估計與檢定具內生性的非條件分量部分效果

Abstract

傳統的分量迴歸主要用於探討被解釋變數的條件分配, 然而政策分析卻可能需要評估該變數的非條件分配。 例如, 我們透過羅倫茲曲線 (Lorenz curve) 的改變, 來闡述所得不均的變化, 而羅倫茲曲線是由所得的非條件分配建構而成。 Firpo, Fortin, and Lemieux (2009, 以下簡稱 FFL), 在不可分離的模型架構 (nonseparable model ) 下, 假設條件分配不變 (unaffected conditional distribution), 提出非條件分量迴歸 (unconditional quantile regression)。 FFL的非條件分量迴歸能估計非條件分量部份效果 (unconditional quantile partial effect), 並以此分析政策。 但是在實證研究的應用上, 由於解釋變數可能具有內生性, 這將導致條件分配不變的假設難以成立, 進而限縮非條件分量迴歸的實用性。 本文延伸 FFL 的非條件分量迴歸。 在不可分離的聯立模型架構 (nonseparable triangular simultaneous equations model ) 下, 我們建構一個內生解釋變數的非條件分量部份效果之估計式, 並在一般條件下, 證明此估計式具有一致性和常態的極限分配。我們藉由引入控制變數 (control variable), 避免了條件分配不變的假設。因此本文的估計方法將更適用於實證研究。 此外, 我們提出在給定分量下, 針對非條件分量部份效果線性假設的檢定統計量。 模擬的結果顯示, 當樣本數充份大時, 本文的估計方法能有效地降低 估計偏誤和均方差。

In this paper, we extend Firpo, Fortin, and Lemieux’s (2009) unconditional quantile regression in the presence of an endogenous variable X. An estimator for the unconditional quantile partial effect (UQPE) of X is constructed in a nonseparable triangular simultaneous equations model via a control variable approach. By introducing a control variable, we avoid the assumption of unaffected conditional distribution imposed in Firpo et al. (2009) so that our estimator is more generally applicable in many empirical studies. We demonstrate that our estimator for the UQPE is consistent and asymptotically normally distributed under some regularity conditions. In addition, a quadratic-form test statistic is proposed to test linear hypotheses on the UQPE of all covariates for a given quantile. Finally, the results of Monte Carlo simulation suggest that our estimation of the UQPE of an endogenous variable effectively reduces the bias and mean square error when the sample size is sufficiently large.