Companion to Econometric Analysis of Panel Data

Badi H. Baltagi is Distinguished Professor of Economics, and Senior Research Associate at the Center for Policy Research, Syracuse University. He is a fellow of the Journal of Econometrics, a recipient of the Multa and Plura Scripsit Awards from Econometric Theory, and the Journal of Applied Econometrics Distinguished Authors Award.

• Preface xi1 Partitioned Regression and the Frisch–Waugh–Lovell Theorem 1Exercises1.1 Partitioned regression 11.2 The Frisch–Waugh–Lovell theorem 21.3 Residualing the constant 31.4 Adding a dummy variable for the ith observation 31.5 Computing forecasts and forecast standard errors 42 The One-way Error Component Model 92.1 The One-way Fixed Effects Model 9Exercises2.1 One-way fixed effects regression 102.2 OLS and GLS for fixed effects 112.3 Testing for fixed effects 122.2 The One-way Random Effects Model 12Exercises2.4 Variance–covariance matrix of the one-way random effects model 132.5 Fuller and Battese (1973) transformation for the one-way random effects model 142.6 Unbiased estimates of the variance components: the one-way model 152.7 Feasible unbiased estimates of the variance components: the one-way model 162.8 Gasoline demand in the OECD 172.9 System estimation of the one-way model: OLS versus GLS 222.10 GLS is a matrix weighted average of between and within 232.11 Efficiency of GLS compared to within and between estimators 242.12 Maximum likelihood estimation of the random effects model 252.13 Prediction in the one-way random effects model 262.14 Mincer wage equation 272.15 Bounds for s2 in a one-way random effects model 302.16 Heteroskedastic fixed effects models 313 The Two-way Error Component Model 353.1 The Two-way Fixed Effects Model 35Exercise3.1 Two-way fixed effects regression 363.2 The Two-way Random Effects Model 38Exercises3.2 Variance–covariance matrix of the two-way random effects model 383.3 Fuller and Battese (1973) transformation for the two-way random effects model 403.4 Unbiased estimates of the variance components: the two-way model 403.5 Feasible unbiased estimates of the variance components: the two-way model 413.6 System estimation of the two-way model: OLS versus GLS 423.7 Prediction in the two-way random effects model 443.8 Variance component estimation under misspecification 453.9 Bounds for s2, in a two-way random effects model 493.10 Nested effects 503.11 Three-way error component model 523.12 A mixed error component model 553.13 Productivity of public capital in private production 574 Test of Hypotheses Using Panel Data 654.1 Tests for Poolability of the Data 65Exercises4.1 Chow (1960) test 654.2 Roy (1957) and Zellner (1962) test 674.2 Tests for Individual and Time Effects 69Exercises4.3 Breusch and Pagan (1980) Lagrange multiplier test 694.4 Locally mean most powerful one-sided test 724.5 Standardized Honda (1985) test 734.6 Standardized King and Wu (1997) test 734.7 Conditional Lagrange multiplier test: random individual effects 744.8 Conditional Lagrange multiplier test: random time effects 774.9 Testing for poolability using Grunfeld’s data 794.10 Testing for random time and individual effects using Grunfeld’s data 804.3 Hausman’s Test for Correlated Effects 81Exercises4.11 Hausman (1978) test based on a contrast of two estimators 824.12 Hausman (1978) test based on an artificial regression 824.13 Three contrasts yield the same Hausman test 854.14 Testing for correlated effects in panels 864.15 Hausman’s test as a Gauss–Newton regression 894.16 Hausman’s test using Grunfeld’s data 894.17 Relative efficiency of the between estimator with respect to the within estimator 904.18 Hausman’s test using Munnell’s data 924.19 Currency Union and Trade 955 Heteroskedasticity and Serial Correlation 995.1 Heteroskedastic Error Component Model 99Exercises5.1 Heteroskedastic individual effects 995.2 An alternative heteroskedastic error component model 1005.3 An LM test for heteroskedasticity in a one-way error component model 1025.2 Serial Correlation in the Error Component Model 105Exercises5.4 AR(1) process 1055.5 Unbiased estimates of the variance components under the AR(1) model 1075.6 AR(2) process 1085.7 AR(4) process for quarterly data 1095.8 MA(1) process 1115.9 MA(q) process 1125.10 Prediction in the serially correlated error component model 1135.11 A joint LM test for serial correlation and random individual effects 1175.12 Conditional LM test for serial correlation assuming random individual effects 1195.13 An LM test for first-order serial correlation in a fixed effects model 1205.14 Gasoline demand example with first-order serial correlation 1215.15 Public capital example with first-order serial correlation 1236 Seemingly Unrelated Regressions with Error Components 125Exercises6.1 Seemingly unrelated regressions with one-way error component disturbances 1256.2 Unbiased estimates of the variance components of the one-way SUR model 1276.3 Special cases of the SUR model with one-way error component disturbances 1276.4 Seemingly unrelated regressions with two-way error component disturbances 1286.5 Unbiased estimates of the variance components of the two-way SUR model 1306.6 Special cases of the SUR model with two-way error component disturbances 1307 Simultaneous Equations with Error Components 1337.1 Single Equation Estimation 133Exercises7.1 2SLS as a GLS estimator 1337.2 Within 2SLS and between 2SLS 1347.3 Within 2SLS and between 2SLS as GLS estimators 1357.4 Error component two-stage least squares 1357.5 Equivalence of several EC2SLS estimators 1377.6 Hausman test based on FE2SLS vs EC2SLS 1397.2 System Estimation 143Exercises7.7 3SLS as a GLS estimator 1437.8 Within 3SLS and between 3SLS 1447.9 Within 3SLS and between 3SLS as GLS estimators 1447.10 Error component three-stage least squares 1467.11 Equivalence of several EC3SLS estimators 1487.12 Special cases of the simultaneous equations model with one-way error component disturbances 1497.3 Endogenous Effects 151Exercises7.13 Mundlak’s (1978) augmented regression 1517.14 Hausman and Taylor (1981) estimator 1547.15 Cornwell and Rupert (1988): Hausman and Taylor application 1567.16 Serlenga and Shin (2007): gravity models of intra-EU trade 1587.17 Cornwell and Trumbull (1994): crime in North Carolina 1628 Dynamic Panels 169Exercises8.1 Bias of OLS, FE and RE estimators in a dynamic panel data model 1698.2 Anderson and Hsiao (1981) estimator 1708.3 Arellano and Bond (1991) estimator 1708.4 Sargan’s (1958) test of overidentifying restrictions 1728.5 Ahn and Schmidt (1995) moment conditions 1748.6 Ahn and Schmidt (1995) additional moment conditions 1758.7 Arellano and Bond (1991) weak instruments 1768.8 Alternative transformations that wipe out the individual effects 1778.9 Arellano and Bover (1995) estimator 1808.10 Baltagi and Levin (1986): dynamic demand for cigarettes 1829 Unbalanced Panels 1879.1 The Unbalanced One-way Error Component Model 187Exercises9.1 Variance–covariance matrix of unbalanced panels 1879.2 Fixed effects for the one-way unbalanced panel data model 1899.3 Wallace and Hussain (1969)-type estimators for the variance components of a one-way unbalanced panel data model 1919.4 Comparison of variance component estimators using balanced vs unbalanced data 1929.2 The Unbalanced Two-way Error Component Model 195Exercises9.5 Fixed effects for the two-way unbalanced panel data model 1959.6 Fixed effects for the three-way unbalanced panel data model 1989.7 Random effects for the unbalanced two-way panel data model 1999.8 Random effects for the unbalanced three-way panel data model 2009.9 Wansbeek and Kapteyn (1989)-type estimators for the variance components of a two-way unbalanced panel data model 2019.3 Testing for Individual and Time Effects Using Unbalanced Panel Data 203Exercises9.10 Breusch and Pagan (1980) LM test for unbalanced panel data 2039.11 Locally mean most powerful one-sided test for unbalanced panel data 2059.12 Standardized Honda (1985) and King and Wu (1997) tests for unbalanced panel data 2079.13 Harrison and Rubinfeld (1978): hedonic housing 20810 Special Topics 21310.1 Measurement Error and Panel Data 213Exercise10.1 Measurement error and panel data 21310.2 Rotating Panels 217Exercises10.2 Rotating panel with two waves 21710.3 Rotating panel with three waves 21810.3 Spatial Panels 222Exercises10.4 Spatially autocorrelated error component model 22210.5 Random effects and spatial autocorrelation with equal weights 22410.4 Count Panel Data 229Exercises10.6 Poisson panel regression model 22910.7 Patents and R&D expenditures 23211 Limited Dependent Variables 235Exercises11.1 Fixed effects logit model 23511.2 Equivalence of two estimators of the fixed effects logit model 24011.3 Dynamic fixed effects logit model with no regressors 24211.4 Dynamic fixed effects logit model with regressors 24411.5 Binary response model regression 24611.6 Random effects probit model 24711.7 Identification in a dynamic binary choice panel data model 24811.8 Union membership 24911.9 Beer taxes and motor vehicle fatality rates 25112 Nonstationary Panels 25712.1 Panel Unit Root Tests 257Exercise12.1 Panel unit root tests: GDP of G7 countries 25812.2 Panel Cointegration Tests 260Exercises12.2 Panel cointegration tests: manufacturing shipment and inventories 26112.3 International R&D spillover 270References 277Index 287