Stephen Williamson Discovers VAR Analysis

A Mark Sadowski post

In his most recent post Stephen Williamson states the following:

“The modern version of the Monetary History approach is VAR (vector autoregression) analysis. This preliminary version of Valerie Ramey’s chapter for the second Handbook of Monetary Economics is a nice survey of how VAR practitioners do their work. The VAR approach has been used for a long time to study the role of monetary factors in economic activity. If we take the VAR people at their word, the approach can be used to identify a monetary policy shock and trace its dynamic effects on macroeconomic variables – letting the data speak for itself, as it were…But, should we buy it? First, there are plenty of things to make us feel uncomfortable about VAR results with regard to monetary policy shocks. As is clear from Ramey’s paper, and to anyone who has read the VAR literature closely, results (both qualitative and quantitative) are sensitive to what variables we include in the VAR, and to various other aspects of the setup. Basically, it’s not clear we can believe the identifying assumptions…”

As Chris Sims (1996) noted in response to similar criticism of VAR by Glenn Rudebusch, issues of “variable selection are universal in macroeconomic modeling” (pp. 9). And as for the issue of identification, the Ramey paper to which Williamson links lists ten different approaches, all of which are associated with VAR modeling to some degree or another.

So what is the alternative to VAR modeling?

Presumably, from his later criticism of Christiano, Eichenbaum and Evan’s (2005) approach to DSGE modeling, which matches the impulse responses from the model to those of actual data, Williamson would prefer models achieve identification by imposing structure based on theory. But DSGE identification is even less straightforward than VAR identification. Canova and Sala (2009), Komunjer and Ng (2011), and others have pointed out some of the many problems with identification in DSGE models.

And, in the final analysis, this criticism of VAR on the basis of identification is ironic given it is no exaggeration to say that it was in fact the “incredible identification” of large scale models that was the primary motivation for Chris Sims (1980) to introduce VAR analysis to macroeconomics.

Williamson goes on to provide another objection to VAR modeling:

“…Second, even if you take VAR results at face value, the results will only capture the effect of an innovation in monetary policy. But, modern macroeconomics teaches us that this is not what we should actually be interested in. Instead, we should care about the operating characteristics of the economy under alternative well-specified policy rules. These are rules specifying the actions the central bank takes under all possible circumstances. For the Fed, actions would involve setting administered interest rates – principally the interest rate on reserves and the discount rate – and purchasing assets of particular types and maturities.”

I think the best response to this is to turn to page 24 of the Ramey paper which Williamson cites in his post:

”Before beginning, it is important to clarify why we are interested in monetary policy shocks. Because monetary policy is typically guided by a rule, most movements in monetary policy instruments are due to the systematic component of monetary policy rather than to deviations from that rule. Why, then, do we care about identifying shocks? We care about identifying shocks for a variety of reasons, the most important of which is to be able to estimate causal effects of money on macroeconomic variables. As Sims (1998) argued in his discussion of Rudebusch’s (1998) critique of standard VAR methods, because we are trying to identify structural parameters, we need instruments that shift key relationships. Analogous to the supply and demand framework where we need demand shift instruments to identify the parameters of the supply curve, in the monetary policy context we require monetary rule shift instruments to identify the response of the economy to monetary policy.”

Failure to correctly identify the effect of an innovation in monetary policy might for example allow us to theorize that raising interest rates causes inflation to increase.

Fortunately, partly thanks to VAR analysis, most economists don’t consider that to be very plausible (just as most people don’t think that it is the act of opening umbrellas that causes it to rain).


In comments Williamson says the following:

“In the quote, you can see roughly what Friedman and Schwartz were up to. They looked at turning points in money supply and turning points in what he calls “general business.” I haven’t read the Monetary History in a long time, but I think “general business” is the NBER “reference cycle,” which is roughly an index of aggregate economic activity – not aggregate output, but presumably highly correlated with it. Basically, Friedman and Schwartz showed that money leads aggregate economic activity. It’s the informal counterpart of what Sims (1972) is about. Sims showed that money Granger-causes output in the the U.S. time series. Of course Granger causation need not imply economic causation. That was part of Tobin’s critique of Friedman and Schwartz. Money could in fact be endogenously responding to output, but appear to lead output in the time series. The endogeneity could come from policy, or from the banking sector, if we’re measuring money as M1 or M2, say.”

Williamson is referring to Tobin’s famous Post Hoc, Proctor Hoc (“after this, therefore because of this”) critique of Friedman.

Williamson implies that Granger causality tests are subject to the very same criticism, when in fact Chris Sim’s 1972 paper was specifically intended as a rebuttal to Tobin’s invocation of the fallacy (which is incredibly clear if one actually bothers to read the paper). Williamson’s comment on the endogeneity of money is even more ironic when one realizes that Granger causality testing is the primary econometric tool of the Post Keynesian empirical literature on endogenous money (e.g. Basil Moore, Thomas Palley, Robert Pollin, Peter Howells etc.).

5 thoughts on “Stephen Williamson Discovers VAR Analysis

  1. “Failure to correctly identify the effect of an innovation in monetary policy might for example allow us to theorize that raising interest rates causes inflation to increase.”

    Contrast with the previous post by Marcus:

    “In other words, the central bank is fast losing the power to control inflation. Worse, the more it tries, by raising interest rates, for example, the higher inflation rises, since the increase in interest rates worsens the debt dynamics, requiring more inflation to produce the requisite seignorage revenues (in addition to reducing the present value of real debt through a rise in the price level).”

    Of course, the real driver is expectations, not the moving around of interest rates in themselves. Expectations are harder to manage unless we all become machines.

  2. I hope you understand that I didn’t just “discover” VAR analysis last week. I discovered it when I read “Macroeconomics and Reality” in 1980.

    This quote illustrates part of the problem with how VARs are used:

    “Failure to correctly identify the effect of an innovation in monetary policy might for example allow us to theorize that raising interest rates causes inflation to increase.”

    The idea here is that you are supposed to think your identification is wrong if you get a result that doesn’t seem to conform with your priors, which of course may have come from some schlock theory. People keep running across the “price puzzle.” And they will torture the data until it relents, and tells them that, just as they thought, raising rates makes inflation go down.

    • Steven, 20 years ago I “scrutinized” the “Price-Puzzle”. Then I wrote:
      …People’s views on inflation could still be influenced by the rising inflation trend and large inflation swings of the 1960’s and especially the 1970’s
      …The persistence of inflation was a dominant factor in shaping peoples expectations. When concern over unemployment is also factored in as a determinant of FOMC actions the impression is that countervailing actions by the Fed would never be sufficient to fully abate the rise in inflation.
      This gave rise to what has become known as “the price puzzle” meaning that an increase in the fed funds rate (interpreted as a tightening of policy) would be followed by an increase in inflation!
      … Comparing figure 5.6 with figure 5.2, the message is that the Fed no longer “leans against the wind” with respect to inflation. This is somewhat surprising given a supposedly (my hypothesis) higher concern (or premium) over price stability in the 1980’s.
      One plausible explanation for the result that reconciles the (apparently contradictory) muted response of the federal funds rate to inflation after 1982 with a postulated increase in the Fed.’s resolve to fight inflation is evidence that the behavior of inflation changed after the 80/82 recession. Inflation after 1982 exhibits substantially less persistence than in the previous years (see figure 3) so that increases in inflation in one month are viewed as temporary. In other words, inflation is much less autocorrelated so that lagged values of inflation provide little information about future inflation. As a result, unexpected movements (or innovations) in inflation no longer require a monetary policy response (which sits well with our initial argument that the fed funds can be a poor indicator of monetary policy)
      The above observations are indicative of a move towards less discretion in the actions of the Fed, consistent with the (unstated) adoption of a more rule-like behavior by the monetary authority. An examination of figures 5.8 and 5.4 indicates that the “price-puzzle” – the positive reaction of inflation to an innovation in the fed funds rate – essentially disappears after 1982.

    • You have to forgive the title of this post Steve, but it does seem to me (as well as to many others) that, at the very least, you display a certain antipathy towards empirical macroeconomics.

      To be clear, the phrase “price puzzle” refers to the occasional finding in the VAR literature that positive innovations to short-term interest rates lead to a temporary increases in the price level. While this may not conform with conventional monetary theory, the main reason it is considered a “puzzle” probably has much more to do with the fact that it is inconsistent with the effects observed using alternative plausible measures of innovations to monetary policy (e.g. monetary aggregates), as well as the fact that it is inconsistent with the nearly universal finding in the VAR literature that positive innovations to short term interest rates lead to unambiguous decreases in the output level. I also think the existence of the “price puzzle” mainly serves to underscore the fact that short-term interest rate changes apparently are a rather imperfect measure of monetary policy innovations.

      In any case, even those VAR studies that exhibit the “price puzzle” don’t exhibit the kind of behavior that Neo-Fisherian theory seems to be proposing. And if a theory finds itself at odds with an entire body of empirical literature perhaps that theory should be questioned.

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