Graduate Macro Theory II: Stylized Business Cycle Facts and the Performance of the RBC Model

The convention within the literature is to look at HP detrended data to examine the business cycle. We focus on deviations from the smooth HP trend. There are, of course, alternative ways in which one can look at the cyclical component of the data (e.g. first differences, the Band Pass filter, linear detrending, etc.). “Business cycle moments” focus primarily on a variety of second moments. In particular, the standard deviation of an HP filtered series is referred to as its volatility. We are also interested in looking at a series’ cyclicality, which is defined as its contemporaneous correlation with GDP. We call the first order autocorrelation of a series a measure of its persistence, and we also look at how strongly a series is correlated with output led or lagged a number of periods, so as to say something about which series are “lagging indicators” and which series are “leading indicators”. The series we are most interested in looking at are the same endogenous variables that come out of a simple real business cycle model – output, consumption, investment, total hours worked, the real wage, and the real interest rate. In addition, we will look at average labor productivity (the ratio of output to total hours worked), the price level, and total factor productivity (TFP). The price level is not in the model as we have thus far specified it, but can easily by added. TFP is the empirical counterpart of the driving force at in the model. We measure it as output minus share weighted inputs: