Lecture 9: Reference-Dependent Preferences

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FRANK SCHILBACH: OK. So let me sort of just recap what we discussed last time fairly quickly, and then I want to move to empirical evidence on a variety of settings. We might not get through all of the slides. That's fine. In that case, we'll just discuss some of this in recitation.

So let me sort of recap what Kahneman and Tversky, in their 1979 article, were proposing based on a bunch of experiments and empirical evidence that they had collected. So their theory, it was called prospect theory what they proposed. Versions of prospect theory is essentially versions of reference dependent utility, have been used or used prominently now in economics.

So the first thing that they proposed was, what matters, what the carrier of utility is, is changes rather than levels. That's to say it doesn't matter for you necessarily how warm it is. It matters kind of what's the change of temperature compared to yesterday.

It doesn't matter that much how much money people have in total. It matters how much that changes relative to what they had previously. More generally, what matters for people is essentially a certain consumption or the like relative to reference point as opposed to in absolute terms.

Second, loss aversion, this is losses loom larger than gains. And we had some evidence of that in the last lecture. That's to say, if you lose some money or some consumption or anything else, grades, et cetera, a loss relative to either your status quo or to your expectation looms larger, is more important, hurts more than a gain of the same magnitude in the positive direction.

And number three, which we talked about quickly, is what's referred to as diminishing sensitivity. That is people are risk averse in the gain domain, but risk loving in the loss domain. That's to say, for example, if you think about distance, time, chance, and the like, going from 0 to 1 or from 1 to 2 or from 2 to 3 is more important for you than going from, like, 100 to 101, 101 to 102, and so on.

Essentially, the further you go away from your status quo, your reference point, any marginal change is diminishing, right? And that's true for both the gain domain and the loss domain. So these are sort of the main three characteristics related to what Kahneman-Tversky called the value function.

We can think of this as essentially version of the utility function. There's a fourth characteristic, which is probability weighting, which we're not going to talk about at least for now. Are there any questions on these three things so far?

OK. So now, prospect theory is then what Kahneman and Tversky were proposing. They were essentially saying, instead of having concave utility, which I showed you last week, instead your utility function may look like this. And what are sort of the features of this utility function?

What are the three key features that I just showed you? How are they showing up in this function here? Yes?

AUDIENCE: C minus [INAUDIBLE] is the change?

FRANK SCHILBACH: Right. So the carrier of the utility function-- so what we have here is c and r. c is like consumption. That could be anything.

That could be apples. That could be bananas. That could be sort of how much money people have available to consume overall.

The carrier of the utility function is not c itself. It's c minus r, so it's c of relative to some reference point r. That's exactly right.

And if r is the status quo, if r is how much we have right now or the person has right now, c minus r is the change relative to the status quo. Notice that r-- we're going to talk about this a little bit-- could be also other things. It doesn't have to be necessarily the status quo.

It could be also people's expectation or their goals or their aspirations for the future, right? The key part is, however, what matters is-- this is the first thing I was saying. It's changes rather than levels, changes relative to some reference point or consumption relative to some reference point. That's number one, yes. Yes?

AUDIENCE: The curve flattens out, which is diminishing sensitivity.

FRANK SCHILBACH: Exactly. The curve flattens out in both directions. That's diminishing sensitivity. It's essentially concave in the gain domain, in the domain where c is larger than r. And it's convex in the loss domain where c is smaller than r, right?

And that's exactly the issue that essentially the first, the marginal change, going from, say, 1 to 2 is relatively large compared to a marginal change going from 10 to 11. That's both going in the right direction in the gains domain and the left direction in the loss domain. Yes?

AUDIENCE: For the loss aversion, the left side is steeper than the right side.

FRANK SCHILBACH: Exactly. In particular, there's a kink in this function. When you look at 0, where c equals r, the gain and loss domain intersect, there we have a kink in the value function, in the utility function, which essentially exactly is the loss domain, the loss aversion which is like going to the right is less steep than going to the left. Put differently, if you lose, if you're sort of below the reference point, that's more painful than being the same amount of units to be above the reference point.

That's number two. That's essentially exactly the loss aversion. So I just wrote down all of that.

Again, let me repeat. Carrier of the utility changes relative to the reference point-- excuse me-- rather than levels. Second, there's loss aversion. There's a kink at 0 in this function. And three, there's diminishing sensitivity, which is concavity in gains and convexity in losses.

Any questions on that? Now, a key question here is-- I want to sort of flag this. We're going to talk about this a little bit at the end of the lecture. We're going to talk to this a little bit in the next problem set is kind of like how is the reference point determined. And does it matter?

As I said before, in Kahneman-Tversky's work, a lot of the reference point is the status quo. So they essentially postulated the status quo is what really matters originally. I think people have moved toward saying the reference point.

And this is what Koszegi and Rabin and others have written down in their models of reference dependence utility and recent more economics work is what really matters is expectation. So what do you expect to consume or to have and so on? That matters. That sometimes coincides with the status quo.

For example, if you have a house, the status quo is that you have a house. You probably assume that you have a house in the future. These things coincide.

If you think about wages, et cetera, what seems to matter often is not so much what people's wages are right now. What matters is what wage gains and so on do they expect to receive in the future. And they evaluate their future, their outcomes in the future, not necessarily to the current wage, but rather what they expect they would get in the future.

OK. And so here's an example. And you'll have some problems set questions. Again, this is a problem set three-- which is not posted yet, but will be-- of that kind, which is you might have reference dependent utility over-- this is just a very simple example-- shirts and money.

So you have essentially two different domains. You have, essentially, losses and gains over both of those domains. You have a reference point, which is rs, is how many shirts you might have. You have a reference point, rm, how much money you might have.

Now, what's important here is that, essentially, when you think about buying a shirt or selling a shirt, there's going to be two dimensions which you have to sort of consider. And when you think about the endowment effect of [INAUDIBLE] and so on, you have to consider not only the losses and gains and shirts, but also the losses and gains and money.

So that's to say, if you're trying to buy something, you're going to get a gain in shirts relative to the reference point if it's unexpected. But you'll also have a loss in money. Similarly, if you're going to sell a shirt, you're going to have a loss in shirts, but a gain in money. And these things then interact.

Now, what's the value function? The value function, as I said before, is usually concave in the gain domain and convex in the last domain. There's a kink at 0. It's steeper on the left than on the right. Usually, we think the relative slope is about 2, 2.5, OK?

So one version of that would be this function that I wrote down. Again, there will be some problem set questions, et cetera, sort of to clarify that. But one key question here is, then what are the different domains?

And that's kind of a question of mental accounting. We'll get to this in the second half of the course. The question's kind of like, what are the different categories?

Do you have shirts? Do you have pants, sweaters? Or is it just for clothes overall?

Or when you think about earnings and consumption, et cetera, is it daily consumption? Is it weekly consumption? Is it monthly consumption?

So there's lots of questions on how to exactly specify this utility function. These questions are mostly unanswered in the literature. So for now, for us in our purposes, we're going to essentially assume there is a value function given and then sort of work with that. Any questions on that?

OK, great. So now, we're going to talk about a number of different applications. We talked a little bit already about the endowment effect and about insurance. I'm going to skip this. There's some of this already in recitation in the problem sets.

We're going to particularly talk about labor supply and employment decisions, essentially how much do people like to work. And is effort or people's work decisions, are they reference dependent? We're going to talk about finances, what was mentioned last time already about investment decisions. When do people sell and buy stocks?

We're going to talk about housing. When do people decide to sell or buy a house and at what price? We're going to talk about sports, in particular marathon running and golf.

There's some papers on domestic violence we're going to talk very briefly about. And then we talk a little bit about firms. How do firms think about pricing and so on? What is sort of the market response to reference dependence?

That's to say, given that we know there's lots of reference dependence in the world, now, as a firm or treating other people, how should we think about, how does that affect, our own behavior or how maybe firms interact with us? OK. So let's start with labor supply. Let's start with a very simple example.

Suppose there's a worker in the following situation. She can freely choose how many hours she works every day. And there are frequent temporary changes in her hourly wage.

Now, there's different relationships between wages and hours per day. You could always work the same number of hours. You could work more hours on the days when wages are high.

Or you could work fewer hours on days when the wages are high. What does sort of standard theory say? What should you do? Yes? Two?

AUDIENCE: Two.

FRANK SCHILBACH: Why is that?

AUDIENCE: Because that maximizes your expected value for time.

FRANK SCHILBACH: Right. So if hours are effortful, you usually don't like to work. You should work during the hours when your payment is the largest. That's right.

So what about option number one? Why might option number one be optimal? So what you're saying is exactly right. It depends a little bit on something else. And what is that? Why might you choose number one anyway?

AUDIENCE: Habit-forming is nice.

FRANK SCHILBACH: Yeah, there could be sort of habits, exactly. Or it could just be that it's really effortful to work 12 hours in one day. Maybe there's kids at home, or maybe it's just really tedious to work. At some point, you just want to go home and do other stuff.

So it could just be that working beyond, say, eight or nine hours per day is really tough to do. So then you might say, I'm always going to work eight hours. I'd love to work more, but it's difficult to do.

So essentially, it's just to say, if the function of the effort as a function of hours is convex, then you might sort of keep it the same. Surely, what you don't want to do is number three, working fewer hours on days when wages are high unless effort costs are particularly high on those days. So it could be that it's really super hot. Or it could be it's tedious to work on those days. And you might say, then you don't want to do it.

But assuming that's not the case, you kind of want to avoid this. Because for the same number of hours, you're going to make less money overall. And so here's a concrete example.

Suppose wage is 5 hours an hour on day one and 10 hours a day on day two. So there's three strategies. You can work 8 hours on both days. You can work 6 hours on day one, 9 hours on day two, or the opposite, 9 hours on day one and 6 hours on day two.

So if you do that, you can sort of calculate how much that is. You can essentially work 8 hours on both days. You get 120 hours. You can work 6 hours on days one and two, which makes $120 as well. Or you can essentially do the opposite, which makes you $105.

This is what I was saying. Option three doesn't make a lot of sense unless effort costs are particularly high on certain days when the wages are high. We're assuming that away for now.

And so now option two-- and this is what you were saying-- essentially saves you an hour overall. You work only 15 hours instead of 16 hours. And you make the same amount of money.

Now, unless the ninth hour is extremely costly for you to do, you might not want to do that. OK. Now, why might you do something else instead? Or where does reference dependence come in here? Yes.

AUDIENCE: I see on the high wage day you make more than the less wage day, so I feel like stopping maybe.

FRANK SCHILBACH: And why would you stop? What's causing you to stop?

AUDIENCE: [INAUDIBLE] wages higher relative to [INAUDIBLE].

FRANK SCHILBACH: Yeah. Yes. And so what are you evaluating? Or what's the-- or what happens, for example, if you work only 6 hours on a different day? How much do you make on the sixth hour day, I guess, which would be $30, right? And so what are you comparing that to, I guess?

AUDIENCE: You're comparing it to the actual money you made at the end of the day.

FRANK SCHILBACH: Right. But so suppose you, on average, want to make a certain amount of money, which is $50, $60 and so on. Now, if on some days you make a lot of money and on some day you make very little money, you might sort of evaluate that separately and say, on that day, I'm essentially in the loss domain. I'm below my target or below my expectation.

And so if you evaluate your utility that way, you might sort of not want that because it feels essentially you're below a certain threshold. It feels kind of like a loss relative to your expectation and so on when you might be inclined to work a lot of hours. Instead, on the days when you make a lot of money, why might you stop? Yes?

AUDIENCE: You might have a target that you expect to meet every day to cover your expenses. And if you feel like the work [INAUDIBLE] reach that target, you might [INAUDIBLE].

FRANK SCHILBACH: Right. So if you target, your reference point, is essentially a certain number, you might reach that target quickly because your wage is pretty high on that day. And once you reach that target, you might say, well, now utility function is relatively not very steep anymore relative to being in the loss domain. So it's flatter.

So then you might just stop relatively soon because, essentially, any marginal earnings are not really valuable for you anymore. OK? Any questions on that or comments?

So why do we want the wage changes to be temporary here? What's an issue here when you sort of try to look at this in the data? Suppose I had persistent wage changes. Yeah.

AUDIENCE: So you can have a frame of reference?

FRANK SCHILBACH: Yeah. You want to kind of keep the reference constant. So in some sense, if wage changes are permanent, then you get essentially income effects. You'll be a lot richer overall.

If they're only temporary, essentially, you can sort of argue that, essentially, your expectation should be the same. And once you reach, once you have a lot more money, the neoclassical model should actually say that there should be income affects. Essentially, the neoclassical model says, you should essentially aggregate all of your income and say, it doesn't really matter whether you earn it on Monday, or Tuesday, Wednesday, or Thursday.

You should look at how much are you earning overall depending whether you earn sufficiently much, you're going to work fewer or more hours. Now, if you earn a lot, because your wages doubles or whatever, you might actually work few hours not because you reach a reference point on a given day. It's just because you got a lot richer, and then you decide it's not worth for you to work that much.

So we're kind of trying to avoid that. We're trying to have only temporary changes, which is to say, for given wealth overall on any given day, it shouldn't matter whether you earn the money on Monday or on Tuesday. So essentially, if the wage happens to be really high on Tuesday, you should be working more, earning more, on Tuesday as opposed to on Monday.

Now, what I was saying is, if you're reference dependent, you might actually care about this. You might care about on Monday you didn't reach your target. Therefore, you want to work more. On Tuesday, you reached your target very quickly. And you work less even though the wage is actually really high. OK.

Now, strategy one might be optimal even in the neoclassical model if effort costs are convex. This is what I was saying is, if it's really sort of costly for you to work 9 hours, you might say, I always work 8 hours. I want to have a certain amount of money for my children and so on.

So the extra hour, if that's really, really painful, you might not want to do that. We don't think that's necessarily the case in so many situations. The question is, can we really say that strategy three-- that's the strategy of doing the opposite, of working essentially a lot of hours when wages are low and few hours when wages are high. Can we really say it's a mistake?

Well, it depends on kind of whether the effort costs are correlated with wages. So if cab drivers, for example, make really high wages on some days and low wages on other days, it could just be on low wage day it's much less effortful to drive around. So you would do more hours.

It turns out, when you actually ask cab drivers, they actually prefer busy days. They actually prefer it when there are customers as opposed to just driving around and looking for people. So we don't think that's actually true. But in principle, you would have to sort think about that.

Now, there's a long literature starting with Camerer et al. On cab drivers. A lot of that essentially is pre-Uber, like collecting trip shifts from cab drivers. Now, there's lots of like Uber data that's essentially much more powerful in some ways. So there will be probably more papers using Uber and Lyft, et cetera, data on that.

But what Camerer et al. did at the time was they essentially looked at typical cab drivers that rent their cab for 12 hour periods for a fixed fee. And within this 12 hour window, a driver can choose their hours freely. So you just get your cab that's not yours. You rent it for the day. And then you can essentially choose how many hours you want to work.

And their wages, how much money they make in any given hour, varies by a lot. The weather varies, the subway breakdowns, conferences and so on and so forth. There's lots of variation in how much money you make on a given day.

So then they have trip sheets that look at how long cab drivers work and their overall earnings. And so they can essentially back out the wages from each day and then look at like how much do people work on days when wages are high versus days when wages are low. And then they essentially find the basic finding. And that's a finding that's sort of been contested in the literature many people have found or confirmed subsequently. And others have not, but I think eventually people have sort of settled on this.

Hours are negatively correlated with wages. So when wages in particular are unexpectedly high, cab drivers tend to work fewer hours. And again, this is not for permanent changes, but for transitory changes. Surprisingly, on a given day people get more money, then drivers work few hours.

And that's very hard to explain for the neoclassical model. Because, essentially, you shouldn't care about whether you make the money on Monday, on Tuesday. As I said, you should care about how much money you make overall and how many hours you work.

And so it's very hard to explain this. And sort of the explanation that Camerer et al. and others were testing or arguing is essentially this has to do with reference dependence. And so what's being evaluated in a reference dependent way? Or how do we think about this? Yeah.

AUDIENCE: I have a question.

FRANK SCHILBACH: Yeah.

AUDIENCE: How did they rule out the possibility that maybe there is reverse causality maybe on a day where none of the cab drivers want to work that much because it's supply and demand that they just go on?

FRANK SCHILBACH: So that's to say effort costs are high. So usually, it's to do with other drivers. So let me actually get through-- so let me defer this for one second.

I have a slide on confounds. And then we can see the rest of your question and then get back to that. But that's a good question.

So what is being evaluated in reference-dependent way? What are people looking at in terms of where's the reference point in the evaluation here? Yes.

AUDIENCE: I guess, if you're a cab driver, you kind of say, oh, I want to make this much money today. And then you just kind of work until you feel like you've made enough, and then you just stop.

FRANK SCHILBACH: Right, exactly. You have to pay your fixed fee for the day or for the month or whatever. But there's an implicit fixed fee for the day. So you kind of want to make at least that much money to make not a loss. You probably have some positive target in some way in saying, like, I want to make pay back for my fee plus you want to make some money for the day and minus sort of expenses.

And once you reach that target, you are in the gain domain. Below that, you are in the loss domain, right? And so the daily income essentially-- and that's essentially sort of money after paying back the fee, but you could also get-- it's essentially what's being evaluated in the reference-dependent way.

What's the reference point is some daily target that you have. Often, it's expectation and so on and sort of, essentially, how much you think you will make. And then what's the feature of the value function that explains the phenomenon?

Well, it's loss aversion. If you're falling short of the target, essentially your marginal utility-- when you drive another hour or another trip, the marginal utility that you get, since the value function is very steep below the target-- is very high. Once you reach the target, it's very flat. And then essentially you tend to stop. Does that make sense?

AUDIENCE: Yeah.

FRANK SCHILBACH: OK, great. So the main takeaway is, so if drivers often stop at their daily income target, driver with a higher wage reach their targets faster. And they work fewer hours. Again, that's variation within drivers across days.

And sort of there's lots of subsequent work and debate regarding this finding. The debate is still ongoing. For example, one recent paper looks at tips that drivers get unexpectedly.

So sometimes drivers get large tips, sometimes get small tips. It depends a lot when in the day they receive the tip, if they receive it really early versus late, if they sort of get to their target. And essentially, the target seems to be adjusting over time.

But overall-- and this is sort of getting a little bit at your question-- we think it's not sort of aggregate supply. But the debate is still ongoing. But overall, we sort of think that lots of labor supply decisions, when people have daily decisions of how many hours to work and their wages vary, depend on reference points and might sort of potentially be at least suboptimal. Or put differently, people could work fewer hours and try to sort of adjust their overall amounts.

For a while, I did this. You can ask your Uber and Lyft drivers what they're doing and so on and see whether they're a reference-dependent driver, sort of where they have reference-dependent preferences. Now, what are sort of potential alternative hypotheses?

One question, one issue, could be liquidity constraints. This is, for example, if you just don't have enough cash. If you have to pay back your fee for the day or for the next day, you might want to not work only very few hours on a given day.

It turns out that drivers who own their own medallion exhibit the same patterns. There could be things like fatigue. Let's just say it's really tedious to work on certain days when wages are high. We don't think that's going on in part because drivers themselves, they say, it's actually easier to drive with more passengers.

Again, recent papers, in fact, can also control for this and so on. So we don't think it's actually fatigue. And this is, I think, what you're saying. The last one is unobserved shocks, so some shocks that affect all drivers' labor supply at the same time.

Example, there are some days in which all drivers get the flu. Fewer drivers will work. And those who will work work fewer hours. And those who work get higher wages.

That's a little bit trickier for them to rule out. In part, there's other papers, other studies afterwards, that sort of try to get at this. Usually, yeah, for this specific data, that's hard to do.

I think for the other data where people have essentially not just daily-- so this is essentially trip sheets. So what they're using mostly is daily wages overall. They don't even have the wage.

They only have the overall earnings and then the hours. And then they sort of compute the wage dividing the two, which causes some other trouble. But once you have Uber data, once you have specific trips and particular also tips and so on, you can look at, on a given day when I get a high tip versus a low tip, you can predict, essentially, how much I'm going to earn on a given day.

So suppose you predict that I'm going to earn $100 in a given day. Now, I have, say, $50 or $60. Now, I get a large trip and a tip and so on that gets me over that threshold.

You can look at whether I stop. You can look at the exact same thing. When I have only $20 and I get a large tip, do I stop and so on?

So you can essentially control for all of that and then do within driver comparisons, like for trips that happen to be large or small that you happen to get in a given hour. And then you can sort of deal with overall market conditions. I think even better, in the future, there will be sort of experiments and so on where you can look at when Uber and Lyft try to incentivize their workers and so just, say, essentially, sometimes pay people more and less randomly, sort of explicitly randomly, because they want to kind of learn about how to best incentivize their drivers.

And then you can control for everything because it's explicitly random whether a certain driver gets high versus low wages or sort of trip fares. Yeah. OK. Any questions on the labor supply? Yes.

AUDIENCE: I'm a bit confused about the unobserved shock. Because if you get a really large tip, that doesn't necessarily predict that the rest of the day you'd have higher wages if you kept working. [INAUDIBLE] you get this really high tip, and then you would be like, oh, today's a lucky day. I can stop early. But if I have worked more this day, I wouldn't necessarily be making continuously more than normal.

FRANK SCHILBACH: Right. So in the unobserved, in the large tip example, the assumption is exactly-- or what they show in the paper. This is subsequent work, not this specific work. What they exactly show in this type of paper, these are sort of random events.

In a sense, it's precisely not predictive of your future earnings. It's random. Now, one interpretation that you have is to say, well, it could be that you kind of have some expectations about your future earnings. They could be particularly high or low. It's like, I got my lucky day and so on and so forth.

That is hard to rule out. In some sense, if you had rational expectations, that's hard to explain for the neoclassical model. What's harder to rule out is to say, you know, I now think I got my lucky draw for the day.

And that's it. And I'm not going to get any lucky draw again. Let's just call it a day. That is hard to rule out.

But what is hard to explain for the neoclassical model-- I think we can sort of reject-- is to say, if you just think this is a shock, which really in reality it is and you just happened to get a bunch of money on a given day just randomly, then the reference-dependent model can sort of explain why you stop early. Because it just gets you over the reference point. The neoclassical model should just say, depends on essentially how many hours you want to work on a given day.

It's nothing to do with a target. Because essentially, again, it doesn't matter whether you make money on Monday, or Tuesday, or Wednesday. You should just care about the overall amount of money that you make overall. But that's a good question. OK.

So now, a second paper is on the housing market. So what is the natural reference point for housing market? Or how do we think about housing prices? Or how do you think about-- I guess a few of you will own a house. But if you owned a house, how would you think about selling a house? What is an actual reference point? Yes?

AUDIENCE: Whatever it was before or how [? changes ?] [INAUDIBLE].

FRANK SCHILBACH: Yeah, so exactly. So the previous purchase price, it turns out it's a very, very salient thing for owners. People really know how much they paid for their house. It's a huge expense in their life.

They really remember it was like 300,00, 500,000, a million, et cetera. They know exactly how much they paid. And when you even ask people, the majority of people know exactly how much they paid for their home.

Now, one claim is that loss aversion makes people unwilling to sell their houses at a loss. And so what they would then do is they ask essentially for higher prices, if a loss, relative to their purchase price. And let me just show you exactly what I mean by that.

Genesove and Mayer have Boston condominium data from 1992 in 1997. Luckily for them, there's lots of variation or fluctuations in the housing market during that time. So the housing market went up a lot, and then it went down a lot and went up a lot.

Now, suppose you have two sellers, A and B, who both want to sell their home in 1994. Now, what we can do is we can look at these two people. Suppose they have very similar houses based on observable characteristics and location and so on and so forth.

So once they have really comparable houses, we can all look at seller A, purchased their home really early on, in 1989. That person happens to be quite unlucky because they just bought the house really at the peak of, I guess, the housing boom at the time. Or seller number B, who purchased in 1991, that person was relatively lucky. They bought essentially at a time when the housing market was relatively low and appreciated quite a bit.

So now, we can look at these two people and ask the question, is seller A or seller B more likely to sell their house? And the hypothesis is that seller A will sort of view this as a loss. This seller will essentially just say I'm losing money here. I don't want to sell. And that seller might essentially ask for a higher listing price and wants make more money for this house because they don't want to make a loss on that sale.

Well, seller B says, I'm actually gaining money anyway. So let's just sort of post whatever you think is actually the expected market price. I might be happy to sell at a lower price compared to seller A.

OK. So one thing we can look at essentially are listing prices. How much do people want for the houses? The second thing they can look at is actual sales prices. Are you now selling this at a higher or lower price?

And number three, we can look at how long is the house on the market. How long does it actually take to sell it? That's a quite costly thing to do to have your house on the market for quite a while because, essentially, often people then don't already move somewhere else. Or they can't really live in the house because they have to sort of show it and make it available for showings and so on.

So it's a costly thing to do. You really don't want to have your house on the market for several months. But is sort of the broad idea clear of what we're trying to do? OK.

So what predictions do we want to test? We want to test whether house owners are reluctant to sell their house when the current market price is below the purchase price. So the ideal specification is essentially the following.

We look at the list price on the left-hand side. And then we are going to run a regression that looks at some constant-- that's just kind of time trends, et cetera-- plus a beta, which is the coefficient of interest. Or one coefficient of interest is of the actual market price. How much is the thing worth? And then delta on the loss is how much do you lose relative to your purchase price.

Now, if people were not reference-dependent, what should we find? Or what would be the predictions? The neoclassical model, what should we find here? Yes.

AUDIENCE: We should find that delta 0 [INAUDIBLE]?

FRANK SCHILBACH: Exactly. Delta should not matter. It shouldn't matter how much you lost or gained in that house. What should matter is what is the actual market value. You should essentially try to be willing to sell it not.

Beta could be-- it doesn't have to be 1. It could be everybody pays above the actual market. There's some housing bubble or whatever. Beta could be 1.1 or whatever you might be. That depends on, essentially, sort of aggregate conditions and so on.

But delta really should not matter. When I'm trying to sell you a house, you should ask, what's the actual market value? And I should, essentially, then based on that, put it on a market on that listing price. But what might be the case is that the loss actually matters.

Now, one problem here is that the actual market value is not observable, right? So I don't actually know what the market value is because that's endogenous. That's part of the transaction. So what can I do instead? Or how do I do this? Yes.

AUDIENCE: By asking people, would you take this trade? And then see what they say. [INAUDIBLE].

FRANK SCHILBACH: Right. So you can look at actually the market outcome overall. You can look at who buys it and what's the actual purchase price. Now, that might also be endogenous to the listing price, right?

So if you think you know that people who are loss averse are listing their houses too high relatively compared to what the market value actually is, it might actually be sold at a higher price. So that's hard to interpret. It could just be that, if you list it at a very high price and wait for a long time, you also sell it at a higher price.

But it doesn't mean that that's actually worth that much. It just means that you happen to find a buyer who happens to be willing to pay a lot. And that's more likely when you wait for a long time, which is not necessarily optimal, because it's actually quite costly to do that.

But you're saying something else which is asking them about what they think. But what are the characteristics that we could look at? Or what data could we look at?

If you had Zillow data or data on essentially a bunch of these apps where you can look at houses, what data could you get? Yes.

AUDIENCE: You'd look at the houses in the neighborhood, similar houses that sold recently.

FRANK SCHILBACH: Exactly. What Redfin and Zillow, et cetera, do these days is essentially they have these algorithms that try to predict the actual market sales price. And what they tend to do essentially is look at, exactly as you say, surrounding houses that are similar in some characteristics.

They look at the square footage. They look at the number of bathrooms and rooms in general. They look at sort of location and so on and so forth.

And then you can predict how much-- and sort of they look at all the time trends and so on. How much is the actual market value? But essentially, fundamentally, it's a prediction exercise. You can try to predict what the actual value is. And that's exactly what Genesove and Mayer do.

They do some more fancy things that try to get it other unobservable characteristics and so on. But the essence of this is exactly the prediction exercise where they say, let's just look at the characteristics of this house. Let's try to predict what the market value is and then look at the loss, which is essentially the difference between the previous selling price and the expected selling price truncated from 0 because, otherwise, it's a gain.

And then we can look at does it really seem that, when people are in the loss domain, when their loss is positive, are they now selling their house or trying to sell their house at a higher price? Yes?

AUDIENCE: How do you account for something like recent renovations since the last listing and relative to any other similar units or houses or [INAUDIBLE] [? nearby ?] [INAUDIBLE]?

FRANK SCHILBACH: Right. So that's tricky to do. And I don't think they have this in their data. So what you'd have to assume here, and that's perhaps reasonable, is to say that when you look at sort of this picture that seller A and seller B did not do differential renovation depending on when they bought the house. Right?

So if you said, it's fine if people have done renovations. For example, this is what I was saying about the beta on the actual market value. If you systematically underestimate or overestimate how much people renovate and so on, or maybe the housing market is really hot or whatever, that's OK.

The main issue is that can't be correlated with the loss here. So if it's the case that people who lost a bunch of money in terms of their housing prices sort of tanked, if those people have done more or less renovations, then you're in trouble with your estimates. Yeah.

AUDIENCE: Is the expected selling price the estimation of actual [? work ?] value?

FRANK SCHILBACH: Correct.

AUDIENCE: OK.

FRANK SCHILBACH: Yes. So now, what Genesove and Mayer find is-- and there's more detail to that. But essentially, the main finding is-- and that's a fairly solid one, there's a bunch of different specifications-- a 10% increase in a prospective loss. So if this loss coefficient, the difference between the expected selling price and the purchase price, if that's 10% higher, then essentially the list price is 2.5% to 3.5% higher.

So people list the price, the house, at a higher price. If the house is at a loss compared to a similar house who's not at a loss or who's in the gain domain, these effects then translate into higher sales prices and a lower hazard rate of sale. That's to say people actually sell it at a higher price. So in fact, it's hard to say here what's optimal versus not.

It could be that, overall, people are like, it's actually a good thing to do. That depends a lot on, essentially, your opportunity costs of money in terms how costly is it for you to keep the house on the market for a while. But essentially, people have a lower hazard right of sale.

That's to say it just takes them a lot longer to sell the house. That tends to be very costly to do. But if you just otherwise would have your money in the bank and you have another place to stay and you don't really care, maybe then that's fine.

But we surely have real effects in terms of people list their houses at higher prices. People sell them at somewhat higher prices. And people also keep them longer on the market. OK. Yeah.

AUDIENCE: Is this the same analysis if it's gains on the value of the house?

FRANK SCHILBACH: So essentially, what we're doing is we implicitly comparing losses versus gains, right? So the gains here would be in the actual market value already as it is. But essentially, what you're implicitly doing is, when comparing implicitly, this is what I was saying here. When you look at this picture, implicitly what we're doing is we look at people who are losing money compared to people who are gaining money. And explicitly or implicitly, we're asking, is the increase and the gain sort of predictive of that-- sorry, the increase in the losses predictive of your listing price?

Now, it's hard to do this at the same time for gains because, essentially, an increase in the market price overall that's sort of collinear. In [INAUDIBLE], essentially that's hard to separate. You could do the same analysis, and you wouldn't find that for the gains in part because essentially explicitly what we're doing is incurring losses to gains. OK.

OK. So then there is another piece of evidence that sort of tells us perhaps this is not optimal. If you look at people who are owner-occupied compared to investors-- so there are people who essentially invest in houses. And they sell houses. And they sell lots of houses over time.

Those people have much lower endowment effect, if you want, for houses. So they exhibit this behavior a lot less. But people who live in that house, who bought that house, for them it's mostly the only house they live in.

It's the main purchase that they have. For them, it's essentially their house for which they don't want to make losses. For them, these effects are twice as large compared to the investors.

And that's perhaps some evidence that this is not optimal behavior in a sense of sort of the professional investors. They presumably know pretty well how to price their houses. So if they do this behavior less, presumably that's a sign that there's some form of a mistake here going on.

Second, there's some evidence-- and John List has some work on this overall-- to say that experience can mitigate reference dependent effects. Essentially, if you do a lot of trading, if you sell a lot of houses and so on, then you might still feel losses and gains, but you might sort of have a lot more experience with this. You kind of know that this is happening sometimes.

And you might be less prone to these types of effects because you kind of know that you shouldn't be doing this. You shouldn't sort of have your feelings of losses and gains get in the way of making profits. So there are some people who would argue that this is very much consistent with markets over time or exposures to markets and several predictions. Experience makes some of these effects go away. And John List has some separate evidence on this on traders of cards and so on. OK.