Non-parametric Panel Data Models with Interactive Fixed Effects

This article studies non-parametric panel data models with multidimensional, unobserved individual effects when the number of time periods is fixed. I focus on models where the unobservables have a factor structure and enter an unknown structural function non-additively. The setup allows the individual effects to impact outcomes differently in different time periods and it allows for heterogeneous marginal effects. I provide sufficient conditions for point identification of all parameters of the model. Furthermore, I present a non-parametric sieve maximum likelihood estimator as well as flexible semiparametric and parametric estimators. Monte Carlo experiments demonstrate that the estimators perform well in finite samples. Finally, in an empirical application, I use these estimators to investigate the relationship between teaching practice and student achievement. The results differ considerably from those obtained with commonly used panel data methods.

[1]  Semiparametric Estimators , 2018, Wiley Series in Probability and Statistics.

[2]  Yuya Sasaki,et al.  Heterogeneity and selection in dynamic panel data , 2015 .

[3]  Yingyao Hu,et al.  Identification and estimation of nonlinear models using two samples with nonclassical measurement errors , 2010, Journal of nonparametric statistics.

[4]  Y. Shao,et al.  Asymptotics for likelihood ratio tests under loss of identifiability , 2003 .

[5]  Bo E. Honoré,et al.  Bounds on Parameters in Panel Dynamic Discrete Choice Models , 2006 .

[6]  K. Judd.  Numerical methods in economics , 1998 .

[7]  Richard Blundell,et al.  Endogeneity in Nonparametric and Semiparametric Regression Models , 2022 .

[8]  Susanne M. Schennach,et al.  Instrumental Variable Treatment of Nonclassical Measurement Error Models , 2008 .

[9]  H. White,et al.  Nonparametric Identification in Nonseparable Panel Data Models with Generalized Fixed Effects , 2009 .

[10]  Serena Ng,et al.  Principal Components Estimation and Identication of the Factors , 2011 .

[11]  Alexander Meister,et al.  On deconvolution with repeated measurements , 2008 .

[12]  M. Shum,et al.  Nonparametric identification of dynamic models with unobserved state variables , 2008 .

[13]  Xiaohong Chen,et al.  Efficient Estimation of Models with Conditional Moment Restrictions Containing Unknown Functions , 2003 .

[14]  Gary Chamberlain,et al.  Binary Response Models for Panel Data: Identification and Information , 2010 .

[15]  M. Weidner,et al.  Linear Regression for Panel with Unknown Number of Factors as Interactive Fixed Effects , 2014 .

[16]  J. Bai,et al.  Panel Data Models With Interactive Fixed Effects , 2009 .

[17]  W. Wong,et al.  Convergence Rate of Sieve Estimates , 1994 .

[18]  J. Powell,et al.  Identification and Estimation of Average Partial Effects in “Irregular” Correlated Random Coefficient Panel Data Models , 2012 .

[19]  Xavier D'Haultfoeuille,et al.  ON THE COMPLETENESS CONDITION IN NONPARAMETRIC INSTRUMENTAL PROBLEMS , 2010, Econometric Theory.

[20]  S. Bonhomme,et al.  Consistent noisy independent component analysis , 2008 .

[21]  Liangjun Su,et al.  Sieve estimation of panel data models with cross section dependence , 2012 .

[22]  Cristina Lopez-Mayan,et al.  Teaching Styles and Achievement: Student and Teacher Perspectives , 2015, Economics of Education Review.

[23]  Arthur A. Hyde,et al.  Best Practice: New Standards for Teaching and Learning in America's Schools , 1993 .

[24]  Daniel A. Ackerberg,et al.  A Practical Asymptotic Variance Estimator for Two-Step Semiparametric Estimators , 2011, Review of Economics and Statistics.

[25]  J. Bai,et al.  Inferential Theory for Factor Models of Large Dimensions , 2003 .

[26]  H. White,et al.  SOME EXTENSIONS OF A LEMMA OF KOTLARSKI , 2012, Econometric Theory.

[27]  J. Bai,et al.  Determining the Number of Factors in Approximate Factor Models , 2000 .

[28]  A. Gallant,et al.  Semi-nonparametric Maximum Likelihood Estimation , 1987 .

[29]  M. Pesaran.  Estimation and Inference in Large Heterogeneous Panels with a Multifactor Error Structure , 2004, SSRN Electronic Journal.

[30]  James J. Heckman,et al.  The Importance of Bundling in a Gorman-Lancaster Model of Earnings , 1987 .

[31]  Albert Madansky,et al.  Instrumental variables in factor analysis , 1964 .

[32]  Xiaohong Chen,et al.  Sensitivity Analysis in Semiparametric Likelihood Models , 2011 .

[33]  M. Weidner.  Semiparametric Estimation of Nonlinear Panel Data Models with Generalized Random Effects , 2011 .

[34]  Kirill S. Evdokimov.  Identification and Estimation of a Nonparametric Panel Data Model with Unobserved Heterogeneity ∗ , 2009 .

[35]  Gary Chamberlain,et al.  Efficiency Bounds for Semiparametric Regression , 1992 .

[36]  G. Imbens,et al.  Identification and Estimation of Triangular Simultaneous Equations Models without Additivity , 2002 .

[37]  Richard M. Dudley,et al.  Invariance principles for sums of Banach space valued random elements and empirical processes , 1983 .

[38]  Xiaohong Chen.  Chapter 76 Large Sample Sieve Estimation of Semi-Nonparametric Models , 2007 .

[39]  Identification of Marginal Effects in a Nonparametric Correlated Random Effects Model , 2009 .

[40]  Stéphane Bonhomme,et al.  Identifying distributional characteristics in random coefficients panel data models , 2009 .

[41]  W. Newey,et al.  Large sample estimation and hypothesis testing , 1986 .

[42]  J. Heckman,et al.  The Effects of Cognitive and Noncognitive Abilities on Labor Market Outcomes and Social Behavior , 2006, Journal of Labor Economics.

[43]  Victor Lavy.  What Makes an Effective Teacher? Quasi-Experimental Evidence , 2011 .

[44]  Jan Bietenbeck,et al.  Teaching practices and cognitive skills , 2014 .

[45]  Kirill S. Evdokimov.  Nonparametric Identification of a Nonlinear Panel Model with Application to Duration Analysis with Multiple Spells ∗ , 2010 .

[46]  Christian Hansen,et al.  Identification of Marginal Effects in a Nonparametric Correlated Random Effects Model , 2006 .

[47]  Azeem M. Shaikh,et al.  On the Testability of Identification in Some Nonparametric Models With Endogeneity , 2012 .

[48]  T. Dee.  Teachers and the Gender Gaps in Student Achievement , 2005, The Journal of Human Resources.

[49]  Jan Bietenbeck,et al.  TEACHING PRACTICES AND STUDENT ACHIEVEMENT , 2011 .

[50]  E. Fama,et al.  Dissecting Anomalies , 2007 .

[51]  W. Newey,et al.  Estimating vector autoregressions with panel data , 1988 .

[52]  J. Heckman,et al.  Formulating, Identifying and Estimating the Technology of Cognitive and Noncognitive Skill Formation , 2012 .

[53]  Arthur A. Hyde,et al.  Best Practice: Bringing Standards to Life in America's Classrooms , 2012 .

[54]  W. Newey,et al.  Instrumental variable estimation of nonparametric models , 2003 .

[55]  H. Bierens.  Consistency and Asymptotic Normality of Sieve Estimators Under Weak and Verifiable Conditions , 2011 .

[56]  Jushan Bai,et al.  NOTES AND COMMENTS FIXED-EFFECTS DYNAMIC PANEL MODELS, A FACTOR ANALYTICAL METHOD , 2013 .

[57]  Daniel Wilhelm,et al.  Identification and estimation of nonparametric panel data regressions with measurement error , 2015 .

[58]  Peter A. Youngs,et al.  Teacher Characteristics and Student Achievement Gains: A Review , 2003 .

[59]  Rosa L. Matzkin,et al.  Cross Section and Panel Data Estimators for Nonseparable Models with Endogenous Regressors , 2005 .

[60]  Manuel Arellano,et al.  Nonlinear Panel Data Analysis , 2011 .

[61]  Rosa L. Matzkin.  Nonparametric Estimation of Nonadditive Random Functions , 2003 .

[62]  D. Andrews,et al.  Cross-Section Regression with Common Shocks , 2003 .

[63]  Jianqing Fan.  On the Optimal Rates of Convergence for Nonparametric Deconvolution Problems , 1991 .

[64]  Helen F. Ladd,et al.  Teacher Credentials and Student Achievement in High School: A Cross-Subject Analysis with Student Fixed Effects , 2007 .

[65]  Peter Schmidt,et al.  GMM estimation of linear panel data models with time-varying individual effects , 2001 .

[66]  J. Heckman,et al.  Estimating Distributions of Treatment Effects with an Application to the Returns to Schooling and Measurement of the Effects of Uncertainty on College Choice , 2003, SSRN Electronic Journal.

[67]  Yingyao Hu,et al.  Identification and estimation of nonlinear models with misclassification error using instrumental variables: A general solution , 2008 .

[68]  Yingyao Hu,et al.  Identification and estimation of nonlinear dynamic panel data models with unobserved covariates , 2013 .

[69]  Guido Schwerdt,et al.  Is Traditional Teaching Really All That Bad? A Within-Student Between-Subject Approach , 2009, SSRN Electronic Journal.

[70]  W. Newey,et al.  Average and Quantile Effects in Nonseparable Panel Models , 2009, 0904.1990.

[71]  Victor Lavy,et al.  What Makes an Effective Teacher? Quasi-Experimental Evidence. NBER Working Paper No. 16885. , 2011 .

[72]  L. Mattner,et al.  Some incomplete but boundedly complete location families , 1993 .

[73]  Advances in Economics and Econometrics: Endogeneity in Nonparametric and Semiparametric Regression Models , 2003 .

[74]  Seung C. Ahn,et al.  Panel Data Models with Multiple Time-Varying Individual Effects , 2013 .

[75]  Xiao Huang.  Nonparametric Estimation in Large Panels with Cross-Sectional Dependence , 2013 .