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NIMBYs and economic theories: Sorry / Not Sorry

This post is not by Andrew. This post is by Phil.

A few days ago I posted What’s the deal with the YIMBYs?  In the rest of this post, I assume you have read that one. I plan to post a follow-up in a month or two when I have had time to learn more, but there are a couple of things I can say right now.

I. Sorry

  1. I apologize unreservedly to YIMBY supporters who know, or think they know, that buiding more housing in San Francisco will decrease rents there or at least will greatly reduce the rate at which they rise. I characterized the entire YIMBY movement as being at least partly motivated by a desire to stick a thumb in the eye of the smug slam-the-door-now-that-I’m-inside NIMBY crowd, rather than by a genuine belief that loosening land use restrictions in SF will decrease rents there. This was simply wrong of me.
  2. There might be something else I need to apologize for too, I’m not sure. (I don’t remember whether or not I said this in the comments; I’ve taken a quick skim through and didn’t see where I said it, but maybe I did). I have seen a few articles that touch on Bay Area housing, and the YIMBY movement, in which people who characterize themselves as YIMBYs say things like “we aren’t talking about turning San Francisco into Manhattan, we are talking about building some more housing to take the pressure off so rents come down.” [That is not a quote, it’s a paraphrase.] I think that in the current economic environment you would need to build an enormous amount of housing in SF to get the price to come down, so I’ve felt that people who say things like that are being disengenuous. It’s possible that I characterized the entire movement incorrectly, based on those examples. If I did, then I apologize to people like Sonja Trauss, who is a leader in the YIMBY movement: Sonja is absolutely up-front about wanting to build however much a free- or nearly-free market would allow, even if this does indeed lead to the Manhattanization of San Francisco. Trauss is not being disengenous at all, there are others in the movement that are also straightforward about the fact that their desired policies might completely transform the city.
  3.  I’m also sorry that I wrote authoritatively rather than speculatively. What I should have said is “Here’s what I think is happening, and I’d welcome comments” rather than, in essence, “Here’s what is happening, and I welcome comments.”

II. Not Sorry.
I proposed a model for San Francisco housing prices that makes sense to me. Quite a few people posted that my economic model is nonsense and I’m an arrogant fool, or worse, for having proposed it…that I should be embarrassed… etc.  But not only do I not think I’m arrogant, I think some of the people who accused me of being arrogant are themselves arrogant. (As for whether I’m a fool, that’s possible but I am not convinced).

Before I get into just a bit more discussion of the economics, let me touch on a few things about the comment stream.

  1. Many people mischaracterized my argument, claiming that I don’t understand the simple “law of supply and demand” , that if you build more of something it gets cheaper. But I do understand that, indeed I said it explicitly in the fifth paragraph of my post! If you build more housing, housing gets cheaper on average. I said that and I believe it. I just believe that the place you build the housing isn’t necessarily the place it gets cheaper, for reasons I explained.
  2. Several people claim that my model — actually I will admit it is an incomplete model, so I should perhaps put it in quotes — that my “model” predicts that when new high-income housing is built in San Francisco, it will be occupied only by newcomers to the city. This is not true. I do think that if N new expensive housing units are added to the city, the population of the city will go up by nearly N high-income households, but this could happen even if current high-income residents move into the new units, as long as their former residences are taken by high-income residents from outside. Some people think I am very wrong about this — they say if N new high-income units are added the number of high-income households will go up by much less than N. One of the people who says I’m wrong is a noted economist, a fact that certainly gives me pause. But I will explain below why I am unwilling to simply accept the judgment of the economist, absent an actual economic model that captures the key characteristics of the system.
  3. A commenter named Sam pointed out a  blog post by economist Nick Rowe in which he demonstrates that local housing demand curves can slope upward — that is, building more housing can lead to higher housing prices, at least over some range of housing density — even if one ignores the distorting effects of land use regulation. Rowe does not claim that this actually happens, he merely points out that under some reasonable assumptions, it could. Well, if it could, maybe it does. However, I must admit that although I said in a comment that Rowe’s model ‘is more or less what I think is happening’, upon reflection that is not true: my ‘model’ is based on the fact that the Bay Area housing market is trapped by regulations in a state that is very far from the free-market equilibrium, whereas Rowe’s model assumes a free market. Still, the effect Rowe posits could be an important part of real-world behavior. People who say I’m obviously wrong — that an increase of housing supply in San Francisco might lead to an increase in housing prices there — might want to read Rowe’s post and ask themselves if they are really really sure.
  4. Several commenters said I am ignoring a large body of published work that clearly proves I’m wrong. This is one of the main pieces of evidence that supposedly proves my arrogance or ill-will. All I can say here is that if I am ignoring such published work it is because I’m ignorant of it in spite of looking for it. If economists have indeed looked at the economics of housing in a Bay-Area-Type situation, my default assumption would be that they have done it right. But I still haven’t seen such work.

#4 requires an explanation. When I said I haven’t been able to find relevant work in spite of looking, I got a few incredulous comments along the lines of “How could you possibly have missed the work of X”. In a couple of cases I actually had seen at least some of the work; in others I had not. But even though I have now looked at some of the papers to which I was referred, I still have not seen what I’m looking for, which is a housing price model that would predict what will happen if you build some new high-income housing in San Francisco.  I think that what these commenters are referring to is the large number of publications on regulatory restrictions on housing prices. For instance, there’s a fair amount of work that compares housing prices across different metropolitan areas, and demonstrates that highly regulated areas with high economic growth have much higher housing prices that less-regulated areas with high economic growth. (When I say ‘highly regulated’ I am referring to land use regulations that limit the construction of new housing). An example, to which economist Steven Berry referred me, is “Urban Growth and Housing Supply”, by Glaeser, Gyourko, and Saks. These are all real heavyweights, and if they had a model that applied to the Bay Area housing system I would be inclined to take it at face value, unless they made obviously questionable simplifying assumptions or something. But in fact that paper explicitly looks at entire metropolitan areas. Housing prices have gone up more in the San Francisco Bay Area than in Las Vegas, and land-use regulations are surely part of the reason… that’s fine, and makes sense, and I don’t dispute it. (I also note that the uncertainty on the magnitude of the effect is extemely large). But I could not find anything in that paper that I think even the authors would suggest can be used to predict what would happen if you have several highly-regulated cities in the same metro area, and you relax regulations somewhat in one of them. I have looked at the work of several other authors who were mentioned by commenters, and so far have not found anything about such a system. I do not claim it doesn’t exist.

Quite a few critics of my post said (paraphrasing):  “you obviously know nothing about economics, because even the basic supply-demand relationship you learn in Econ 101 disproves what you say.”  One of the people who said this is the aforementioned economist Steven Berry, who posted a response that began with “1. Go to ebay and buy a used intro microeconomics textbook 2. Read the chapter on supply and demand” and then laid out the standard free-market equilibrium model of supply and demand, which, ironically, is about the only thing I do remember from Econ 101.  He then points out the undisputed fact (undisputed by me, anyway) that under the assumptions of that model, an increase in the demand for housing in San Francisco will cause a lower price increase if more housing is built in San Francisco than if it isn’t.

But…but…but…if even an Econ 101 student were to propose modeling the current Bay Area housing market as a free market that is near equilibrium, surely Berry would give him a very poor grade. If the Bay Area housing market really worked that way, there would be no need for a YIMBY movement and indeed no point to having one.  The whole point of the YIMBY movement is that the difficulty in building new housing has moved the market far from free-market equilibrium and is holding it there. This applies to the whole Bay Area, but since demand is highest in San Francisco the effect on housing prices has been especially large there.  I think it’s just wrong to look at a system like the one we have, and apply a model that assumes we are at equilibrium in an environment where additional housing can be built instantaneously at the construction cost.  So I pointed that out to Berry. And Berry told me to quit bothering him and go pound sand.

No, actually he didn’t. He said “You treat the supply side as fixed, which as you say given the NIMBY success is maybe first-order correct…”  And then he went on to suggest how to model a system like this, and gave a reference to a relevant paper (which I have not yet looked at, but will).  On the whole he put in quite a bit of time writing several comments, and I appreciate it. Berry still said I’m an ignoramus, and questioned both my motivation and my character, but on the whole I think his behavior has been quite good: he didn’t just call me names, he made constructive comments and pointed out where he believes I have made an error.  This certainly contrasts favorably with the behavior of some of the other commenters, who simply referred to the inappropriate free-market model and refused to even consider the fact that it is a terrible model for the actual market here.  This is what I meant above when I said “I think some of the people who accused me of being arrogant are themselves arrogant”: if you are one of the people who gave a knee-jerk shout-out to the free-market-equilibrium model and then dropped the mic, you are in this category.  Kudos to Berry, who I think was the only one to acknowledge that that model is (or at least may be) inappropriate, and to give actionable advice on how to create a reasonable model.

I’m reminded of a brief anecdote in Landsburg’s “The Armchair Economist.”  Landsburg recalls a fellow economist posting a bunch of questions that he claimed were interesting — things like “why does candy cost so much at a movie theater” — and that Landsburg and some of his buddies sat around making fun of the questions, and the guy who posed them. Landsburg says he thinks they laughed some of them off by simply saying “supply and demand!”  But, as he was writing the book years later, Landsburg said he now recognizes that he and his buddies were wrong, and that the answers to the questions are in fact non-trivial and that the questions really are interesting.

To get back to the economics model: Berry does not claim to have a model of the system we actually have, or at least he didn’t claim it in the blog comments. He nevertheless claims that building N high-income apartments in San Francisco will not, in fact, result in approximately N new more high-income households moving there, but rather some number very much less than N. He’s an extremely competent economist and I am not, so I take his intuition on this subject very seriously. But I don’t think I need to apologize for not simply accepting his intuition, or anyone else’s. I think we agree the equilibrium model is not a reasonable one to use. So what is a simple model that can be used?

So, I am not sorry for not simply caving to the people who are calling me an idiot, especially the ones who beat me over the head with an inappropriate model and then stalked off!

I will post again when I can figure out whether or not I really am completely wrong. Or, if I can’t figure it out, I’ll say that.







  1. Phil, as one physicsy guy to another, I think what you want is a Fokker-Plank type equation for the time-evolution of the distribution of prices of occupied housing within the actual real world SF city in the months after they open doors on a new 5000 unit apartment building, and especially you’d like to know what happens to the right tail of the distribution where the “affordable” units are, and I don’t think you’re going to get it from the Economists, and especially I don’t think you’re going to get it from the Economists who basically said “Supply and Demand” and dropped the mic.

    If this resonates or doesn’t I’d like to hear it, because it made perfect sense to me, and I think it went WHOOSH over the heads of most of of the commenters on the previous post.

    • ack, LEFT tail of the distribution where the affordable units are… typo.

      • Matt says:

        But Daniel, if you observe the left-tail prices go up…what do you make of this? You need to be able to separate supply and demand, looking at the evolution of equilibrium housing prices doesn’t get you anywhere…

        • If inherently you are interested in the question of what is going on in the left tail of the distribution (ie. how many places are there where low income people are affording them)… then seeing it thin out is itself end of story what you’re interested in. Stop thinking like an economist and start thinking like a demographer, who is in the bay area? what are they paying for rent? How has that changed in time? After building a bunch of new apartments, will we or will we not see the left tail shrink upward?

    • Phil says:

      Daniel, for god’s sake, don’t cop to being a physicsy guy! Our name is mud around here.

      If you brought up the Fokker-Plank equation specifically because it deals with entire distributions rather than, say, the behavior of a single particle, then yes, absolutely I am struggling with how one boils the real-world housing situation down into a single point in a two-dimensional parameter space, or even a single curve in that space, which is what economists seem to be able to do somehow.

      So, yeah, if what you mean is that I want a model that works with distributions rather than points, I agree.

  2. Carlos Ungil says:

    Phil, just one question: when you say that if you build more housing in SF, housing will get more expensive in SF what do you mean?

    A) median rent of occupied units will go up
    B) median market rate will go up
    C) market rate for every unit will go up
    D) something else

    • Phil says:

      Eh, I’ve been dodging this one ever since you posed it in a comment on my original post. My ‘model’ is incomplete and my inability to answer this is one of several effects of that.

      I am assuming that building N more expensive units in SF leads to approximately N more wealthy households living SF compared to how many would arrive if no units were built — an assumption Berry, for one, does not believe. Berry points out this should not be an axiom but needs to be justified (or not) by constructing a reasonable demand curve and seeing whether it leads to this conclusion. I agree with him on this, but this is not easy: you end up with a coupled series of equations, and statistical distributions of various parameters. I would very much like to find a publication that at least writes out the model, which I can then solve numerically if necessary.

      Anyway, for better or worse I am assuming, essentially axiomatically, that building expensive units draws in additional high-income renters and buyers from among the large number of wealthy people who would like to live in SF. This leads to an increase in the already-occuring effects of gentrification, thus further revving up the local economy and leading to higher demand for lower-income workers for whom no additional housing has been provided. I think in such a situation every unit will be occupied, so there’s no need to specify ‘occupied’ in your item A, but anyway I do think median rent of units will go up..also that median market rate will go up. As for whether market rate for every unit will go up…I dunno…Yes, I guess? I think one could look at areas that gentrify, and see what happens to them: basically I am claiming that building additional high-income units, in a situation in which there is large demand for such units, increases the rate of gentrification. So I think looking at areas that undergo gentrification for any reason would be a reasonable way to answer your question.

      • The key importance of this question Phil is that Economists think “median rent” means “the median of market advertised rental rates” (ie. the rents on what’s available) whereas “gentrification” involves looking at all the rented apartments and seeing that most of them are rented at high rents, that is it’s a question not about the market rate (a marginal unoccupied unit) but the distribution of *occupied* units.

        I think this is almost the entirety of the “mic drop” effect, that you say “median rent” meaning “median rent that a person living in SF is currently paying” and economists here “median rent that it would cost to move into SF today”

        • John Hall says:

          Because when economists say that wages are sticky, they are referring to wages of jobs that have not been filled, not the wages of all jobs. He said sarcastically…

        • jrkrideau says:

          The key importance of this question Phil is that Economists think “median rent” means “the median of market advertised rental rates

          Then it might have helped if they had said so. I am NOT an economist. To me median rent for rental units in San Francisco is take all the rents and take the midpoint.
          Basic Stats 101. I think this was what Phil meant and certainly what I understood.

          From an economics’point of view “the median of market advertised rental rate” may even have some use. Who knows, not me, I’m not an economist.

          For a number of policy issues I have dealt with, the actual “median rent” would be what was important. In some (many?) cases the “the median of market advertised rental rate” would have been a meaningless term whatever it means in economics. When you don’t have a “market advertised rental rate” it is very difficult to take its median.

          • Carlos Ungil says:

            I agree that what you call the actual rental rate (taking all the rents applied) may be more relevant in some cases. But for someone who wants to find an available appartment at an atttractive rate (the YIMBYs) the market rates are more relevant (and the median is not the best indicator).

            If you wanted to move to SF and were looking for an appartment there what would you rather have?
            A) the median of all the rents going down while the rents for the units available in the market increases
            B) the median of all the rents going up while the rents for the units available in the market decreases

      • Carlos Ungil says:

        Thanks for your reply. I have to say I find the answer disconcerting. The previous discussion could have been much less frustrating for everyone if you didn’t dodge the difficult questions. Maybe people wouldn’t have mischaracterised your “model” if you had explained better what does it predict precisely.

        I assume your answer is A. “if expensive units are added, the median rent (including available – in the market – units and unavailable – already occupied – units) would rise”.

        You might be right on that, but if market rates go down your original post doesn’t make much sense. The YIMBY people want, according to you, to find a place to live that they like and can afford. Why is it perplexing that they favour adding expensive units if the consequence is that market rates will go down? Why is this policy bad for them?

        You “guess” (maybe, there is a question mark) that market rates will go up. Why? How do you expect to convince anyone of that if you’re not convinced yourself?

        • Phil says:

          You asked about whether I think the rate for EVERY unit will go up. Every single unit. I feel very comfortable talking about the median unit and the 25th percentile unit and even the 10th percentile, but the 0.000000th percentile? Is there some mechanism by which the central region of the distribution could go up but the distribution could get so much wider that the very lowest parts actually go down? I can’t think of one but I can’t rule it out. I _definitely_ can’t rule it out in the real world rather than the simplified world of the models. Maybe at some point the police and fire department give up on enforcing some laws, and landlords start subdividing unfinished basements with plastic sheeting and renting out cot space for $5/day.

          I think if you move a bunch more rich people into SF, they bring their money with them and demand for goods and services goes up, causing an increased demand for non-rich workers. Wages for those workers tend to rise; pressure on the low end of the housing market goes up; rents in general go up. Does EVERY rent go up? I don’t know.

          I’m sorry you find my answer disconcerting.

          • Carlos Ungil says:

            What I did ask you is what do you mean by “prices will go up”.

            Between the option you selected (A: median rent of occupied units will go up) and the option that you reasonably decline to select now (C: market rate for every unit will go up) there are several intermediate claims you didn’t choose which would be much more interesting than A.

            I gave one explicit alternative (B: the median market rate will go up). Actually that’s not very interesting either, because it could be true even if the market rate for every single unit goes down (making YIMBY people policy choices perfectly reasonable).

            A much more meaningful claim would be B’: the market rate of the previous median unit will go up. I’m sure you can see the difference. Or B”: the market rate of most of the units will go up.

            Does you model predict at least that the market rate for some units will go up? I’m not saying that won’t happen but it’s far from obvious.

          • Ryan Moulton says:

            I think you should stop using percentiles and talk only about ordinal rank. If you build more apartments equivalent to the 1000th most expensive, what happens to the rent for the 10,000th most expensive? Working with percentiles just muddies things because the quantity is growing and makes all your statements really slippery.

      • Sonja Trauss says:

        This is the biggest problem I have with this whole exercise:
        “Anyway, for better or worse I am assuming, essentially axiomatically, that building expensive units draws in additional high-income renters and buyers …”
        Whether this is true or not has a HUGE impact on the conclusion you reach. This is a question about the material world that you could investigate but instead you just guess. By guessing at this point, assuming you have a can opener, you’re ensuring you reach the conclusion you want to reach. It’s fine to like what you like, but what’s the point of all of the reasoning between this axiom & your conclusion, of (1) it might be wrong and (2) whether it’s right or wrong totally impacts your conclusion? Can assume the opposite and still reach your conclusion?

        It happens all the time that people make axiomatic assumptions about things they think they can’t know, in order to get to the outcome that _feels_ right. Does life begin at conception? If you want to punish women for having sex, you’ll answer yes. If you want women to be able to ‘choose their own future’, you’ll answer no. This is perfectly fine, whatever your metaphysics. But reasoning from your guess about a state of the word to the outcome you already believe isn’t social science. It’s rationalization.

        • Andrew says:


          I don’t see the problem with thinking that life begins at conception but still wanting abortion to be legal. I mean, sure, I see some tradeoffs here, and I can see how it would be easier to argue in favor of abortion if you want to say that a fetus is not alive, but I don’t see that just because someone favors abortion rights, that they’ll answer no to the question, Does life begin at conception?

          • Sonja Trauss says:

            That was an example, so this is a tangent, but, sure – you’re right. There are pro-choicers who have put in the extra reasoning effort to argue for their conclusion starting from a number of different axiomatic assumptions. And you might notice- that’s what I’m asking Phil if he can do here. If he assumes the opposite, that N new units results in <N new households can he still reach his desired conclusion that YIMBYs are stupid jerks?

            • Sonja Trauss says:

              New *rich* households

            • Sonja: under what assumptions does adding say 100 new apartments at $4500/mo result in significantly less than 100 new rich people?

              For purpose of that question, I am going to define a “rich” person as someone who makes more than 1.5x GDP/capita which is about 85k, and “afford” as spends 0.35 times gross income or less on rent, so $2500/mo and “significantly less than 100” as around 80 or less, i’m not too interested in the possibility that 1 or 3 or even 5 for example new people at under 85k appear, that seems within the random fluctuations of the believable range

              I think we all agree that adding 100,000 new apartments would do a lot, but at the margin, 100 new “rich” apartments, by what mechanism do we get fewer than 80 new rich people? This is a fully serious honest question, I’d like to incorporate the possibility of that mechanism in any agent based model I create, so we can investigate whether that mechanism seems plausible or not.

              • sonja trauss says:

                When new 1 bedroom apartments are not inhabited by 1 or 2 high income people, but instead by 4 low income people: 2 sharing one bedroom and 2 in the living room. also look at this: Lower income people with a higher tolerance for crowding & a higher preference for a short commute will always be able to pay more for housing than higher income people who believe they need more space & don’t mind commuting. That’s why there are any low income people in high demand areas at all right now.

                Or when the new apartment building opens onto a declining market. The economy ebbs and flows. Because there is necessarily a lag time between planning a new housing development & delivering it, developers will always overbuild, if we let them: Jobs are not being created as quickly in SF as they had been, not as many people are coming and more people are leaving. Rents are going to continue to at least not rise. If we hadn’t been so stupid since 2013, and we had allowed more people to start the 18-24 month process of building on 2015 then there would be even more housing opening into a declining market.

                The above example is a specific case of the general case – you get < N high income households moving in when N is greater than the number of high income households that want to live in SF? You, and Phil, are 'quite sure' that it's Totally Obvious, that there is no amount of building in one year that could ever exceed the amount of high income households that want to live in SF. You just know it in your bones.

                Unmet demand is notoriously hard to measure, Keynes wrote an entire book on that premise. Since it's so hard to know, you (and Phil) should be way more circumspect about your assumption that rich people demand for SF is totally unlimited.

                Since 1990, SF builds around 1500 units per year. Three times since then has SF gone above 3000 in one year: 2008, 2015 and 2016 where 2016 is the first time we broke 5000. Keep in mind that the number of housing units in SF is about 350,000, so except for 3 years, SF housing capacity has been growing at less than 0.5%. The rate of population growth in the whole US over that same time period has been about 1%. That includes shrinking places like Buffalo. SF has had particularly intense economic growth over that time period, so we should have seen growing our housing stock at MORE than 1%/ year, more than the US rate of population growth – at least 5,000 units per year, on average.

                You and Phil seem to be confusing "SF has not been building enough housing over the last 27 years" with "SF could never build enough housing," which is not at all warranted.

                I made this a couple of years ago:

                Agent Based Model of the Housing Market
                CfA Presentation of the Model
                Written explanation of the Model
                Video explanation of the Model

                Maybe it will help you

              • Sonja: thanks for your comments, and seriously thanks for taking my request seriously. You way over-state how much I “feel it in my bones” but of course we are communicating indirectly across a splattered spray-paint of comments. It’s interesting that you also went towards agent-based models.

                I have *absolutely* no problem with saying things like “building more housing will increase xyz important overall measures of well-being” it seems very plausible to me that building could increase *or* decrease well being. I do however think that due to the rent-controlled friction which is relaxed by small increases in housing quantity, observed rental prices of basically all *rental units* will jack up for marginal increases in quantity. I don’t know whether I buy into Phil’s second order demand effect being as large as he seems to think.

                Now, you can argue for example that you’ll be able to have *more* overcrowding and that people who are willing to overcrowd are made better by enabling this, and soforth. That’s all very plausible. But I think those are very very different statements than the kind of thing Phil was originally responding to, claims that basically nominal rental prices of low end units will drop.

                To be clear, politically, I support building, and I support eliminating rent control. I’d like to see a law at the state level that said something like “regardless of any local ordinances, no ordinance may prevent a landlord from raising the rent on a rental unit by the percentage change in the CPI last year plus 10 percentage points” and then let-er rip. Within about 6 or 7 years pretty much everything would have equilibriated to a free market, and stay there because very rarely would CPI + 10% be smaller than the increase in rents.

                So, politically I support things closely aligned with your cause, but I don’t necessarily support the simplistic version in which some seem to argue that low end places will come into being or rents will drop at the low end of the market, or service workers will be able to start moving into SF or any of those implied conclusions. Perhaps those are straw men, but I don’t think so, I think some people do advocate those positions, and I strongly suspect they are wrong, while still believing that *you* could well be right that people will be better off by other very important measures!

    • Gabi says:

      My own reading of it is A) but I am curious as well. I am voting A) because Phil is specifically talking about high-end housing. The way I see it, Phil is saying that as the supply of housing that the rich can afford grows in SF, the rich move in from Oakland. In doing so, they increase the demand for services delivered by the poor in SF, but as the supply of housing that the poor can afford is unchanged in SF, this just means a bidding war at the lower end of the housing supply as the resident poor must now compete with commuter poor who are willing to commute from further afield, drawn by the new jobs.

      • Phil says:

        Gabi, yes, that’s what I’m saying! I am definitely predicting the median rent to go up (even more than it would without that high-income housing). I’m also predicting the 25th percentile to go up, and the 10th percentile. As for _every_ rent…see my response to Carlos, above.

        • Gabi says:

          OK. For simplicity, let’s just assume that _every_ rent goes up in the part of town where the poor live. That’s unfortunate, on the face of it, but I believe that it’s not the worst possible outcome. For more simplicity, imagine this: the 7×7 mile square that is San Francisco is split into two sections. One, say South Beach, is where we may stack the rich into market-rate luxury high-rises. The other is everywhere else, where through myriad regulations we keep the supply of housing fixed to what it is today. The YIMBY question becomes this: are the poor better off if we can stack the rich? I’d argue that the answer is yes, in _relative_ terms. Sure, the poor people’s rent will go up by the mechanism that you described. But it would go up by more if instead of _stacking_ the rich in market-rate high-rises in South Beach we allowed them to _spread_ into areas now covered by housing available to the poor. So, the poor people’s housing costs won’t go down, but they’ll go up by less than they would otherwise. It’s the best that anybody can do, it seems to me. What am I missing?

        • Alex Godofsky says:

          Phil: to clarify, is your claim essentially that the median goes up because you’ve added more units at the top? Like, if I have 100 apartments with prices from 1-100, the median price is 50.5; if I add 10 more units at 100, sure, the median goes up to 55.5, but that just seems like an uninteresting result? No one who is currently renting should care that this particular median has gone up, it doesn’t affect them.

  3. Possibly some data could be useful and since I have it I’ll drop this here:

    click the image to get a big version if you want to see details.

    • Things I’d like to know after seeing this distribution:

      1) on the left end of this distro, did the increase in “affordable” housing come from SF allowing some building and then having required “affordable” units available by lottery?

      2) How much housing was built / opened between 2011 and 2012? Because things changed a lot, abruptly, and median rents of occupied housing definitely went up, and it’d be useful to know if any new housing came on line that year, because that’s a big jump in distribution. Of course, probably this coincides with the major influx of demand, so there’s that.

      3) Between 2011 and 2015, pretty clearly the left tail (in the vicinity of 0.4 x median 2010 level) thinned out and the right tail (vicinity of 2.5x the 2010 median) moved up, how much additional housing was added between 2011 and 2015? If a bunch of market rate housing was brought online in the $2900 range, then if I’ve understood Phil’s point, EXACTLY what he said would happen DID happen.

      I could maybe back out the housing unit increase numbers from the ACS data but I think the statistical errors would be larger than if someone just found out how much housing was approved by SF City.

      • Also, ACS separates households if they’re independent financially, so two friends sharing one apartment would be TWO households. So perhaps the “affordable” end is actually just the fact that people took on roommates and split the rents as everything got expensive. That’s important to consider.

  4. Lord says:

    The historical evidence of San Francisco is indeed consistent with your model. It simply isn’t possible to build enough fast enough to lower rents, even without legal restrictions, physical restrictions are significant. New housing always enters at above average, partly because it is new. It does move those living in outlying areas who work there to reduce their commute and live closer to where they would like to live. It won’t lower rents in the city, but it will raise the standard of living by eliminating some old, tired, less functional housing with more new, more pleasant and functional housing, at a cost but even higher increases over time as more move in providing more growth and opportunities. It will keep down rents in outlying areas as those who want to will be able to find more attractive suitable options in the city than they have now.

    It is always hard to know what others believe and think. Some might expect they might be tiered in to affordable housing or rent controls might be added later. Some might like to move up or buy or move in from outlying areas with it being less an issue of price than availability and quality. Some might like to buy or already own and anticipate the increased appreciation that would result. Some may look forward to the greater opportunities it would present and greater dynamism from the influx, most living things growing or dying.

  5. David18 says:

    Harvard Economist Edward Glaeser: Build Big Bill [NYC Mayor DeBlasio]

    As pointed out by others in the comments in the original post, Japan instituted federal laws that override the local laws so that enough housing could be provided in Tokyo. We need the same for the US and market forces will fix the rest as they did in Tokyo.

    • Phil says:

      As I pointed out in the comments of the previous post (what, you didn’t read all 250 of them? ;)
      A Bloomberg article from a year ago says “The average price for apartments in Tokyo and commuter regions has climbed 22 percent during the past three years, according to the Real Estate Economic Institute. The price for an apartment in Tokyo’s main urban area, where more than 9.2 million people live, rose 12 percent on average to 67.3 million yen in 2015. The increases are coming even as average Japanese base wages in November fell 1.4 percent from three years earlier to about 239,250 yen, data from the Labor Ministry show.

      With building costs and land prices rising, it has become increasingly difficult to pass on those charges in suburban developments, so large developers have been building more luxury apartments targeting the wealthy, according to a report last week by analysts Tomoyoshi Omuro and Junichi Sano at Morgan Stanley MUFG Securities Co.”
      But I wonder about the whole comparison to Tokyo because Japan is still in an economic slump — note the falling base wage in Japan — and the Bay Area is not.

      As I also pointed out According to Japan Property Central, “The ratio [of housing costs to salary] was the highest in the Tokyo metropolitan area, with a price-to-income ratio of 9.79 times for new apartments and 7.20 times for second-hand apartments. Kyoto Prefecture had the second highest ratio for new apartments with the average apartment costing 9.78 times the average income for the prefecture.” A quick look at their website didn’t turn up a time series plot of price/salary for second-hand apartments, but they do have it for new apartments, and the ratio has increased from a low of about 7 (in 2000) to its current level of 9.8. That’s a 40% increase.

      But mostly: I agree that land use restrictions increase the cost of housing in the Bay Area. I don’t know about the history of Tokyo but presumably they did so there too, until they were removed. But even now it doesn’t look like Tokyo is particularly cheap.

      • David18 says:

        People referenced the FT article within the past year.

        “Here is a startling fact: in 2014 there were 142,417 housing starts in the city of Tokyo (population 13.3m, no empty land), more than the 83,657 housing permits issued in the state of California (population 38.7m), or the 137,010 houses started in the entire country of England (population 54.3m).” For NYC 20,000 built in 2014.

        “Tokyo’s steady construction is linked to a still more startling fact. In contrast to the enormous house price booms that have distorted western cities — setting young against old, redistributing wealth to the already wealthy, and denying others the chance to move to where the good jobs are — the cost of property in Japan’s capital has hardly budged.

        This is not the result of a falling population. Japan has experienced the same “return to the city” wave as other nations. In Minato ward — a desirable 20 sq km slice of central Tokyo — the population is up 66 per cent over the past 20 years, from 145,000 to 241,000, an increase of about 100,000 residents.”

        “In the 121 sq km of San Francisco, the population grew by about the same number over 20 years, from 746,000 to 865,000 — a rise of 16 per cent. Yet whereas the price of a home in San Francisco and London has increased 231 per cent and 441 per cent respectively, Minato ward has absorbed its population boom with price rises of just 45 per cent, much of which came after the Bank of Japan launched its big monetary stimulus in 2013.”

        US rate of inflation in the past 20 years is about 55%, so in US terms at least the price of desirable Tokyo property hasn’t really increased when taking inflation into account while the population has grown 66%. Meanwhile the SF population increased only 16% with price increases of about %180 adjusting for inflation.

        • Phil says:

          Tokyo has indeed been building like crazy. If the entire Bay Area had the same permissive building rules as the entire Tokyo area, we might see the same. But I don’t think this tells us what happens if you are very nearly in the opposite situation — very little building is permitted anywhere in a region of high demand — and then you relax that demand in one portion of that region.

          I ‘m not sure whether that last paragraph is yours or someone else’s. If it’s yours I think it’s very misleading: yes, US inflation has been about 55% in the past 20 years but Japan’s has not. In the past 20 years Japan has had periods of slight deflation and periods of slight inflation. If I’m interpreting correctly, the total increase in the Japanese consumer price index in the past 20 years is only about 2%. Not 2% per year, but a _total_ of 2%, which means Tokyo housing prices increased about 40% above inflation. Of course, that’s still a lot less than SF’s 120% above inflation! I’m not arguing with your main point, but I think it’s wrong to look at Japanese housing prices in the context of US inflation rates.

          • David18 says:

            The last paragraph is mine, but the SF housing price rise was about 180% above US inflation. According to the FT as quoted in my previous comment, the SF rise in housing prices is 231%% which would be about 180% after inflation adjustment.

  6. Matt says:

    Phil: Could you outline the basic empirical facts that have motivated your model? What is consistent with your model, but inconsistent with a simple S&D model where demand is outracing supply in SF?

    • Phil says:

      Well, the main thing is that over the past ten or fifteen years rents and housing prices have raced upwards both in SF and in the surrounding areas, but not a lot of new housing has been built. In contrast, other cities with hot economies, such as Houston and Las Vegas, have built much faster.

      You might point out that are some differences: Las Vegas and Houston can expand in area, but San Francisco proper cannot (and even the Bay Area is partially blocked in, both by physical barriers such as the East Bay Hills and land use barriers such as the East Bay Regional Parks system). San Francisco is pretty much built out (unless you talk about something radical like building in Golden Gate Park) so building more housing often requires tearing down what is there, and replacing it with something taller or at least bigger. I suppose the same is true of Manhattan. Conceivably this could add to construction time, even absent any regulatory barriers, perhaps that’s the thrust of your question?

      I can certainly attest to the fact that it is hard to get new housing built in a lot of cities in the Bay Area.

      Many economists have looked at the situation and concluded that regulatory barriers are preventing housing from expanding as rapidly as it would under a less regulated market. This makes sense to me, and is what many good economists have concluded, so I believe it.

      • Matt says:

        Honestly, I’m lost. How is this inconsistent with a simple S&D model? Prices are higher in SF because supply is restricted – just look up econ 101 S&D with a quota (i.e. can’t build more than N houses). I thought you were proposing this model because you think that building more houses is causing rents to be higher than they otherwise would be…I just don’t see where the empirical evidence is..

        • Phil says:

          Oh, I see what you’re asking. Sorry, I misunderstood.

          The simple S&D model, or at least the one Berry initially told me was applicable, is an equilibrium model: assume supply and demand are matched, so if there’s demand for nice new apartments in SF that is less than the cost to build them, they get built. Then assume that the reason more apartments get built is that the demand for them goes up, and see what happens to the predicted price.

          All economists believe (and I do too) that we are very far from that equilibrium. If building were unregulated, there would be far more housing in SF than there actually is. So the equilibrium model just doesn’t apply. For one thing, demand could drop quite a bit and you’d still be able to rent out apartments for far more than the cost to build more.

          • Matt says:

            I mean yeah you don’t have to believe you’re in equilibrium (it’s a model, we’re never actually in eq’m) for the model to be useful. It can explain exactly what’s going on – just draw your S&D with P on the y-axis and Q on the x-axis and then put a vertical line in at some Q < Q*. You'll see that price is way higher than eq'm price and quantity, and demand greatly exceeds supply. Your last comment can just be accommodated by shifting the vertical line closer to Q* (but still < Q*). Berry obviously was not suggesting that we are in equilibrium, but the intuition of the model suffices.

            • Phil says:

              I don’t think that’s true, I don’t think you can trust an equilibrium model when the real world is far from equilibrium.

              I’m trying to figure out what (if anything) is wrong with this way of thinking of things:

              Consider a world in which no new building is allowed whatsoever, anywhere in the Bay Area. (Let’s also pretend the economy is stable, there’s no bubble that will burst, etc.) The distribution of housing prices in San Francisco eventually stabilizes with some statistical distribution…I picture it as being roughly lognormal but I don’t really know. The distribution of housing prices in not-San-Francisco also stabilizes, with some other statistical distribution (I picture this one as lognormal too). People will pay a premium to live in San Francisco, so the distribution of prices (or at least price per square foot) is much higher in SF than in the rest of the area. So this is a static model in which housing is fixed.

              Now I build a chunk of high-end housing in San Francisco. What happens? Well, for one thing, unless it is crazily mispriced it will be occupied by wealthy people. Some will come from outside the city, some from inside…but, since some people think it makes a big difference which of these occurs, let’s pretend that there’s some sort of regulation such that only San Franciscans can move into these apartments. OK, but if a wealthy person moves into one of these apartments, they are moving out of some other place expensive place, which is now vacant. Those places now get rented out, either to other San Franciscans or to people who came from elsewhere. Consider those other San Franciscans: they, too, have left someplace vacant, which now gets rented out. When you follow the game of musical chairs, if you have added N apartments for wealthy people, then you have N additional households of wealthy people…possibly not _quite_ as wealthy, but wealthy. Those N additional households of wealthy people create additional demand for goods and services in San Francisco, which means (among other things) more workers who would like to live in the city so they don’t have to commute, thus increasing demand for housing…which has not been provided.

              This is very different from the free-market-equilibrium model. I don’t think the free-market-equilibrium model is useful here. And I think the system I have described above — I won’t call it a “model”– is closer to the current Bay Area reality than the free-market-equilibrium model is.

              Berry strongly disagrees with one aspect of what I’ve just described: he disagrees that if you build N more high-end apartments, you get approximately N more wealthy people. He says it is much less than that. You would be doing me a great service if you would explain why!

              • Sam Bailey says:

                >Those N additional households of wealthy people create additional demand for goods and services in San Francisco, which means (among other things) more workers who would like to live in the city so they don’t have to commute, thus increasing demand for housing…which has not been provided.

                But this rationing is not something that does not appear in equilibrium models. Indeed, in the textbook sketch of a straight line sloping down for demand a straight line sloping up for supply, all the potential buyers and sellers to the right of the equilibrium point are not going to be participating in the market. In this scenario, the people who commute to the city are those to the right of the intersection. This is not to say this is the best possible outcome or its Pareto efficient or any of that stuff, just that it is explicable with standard equilibrium models.

              • JPK says:

                So ask the question in reverse. Still assume no building allowed. Why aren’t the rich people who currently do not live in San Francisco but who want to, not bidding up the price of existing housing further than it already is? Prices are something, they’re X right now, and could be bid higher if some people were willing to pay more now, but by definition they’re not, they’re X. If what you’re saying is true, that they would gladly come in (or come from wherever, there could be shuffling where existing residents take the new housing and new residents take their old stuff) if new housing is built, but not with the current supply. They’re not willing to pay current market prices (after all, it’s not really the case that you can’t move in if you don’t want to, there’s always stuff in inventory at most quality levels if you’re willing to pay enough, and if you’re assuming that away in your model you’re really throwing all realistic assumptions about quasi-rational behavior out the window).

                But if more housing is built in SF and they are all of a sudden willing to pay higher prices than they were before, what gives? Well, maybe these people prefer increased density, increased gentrification that the simple presence of the new structures brings. How much is that worth to them, I don’t know, you’re right that newer housing and newer development itself makes a place more desirable. Just like people like newer cars more than older cars, but I don’t see that in and of itself as a reason to forbid the construction of new cars to keep the price of transportation down. In fact it’s the new cars, we might tell the story, that drive down the price of old cars (sound like a familiar argument). Which, by the way, all (or most) of the old housing will still be around, so why are those prices also going up (or not going down) in this situation. Who’s now willing to pay more for that?

                Again, all of these stories are plausible, economists have models to describe them, e.g. models with luxury goods, price controls, constrained supply, there’s no law that supply and demand curves have to be a certain way, it’s just that if they’re not you better have a decent story for why, and for sure some empirical evidence. (There’s plenty of that actually looking at building restrictions and prices.) It’s not like housing and urban economics is a brand new topic. I don’t have particular studies at hand, and I’m not much of one for throwing out random studies that conveniently support my arguments, but I think a few have been mentioned here already.

                So just how many people out there really are willing to pay more for something in the future they could basically get for less right now? Are there hordes of suburban retirees just waiting for enough dense housing to be built and for it to be expensive enough that they’ll pile in once it’s built, they’re all just waiting until the right moment to all go together?

                And even then, it Kind of requires a heroic effort to view the new housing as a bad thing in and of itself if it has all these other positive effects. And remember, eventually that new housing will be old housing, we’d probably be in a better situation now if there were more new housing 20-30 years ago.

                I’m not an expert myself, but I am a thirtysomething with kids in another big city that is sick and tired of housing costs, and sorry for what working people have to go through, the long commutes, the inability to save up large down payments, and most of all the toll it takes on families. That we’ve built less housing than is needed in a great many large cities is unquestionably true. It seems perverse to me to want to weasel out an excuse for not building more.

                And no one is saying specifically that prices will go this way or that way if you build, the argument is a counterfactual, that all else being equal, new construction versus no construction, prices will be higher than they otherwise would have been if there’s never any new construction. They may still be higher if other factors that apply regardless (tech booms, global warming, interest rates) are having effects.

                Another pet peeve, just consider basic efficiency of getting people around. Compare areas around BART stations (in SF, Berkeley, etc) to (most) DC Metro stations. Similar metro areas in size and demographics, with transit systems built at the same time, yet there’s much more dense development in much of the DC area, again probably largely due to differences in local politics more than anything. And those parking lots are such a waste. Regardless of other effects, more people living without cars, getting around quicker and more efficiently because there are more people living closer to more things, is in and of itself a good thing, for the environment and people’s health and wellbeing.

                THe one thing I’m not getting into here is fairness and equity, that is indeed a big topic, and frankly I’ve never understood how they lean in favor of NIMBYism given the immense power and influence it gives to incumbent property owners and the lucky few developers that hit the jackpot, but I’ll point out that a great many, if not most working people have no choice but to pay market rates, many if not most already have to live at great distances, and many more would be able to live and work in the area if there were more housing.

              • JPK: let’s define equilibrium like finance people do: the bid is below or at the advertised asking price, and the clearing price is somewhere in that spread.

                Now, here’s what Krugman wrote in the NY Times about SF in THE YEAR 2000 (OMG I’m quoting Krugman, well in this case he’s not being obtuse)


                “On the other side, consider an article that appeared in yesterday’s New York Times, ”In San Francisco, Renters Are Supplicants.” It was an interesting piece, with its tales of would-be renters spending months pounding the pavements, of dozens of desperate applicants arriving at a newly offered apartment, trying to impress the landlord with their credentials. And yet there was something crucial missing — specifically, two words I knew had to be part of the story.”

                The same thing has been going on during this second tech bubble, at least since 2010, but the truth is, it never really ended from 2000… 17 years of a lot of this going on. Landlords ask a low price to attract supplicants, and the supplicants have a bidding war until the price of this apartment fully equilibriates, and then those two people the tenant and the landlord are the only two to observe the actual settling price. So, evidently that bidding war suggests *the prices aren’t in equilibrium*

                The real key to Equilibrium is that information about supply and demand is widely available, and so people *know* what the clearing prices are without having a bidding war, at least to within a bid-ask spread that’s a small fraction of the clearing price. How do you decide if you can build an apartment complex if you don’t even know approximately what you’ll be renting it for? $2500, $2800, $3600? no one has the slightest idea, because information hasn’t percolated in the market because latent demand can’t register its “vote” and because demand is shifting continuously without the slightest bit of information flowing into the market due to lack of liquidity. Nothing stays advertised long and the hidden clearing price is different and higher than the asking price.

                Why don’t more people just show up to outbid the existing tenants at higher prices? Oh yeah, they can’t it’s illegal to NOT renew a lease at government prescribed prices.

                Let’s not forget that in the face of all of this, HUGE quantities of apartments have been taken off the market and converted to tenancy in commons or other forms of *ownership* instead of leasing, and so supply of rentable apartments may actually be *shrinking* on a daily basis, I don’t know. Let’s not forget that in order to convert like this you have to buy out your tenants, and so some people hang out looking for that buyout even if they’d like to move.

                So, here are two things that Phil *has not* disagreed with:

                1) That building housing will result in prices lower than they otherwise would have been in the broad bay area. Phil explicitly AGREES with this.

                2) That building housing in SF will result in prices otherwise lower than they would have been in SF. I think he’s open to being convinced either way, but he has a prior that tells him the second order effects of increased demand at the lower end might lead to higher prices at the lower end (not even necessarily higher prices overall, say on average just higher prices and/or lower supply of stuff in the less than 1x the 2010 median range, stuff that you could afford with current barista salaries). So far, the data shows Phil is right that at the lower end prices have increased, but there’s no specific counterfactual predictions that he can compare to, and economists who yell “supply and demand, it HAS to be true” are not convincing him. That’s just religiosity not empiricism.

                Phil seems to be open to the point that perhaps absolute dollar prices of lower end apartments increase, but by less than the wages of baristas, and so the dimensionless ratio rent/wage might decrease. But, he is talking about people who actually claim on the radio that building market rate apartments will *decrease the nominal dollar cost of low end apartments*. And he’s not convinced, and there’s absolutely no reason he should be.

                In fact, Brian, below, an economist with actual data and who actually *does* study this stuff, has weighed in saying essentially that it’s never going to happen, that you’d have to build 4-5x as much market rate housing to get to the point where low end stuff is available.

                So there you have it. Physics guy may not know the jargon, but Physics guy’s intuition about non-equilibrium pricing agrees with the quants on wall-street who make big bucks arbitraging non-equilibrium prices, and Physics guy’s intuition on whether housing prices at the low end will *decrease in time, in nominal dollar terms* agrees with research by professional economist who actually studies the housing market in SF.

              • Matt says:

                Unfortunately the fundamental problem remains for both Daniel and phil, neither understands the basic s and d framework. I assume that’s why berry hasn’t come back, because this is just pitiful. Phil, you need to understand that people that aren’t in sf before that new housing comes BY REVEALED PREFERENCE do not want to pay market prices. Now, when a new chunk of housing is built, the whole point is that people aren’t going to move in if they cost more. Who are these people?? You say wealthy people will move in, where were they before? I’ll tell you where they were, they were somewhere else saying I don’t want to pay market price in sf, and they won’t be paying it after they build houses either. You simply do not understand the simple s and d model. Call me arrogant, but it is abundantly true. I am only a 3rd year phd student but I have never been a serious adults attempt to understand economics and be so wrong yet think they are so right (this is mostly Daniel, who thinks he has written some great new model that doesn’t even have consumer preferences in it).

                The quote that really baffles me was when you said “unless it is crazily mispriced” in regards to the new units…. good God. It is a market, these prices are determined by supply and demand. There is no central planner, this isn’t soviet Russia. The basic fact is that you don’t understand that there are no people willing to pay market price before the housing is built, if they were than market price would be higher. This is true to a first approximation. Please just look up Econ 101 quota supply and demand model.

              • Matt says:

                After reading Daniels latest comment below, I think he more or less knows what he’s saying. But it’s a far cry from what you have been pushing phil, I don’t know why Daniel keeps putting words in your mouth.

              • Matt, so in two posts back to back you’ve flip-flopped from something like “Daniel has no idea what he’s saying” to “actually Daniel pretty much knows what he’s saying but it’s not what I understand Phil is saying”

                Perhaps you should read things carefully and think about the idea that maybe other people are talking about something you are misinterpreting and that it’s not external to you that other people have no idea what is going on, it’s that you don’t get what they’re saying.

                Below you will see that *phil is explicitly interested in the behavior of the statistical distribution of housing type, quality, and rental price in the presence of severe regulatory constraints on changes to the rental price* and that this can’t be modeled by supply and demand curves because *those are explicitly about the spot prices in the market*

                That you can’t fathom this should maybe give you pause.

                That other people keep coming back here and saying “well why aren’t those rich people already living in SF” they should maybe think about that fact that unlike a situation where a rich person can simply go to a landlord and say “i’ll give you $X if you don’t renew your current tenant’s lease”, in fact *no amount of money can force a person in a unit to move out* and so if you want to force that person out, you need to pay the tenant directly.

                Now, how much should the tenant hold out for? Suppose you have a 50 year old healthy tenant with a life expectancy of 90 years currently paying $800/mo for an apartment that would probably list on craigslist for $3500. This means they’re receiving $2700/mo in amenities. Further, housing prices are increasing something like let’s say 8% per year over the last 20 years, so let’s extrapolate that into the future with 2%/yr inflation so net 6% increase in real amenity per year. I’ll simply calculate the monthly Net Present Value:

                sum(2700*(1+.06/12)^i,i,0,40*12) = 5.4 Million Dollars

                So, yeah, definitely there are not very many people willing to pay $5.4 million dollars for first months rent, and then $3500 a month after.

              • Jonathan (another one) says:

                You’re right that you can’t get distributional considerations out of the Econ 101 supply curve. But it’s not necessarily always true that the top end of the market is where it’s most profitable to build. it’s of course a question of relative demand. It might be possible (albeit politically extremely damaging) to build really bare bones accomodations for less wealthy people and make more money doing that than you do building luxury condos. (Picture 150 square feet or so per apartment… way below code.) So that building is stopped by (a) the same regulations that stop you from building anything; (b) residential zoning laws; and (c) human decency. Merely freeing up (a) won’t get you there. In any case, there are well-defined economic models of supply and demand with heterogeneous capacity choice. Those are the models you’re looking for, I think. Something like: (I read the introduction on Google and it seems like just what you’re looking for.)

              • Matt says:

                Daniel, ok; I await the appearance of your publication in Econometrica.

              • Phil says:

                Thank you for using your time and patience to comment. It is obviously frustrating to you. And thank you for suggesting a simplified model. As I write this I’m not 100% sure it will capture all of the key features, but let’s find out.

                You do not need to introduce a third type of housing, or at least I don’t think so. I am perfectly happy to have all units be one of just two types, although this obviously greatly limits the realism of the model.

                So in this model we aren’t talking about San Francisco, which has essentially a continuum of housing sizes and ages and charmingness-es and resident incomes, but rather an alternative San Francisco in which there are only rich people and proles, and there are nice big sunny pleasant apartments that only the rich can afford (type H), and tiny cramped dark apartments that the rich people would never deign to live in (type L).

                In addition to alt-San Francisco, there’s an alt-Rest-of-the-Area, which also has only type H and type L housing.There are fixed supplies of housing of type H and L in both alt-SF and alt-Rest-Of-The-Area. Both types of housing are more expensive in alt-SF than in alt-ROTA. We have a stable equilibrium. Fair enough, Matt?

                I suppose we might also need an alt-outside-the-area, which is a reservoir of people who could potentially move to the area given the right housing costs and income potential.

                Now we build more type H housing (but not more type L housing) in alt-SF. If the people living in alt-ROTA had been willing to pay alt-SF prices to live there, they would have, so the price of type H housing has to come down…but it doesn’t have to come down very much, because (in the real world, I believe) there are plenty of high-income people who would like to live in SF if it were just a little cheaper.

                So we’ve built more Type H housing and thereby moved more high-income people into SF, with the newcomers paying slightly less than the ones who were here already. Or do we assume all type H people get exactly the same lease, so the price comes down a little bit for ALL the high-income people? Do we charge everybody the marginal rate to fill the final unit? It is surely simplest if we assume that, but it’s also less realistic. I don’t think it will matter for my qualitative claims, so for simplicity I’ll assume everyone in Type H housing pays the marginal price to get the last unit occupied, so when we build more Type H apartments the price for everybody comes down. All of the high-income people who were already in SF are now paying a bit less than they were before, and all but one of the newcomers is paying slightly less than they would have been willing to pay for a place in SF. We have made a lot of high-income people very happy. (Or, if you prefer, we could have each type H person pay as much as they’re willing to pay, in which case we haven’t made anyone happy — ah, economics, the dismal science.)

                These additional high-income people create an increased demand for proles in alt-SF. They either have to live in the type L housing in alt-SF or they have to commute from alt-ROTA, so the price of Type L housing in alt-SF gets bid up a bit.

                The wealthy people who moved to alt-SF have vacated Type H apartments in alt-ROTA that will not sit empty, they’ll be filled by people from alt-Outside-The-Area (uh oh, poorly chosen name, we now have alt-ROTA and alt-OTA…well, I’m not going back to change it). Of course, to get them in from outside the area, the price of H housing in alt-ROTA has to come down just a bit.

                This all agrees with what I’ve been saying, doesn’t it? We’ve built more Type H housing in alt-SF, and the result is lower prices for Type H housing there, but higher demand for Type L housing there.

                We have moved some wealthy people out of alt-ROTA, and replaced them with people who are less willing to pay for housing in alt-ROTA, so the price of Type H housing in alt-ROTA has come down.

                I’m trying to anticipate what you, Matt, might say to this. Do I have something wrong? I don’t see where (obviously, because if I did I would fix it!). Maybe you will say I have it right, but even though the price of type-L housing has gone up in alt-SF the welfare of the proles has not decreased because we have to bring in another component, which is wages, which will go up?

                I fear you have thrown up your hands in disgust and won’t even read this comment, and that would be a pity, because I would be very grateful to be shown what I have wrong. I mean, yes, it will be embarrassing, but I’d still vastly prefer to know. I hope you will respond to this.

                And for the record, you attribute to me a certainty that I don’t have. I’m not sure I’m right. Obviously I think I am, but I assure you, I am willing to be convinced that I am not, even (or perhaps especially) with the use of simple models like the one above.

                Thanks very much for carrying so much water on this. I have to confess don’t think I’ve read everything you’ve written (you’ve been very prolific), although I’ve read quite a bit. I know you have put a fair amount of emphasis on rent control, which is clearly a large distorting force but I think (see above) that the effect I’m talking about does not rely on rent control.

                I see you have also written about things like lack of transparency in the markets, and other real-world issues that I had not thought about. I see what Matt means when he says you seem like you know what you’re talking about, and that I don’t!

                I, too, think an agent-based model might be the best or at least easiest way to model these systems. You have a bunch of agents with different preferences and different abilities to pay, you have a bunch of units with different characteristics, you create a system for the agents to bid on units…it seems reasonably straightforward, although to actually implement it seems quite daunting to me. If you are willing to try, well, shucks, go for it!

            • Sam Bailey says:

              I’m in the same boat as Matt, I don’t quite understand where the equilibrium style of model breaks down.

              > All economists believe (and I do too) that we are very far from that equilibrium. If building were unregulated, there would be far more housing in SF than there actually is. So the equilibrium model just doesn’t apply.

              From that equilibrium, maybe, but that’s just because the supply and demand functions for the “free market” (if such a thing has ever existed in housing markets) aren’t the ones describing the scenario here. There could very well be an equilibrium for a supply and demand system that factors in the regulatory costs of building. (For example, the system Matt suggests where supply becomes vertical at some point.)

              • Jack pq says:

                @Phil you may be right that a simple 101 model misses things, but I don’t think it makes sense to talk about being out of equilibrium or about S and D matched or not ( if you want to talk economics you have to use the concepts correctly). If supply is fixed in SF then this function is a vertical line and you still get an equilibrium. Then if demand increases price increases and Q stays fixed. If supply is relaxed this function now has a less than infinite slope, and so the new equilibrium has a lower price and higher Q.

                The angry responses are probably because economists are tired of hearing physicists, biologists and other natural scientists spout crank theories without bothering to learn a little economics first. I’m Not saying that describes you. But it’s a commonplace phenomenon and economists are tired of this arrogance. You were just caught in the cross fire.

              • Jonathan (another one) says:

                I’ve stayed out of this up until now, but I’m with those who are really confused by what you’re calling “equilibrium.” Equilibrium simply means (a) no one wants to live somewhere they don’t *at the current asking prices,* and (b) no one *allowed* to build wants to do so given the profits they can earn from building. So why do you say the market is “far from equilibrium?” Under (b) supply is in equilibrium because no new building is allowed and no one, including you, is doubting (a), which is a fundamental part of your model.

              • Phil says:

                Matt, Sam, JPK:

                I agree the market is in equilibrium — well, actually no, the economy is very dynamic, but I’m happy enough with the thought experiment that the market could be in equilibrium, or I guess we could talk about dynamic equilibrium — it’s just not the “free market equilibrium” that would be attained if builders were allowed to build what they want. You guys don’t think that matters because you can just make the supply-vs-price curve vertical at the current price. Maybe you’re right but I don’t think so: I think the current situation distorts the statistical distribution of housing prices (not just the mean or median price) and I think this matters. I think this is germane to JPK’s question/comment as well: (his question is, if there’s all this pent-up demand for apartments in SF, why don’t rich people outside SF bid up housing prices even farther, and he goes on from there with related questions/observations/etc?)

                I think that if the market were in or near free-market equilibrium, then when builders build more units they would (collectively) build units for both wealthy people and non-wealthy people. Some builders would build big buildings with spacious high-ceilinged apartments with nice wood floors, stocked with high-end appliances, and others would build tiny apartments with vinyl floors and refrigerators rescued from the junkyard, and others would build for the market in between.

                In the current state, though, there’s far more money to be made at the high end of the market than elsewhere. Nobody is going to build apartments for hoi polloi (except as forced to do so by legal requirements to provide such apartments).

                You guys tell me: am I wrong about this? If you simply make the supply curve vertical at the current price, does that somehow tell you about the statistical distribution of what units get built?

                Economists seem to be able to compress the state of any market into two curves on a plane (an aggregate supply curve and an aggregate demand curve) and to describe the whole system by changes to those curves. I won’t claim that that is wrong but I can certainly say that I don’t understand it. My understanding of supply-demand curves is at Econ 101 level: a widget-maker is trying to decide how many widgets to make, and at each price he is willing to make a certain number. Widget-buyers are trying to decide how many widgets to buy, and at each price they’re willing to buy a certain number. Where the curves intersect is where you end up.

                At least with my simple understanding of that model, I cannot describe the housing market that way and I’m skeptical whether anyone can (which is not the same as saying I refuse to be convinced). The housing market includes a wide distribution of houses and apartments, even within a single neighborhood of San Francisco: there are big apartments and small ones, big houses and small ones, old buildings and new buildings, sunny units and shady ones, units on noisy streets and on quiet streets, etc. etc. The owner has some limited ability to change a few of these characteristics: they can subdivide an existing unit (up to a point), or they can knock out some walls and convert multiple units into a single one, and so on. All of these changes cost money. Many characteristics can’t be changed at all.

                For any single unit, every potential customer has their own demand curve. The aggregate choices of all customers over all units leads to the housing market that we see: there is a very wide statistical distribution of housing prices, in San Francisco and elsewhere. There are people of all income levels who would be willing to pay a premium over their current housing costs in order to live in San Francisco, but the market is in equilibrium (!) and these people aren’t quite willing to outbid people who are already in the city for the units that they already occupy. Now build some more high-end housing in SF. Let’s make it really simple and say there are 1000 new apartments that all rent for $4000/month, and they’re just a teeny tiny bit nicer than 1000 apartments that people in SF are already paying $4000/month for, so 1000 current SF households move out of their old $4000/month apartments and into these new ones. Well, now the people outside SF who would have been willing to pay $3999 for one of those now-vacated apartments, but not $4001, are able to move in at $4000. So they do.

                I’m sorry — genuinely — that I can’t really address your criticisms/comments in the supply-and-demand-curve language that you prefer. I just don’t know how. Could I ask you guys to try the opposite exercise? Would you take a look at what I’ve written in this comment, and in the one above that starts “I don’t think that’s true”, and explain how I can understand/explain this in your terms? Or, if you think I have it completely wrong, then you could point out where. Or you may conclude (as I think is the case) that the system simply can’t be modeled sufficiently well with a single demand curve and a single supply curve.

                (I don’t want to draw Andrew into this, but I see some analogy with Andrew’s feelings about causal models, which you might be familiar with if you are followers of this blog: he always wants to see things analyzed in terms of the effects of a clearly specified intervention, rather than as parameters from a causal model, because he doesn’t understand the causal models. Some modelers tell him that he’s being silly, but Andrew says (paraphrasing) that if you can’t use your causal model to predict the effect of an intervention then what good is it and in what sense is it a causal model?.

                Similarly, I’m saying I don’t understand how to get distributional information out of the supply-demand curves, and asking you to do it for me, if you’re willing.

              • Matt says:

                Phil, you are correct that the econ 101 model can’t describe the statistical distribution of housing prices, but it is a very powerful tool that can provide good intuition on a lot of problems.

                Why don’t we meet somewhere in between – it will be hopeless to provide an economic model for the entire distribution of housing, so why don’t we just say there are two types of housing – low-end (L) and high-end (H). Suppose both markets can be characterized by standard supply and demand curves. You can think of the slope of the supply curves as reflecting land regulations, building costs, etc (so if housing is fixed due to regulations, the supply is vertical). So, from what you’ve been pushing, you say suppose more type H housing gets built. But wait, maybe that’s not what you are saying. Here you write:

                “Now build some more high-end housing in SF. Let’s make it really simple and say there are 1000 new apartments that all rent for $4000/month, and they’re just a teeny tiny bit nicer than 1000 apartments that people in SF are already paying $4000/month for, so 1000 current SF households move out of their old $4000/month apartments and into these new ones. Well, now the people outside SF who would have been willing to pay $3999 for one of those now-vacated apartments, but not $4001, are able to move in at $4000. So they do.”

                This actually isn’t that simple. This sounds like you are introducing an entirely new product into the market – these slightly nicer houses (H* lets call them). I think we would agree that if they were the exact same type of houses as the H-type, then prices would have to fall a bit for people to move into these houses (assuming demand is unchanged), because we know that the people not already in SF have a slightly lower willingness to pay then those who are in SF.

                So now you are saying that this brand new market of H* houses attracts some demand (people move from the H houses to the H* houses). Then, you say that the people who were not quite willing to pay for type H houses before, are now willing to pay. But, to me this means the price has to drop, at least slightly. They weren’t willing to pay for a type H house before, but now that there is a new supply of H* that has pulled some of the H market tenants away, there is some downward pressure on the H-type price which allows new tenants to move in. If there is no downward pressure, then nobody moves in. Then, suppose some of the L market moves to claim the type H market houses as you have said, by the same logic prices will fall for the L market housing.

                This to me has to be the first-order effect of adding new housing. You have then gone on to say that because there are now more people in SF, there will be increased demand for other goods and services in SF. This is true, and this new excess demand will cause an increase in labor demand which will attract workers and put upward pressure on housing prices in the L market (if these are the people who work in services). But, this second-order effect will not overpower the first-order price decrease. If it did, then workers would not move in. The logic is that, although a worker could get a higher wage in SF, if he has to pay an even higher rent, then his real wage is probably lower in SF than it is elsewhere, and he will not move in.

                Daniel has provided a model where rent control play an important role. The problem as I see it is that his model is not really tractable, and I can’t understand how things will play out in equilibrium in his model.

              • Phil,

                I’ve been crusading for you a bit on this, and it’s because it’s a question very close to my interests, and I think standard models of economics are simply unable to address the questions that you have. That’s not to say that economists have no ideas here, just that there’s something missing from the textbooks, there are lots of simplifications in that textbook description.

                I do actually know something about both economics and finance, though I’m not a professional economist, nor am I any more a professional finance quant (though I played one in my early career and still have friends in the financial quant world)

                So, here are some ideas about how you’d get information about distributions of houses:

                There are let’s call it 300,000 apartments in SF, each one has some unique features, and a unique location. Yes, nearby apartments of similar sizes are more or less exchangeable in terms of preferences, but the farther away two apartments are, the less exchangeable they are. So, it makes sense to model this as a single supply and demand curve for *each* apartment, with statistical coupling between nearby apartments, like some kind of covariance function.

                Furthermore, there are people with rent control. People with rent control hold a lease which is *in essence* a very valuable bond. See where I calculate that a person with a pretty sweet rent control deal owns a bond worth on the order of $5 Million dollars under “all else equal” assumptions.

                Now, what we have is a situation where for apartments indexed by i, there is a market price for that apartment *without* the bond, and there is a market price for the apartment + buyout of the bond. The market price of the rent on the apartment may be something like on the order of $3500 but this is more or less made irrelevant by the fact that the bond is worth somewhere between 0 and $5M depending on conditions UNIQUE to that apartment and renter.

                *each apartment* has a supply curve. If it’s a market rate apartment, then it’s 0 up to some value like $3500 or $4000 (outbidding the current renter) and 1 afterwards. That’s a very very different curve than the smooth supply curve you see in textbooks. It is a step function. If it’s a rent controlled apartment, the supply curve is 0 up to potentially some multi-million dollar amount, and then 1 afterwards. Of course as I say there are some nearby apartments that might be exchangeable and you could statistically aggregate them into a slightly less rough curve, but it’s still maybe a few hundred steps not a smooth curve.

                Now, also each apartment has some demand curve. But this demand curve is a constantly changing function like the absolute number of atoms in a crystal of sugar at equilibrium in sugar water. it’s just constantly the case that atoms bind to and release from the crystal. But unlike atoms where the quantities are 10^23 molecules, we’re talking about a few tens to hundreds of thousands of latent “sugar molecules” = families in Oakland, Berkeley, Emeryville etc, and probably only a few thousand who are interested in any particular small region of SF (like a 6 block radius or whatever). So, the demand curve isn’t a curve, it’s a discrete step function with 100 or 1000 steps, one for each of the 1000 people who are hunting for apartments in that 6 block radius, and It is constantly churning in time.

                Given this something like 300,000 apartment + 350,000 person system, you have a 650,000 dimensional dynamical system, with correlations (because each person maybe cares about a few hundred apartments for example). I personally think Physicists are more comfortable with this kind of concept than Economists are, it looks like solid state quantum physics more than anything in an economics textbook. That’s why economists talk about perfect substitutions, because it collapses the system down to 1 smooth S curve and one smooth D curve as you average out everything.

                But that’s just not what we have in SF.

                So, when you build market rate housing, what happens? Only people whose bond value is smallish (so they’re not renting way below market) will consider moving, and they’ll move if they like the new housing better than the old. This essentially transfers the bond from the renter back to the landlord. Now the landlord has a single supply curve which is 0 up to some value and then 1 afterwards. This value is uncertain, because information in the market is scarce because liquidity is scarce and turnover is not that much. So, they advertise at some low price, attract people to bid, the advertisement causes a step-function demand curve to accumulate of only a few tens of people (who show up in the first day and start bidding) and so some market rate gets determined for this individual unit that is based on the very specific conditions of who finds out about the apartment in the first few hours. Now, not every apartment goes like this, perhaps some get put up on craigslist at high rates and lower until they find a taker, but that again is a very stochastic rough discrete dynamical process. We’re not talking about smooth curves, we’re talking about constantly churning step-functions.

                Now, what about supply of new housing. Well in the “build nothing” scenario, it simply doesn’t exist. But in the scenario where you have “build a little bit” because of space constraints etc you get building that is very expensive. You have to buy things, tear down, put up, and get approval for the plan. Also building materials are expensive in the bay area, and labor is expensive. So the supply curve for “build more” looks like zero out to some minimal cost of building and then steps up to a few tens or hundreds of units out in the region of say 20 million dollars to build a 100 unit apartment complex. Furthermore, there are only a few locations where it can be done. Again, a step function, very rough. Now what does cost of building make the minimum rent look like? Let’s say $20M to build 100 apartments, that’s $200k per apartment, so it has to be more than the cost of borrowing $20M at say 4%, and so when I go to google’s mortgage calculator, and put in 20M at 4 percent for a 10 year commercial loan I get $202k/mo in mortgage payment, divide by 100 and you get something like $2025 is the minimum rent you can supply at and make no profit at all.

                But, also, there’s some risk involved, and some need to earn profit to make it worthwhile, and it takes a couple years to do all the paperwork and get all the construction finished, and there’s market uncertainty about whether the whole thing will crash before you finish. So realistically market supply curves at individual sites involving building 100 unit complexes are something like zero out to say $2500 a month and then 100 after that.

                Now it’s pretty clear why it is that people don’t build tiny apartments with refrigerators scrounged out of recyclers… because even doing that you’d rent at something like $2500/mo and no one wants to live in a dump for $2500/mo, so the demand curve is zero for low quality at 2500 per month. So you have to raise the quality, which isn’t that expensive, it goes maybe from $19M to build the 100 unit apartment complex as a dump to $20M to build it as a pretty nice place. All the cost is in labor and base materials and bribing officials or whatever, it doesn’t cost that much to put nice carpet and good refrigerators and a nice kitchen in each one. Let’s say an additional $10k each times 100 units is the $1M marginal that I mentioned.

                So, here we are. The distribution of what it is possible to build is based on the fact that due to the cost of capital, minimum rent to get started is around $2500/mo and the distribution of what people are doing in terms of dynamics in the market are down to this enormous number of highly variable virtual bonds holding the system into place with high friction. It’s not a LITTLE friction that the mic-drop economists are discussing here. It’s millions of dollars each apartment, at least until the crash.

                So, if you want to play with some kind of agent based model of the rental market with 500,000 agents and 300,000 apartments and some externally imposed distribution of desirability of a given region for each agent, you could get decent information about what is really going on.

              • Matt says:

                Daniel, so you don’t think any simplifications can be made in a model of housing in SF and still get useful information out of it? You can’t, for example, assume that preferences are identical for people with similar characteristics (age, education, marital status). You aren’t willing to group houses into rough groups and call them perfect substitutes within that group? C’mon.

                I would love to hear your take on macroeconomics, things get a little more complicated in the aggregate. Economics isn’t physics, we are modelling human behavior which is a little less predictable than physical nature. You have to make assumptions. Your model is completely intractable, and I don’t see what anyone can take away from it. My take away from your comment is “Well, this is really complicated so let’s just not model it”.

              • Matt. au contraire, I think it’s totally tractable, you just don’t have enough background in those kinds of models because you’re not a physicist ;-)

                Here’s where I describe how to get started and extract a lot of interesting information about this treatment:


                An agent based model can take these things into account. A model should be as simple as possible but not simpler. I don’t think you can simplify a lot below the level of this agent based model and get much meaningful information *about the time evolution of the statistical distributions of housing and how they change in counterfactual situations of build/nobuild*

                Sure, you could get lots of simpler information. Like you and I and Phil will agree that if they build housing in SF the average cost of housing across the whole bay area will go down, and that the most likely place where more affordable housing appears is way out on the edge… and that is deducible from a much simpler aggregate supply and demand model.

                But, if you want to understand how spatial preferences + highly variable distributions of income + rent control work together, you should just attack that problem directly and it’s very tractable, could be done on a desktop computer with a few minutes of computing time per simulation I think. Less demanding than many of my Stan models.

    • Asa says:

      I had this same question below. Downtown brooklyn is certainly an example of a place where “overbuilding” of high end new housing appears to have brought rents down:

      Of course there is plenty else going on as well…markets and public policy are complicated. Counter intuitive hypotheses are great but its really helpful to see evidence in addition to theory.

  7. Brian says:

    A few points to consider.

    (1) Demand to live in a world city like San Francisco is not fixed but grows over time as the population and wealth of the planet increases. Satisfying this baseline growth in demand requires a baseline growth in housing. This is why the argument that Manhattan has added lots of people over the years but is still expensive is not persuasive.

    (2) Even if we accept that building N new houses will mean N new residents move to San Francisco, it does not imply that prices would increase (or even stay the same). The process that determines how much new housing gets built in San Francisco certainly cannot be described by an Econ 101 supply and demand model, but the process that determines who gets to live in that new housing (note I say new housing to which rent control doesn’t apply) is much closer to being reasonably approximated by the Econ 101 model. If X number of people compete for Y available rentals and X>Y, then generally speaking we might expect a subset A of X that is willing to pay the most money will get the rentals. The prevailing rent will be based on what subset A is willing to pay. This leaves a subset B of X who want to pay less without an apartment. If you then increase Y, then these additional units would be competed for by those in B. The prevailing rent would then be based on what B is willing to pay, which is likely to be lower than the prevailing rent based on A, because if B was willing to pay more than A, then they would already be In A.

    • Right, so I propose the following model consistent with Phils ideas:

      1) The latent demand for SF apartments at market rate is something like 30,000-50,000 families currently living in Oakland, Berkeley, Emeryville, South San Francisco etc and just hoping that some place will open up in the range 1.5-3x the 2010 median (see my graph ). The fact that they don’t already live in SF is down to they can’t force out renters who have rent control by bidding higher, so their latent demand is not met. The demand for apartments in the range 0.5 to 1x the 2010 median is truly astronomical, perhaps 200,000 people. It’s just order of mag guesses, but lots of people like SF and huge numbers of people work in SF but commute and would rather not especially if they could get some low-income type housing.

      2) Every existing apartment freed in SF will increase its rent somewhat before going on the market due to the fact that all the rents are held low by rent control, even those that are pretty crappy quality.

      3) It is politically infeasible to build more than say 5000-10000 apartments in SF in the next few years.

      4) The demand from people currently living in SF or in surrounding areas for the high end apartments that will be built (say in the $3500/mo + range, +3x the 2010 median) exceeds the number of apartments that can actually be built in the next few years.

      Now, under these conditions, if you open up fancy apartments, either people outside SF will flood in and take them at $4000/mo or people inside SF will move out of their apartments and take them because they like them better and why not, they’ve got crazy salaries and can afford them.

      Every person who moves out of an SF apartment into a fancy new one will free up an SF apartment and those will now be rented at higher rates than they were before, causing more people who are “rich” to flood in from Emeryville or the Berkeley hills or whatever, or from some other part of SF causing further cascade of reset-to-market rates.

      To the extent that there is now more demand for daycare teachers and baristas and soforth, there ARE more people doing those jobs who will be working in SF, and they’d like to cut their commute times and so their demand for apartments at the lowest end of whatever is available *is* higher, maybe up from 200k people to 220k or something like that. HOWEVER, most likely there just isn’t much available. you’ll see them apartment sharing and squeezing several people into one bedroom etc (and yes, I’ve got friends of friends who do this so I know it happens) so prices at the low end ARE expensive, whether the marginal price of that “low end” housing is higher or lower than if the new fancy apartments had been opened is an empirical question requiring much more than equilibrium theory to determine because … definitely not equilibrium conditions.

      Regardless of whether the marginal price at the low end is higher or lower after building the high end apartments, every bit of liquidity causing turnover moves an apartment from being rented at lower rent controlled rents to being rented at market which is higher, and so every single move out in SF causes the price *of that apartment* to increase somewhat.

      Under these conditions, all you will ever see is “gentrification” defined as whatever price is being paid for each and every apartment only ever goes up in time and often by a lot.

      Note all of this is specific to a short time horizon while tech boom continues, say 1-7 years. There is exactly zero chance that SF will equilibriate to a free market supply-demand in 7 yrs because… no more than the few thousand houses will be built thanks to building restrictions.

      Now, is this so hard to believe? I think even though maybe Phil doesn’t know how to explain his idea, reality looks a lot like this and he’s intuited it.

      • Brian says:

        It seems that all the action is in existing units you discuss in (2). That is, most of the available rental market at any given time is existing housing turning over. So it is really the cost of these units that determines what most people pay. So let’s consider what happens to the rent of those units under your reasonable enough assumptions if instead of 5000-10000 new units you build 0. All those people outside of SF still want to live there and are waiting for apartments to become available. If you build nothing new, then that is even more higher income people competing for the existing apartments as they turnover leading to higher rents.

        As a side note, rent control does not apply to anything built in the last two decades.

        • Right but *number of turnovers* is way way smaller. So rate of “gentrification” is less, so in any given region, median housing prices are increasing slower under the “build zero” scenario, and at no point under either scenario does the number of apartments at the very low end increase (ie. it’s not true that building more market rate apartments lets plumbers and daycare workers who can only afford 0.5 the 2010 median or so, move to SF).

          Note: I did NOT know that about the built in the last 2 decades thing. Of course, how many units is that? Probably not that many right?

        • and so again I think it’s important to distinguish between the two meanings of “higher rents”

          1) Higher spot prices

          2) Higher observed prices in occupied units.

          Under the “build more units” scenario:

          (1) probably happens less, maybe things go up, but they go up less than they would have if all those units hadn’t been built, but (2) happens more.

          under the build no units scenario

          (1) happens a lot, spot prices continue to skyrocket on the tiny number of vacancies, but because the number of vacancies per year is small (2) happens less.

          It’s this confusion that needed to be ironed out in Phil’s last post.

          • Matt says:

            What is your model providing as far as empirical predictions go that the S&D model cannot? Now that we’ve clarified that you agree that prices will be higher if no building is done (as a simple S&D model predicts when there has been a demand shift), I don’t see a difference as far as empirical predictions go.

          • Put mathematically

            “Build more market units”

            will drive d(integrate(X*p(X),dX))/dt higher while at the same time driving d(integrate(p(x),x,3,inf))/dt lower (ie. very high spot prices will not accure as quickly).

            “Don’t Build”

            will drive d(integrate(X*p(X),dX))/dt lower than the build scenario, but at the same time driving d(integrate(p(x),x,3,inf))/dt higher than the build scenario, as spot prices continue to jack up rapidly even while turnover declines. Actually the decline in turnover is an interesting point, at zero turnover, there will be zero change in the p(x) curve so it’s conceivable that although spot prices could skyrocket to a bajillion dollars, basically nothing would clear and the whole market would lock up eventually.

            In this, p(x) is the probability that a unit will be observed to be rented at x = Price/median2010Price and 3 is pretty high up in the right tail of that distribution as seen in my posted graphs.

          • Brian says:

            I think you are overestimating the proportion or vacancies that are made up of new units. SF builds a few thousand units per year, maybe 10,000 at economic peaks. But between 2010 and 2015 about 120,000 of San Francisco’s 350,000 units turned over, according to American Community Survey data.

            • My point isn’t that tons of vacancies are *in new units* my point is that given the statistic about 85 percent of moves occur between units in SF (from the last debacle post) then for every 100 new units on the market we expect something like 567 turnovers in existing units in SF, if they build 10,000 units in a given year, you’d expect 57k turnovers since sum(0.85^n,n,1,1000) = 5.666. That’s a lot of extra liquidity, and a lot of reset to market, it drives prices towards an equilibrium distribution faster, and it increases the time rate of “gentrification”.

              What it doesn’t do is drive prices down into the “affordable to pre-school teachers at 0.5 the 2010 median type range” which is what Phil suggested was the hype.

          • Also, under the “build” scenario where no subsidized housing is created, we expect to see overall costs of living increase as more people, especially more wealthy people, compete in SF for other goods and services.

            This drives d(integrate(p(x),x,0,1))/dt less than or equal to 0, to the extent that there are turnovers caused by people who simply can’t afford to live in SF (buy food, etc) their turnover frees up a rent controlled unit which has a high chance of leaving the “low” end and moving upwards into the middle or high end due to rent control reset. The more general gentrification we see, the more general cost of living goes up, and these people get displaced.

            under the build *subsidized* housing scenario this would be greater than zero, but would be distributed by lottery.

            Under the don’t build scenario, it’s hard to know what happens but it depends a lot on how economic opportunities accrue to these renters. THe people renting at the low end are not all low income, some are just long-term residents with a rent controlled apartment.

            • Brian says:

              The flip side of the cost of living argument is that more rich people demanding more goods and services means higher pay for people providing those services, i.e. working class people.

              • I have no dog in the fight of which scenario is better, my main point is I’d like economists to engage this model which accords with Phil’s intuition and talk about what the various good vs bad aspects of thinking about things in this way is and whether or not it does accord with Phil’s point about building high end housing not improving the availability of affordable housing at the low end.

              • Martha (Smith) says:

                Brian said: “more rich people demanding more goods and services means higher pay for people providing those services, i.e. working class people.”

                What is the empirical evidence for this assertion? And one also needs to address the question, “How much higher pay?” even if there is evidence of higher pay. Pay can go up yet still below “living wage”.

              • Brian says:

                See the bit is the blog post below about residual incomes (income left over after housing and transportation costs). 25th percentile residual income higher in Bay Area than rest of California. That being said, I’m not arguing for or against the notion that working class people in SF (or anywhere else) earn a “living wage”, however one chooses to define that. Just pointing out that there can be effects on both sides of the ledger.


              • Martha (Smith) says:

                Brian: The residual income data are indeed interesting. I wonder how much of this is because of decreased transportation expenses for those living as well as working in the Bay area (i.e., housing close to work means less income spent commuting. And less time commuting might possibly also translate into more home cooking, hence less income spent on food.)

              • Martha (Smith) says:

                It belatedly occurred to me that the rent control situation might have influenced the residual income data. And what would be most informative would be “within subject” comparisons, since factors such as rent control can make a big difference between people’s income use.

              • Yes, yes, Martha +1000!

                People with high income potential in an SF job come to SF! And people who’ve been in SF for years with a cushy rent controlled place have WAY more residual income than they would have otherwise. You can make residual income of people go up by just freezing their rent and letting their salaries inflate with everything else. Now, of course, you make the income of people who own apartments go down… but no-one cares about them ;-)

                I don’t think observed residual income is a good measure of “economic health” in a rent controlled situation, what’s probably a better measure is Wages/SpotPrices or Wages/AverageRentofAparmentsInLast3Years or something like that. If lots of people have residual income because of rent control, of course it makes *them* better off, but it makes averages across society worse, it makes young people who are just getting their first jobs worse off, it makes the cost of producing things for society higher because it drives up wages paid to tech workers above their otherwise free market rates… It’s a big distortion of resource allocation.

              • Also note that SF is not the only rent-controlled area. Both Berkeley and Oakland have rent control (total population about 500k people), and there are probably rent controls in other cities nearby I’m not aware of. Doing a google search, apparently Richmond and Mountain View, and Alameda just enacted them. Oakland, Berkeley, and Palo Alto increased their strictness



                So, residual incomes are higher in areas where wide swaths of people are in a situation where landlords are forced to renew leases at below market rates. That’s not very surprising information.

              • Brian says:

                I don’t have a good answer on how much of the residual income results are being driven by rent control. I would just offer two counterpoints. First, Los Angeles, Santa Monica, and West Hollywood all have some form of rent control, yet residual incomes in Los Angeles county are below the state average. Also, none of the major cities in San Mateo County have rent control (or at least did not at the time the referenced residual income data was collected), yet residual incomes there are high. Second, despite rent control, rents across the distribution are still higher in the Bay Area than most of the California.

          • Brian says:

            Ultimately, I want to say, I agree that if we take as given the political constraint that 10,000 units is the max possible production, then housing costs in SF will never go down for anyone. I think this is what the YIMBY movement is ultimately about, changing that political reality. Undeniably that change would be extremely difficult, both politically and physically. You can argue that those changes would just be too painful and that’s understandable. But YIMBYs argue that the status quo is the worse of two evils. They are argue that access to a culturally and economically vibrant city should not have to be rationed by a lottery or any other mechanism.

            • Those arguments accord with pretty reasonable ideas, but to the extent that Phil has heard arguments that building more housing in SF at politically realistic rates will actually drive decline in prices to the point where housing will become affordable to baristas and pre-school teacher and whatnot… I think they’re being disingenuous, or just wrong and I agree with Phil on that on the basis of the kind of analysis I’ve done here, and which I think you have just agreed with. So I think that’s progress from where we were in the last post where people piled on with virtually the equivalent of “duh U R StOOpiD Physics DUde”

              • Brian says:

                To be blunt, there really is not scenario where baristas will find affordable housing in SF for the foreseeable future. It’s the sad reality of the current situation. In the report linked in my comment below, I and my colleague tried to put a rough estimate on the “how much would be enough” question. For SF, it was something like a 4 to 5 fold increase from historic building levels, which I often refer to as “as much as you can imagine, plus some.” There are no easy solutions.

              • Yep, that’s exactly what I think, if you build 200k units you could maybe get some baristas into 1bedrooms.

              • Martha (Smith) says:

                And if there were “something like a 4 to 5 fold increase from historic building levels”, would SF remain “a culturally and economically vibrant city”?

              • Brian says:

                Martha: Under the 4 to 5 fold increase scenario, the density of SF would be somewhere between Brooklyn and Manhattan. I think people generally consider those places culturally and economically vibrant. Would SF’s culture be identical to what is it today. Clearly not. But neither would a zero build scenario preclude cultural change.

  8. Brian says:

    I would also offer the following (see technical appendix) as some empirical evidence that demand for housing generally slopes downward. I acknowledge that it’s not a highly technical treatment of the issue and was authored by me, a humble public servant, for a more general audience.

    • Phil says:

      That is a very good report…or at least, a very well-written one. I’m just taking it on faith that the numbers are right.

      I realize there are space constraints (and constraints on how much time you can spend preparing it) but I wish it included just a bit more on salaries. Figure 2, for instance: you show the average monthly rent and average home price in different cities, but not average income.

      There is a graph that shows median share of household income spent on housing that I found quite surprising: I would not have guessed how low San Francisco is compared to some of the other cities, nor how close it is to the national average…although, as you point out, this share is at least slightly above average in all of California’s major metropolitan areas.

      I have some quibbles but in general I like this, thanks for pointing it out.

  9. Sohier says:

    Honestly, I think bringing math into the discussion is unhelpful. There are two core choices we as a society face:
    1) How many people total will get to live in SF.
    2) Which people get to live there, given that many, many more people would like to than currently can. This boils down to how much is allocated via a lottery (affordable housing or inheritance/birth lottery) and how much via the market.

    Under the current path, many people who would like to live in San Francisco will be unable to do so. Families will continue to be ripped apart no matter which allocation method we use. To me, that is more important than a precise estimate of the impact of the trivial number of new units that are currently proposed.

  10. gdanning says:

    I think you might need to post another apology. You say, “I think that in the current economic environment you would need to build an enormous amount of housing in SF to get the price to come down, so I’ve felt that people who say [that they don’t want to turn SF into Manhattan] are being disengenuous.” But, as I understand it, the amount of new housing needed to reduce the market price thereof depends on the elasticity of demand for housing. If demand is highly inelastic, then a relatively small increase in supply will cause a relatively large decrease in the market price. So, unless you are very sure that demand for housing in SF is fairly elastic (and I am pretty sure you don’t have any idea whether or not that is the case), you are on awfully thin ice accusing those people of being disingenuous.

    • Brian above who studies this stuff professional agrees that you’d need to turn SF into Manhattan to get much in the way of low end housing a Barista could afford. So, I don’t think Phil needs to apologize for anything.

      • gdanning says:

        But, “affordable to baristas” is a bit of a red herring, no? Phil referred to “getting the price to come down,” not “affordable to baristas.” How about, “affordable to people who earn the median income in the Bay Area”? Or, some other measure of affordability? Also, Brian does not say that you’d need to turn SF into Manhattan to make it affordable for baristas – he said a density “somewhere between Brooklyn and Manhattan.’

        Finally, Phil accused the YIMBYs of being disingenuous (i.e., lying) before talking to Brian, and without any apparent attempt to consider the elasticity of demand, but rather because their claim was inconsistent with his purely subjective guess about how much housing would be needed to be built in order to reduce prices. That simply isn’t kosher, especially on a blog that is supposed to be devoted to empiricism.

        • Phil, to follow up on my suggestion of an agent based model from comment:

          Suppose you actually want to run this model, how would you go about doing it? First off, I recommend taking a look at NetLogo:

          Second of all I could imagine the following, set up the model by having agents mill around randomly for a while, and then freeze them in place. Hundreds of thousands of agents is probably not that tractable, so start with something like 10k. Make them small black squares that represent houses, and assign them normal(1,0.25) occupation price which is not too far off what my graphs show here for 2010, though the tails aren’t right, it’s not that important for first look. Also assign rent control to say 90% of them, with 10% un controlled.

          Put a turtle on top of each house, and assign a desirability function for each turtle as a normal distribution in space, which has a center uniformly randomly distributed in the field, with a wideish standard deviation. So now, we have each person would like to move to somewhere else all else equal. Assign a willigness to pay for each turtle for their “most desirable” location, and have their willingness simply decline proportional to desirability (why not, it’s a start, revisit this assumption later).

          Now create an additional 5000 agents on the edge of the screen, maybe with a different color, and assign each of them a spatial distribution of desirability, and a willingness to pay for their most desirable location which is randomly distributed between say 2 and 4. These are wealthy recruits who have nice tech jobs and arrived recently.

          At each time-tick, have each turtle find the top 10 available locations (either not rent controlled, or unoccupied) by willingness to pay, and bid on each non-rent-controlled house and each unoccupied house according to their willingness to pay, and let each turtle move. Don’t have them bid if their current digs including rent control value exceeds every other option available to them. Just have them stay where they are.

          Let the system churn for a while, and keep track of the statistics of the distribution, and the rates of transitions etc. Then do it but with some small number of additional market rate houses added to the mix. Vary the parameters, and see what you get.

          This is why I say it looks more like a physicists Ising model than anything you’d find in an Econ 101 text.

          • Ack, it’s not clear to me why this wound up here. It was meant to go at the very bottom of the page.

          • More thoughts. Initial set up should probably involve letting the distribution equilibriate before you put in the additional “new recruits” so that churn is stable and a relatively stable spot price develops. Also, I’d recommend leaving at least a few apartments unoccupied initially. So if you put down an initial 10k houses, put down say 9800 agents in them, and have 200 unoccupied, then let things churn until it stabilizes, then add the 5000 outside recruits. In fact you’d probably do well to add the 5000 new recruits a few at a time ramping up in time.

            Statistics you should track include the median clearing price at each time tick, the total value of the rent-control bonds, and the number of houses cleared per tick.

            It might make sense after running the model forward to a certain point, to save the state and then run it forward from that state with different assumptions on the building rates, look at the counterfactuals regarding what happens to the price of housing in each decile of the distribution, and what happens to the bond values etc.

            Also you should track the demand curve for each house and when you drop in new houses, put them in highly desirable areas in the same way that most builders would like. Next compare to where you have to put them in less desirable neighborhoods. You could allow preferences to shift, under an assumption that people with high levels of income like to live together, so track local averages over patches in Netlogo of the rental prices, and have individual turtles shift their spatial preferences towards regions where people of similar willingness to pay live…

            It’s actually a really fascinating dynamical system to study I think. I’m tempted to do it myself, but at the moment I don’t think I’ll be able to do it.

            • NetLogo is really quite easy to use, and so I do think a person who’s programmed a fair amount in something like R, or Python could get a model like this running in a day or two of concerted effort, certainly less than 5 days of coding and testing. It’d be real concerted multi-hour sessions of programming, but it wouldn’t be a 6 month project it’d go from figuring out the technicalities of the implementation to figuring out what features you need in the model some time in the first few days.

            • AnonAnon says:

              At one point in my graduate career, I worked pretty extensively with Netlogo. I think it’s a wonderful tool for problems formulated like this but I just want to throw out the caveat that in my experience it doesn’t scale well. Largely because it wasn’t built to scale well. It was built to make ABM accessible. So it might choke before you get to a model you can believe in. Not a criticism, just an observation from experience.

              • Yeah, good to know. What you say doesn’t surprise me. And I’m sure there are computational tools that are more performance oriented. How long ago was it that you were working with it? I’ve done some stuff recently with it involving up to several thousand turtles in a reaction-diffusion-growth sort of model, and it ran reasonably well. It’s written in Scala and of course benefits from improved Java virtual machine software, so it is possible that it’s somewhat more performance enhanced now than at various times in the past, not to mention that machines are also a lot more powerful than 5 to 7 years ago say.

                I definitely doubt you’d do well scaling a model like this to 500,000 turtles bidding on 300,000 apartments… but 1/10 to 1/20 of that size I think would probably be ok, just a guess, and of course based on your coding skills and soforth.

                Do you have any suggestions for alternative ABM systems, maybe something that compiles to machine code?

              • AnonAnon says:

                From memory, I recall swarm was supposedly less user friendly but did scale somewhat better. but the site hasn’t been updated in almost a year and it’s looking pretty sparse.

                The last large scale model I remember seeing back in 2010.

                Its ABM component is MASON (built in java … haha programer jokes).

                But at this point I’d probably start with the site and dig around from there. Keeping an eye out for any work moving the computations of to the GPU using something like CUDA.

              • AnonAnon says:

                Oh and to answer your other question, most of my work with Netlogo was early on in grad school (’08-10). So while I’ve tinkered with it since then, it certainly sounds like you’ve done more recent work.

              • I think the way to go with this is to start with netlogo and if it struggles work with small models until you have all the model components specified and then code the model in Julia and run bigger versions there.

              • I did a little reading on NetLogo performance, and it seems that at some point in the past it changed from being an interpreter of the NetLogo language to being a compiler from NetLogo language to JVM bytecode. After a while the modern JVM will just-in-time compile your stuff, so basically if you want to run a big simulation, you have some start-up inefficiency, and then you run at full JIT compiler machine code speed. This may explain part of why I experienced pretty good performance.

                Also, a stackoverflow thread pointed me to this paper on how to optimize NetLogo code:


                and a lot of it is related to pre-computing agent sets so that inside loops you don’t have essentially a further loop inside NetLogo’s libraries to find which agents satisfy some property.

              • AnonAnon says:

                Thanks for the links! It looks like I might have to revisit some of the old models I have and play around with them to see the performance.

            • Phil says:

              I was mulling this over on my bike ride this morning. The basic structure of the agent-based model would not be hard but it’s hard to choose a level of complexity that works for the real world but is not too hard to code.

              I’m imagining three groups of houses, each representing a different region: SF, Bay Area Not SF (BANS), and Outside. I am not sure whether Outside is really necessary to capture the dynamics, but it is probably necessary for making a model that looks something like the Bay Area.

              Wihin each group, there’s a distribution of ‘niceness.’ If I were to decide, for each unit, how much I am willing to pay for it, then within any of the three areas my price depends on the ‘niceness’, as well as on my income. As for the difference between groups, I might assume everyone would pay more in SF than in BANS or Outside for a unit of equal niceness, and that everyone would pay more in BANS than in Outside. I wouldn’t want to try to model different areas within SF as different niceness, etc., unless I wanted to study the local effects of gentrification. Start with a distribution of niceness across the homes in each group.

              So far, so easy.

              But there’s still lots of stuff that needs to be specified, so the number of functions and parameters that need to be specified can get fairly large, though not huge. We need some concept of the economy associated with each group, so if we build more housing in a group and thus bring more people into it, there is some increase in the income of the people who work in that group. Does this mean we need to keep track of not just where people live but where they work? Maybe so. But then we need to include the preference that people have for living near where they work (and vice versa).

              If we had such a model, it’s easy to think of nice things to do with it. But it’s a fairly hard model to write. It also seems like the kind of thing someone should have done already, so maybe they have.

    • Phil says:

      In contrast to the essentially nonexistent amount of work I was able to find on economic modeling of the actual situation in the Bay Area, there has been a ton of work on what the situation would be like if building were unconstrained, so that building could take place as long as the price people are willing to pay is greater than the marginal cost of buildng. An example is Hsieh and Moretti, which says “San Jose and San Francisco would grow by more than 500%, while Austin would increase by 237%.” They are up-front about caveats, but they really do think San Francisco would grow an enormous amount. There are other papers that have looked at this (by Glaeser et al., for example) and they also predict very large population increases for SF under a free-market scenario. Oh, and it’s worth noting that even under the free-market models I’ve seen, rents would still increase over what they are now. To actually get them to decline, you’d have to “overbuild” compared to the free market.

      • gdanning says:

        Isnt that quote from Hsieh and Moretti about the size of the labor market? Not about the size of the population? It also says that NYC would increase by 787% if there were a free market in housing – are they saying that NYC would almost 9-tuple in size? Over what time period?

        More importantly, that paper is not about “how do we get the price of housing to come down,” nor about “how will an increase in supply affect housing prices.” It is about “what will happen to the US economy if NYC, SF and San Jose had completely free housing markets.” That is a very, very different question. Do we even know if the YIMBYs are advocating for a “free market scenario” as that is defined in the Hsieh & Moretti and Glaeser papers?

        it is perfectly plausible for YIMBYs to argue for a much denser SF, yet one that is not nearly as dense as Manhattan. They might simply believe, “we want housing supply to be as high / prices to be as low as possible, without becoming too much like Manhattan.”

        And, most importantly of all, even if you are correct, unless you know that the YIMBY’s were aware of the studies you cite, you should not have called them disingenuous. There are many other adjectives you could have used.

        • Phil says:

          If you can figure out how to get 9x more laborers without having an increase in population of approximately the same magnitude, let me know. Even if you put all of the children and retirees to work, but that’ll only get you like a factor of 2.

          I think it is entirely reasonable to say “I want enough housing to be built that I can afford to stay in the city, but not more than that because I want the city to change as little as possible.” But if you say that, you have to also acknowledge that once that density has been achieved you are going to be in exactly the same moral position NIMBYs are in now: yes, we know we would need to allow a lot more building in order to reduce rents (or to prevent them from rising) but we are not going to do that because we don’t want the city to change too much.

          • Carlos Ungil says:

            Are you changing your position or is it just a rhetorical argument?

            Your original claim was “YIMBY people want more housing but this will make prices go up”.

            Now it seems to be “YIMBY people want more housing to make prices go down, but once they can afford to live in SF they will join the NIMBY camp” which is a completely different argument.

            • Phil says:

              Carlos, No, not changing my position. I believe that in the current situation, building more market-rate housing in SF will make housing prices in SF go up. Of course the population will go up too.

              I think that if impediments to building are relaxed in the entire Bay Area, a lot more building will happen in the whole area. The population of the area will go up by a huge amount (Hsieh and Moretti estimate a 6x increase in SF and Silicon Valley). They say that if that is allowed to happen then housing prices will stabilize. I don’t have any reason to disagree with them.

          • gdanning says:

            Sure, at that point the YIMBYs will be NIMBYs, and moral equals. But, how is that relevant to your claim that YIMBYs are being disingenuous when they say that they are not advocating the Manhattanization of SF?

            Re the pop increase v. the laborer increase, I am sure that the workforce of SF has increased far more than has its population over the last 30 yrs. But my main point is that the study you cite might not quite be saying what you think it is saying – a NYC with 9x the population would be far, far larger than any other city in the world, so one wonders what the time frame of the model is, or what the assumptions are — they might well be such that the study doesn’t really support your argument.

            And, moreover, I have yet to hear someone explain why I am incorrect in my understanding that 1) demand for housing is highly inelastic; and 2) therefore, a relatively small increase in supply will yield a relatively large decrease in price. I might well be wrong – there might be complexities to the housing market in places like SF that I am unaware of, and/pr the effect might be very short term – but I am pretty much sure that that is what basic S/D says.

            • Phil says:

              I speak subject to correction from a real economist, but I think if we were near the free-market equilibrium then you would be right. Go to a city that is neither shrinking nor growing, build 10,000 new homes, and you’ll have to sell them really cheap, because if people in those cities were willing to spend much more than the cost of building a new house in order to have a new house, then someone would have already built those houses and sold them for a nice profit.

              But the Bay Area isn’t like that (neither is Austin, Manhattan, or many other places with restrictive zoning and strong economies). There are people commuting from outlying suburbs who would be thrilled to buy a new house here at twice what it costs to build (or to rent at a rate that corresponds to a net present value of twice what it costs to build the unit). And if you build a bunch of those homes and fill them, there will still be a ton of people who would be thrilled to buy or rent at 1.9x what it costs to build…and so on. You have to build a huge amount of housing here to get to the point that you get a big reduction in prices when you add another unit. How huge an amount? That’s the kind of thing Hsieh and Moretti, and Glaeser and Gyourko and Saks, and a bunch of other economists, have looked at. They all conclude: huge.

              • Sam Bailey says:

                > And if you build a bunch of those homes and fill them, there will still be a ton of people who would be thrilled to buy or rent at 1.9x what it costs to build…and so on. You have to build a huge amount of housing here to get to the point that you get a big reduction in prices when you add another unit. How huge an amount? That’s the kind of thing Hsieh and Moretti, and Glaeser and Gyourko and Saks, and a bunch of other economists, have looked at. They all conclude: huge.

                So, it sounds like there are two arguments you’re making, which don’t fully mesh:
                1) In this post, it sounds like you’re just saying there are lots of people willing to pay lots to live in San Francisco, and who can’t because they are constrained by quantity, not prices. Thus, more building would not lower prices for a long time. That would not necessarily raise rents, though, they just won’t go down.
                2) There’s another argument, which I think is your main one, that as wealthier people rent in San Francisco, they increase the demand for low-paying services like barista or barber. Thus, if we build an additional unit, it will get filled by a rich person, who will increase the pressure on other units because his or her “real” demand for housing includes all the people who need to serve him or her coffee, cut hair, and so on.

                Is this correct?

              • Phil says:

                Re your point 1, of course everyone is constrained by prices. I think there are a lot of rich people outseide SF who would like to live there, and could afford to if they were willing to outbid someone who already lives there, but they don’t think they’d get enough for their money. For that matter there are a lot of low and medium income people who fit that description too. The key point here — and this is genuine economists talking, not just me — is that these people are willing to pay far more for housing than the cost of building that housing. In a free market that would not be the case (they say, and I don’t disagree): people would have already built housing and made a profit off the difference between what it cost to build and what they can sell it for or rent it for. This would have continued until there is no profit left to be had.

                As for your point 2, yes, that’s what I think. Actually i think 2 is trivially true and no one would disagree with it; the disagreement is whether this means that more market-rate housing in SF will decrease, increase, or leave unaffected the cost of housing in SF. As more than one correspondent has pointed out, in order to fill that new unit you have to charge slightly less than the rate for existing units of the same attractiveness, because if someone were willing to pay more for a unit of that attractiveness they would have outbid someone who is in one. So building more market-rate housing decreases the price of housing. However, whoever moves into that unit brings money and economic activity to the city, as mentioned, thus creating more demand for workers. Near free market equilibrium you have to make some funny assumptions to make the second effect bigger than the first. I agree with all of that.

              • Sam Bailey says:

                >I think there are a lot of rich people outseide SF who would like to live there, and could afford to if they were willing to outbid someone who already lives there, but they don’t think they’d get enough for their money. For that matter there are a lot of low and medium income people who fit that description too. The key point here — and this is genuine economists talking, not just me — is that these people are willing to pay far more for housing than the cost of building that housing.

                Sorry, I’m still a little confused by this. There are rich people who want to live in San Francisco, and can afford to live there, but don’t because they’re not willing to pay the rent? That sounds like not wanting to live there. (Or if they do want to live there, it’s in the same way I’d like to exercise more, or learn another language, or one of the many other things my actual habits suggest I don’t want to do.)
                It sounds like in your setup everyone has a minimum quality threshold *regardless of price*, and the rich have a higher threshold than the poor. There are also luxury apartments the poor will never live in, again, regardless of price. So, there are some places only the poor will live in, and some places only the rich will live in. I don’t see why that is true, but perhaps I’ve messed up something?
                As far as willingness to pay exceeding cost: I think the YIMBY argument is it actually doesn’t exceed cost as it currently exists, but part of that cost we could remove through policy change. So if by cost you mean “what you spend on labor and materials to erect a new structure,” I agree, but I’m not sure that’s the only things that matter.

              • gdanning says:

                I guess I am not sure what you mean by not being near free market equilibrium. Yes, there is rent control in SF, but not on vacant apartments, since that is illegal in CA. (unless the law has changed recently) Nor does rent control usually apply to new construction. And, I don’t think that restrictive zoning affects whether we are at equilibrium – restrictive zoning shifts the supply curve left, so that the equilibrium price is higher than it otherwise would be, but is does not place the market out of equilibrium the way that rent control does.

                So, I think that is where we are disagreeing re the relevance of the studies you cite – I am guessing when they say “here is what would happen in a free market,” they are hypothesizing what would happen with no zoning and no rent control. But that is not really the issue here, in don’t think; I think the issue is, what will happen if more housing is built, given current laws, etc?

                If I may, this is what I do not understand about your basic argument. The price of housing is determined by supply and demand. Demand is the willingness and ability of buyers in the market (ie, everyone interested in living in SF) to buy different amounts of a good at different prices. Eg: there might be 10,000 people willing and able to rent a 1-bed at $4000/mo, 12,000 at $3000/mo, etc. An increase in supply shifts the supply curve right, and lowers the market price. Indeed, if as you state, more housing = a higher population, then the price must have gone down – ie, to use my hypothetical data above, if there are 12000 people renting a 1-bd where only 10,000 were before, the price must have gone down.

                The only way that would not be the case is if the demand curve shifts right as well (ie. if demand [rather than quantity demanded] increases). So, I think you must be claiming that would happen, but I do not understand the basis for that claim. I think you mention that “more rich people will move to SF,” but those people are all in the market now. (Heck, I am on the East Coast, but I am in the SF rental market – I would retire and move to SF iif rent were low enough, so my demand for a 1-bed in SF is 1 apt at $500, and zero at all prices above that).

                So, I think that is the basis for much of the criticism of your posts – that your posts don’t make clear why you think that the demand curve will shift. (Perhaps someone has raised that point already – I have tried to read all of the posts, but …)

                PS: I believe that even building “luxury housing” should lower the rent for less-nice housing: If a luxury 1 bed rents for $5000/mo, and average one for $4000/mo, and the proverbial shitbox for $3000/mo, and a bunch of luxury apts are built, lowering the rent to $4000, the price of the average apt will no longer be $4000 – it will be less, because no one will pay $4000 for an avg place if the market price of a luxury place is also $4000.

            • Phil says:

              gdanning, I’m not referring to rent control, although as many people have pointed out (inclu Daniel Lakeland in these comments) it is a major factor.

              The non-free-market effect that I’m referring to is restrictions on building new buildings (or enlarging existing ones). I think everyone who has looked into the subject thinks there would be a huge amount more building in the Bay Area if those restrictions did not exist.

              • gdanning says:

                But, if you are not referring to rent control, then how can you say that the market is not in equilibrium? As I understand it, that only makes sense if you are referring to rent control – under rent control, the rental price of housing is below the equilibrium price, and quantity demanded is above quantity supplied (unlike at equilibrium, where quantity demanded equals quantity supplied). Restrictions on building new buildings moves the supply curve (or, really, prevents the supply curve from shifting left // supply from increasing in response to high prices), but that just means there is a different equilibrium, not that the market is not at equilibrium.

                Also, I am sure that the studies you posted re what would happen to employment in a “free market” for housing defines “free market” as one in which there is no rent control, so I don’t think they help your argument much.

                Lastly, how is it relevant that “everyone who has looked into the subject thinks there would be a huge amount more building in the Bay Area if those restrictions did not exist.” How does that fact imply that increasing the supply of housing will not reduce prices (which will happen, as I said above, only if the increased supply causes the demand curve to shift right – which is very unlikely – by what mechanism would that happen? If anything, the opposite is likely to happen, if the increase in housing and population robs SF of some of its charm, leads to overcrowding, etc. That would cause a decrease in demand, not an increase).

                So, again, what is the proposed mechanism in your model whereby, if more housing is built, demand (note: not quantity demanded) will increase / the demand curve will shift right? If that doesn’t happen, prices have to go down when supply increases.

              • Phil says:

                The market may be in equilibrium, but it is not in the same equilibrium that it would be in if construction were not restricted. Even with rent control the market can be in equilibrium; it just isn’t the free-market equilibrium.

                Increasing the supply of housing in the Bay Area will decrease housing prices in the Bay Area on average. I said that in the fifth paragraph of my original post! And I reminded people of it in this post!

                I think I have gotten better at explaining myself, so I will try it one more time.

                Assume one additional market rate apartment is built in San Francisco. When I say “market rate” I mean I let the builder pick what apartment he will make: a big one or a little one, one in a nice neighborhood or a bad neighborhood, etc., and I let him charge whatever the market will bear. I want to look at the effect that this has.

                Of course a lot of what is actually going into SF is big new apartment towers, nobody builds a single apartment. This is a model. But anyway, those apartment towers are renting for very high rents. Empirically, “market rate” means expensive.

                So we add one expensive apartment in SF. Somebody rents it. This can be someone from inside SF, or someone from outside SF. If the market were in free-market equilibrium, this apartment would not get built: the market would already be at the point where, if there was money to be made by building an apartment, someone would have done it already. But because the market is not in free-market equilibrium there is a difference between what it costs to build the apartment and what someone is willing to pay for it, so you do not need to assume any change in the demand curve in order to have someone be very eager to rent it out and charge as much as they can.

                The apartment rents to someone. Who? Well, a wealthy person, of course, but is it a wealthy person from San Francisco or a wealthy person from outside San Francisco? If it’s a wealthy person from outside San Francisco, it’s because there was previously no SF apartment that was worth the price to them, but now there is. This apartment is either cheaper at the same quality as other apartments they’ve had, or it’s more expensive but a lot nicer…for simplicity let’s assume it’s cheaper. So there is a new high-end apartment in SF that has to be rented slightly cheaper than similar apartments that are already occupied, in order to induce someone to rent it. The market has come down a little…but, I believe, just a little teeny bit, because I think there are a lot of wealthy people who would move to SF if the rent were just a teeny bit cheaper for the nice apartment they want.

                What if the apartment doesn’t rent to someone from outside SF? Then it rents to someone inside SF who prefers it to the one they’ve been living in (again, let’s assume this is because it’s cheaper). But what about the apartment this person has vacated? It is not going to sit empty, it will be occupied by someone. Will that person be from inside SF or from outside? If from inside, then that creates a new vacancy, which someone will fill…and so on. We keep going down the chain, with one renter displacing another, until we finally bring someone in from outside SF who fills the final vacated slot. At that point the chain stops. Everybody who is involved in this chain is now in a cheaper apartment than they used to be. Building the high-end apartment has decreased the price (a tiny bit, but hey, it’s only one apartment) for everybody in the chain.

                But that is not the only effect. We have also moved one new household into the city, and this household will spend money in SF. This will increase the cost of goods and services in SF, and thus the demand for people who provide those goods and services. Those people would prefer to live in SF rather than elsewhere, so the demand for housing will go up.

                I think that in free-market equilibrium, that initial chain of displacements would (in expectation) go way down into the distribution of apartments, with each person getting to move into a cheaper apartment: Adam moves from his current apartment in SF into the new one, leaving his current one vacant; Beth leaves her apartment and takes over Adam’s; Charlie takes over from Beth; and so on, and on, and on, until finally we come to Zachary, who is happy to move from Oakland into the tiny downmarket apartment in SF that was freed up by Yolanda. This chain of rent decreases more than counteracts the increased demand due to a slightly increased economy in SF, so prices come down. I think for a market in free-market equilibrium this is what happens…this is what economists think happens, anyway.

                But the market is not in free-market equilibrium, and I think that matters. I think that if Adam’s family moves out of their $5000/month place into the new apartment, Adam’s old landlord only has to reduce the rent to $4990 to induce Beth to take over, and then Beth’s old place goes to Charlie for $4980, and so on, until we get to Frances, who moves over from Piedmont into Ethan’s old place at $4940. The new person we have moved into the city isn’t low-income Zachary as in the free-market case, it’s high-income Frances. The high-income people in the chain of displacements have all benefitted from reduced rents, but this doesn’t affect the lower income tiers at all…whereas when Frances moves to the city, he doesn’t bring the $10K/year in spending that Zachary would have, she brings $120K instead. Rents have only been reduced at the top, in contrast to the free-market-equilibrium case, and the increased demand for workers is a lot higher than in the free-market-equilibrium case.

                Of course, when Frances moved out of Piedmont and brought her money with her, she decreased the amount of spending in Piedmont and thus the demand for workers there, so rents in the Piedmont area can come down.

                I think this actually happens. I think that, in the current market, if market-rate apartments get built in SF it drives rents for low-income people up, not down.

                I might be wrong but I don’t think the mechanism I have proposed is ridiculous.

              • gdanning says:


                It seems to me that “free market equilibrium” is doing a lot of work in your explanation, but I am not sure it is up to the task.

                First, you say, “If the market were in free-market equilibrium, this apartment would not get built: the market would already be at the point where, if there was money to be made by building an apartment, someone would have done it already.” Well, that is true only in the long run. In the short run, the market starts at equilibrium. Then, 1) there is an increase in demand, which has happened over the last few yrs in SF (I recently read that the avg “millennial” in SF earns over 100K). 2) The increase in demand causes prices to rise. 3) The high prices act as a signal to suppliers – build more housing! 4) Supply increases, and prices drop back down, until we are at a new equilibrium. But that takes time, esp in the housing market. SF is almost certainly not at the end of that cycle.

                Second, you said earlier that when you say SF is not at free market equilibrium, you mean that there are restrictions on increasing the supply of housing. That is certainly true. But that just means that SF is stuck at point 3 – it can’t move to step 4. As I understand it, the YIMBYs want to reduce impediments to building housing – ie, they want to get closer to a free market, which will enable step 4 to take place, at least to some extent. So, when you say that YIMBYs are wrong, prices won’t drop if we build more housing because SF is not a free housing market, you seem to relying on the very assumption that they want to change.

                Third, you say that “new residents will spend money in SF, increasing the cost of goods and services in SF, and thus the demand for people who provide those goods and services. Those people would prefer to live in SF rather than elsewhere, so the demand for housing will go up.” But, will demand increase more than supply did? A lot depends on the slopes of the demand and supply curves for housing, ditto for goods and services, ditto for the labor to provide those services, etc. That is a LOT of assumptions.

                Fourth, demand for goods and services will also increase if housing is not built. Without more housing, prices will rise, and the average resident will become richer and richer, since only relatively affluent folks will be able to afford rent. An increase in income increases demand (because one component of demand is ability to pay). As a result, businesses will stay open later, fast food places will be replaced by restaurants which employ more people, etc, etc. So, either way, demand for goods and services will increase — your mechanism will be triggered regardless of whether more housing is built.

                Fifth, you spoke earlier of the amount of new housing needed to make SF affordable for baristas. Yet, here, you are assuming that all those baristas will be moving to SF. A mentioned, demand is not just the desire to buy X amount of a good at various prices; it also includes the ability to do so. I believe the govt defines “affordable” housing as “costing no more than 30% of your income.” At $15/hr, that is $750/mo. I don’t think that barista is going to have much of an effect on SF housing demand. So, I think your assumptions about the effect of demand for services on demand for housing are iffy.

                Sixth, you explicitly say that building one apt will cause prices to drop, if only just a teensy bit. Well, what about 10,000 apts, or 50,000? Now, it might well be that the economics of the housing market in SF are such that profits will evaporate after 5000 apts are built, so supply will never drop enough to lower prices. But I don’t think either of us has any idea of whether that is true.

                Seventh, you say, “I think that in free-market equilibrium, that initial chain of displacements would (in expectation) go way down into the distribution of apartments, with each person getting to move into a cheaper apartment” but that “because we are not in free-market equillibrium,” that chain will stop early. But if so, that reinforces the YIMBY argument that reducing restrictions on supply is necessary for lowering prices for everyone.

                Finally, re lowering prices for the poor – what will happen in the future if the YIMBYs lose the argument, and more housing is not built? Demand for housing in SF will continue to increase regardless, and places like Hunter’s Point will gentrify, driving up prices for the lower income people who live there. If instead more housing is built elsewhere, those areas are more likely to remain (relatively) affordable.

            • Phil says:

              Sam, it’s funny, an economist who commented suggested that I consider the case of two discrete housing types, high-end and low-end. If you search these comments you’ll see what I think happens in such a case.

              But I complete agree with you that that is not the case.

              Please look below, where I respond to Raghu. I think I am getting better at explaining what I think and why, and perhaps that comment is my best attempt.

              • Sam Bailey says:

                The issue is not that there are two discrete housing types. The issue is that you treat them as two separate markets, one for the rich, one for the poor. If prices in the “high-end” market fall enough, poor people will move in. Similarly, if prices in the high-end rise, rich people will move to the low-end. You do address this somewhat in the reply to Raghu as you allow people from “nice” apartments to move to less nice ones, but there is still this issue where the rich have a high quality cutoff than the poor regardless of the apartment’s price. This seems suspect, and I think inspired the comment below:

                > And yes, I know the response is going to be that adding housing attracts rich people, while removing housing makes the rich people compete for the poorer people’s housing, as if the rich people were previously unaware of the existence of those places. (This whole model reminds me of some sort of ecological two-species scenario, in which the “rich” really are totally different from you and me.)

      • Martha (Smith) says:


        A simple search of the linked paper did not get me to the quoted information, “San Jose and San Francisco would grow by more than 500%, while Austin would increase by 237%.” Is this perhaps the wrong paper, or is the item in quotes a consequence of what’s in that paper?

        • Phil says:

          The quote is the second sentence on page 27 of the pdf at . I don’t know why it didn’t come up when you searched for it. I can find it just fine by searching for the quoted text. Uh, wait, I lie: it’s on the page that is numbered 27, which is actually the 28th page of the pdf.

          I wouldn’t take the exact numbers too seriously; indeed, the authors say not to. But they do think the Bay Area would grow enormously if allowed to. So do other economists whose work I’ve seen.

          • Martha (Smith) says:

            The second sentence on the page labeled 27 (called p. 28 in the pdf) of what I downloaded reads “Suppose instead that each city makes a
            differentiated product with a production function given by Yi = AiLi.”

            So maybe I downloaded the wrong thing? The title of what I have is “Housing Constraints and SpatialMisallocation”

            I just downloaded again from the link you gave in your reply — I get the same thing; the only mention of Austin is on p. 20 (21 in pdf labeling). So maybe you linked the wrong paper? Or an earlier version of it? (What I downloaded is dated May 18, 2017 on the first page)

      • Sam Bailey says:

        > In contrast to the essentially nonexistent amount of work I was able to find on economic modeling of the actual situation in the Bay Area

        The study Brian posted seems like good work on the actual situation in the Bay Area. Also, while it’s maybe not the focus on the Hsieh and Moretti study, they are implicitly modeling the actual situation by comparing it to a counterfactual. People have also brought up the example of Tokyo, which is obviously not in the Bay Area, but does seem suggestive.

        I’m very sympathetic to being irritated when people say “oh, this is just Econ 101” when it’s obviously not Econ 101–it’s complicated! I don’t think policy is super obvious either way. The idea that richer people have a higher demand for low-paying services intuitively makes sense, and probably has interesting effects on the makeup of a city. But multiple people have given pretty good evidence your theory doesn’t hold, at least not the final results, and the reaction has been “yes, but that’s not EXACTLY what I’m thinking about” and then complaining no one is studying this and trying to reinvent the wheel by coming up with a model lifted from quantum solid state physics (a subject, funnily enough, that many of the people presenting counterexamples are not familiar with and thus unprepared to engage with).

  11. Carlos Ungil says:

    From physicist to physicist, let’s try a little Gedankenexperiment. Let’s say I accept you thesis (adding upscale rental units drives prices up and makes housing less affordable in SF). Now imagine that the appartment tower recently built at 55 9th street has to be vacated for some reason (fire, construction defects, whatever). These 273 rental units are retired from the market for a very long time, maybe forever. Will this result in lower prices and more affordable housing in SF?

    • Also as a physicist, I was thinking exactly the same thing! The proposed model seems to imply either (i) that the solution to the affordable housing problem is to eliminate as much housing as possible, or (ii) that somehow we happen to be in a particularly special local minimum such that making more housing increases prices *and* making less housing increases prices. Panglossian urban planning?

      And yes, I know the response is going to be that adding housing attracts rich people, while removing housing makes the rich people compete for the poorer people’s housing, as if the rich people were previously unaware of the existence of those places. (This whole model reminds me of some sort of ecological two-species scenario, in which the “rich” really are totally different from you and me.)

      • Sam says:

        I think this is the main shortcoming of Phil’s model. He’s right that treating housing as a homogeneous good is a gross simplification, and maybe others (including myself) were wrong to think of it as a single market. I think he errs in the other direction, though. Apartments can be differentiated and still be partially substitutable. So, even if it true that there are now more poor people competing for units, it’s not true the supply for the poor has remained fixed.

        It’s also unclear why the new poor people want to move to San Francisco, unless wages went up. (Just wantinga barista doesn’t make one appear, sadly.) That’s another element assumed to be fixed that probably isn’t.

      • I have it on good authority from an estate planning lawyer in the area that there are plenty of people in the Bay Area with over $6,000,000 in cash in their checking account.

        So, yes, in this case I think the rich really ARE different from you and me.

      • Phil says:

        Raghu, you will be amused to find (if you search these comments) that a third-year Econ grad student suggested modeling the system as if there are only two kinds of housing, high-end and low-end! I actually worked through a little exercise of how I think the market would work in that system. I am hoping the grad student will return and tell me why I’m wrong.

        As for Carlos’s gedankenexperiment, i like it a lot. If I say yes, I think rents will go down if some expensive housing is removed (or at least that they will increase less than if the housing isn’t removed), that certainly seems counterintuitive even to me (whereas, in the forward direction, my claim is not counterintuitive to me). Do you guys know Feynman’s story about discussing which way a garden sprinkler will spin if you submerge it in water and suck water out through it, rather than forcing water into it, To me it’s a bit like that, intuitive in one direction but not the other.

        But I still say yes. I doubt I can make you agree (except possibly Daniel) but I hope to make you scratch your chin and say “hmm, there something wrong here I think, but I’m not sure what.”

        With that limited goal, I proceed. Actually im going to simplify the thought experiment even farther: only a single unit is rendered permanently uninhabitable, and moreover it happens to be a very special unit: it is the one that was occupied by the marginal household, the one that was just barely willing to pay the cost of living there. These people now need a new place to live. They can either pay the premium to stay in SF, or they can move out.

        If they choose to move out of SF, then I think I ‘win’, don’t I? They have no effect on the rest of the SF market, and are now bidding up the price of high-end housing elsewhere. They now spend 50 or 100 or 200 thousand fewer dollars per year in SF so the demand for workers in SF goes down by 0.5 or 1 or 2.

        But of course, they probably don’t move out of SF. They were just barely willing to pay to move into that specific building, but they are probably still willing to outbid someone for a slightly less nice place that is cheap enough that they’ll choose it. So they outbid someone else in SF and now that person has to decide whether to stay in SF or move elsewhere.

        And so on down the line until someone says Screw it, I can’t afford to live in San Francisco anymore, and moves away.

        The question is (I think) what is the income of that person, in expectation? If they are wealthy then removing the high-end unit from the market raises housing costs for the wealthy and displaces a wealthy person from SF, and they take their money them, etc.But if we have to go far down the chain in order to find the displaced person then removing the unit has increased rents for middle- or low-income people.

        How far down the chain do we have to go to find the displaced household? That’s an empirical question; I can’t think of any way to derive it purely from the structure of the system. If Adam’s condo is destroyed, and he outbids Beth on a replacement place in SF, causing her to outbid Charlie, who then outbids Dora, whom outbids Ethan, who leaves the city, how rich is Ethan?

        A commenter on my previous post said only about 15% of people in new SF housing moved there from outside the city, so (if true) we can come up with a rough estimate of how many steps there are before someone is displaced: 15% chance that Adam is displaced; if he isn’t displaced then there’s a 15% chance that Beth is displaced; and so on. By the time we’ve gotten to Frank or Gina we have probably displaced someone, and it’s pretty much a sure thing by the time we reach Mark and Nancy.

        I’m pretty sure that if someone is paying $5000/month and they’re outbid for their place, so they have to outbid someone else for -their-place, that is still going to be a very expensive unit. They might end up paying $5000 but for a place that isn’t quite as nice but almost, or they might pay $4800 for a place that is noticeably not quite as nice, but I don’t think they’re going to settle for a $3000/month place that is a big step down. I mean, sure, some people might do this, but I think it would be rare. So I think that even if you have to take seven or eight steps, you still aren’t displacing someone with below-median income.

        Have I made you scratch your chin and say ‘hmmm’? If not, that’s actually good in a way, because it means my error is obvious and you can easily point it out to me.

        • But Phil, now I’m definitely not following you. You just described how by shutting one expensive unit, a bidding war cascade occurred that *RAISED the prices of all the other downstream units*. Paradoxically, if the unit was rented at high rents, and catches fire, and the person just moves out of SF, then the distribution of housing prices actually *does* go down, but it’s “mechanical” because you’ve just removed some houses from the right tail, they no longer exist.

          So I think your fault is that you’re not looking at Carlos’s question. he asked whether closing this high end unit would *make the affordable houses in SF GO DOWN*

          I agree with you that all that bidding will occur, and the price of other downstream units goes *UP*.

          The thing is, I also agree with you that opening new market rate housing and thereby attracting people out of their marginal rent controlled units *also makes things go up*.

          Basically because we’re standing on a board on the side of a mountain, any movement at all that temporarily disrupts the friction makes the board move towards its equilibrium. which in the case of the housing market is *up*

          And yes, I love that Feynman water sprinkler thing.

          • Ok, there’s something subtle here, because I think we’ll all agree that each of the individual houses went up in price after the bidding war, BUT one house was removed from the distribution. Also, we’re assuming the displaced person finds a slightly less good apartment at a slightly lower price, and cascading down… the prices paid by each person are slightly lower than they used to be, until the marginal person leaves SF. So the empirical question of what the distribution looks like after you remove the one house is nontrivial because it’s conceivable that it could have say the average or the median shift slightly either way depending on very specific facts about what happens.

            But I think what we should all agree with is, each individual apartment that changed hands went up.

            • Phil says:

              Yes, each apartment that changed hands went up. I agree. But I believe that, in the scenario given, all of those apartments are above the median price. It doesn’t matter what you do with them-and-only-them, it doesn’t change the median one way or the other…except that, as you point out, we have now removed one apartment, so the median is no longer the Kth apartment, it’s now the K-0.5th apartment. Perhaps this though experiment would be nicer if we render two high-end apartments permanently uninhabitable, so the median isn’t the Kth apartment, it’s the K-1th apartment.

              At any rate, if (as I believe) eliminating a high-end apartment has led to a wealthy person leaving the city, then expensive apartments get a bit more expensive but the median goes down a hair mechanically. This is a tiny effect, but then, we have only made a tiny perturbation in the market, so how big an effect do you want?

              But in addition to the mechanical reduction in the median by removing someone from the high end, we have also removed from the city one high-income household, with their…I dunno, $100K in annual spending in the city, or whatever it is. I think this leads to slightly less demand for lower-income workers in the city, and thus reduces the premium such workers are willing to pay to live in SF. So rent prices for such workers should go down a little. Again, it’s a very small effect, but how big an effect would we expect when we eliminate only a single unit?

              From my perspective all of this is self-consistent and intuitive, but from your perspective (and everyone else’s) I am wrong…so, what’s my error?

              • All this has a lot to do with the median, which is a bit of a weird statistic. Suppose you remove an apartment that is say 5 apartments above the median? Now you probably agree that the cascade effect goes down below the median, and the below median houses are bid up. Further, perhaps the person who leaves the removed apartment bids up an apartment enough so that it is above the old median.. All this “crossing a threshold” is a very unnatural and unintuitive way for me to think about it.

                Let’s go with the mean value. We remove one apartment and have a bidding war and one person leaves SF, the average over the remaining apartments goes up because as you say each and every apartment involved in the bidding war went up.

                Whether it affects apartments in the far left tail is a question of how big an avalanche we get, but we both agree that every single apartment in the avalanche does go up right?

              • Phil says:

                Oh, Daniel, please don’t go moving the goalposts on me now!

                What I said in my original post was “that is, there will be more jobs for the kinds of people who already have trouble affording a place in San Francisco. Those additional people will need to live somewhere, so there will be increased competition at the lower end of the market, which means higher rents. Most of these people will end up commuting from other cities.”

                By focusing on the median I suppose I am implicitly defining ‘the lower end of the market’ to be the bottom half. Isn’t that more than fair?

                My claim is/was that building market-rate units in SF (which, in the current market, are high-end units) makes things worse for the kinds of people who are active in the YIMBY movement there. I don’t think the median is a ‘weird statistic’ in this context. If you want to argue that a mechanical reduction of half a unit simply be removing a high-end unit shouldn’t count, since it doesn’t change the actual dollar rent of anyone who is below the median, I would agree. I’m perfectly happy to look at the bottom K units (where K is some fixed number that is near 1/2 of the total number in San Francisco) rather than the moving target of the median when the number of units changes…indeed I think that makes sense.

                Anyway: yes, I agree that under this model (which is of course highly simplified, full-information, instant-bidding, frictionless market blah blah) if we destroy Adam’s high-end apartment so that Adam displaces Beth and Beth displaces Charlie etc. until we reach someone who leaves the city, at which point the chain ends, then in every one of those units the rate goes up. But I think that in the current environment every one of those units is an expensive apartment. (I also think the chain isn’t all that long). Higher end of the market goes up, yes. But I also think that by removing a wealthy person’s income from the city and thus decreasing the demand for goods and services and the people who provide them, the lower end of the market goes down.

                So…what do you think of that proposition? We can talk about the mean later, if you want — I don’t know what, if anything, I will have to say about it…I don’t have a prediction, I think.

                One possibility: you think the chain of displacements goes all the way down into the lower parts of the distribution…that the person who is ejected from the city is from the lower part of the distribution. This means removing that high-end unit causes rent to increase in the lower part of the distribution.

                Another possibility: You agree with me that the chain of displacements will not be long enough to reach down into the lower parts of the distribution (I, for one, do not think it would be remotely close), so the person who is ejected from the city is indeed a wealthy person, but you think the lower parts of the distribution nevertheless move downward. I can’t think of a reason for that, but perhaps you can.

                What else is there…I don’t know, you tell me!

                For what it’s worth I think the first of those possibilities is what Berry would say, and since he’s a good economist perhaps this is where we (or at least I) should focus our attention. I think he thinks Adam displaces Beth, who displaces Charlie, who displaces Donna, who displaces Ethan, … and that this continues many many steps until poor old Zachary has to abandon San Francisco, freeing up an apartment at the 19th percentile or something, so that even though we have destroyed the apartment of a rich person it’s ultimately a low-income person who is priced out. Why is he so sure of this? Or, to flip it around, why am I so sure this is not the case? I do have an answer, but I’ve gotta go get some work done.

              • Ok, Phil, good we’re getting clarity I think. First off, I agree that the removal of a unit mechanically adjusting the median is weird, so let’s just fix the percentile points as they were right before the expensive unit was removed.

                How far down does the avalanche go? I would expect this avalanche to have a statistical distribution that was not narrow. Sometimes it might go 1 or 2 or 3 apartments, other times it might go much further. What’s the time-scale for this avalanche? It’s potentially months because maybe Alice stays with friends for a few weeks while she looks for a place, and outbids Bob, who stays with friends for a few weeks, and then outbids Carol, who stays with friends for a few weeks and outbids Dan and …

                One thing I can tell you is that you can’t kick a rent-controlled person out, so that cuts off the tail of the avalanche distribution. And since most of the left tail *is* rent controlled, it’s the case that the avalanche doesn’t penetrate down into the left tail *because* of rent control. On the other hand, perhaps Zachary loses his job because say Dan leaves town and doesn’t spend so much money, and then Zachary’s far left tailed rent controlled apartment resets to market and goes WAY up. The dynamics are pretty intricate with deep feedbacks.

                In a free market, this avalanche could go way way deep into the left tail, indeed, in a free market, it would have LONG AGO and there WOULD BE NO apartments renting in the deep left tail.

              • As for the mean, if we condition on just the apartments not removed from the market, you’ve already said that each apartment in the avalanche chain increases in price, so the mean over all-but-the-removed-apartment obviously goes up. A prediction, and it agrees with economic theory! ;-)

                I think where we are is that removing apartments doesn’t help anyone, and hurts some people. Adding apartments helps people who are very wealthy a lot. They get fancy apartments in the city where they want to be. The effect on rent controlled apartments at the lower end is virtually nil, except that overall cost of living rises a little and if you’re a rent controlled elderly person with low income, you might be hurt by that.

                The effect on job creation at the lower end is probably positive, more demand for service workers would tend to push up wages for service workers, and maybe a few additional service workers can move into crowded apartment-sharing situations with their additional wages at the lower region of the current spot prices, the lower tail of spot prices may shift downward a little as some fancy pants people free up some mid-range apartments so they can get into the fancy apartment they always wanted.

                And I don’t think any of that is actually counter to economic theory. The thing I think we’ve ignored is that as in all real-world situations, what matters is NOT the dimensional measures such as “Dollars paid in rent” but rather dimensionless ratios such as “Dollars Paid In Rent” / “After Tax Wages”, and while you’re right that building more fancy apartments will result in more rich people, and more demand for service workers, and higher competition for service worker apartments, the net effect of avalanches of freeing up apartments will be each apartment rises in price due to rent-control, and due to greater demand at the left tail of spot prices, *but* only because wages for service workers increased, or at least opportunities for service workers at current wages increased.

                What matters is Rent/Wage and basically adding apartments is going to make *that* stay constant or go down for service workers even while rent may well go up.

              • Bryan K says:

                “At any rate, if (as I believe) eliminating a high-end apartment has led to a wealthy person leaving the city, then expensive apartments get a bit more expensive but the median goes down a hair mechanically.”

                This is a profound misunderstanding of what it means to be wealthy.

    • I too am interested in Phils answer to this question. I will point out that the day after this thing closes, if its houses rent below median then the median mechanically shifts up, if they rent above median, then the median mechanically shifts down. The real question is what happens in the few months after this event during a re-equilibriation phase to the distribution of houses.

      • Some thoughts. Those million dollar bonds (ie. rent controlled leases) I discuss above are a lot of friction in the market. Suppose we’re all standing on a big board on the side of the mountain. Anything that happens makes us slide downward, it’s only the forces at the contact points that keep us in place…

        Also, question: suppose there’s a penny stock, the last time it traded was 3 weeks ago, 100 shares for $1 each. The bid is currently $0.05 and the ask is $35.00 what is the price of this stock?

        • Phil says:

          Daniel, have now read all of your comments I think. Your arguments/model is far more sophisticated than mine…and also seems to be far less related to non-equilibrium conditions and far more related to market inefficiencies, friction, etc. it’s all quite interesting. You give me too much credit for intuiting things I know nothing about (but thank you).

          I’ve got a lot to think about!

          • Well the market friction stuff is what holds the market out of equilibrium. Like an earthquake slip system on a fault. The plates are constantly moving and yet the fault doesn’t slide into it’s equilibrium position because those transactions are prevented.

          • Also the unique aspects of each individual apartment put the landlord in a position similar to the penny stock owner. The way they set the price is to run an auction. Ask below market on Craigslist, and wait for 10 or 20 people to bid each other up into an equilibrium price for that unit. The fact that this bidding war happens is evidence again of lack of information in the market and once again non-equilibrium conditions.

            Here’s a question for you Phil, what happens if we end rent control and housing subsidy tomorrow? What I think happens is that there will be a LOT of turnover. People outside SF will flood in and start bidding on occupied apartments, to stay in your previously rent controlled apartment you’ll have to participate in this auction, and basically every single apartment below the current 70th percentile or so in SF will increase in price. Like an avalanche, or an earthquake.

            What happens to the distribution?


            I think the super diffuse distribution we see now would congeal around a more narrow price range that looks like the 2010 distribution but shifted upward to have a median around say 2. In other words, at the lower end of things in the range 0-1 on the x axis there would be basically nothing. On the other hand, I also think that on the high end at 2.5+ things would shrink inward toward the new median. I suspect the market spot price would decline as more liquidity was available, and renting has less risk to the landlord (the landlord doesn’t have to worry that you’ll rent your apartment for life and they’ll never be able to increase the rent). Right now, market spot prices are basically around 2.5 to 3 for everything.

            So, in the sense of *the spot price* the clearing spot price is too high now because of rent control. In the sense of the advertised price, the advertised price is too low because low liquidity and pent-up demand prevents people from knowing what price to advertise, it’s better to advertise low, and run an auction. In the sense of the observed distribution of prices at which apartments are rented, the left tail of the distribution is too low relative to a free market because of rent control and the right tail is too high because supply is artificially low.

            Now, how about the demographic composition of the city, and wages? Suppose we eliminate rent control right away. “Rich” people flood into SF displacing people who have rent controlled apartments. Rent controlled people who have good jobs have to bid more for their current apartment and their rents go up but they aren’t displaced because they have good jobs, so more of the economic activity accrues to landlords making being a landlord a more attractive thing. Now, we have a lot of “rich” people in this area, and they’d like services, but they just displaced all the low-earning service workers. There’s no one to make coffee, give haircuts, be a bank teller, clean carpets, paint interiors, fix plumbing, etc.

            So, offer prices for those jobs will jack up, a bunch! So wages for service workers rise, and then they can come back into the area and squeeze into the lower end of apartments (remember, no more rent control). So the left tail of the rent distribution rises *further* but the service worker wages rise *even more*. More of the benefits accruing to the high paid tech workers pour down into the job market for generally young and less skilled service workers.

            As for building restrictions, being a landlord just became YOUGELY more attractive ;-) it now becomes an unambiguous positive to maintain and improve building quality, and to build more buildings or at least free up space within buildings. So quality of apartments rises, fewer firetraps, fewer cockroaches, many many people who want to build in-laws or rent out rooms or convert 2 story single houses into duplexes. Every accidental fire that occurs has a slightly larger or at least more accommodating (perhaps 2 small duplexes) building put up, big ugly 1970’s apartment buildings get taken down and nicer more modern apartment buildings with maybe slightly smaller but higher quality apartments get put up, an improvement to neighborhood quality…

            And so, in the longer run, there is automatically more and better housing even if major construction projects aren’t green-lighted, and all else equal on the 3 to 6 year time horizon (which of course it isn’t) the distribution of prices might relax further downward as supply increases through inlaws, apartment sharing, duplexification, conversion, 3 bed single family homes becoming available to rent. You don’t even need to posit massive SOMA towers.

            So, I really do think it all comes down to rent control. In the absence of rent control the place wouldn’t have filled in and have so much pent up demand, because advertised prices would be equal to clearing prices, wages and salaries at the lower end would converge upwards, and pent up demand would dissipate to some extent, and if it didn’t, *the whole price distribution* would jack up until it did. Then we’d see some vibrant growth in Sacramento, Fresno, Salinas, Santa Rosa, etc instead of an artificial sense that “if I could just get into one of those $1300/mo 1 beds advertised on Craigslist in SF things would be great… run around trying to get one… and every single one clears in an auction at $2500”

            So, it’s not that *prices are too damn high* in SF. it’s that *advertised prices are too low*, *spot clearing prices are too damn high* and *the price distribution is WAY too low*, and *service worker salaries are artificially way too low*, and *too many people are occupying way more square footage than they would if the rents reset*

  12. Ian says:

    Phil, is your claim essentially that adding one more house + resident to SF causes demand to increase (via network effects) enough to more than offset the decrease in market rate from the additional supply?

    • Phil says:

      No, or at least not without putting in a few modifiers.

      My claim is that putting in one more market-rate unit in San Francisco will increase the median rent in San Francisc, although it will decrease the median rent in the Bay Area.

      I have learned that I need to emphasize that I believe this is only true because the market is far out of free market equilibrium. I think that near equilibrium.

      It is also possible (see what I say about Rowe and click on the link) that even if building were not tightly restricted in the Bay Area, more building would beget higher rents over some range of housing density, but that’s not what I’m asserting.

      • Asa says:

        I don’t get why this is controversial or interesting. Adding a market rate unit mechanically increases the median rent because the new unit is worth more than the previous median. But that’s not what people care about – this new unit doesn’t directly affect the number or price of below-median rental units. If Bill Gates walks into my office the median income goes up but mine stays the same.

        Maybe there is one more rich person demanding services from workers who cant afford to live in SF. Maybe their wages go up in response to this increased demand for their labor (and anecdotally this is something I have heard from friends in the SF restaurant industry). I also think much is being made out of relatively meaningless political boundaries. If you build new above-median luxury housing in Beverly Hills or Tribeca then prices mechanically rise in those places. But the point is not for everyone to afford the wealthiest parts of the city – the point is for people to afford NYC or LA more broadly.

        • Phil says:

          Good timing, Asa: as I just mentioned in a response to Daniel, about ten comments above (the comment that starts “Oh, Daniel, please don’t go moving the goalposts on me now!”)

          I understand your objection. I am not talking about the mechanical increase in the median; happy, instead, to talk about the Kth-highest price, where K is a fixed number. Does the rent go up, down, or stay the same, for the lowest 200,000 apartments or whatever number. See above if you’re willing to take a look.

          • Asa says:

            Ok I see your proposed mechanism now. Its not clear to me that increased demand for service workers would have such a big impact on low-end rents. In 2017 most SF service workers are not living in SF before or after the hypothetical new housing unless they have some other income source (student loans, etc.). And each marginal new rich person certainly requires less than one additional new service worker (how many lattes can you drink in a day anyway).

            I don’t claim to be an expert but I’ve studied urban policy and worked in city government and at policy think tanks. These second order and/or multiplier type effects often tend to be overstated (e.g. number of jobs from the new stadium, etc.). What evidence have you seen that makes you think this effect is so large in this case? It seems like you’ve stated a hypothesis without making a case against the prevailing understanding that rents are rising, but would be even higher without new housing.

            • Asa says:

              For example, if your theory holds why has a building spree of new high end housing in downtown brooklyn led to a fall in prices?


              • Sam Bailey says:

                Part of the frustration I and possibly others have had with this discussion is the evidence seems pretty firmly on the other side of what Phil’s model explains. There are more minor modeling issues as well, some assumptions that seem a little weird, but the Achilles’ heel of it is the stylized fact it’s explaining is not factual.

                For instance, I’m still not sure why the evidence Brian presented hasn’t been a sufficient answer to the question “does increased housing raise rents?” Is the concern that, even though the predictions of traditional methodology line up with what actually happens, the traditional model is clearly flawed and needs to be reworked to be more realistic? Or are you taking as given that increased housing actually does raise rents, at least in the city of San Francisco?

                (Which is another question I’m concerned about: you’ve said multiple times you’re talking about rents just in San Francisco, not the greater Bay Area. You do think rents would fall in the larger region. But why is the city border the cut-off? Why not say, “rents will rise in the city and inner suburbs, but fall overall?” Or “rents will rise in the toniest neighborhood, but fall in the rest of the city and surrounding area?”)

              • Asa, that article is talking about *spot prices* of new leases. Phil is talking about *the distribution of rented apartments* especially for low end service workers. If 35 new plumbers all sign leases that are 20% higher than the leases other plumbers have, but are 10% lower than they were advertised at 1 month ago, then the *spot prices* went down 10% but the *cost of housing for plumbers* went up 30%

              • ack, went up 20%, typo

              • Phil says:

                Daniel makes an important point about spot prices…I think the comment I am writing will appear just below his.

                I know Brooklyn is hot these days, but other than that I know little about the New York area housing market…and I’m deliberately not going to look, because I don’t want to be one of those people who sees the facts first and then says “that’s exactly what my theory would predict” and then makes up a just so story. Ultimately I need to realize my model in either mathematics or a computer program and that will be the real test.

                So to try to answer your question…eh, let me come at it another way. In what circumstances do I think building more housing makes the median local rent come down? (Actually I already touched on this in one of the approximately comments on…uh, I think it was the previous post: someone pointed out that in Berkeley, where I live, new housing is being built and rented for rates not much higher than the current median rent. I said in that case it will make the median rent come down).

                My conceptual model says that if the market rate housing that is being built is at far above the median rent, and if a non-negligible fraction of people from outside the city are willing to pay for those units, then building more market rate housing will make the low end of the market go up in price rather than down. If you search for my response to Raghu, you’ll find what I think is my best explanation of why I believe that.

                If market rate housing is coming in anywhere near the median rent, even if it is somewhat above, then I think adding that housing will decrease rents at the low end. I guess that would also be true if pretty much everyone who occupies the new market rate housing is from within the city, with no outsiders paying it.

                So, flipping this around to answer your question: my conceptual model says that if new market rate housing is being built in Brooklyn and is driving the low-end rents down — and, to Daniel’s point, I am talking about the low-end rents that people in the city are paying, not the rental price of newly built housing! — then the market is such that the units that are being built must contain a non-negligible number of units that aren’t priced far higher than the current median rent in the city. That would be closer to the situation in Berkeley or Oakland than San Francisco.

                Perhaps there’s an analogy like Brooklyn:Manhattan :: Oakland:San Francisco. If that’s the case, I’d predict that new market-rate housing in Brooklyn would reduce low-end rents in Brooklyn (and maybe even in Manhattan), but new market-rate housing in Manhattan would increase low-end rents in Manhattan while reducing them in Brooklyn.

                I’m going to post this comment before looking at the data from Brooklyn. I hope I’m right because otherwise this will be slightly embarrassing.

                As for Sam’s claim that “evidence seems firmly on the other side”, of course I disagree. I think the market situation in San Francisco and the rest of the Bay Area is consistent with my conceptual model. (Actually I also think San Francisco might be experiencing a housing bubble, and I wouldn’t be shocked if housing prices decline 20% in the next few years even if nothing new gets built. I’m not claiming this will happen, just saying it wouldn’t shock me.)

              • Sam Bailey says:

                I don’t mean to say the evidence is conclusive either way. However, it seems suggestive in the other direction, and so I think there’s an onus to not only explain why your theory makes sense but why what we think we’re seeing is not really what we’re seeing.

                > …to Daniel’s point, I am talking about the low-end rents that people in the city are paying, not the rental price of newly built housing!
                I don’t think the price index Asa linked to uses only rates of newly built housing. It looks like it’s the price of any place listed for rent in the given time period. Isn’t that the price of interest? If you’re arguing “low-end rents” (which I still don’t think is a well-defined concept) are going to rise, then in an environment with rent control it seems like you’d have to be talking about the selling price.

              • “It looks like it’s the price of any place listed for rent in the given time period. Isn’t that the price of interest? ”

                No. see this is the problem, unless I’m misunderstanding Phil is interested in




                He’s talking about the fact that unless you build a LOT of housing, service workers are not going to see a general reduction in their rental rates.

                The fact that Economist after Economist seems to come here and just can’t wrap their head around this idea is kind of staggering.

              • Sam Bailey says:

                > He’s talking about the fact that unless you build a LOT of housing, service workers are not going to see a general reduction in their rental rates.

                Phil is arguing that more housing (which he’s refined to “more housing above the median rent”) will lead to service workers paying higher rents. (I assume he means high enough to still be worse off after any wage increases, though he hasn’t said that.) I realize he’s interested in people who have been living in the same unit for years, not just people entering new leases. There are two arguments that seem contradictory:
                1) Rent control means the actual median rent is very different than what I would pay if I were entering a new lease. That is, the rent for vacancies could increase 100 fold, and rent-controlled units would stay untouched. When we’re considering welfare we should also consider people who aren’t moving, so we should think about the entire distribution of rent, what actually comes out of people’s checkbook.
                2) Greater demand for apartments and services will raise all rents. (Phil clarifies maybe not all, but well below the median).

                I don’t think these can co-exist. What am I missing?

              • Sam Bailey says:

                > …to Daniel’s point, I am talking about the low-end rents that people in the city are paying, not the rental price of newly built housing!

                I don’t want to harp on this because I think everyone here is arguing in good faith, but this sentence highlights the sloppy regard for evidence that has been employed more generally. From the initial post, when Phil gets the density of Manhattan off by a magnitude of eight, to when Daniel cites Brian as saying San Francisco would require Manhattan levels of density (he said “between Brooklyn and Manhattan”), to the point here, where Phil seems to think the index charts only new housing (given they are tracking units over time, by definition they are looking at more than new housing). For a theory that seems to depend an awful lot of small subtleties that most people don’t pick up, the handling of evidence seems more slipshod that one would like.

                To his credit, Phil admitted his mistake about Manhattan, but the way he says he came at that number (one of the first things that comes up when you Google it) suggests he maybe hasn’t delved as deeply into the evidence as one might like.

              • Sam: when you say “I assume he means high enough to still be worse off after any wage increases, though he hasn’t said that”

                I don’t think this is correct either. Phil hears some people on the radio say that building fancy apartments in SF will make rent prices come down in a way that implies the nominal dollar amounts should decrease, and specifically decrease enough to make it so that service workers rent comes down. They are, politically, implicitly, appealing to service workers to support this measure.

                Now, Phil comes along and says that every bit of Tony housing is going to add a high earner and some demand for services, and raise demand for service workers, but it isn’t going to drop the spot price enough that d/dt median(AllServiceWorkerNominalActualRents) will head negative any time soon, and every service worker entering SF will have to pay way higher than current median service worker rents, in nominal dollars. And he makes an effort to explain this with a cartoon 2 compartment “service worker” and “tech worker” scenario. Economists complain that this is two markets and is clearly wrong. And sort of it is, there’s no literal energy gap between the electrons so to speak, but in point of fact, spot prices for 1 beds are $2500/mo to $3500/mo and this is something like 2-4x what a service worker could typically afford, so there kind of *is* an energy gap for the moment at least. I don’t think you’ll find wages going up so that Baristas and cut rate hair cutting employees are making $85,000/yr any time soon.

                He really hasn’t acknowledged is the issue of service worker wages going up, or whether rent/Wage goes up or down for service workers. I’ve mentioned that in another comment, but this comment thread is again pretty dense and split up (WordPress isn’t exactly perfect for this kind of multi-party multi-conversation)

                Another thing that I haven’t been able to get totally clear on is whether he thinks building this extra housing makes the nominal dollar *spot price* of available low end quality apartments stay the same, go up but not as much as before, go up more than before, or come down. Perhaps his point is that there’s basically no supply for service workers at low end rents, and whatever happens to the spot price is irrelevant because it stays way above service worker affordability, and service workers to the extent that they come into the area do so at very high prices, which might be slightly less than they would have been, but still way above what the other service workers are paying with their rent control. Mostly likely if more service workers come into SF it’s by squeezing into black-market situations anyway, there are a certain number of people renting out large closets for cash under the table etc.

              • Sam, one thing that I think is clear, is that Phil doesn’t know the econ jargon, and he uses physics jargon. So part of what I keep trying to do is bridge that gap, with things like “nominal rent” and “spot prices” and “median rent of occupied housing” and soforth so that the concepts that I am guessing he means can be translated to concepts that might make more sense to an economist.

                So, how am I doing? Do you understand my hopefully correctly translated version of his point yet?

              • Sam Bailey says:

                > I don’t think this is correct either. Phil hears some people on the radio say that building fancy apartments in SF will make rent prices come down in a way that implies the nominal dollar amounts should decrease, and specifically decrease enough to make it so that service workers rent comes down.

                Perhaps, but he also suggests that many service workers will be worse off as a result of more housing. He says later than he expects rents to rise for service workers. So while it’s true that rent controlled units are unlikely to lower their price without an enormous amount of new housing, I think Phil’s argument is stronger than that: he predicts nominal wage across the distribution will rise, not fall or stay constant, and he predicts wages will not rise enough to make the difference.

                > …in point of fact, spot prices for 1 beds are $2500/mo to $3500/mo and this is something like 2-4x what a service worker could typically afford, so there kind of *is* an energy gap for the moment at least. I don’t think you’ll find wages going up so that Baristas and cut rate hair cutting employees are making $85,000/yr any time soon.

                No, that’s true, but I’m not sure if “baristas in one-bedrooms” makes sense as a minimum indicator of improvement. Three people instead of four in a three-bedroom apartment would be an improvement closer to the margin, or roommates moving to a slightly larger unit. A large part of the report Brian posted was about overcrowding, and this seems like an area where marginal changes could have real effects.

                > He really hasn’t acknowledged is the issue of service worker wages going up, or whether rent/Wage goes up or down for service workers. I’ve mentioned that in another comment, but this comment thread is again pretty dense and split up (WordPress isn’t exactly perfect for this kind of multi-party multi-conversation)

                I did see that and agree it’s something that needs to be addressed. I actually don’t really see a way wages can do anything but go up (relative to the outside option) if he is also positing more service workers come to the city (not even necessarily to live there, just as workers). I suppose it’s possible the nominal wages in San Francisco don’t change, but because all the rich people have moved from Oakland to the city there’s no longer any demand for coffee in Oakland, so it’s not so much wages rising in San Francisco as it is them falling in Oakland. That’s…possible, maybe, but seems unlikely (especially if we imagine there are plenty of slightly less rich people who’d like to live in Oakland ready to pounce, etc.)

                This is related to my confusion on how Phil is drawing boundaries. He seems to be treating the whole Bay Area as a unified market, very well, but then says more housing will have opposite effects in clearly demarcated areas. If the rent control policies were very different across municipalities, maybe, but that doesn’t seem to be the case.

                As for the language used in describing the model, if physical models are actually helpful in clarifying thoughts and setting things out, more power to you. In communicating the ideas, though, I’d say it’s better to express things in a way that other people studying the issue understand. That doesn’t mean economics technical language is necessary–plain English also works! (And is in fact preferable, given there are plenty of people who study this and are not economists.)

              • Sam: regarding the plain english. Yes I think plain english is good, but I think it also can be confusing. For example when Phil says “prices” he needs to be more clear what he means so that for example we don’t have 3 or 4 people each thinking he means a different thing: 1) Nominal Prices of all apartments available on the market 2) median prices across the apartments occupied by service workers 3) Median nominal spot prices for available apartments similar to apartments service workers are currently living in 4) Prices as a fraction of wages…. etc

                One of the biggest points I hope eventually comes across is that, no this isn’t Econ 101, and no it’s useless to just define essentially “anything that actually happens” as “equilibrium” and that housing is not a perfectly fungible good, and that spatial distribution of prices makes a difference, and some markets have a *crap ton* of friction (rent controlled leases are essentially an appreciating bond asset worth sometimes upwards of 2 to 5 Million dollars), and soforth.

                I’m not so sure what to make of Phil’s 2nd order demand feedback effect on service workers. It’s not clear to me how big that effect should be, and I don’t think it should be clear to anyone, because it’s a dynamically changing market with highly imperfect information and a bubble that *will* pop eventually…

                So, more power to those who want to engage it seriously and based on both data, and real-world models. I’m particularly thankful for Brian’s data based input.

                I particularly think Phil would do well to formulate his model more mathematically, decide what quantities he’s interested in discussing. Like, is he really talking about:

                d/dt median(ObservedRent(ServiceWorkersInSF))

                or is he talking about

                d/dt median(ObservedRent(ServiceWorkersInSF)/TotalWage(ServiceWorkersInSF))


                d/dt median(SpotPrice(ApartmentSimilarToOneAServiceWorkerIsCurrentlyLivingIn))



                Phil? Can you write down a pseudo-code expression that could at least define the quantities of interest to you very clearly?

              • Sam Bailey says:

                > Yes I think plain english is good, but I think it also can be confusing. For example when Phil says “prices” he needs to be more clear what he means so that for example we don’t have 3 or 4 people each thinking he means a different thing:…
                I think this is on Phil, not the English language. That’s okay, he never claimed to have it completely worked out and some aspects of the story have evolved over time, but I would hope that at least the intuition of a “finished” version could be expressed in plain English. It would be suspect if it could not.

                > One of the biggest points I hope eventually comes across is that, no this isn’t Econ 101, and no it’s useless to just define essentially “anything that actually happens” as “equilibrium” and that housing is not a perfectly fungible good, and that spatial distribution of prices makes a difference, and some markets have a *crap ton* of friction (rent controlled leases are essentially an appreciating bond asset worth sometimes upwards of 2 to 5 Million dollars), and soforth.

                Sure, but I wasn’t saying it was. In fact, I made a point to say it isn’t Econ 101. The first thing I mentioned was a post by Nick Rowe that is one possible explanation for results very different from what you would see in Econ 101.

                What I did say was there is a lot of wheel reinventing going on. This isn’t a field I’m very knowledgeable in, but many of the things you argue don’t show up (can’t show up?) in existing models have, in fact, shown up in existing models.

                I think the best resource is still the link Brian posted because 1) the link is conveniently located on this very page, 2) it lays out data (real data!) concisely and clearly, and 3) it’s on exactly the same question that Phil is asking. (Exactly!) But there’s other stuff as well. I haven’t read all of it, but Christine Whitehead’s chapter in the Handbook of Urban and Regional Economics seems a good overview. (In fact, the Handbook in general has lots of material, including empirical work.) Some of the previous research she cites is simulations done at NBER and the Urban Institute by de Leeuw and Struyk in the late 1970s that sound very similar to what you are talking about in an agent-based model.

                But if Phil’s story doesn’t look like any of those existing models, that’s fine. Here is where I will continue my stint as a broken record and say that regardless of what the final story looks like, it should be able to explain patterns we see in the data, and so far I don’t think it does.

              • Sam, I’ve tried to be careful not to impugn economists who actually work on these questions, or to argue that existing sophisticated models of this process don’t exist. And in talking to you here I am not claiming that you said Econ 101 is sufficient. There are many people who have been involved in this conversation. (Public multi-thread conversations like this can get confusing) My only suggestion has been that standard *textbook* models of this stuff like you’d find in an advanced undergrad course or something are not sufficient regardless of what various people piling on to Phil about “supply and demand” and “the market is in equilibrium” and soforth say.

                The main thing Phil’s model (or my agent based model, if I get it running) needs to explain is the observed changes in the distribution of rents in SF, and the observed changes in spot prices, and then make predictions about what would have happened if more housing of various types had been built, under various assumptions about what the various parameters of the model such as external driving factors, wage changes, etc are. We can then argue about which of those parameters best meets the actual observed stuff going on in SF, and see what the predictions are under that parameter set.

                Could be good times. I have to admit I started working on the Agent based version, but I don’t know how far I’ll be able to get.

              • Phil says:

                This discussion has gotten so fragmented that I’m not sure where to put this comment. Under ordinary circumstances I’d post a brand new post that summarizes where things stand on the discussion, but I have posted twice in the past week and am reluctant to do so again so soon on the same topic. Plus I want to take some time to figure out some things and do some reading before I say anything else. And I think this discussion is probably being read by fewer than a dozen people at this point.

                I’m going to hit a whole bunch of topics in this one comment.

                Daniel, Sam, and others have made the point (correctly and repeatedly) that I haven’t used precise enough language. It’s true I don’t know the terms of art. When I say low-end rents will go up in a certain scenario, what do I mean by low end and what rents am I talking about etc. What I think is that there will be some number N for which the rent for the Nth-cheapest apartment in SF is higher if more market-rate housing is built in SF than if it isn’t. I am not talking about the Nth-cheapest apartment on the market at a given time or in a given year, I’m talking about the rents people are actually paying.

                I also think that building more market rate apartments in SF will make the upper end come down (and when I say upper end, just flip the definition of lower end around).

                In another comment, perhaps on the other post, Sonja the activist says the real problem with SF isn’t that the median is too high, it’s that the bottom end is too high, there’s nothing under $800/month. Presumably she means nothing that isn’t rent controlled. I think that problem will get worse not better, I.e. I think even (indeed especially) if you pick an N that is way below half the number of units in the city, the rent on the Nth-lowest unit will go up more if you build the market rate housing than if you don’t.

                I don’t know what to do with rent control. It’s surely a huge influence on the market, and if it were phased out (or expanded) the effect would be far far bigger than what I’m talking about.

                Prop 13 is also a huge effect, while we’re at it. If you bought a house 20 years ago, and are considering selling it and buying another house instead, your property taxes are going to skyrocket because they’ll be based on the purchase price of the new place rather than the (price of the old place plus a modest adjustment). As with rent control, the effect is to lock people in place and the effect is huge.

                I do not believe the two-type high/low market model at all. I did that as an exercise because it’s how I interpreted the suggestion of a commenter. There is a continuous distribution of willingness-to-pay and a nearly continuous distribution of unit desirability.

                There is a lot of friction in the housing market — e.g., moving is a pain, and the more stuff you own the more that is true, so people do not in fact jump ship for a slightly cheaper apartment at the same level of attractiveness; similarly it is a pain to deal with signing up new renters, and there is a period when the unit isn’t rentable, so landlords do not in fact raise the rent to exactly what the market will bear every month. The specific effects I have mentioned here act mostly to greatly increase the relaxation time of the system. Even the renter who doesn’t want to hassle with moving into a slightly nicer place at the same rent will eventually do so if the rent differential is big enough; even the wealthy homeowners who dread having to pack up all their possessions and unpack them across the bay will do so if the inducements are big enough. Indeed, even people in rent controlled apartments will eventually move out (or die). But you might have to wait decades for some of these things.

                I might be completely wrong about the effect that I believe exists. I think my response to Raghu is my best description for whi I believe the effect exists, even in a world without rent control.

                I understand and agree with the comment that claims about what happens in the real world must be tested against real-world data. Since I don’t have a complete model, only a conceptual one, I can’t really do this. I note that this is also a huge problem for the whole field of economics, and is one of the reasons economists have it so much harder than physicists: in the real world everything is economically coupled to everything else, so you can’t even hope to make a model that captures the full complexity of it all. Famously, you’ll find that if you try to get a concrete prediction out of a bunch of economists you’ll find that every economist has two hands. This is not a moral reflection on economists, it’s a reflection on the complexities of the world. Economists are great at explaining things once they know the right answer, but often not good at predicting them in advance. The housing bubble couldn’t have happened if every bank didn’t have a team of economists explaining why it was perfectly ok to loan $400,000 to a self-employed day laborer to buy a house in Modesto. Of course after the bubble burst the whole mechanism of the bubble was easily explained by every economist. This sounds harsher than it should. I think economists should have more humility, under the circumstances. So should I.

                One thing economists have going for them is supply and demand, and utility-maximizing rational choice decision-making in general. There is a ton of real-world behavior that is beautifully explained by this stuff. And after you get past Econ 101 (the only Econ class I ever took) you can extend the theories farther…especially if you make simplifying assumptions. (Economics has a lot of similarity with physics). Assume everyone is rational and has a utility function, assume everyone has complete information about everything, etc., etc. You end up with a model system whose behavior you can study, so you do. I think it’s totally cool. But when you say this is the way my model works, so this is the way the world works, you have to really worry about those simplifying assumptions…and here, I have to say, I think economists sometimes take their models way way too seriously, or perhaps I should say they aren’t careful enough to include important real-world effects.

                An example is an economics paper I just read (on recommendation) about the housing market. The economists started by making a somplified model that is still pretty complicated (which is fine…indeed inevitable). Among the simplifications: assume all workers can instantly and freely move from city to city, and assume there is only one type of worker and one type of industry so any worker can move from one city to another and instantly receive the prevailing wage in that city. I have no problem whatsoever with investigating such a model and I think you can learn an enormous amount from a model like this. My problem comes next, when the authors compare the prediction of the model to the real world and attribute 100% of the difference to regulations restricting housing supply, as if none of those model simplifications make any difference at all! Sure, they put in the usual caveats in the text, but all of their figures and tables and discussion implicitly suggest that the model simplifications have relatively small effects. To me this seems like saying “we are going to investigate the motion of a projectile in absence of air resistance” — totally fine on its own — and then saying that goverment rules about parachuting are having a huge effect, because the parachutists descend much slower than your model predicts. Eh, ok, I exaggerate (enormously) but you see what I’m saying.

                Economists have a genuinely powerful free-market theory but when markets aren’t free they have a problem. In the specific case of the Bay Area housing market, the market is nothing like the frictionless-free-market model. Economists seem to think that if you were to relax the constraints that distinguish the actual market from the free market, you would approach the free-market equilibrium. There are few systems that work that way (I’m talking about both mathematical systems and real-world systems). I’m not saying it’s impossible but you certainly can’t expect it to be true. If you want to know where the Bay Area housing market would go if you relax some constraints on it, you need a model for the effects of those constraints as they are relaxed.

  13. Phil, I noticed your 2 compartment High and Low quality apartment model above:

    I think now we’re getting somewhere. Yes, your model is simpler than mine because your model is of course 2 compartment and considers only the effect of this compartmentalization and building. But think about it a little and you’ll see that the “energy band gap” you’ve created between H and L apartments is a kind of market friction that has the same type of character as rent control, it keeps things from happening like a couple new H apartments are created, and rather than more H people moving in, one of the existing H apartments becomes an L… in other words it prevents realistic things from happening, it artificially holds the entropy of the system down. Under rent control, in actual SF, there are plenty of people living in what should be a very expensive “H” house but paying only “L” rents and so again, rent control holds the entropy of the system down, we don’t get equilibriation to a market type situation.

    Now, as to your specific 2 compartment model. I think the Economist response is “why would there be more demand for L apartments without some reason?” and the reason is either that the supply of low end service worker jobs increases at constant price, or the price increases to attract workers. In either case, you’re right there’s more demand for services.

    If the supply of jobs (or put better, the demand for workers) increases at constant price, this is a little like a phase change right? We can’t actually raise the temp of boiling water until we boil away all the liquid. So perhaps there are tons of people outside SF just dying to work service worker jobs in SF but there aren’t enough jobs, so building some H housing increases the number of jobs for Proles and the Proles flood in to those jobs at constant wage. Or, possibly wages go up somewhat, or go up a lot, we just don’t know. But wages for prole jobs DO NOT go DOWN in this scenario.

    Now, suppose all the L houses are rent controlled. Then prices of L houses don’t go up, but neither is there ANY turnover in the L houses, L houses become like that penny stock with no liquidity, no-one knows what they’d really rent for. All the extra service workers have to commute, and this means extra expenses, and so depending on the facts of the matter perhaps this causes service worker job wages to go up quite a bit, but no amount of increasing service worker wages can get a service worker into a rent-controlled L house… so depending on the facts of the matter, perhaps eventually maybe service worker wages rise enough that a service worker can get into an H house! But again, it depends crucially on the facts, and the H/L band-gap type model is very poor at modeling SF compared to a continuous model. So, I agree an agent-based model seems like the way to go. I really am tempted to work on it, but I’d be a lot more tempted if someone gave me money! ;-)

    • Note another thing… rich guys in SF may say things like “gee it’s really expensive to get a coffee, and that’s because the barista can’t afford to live here. let’s impose regulations on builders to force them to give out a certain number of “affordable” houses” and so, even though supposedly “there’s no rent control on stuff built in the last 20 years” in fact “affordable houses” are just rent controlled houses!!! so there *is* rent control on 10-20% of the stuff built in the last few years.

      Of course, it just drives up rent in the new H apartments, but many of the H workers are living in older apartments with rent control, and so they’ve got lots of moral hazard in this, they don’t have to pay the high rents in the H apartments, because they’ve got theirs under rent control!

      Seriously, now I really want to do that agent based model.

    • Phil, another point about Equilibrium:

      In a free market, if there were say 300 apartments that the vast majority of people would consider equivalent (like say they’re all in one apartment building, and none of them have particularly great views or anything), then you’d observe their rented prices would all be basically the same, and if you had say 50 of them that were just finishing with being painted or whatever, and you put them all on the market, then a year later or so, all the apartments would be rented at the same price, and all else equal that price would be a little lower than when you only had 300 supply instead of 350.

      And so, the distribution over these prices is near-delta-function like, a normal(mean,sd) with sd/mean pretty small. So if you observe a distribution across SF that is really broad it’s either because there’s a broad range of desirability, or something else. I vote something else, because in 2010 you saw a pretty narrow spread relative to now, and now you’ve got a wide spread, and it’s because the liquid housing was dragged up, but the rent controlled housing wasn’t. The spot price is very relevant for the liquid housing, but the liquid housing is a small fraction of the housing stock. Most of the stock is rent controlled.

      Now, Economists are not used to this situation. Of course some of them might think about it, but it’s a special issue in Econ, not the norm. And so they’re here saying things like “see the price of housing went down in Brooklyn after building” and they’re talking about the spot price, and in a market economy, the spot price and the observed price distribution across essentially equivalent units…. is tightly coupled. In SF it’s not even remotely coupled. I don’t know about Brooklyn, but I suspect that if it’s rent controlled, it also has a pretty broad spread of rents across fairly similar apartments, all depending on *when* the apt was rented.

  14. Sonja Trauss says:

    I’m glad I disabused you of the notion that YIMBYs are aesthetically invested in the current, typical suburban form of the Bay Area. There is disagreement among YIMBYs about how much housing it would take to make a noticeable difference in people’s lives. But the disagreement doesn’t really matter because everyone agrees that the right amount of housing is “more than we have now” and the right speed of building is “faster than we have now.”

    I’m sorry I didn’t make another point more clear: median rent isn’t that interesting of a statistic. If median rent went up, but so did standard deviation, that would be success. SF’s problem isn’t even really high median housing costs, it’s that all the prices are clustered tightly around the median. Median rent can be $3500 as long as there exist $500 a month options. But there aren’t. Below about $800/ bedroom there is nothing available anywhere within a half hour of SF. As little as 5 years ago there was.

    A few other people also already said, and I want to repeat, focusing on SF only is arbitrary. The first club I started was called SF BAY AREA Renters Federation. I was living in West Oakland, and I started organizing people on both sides of the bay to testify in favor of more housing in SF _specifically_ to protect existing low cost housing in West Oakland. The focus has always been on political involvement across political borders because our housing and job markets sprawl across those borders.

  15. Phil, I’ve put up some brief sketches of how a continuous model of this system might look here:

    You might want to scavenge that as a start to formulate a dynamical model if you don’t want to go the Agent based route.

  16. Rob says:

    Noah Smith (journalist and academic) has written a blog post in response to Phil which I think more clearly and simply explains the YIMBY stance on this than any of the comments I’ve read:

    If you’re reading through the comments and feeling confused, probably start with that blog post.

  17. Martha (Smith) says:

    Thanks for the link. I read the post and the comments. A lot of the comments do seem shallow, based on one prejudice or another. Still, there are a few comments (although I think fewer than here) that point to differences in different localities. Also less true discussion (e.g., the type where person B critiques what person A said, and person A or C (or each) says, “Now I see your point”) than here. But it does add to the picture.

    One comment I did find interesting is that one attraction to the Bay area is the weather, which makes it a more desirable place to live than the northern east coast. I, of course, can’t help but think of what in all this discussion applies to Austin — and weather here can get brutal in summer. One point I have heard raised here recently is that the hot summer weather makes people less likely to use public transit, so that city planning that assumes high use of mass transit use might not pan out as hoped. Also interesting: Current discussion here is about a proposed “revamping” of the land development code, and the proposed plan was contracted out to a “consultant” firm in Berkeley, California.

  18. Michael G says:

    This entire set of posts and endless arguments over trivia should never have happened. The spatial economic development of urban areas has been extensively researched for centuries and a widely accepted set of models have been developed. Summary of key points with references:

    part 1:
    part 2:
    part 3:

    Some highlights
    “First an increase in the population size has fairly straightforward effects. Indeed, a rising population makes competition for land fiercer, which in turn leads to an increase in land rent everywhere and pushes the urban fringe outward. This corresponds to a well documented fact stressed by economic historians. Examples include the growth of cities in Europe in the 12th and 19th centuries as well as in North America and Japan in the 20th century or since the 1960s in Third World countries.” (From page 83 section 3.3.2: Economics of Agglomeration:… by Fujita, Thisse).

    (2015) “SPATIAL DISTRIBUTION OF LAND PRICES & DENSITIES – The Models Developed by Economists” by Alain Bertaud at NYU – former principal urban planner at the World Bank. A paper specifically to teach basic economics of cities to urban planners. His (very readable) paper is available for download at:

    Mr. Bertraud writes “…an increase in population, everything else being equal, would increase both land prices and densities.”

    The finite supply of land is key. Building up costs more money, but increases rental income per acre. This causes the value and price of land to increase concomitantly. Further new construction must incorporate the newly higher cost of land into the rents to be charged raising rents on new construction. Land is not finite in Dallas or Houston since they can incorporate contiguous land. The population density of Houston is about half that of Silicon Valley and so rents/acre are higher in the denser areas.

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