A Comparison of the Michigan and Fair Models

This chapter compares the predictive accuracy of the Michigan and Fair models using the method developed in Fair (1980). These models are compared to each other and to an eighth-order autoregressive model. The method accounts for the four main sources of uncertainty of a forecast: uncertainty due to (I) the error terms, (2) the coefficient estimates, (3) the exogenous variables, and (4) the possible misspecification of the model. Because it accounts for these four sources, it can be used to make comparisons across models. In other words, it puts each model on an equal footing for purposes of comparison. The method has been used to compare the Fair model to autoregressive models, vector autoregressive models, Sargent’s classical macroeconomic model, and a small linear model, but this is the first time it has been used to compare two relatively large structural models. Ideally, model builders should not be the ones comparing their models to others. Although one may try to be objective, there is always the suspicion that one has stacked the cards in favor of her or his model. This chapter is not intended to be the final word on the relative merits of the Michigan and Fair models. Its primary aim is to demonstrate the application of the comparison method to large models. As will be seen, the application of the method to the Michigan model reveals two potential shortcomings of the method. First, the results for the Michigan model are highly sensitive to plausible alternative assumptions about exogenous variable uncertainty. This makes comparison difficult because there is no obvious criterion for choosing between the competing assumptions. Second, the Michigan model relies fairly heavily on the use of dummy variables, and the part of the method that accounts for exogenous-variable uncertainty cannot handle dummy variables. It must be assumed that the dummy variables are known with certainty. The method may thus bias the results in favor of models that are heavily tied to dummy variables. It is uncertain how large this bias might be.