Sunday, August 18, 2013

Krugman to Farmer: "Show Me Your Trailer, or I Won't Watch Your Movie"

Paul Krugman has replied to Roger Farmer's letter of complaint. The bottom line is that Krugman finds Farmer impenetrable:
I’ve tried [to read Farmer's stuff], a couple of times, but found it very hard to penetrate and gave up — and several other economists I’ve talked to had the same reaction.

Krugman is on to something here. Though not always a paragon of transparency myself, I have at times found Farmer's work confusing. But there can be a nugget in there that is worth taking the trouble to dig for. Here's a tip for Krugman: Ignore the words that Roger writes, and just try to sort through the model. Typically, he's not doing anything that's technically difficult for the average economist with a PhD - the models typically have standard features.

A couple of years ago, I was confused by this paper by Roger. But, I think I figured it out, and the idea is fairly straightforward, and interesting enough that I wrote this paper, to explain Roger's idea and extend it. Krugman says:
Sorry, but I won’t commit to sitting through your two-hour movie if you can’t show me an interesting three-minute trailer.
So, here's the "trailer" for Roger's idea (different from the subject of his complaint - that's another idea):

Workers and firms are in the business of bargaining over the surplus from exchange. But how they split that surplus is indeterminate - we don't have good theories of bargaining power. What this can lead to is indeterminacy in real wages, aggregate economic activity, and the unemployment rate. There are multiple equilibria. If the unemployment rate is high, the expected payoff from searching for work tends to be low, and if the real wage is high, the expected payoff to searching for work tends to be high. In the model, equilibria with high unemployment rates and high real wages coexist with equilibria with low unemployment rates and low wages, and across these equilibria, the expected payoff to searching for work is equal to the best alternative. This encapsulates the basic Keynesian idea - private economic agents find it difficult to agree on socially beneficial terms of exchange - but in the model there is nothing left on the table. Everyone is optimizing in equilibrium, and no prices or wages are fixed. The government can fix things - this is an essential element of Keynesianism - but they do it in non-Keynesian ways. For example, Taylor rules don't work.

Though Krugman has a point, we can get carried away with sound-bite economics. As with good music, sometimes you have to live with it for a while before you get it. Then, there's no turning back. Examples:

1. Expectations and the Neutrality of Money was part of a revolution, but almost nobody got it when it was first written. And the people who got it initially were not waiting for the trailer to convince them. They were moving the research forward, and getting credit for it. Ideas progress quickly, and young economists who want to make a splash are not waiting for a three-minute spiel to convince them what the big new ideas are.

2. The economics job market: It's well-known that lazy recruiting strategies don't work. Every January, 10,000 economists converge on some city in the United States, and various academic and non-academic institutions conduct 30-minute interviews of newly-minted (or about-to-be-newly-minted) economics PhDs. Recruiters can show up for interviews without preparation, and screen candidates based solely on the 30-minute interview. That guarantees that the people who are hired are the ones who can give a 30-minute interview. Of course it's no guarantee that the candidates can actually do good research and teach effectively. The conclusion of this paper seems to be that: (i) the research payoff from the median economics PhD is pathetic; (ii)quality falls off quickly in the top-ranked schools: the top graduate from the University of Toronto is roughly as good as the #3 from Yale. Everyone knows that it is worthwhile to spend time reading job market papers - carefully. A job candidate can be an inarticulate nerd, but have the power to create beautiful research that will pay off big-time in the future.


  1. Hi Stephen,

    Here's my "trailer" on the Williamson on Roger Farmer on Keynes discussion:

    1. No, you didn't get it. What I wrote down is literally Farmer's model, just simpler. As I state in this post, don't read Roger's words, work through his models.

    2. SW, your paper on Farmer's model says, “We can imagine a world – Farmer’s Keynesian world - where a matched worker and producer in our model have difficulty splitting the surplus."

      And you summarize, “Inefficiencies arise in Keynesian models because private sector economic agents somehow do not get the terms of exchange right. In our model [i.e., SW's model], what goes wrong is that there are no incentives determining how producers, workers, and consumers split up the gains from trade.”

      With due respect, your description finds no expression in either Farmer's words or his equations. "What goes wrong" in Farmer's model is that demand depends on self-fulfilling expectations about future asset values, not that producers, workers, and consumers can't figure out how to split up "the gains from trade."

      Here's Farmer's own description, “In this article, I propose a new approach. Instead of searching for a fundamental explanation to close an indeterminate model of the labour market, I close the model with the assumption that firms produce as many goods as are demanded. Demand, in turn, depends on beliefs of market participants about the future value of assets. By embedding the indeterminate labour search market into an asset pricing model, I show that the unemployment rate can be explained as a steady-state equilibrium where the indeterminacy of equilibrium is resolved by assuming that the beliefs of market participants are self-fulfilling.”

    3. No, clearly you don't understand how his model works. The stuff about "demand," future asset values, etc., is a red herring. The indeterminacy in the model is purely static - it's bargaining indeterminacy. I can understand that you want to cling to this "demand deficiency" language, but in this instance it doesn't work - when you use those words, it's just confusing.

    4. I have not read the model, but based on Farmer's description I suspect that expected asset prices influence unemployment by affecting how the surplus generated from an employment match is divided. Am I correct? If so, then it would seem to me that the multiplicity of equilibria indeed results from bargaining indeterminacy. Animal spirits may be one way to generate persistent deviations in unemployment, but there should be other ways to do the same.

      My problem with animal spirits is that they seem "too easy" an answer. Where do market design, asymmetry of information, and financial innovation come into play? I think it would be a mistake to ignore these issues and instead conclude that the role of the government is to manage expectations or asset prices.

    5. SW, if you can read the Farmer's own description of his model in my comment above and conclude, "The stuff about 'demand,' future asset values, etc., is a red herring," then you're claiming that Farmer, himself, has no clue about what he's doing. I doubt it.

      You write, "The indeterminacy in the [Farmer's] model is purely static - it's bargaining indeterminacy." But Farmer is working with Peter Diamond's search model, which focuses on search externalities rather than bargaining problems. And Farmer finds “no reason to treat the search model differently from any other competitive model with externalities,” adding that he views “the addition of the bargaining equation as arbitrary.”

      For your interpretation of Farmer's model to be correct, given what Farmer, himself, says in several places, I think you'd have to invoke a conception of unconscious economic modeling, coupled with a degree of self-deception, which would make a psychoanalyst blush.

    6. "But Farmer is working with Peter Diamond's search model, which focuses on search externalities..."

      It's not increasing returns in the matching function. This is like talking to a fence post.

      CA: The model is basically static. Farmer pastes it together into a dynamic setting, does standard asset pricing, then acts as if it's "animal spirits" in the asset market that picks out the equilibrium. It's actually just the bargaining indeterminacy that does the trick.

    7. "It's not increasing returns in the matching function. This is like talking to a fence post."

      I didn't say there were increasing returns in the matching function. I was merely supplying the background to Farmer's declaration, "I see no reason to treat the search model differently from any other competitive model with externalities and I view the addition of the bargaining equation as arbitrary."

      Now, you may have convinced yourself that Farmer "acts as if it's 'animal spirits' in the asset market that picks out the equilibrium," but that "it's actually just the bargaining indeterminacy that does the trick." But Farmer doesn't see it this way, and, leaving all the bluster aside, you haven't shown that it's "bargaining indeterminacy that does the trick."

    8. Let's make a deal. Don't discuss economics with me, and I won't discuss philosophy with you.

    9. I see one of the Horsemen has returned. Greg Hill, your tinfoil hat has fallen off.

    10. Steve, I got it, thanks. I should read the model though, as it seems that in Farmer the equilibria are different points on the same Beveridge curve. It would be worthwhile to examine how much of the persistent historic variation in unemployment is due to such movements as opposed to shifts of the curve itself.

      In an empirical paper currently under review (for about two months), using time series from 1967 to 2008 I find that the efficiency of matching experiences persistent changes that are negatively correlated with the dispersion of IT capital across sectors. Dispersion rises in the early stage of IT adoption during the 1960s and 1970s, drops in the late 1980s (after the introduction of PCs) and rises again somewhat after 1995, following the introduction of the internet. The efficiency of matching moves in the opposite direction. The finding is consistent with Acemoglu (1999) in which when the adoption of a skilled-bias technology by some firms leads to greater technical diversity the search lasts longer, because firms and skilled workers become more selective. If you are interested, I would be happy to email you a copy.

      P.S. Guys, take it easy on Greg, he usually is quite reasonable. Most people, including many economists, are not familiar with search models.

    11. CA, +1 to both of your comments.

      Also, Greg actually has a point. By itself, the Nash bargaining assumption doesn't lead to multiple equilibria. In the bargaining model in Farmer's paper, employment is constant in equilibrium.

      The way Farmer produces multiple equilibria in the search model is by introducing "animal spirits" in what he calls an "old-Keynesian search model". Now, as CA argued in his first comment, "animal spirits" are not the only way of generating persistent employment deviations.

      Regardless, you need the bargaining + something else to make the point that Farmer is trying to make.

    12. Sorry, my mistake here. I misinterpreted the model. Sigh.

      Both the bargaining assumption and the "old-Keynesian search model" have a continuum of equilibria, so Williamson is right.

      There is a difference in how the equilibria is characterized in each model though.

    13. CA: Yes, that's right. A higher wage gives you higher unemployment and lower vacancies, so across equilibria you trace out a Beveridge curve. Sure, I'd be interested in the paper. There is some work I've seen - not in presentable form yet - that links credit market frictions with matching efficiency. All of this is interesting.

  2. Is there any merit to Farmer's passive-aggressive suggestion that Krugman plagiarises his commentary? This passage unfortunately did not provide supporting examples: "Perhaps you have read some of my recent work: Perhaps not. I infer that you may be aware of it since your columns often select themes that closely mirror my writings, usually a day or two after they are circulated. Perhaps that is due to the coincidence fairy."

    Meritorious complaint, or just another example of self-serving conceit in a field that frustrates empirical validation?

    1. I think we can take Krugman's word for it that he is oblivious to Farmer's formal work. Roger writes more accessible things though, so maybe Krugman has read those. Without supporting evidence, it's hard to judge Farmer's claim.

  3. If your trailer is correct, than Farmer should really agree with Krugman. Whether you take some action (be it reading a paper or looking for work) depends on the expected payoff. For this, you need an expectation of that payoff. If you, as writer, don't provide that expectation using a leader, (or as a government through creating full employment), the expected payoff will be lower than it otherwise could be. And that has a direct effect on which equilibrium is taken (by the reader or the job seeker.) It's elementary, dear Roger.

    1. Very good. It's not quite Farmer's model, though. This is more like a signalling model. In this world, suppose there are two kinds of people, purveyors of ideas, and consumers of ideas. For a purveyor, a low-quality idea can be created with certainty at low cost. The purveyor can also pay a high cost and produce an uncertain outcome - low-quality or high-quality. From the consumer's point of view, there are two kinds of purveyors. One has a low-quality idea, accessible at low cost. The other has an idea of uncertain quality, but the consumer has to pay a high cost to find out. The purveyors can signal whether they have a high-quality or low-quality idea. Maybe there's some heterogeneity in purveyors, and/or there are lazy consumers, and not-so-lazy consumers. You can add the details and work out the equilibrium.

  4. "But how they split that surplus is indeterminate - we don't have good theories of bargaining power."

    OK, I'm sure you know this, but there have been so many examples of the elements of a model being mistaken for reality that I think it needs to be said:

    How they split that surplus is indeterminate in the model, because we don't have good theories of bargaining power. In reality, there may be little wiggle room in how the surplus is split up. The short-comings in our formal understanding means we are limited in what we know about reality, but often we go ahead and assume we "know" what the model shows.

    1. I'm not sure what you are trying to get across. Models are not reality. We know that. A model is only an abstraction - an artificial construction we put together to try to simplify what is going on in the world, and come to grips with some small element of reality.

  5. Now that I've managed to exasperate Stephan, and to awaken Anon from his self-loathing slumber, perhaps SW will permit me one more comment in reply to CA and Rick, who seem to remain in a looser frame of mind.

    CA, you write, "I have not read the model, but based on Farmer's description I suspect that expected asset prices influence unemployment by affecting how the surplus generated from an employment match is divided. Am I correct?"

    No, I don't think this is correct. I think it's more accurate to say that in Farmer's model: 1) producers choose a level of output based on their expectations about demand/sales revenue; and 2) actual demand/sales revenue is determined by expected returns to assets now and in the future. This is obviously much oversimplified, but I think it's closer to what Farmer actually says and does (in building his model) than the alternative you suggest.

    Bear in mind that Farmer calls his model, "Old Keynesian," which is, I believe, a plausible characterization of the "model" described above. SW's model, by contrast, has nothing "*Old* Keynesian" about it. It's composed of agents who choose whether to be producers or hired hands or couch potatoes at the beginning of each period, and who then divide up the exchange surplus, first between producer and hired hand, and then between producer and consumer. It's easy to see how all the bargains (i.e., the sharing of the many surpluses) required for efficiencies may not be struck, but this is not an Old Keynesian "insight."

    In Farmer's model, by contrast, the obstacle to efficiency is our inability to predict the course of many economic variables, even probabilistically. Or, if the obstacle is not our inability to predict the future, then the problem is our lack of confidence in the predictions we are willing to make regarding asset prices, technological advances, the strength of unions, etc., many years hence. Or, it's a combination of the two. (CA, I'm merely giving my version of Farmer here, I'm not defending the concept of "animal spirits" [though I certainly would]).

    If you read both SW's and Farmer's papers, I'd be very interested in your explanation of how SW gets from Farmer's model to SW's conclusion that it's not expectations of asset prices and demand that determine the rate of unemployment in Farmer's model, but bargaining indeterminacy.

    Rick, you write, "Both the bargaining assumption and the "old-Keynesian search model" have a continuum of equilibria, so Williamson is right."

    I don't follow your chain of reasoning. I think the original issue was whether Farmer's model is really a bargaining model with indeterminate outcomes disguised as an Old Keynesian model (with an emphasis on the production decisions of firms and the uncertainty surrounding future asset prices and other important variables).

    Table 1 in Farmer's paper lists six basic equations in each of three models: 1) Competitive Search; 2) Bargaining Search; and 3) Old-Keynesian Search. Equations 1-4 are identical in all three models; equations 1-5 are identical in the Bargaining Search and Old-Keynesian Search models, but equation 6 is not (the two models are closed with very different equations).

    Now, if anyone can show how equation 6 in the Farmer's Old-Keynesian Search model can be derived from equation 6 in Farmer's Bargaining Search Model, and you're ever in Seattle, then I promise to buy you a nice lunch and to sit quietly even if you say I'm dumb as a "fence post" or that I'm one of the four horsemen of the Crackpotolis (help with spelling here anon?) who has also misplaced his "tin foil hat."

    p.s. CA, thanks for sticking up for me as a generally reasonable commentator.

    1. Hi Greg,

      Truth is, I haven't worked through this type of model since my MA some years back, and I didn't have time to go through Farmer's model in detail, as Williamson had suggested.

      From quickly going through Farmer's paper, it seemed to me that he's suggesting two ways to "close" the search model, as he puts it: one is the Nash bargaining equilibria; the other is through the introduction of beliefs. Each way leads to different equilibria.

      I'm not sure why Williamson is downplaying the "old Keynesian model" where beliefs play a key role. But then again, I'm not a macroeconomist. It would be great if Williamson were a little bit more forthcoming about this point, but I don't think it's going to happen.

    2. Greg,

      Well, sorry for getting a little short with you. CA is correct that you are generally a polite commenter, and seem willing to learn something.


      Maybe this will help Greg too. Indeed, it is true that beliefs play an important role. You can exposit Farmer's idea in most standard labor-search models, e.g. Mortensen-Pissarides works. There's a matching function, which matches firms searching for workers with workers searching for firms. The matching function is constant returns to scale. Note the difference from Diamond (1982), for example. In Diamond's paper, you get multiple equilibria because there is increasing returns in the matching function. Then, there is a kind of "thick market" effect - it's easier to find a match the more people are searching. But that's not what's going on in Farmer's model. Suppose you thought about simple Mortensen-Pissarides, but made it static, i.e. all matches break up at the end of the period - the separation rate is 1. Then the typical solution would be the following: There are two conditions:

      (1) A firm pays a cost to search, and firms enter until the expected payoff to searching is zero.
      (2) Nash bargaining (typically) determines how a firm and a worker split the surplus from a match.

      In Mortensen-Pissarides, would-be workers search no matter what. Then, (1) and (2) determine the market wage and the vacancy/unemployment ratio, which in turn determines the unemployment rate and vacancy rate.

      If we take a Farmer approach to that, we just drop (2). That's not as crazy as it sounds. For example, in the typical Nash bargaining solution, there's a bargaining parameter that lies between zero and one. Who's to say what that should be?

      So, once we have that approach, there is a continuum of equilibria - there are two unknowns and one equation. Then, I can argue that beliefs, animal sprits, whatever I want to call it, picks out an equilibrium. Start with a belief about what the wage is, for example, and there are a set of beliefs that are self-fulfilling.

      What I do in my paper is to construct the model a bit differently from a standard Mortensen-Pissarides model, but it amounts to the same thing ultimately, and actually looks more like what Farmer does. I say that the agents in the model can choose to be producers or workers, and instead of (1), I have an indifference condition for the representative agent.

      The next step Farmer takes is to make this model "dynamic." There's really fundamentally no dynamics, as there's no capital, and the matches all break up at the end of the period. He prices assets, and then ties beliefs to asset prices, but the fundamental indeterminacy is from dropping (2).

  6. Greg,

    If Steve would allow me to add a few things now that I read Farmer's model (instead of working on my own research-you guys are going to cost me tenure), here is what is wrong with using the "demand deficiency" language. This usually implies that there is a labor market equilibrium to which the economy converges in the long run, and that low aggregate demand in conjunction with other frictions is preventing us from getting there. In this case, stimulating aggregate demand may make sense. But this is precisely Samuelson's approach that Farmer is so critical of. Using that language is antithetical to what Farmer is trying to do.

    To understand what Steve is saying, you need to look at equation (60) in Farmer. It contains six endogenous variables (the variables the model is trying to explain). Namely, the level of consumption (which in the model is equal to GDP because there is no investment), the real wage (wage adjusted for the price level), the real interest rate, the relative price of capital, the level of employment, and the real return to capital. However, there are only five equations. This means that the solution is indeterminate. Unless one closes the system by introducing a sixth equation, there is no way to pin down the level of employment (and therefore unemployment). Any initial level of unemployment can be an equilibrium so long as the other five equations are satisfied. In this respect it makes no sense to talk about deficient demand, in that there is no equilibrium level of employment that we can look forward to return to. The starting point IS the equilibrium, and all equilibria entail unemployment. Farmer does compute an optimal level of unemployment (this is U*, the solution to the social planner's problem), but this is not necessarily the lowest possible one. Instead, it depends on the efficiency of recruiters. If recruiters are inefficient, the optimal level of unemployment is high. If policy-makers knew how efficient recruiters are they could perhaps try to target the optimal level (which may mean increasing unemployment, if it is below that level). However, it is highly unlikely that they can figure out what the value of that parameter is.

    But, in any case, Steve is correct that employment fluctuations do not arise from animal spirits per se. So long as one models the labor market using the search model, the economy is inherently capable of permanently shifting from one unemployment level to another.

    What farmer does is to add, as the sixth equation, a belief function about future asset prices. The equation pins down the level of unemployment. And, by adding a stochastic element (allowing people's beliefs to be random), Farmer generates shifts in the equilibrium level of unemployment. But as Steve notes above, this is only one way to explain why such shifts may take place. Any other stochastic sixth equation (e.g. Nash bargaining with a twist) could do the same. So there is a number of plausible explanations, probably a large number, why unemployment may experience persistent fluctuations. You do not need animal spirits for that, all you need is search theory.

  7. Rick, Stephen, and CA,

    Very interesting elaborations, and worth thinking about. Thanks, Greg.

  8. Steve, Greg, CA and Rick
    Sorry for not weighing in on this sooner. It's been a busy week.
    First, thanks to all of you for taking the time to read my work carefully and for the really interesting discussion of my main themes. You all seem to have sorted out that dropping Nash bargaining is central. But then the issue is how to close an otherwise indeterminate model.

    Suppose I place myself, conceptually, as an agent in a model where the future matters to me, perhaps through uncertainty about prices. I need some way of forecasting the future. This is an issue faced by ANY dynamic model. Before the advent of RE, economists looked at that problem and added an equation, adaptive expectations was a favorite, to specify how beliefs about future prices would depend on past beliefs and on realized prices.

    Along comes Lucas and we start to write down very simple RE models where there is a unique RE equilibrium. Lucas and Sargent argue that it doesn't matter how we form our beliefs. Whatever mechanism we use, it has to lead to unbiased forecasts in a stationary equilibrium. Presto. We have 'solved' the problem of expectations.

    When we started to look at RE models with multiple RE equilibria, e.g. Benhabib Farmer models from the 1990s, most of us had relegated adaptive expectations to the history books. But in a multiple equilibrium environment, the way we form our beliefs becomes central. That's true of ANY multiple equilibrium model, not just one where the indeterminacy is in the steady state.

    In a multiple equilibrium environment, the way we form our beliefs becomes part of the fundamentals of the economy. In my view, we should treat the belief function in the same way as we treat preferences. (Incidentally, I see learning rules a là Evans and Honkapohja as complementary to this idea).

    That brings me back to the debate between Steve and Greg. Here I'm more on Greg's side than Steve's. Yes, we could close the model in other ways. For example, more sophisticated bargaining equations of the kind the NK's have started to use. But that approach leads us back to a world with a unique stationary equilibrium that agents are learning about.

    There is an empirical issue here too that I point to here

    The unemployment rate (or a transformation of it) appears to be non-stationary. Whatever equation we use to close the model needs to account for that fact. I do it through the belief function but I can see that there may be other ways. That will lead to some interesting empirical questions since, one would hope, that different ways of closing the model will have different implications for the data.

    On the Beveridge curve, let me put in this plug for the Farmer and Farmer UTube video

    There should be grist there Steve for the mill of a new monetarist.


    1. That last link seems to be broken but you see an embedded link here

    2. "In a multiple equilibrium environment, the way we form our beliefs becomes part of the fundamentals of the economy. In my view, we should treat the belief function in the same way as we treat preferences."

      Actually, with multiple equilibria, the interesting feature is that the beliefs are NOT fundamental. Some models of crises, for example Diamond-Dybvig banking models, work like that, and you can have models of aggregate fluctuations where there is nothing going on with the fundamentals, but self-fulfilling beliefs are driving the business cycle. That's interesting, and it's surprising that NK people pay no attention to it. Maybe that's part of what bugs Roger. NK is essentially Prescott-style unique rational expectations equilibrium with some relative price frictions.

      "For example, more sophisticated bargaining equations of the kind the NK's have started to use."

      Not sure what you mean.

      "The unemployment rate (or a transformation of it) appears to be non-stationary."

      The unemployment rate cannot be non-stationary as, in percentage terms, it's bounded by 0 and 100.

    3. I use the log of a logistic transformation of the unemployment rate. That object lives in the real line.

  9. "For example, more sophisticated bargaining equations of the kind the NK's have started to use."
    I mean the Hall-Milgrom model that was picked by Gertler and Trigari.

    1. I see. Sorry, above, I wasn't reading carefully, and thought I was still talking to Greg. I was impressed, as he seemed to have learned a lot. However, I'm wondering why you want to think of beliefs as a fundamental. Is that just an approach to selling the idea? On the unemployment rate: The unemployment rate can't be non-stationary, but if I take the log of a logistic transformation of the unemployment rate, that appears to be non-stationary. But does that mean that, for example, that there could be some slow-moving demographic factors at work in the time series you are looking at, that could have produced this?

      Bargaining solutions: I see what you mean.

  10. Regarding the non-stationarity of the unemployment rate, I defer to Cochrane (1991). While more efficient tests, like the Generalized Dickey-Fuller (Elliot et al, 1996), have been introduced, it is still difficult to distinguish between highly persistent but stationary processes, trend-stationary processes, and unit roots, especially with only 40 or so years of data. In the case of unemployment not only demographic change, as Steve suggests, but also technical change can cause persistent movements in unemployment. The difference is that these movements are driven by shifts of the vacancy/unemployment locus, rather than shifts along the locus. So this is perhaps one way to evaluate the theory.

    As for beliefs, the way I see it the issue is the absence of a Walrasian auctioneer to dictate a wage. Thus, there are two ways one can go about this. One is to have firms decide first how much to produce, perhaps based on demand, and then offer a wage that makes producing that amount worthwhile. This, I think, is the approach Roger is taking. Another is to have firms first decide what wage to pay, and then produce the amount corresponding to the profit-maximizing level of employment. But beliefs matter either way, since firms do not know what wage they should offer to attract a worker with the desired characteristics within the allotted time. Is uncertainty in consumer beliefs more important than uncertainty in employer beliefs? I am not sure. Maybe both are important.

    Finally, I am not sure that modelling beliefs as a martingale is the way to go. When people form expectations about future asset prices, do they only take into consideration the current price? Well, this may make sense if earnings adjust to asset price expectations as in Roger's model. But in the data we see big historical fluctuations in the P/E ratio. How does the theory square with that? In the real world, should a person's expectations about the future path of stock prices be independent of whether the P/E ratio is at historic highs versus historic lows? My guess is, Shiller doesn't think so.

    1. By the way, out of curiosity, I just performed a DF-GLS test on the annual average unemployment rate from 1948 to 2012, and the hypothesis of a unit root is rejected at the 5% level.