Monday, January 13, 2014

Where I differ with Bob Hall on Modelling Unemployment

My former class mate Nick Rowe, in a comment on Saturday's blog post, asks: 
Start with a standard model with perfectly flexible prices and wages. Delete one equation, for example the labour market clearing condition. We are now one equation short of a solution, so we have multiple equilibria. Does that mean we are now free to add any additional equation we feel like? Mathematically, we can do that, of course. But one would like some sort of intuition for that extra equation. Why, for example, should it be an equation for stock prices? Why not a different equation for wages?
That's a great question. Until recently, new-Keynesian economists didn't bother to model unemployment. Instead, they followed the new-classical approach in which all that matters is labor hours spent in paid employment. More recently, a number of authors including  Bob Hall, and Mark Gertler and Antonella Trigari have incorporated explicit models of search unemployment into otherwise standard macroeconomic DSGE models. That idea is not new; David Andolfatto and Monika Merz introduced search to RBC models in the 1990s. What is different about more recent work, building on Hall's 2005 paper, is the way the model is closed.

Bob Hall was following up on an insight from Peter Howitt and Preston McAfee: When a firm meets a worker in a search model, the worker and the firm enter a bilateral bargaining situation. The worker would be willing to accept a job, and the firm would be willing to employ the worker, for any wage that is greater than the worker's reservation wage and less than the worker'r marginal product. In his 2005 paper, Bob showed that one way to close the model,is to assume that the wage is fixed.

Presto. Search in a DSGE model has equilibria with rigid wages. That idea has led to a huge industry as new-Keynesians seek to study different bargaining protocols in an effort to explain slow wage adjustment endogenously.

That way of attacking the problem is, in my view, a mistake. The new-Keynesians are squeezing the square peg of labor market search theory into the round hole of Samuelson's  neoclassical, synthesis.

There is an alternative approach that has a better shot at understanding the data. By dropping the bargaining assumption completely and assuming that firms and workers are price takers in the labor market, we arrive at a microfoundation to a model we used to teach to undergraduates.  The Keynesian Cross.

The Textbook Cross Keynesian Model

The Keynesian story for this picture is that upward sloping green line, at 45 degrees to the origin, is a Keynesian aggregate supply curve. It represents the assumption that whatever is demanded will be supplied. The upward sloping red line is the Keynesian aggregate demand curve. The aggregate demand curve slopes up because consumption increases with income. Shifts in the aggregate demand curve call forth shifts in aggregate supply as the equilibrium moves up and down the 45 degree line.

According the parable of the Keynesian Cross, the Great Depression was caused by a downward shift in the aggregate demand curve as investors lost confidence in the value of assets. The labor search theory, with its continuum of possible equilibria, offers a way to tell this story that is consistent with microeconomic theory.  All we need,  is an explanation for what causes shifts in aggregate demand. And for that, we need to think carefully about market psychology and animal spirits.

That takes me full circle; and back to Nick's question. One way of closing the model is to assume a bargaining protocol that explains why wages are sticky. A second way, is to provide a theory of  animal spirits that explains movements in aggregate demand. Why is one way of closing the model better than another? 

I show here, that these two ways of closing the model are observationally equivalent. For every theory of wages, there is a sequence of asset price movements that is consistent with those we observe in the  data.  And for every theory of animal spirits there is a sequence of bargaining weights that rationalizes wage movements in the data. But these theories have very different implications for what caused the Great Recession.

If the sticky wage theory is correct, movements in labor market fundamentals cause movements in the stock market. Standing in 2008, savvy investors, looking forward at future returns, must have foreseen some fundamental event that would shift bargaining power in favor of workers.  That prescience caused them to downgrade expectations of future profitability leading a to a big crash in the stock market.

If the animal spirits story is correct, movements in the animal spirits of investors cause movements in the labor market. Standing in 2008, investors lost confidence in the value of assets. The resulting destruction of paper wealth caused households and firms to cut back on spending and firms to layoff workers. We are, only now, digging our way out of the hole.


  1. From where I stand, the "animal spirits" argument makes far more sense. Gary Gorton and others have shown that both the 2008 financial crisis and the Eurozone crisis were due to the sudden revelation that assets believed to be safe were anything but, causing a massive loss of confidence among investors and a flight to traditional safe havens (gold, USTs, yen). I find it difficult to see how expectations of a change in labour market dynamics would have caused a sudden failure of safe assets. I guess an explanation could be contrived to somehow blame the failure of safe assets on sticky wages, but it's hardly Occam's Razor.

    1. I agree. I will sign you up as a convert to neo-paleo-Keynesianism...

  2. "If the sticky wage theory is correct, movements in labor market fundamentals cause movements in the stock market."

    This sounds more ridiculous than it really is. I think the story is pretty straightforward: as certain forms of near-money lost their money-like characteristics, there was an increase in the demand for money. This caused money to become more valuable. Whatever causes wages to be sticky, therefore effectively caused all workers (the ones that kept their jobs) to get a raise in real terms, because they were all being paid in this newly valuable commodity called money. And it caused firms to become less profitable, because they were obliged to pay all this newly valuable money to their workers (and indeed, some firms went out of business because they didn't have enough access to money). So the stock market went down. Surely the Great Recession didn't start in the stock market; it started in the mortgage derivatives market, which is to say, in the market for near-monies.

  3. Agreed. The Great Recession started in the housing market; not the stock market. But the trigger was the re-evaluation of the worth of an asset; in this case a house. We should also not be so quick to assume that wages are rigid. There is a nice summary here of a piece by Elsby Sin and Solon that finds remarkable downward flexibility in UK wages

    1. I'm not so sure it was the re-evaluation of the worth of houses per se that triggered the Great Recession. US house prices started dropping in early 2006, and the recession didn't start until the end of 2007 and didn't become "great" until the fall of 2008. The direct trigger for the Great Recession seems to have been the collapse of the financial system. That's a bit different from houses or stocks, because it relates directly to the supply and demand for money and therefore to conditions in the labor market if wages are sticky in terms of money. Granted, there is room for a lot of empirical disagreement as to how sticky wages actually are, but in the post, you make the sticky wage explanation sound kind of silly, whereas I think it's actually fairly plausible on the face of it. My guess is that there's some of both going on -- a change in labor market conditions induced by a shortage of money and a drop in animal spirits -- and that they reinforce each other. Not that I would want the job of having to come up with a formal model in which that happens.

    2. That's a fair comment. It is certainly true that nominal variables, both prices and wages, are much smoother than predicted by equilibrium models. But again, I don't think we need to appeal to frictions to explain that observation. My preferred explanation is that beliefs are smooth and persistent and that is translated into what looks like sticky prices. Here is a reference that explains that idea

    3. Yes, I looked at that paper when you linked it from your previous blog post. Very interesting. Again, I think there's some of both going on. One thing to consider: if there are flexible-price equilibria that are consistent with prices not changing, that lowers the bar for rigidities. In other words, if you're an agent choosing which equilibrium to believe in, and if you also have menu costs, that gives you more reason to behave as if you believe in the equilibrium where prices don't change. If you attach equal subjective probabilities to constant-price and rising-price equilibria, your menu costs, even if they are very small, will lead you to choose the constant-price one. (And moreover, if you believe that other agents have menu costs, then you will expect them to choose the constant-price equilibrium, so small rigidities can operate as a coordinating mechanism.)

  4. Very nice post, Roger. Just one thing regarding this:

    "But these theories have very different implications for what caused the Great Recession."

    Do the two theories have different implications for the design of optimal policy?

  5. Thanks David. The answer is yes. If financial crises are caused by inefficient swings in asset prices; then intervention in the asset markets is the solution. I argue that case here. in my John Flemming lecture at the Bank of England.

    1. If that's the case, then I think it's a point well worth emphasizing. Without having read your paper, however, I suspect that there may be more than one solution. But maybe not. Is your claim that inefficient swings in asset prices cannot be remedied by an appropriately designed labor market intervention (in your model)? Or just that intervention in the asset market is sufficient?

    2. I can sustain the view that inefficient swings in asset prices are the problem even when I'm in a single-equilibrium New Keynesian mood. If the Wicksellian natural interest rate is far below the growth rate and the risk premium is volatile, there will be excessive asset price fluctuation. Combine with nominal rigidities, and you can get asset prices as the major source of macro fluctuations in spite of having a single equilibrium at any given time.

  6. Thanks Roger. I've been thinking about this, and reading some of the very interesting papers you link to in your previous post. I tend to approach this roughly the same way as Andy Harless does above. I tend to think of these models as similar to "infinitessimally small menu cost" models. But with one difference. It's more like a Schelling focal point determining prices (or wages) than literal stickiness. So that, for example, if every firm thinks that every firm will raise prices by 2%, then it is 2% inflation that is sticky. Whatever is customary, is sticky.

    We can think of monetary policy as, in a sense, "intervention in asset markets", because money is an asset. Though monetary policy is normally framed, nowadays, as temporarily setting nominal interest rates, it could also be thought of as temporarily setting the stock price index, a perspective I am sympathetic towards.

    This goes back to Keynes' old point, about it being more sensible to use monetary policy by the Bank of England than "monetary policy by the trades unions" (probably not an exact quote).

  7. Roger,
    I'm still not sure if unemployment is so painful if your story doesn't result in a large number of people who would be willing to accept lower pay temp jobs (e.g with a lower entry title) + possibility of eventual upgrading if times improve? So does your theory or Hall's really answer the Barro critique, that if not having a job/firing workers is so painful then employers and job seekers would find a way to make a deal. Looking for possible barriers to a deal leads us back to more fundamental theories like efficiency wages (either shirking or fairness issues), but that doesn't lead to indeterminacy.
    Also why not put this inefficiency in product markets like the baseline new keynesian approach, in which animal spirits cause a reduction in demand which gets accomodated by firms at sticky prices? You have search frictions in product markets, so that also leaves room for the indeterminacy you're using in your theory? What do you think of the paper by Saez and Michaillat on this
    Also, can you distinguish your theory from models that have unique equilibria conditional on sentiment shocks or demand shocks that affect the economy's matching efficiency e.g by reducing search effort in recessions? Thinking of the paper on sentiments by Anegeletos and Lao and recent papers on demand shocks that look like productivity shocks by Rios Rull and co.,

    1. daniels...

      Unemployment can be VERY costly in these models. If the wrong mix of unemployment and vacancies is used in the search technology GDP can be anything between potential output (the social planning optimum) and ZERO.

      There is a nice paper by Kaplan and Menzio that has search in both roduct markets AND the labor market.

      I like the paper by Michaillat and Saez; but I don't like the way they close their model, which is much closer to Bob Halls fixed wage assumption.

      As for Angeletos Lao -- and related work where sentiments matter -- the key, for me, is to link these models to multiple steady state unemployment rates to explain what Larry Summers has called :secular stagnation". Search theory without the Nash bargain is a simple and attractive way to do that. I'm sure there are others.

    2. But the problem with the bargaining indeterminacy result is that it is only robust to the Barro critique at the individual job level. Once you have large firms posting many vacancies, and you have unions or employment agencies representing many workers at once then solutions to the bargaining problem like competitive wage posting make more sense, i.e firms at least don't just take wages as given, they actively try to influence their hiring prospects and employee quality by setting the prices in labour markets. The more medium-long run you think, the more I have trouble with combining price taking with inefficient labour market outcomes, the more I expect to see some combination of wage posting and bargaining la Nash-Binmore-Rubinstein (last 2 references establish that Nash bargaining is like the limit of a large number of fast offers/counteroffers in a sequential bargaining game). In modern exogenous long run growth theory (the one which takes firm level heterogeneity and endogenous TFP seriously), we have lots of models where long run output is lower if you have long run increases in uncertainty about investment outcomes, or if the financial sector becomes more cautious and increases collateral requirements on a (quasi) permanent basis. Not to mention all the issues we're now facing with the demographic imbalance, which according to very neoclassical growth models (extended for finite life cycle efffects) calculations lead to suggestions that Japan may gradually have to raise consumption tax rates to around 30-35% if it wants to avoid default either on bondholders or on pensionners or high inflation to reduce the real debt burden. And I suspect similar calculations can be made for many Western European countries and the US? Aren't there enough mechanisms for a possible secular stagnation with flexible prices and wages in the medium-long run? Though separating a unique equilibrium model in which you allow shocks to parameters from a multiple equilibrium model seems like more an issue of semantics (or am I missing something in thinking this way)?


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