This is Jeff Hallman's Typepad Profile.
Join Typepad and start following Jeff Hallman's activity
Jeff Hallman
Recent Activity
Thanks for noticing, Nick. I wouldn't refer to myself as a serious econometrician these days, mostly I do programming. But I used to be. On the BVAR: It is well known in economic forecasting circles that simple models with few parameters tend to forecast better out of sample than more elaborate models with many parameters. Suppose you simulate a model like: y(t) = a + b1*x1(t) + b2*x2(t) + ... + bk*xk(t) + e(t) (1) where e(t) and xi(t) are independent and identically distributed, and with 1 > b1 > b2 > .... bk > 0. If the number of observations you have is large relative to k, then estimating a model that includes all k of the xi(t) will give you good out of sample forecasts. But if you don't have very many observations, you'll find that dropping some of the xi variables with small coefficients from the regression improves the model's forecasting ability. The variance of the estimated coefficients is smaller if you estimate fewer of them, and for prediction purposes, a precisely-estimated incorrect model is often better than an imprecisely-estimated correct model. A typical conventional vector autoregression (VAR) in macro has 4 lags of six variables. Throw in a constant, and this means each of the six equations has 25 parameters to estimate. You also have estimate the 21 parameters of the symmetric 6 by 6 covariance matrix. You typically only have 20 or 25 years of quarterly data to work with, which means you're estimating 171 parameters with only 480 to 600 observations. That doesn't sound too bad until you realize that there's likely to be considerable collinearity amongst your six variables. You are going to end up with estimated standard errors on your coefficients that are so large as to render most of them meaningless, and the out of sample forecasts will be quite poor. Litterman's BVAR is a form of ridge regression, an old technique used by statisticians to reduce the effective number of parameters estimated by biasing the estimates in a particular direction. It is one of a number of so-called "shrinkage" estimators. In traditional ridge regression, the coefficients are shrunk (biased) towards zero. The Litterman prior biases the coefficients towards the "six independent random walks" model. However, you can use the same technique to bias coefficients in some other direction. As a grad student many years ago, I worked for a while on shrinking a VAR towards a cointegration prior, but I never really finished it. One day somebody ought to pursue it. At any rate, the fact that BVAR's with the Litterman prior do about as well at forecasting most macroeconomic series as the big econometric models that used to be popular is one reason those big models have fallen out of favor. What's important in the context of this discussion is that they contain zero economic theory content, and yet they perform about as well as models with lots of built-in economic theories. It's true that BVAR's are lousy at predicting things like turning points or evaluating the effect of policy changes. But then again, that's also empirically true of the theory-based models.