Conditional inference for binary panel data models with predetermined covariates

Abstract A fixed-effects logit model that accounts for feedback effects of the dependent variable on the covariates is proposed. The model is formulated by including leads of the predetermined covariates among the regressors and it is proved to satisfy certain theoretical properties under some regularity conditions on the distribution of the covariates. Estimation is based on the Conditional Maximum Likelihood ( cml ) method for the static logit model and the Pseudo- cml ( pcml ) method for the corresponding dynamic formulation. Both methods have good finite-sample properties even when the required regularity conditions are not satisfied. An application is provided about female labor supply where we jointly account for the predetermined number of children and husbands’ income. Differently from previous studies, it emerges that female employment history does not affect future fertility choices and the husband’s earnings, as no evidence of feedback effects is found.

[1]  L. Hansen.  Large Sample Properties of Generalized Method of Moments Estimators , 1982 .

[2]  Jinyong Hahn,et al.  JACKKNIFE AND ANALYTICAL BIAS REDUCTION FOR NONLINEAR PANEL MODELS , 2003 .

[3]  Furkan Emirmahmutoglu,et al.  Testing for Granger Causalityin Heterogeneous Mixed Panels , 2011 .

[4]  Gary Chamberlain,et al.  Analysis of Covariance with Qualitative Data , 1979 .

[5]  Jinyong Hahn,et al.  BIAS REDUCTION FOR DYNAMIC NONLINEAR PANEL MODELS WITH FIXED EFFECTS , 2011, Econometric Theory.

[6]  R. Blundell,et al.  Initial Conditions and Moment Restrictions in Dynamic Panel Data Models , 1998 .

[7]  Jeffrey M. Wooldridge,et al.  Solutions Manual and Supplementary Materials for Econometric Analysis of Cross Section and Panel Data , 2003 .

[8]  Francesco Bartolucci,et al.  Pseudo Conditional Maximum Likelihood Estimation of the Dynamic Logit Model for Binary Panel Data , 2009 .

[9]  J. Heckman.  Heterogeneity and State Dependence , 1981 .

[10]  J. F. C. Kingman,et al.  Information and Exponential Families in Statistical Theory , 1980 .

[11]  P. Michaud,et al.  Fertility and Female Employment Dynamics in Europe: The Effect of Using Alternative Econometric Modeling Assumptions , 2008, SSRN Electronic Journal.

[12]  C. Granger.  Investigating Causal Relations by Econometric Models and Cross-Spectral Methods , 1969 .

[13]  M. Arellano,et al.  Another look at the instrumental variable estimation of error-components models , 1995 .

[14]  Raquel Carrasco,et al.  Binary Choice With Binary Endogenous Regressors in Panel Data , 2001 .

[15]  Bo E. Honoré,et al.  Panel Data Discrete Choice Models with Lagged Dependent Variables , 2000 .

[16]  J. Neyman,et al.  Consistent Estimates Based on Partially Consistent Observations , 1948 .

[17]  C. Sims.  Money, Income, and Causality , 1972 .

[18]  J. Florens,et al.  A Note on Noncausality , 1982 .

[19]  Gary Chamberlain,et al.  Longitudinal Analysis of Labor Market Data: Heterogeneity, omitted variable bias, and duration dependence , 1985 .

[20]  Y. Mundlak.  On the Pooling of Time Series and Cross Section Data , 1978 .

[21]  Raquel Carrasco,et al.  Binary choice panel data models with predetermined variables , 2003 .

[22]  D. Cox.  The Analysis of Multivariate Binary Data , 1972 .

[23]  Francesco Bartolucci,et al.  A Dynamic Model for Binary Panel Data With Unobserved Heterogeneity Admitting a √n‐Consistent Conditional Estimator , 2007 .

[24]  Gary Chamberlain,et al.  Chapter 22 Panel data , 1984 .

[25]  M. Arellano,et al.  Some Tests of Specification for Panel Data: Monte Carlo Evidence and an Application to Employment Equations , 1991 .

[26]  Jeffrey M. Wooldridge,et al.  The Initial Conditions Problem in Dynamic, Nonlinear Panel Data Models with Unobserved Heterogeneity , 2002 .

[27]  Cheng Hsiao,et al.  Analysis of Panel Data , 1987 .

[28]  E. Dumitrescu,et al.  Testing for Granger Non-causality in Heterogeneous Panels , 2012 .

[29]  Ivan Fernandez-Val,et al.  Fixed effects estimation of structural parameters and marginal effects in panel probit models , 2007 .

[30]  Gary Chamberlain,et al.  The General Equivalence of Granger and Sims Causality , 1982 .

[31]  Francesco Bartolucci,et al.  cquad: An R and Stata Package for Conditional Maximum Likelihood Estimation of Dynamic Binary Panel Data Models , 2017 .

[32]  Bo E. Honoré,et al.  Semiparametric Binary Choice Panel Data Models without Strictly Exogeneous Regressors , 2000 .

[33]  Cheng Hsiao,et al.  Estimation of Dynamic Models with Error Components , 1981 .

[34]  Alessandra Salvan,et al.  Modified Profile Likelihood for Fixed-Effects Panel Data Models , 2016 .

[35]  Jeffrey M. Wooldridge,et al.  A framework for estimating dynamic, unobserved effects panel data models with possible feedback to future explanatory variables , 2000 .

[36]  E. B. Andersen,et al.  Asymptotic Properties of Conditional Maximum‐Likelihood Estimators , 1970 .

[37]  Jesus M. Carro.  Estimating Dynamic Panel Data Discrete Choice Models with Fixed Effects , 2003 .

[38]  Raffaello Seri,et al.  Non-Causality in Bivariate Binary Time Series , 2006 .