The Great Vacation: Recessions In DSGE Models (Part I)

Neoclassical models are built around optimizing behavior. The logic for this is somewhat reasonable: one should expect the private sector to look out after its own interests, and not be tricked by policymakers into self-defeating behavior. The aspiration is hard to argue against, the problem is the implementation. When it comes to recession analysis, the most blatant problems are in the modeling of household sector behavior. Since working is voluntary, the hours worked in a period is allegedly a decision variable that can be controlled unilaterally by the household in order to optimize its utility. However, since employment is voluntary — so is unemployment. The result is that recessions can be seen as the optimal decision of households to stop working. As wags have described it, The Great Depression was actually The Great Vacation.

Time, Time Management, Stopwatch, Industry, Economy

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The Great Vacation Effect is a pathological result that few people take seriously. The implication is that it is easy to avoid recessions — tell people to stop cutting back their work hours! However, no matter what one's opinions of politicians are, it is safe to say that no politician would make such a silly suggestion. Even if we put aside the quite obvious criticisms one can make about the silliness of voluntary unemployment, we are stuck with pathological dynamics embedded in the model, hampering recession analysis.

(Note that this topic was broken into two parts. This part sets up the background of The Great Vacation Effect. For many people, this may be the most interesting part — since it makes DSGE models look silly. However, even if we want to put aside the question of silliness, practical issues remain, which are deferred to the second part.)

Not Easily Avoided

Most verbal descriptions of dynamic stochastic general equilibrium models give the mistaken impression that The Great Vacation Effect is just a feature of Real Business Cycle (RBC) models. These models were the first generation of dynamic stochastic general equilibrium models. My guess that RBC models are associated with The Great Vacation Effect because RBC model supporters tended to be free-market absolutists who take voluntary unemployment literally. Robert Chernomas and Ian Hudson give some statements to this effect in Chapter 6 of their book "The Profit Doctrine: Economists of the Neoliberal Era."*

However, adding innovations like price stickiness (which converts an RBC model into a so-called New Keynesian model) generally does not eliminate the vacation effect. However, the New Keynesians realize that The Great Vacation Effect is embarrassing to the credibility of the DSGE project, so they change the subject to other features of this model. Nevertheless, so long as hours worked is a voluntary choice in the household optimization problem, the effect remains. I discuss means the implications of trying to eliminate this effect later.

Two Optimizations Mashed Together

There are a wide variety of DSGE macro models, but my concern are the class of models where there are at least two optimization problems that are meant to be joined via general equilibrium: a household problem, and a firm problem. In the context of recessions, the firm's problem seems more plausible, so that it was adherents of DSGE macro wish to discuss. I will turn to it in a later article. For now, I will focus on the household problem, but offer a minimal discussion of its linkage to the business sector.

An optimization problem normally consists of two mathematical structures.

  1. There is an objective function, which maps the possible choices of decision variables to a numerical (real) value. We want to find the choice of decision variables that gives the maximum (or minimum) of this function. A choice of the decision variables that results in the maximum (minimum) objective function is termed the optimizing solution.
  2. Constraints on the decision variables are then specified. This specification can be done in a multitude of ways. Note that the decision variables can be quite complex -- a set of time series variables (a variable defined on either a discrete or continuous-time axis). In economic problems, the constraints are the mathematical relations that define the "laws of motion" of the model economy. For example, the production function will map the hours worked, capital, and productivity variables to the level of production. The set of all possible choices of variables are termed feasible solutions. For example, economic trajectories that violate accounting identities within the model are not feasible, and so it does not matter if they generate a greater utility.
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