|
|||||
|
|||||
| |
|
|
|
|
|
|---|---|---|---|---|---|
|
Everything I know about VARS, I learned at the St Louis Fed Everything I know about VARS, I learned at the St Louis Fed-1December 06, 2004
Kevin D. Hoover and Oscar Jordá, "Measuring Systematic Monetary Policy" (PDF) In plain English, VARs was intended as a computational tool to determine what was a shock to the economic system, which would in turn stimulate an adjustment in the rate of accumulation driving economic growth, and what was actually a development predicted by the monetary authorities (and presumably knowable to the money markets—included business managers, who select pricing and output strategy). Since that time, VARs has been used to test Rational Expectations itself—as in Hoover & Jordá, cited above—and has come under some analytical scrutiny as well—as in Evans & Kuttner (below).
The main concern of analysts is whether or not VARs produces useful results based on the data input. If these results are useful, what do they mean? What do they prove? The object of an autoregression is to establish a statistically stable estimate of the future by regressing all the dependent variables on themselves; vector autoregression means that if some It stands to reason that Christopher Sims carefully selected variables to ensure that there were none that were perfectly collinear—such as, say, the consumer price index and the GDP deflator, which are reciprocals of each other. Even so, with 89 variables there is a high level of correlation; as with all systems of linear equations (which is what a vector autoregression is), you can eliminate all of these by patiently multiplying one member of each pair of correlated equations by some μ and subtracting it from the equation it's correlated with, to get a new equation that takes the place of the other one in the pair. This process is called a "transformation," and by transforming all pairs of correlated equations, you should achieve an extremely rich, stable predictor. There is, however, a slight problem. The transformation procedure I just described can be done many different ways; in linear algebra, where the object is to achieve a unique vector solution, all of these ways will result in the same answer. In VARs, it turns out that different transformations will lead to different definitions of what is a "shock" (Hoover & Jordá, p. 4a). This is not an entirely fatal flaw, since the analyst may have a rigorous explanation for preferring one transformation to another. I have spent much more time explaining the math and statistics of VARs than I intended to, partly because the method of analysis imposes its own structure of ideological assumptions. Most economists today perform quantitative analysis of monetary policy on VARs, while assuming that the monetary authorities cannot really take advantage of what they determine from it. While Hoover and Jordá make the [snide?] rejoinder that If Lucas was right in the first place, how does knowing the response of the economy to shocks help the policymaker when shocks cannot be systematically exploited? We cannot help but think that some practitioners want to have it both ways: to have a method that is immune to the Lucas critique because its VARs are estimated over periods in which, in fact, there have been no regime changes and, at the same time, to formulate advice for systematic policy on the basis of the impulse-response functions of these VARs.It would appear the real purpose of the Lucas Critique has evolved over time: instead of actually "proving" that the monetary policy is doomed to ineffectiveness, it has instead altered the character of the relationship between policymaker and money market participant. Hereafter, the power relationship of the markets to the state is symmetric; just as unbridled state tyranny ultimately defeats the purpose of any ideology that creates it, so the power of a national government to redress its policy failures by sheer force of macroeconomic action (Part 2)
One unresolved question is how well simple econometric procedures, like VARs, can describe the monetary authority’s response to economic conditions, and by extension, the policy shocks used to identify policy’s effects on the economy. There are several reasons to be skeptical of the VAR approach. VAR models (indeed, all econometric models) typically include a relatively small number of variables, while the Fed is presumed to “look at everything” in formulating monetary policy. By assuming linearity, VARs rule out plausible asymmetries in the response of policy, such as those resulting from an “opportunistic” disinflation policy. VARs’ coefficients are assumed to remain constant over time, despite well-documented changes in the Fed’s objectives and operating procedures. Evans and Kuttner resist the temptation to throw in the towel and condemn VARs as a predictive tool. Nevertheless, they explain some rather significant issues with the predictive powers of the program: the series plotted in figure 1 shows that the VAR’s forecast errors bear little resemblance to the futures market surprises. The correlation between the two is only 0.35 for one-month-ahead forecasts, comparable to the R2 of 0.10 reported in Rudebusch (1997). The correlations between two- and three-month ahead shocks are somewhat higher. If the futures market surprises are interpreted as the “true” shocks, this immediately calls the VAR approach into question.Evans and Kuttner argue these are the result of statistical noise and can be readily fixed with minor technical fixes. If so, I admit I'm surprised that it's taken so long for coders to devise fixes to the program, but of course the Evans & Kuttner paper is six years old. NOTES: 1 "Rational expectations" is usually explained in words to the effect that "markets [or the participants in them] do not make consistent errors when anticipating future conditions," and applies more precisely to the Lucas Critique of monetarism. This Critique objected to the aspect of monetary/Keynesian theory that believed policymakers could guide the economy through manipulation of the money supply; if bond traders, for example, were expecting a tight money policy and the Fed expanded money faster than predicted—in order to get the President re-elected, for example—then the bond traders would be burned because they had bought the bonds at an unreasonably high price (the yields were unreasonably low). In the future, therefore, they would anticipate this, pushing interest rates up, and compelling the authorities to either accelerate inflation to achieve the same level of low employment, or else "eat" high unemployment by tightening the money supply. The only way monetary policy can work is if authorities consistently deceive the markets. This is actually a very good critique, and Lucas deserves a lot of honor for not only making it, but also developing a system of incorporating it into a rigorous system of equations. Under the new "dynamic general equilibrium analysis," economists sought to describe the economy as a large number of identical households who seek to maximize their incomes based on predicted real interest rates and returns to labor. They could then use computer programs to parameterize these equations to determine how rapidly the economy responded to "shocks" (basically, stimuli that are exogenous to the model, like a sudden massive increase in the price of crude oil). "Quasi-rational expectations" are similar to the systems developed for rational expectations except that the assumption that participants can or do predict the future in a "rational" way are relaxed. In one version of this (John Cochrane, "What Do the VARs mean?" 1997), some actors are "rational" and some rely on a rule of thumb. Another, more accurate use of the concept is the Shefrin & Thaler "planner-doer" model (or see this hilarious PDF, "Self-Control for the Righteous," Kivetz & Simonson, 2002; unfortunately, Hersh Shefrin and Richard Thaler's essay is no longer online; it is anthologized in Quasi-Rational Economics, 1981), in which quirks in human behavior are modeled as affecting their intertemporal utility maximization function.
Everything I know about VARS, I learned at the St Louis Fed-2December 09, 2004
Kevin D. Hoover and Oscar Jordá, "Measuring Systematic Monetary Policy" (PDF) (Part One)
On to the VARs role in describing monetary policy: The authors develop a more complex, nuanced version of the Lucas Critique (the [monetary] "policy ineffectiveness proposition") than the customary interpretation—which is that only unanticipated, unanticipated shocks have any effect on real output. Yes, excellent, so what is this "relative invariance below the aggregate macroeconomic phenomena"? Second, even with only half the economy in the rule-of-thumb camp, the economy behaves quantitatively and qualitatively substantially as if Lucas had been wrong altogether about the unimportance of systematic and anticipated monetary policies.
Third, Lucas is correct, nonetheless, that the aggregate reactions of the economy are conditioned on policy regimes and the analysis of what happens when a regime changes—in practice as well as in theory—requires some structural knowledge. The key assumption of this paper is that the coarse structural knowledge suggested in Cochrane’s decomposition of the effects of monetary policy into anticipated and unanticipated components is sufficient—and very likely the best that we can practically accomplish—to reach substantive results. This post—including its first part—would not be complete if I did not at least discuss the concept of "physics envy." Lukelea (who wrote the web log entry on physics envy above) makes some compelling points about the fact that economics is not comparable to physics—which strikes me as clamorously obvious—but seems to overlook an alternative hypothesis, that it does seek to take full advantage of statistical technology. Statistics is often used in a rash way, as when policymakers seek to confirm or deny meaningless propositions, and economics in all its variant schools is the same way.
When I began researching economics for my own interest, I believed that it had taken a wrong turn in focusing on a controversy over which system of linear equations most coherently captured how the economy worked. I believed, in fine, that since no such system could ever describe the whole of capitalism, it followed that all the energy was being directed at describing a parallel universe with no urgent attachment to this one. I further believed that the ideal would have been to study case histories, with a parsimonious use of entirely certain parameters. Perhaps this ideal of mine did not develop because it was an absurd ideal. I rather cheerfully propose that it is the next turn in the road of economic analysis, since the limits of what is statistically meaningful have been reached.
|
