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Theoretically, How Long is This Recovery Supposed to Take Anyway?

The first estimate for GDP and its components in the third quarter of 2010 is out and it is not a very encouraging one, at least as far as the recovery goes. The positive contributions from personal consumption expenditures and from changes in private inventories were attenuated by strong import growth and a further decline in residential investment. In all, GDP is estimated to have grown at an annual pace of 2 percent in the third quarter. To put things in perspective, just to keep up with its trend, GDP should be growing at an annual rate slightly above 3 percent, but since we are recovering from a recession it should actually be growing at an even faster pace.

It is no wonder then that people are throwing out words like subpar or anemic to describe the current recovery. But compared to what? One way to establish a point of reference is to look at past recoveries. This is what I did in a previous Trends article, in which I argued that yes, compared to other recoveries the current one looks pretty weak, but no worse than the recovery from the “Tech Bubble” in the early 2000s. My colleague Ken Beauchemin took a different route in a recent Commentary and instead of looking only at the behavior of GDP during recoveries he used data on other variables, like the unemployment rate, the inflation rate, and the federal funds rate, from 1959 on and concluded that the current recovery is just slightly below what a vector auto-regressive (VAR) forecast would predict. In fact, if one uses only data after 1983 in this exercise, the current recovery would be slightly stronger than the VAR forecast.

What these two approaches have in common is that they are solely predicated on data and lack a theory of how the economy works. Actually, a VAR has an underlying theory, just not a very deep one. It assumes that the values of the current variables depend on past (or forecast) values of all variables in a linear way.

Economists have developed “deeper” models of how the economy works, by making assumptions about how individuals and firms that are constrained by their current resources and information behave when facing an uncertain future. One class of models known as Real Business Cycle (RBC) models sees the economy as being constantly buffeted by random shocks to firms’ production opportunities. Given the last shock and their current wealth, consumers form expectations about future shocks and use them in choosing how much to consume, work, and save, with the ultimate goal being to maximize their well-being. Their future income is uncertain, as it depends on the wages and interest income they obtain from renting their labor and capital to firms, whose opportunities for production are subject to the random shocks. These shocks and other parameters in the model are then constrained so that the model economy replicates some properties of the real U.S. economy, like how much GDP varies, how long people work, how income breaks down between labor and capital, and so on.

One of the problems economists struggle with when putting this recovery in perspective is that, except for the Great Depression, there is no other recession of this magnitude to compare it to. This is where we can use the theoretical model to our advantage. By simulating a series of shocks hitting the economy, we can create our own (simulated) data. I simulated 20,000 runs of the model economy, each lasting about 60 years. It’s like looking at 20,000 possible paths for GDP, given different levels of the kinds of shocks that can occur, hitting at various times. I then looked at the instances where GDP fell between 4 percent and 4.5 percent in 6 quarters (U.S. GDP actually fell 4.1 percent from the fourth quarter of 2007 to the second quarter of 2009). Finally, I looked at what the recoveries from these episodes looked like. The results are in the figure below. The grey lines represent each individual simulation, the blue line is the median of all simulations and the red line is the actual behavior of U.S. GDP.

Actual and Simulated Recoveries

First, it should be noted that this simple RBC model has some trouble generating recessions of this magnitude. Out of the 20,000 simulations, only 39 produced episodes comparable to the latest recession, and more severe recessions were even rarer. But more importantly, this experiment tells us that, at least when seen through the lens of the RBC model, our current recovery is a bit on the slow side. The median time it takes the model economy to get back to the level we had back in the fourth quarter of 2007 is four quarters. By that yardstick we will be at least half a year late.

This is, of course, just what a standard, no-frills, RBC model implies. In particular, it lacks a lot of features some economists have deemed crucial in shaping the current recession and subsequent recovery. For example, it is missing both a financial intermediation sector and a housing sector, so it is, by definition, unable to capture any frictions in these markets. It is nevertheless a benchmark that is informed by theory, although what that means regarding its usefulness ultimately depends on how good the theory is.

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