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The Behavior of the Real Rate of Interest Michael Dotsey (bio), Carl Lantz (bio), and Brian Scholl (bio) Abstract This paper presents new facts regarding the behavior of the ex-ante real rate of interest. These facts are notably different from conventional wisdom about the cyclical properties of the real rate. In particular, we find that the ex-ante real rate is contemporaneously positively correlated with GDP and positively correlated with lagged cyclical output. There is also evidence that high real rates are associated with strong cyclical output one quarter into the future. Our results generally are not sensitive to the estimation methodology, but are quite sensitive to the price series used. This sensitivity is especially true for the Consumer Price Index. Thus, we find evidence of specification uncertainty. We also find that real rate behavior varies over different sample periods and that the cyclical properties of the ex-ante and ex-post real rates are not identical. Therefore, inferring ex-ante real rate behavior using ex-post data is inappropriate. This paper presents new facts regarding the behavior of the ex-ante real rate of interest. These facts are notably different from conventional wisdom about the cyclical properties of the real rate. In particular, we find that the ex-ante real rate is contemporaneously positively correlated with GDP and positively correlated with lagged cyclical output. There is also evidence that high real rates are associated with strong cyclical output one quarter into the future. Stylized facts presented in Stock and Watson (1999) are exactly the opposite and we investigate the reasons for these differences. We do this by looking across a wide variety of constructed real rate series. These series are obtained by using a number of different methodologies for estimating expected inflation, using several different price series, and looking over different time periods. Our results generally are not sensitive to the estimation methodology, but are quite sensitive to the price series used. This sensitivity is especially true for the Consumer Price Index (CPI). Thus, we [End Page 91] find evidence of specification uncertainty. We also find that real rate behavior varies over different sample periods and that the cyclical properties of the ex-ante and ex-post real rates are not identical. Therefore, inferring ex-ante real rate behavior using ex-post data is inappropriate. Understanding the cyclical behavior of the real rate is important to macroeconomic theorists. One challenging area of model development is matching modeled asset price behavior to data. In order to do so, one must have an accurate representation of autocorrelation and cross-correlation functions in the data. The paper is organized as follows. In Section 1 we outline the various methodologies used in constructing the ex-ante real rate. In Section 2 we present our preferred estimate, investigate its cyclical properties, and compare the behavior of the exante and ex-post real rates. In Section 3 we discuss the robustness, paying particular attention to the question of why results that use the CPI differ from those of our other series. To complete our study of the behavior of the ex-ante real rate of interest, Section 4 investigates its stationarity properties. We do this by looking at augmented Dickey-Fuller statistics and by using the Horvath and Watson (1995) procedure in the case where the cointegrating vector is assumed to be known. Given the results in the literature, it is not surprising that our conclusions regarding the stationarity of the ex-ante real rate depend on the sample period. These conclusions also depend on the price series and methodology used for calculating the real rate. The conclusions are given in Section 5. 1. Construction of Real Rates In this section we describe our various methods for constructing the real rate of interest. We use five basic methodologies and four different price series. 1.1 The Data In order to ease comparison of our results with those presented by the benchmark model of Stock and Watson (1999), except where otherwise noted, data are taken from the Stock and Watson (SW) data set.1 We select four different price indices to use as measures of inflation: the monthly CPI; the monthly CPI excluding food and...
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