Implementations of tests on the exogeneity of selected variables and their Performance in practice ACADEMISCH PROEFSCHRIFT ter verkrijging van de graad van doctor aan de Universiteit van Amsterdam op gezag van de Rector Magnificus prof. dr. D.C. van den Boom ten overstaan van een door het College voor promoties ingestelde commissie, in het openbaar te verdedigen in de Agnietenkapel op vrijdag 29 mei 2015, te 14:00 uur door Milan Pleus geboren te Naarden
Contents 1 Introduction 1 1.1 Outline of the thesis 4 2 The performan.ee of tests on endogeneity of subsets of explanatory variables scanned by Simulation 7 2.1 Introduction 7 2.2 Testing the orthogonality of subsets of explanatory variables 10 2.2.1 The model and setting 10 2.2.2 The source of any estimator discrepancy 12 2.2.3 Testing based on the source of any discrepancy 15 2.2.4 Testing based on the discrepancy as such 19 2.2.5 Testing based on covariance of structural and reduced form disturbances 21 2.2.6 Testing by an incremental Sargan test 22 2.2.7 Concerns for practitioners 23 2.3 Earlier Monte Carlo designs and results 23 2.4 A more comprehensive Monte Carlo design 26 2.4.1 The simulated data generating process 26 2.4.2 Simulation design parameter space 27 2.5 Simulation Undings on rejection probabilities 31 2.5.1 At least one exogenous regressor 32 2.5.2 Both regressors endogenous 36 2.6 Results for bootstrapped tests 38 2.6.1 A bootstrap routine for subset DWH test statistics 38 2.6.2 Simulation results for bootstrapped test statistics 39 2.7 Empirical case study 41 2.8 Conclusions 42 iii
3 On overidentifying restrictions tests and their incremental versions 53 3.1 Introduction 53 3.2 Testing overidentifying restrictions 55 3.2.1 Test statistics and distributions 56 3.2.2 Power properties 61 3.3 Neglecting heteroskedasticity 65 3.4 A higher order refinement to the Sargan test 67 3.5 Simulation design 69 3.6 Simulation Undings on rejection probabilities 71 3.7 Conclusions 73 Appendix 3.A Proofs of theorems 75 Appendix 3.B Details on the correeted statistic 77 4 Accuracy and efficiency of various GMM inference techniques in dynamic micro panel data models: theory 85 4.1 Introduction 85 4.2 Basic GMM results for linear models 88 4.2.1 Model and estimators 88 4.2.2 Some algebraic peculiarities 90 4.2.3 Particular test procedures 91 4.3 Implementations for dynamic micro panel models 93 4.3.1 Model and assumptions 93 4.3.2 Removing individual effects by Erst differencing 94 4.3.3 Respecting the equation in levels as well 100 4.3.4 Coefficient restriction tests 105 4.3.5 Tests of overidentification restrictions 107 4.3.6 Modilied GMM 109 4.4 Intermediate conclusions 111 Appendix 4.A Correeted variance estimation for 2-step GMM 112 Appendix 4.B Partialling out and GMM 114 Appendix 4.C Extracting redundant moment conditions 115 5 Accuracy and efficiency of various GMM inference techniques in dynamic micro panel data models: practice 117 5.1 Introduction 117 5.2 Simulation design 118 5.3 Simulation results 125 iv
5.3.1 DGPs under effect stationarity 128 5.3.2 Nonstationarity 142 5.4 Empirical results 146 5.5 Major Undings 151 Appendix 5.A Derivations for (5.17) 153 6 Refined exogeneity tests in dynamic panel data models 155 6.1 Introduction 155 6.2 Exogeneity tests 157 6.2.1 Estimators and assumptions 157 6.2.2 Incremental Sargan-Hansen test 159 6.2.3 Hausman test 161 6.3 Some possible refinements 162 6.3.1 Diagonal Sargan-Hansen test 162 6.3.2 Finite sample corrected variance for the Hausman test 164 6.4 Testing exogeneity in dynamic panel data models 166 6.4.1 Model and assumptions 166 6.4.2 Füll comprehensive internal Instrument matrices 168 6.4.3 Estimators 169 6.4.4 Establishing endogeneity 171 6.4.5 Establishing weak exogeneity 173 6.5 Simulation design 174 6.6 Simulation results 176 6.6.1 Results under strict exogeneity 178 6.6.2 Results under weak exogeneity 180 6.6.3 Results under endogeneity 180 6.7 Empirical case study 181 6.8 Conclusions 184 Appendix 6.A Non-negativeness of Jj 2 ' 186 Appendix 6.B Proof of Theorem 6.1 188 Appendix 6.C Estimating the variance of the vector of contrasts 189 Appendix 6.D Correcting H 190 Bibliography 197 Surnmary 207 v
Samenvatting (Summary in Dutch) vi