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.