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.

翻译：本文提出一种确定性前沿模型，其中效率由Matsuoka分布控制——这是一种定义在$(0,1)$区间上的简约单参数设定，旨在反映效率数据中常见的典型模式。基于此设定，我们开发了一种两步半参数估计程序：首先对回归分量进行非参数平滑，随后通过可行的矩估计方法结合前沿函数的插件重构来估计效率参数。理论结果确立了效率参数估计量的收敛速率、渐近正态性及预言机性质。蒙特卡洛研究表明该方法的实际表现与理论结果一致，且优于完全非参数的替代方法。将本方法应用于以土地和农用化学品作为投入的巴西短期作物数据，我们发现两个地区的等产量线均接近常替代弹性形式，但在投入要素的相对生产率方面存在差异。尤为重要的是，统计检验证据表明南部地区相对中西部地区具有更高的生产效率，这凸显了所提方法的实证价值。