Expectations hypotheses tests at long horizons

Many rational expectations models state that an economic variable is determined as the present value of future variables. These restrictions have traditionally been tested on VARs where variables appear either in levels (or cointegrating relationships) or first differences. When variables are highly persistent, commonly used test statistics may lead to overrejections in small samples. We propose an alternative method based on local-to-unity asymptotic approximations that has good coverage properties, and can be applied to jointly test across horizons. We apply this method to the Term Structure of Interest Rates, the Uncovered Interest Rate Parity condition, and the Permanent Income Hypothesis. The method can also be used to perform inference in long-horizon predictive regressions.