Partial effects in non-linear panel data models with correlated random effects

2021 ◽  
Author(s):  
Jason Abrevaya ◽  
Yu-Chin Hsu
Keyword(s):  
Panel Data ◽  
Random Effects ◽  
Unobserved Heterogeneity ◽  
Data Models ◽  
Panel Data Models ◽  
New Concepts ◽  
Correlated Random Effects ◽  
Non Linear ◽  
Partial Effects

Summary Nonlinearity and heterogeneity are known to cause difficulties in estimating and interpreting partial effects. This paper provides a systematic characterization of the various partial effects in nonlinear panel data models that might be of interest to empirical researchers. The interpretation of the partial effects depends upon (i) whether the distribution of unobserved heterogeneity is treated as fixed or allowed to vary with covariates, and (ii) whether one is interested in particular covariate values or an average over such values. The characterization covers partial-effects concepts already in the literature but also includes new concepts for partial effects. A simple panel probit design highlights that the different partial effects can be quantitatively very different.

NONLINEAR PANEL DATA MODELS WITH DISTRIBUTION-FREE CORRELATED RANDOM EFFECTS

2021 ◽  
pp. 1-25
Author(s):  
Yu-Chin Hsu ◽  
Ji-Liang Shiu
Keyword(s):  
Panel Data ◽  
Data Model ◽  
Conditional Distribution ◽  
Unobserved Heterogeneity ◽  
Random Effect ◽  
Data Models ◽  
Panel Data Model ◽  
Panel Data Models ◽  
Likelihood Functions ◽  
Correlated Random Effects

Under a Mundlak-type correlated random effect (CRE) specification, we first show that the average likelihood of a parametric nonlinear panel data model is the convolution of the conditional distribution of the model and the distribution of the unobserved heterogeneity. Hence, the distribution of the unobserved heterogeneity can be recovered by means of a Fourier transformation without imposing a distributional assumption on the CRE specification. We subsequently construct a semiparametric family of average likelihood functions of observables by combining the conditional distribution of the model and the recovered distribution of the unobserved heterogeneity, and show that the parameters in the nonlinear panel data model and in the CRE specification are identifiable. Based on the identification result, we propose a sieve maximum likelihood estimator. Compared with the conventional parametric CRE approaches, the advantage of our method is that it is not subject to misspecification on the distribution of the CRE. Furthermore, we show that the average partial effects are identifiable and extend our results to dynamic nonlinear panel data models.

The Robustness of Conditional Logit for Binary Response Panel Data Models with Serial Correlation

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Do Won Kwak ◽  
Robert S. Martin ◽  
Jeffrey M. Wooldridge
Keyword(s):  
Panel Data ◽  
Unobserved Heterogeneity ◽  
Data Models ◽  
Monte Carlo Experiment ◽  
Parameter Estimates ◽  
Panel Data Models ◽  
Time Dimension ◽  
Conditional Logit ◽  
Serial Independence ◽  
Correlated Random Effects

Abstract We examine the conditional logit estimator for binary panel data models with unobserved heterogeneity. A key assumption used to derive the conditional logit estimator is conditional serial independence (CI), which is problematic when the underlying innovations are serially correlated. A Monte Carlo experiment suggests that the conditional logit estimator is not robust to violation of the CI assumption. We find that higher persistence and smaller time dimension both increase the magnitude of the bias in slope parameter estimates. We also compare conditional logit to unconditional logit, bias corrected unconditional logit, and pooled correlated random effects logit.

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