A General Panel Model for Unobserved Time Heterogeneity with Application to the Politics of Mass Incarceration

Scott W Duxbury

doi:10.1177/00811750211016033

Abstract

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.

Highlights

Panel data analysis is common in the social sciences
Two-way fixed effects models that allow for covariance with unmeasured period effects are the dominant approach for addressing time heterogeneity (Imai and Kim forthcoming; Wooldridge 2010), but two-way fixed effects models eliminate common trends: the portion of variance in a time-varying variable that is invariant across cross-sectional units
This study introduced a general panel model for unobserved time heterogeneity that allows for covariance with unmeasured between effects, can include timeinvariant and unit-invariant variables, and provides the coefficient for common trends

Summary

A GENERAL PANEL MODEL FOR UNOBSERVED TIME HETEROGENEITY

I introduce a panel model for unobserved time heterogeneity that provides the homogenous-within effect of common trends, the between effect of unit differences, and the idiosyncratic effect usually provided by two-way fixed effects models. X :tbHW e:t uit means and between effects; unmeasured between effects; unmeasured period effects; random error Idiosyncratic variation and idiosyncratic effect; time over time (bHW ), and specific-city change whereby crime rates in some cities increase more rapidly than others (bI ). In an analysis of students’ academic performance, we could examine the section means and between determinants of within-student effects; unmeasured change (bW ) and between-student between effect; unmeasured period effect; random error differences (bB) while allowing for unmeasured time heterogeneity, assuming the unmeasured period effect does not correlate with X. In an analysis of students’ performance, we could examine the determinants of within-student change (bW ) allowing for unmeasured time heterogeneity, assuming the unmeasured period effect does not correlate with X, but we could not examine betweenstudent differences (bB).

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Summary

Findings

CONCLUSION