Measuring Uncertainty about Long-Run Predictions

Long-run forecasts of economic variables play an important role in policy, planning, and portfolio decisions. We consider forecasts of the long-horizon average of a scalar variable, typically the growth rate of an economic variable. The main contribution is the construction of prediction sets with asymptotic coverage over a wide range of data generating processes, allowing for stochastically trending mean growth, slow mean reversion and other types of long-run dependencies. We illustrate the method by computing prediction sets for 10 to 75 year average growth rates of U.S. real per-capita GDP and consumption, productivity, price level, stock prices and population. JEL classi…cation: C22, C53, E17 Keywords: prediction interval, low frequency, spectral analysis, least favorable distribution We thank Frank Diebold, Graham Elliott, Bruce Hansen, James Stock, Jonathan Wright, three referees, and the Editor, Stéphane Bonhomme, for useful comments and advice. Support was provided by the National Science Foundation through grants SES-0751056 and SES-1226464. Replication …les and a supplementary appendix is available at http://www.princeton.edu/~mwatson.