نرخ واقعی تعادلی متغیر زمان و تجزیه و تحلیل سیاست های پولی

We show how a positive correlation between the equilibrium real interest rate (ERR) and trend growth matters for two widely debated issues in monetary policy. First, a simple Taylor rule is more robust to uncertainty about the trend growth rate than suggested by some analyses of the increase in U.S. inflation during the 1970s, because the policy mistake made when measuring the change in trend growth gets offset by the accompanying mistake in measuring the change in the ERR. Second, ignoring this correlation when estimating policy rules results in coefficients that exaggerate both the degree of interest rate smoothing and the strength of the monetary authority's response to inflation.

The ‘Taylor rule’ provides a benchmark for monetary policy in terms of three arguments: the equilibrium real interest rate, the output gap, and the inflation rate. Despite its apparent simplicity, it turns out to describe recent monetary policy in the U.S. rather well. It has also been used extensively to analyze the conduct of policy, both in the U.S. and abroad (Taylor, 1999). Most of this analysis has been carried out under the assumption that the equilibrium real rate (ERR) is constant. By contrast, recent empirical evidence suggests that there is significant time variation in the ERR (Laubach and Williams, 2003 and Clark and Kozicki, 2004). In this paper we examine how a time-varying ERR can alter the evaluation and interpretation of monetary policy. More specifically, we use a simple, backward-looking quarterly model of the U.S. economy to look at two well-known arguments involving the Taylor rule. First, several authors have argued that a central bank which uses a Taylor rule to set policy could accidentally generate large changes in the inflation rate following an (initially) unperceived change in the trend growth rate. In a series of widely known papers, Orphanides, 2001 and Orphanides, 2003 explores the implications of mismeasuring potential output (or, equivalently, the natural rate of unemployment) in real time and concludes that the Federal Reserve's inability to detect a slowdown in trend growth was the primary cause of high inflation in the 1970s. Bullard and Eusepi (2003) use a well-specified DSGE model to examine how the economy reacts to an unexpected change in trend productivity growth under learning and conclude that misperceptions about trend productivity growth could lead to substantial inflation even if a Taylor rule is implemented. Similarly, Orphanides and Williams (2002) argue that the fact that inflation did not fall noticeably when productivity accelerated in the 1990s suggests that the Federal Reserve was no longer using a rule that depended upon the level of the (unemployment) gap. We show that these arguments capture only part of what happens in a world where the ERR varies over time, and in particular, where it is positively related to the trend growth rate. In such a world, slower trend growth (for example) will be accompanied by a lower ERR, so that a policy authority which takes a while to recognize that the rate of growth has slowed will also take a while to recognize that the equilibrium interest rate has fallen. These two mistakes will tend to offset each other: policy will be ‘too easy’ because it will fail to realize that growth has slowed and ‘too tight’ because it will fail to realize that the ERR has fallen. As a result, policy will not be as stimulative as suggested by analyses which ignore the link between the trend growth rate and the ERR. A key implication of this argument is that the simple Taylor rule is likely to be more robust to productivity or trend growth uncertainty than previous research would suggest. As we show below, the inflation path generated in such an exercise depends crucially upon how quickly the monetary authority learns about the change in the economy. A monetary authority which knows the structure of the economy (but not the shocks hitting the economy) can filter the data in an efficient manner and so learn about changes in the trend relatively rapidly; as a consequence, it does not generate very large changes in the inflation rate when the trend growth rate changes. However, more realistically, a monetary authority that does not know the structure of the economy will not be able to filter the data as efficiently and so will take longer to learn about the change in trend growth (and in the ERR). Consequently, it will generate larger changes in the inflation rate following a change in trend growth. The second argument we take up has to do with ‘interest rate smoothing’ or ‘interest rate inertia’. Estimation of the Taylor rule in the U.S. generally leads to a large AR(1) coefficient on the lagged funds rate (see Clarida et al., 1999, for instance), and this is usually interpreted as evidence that the Federal Reserve adjusts interest rates gradually or ‘smooths’ intended changes in interest rates (Woodford, 1999). On the other hand, Rudebusch, 2001 and Rudebusch, 2002 argues that the observed inertia may reflect the omission of one or more persistent variables from the Taylor rule regression equation. The results of our estimation, shown below, suggest that the ERR is a highly persistent variable; note also that almost all the studies which attempt to measure how much the Fed smooths interest rates do so under the assumption of a constant ERR. Thus, it seems natural to investigate the extent to which this assumption of a constant ERR might bias the empirical estimates of the Taylor rule. Our model simulations indicate, first, that ignoring time variation in the ERR leads to estimates that substantially exaggerate the amount of interest rate smoothing carried out by the monetary authority. For example, it is not hard to find estimated values of about 0.9 for the AR(1) coefficient in the literature (when the Taylor rule is estimated using quarterly data). This implies that it takes the Fed more than six quarters to eliminate half the gap between the desired and the actual funds rate; our results below suggest that this estimate would fall to less than two quarters if the constant ERR assumption were dropped. Second, we find that ignoring time variation in the ERR leads to a substantial upwards bias in the estimated coefficient on inflation, that is, it tends to exaggerate the monetary authority's response to inflation. We conclude our exercise by showing that the estimation of a Taylor rule regression that allows for serially correlated shocks – as suggested by English et al. (2003) – largely eliminates the bias in both the inflation and lagged interest rate coefficients – without requiring an estimate of the ERR. The remainder of the paper is organized as follows. In Section 2 we lay out the empirical framework and display the estimation results. In Section 3 we simulate our model economy to show what happens in response to an unexpected trend growth slowdown, and investigate the kinds of mistakes the monetary authority might make under different assumptions regarding how much it knows and how it learns. In Section 4 we turn to the debate about interest rate smoothing and explore what happens to the estimated Taylor rule parameters if the econometrician ignores time variation in the ERR. Section 5 concludes.

In this paper we have shown that taking account of time variation in the equilibrium real interest rate can make a substantial difference to how one interprets and evaluates monetary policy. First, we showed how the positive correlation between trend output growth and the ERR can complicate the analysis of what happens when there are unperceived changes in the productivity trend, such as in the 1970s or the 1990s. The complication arises because unperceived changes in trend growth tend to be accompanied by unperceived changes in the ERR. Thus, while an unperceived downwards (upwards) shift in the growth trend is likely to lead to a monetary policy that is too easy (tight), the accompanying unperceived decrease (increase) in the equilibrium real interest rate will lead to a policy that is too tight (easy). While the extent to which these two mistakes offset each other depends upon the model structure and parameter values, the general point is that incorporating time variation in the ERR makes it harder to generate a substantial change in inflation as the result of a empirically plausible change in the trend growth rate. This means that the Taylor rule is likely to be more robust to such trend shifts than previous research would suggest. Second, an econometrician who ignores time variation in the ERR is likely to end up with biased estimates of the policy rule parameters. In the most plausible case, the econometrician will end up overestimating both the extent to which the monetary authority smooths interest rates and the strength of the authority's response to inflation. Although we have only examined a few of the possible combinations of parameters (relating to the degree of interest rate smoothing by the authority and the serial correlation of the shocks), our analysis suggests that estimating a Taylor rule with serially correlated errors will tend to significantly reduce (if not eliminate) the bias in the estimated coefficients.