Estimating the productivity of US agriculture: The Fisher total factor productivity index for time series data with unknown prices

Abstract

In this paper, we propose a straightforward way to estimate the Fisher ideal total factor productivity (TFP) index (FI) in cases where price information is unavailable, using ‘shadow prices’ derived from data envelopment analysis (DEA). A Monte Carlo experiment shows that the shadow price Fisher ideal TFP index (SPFI) can effectively estimate the ‘true’ FI with relatively small (and stable) errors. The empirical application to the US agriculture sector (1948–2017) further suggests that the SPFI is a (superior) alternative to the traditional Malmquist DEA, especially in dealing with unbalanced panel or time series data when price data are unknown.