Panel data analysis is common in the social sciences. Fixed effects models are a favorite among sociologists because they control for unobserved heterogeneity (unexplained variation) among cross-sectional units, but estimates are biased when there is unobserved heterogeneity in the underlying time trends. Two-way fixed effects models adjust for unobserved time heterogeneity but are inefficient, cannot include unit-invariant variables, and eliminate common trends: the portion of variance in a time-varying variable that is invariant across cross-sectional units. This article introduces a general panel model that can include unit-invariant variables, corrects for unobserved time heterogeneity, and provides the effect of common trends while also allowing for unobserved unit heterogeneity, time-varying coefficients, and time-invariant variables. One-way and two-way fixed effects models are shown to be restrictive forms of this general model. Other restrictive forms are also derived that offer all the usual advantages of one-way and two-way fixed effects models but account for unobserved time heterogeneity. The author uses the models to examine the increase in state incarceration rates between 1970 and 2015.

面板数据分析在社会科学中很常见。固定效应模型在社会学家中是最喜欢的，因为它们控制横截面单元之间的未观察到的异质性（无法解释的变化），但是当基础时间趋势中存在未观察到的异质性时，估计值会产生偏差。双向固定效应模型可针对未观察到的时间异质性进行调整，但效率低下，不能包含单位不变变量，也不能消除常见趋势：时变变量中的变化部分在横截面单位上是不变的。本文介绍了一个通用面板模型，该模型可以包含单位不变变量，校正未观察到的时间异质性，并提供共同趋势的效果，同时还允许未观察到的单位异质性，时变系数和时不变变量。单向和双向固定效应模型显示为该通用模型的限制性形式。还导出了其他限制形式，这些形式提供了单向和双向固定效应模型的所有常规优点，但也说明了未观察到的时间异质性。作者使用这些模型研究了1970年至2015年之间的州监禁率上升情况。