Getting Implicit Shadow Prices Right for the Estimation of the Malmquist Index: The Case of Agricultural Total Factor Productivity in Developing Countries

The Malmquist index has become extensively used in international comparisons of agricultural productivity since it does not require prices for its estimation, which are normally not available. However, the DEA approach used to estimate this index still uses implicit price information. This entails potential problems because these methods are susceptible to the effect of data noise, and shadow prices can prove to be inconsistent with prior knowledge on cost shares. In this paper we analyze implicit input shadow shares used in the DEA approach to estimate agricultural productivity using the Malmquist index for 72 developing countries. We then set bounds to the implicit input shares introducing information on their likely value and compare constrained and unconstrained input shares. We conclude that the incidence of zero shadow prices justifies the introduction of constraints in the estimation of the Malmquist index. The paper also presents detailed results of TFP growth in developing countries using constrained shadow shares for their estimation. We find that agricultural TFP has been growing steadily in the past 20 years even if countries like China, Brazil and India are not considered. Remarkably, we find a clear improvement in the performance of Sub-Saharan Africa since the mid 1980s.