## Serially-correlated shocks and DSGE models (wonkish)

30 Sep, 2014 at 15:02 | Posted in Economics | 1 CommentNow it is “dynamic stochastic general equilibrium” (DSGE) models inspired by the Lucas critique that have failed to predict or even explain the Great Recession of 2007–2009. More precisely, the implicit “explanations” based on these models are that the recession, including the millions of net jobs lost, was primarily due to large negative shocks to both technology and willingness to work … So can the reputation of modern macroeconomics be rehabilitated by simply modifying DSGE models to include a few more realistic shocks? …

A simple example helps illustrate for the uninitiated just how DSGE models work and why it should come as little surprise that they are largely inadequate for the task of explaining the Great Recession.

For this simple DSGE model, consider the following technical assumptions: i) an infinitely-lived representative agent with rational expectations and additive utility in current and discounted future log consumption and leisure; ii) a Cobb-Douglas aggregate production function with labor-augmenting technology; iii) capital accumulation with a fixed depreciation rate; and iv) a stochastic process for exogenous technology shocks …

It is worth making two basic points about the setup. First, by construction, technology shocks are the only underlying source of fluctuations in this simple model. Thus, if we were to assume that U.S. real GDP was the literal outcome of this model, we would be assuming a priori that fluctuations in real GDP were ultimately due to technology. When faced with the Great Recession, this model would have no choice but to imply that technology shocks were somehow to blame. Second, despite the underlying role of technology, the observed fluctuations in real GDP can be divided into those that directly reflect the behavior of the exogenous shocks and those that reflect the endogenous capital accumulation in response to these shocks.

To be more precise about these two points, it is necessary to assume a particular process for the exogenous technology shocks. In this case, let’s assume technology follows a random walk with drift [and assuming a 100% depreciation rate of capital]…

So, with this simple DSGE model and for typical measures of the capital share, we have the implication that output growth follows an AR(1) process with an AR coefficient of about one third. This is notable given that such a time-series model does reasonably well as a parsimonious description of quarterly real GDP dynamics for the U.S. economy …

However, the rather absurd assumption of a 100% depreciation rate at the quarterly horizon would surely still have prompted a sharp question or two in a University of Chicago seminar back in the days. So, with this in mind, what happens if we consider the more general case?

Unfortunate-ly, for more realistic depreciation rates, we cannot solve the model analytically. Instead, taking a log-linearization around steady state, we can use standard methods to solve for output growth … This simple DSGE model is able to mimic the apparent AR(1) dynamics in real GDP growth. But it does so by assuming the exogenous technology shocks also follow an AR(1) process with an AR coefficient that happens to be the same as the estimated AR coefficient for output growth. Thus, the magic trick has been revealed: a rabbit was stuffed into the hat and then a rabbit jumped out of the hat …

Despite their increasing sophistication, DSGE models share one key thing in common with their RBC predecessors. After more than two decades of earnest promises to do better in the “future directions” sections of academic papers, they still have those serially-correlated shocks. Thus, the models now “explain” variables like real GDP, inflation, and interest rates as the outcome of more than just serially-correlated technology shocks. They also consider serially-correlated preference shocks and serially-correlated policy shocks …

[h/t Brad DeLong & Merijn Knibbe]

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“. . . for more realistic [fill in the blank], we cannot solve the model analytically.”

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Famous last words of the economist!

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I think it might almost be a truism, that any analytic model with a solution, is going to be a very, very poor analogue for the actual economy, where radical uncertainty means that people often do not solve problems optimally so much as they just muddle through, disagreeing about the outcome of the horse race, even after the race has been run.

Comment by Bruce Wilder— 30 Sep, 2014 #