Identifying the elasticity of factor substitution under biased technical change: a structural panel GMM (P-GMM) estimator for the agricultural sector

Recent studies of farm technology conclude that capital and labour are gross complements in agriculture, but most treat factor prices as exogenous. We take the structural panel GMM (P-GMM) estimator of von Brasch, Raknerud and Vigtel, which allows factor prices to respond to supply shocks under biased technical change, to agricultural data for the first time. Using a panel of agricultural employment, capital, off-farm wages and the user cost of capital for thirteen Uzbek regions over 2010–2024, fixed effects yield an elasticity of 0.11, whereas P-GMM yields 1.83 (unit-clustered s.e. 1.16; cluster-bootstrap percentiles 0.74–3.42). The contrast has the sign expected when simultaneity biases fixed effects towards zero, but we show that it cannot be read as evidence of substitution. Monte Carlo experiments with 500 replications show that Wald intervals cover the true elasticity in only 47–62% of samples with ten to thirteen units and up to 80% with 150 units, and that up to a third of estimates lie on the boundary. Stock–Wright S-sets constructed by projection retain 99–100% coverage but have essentially no power with thirteen units and fourteen periods; power rises mainly with the number of periods. In the regional data, no value of the elasticity on the evaluated grid is rejected. These findings establish a decision-oriented interpretation of econometric uncertainty, demonstrating why statistical identification must be assessed before elasticity estimates are used to support agricultural investment and mechanisation policies. Credible estimates require longer and more disaggregated factor data: district agricultural investment is now published, but district agricultural employment and suitable factor prices are not. Policy analyses of mechanisation that assume complementarity rest on weaker evidence than the literature suggests.