A two-step approach to production frontier estimation and the Matsuoka's distribution

In this work, we introduce a deterministic frontier model in which efficiency is governed by the Matsuoka distribution, a parsimonious one-parameter specification on $(0,1)$ designed to reflect patterns typically observed in efficiency data. Based on this formulation, we develop a two-step semiparametric estimation procedure: a nonparametric smoothing for the regression component, followed by a feasible method of moments estimation for the efficiency parameter with plug-in reconstruction of the frontier. Theoretical results establish convergence rates, asymptotic normality, and an oracle property for the parametric estimator of the efficiency parameter. A Monte Carlo study demonstrates that the procedure performs consistently with the theoretical results and improves upon a fully nonparametric alternative. Applying the method to Brazilian temporary crops with land and agrochemicals as inputs, we find that both regions exhibit isoquants close to the constant elasticity substitution form, but differ in the relative productivity of inputs. Most notably, statistical tests provide evidence that the South is relatively more efficient than the Center-West, highlighting the empirical relevance of the proposed approach.