Working Paper: NBER ID: w20374
Authors: Marinho Bertanha; Petra Moser
Abstract: Count data regressions are an important tool for empirical analyses ranging from analyses of patent counts to measures of health and unemployment. Along with negative binomial, Poisson panel regressions are a preferred method of analysis because the Poisson conditional fixed effects maximum likelihood estimator (PCFE) and its sandwich variance estimator are consistent even if the data are not Poisson-distributed, or if the data are correlated over time. Analyses of counts may be affected by correlation in the cross-section. For example, patent counts or publications may increase across related research fields in response to common shocks. This paper shows that the PCFE and its sandwich variance estimator are consistent in the presence of such dependence in the cross-section - as long as spatial dependence is time-invariant. In addition to the PCFE, this result also applies to the commonly used Logit model of panel data with fixed effects. We develop a test for time-invariant spatial dependence and provide code in STATA and MATLAB to implement the test.
Keywords: Count Data; Poisson Regression; Spatial Dependence
JEL Codes: C23; C33; O3
Edges that are evidenced by causal inference methods are in orange, and the rest are in light blue.
| Cause | Effect |
|---|---|
| spatial dependence is time-invariant (C49) | PCFE estimator remains consistent and asymptotically normal (C51) |
| spatial dependence exists across the cross-section (C21) | PCFE estimator remains consistent and asymptotically normal (C51) |
| spatial dependence is time-invariant (C49) | asymptotic distribution of PCFE under spatial dependence does not differ from that under spatial independence (C21) |
| asymptotic variance of PCFE when accounting for time-invariant spatial dependence = variance under spatial independence (C21) | sandwich variance estimator is consistent (C20) |
| spatial dependence is time-variant (C49) | sandwich variance estimator may be inconsistent (C20) |
| Wald test statistic tests for time-invariant spatial dependence (C21) | if null hypothesis of time-invariance is rejected, sandwich variance estimator may not be reliable (C20) |