An Introduction to Modern Econometrics Using Stata

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1 An Introduction to Modern Econometrics Using Stata CHRISTOPHER F. BAUM Department of Economics Boston College A Stata Press Publication StataCorp LP College Station, Texas

2 Contents Illustrations Preface Notation and typography xv xvii xix 1 Introduction An overview of Stata's distinctive features Installing the necessary software Installing the support materials 5 2 Working with economic and financial data in Stata The basics The use command Variable types _n and _N generate and replace sort and gsort if exp and in range Using if exp with indicator variables Using if exp versus by varlist: with statistical commands Labels and notes The varlist drop and keep rename and renvars The save command insheet and infile 21

3 viii 2 2 Common data transformations The cond() function Recoding discrete and continuous variables Handling missing data mvdecode and mvencode String-to-numeric conversion and vice versa Handling dates Contents Some useful functions for generate or replace The egen command 30 Official egen functions 30 egen functions from the user community Computation for by-groups Local macros Looping over variables: forvalues and foreach Scalars and matrices Command syntax and return values 39 3 Organizing and handling economic data Cross-sectional data and identifier variables Time-series data Time-series operators Pooled cross-sectional time-series data Panel data Operating on panel data Tools for manipulating panel data Unbalanced panels and data screening Other transforms of panel data Moving-window summary statistics and correlations Combining cross-sectional and time-series datasets Creating long-format datasets with append Using merge to add aggregate characteristics

4 Contents ix The dangers of many-to-many merges The reshape command The xpose command Using Stata for reproducible research Using do-files Data validation: assert and duplicates 63 4 Linear regression Introduction Computing linear regression estimates Regression as a method-of-moments estimator The sampling distribution of regression estimates Efficiency of the regression estimator Numerical identification of the regression estimates Interpreting regression estimates Research project: A study of single-family housing prices The ANOVA table: ANOVA F and R-squared Adjusted R-squared The coefficient estimates and beta coefficients Regression without a constant term Recovering estimation results Detecting collinearity in regression Presenting regression estimates Presenting summary statistics and correlations Hypothesis tests, linear restrictions, and constrained least squares Wald tests with test Wald tests involving linear combinations of parameters Joint hypothesis tests Testing nonlinear restrictions and forming nonlinear combinations Testing competing (nonnested) models 100

5 χ Contents 4.6 Computing residuals and predicted values Computing interval predictions Computing marginal effects 4.A Appendix: Regression as a least-squares estimator B Appendix: The large-sample VCE for linear regression Specifying the functional form 5.1 Introduction Specification error Omitting relevant variables from the model 116 Specifying dynamics in time-series regression models Graphically analyzing regression data Added-variable plots Including irrelevant variables in the model The asymmetry of specification error Misspecification of the functional form Ramsey's RESET Specification plots Specification and interaction terms Outlier statistics and measures of leverage 126 The DFITS statistic 128 The DFBETA statistic Endogeneity and measurement error Regression with non-i.i.d. errors The generalized linear regression model Types of deviations from i.i.d. errors The robust estimator of the VCE The cluster estimator of the VCE The Newey-West estimator of the VCE The generalized least-squares estimator 142 The FGLS estimator 143

6 Contents xi 6.2 Heteroskedasticity in the error distribution Heteroskedasticity related to scale 144 Testing for heteroskedasticity related to scale 145 FGLS estimation Heteroskedasticity between groups of observations 149 Testing for heteroskedasticity between groups of observations. 150 FGLS estimation Heteroskedasticity in grouped data 152 FGLS estimation Serial correlation in the error distribution Testing for serial correlation FGLS estimation with serial correlation Regression with indicator variables Testing for significance of a qualitative factor Regression with one qualitative measure Regression with two qualitative measures 165 Interaction effects Regression with qualitative and quantitative factors 168 Testing for slope differences Seasonal adjustment with indicator variables Testing for structural stability and structural change Constraints of continuity and differentiability Structural change in a time-series model Instrumental-variables estimators Introduction Endogeneity in economic relationships SLS The ivreg command Identification and tests of overidentifying restrictions Computing IV estimates 192

7 xii Contents ivreg2 and GMM estimation The GMM estimator GMM in a homoskedastic context GMM and heteroskedasticity-consistent standard errors GMM and clustering GMM and HAC standard errors Testing overidentifying restrictions in GMM Testing a subset of the overidentifying restrictions in GMM Testing for heteroskedasticity in the IV context Testing the relevance of instruments Durbin-Wu-Hausman tests for endogeneity in IV estimation A Appendix: Omitted-variables bias Β Appendix: Measurement error B.1 Solving errors-in-variables problems Panel-data models FE and RE models One-way FE Time effects and two-way FE The between estimator One-way RE Testing the appropriateness of RE Prediction from one-way FE and RE IV models for panel data Dynamic panel-data models Seemingly unrelated regression models SUR with identical regressors Moving-window regression estimates Models of discrete and limited dependent variables Binomial logit and probit models The latent-variable approach 2 4 8

8 Contents xiii Marginal effects and predictions 250 Binomial probit 251 Binomial logit and grouped logit Evaluating specification and goodness of fit Ordered logit and probit models Truncated regression and tobit models Truncation Censoring Incidental truncation and sample-selection models Bivariate probit and probit with selection Binomial probit with selection 272 A Getting the data into Stata 277 A.1 Inputting data from ASCII text files and spreadsheets 277 A.I.I Handling text files 278 Free format versus fixed format 278 The insheet command 280 A.I.2 Accessing data stored in spreadsheets 281 A.1.3 Fixed-format data files 281 A.2 Importing data from other package formats 286 Β The basics of Stata programming 289 B.I Local and global macros 290 B.I.I Global macros 293 B.1.2 Extended macro functions and list functions 293 B.2 Scalars 294 B.3 Loop constructs 295 B.3.1 foreach 297 B.4 Matrices 299 B.5 return and ereturn 301 B.5.1 ereturn list 305

9 xiv Contents Β.6 The program and syntax statements 307 B.7 Using Mata functions in Stata programs 313 References 321 Author index 329 Subject index 333

List of Figures. List of Tables. Preface to the Second Edition. Preface to the First Edition

List of Figures. List of Tables. Preface to the Second Edition. Preface to the First Edition List of Figures List of Tables Preface to the Second Edition Preface to the First Edition xv xxv xxix xxxi 1 What Is R? 1 1.1 Introduction to R................................ 1 1.2 Downloading and Installing