
Contents
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7.1 Introduction 7.1 Introduction
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7.2 Static Panel Conditional Logit 7.2 Static Panel Conditional Logit
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7.2.1 Log-likelihood Function for Static PCLE 7.2.1 Log-likelihood Function for Static PCLE
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7.2.2 Special Cases with Two and Three Periods 7.2.2 Special Cases with Two and Three Periods
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7.2.3 Further Remarks 7.2.3 Further Remarks
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7.2.3.1 PCLE Literature 7.2.3.1 PCLE Literature
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7.2.3.2 PCLE for Grouped Cross-Section Data 7.2.3.2 PCLE for Grouped Cross-Section Data
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7.2.3.3 Odds Ratio and Marginal Effect 7.2.3.3 Odds Ratio and Marginal Effect
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7.2.3.4 Time-Varying Parameters 7.2.3.4 Time-Varying Parameters
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7.2.3.5 Dynamics in Panel Logit Model 7.2.3.5 Dynamics in Panel Logit Model
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7.3 Dynamic Panel Conditional Logit 7.3 Dynamic Panel Conditional Logit
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7.3.1 Four Periods or More with No Regressor 7.3.1 Four Periods or More with No Regressor
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7.3.2 Four Periods with the Same Last Two-Period Regressors 7.3.2 Four Periods with the Same Last Two-Period Regressors
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7.3.3 Three Periods or More With Regressors 7.3.3 Three Periods or More With Regressors
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7.3.3.1 Three Periods or More without yT Conditioned on 7.3.3.1 Three Periods or More without yT Conditioned on
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7.3.3.2 Four Periods or More with yT Conditioned on 7.3.3.2 Four Periods or More with yT Conditioned on
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7.3.3.3 Three Periods or More Using an Estimator for δi 7.3.3.3 Three Periods or More Using an Estimator for δi
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7.4 Panel Conditional Ordered Logit 7.4 Panel Conditional Ordered Logit
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7.4.1 Three Categories 7.4.1 Three Categories
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7.4.2 Four Categories 7.4.2 Four Categories
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7.4.3 PCLE with More than Enough Waves 7.4.3 PCLE with More than Enough Waves
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7.5 Panel Conditional Multinomial Logit (PCML) 7.5 Panel Conditional Multinomial Logit (PCML)
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7.5.1 Conditional Likelihood for Three Alternatives and Two Periods 7.5.1 Conditional Likelihood for Three Alternatives and Two Periods
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7.5.2 General Cases 7.5.2 General Cases
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7.5.3 PCML Model Variations and Applied Studies 7.5.3 PCML Model Variations and Applied Studies
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7.6 Conclusions 7.6 Conclusions
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Acknowledgments Acknowledgments
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References References
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7 Panel Conditional and Multinomial Logit Estimators
Get accessProfessor in the Department of Economics at Korea University
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Published:05 May 2015
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Extract
Introduction
Micro panel data models for many individuals over only a few periods are often postulated to contain ‘incidental parameters’ which vary across individuals, along with ‘structural parameters’ which are common for all individuals. For instance, consider a panel linear model
...
where yit is a response variable of individual i at time t, xit is a kx × 1 regressor vector, β is a parameter, δi is a time-constant error (‘individual-specific effect’) and uit is a time-varying error. Here δi may be taken as a parameter to estimate, in which case δi is an incidental parameter whereas β that is common to all individuals is a structural parameter (of interest).
Clearly, δi cannot be consistently estimated in short panels, and thus it should be taken as a random variable just as yit, xit and uit are. In this case, the main concern has been that δi might be the main source of xit endogeneity; e.g., δi may represent genes or innate ability that influence yit. In cross-section data, there are several approaches to deal with an endogenous xit as reviewed in Lee (2012), but all of them require an instrument one way or another. In contrast, panel data do not necessarily need an instrument, as they provide a number of ways to get rid of δi.
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