Comparing Luenberger and Luenberger-Hicks-Moorsteen productivity indicators: How well is total factor productivity approximated?

We empirically compare both the popular Luenberger indicator with the less popular Luenberger-Hicks-Moorsteen productivity indicator on an agricultural panel data set of Chinese provinces over the years 1997-2014. In particular, we test for the differences in distribution when comparing these indicators. These tests are crucial to answer the question to which extent the Luenberger indicator can approximate the Luenberger-Hicks-Moorsteen productivity indicator that has a Total Factor Productivity (TFP) interpretation.