Identification and Estimation of &Apos;Irregular&Apos; Correlated Random Coefficient Models
Identification and Estimation of &Apos;Irregular&Apos; Correlated Random Coefficient Models
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识别和估计
DOI：
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发表时间：
2008
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通讯作者：
J. Powell
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文献类型：
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作者：
B. Graham;J. Powell
本文研究了相关随机系数（CRC）面板数据模型的辨识与估计。感兴趣的结果随内生回归量的向量线性变化。这些回归量的系数在单位之间是异质的，并且可能与它们共变。我们考虑回归向量的微小变化对结果的平均偏效应（APE） （cf., Chamberlain, 1984; Wooldridge, 2005）。Chamberlain（1992）计算了我们模型中APE的半参数效率界，并提出了&radic；<span style="text-decoration:overline；"><i>N</i></span>一致性估计。ape的非奇异性；我们的信息是有限的，因此张伯伦的说法是恰当的。s（1992）估计量，要求(i)面板的时间维数（<i>T</i>）严格超过随机系数的个数（<i>p</i>）和（ii）回归量向量的时间序列性质的强条件。当<i>T</i> = <i>p</i>和更持久的回归过程时，我们证明了APE的不规则识别。我们的方法利用了滞留者亚群中不同的识别信息。——或者回归量值在不同时期变化不大的单位——以及移动量；——或回归量值在不同时期发生重大变化的单位。在此基础上提出了一种可行估计器，并对其大样本特性进行了表征。虽然不规则性使我们的估计器无法获得参数收敛率，但它的极限分布是正态的，推理是直接进行的。标准软件可用于计算点估计和标准误差。我们使用我们的方法来估计卡路里消费的平均弹性相对于总支出为一个贫穷的尼加拉瓜家庭的样本。
In this paper we study identification and estimation of a correlated random coefficients (CRC) panel data model. The outcome of interest varies linearly with a vector of endogenous regressors. The coefficients on these regressors are heterogenous across units and may covary with them. We consider the average partial effect (APE) of a small change in the regressor vector on the outcome (cf., Chamberlain, 1984; Wooldridge, 2005a). Chamberlain (1992) calculates the semiparametric efficiency bound for the APE in our model and proposes a √<span style="text-decoration:overline;"><i>N</i></span> consistent estimator. Nonsingularity of the APE's information bound, and hence the appropriateness of Chamberlain's (1992) estimator, requires (i) the time dimension of the panel (<i>T</i>) to strictly exceed the number of random coefficients (<i>p</i>) and (ii) strong conditions on the time series properties of the regressor vector. We demonstrate irregular identification of the APE when <i>T</i> = <i>p</i> and for more persistent regressor processes. Our approach exploits the different identifying information in the subpopulations of 'stayers' -- or units whose regressor values change little across periods -- and 'movers' -- or units whose regressor values change substantially across periods. We propose a feasible estimator based on our identification result and characterize its large sample properties. While irregularity precludes our estimator from attaining parametric rates of convergence, it limiting distribution is normal and inference is straightforward to conduct. Standard software may be used to compute point estimates and standard errors. We use our methods to estimate the average elasticity of calorie consumption with respect to total outlay for a sample of poor Nicaraguan households.