Likelihood Inference on Semiparametric Models: Average Derivative and Treatment Effect
Likelihood Inference on Semiparametric Models: Average Derivative and Treatment Effect
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DOI：
10.1111/jere.12167
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发表时间：
2018-06
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通讯作者：
Yukitoshi Matsushita;Taisuke Otsu
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作者：
Yukitoshi Matsushita;Taisuke Otsu
在过去的几十年里，计量经济分析中的半参数建模和估计方法取得了很大的进展。本文涉及推理（即，半参数模型中的置信区间和假设检验）。与传统的基于t比的方法相比，我们提倡基于似然性的推理。特别是，我们研究了两个广泛应用的半参数问题，加权平均导数和治疗效果，并提出半参数经验似然和刀切经验似然方法。我们推导出这些经验似然统计量的极限行为，并通过Monte Carlo模拟研究其有限样本性能。此外，我们扩展（删除-1）刀切经验似然删除d版本与增长的d和建立一般的渐近理论。这种扩展对于处理非光滑对象（如分位数和分位数平均导数或治疗效果）至关重要，因为非光滑下的刀切现象是众所周知的不一致现象。
In the past few decades, much progress has been made in semiparametric modeling and estimation methods for econometric analysis. This paper is concerned with inference (i.e., confidence intervals and hypothesis testing) in semiparametric models. In contrast to the conventional approach based on t-ratios, we advocate likelihood-based inference. In particular, we study two widely applied semiparametric problems, weighted average derivatives and treatment effects, and propose semiparametric empirical likelihood and jackknife empirical likelihood methods. We derive the limiting behavior of these empirical likelihood statistics and investigate their finite sample performance via Monte Carlo simulation. Furthermore, we extend the (delete-1) jackknife empirical likelihood toward the delete-d version with growing d and establish general asymptotic theory. This extension is crucial to deal with non-smooth objects, such as quantiles and quantile average derivatives or treatment effects, due to the well-known inconsistency phenomena of the jackknife under non-smoothness.