Interpolation and Shock Persistence of Prewar U.S. Macroeconomic Time Series: A Reconsideration

The U.S. prewar output series exhibit smaller shock-persistence than postwar-series. Some studies suggest this may be due to linear interpolation used to generate missing prewar data. Monte Carlo simulations that support this view generate large standard-errors, making such inference imprecise. We assess analytically the effect of linear interpolation on a nonstationary process. We find that interpolation indeed reduces shock-persistence, but the interpolated series can still exhibit greater shock-persistence than a pure random walk. Moreover, linear interpolation makes the series periodically nonstationary, with parameters of the data generating process and the length of the interpolation time-segments affecting shock-persistence in conflicting ways.

JEL Classification: C01, C02, E01, E30, N10

Keywords: Linear Interpolation, Random Walk, Shock-Persistence, Nonstationary series, Periodic nonstationarity, Stationary series, Prewar US Time Series