Phillips curve forecasts. The expectations-augmented Phillips curve constitutes an important tool of empirical macroeconomics and is considered by many to be a reliable tool for forecasting inflation, cf Gordon (1982) and, more recently, the Congressional Budget Office (1996), Fuhrer (1995), Gordon (1997), Staiger, Stock and Watson (1997), and Tootel (1994). For this reason, forecasts based on two variants of a Phillips curve are also included for comparison purposes. These specified the twelve-month inflation rate as the dependent variable:
w6702-29
where pt = ln(CPIt), 7rt = 1200*Apt is monthly CPI inflation at an annual rate, ut is the unemployment rate, and Zt is a vector of variables that control for supply shocks and/or measurement difficulties. The two variants differ in the supply shock variables Zv In one, zt consists solely of the relative price of food and energy; in the other, this relative price is augmented by Gordon’s (1982) variable that controls for the imposition and removal of the Nixon wage and price controls.


The parameters of (5.4) were estimated recursively by ordinary least squares. For each of the two variants, the lag lengths q and p were chosen by recursive BIC, where 0 —Я — 5 and 0<p<5.

Estimation

The estimation and forecasting was carried out in a way to simulate real-time forecasting. This entailed fully recursive parameter estimation, factor extraction, model selection, etc. For example, to construct the first forecast, the parameters and factors were estimated, and the models were selected, using data available from 1959:1 through 1970:1 (the first date for the regressions was 1960:1, with earlier observations used for initial conditions as needed). These parameters and models were then used to forecast IP growth and CPI inflation from 1970:1 to 1971:1.

All parameters, factors, etc. were then reestimated, and information criteria were recomputed, using data from 1959:1 through 1970:2, and forecasts using these models and parameters were computed for twelve-month growth from 1970:2 to 1971:2. Because all order and model selection is fully recursive, this means that the actual model used to produce the forecasts for a method that uses an information criterion in general changes from one month to the next; what is constant is the rule by which that model is selected.