What univariate models tell us about multivariate macroeconomic models

A longstanding puzzle in macroeconomic forecasting has been that a wide variety of multivariate models have struggled to out-predict univariate representations. We seek an explanation for this puzzle in terms of population properties. We show that if we just know the univariate properties of a time-series, yt, this can tell us a lot about the dimensions and the predictive power of the true (but unobservable) multivariate macroeconomic model that generated yt. We illustrate using data on U.S. inflation. We find that, especially in recent years, the univariate properties of inflation dictate that even the true multivariate model for inflation would struggle to out-predict a univariate model. Furthermore, predictions of changes in inflation from the true model would either need to be IID or have persistence properties quite unlike those of most current macroeconomic models.