Convex non-parametric least squares, causal structures and productivity

In this paper we consider Convex Nonparametric Least Squares (CNLS) when productivity is introduced. In modern treatments of production function estimation, the issue has gained great importance as when productivity shocks are known to the producers, input choices are endogenous and estimators of production function parameters become inconsistent. As CNLS has excellent properties in terms of approximating arbitrary monotone concave functions, we use it, along with flexible formulations of productivity, to estimate inefficiency and productivity growth in Chilean manufacturing plants. Inefficiency and productivity dynamics are explored in some detail along with marginal effects of contextual variables on productivity growth, inputs, and output. Additionally, we examine the causal structure between inefficiency and productivity as well as model validity based on a causal deconfounding approach. Unlike the Cobb-Douglas and translog production functions, the CNLS system is found to admit a causal interpretation.