## Wednesday, October 21, 2015

### Feels Like Science

 Figure 1: Evolution of Two State Variables along Two Dynamic Equilibrium Paths

I continue to explore a micro-founded macroeconomic model from Frank Hahn and Robert Solow, generalized to allow a positive rate of growth of households. Hahn and Solow put forth this model as a strawman, to show that even with perfectly flexible prices and wages, markets clearing always, and rational expectations, room for government macroeconomic management can arise. In their book, they then move on to consider imperfectly competitive markets, norms for wages, and so on.

A dynamic equilibrium path, in the model, defines the values of three state variables at the end of each time period in the model. One of these state variables, the real quantity of money in circulation is easily calculated from the other two. The other two, taken here as the real rate of return on corporate bonds and on money, must be found, in general, by solving a recursive system of two equations at each point in time. I found the code I wrote for this post helpful here.

Figure 1 illustrates the evolution of two state variables for two dynamic equilibrium paths. (The model parameters are β = 2/5, ξ = 2.11, and G = 2. The household utility function is of the form specified by Example 1 in Hahn and Solow, with ε = -1/2.) The stationary, dashed-line, path is for a steady state, which is asymptotically approached by the other dynamic equilibrium path. The oscillations seen in this approach are not in the linear approximation about the steady state. One might view these oscillations as a decaying business cycle. One should be clear, however, that even though economic output varies along such a path, neither unemployment nor disappointed plans arise in this model. Households foresee all future variations in prices and quantities along a dynamic equilibrium path.

One could add various complications to make the model more realistic. Households could live for multiple periods more than two, thereby perhaps modifying the time period for the business cycle. One could add leisure into the utility function and model the supply of labor as the result of trading off the earning of wages for consumption and leisure. Employment would then vary along a business cycle; in this theory, recessions are long vacations. One could add noise terms, from known probability distributions, for various terms. So agents would be continually adjusting their plans to accommodate realizations of stochastic processes. One could add imperfect competition, as modeled by Avinash Dixit and Joseph Stiglitz. I suppose one could describe the parameters of utility functions as lying along a continuum, therefore adding a sort of diversity in the model of households. And so on.

I suppose one would find it difficult to add all of these refinements at once. So one could empirically compare a basic model with each refinement. And a model with one refinement might fit better here and with another there. Room for technical innovation for modelling then arises. Can you add two or more refinements, perhaps simplified, where others could could only add one before? Can you take a model that previously was only described for a linear approximation and analyze at least some non-linearities (as I do above)?

I gather I have just briefly outlined the direction of research in mainstream macroeconomics over the last third of a century, albeit the freshwater school did not start, I take it, with overlapping generations models and a Clower constraint.

None of these refinements would even hint at an approach to addressing the question of how economies get into equilibrium. At the end of each year, the economy is automatically in equilibrium in the model, and this instantaneous magic has been foreseen for all time. Head of households and managers of firms have no need to learn a model of the economy. Agents never have disagreements among themselves about what is the true model. And they never change their minds about the structure of the model. J. R. Hicks, the inventor of the model of temporary equilibrium, came to see that it was set in logical time, not historical time. In other words, John Hicks chose to ally himself with Joan Robinson on this theoretical point.

Without an acceptable understanding of disequilibria, mainstream economists should be tolerant of polyvocality in methodology. Why should some economists not be exploring models that are not microfounded? Why not consider the impact and evolution of social norms, without first insisting that they they be justified by methodological individualism? I consider some work in complexity and agent based modeling to be of interest along these lines and not even all that non-mainstream.