Cohort Projection Models for School Enrollment Are a Special Case of Vector Autoregressive Models in Macroeconomics (and Why This Might Help Us)

Herbert L. Smith, University of Pennsylvania

Current forecasting practice, which is mandated administratively, and sometimes legally, makes use of the cohort projection framework--the useful demographic observation that the number of 9th graders in year t+1 looks a lot like the number of 8th graders in year t. In this paper, I outline the standard cohort projection framework and show that it is a special, deterministic case of a familiar macroeconometric model for forecasting, the vector autoregressive model (VAR). In macroeconometric forecasting, there is a tendency to let the data "decide" the parameters of these models (which can be rearranged as cohort projection ratios); or the data are blended by Bayesian methods with some "prior" about the parameters, such as a random walk. Viewed from this perspective, what we do in school forecasting amounts to a prior so strong that we ignore the data! Maybe we should relax this unrecognized habit. I illustrate with data.