摘要：本文的目的在于探讨和解释面板模型不同的固定效应估计的本质，说明面板数据的二维特性及由此带来的横截面维度和时间序列维度的变量之间相关关系的异质性问题，并对过去一些传统的关于面板数据的可能有偏差的理解予以说明更正。

　　我们在文中展示了：截面固定效应实际上是有线性约束的时间序列回归，回归系数是每个截面的时序回归的加权平均，时间固定效应实际是有线性约束的横截面回归，回归系数是每个时期的截面回归的加权平均；双向固定效应估计量则是混合效应，截面固定效应和时间固定效应估计量的加权平均；与Mundlak(1978)的结论类似，所谓“不可观测的异质性”实际上并不是完全不可观测的，过去传统的面板模型设置有一定的遗漏变量问题，真正不可观测的固定效应与回归元是无关的。

　　关键词：面板数据，固定效应，不可观测的异质性，相关异质性

The heterogeneity of correlation between cross-section

　　 and time series:

　　An Essay Revisiting Panel Data Model and its Fixed Effects Estimation

　　

Abstract: In the paper we aim to investigate and explain the essence of panel data model with varieties of fixed effects, discuss the two dimensional nature of panel data and the possible correlation heterogeneity between cross-section dimension and time series dimension, question and amend the conventional understanding and explanation that may be wrong. We show in the paper that: Cross-section fixed effects estimation is actually a time series regression with a linear constraint, the coefficient of estimation equals the weighted average of time series regression result for each Cross-section, Time fixed effects estimation is actually a cross-section regression with a linear constraint, the coefficient of estimation equals the weighted average of cross-section regression result for each period; Two way effects estimator whereas is the weighted average of pool, cross-section fixed and time fixed effects estimator; Silimar to the conclusion of Mundlak(1978), The so called “unobserved heterogeneity” actually is not really completely unobservable, the conventional panel data model setting is flawed by variable omission, and the real unobservable heterogeneities, in other words fixed effects, are uncorrelated with regressors.

Keywords: Panel data, Fixed effects, Unobserved Heterogeneity, Correlation Heterogeneity

　　JEL Classification Codes: C23, C51, C52