Estimating Changes in Trend Growth of Total Factor Productivity: Kalman and H-P Filters versus a Markov-Switching Framework

Abstract

Trend growth in total factor productivity (TFP) is unobserved; it is frequently assumed to evolve continuously over time. That assumption is inherent in the use of the Hodrick-Prescott or Bandpass filter to extract trend. Similarly, the Kalman filter/ unobserved-components approach assumes that changes in the trend growth rate are normally distributed. In fact, however, innovations to the trend growth rate of total factor productivity are far from normal. The distribution is fat-tailed, with large outliers in 1973. Allowing for these outliers, the estimated trend growth rate changes only infrequently. A nonlinear filtering approach is probably better suited to capturing the infrequent past and possible current shifts in trend growth of TFP. One such approach is the Markov-switching model, which is estimated and tested in this paper. The Markov- switching approach appears to have several advantages over repeated Andrews tests.