## The Great Vacation: Recessions In DSGE Models (Part II)

**<< Read More: The Great Vacation: Recessions In DSGE Models (Part I)**

*The Great Vacation Effect* is what I term one well-known pathological side effect of almost all macro dynamic stochastic general equilibrium (DSGE) models: since employment hours are a voluntary decision in the household optimization problem the direct implication that unemployment is voluntary as well. As such, The Great Depression can be interpreted as The Great Vacation. Although this silliness is well known, the silliness has nasty side effects for recession analysis. This article continues the discussion of the previous part, turning to the question of why this effect matters even if we suspend disbelief with respect to the interpretation of unemployment.

*Image Source: Pixabay*

### Background

My assumption in this article is that the reader is somewhat familiar with the structure of macro DSGE models. Key points were discussed in the first part, but I am not assuming that readers would have gone through it. Nevertheless, I will review the part of the model structure that I am interested in.

It is difficult to generalize about DSGE models, since this is an extremely wide class of models, and researchers are continuously adding new variations. There are classes of DSGE models that I do not classify as being macro models; at the minimum, they need to include two optimization problems that have been fused together by a general equilibrium assumption. The first problem is the Household Optimization Problem, the second is one for firms. This article only looks at the household problem, which is luckily broadly similar across DSGE macro models.

As discussed in Part I, the mathematical assumption is that households can take prices as given, and find an optimal path to maximize utility. When I write prices that refers to at least three prices: wages, goods prices, and interest rates (bond prices). Note that these variables are not just the spot levels, they include forward values (which are not directly measured in the case of wages). Since we are taking these prices as given, we can examine the behavior of the household optimization as a stand-alone problem. *(As noted in Part I, I have to make the heroic assumptions that a solution to the DSGE model exists, is unique, and this model solution corresponds to the optimal solution of the household problem. If these assumptions are not true, the model is nonsensical, and we can learn nothing from it.)*

### Utility Maximisation

Let us now look at the utility maximization problem. Although the details can vary, the following statements capture the behavior of the variables that appear in almost all cases.

- Prices (wages, goods prices, interest rates) are taken as given, or exogenous to this problem.
- The level of utility is the discounted sum of single period utility values, with those values generally being a function of the consumption and hours worked in that period. (Some models might sneak in a money balances term, which I will ignore.) Future values are discounted back to a current value since the sum of non-discounted utility terms on an infinite horizon would be infinite. (The discounting horizon is equal to the lifetime of the household agent, which is either a few periods of an overlapping generations model or out to infinity for the representative household version.)
- There is diminishing returns to consumption for adding to the utility. Typically, consumption will be taken to a power of less than 1. As an extremely simplified explanation as to why this is the case, imagine that a household can consume two units of goods over two time periods, with no discounting. If utility is given by the square root of consumption in each period the optimal choice is to consume 1 each period, giving a total utility of two. If the household decided to front-load consumption, they might consume 2 units first, then zero. The utility would be the square root of 2 (about 1.41), which is sub-optimal. Conversely, if the utility was the square of consumption, the optimal strategy is to front-load, since the utility is 4, versus 2 for even distribution.
- In order to get a labor market that meets assumptions about supply and demand, there is negative utility associated with working. This prevents the household from working infinite hours to fund infinite consumption: at some point, the disutility of working overpowers the utility gains from consumption.
- The amount of consumption allowed is determined by a budget constraint. The household has to pay for all consumed goods from wages, or by selling financial assets, and possibly borrowing against future cash flows. (The identity of the lender is often not pursued, although there are variants where one representative household lends to another.)
- The effect of interest rates and financial asset holdings shows up via this budget constraint, which represents the remaining measurable variables in the model.
- Finally, there are parameter values within the functions that determine behavior. When these parameter values shift, they represent a change in behavior. These changes can be viewed as external shocks to the model, which do not readily forecast.

Disclaimer: This article contains general discussions of economic and financial market trends for a general audience. These are not investment recommendations tailored to the particular needs of an ...

more