Proxy variable estimation of productivity and efficiency

We model productivity and inefficiency jointly, instead of modeling and estimating either only productivity or only inefficiency with many variable and quasi-fixed inputs. In the first model, we use a multi-step procedure. We use the proxy variable method based on the first-order condition (FOC) of expected profit maximization with respect to the single variable input to take care of the endogeneity problem arising from both productivity and inefficiency. To separate mean inefficiency from mean productivity we assume them nonparametric functions of different sets of exogenous variables. In the second model, we consider a novel system consisting of the production function and the FOCs of expected profit maximization for the multiple variable inputs. Distributional assumptions are made on all the random errors associated with the production function, the FOCs, productivity, and inefficiency functions in the second model. We use the Colombian food manufacturing data as an application of our model.