انحرافات و نوسانات : سیاست های پولی و نتایج در گذشته ی جنگ جهانی دوم ایالات متحده

For a VAR with drifting coefficients and stochastic volatilities, we present posterior densities for several objects that are pertinent for designing and evaluating monetary policy. These include measures of inflation persistence, the natural rate of unemployment, a core rate of inflation, and ‘activism coefficients’ for monetary policy rules. Our posteriors imply substantial variation of all of these objects for post WWII US data. After adjusting for changes in volatility, persistence of inflation increases during the 1970s, then falls in the 1980s and 1990s. Innovation variances change systematically, being substantially larger in the late 1970s than during other times. Measures of uncertainty about core inflation and the degree of persistence covary positively. We use our posterior distributions to evaluate the power of several tests that have been used to test the null hypothesis of time-invariance of autoregressive coefficients of VARs against the alternative of time-varying coefficients. Except for one, we find that those tests have low power against the form of time variation captured by our model.

This paper extends the model of Cogley and Sargent (2001) to incorporate stochastic volatility and then reestimates it for post World War II US data in order to shed light on the following questions: Have aggregate time series responded via time-invariant linear impulse response functions to possibly heteroskedastic shocks? Or is it more likely that the impulse responses to shocks themselves have evolved over time because of drifting coefficients or other nonlinearities?We present evidence that shock variances evolved systematically over time, but that so did the autoregressive coefficients of VARs. One of our main conclusions is that much of our earlier evidence for drifting coefficients survives after we take stochastic volatility into account. We use our evidence about drift and stochastic volatility to infer that monetary policy rules have changed and that the persistence of inflation itself has drifted over time. 1.1. Time invariance versus drift The statistical tests of Sims (1980, 1999) and Bernanke and Mihov (1998a, 1998b) seem to affirm a model that contradicts our findings. They failed to reject the hypothesis of timeinvariance in the coefficients of VARs for periods and variables like ours. To shed light on whether our results are inconsistent with theirs, we examine the performance of various tests that have been used to detect deviations from time invariance.We find that those tests have low power against our particular model of drifting coefficients, except for one test. And that test actually rejects time invariance in the data. These results about power help reconcile our findings with those of Sims and Bernanke and Mihov. 1.2. Bad policy or bad luck? This paper organizes evidence within a formal statistical model. We use the patterns of time variation that our statistical model detects to shed light on some important substantive and theoretical questions about post WWII US monetary policy. These revolve around whether it was bad monetary policy or bad luck that made inflation–unemployment outcomes worse in the 1970s than before or after. The view of DeLong (1997) and Romer and Romer (2002), which they support by selecting interesting anecdotes and passages from government reports, asserts that it was bad policy. Their story is that during the 1950s and early 1960s, the Fed understood a correct model (which in their view incorporates the natural rate theory that asserts that there is no exploitable trade off between inflation and unemployment); that Fed policy makers in the late 1960s and early 1970s were seduced by Samuelson and Solow (1960) promise of an exploitable trade-off between inflation and unemployment; and that under Volcker’s leadership, the Fed came to its senses, again accepted the natural rate hypothesis, and used monetary policy to arrest inflation. Aspects of this “Berkeley view”1 receive backing from statistical work by Clarida et al. (2000) and Taylor (1993), who fit monetary policy rules for subperiods that they choose toisolate differences between the Burns and the Volcker–Greenspan eras. They find evidence for a systematic difference of monetary policies across the two eras, a difference that in Clarida et al.’s ‘new-neoclassical-synthesis’ macroeconomic model would lead to better inflation-unemployment outcomes under the Volcker–Greenspan policy. But Taylor’s and Clarida et al.’s interpretation of the data has been disputed by Sims (1980, 1999) and Bernanke and Mihov (1998a, 1998b). They presented evidence that the US data do not prompt rejection of an hypothesis of time invariance of the autoregressive coefficients of a VAR. They also present evidence for shifts in the variances of the innovations to their VARs. If one equation of the VAR is interpreted as describing a monetary policy rule, then Sims’s and Bernanke and Mihov’s results say that it was not the monetary policy strategy but luck (i.e., the volatility of the shocks) that changed between the Burns and the post-Burns periods. 1.3. Inflation persistence and inferences about the natural rate The persistence of inflation plays an important role in some widely used empirical strategies for testing the natural rate hypothesis and for estimating the natural unemployment rate. In particular, as we shall see, inflation persistence also plays an important role in lending relevance to instruments for estimating monetary policy rules.2 Therefore, we use our statistical model to portray the evolving persistence of inflation. We define a measure of persistence based on the normalized spectrum of inflation at zero frequency, then present how this measure of persistence increased during the 1960s and 1970s, then fell during the 1980s and 1990s. 1.4. Drifting coefficients and the Lucas’s Critique Drifting coefficients have been an important piece of unfinished business within macroeconomic theory since Lucas (1976) emphasized them in the first half of his 1976 Critique, but then ignored them in the second half.3 Sargent (1999) reevaluated how drifting coefficients bear on the theory of economic policy in the context of recent ideas about self-confirming equilibria. A self-confirming equilibrium is a subtle extension of the concept of a rational expectations equilibrium that allows different decision makers to have models that differ, but only about the probabilities of events off an equilibrium path. In particular, in a self-confirming equilibrium within a macroeconomic context, a government’s model correctly describes conditional probabilities of events that occur infinitely often on the equilibrium path, but it can be wrong about off-equilibrium path occurrences that are important because they enter the thought process by which the government designs its policy. The idea that the observations conform strictly to a self-confirming equilibrium can bolster the time-invariance view of the data taken by Sims and Bernanke and Mihov. However, Sargent (1999) and Cho et al. (2002) show how a slight modification ofa self-confirming equilibrium, attained by attributing adaptive behavior to the government, produces a macroeconomic model whose tendencies toward a self-confirming equilibrium are interrupted by recurrent escapes that generate nonlinearities in the data that can show up as drifting coefficients. 1.5. Method We take a Bayesian perspective and report time series of posterior densities for various economically interesting functions of hyperparameters and hidden states.We use aMarkov Chain Monte Carlo algorithm to compute posterior densities. 1.6. Organization The remainder of this paper is organized as follows. Section 2 describes the basic statistical model that we use to develop empirical evidence. We consign to Appendix A a detailed characterization of the priors and posterior for our model, and Appendix B describes a Markov Chain Monte Carlo algorithm that we use to approximate the posterior density. Section 3 reports our results, and Section 4 concludes.

One respectable view is that either his erroneous model, his insufficient patience, or his inability to commit to a better policy made Arthur Burns respond to the end of Bretton Woods by administering monetary policy in a way that produced the greatest peace time inflation in US history; and that his improved model, more patience, or greater discipline led Paul Volcker to administer monetary policy in a way that conquered American inflation.24 Another respectable view is that what distinguished Burns and Volcker was not their models or policies, but their luck. This paper and its predecessor (Cogley and Sargent, 2001) fit time series models that might help distinguish these views.This paper also responds to Sims’s (2001) and Stock’s (2001) criticism of the evidence for drifting systematic parts of vector autoregressions in Cogley and Sargent (2001) by altering our specification to include stochastic volatility. While we have found evidence for drifting variances within our new specification, we continue to find evidence that the VAR coefficients have drifted, mainly along one important direction. For reasons discussed by Sargent (1999) and Luca Benati (2001), the presence of drifting coefficients contains clues about whether government policy makers’ models or preferences have evolved over time. It is prudent to be cautious in interpreting evidence either for or against drifting coefficients. For reasons that are clearest in continuous time (see Anderson et al., 2003), it is much more difficult to detect evidence for movements in the systematic part of a vector autoregression than it is to detect stochastic volatility. This situation is reflected in the results of our experiments that implement Bernanke and Mihov’s tests under an artificial economy with drifting coefficients.