INSEAD Library

Includes bibliographical references and index

Digitized

An Introduction to Modern Econometrics Using Stata Contents Illustrations Preface Notation and typography xv xvii xix 1 Introduction 1.1 1.2 1.3 1 An overview of Stata's distinctive features ...................................................... 1 Installing the necessary software ...................................................................4 Installing the support materials ................................................................... 5 7 2 Working with economic and financial data in Stata 2.1 The basics ...................................................................................................... 7 2.1.1 2.1.2 2.1.3 2.1.4 2.1.5 2.1.6 2.1.7 2.1.8 2.1.9 The use command .............................................................................7 Variable types ...................................................................................... 8 _n and _N............................................................................................... 9 generate and replace........................................................................ 10 sort and gsort ................................................................................ 10 if exp and in range ........................................................................... 11 Using if exp with indicator variables ................................................ 13 Using if exp versus by varlist: with statistical commands . . .......... 15 Labels and notes ............................................................................. 17 2.1.10 The varlist ...........................................................................................20 2.1.11 drop and keep .................................................................................. 20 2.1.12 rename and renvars ........................................................................ 21 2.1.13 The save command ............................................................................ 21 2.1.14 insheet and infile................................................................................ 21 viii Contents 2.2 Common data transformations ...................................................................... 22 2.2.1 2.2.2 2.2.3 The cond() function .......................................................................... 22 Recoding discrete and continuous variables ................................. 23 Handling missing data .................................................................. 24 mvdecode and mvencode ................................................................ 25 2.2.4 2.2.5 2.2.6 2.2.7 String-to-numeric conversion and vice versa.................................. 26 Handling dates ............................................................................... 27 Some useful functions for generate or replace ............................... 29 The egen command ......................................................................... 30 Official egen functions ...................................................................... 30 egen functions from the user community ...................................... 31 2.2.8 2.2.9 Computation for by-groups ............................................................ 33 Local macros .................................................................................... 36 2.2.10 Looping over variables: forvalues and foreach .................................. 37 2.2.11 Scalars and matrices ........................................................................39 2.2.12 Command syntax and return values ............................................... 39 3 Organizing and handling economic data 3.1 3.2 43 Cross-sectional data and identifier variables ...............................................43 Time-series data .......................................................................................... 44 3.2.1 Time-series operators ...................................................................... 45 3.3 Pooled cross-sectional time-series data ....................................................... 45 3.4 Panel data ....................................................................................................... 46 3.4.1 Operating on panel data ............................................................... 47 3.5 Tools for manipulating panel data .................................................................... 49 3.5.1 3.5.2 3.5.3 3.6 Unbalanced panels and data screening......................................... 50 Other transforms of panel data ..................................................... 53 Moving-window summary statistics and correlations ................... 53 Combining cross-sectional and time-series datasets ................................. 55 3.7 Creating long-format datasets with append .................................................... 56 3.7.1 Using merge to add aggregate characteristics .............................. 57 Contents 3.7.2 ix The dangers of many-to-many merges ........................................... 58 3.8 The reshape command .................................................................................... 58 3.8.1 3.9 The xpose command ....................................................................... 62 Using Stata for reproducible research .......................................................... 62 3.9.1 3.9.2 Using do-files ..................................................................................... 62 Data validation: assert and duplicates .......................................... 63 69 4 Linear regression 4.1 4.2 Introduction ................................................................................................. 69 Computing linear regression estimates.......................................................... 70 4.2.1 4.2.2 4.2.3 4.2.4 Regression as a method-of-moments estimator ............................. 72 The sampling distribution of regression estimates .........................73 Efficiency of the regression estimator ............................................. 74 Numerical identification of the regression estimates ..................... 75 4.3 Interpreting regression estimates .................................................................75 4.3.1 Research project: A study of single-family housing prices . . .........76 4.3.2 The ANOVA table: ANOVA F and R-squared .......................................... 77 4.3.3 4.3.4 4.3.5 4.3.6 4.3.7 4.4 Adjusted R-squared ......................................................................... 78 The coefficient estimates and beta coefficients ............................... 80 Regression without a constant term .............................................. 81 Recovering estimation results ......................................................... 82 Detecting collinearity in regression ................................................. 84 Presenting regression estimates ................................................................... 87 4.4.1 Presenting summary statistics and correlations............................ 90 91 4.5 Hypothesis tests, linear restrictions, and constrained least squares . . . 4.5.1 4.5.2 4.5.3 4.5.4 4.5.5 Wald tests with test ........................................................................ 94 Wald tests involving linear combinations of parameters . . . . 96 Joint hypothesis tests .................................................................. 98 Testing nonlinear restrictions and forming nonlinear combinations ........................................................................................ 99 Testing competing (nonnested) models ........................................... 100 x Contents 4.6 Computing residuals and predicted values .................................................. 102 4.6.1 Computing interval predictions ................................................... 103 4.7 Computing marginal effects ........................................................................... 107 4.A Appendix: Regression as a least-squares estimator ..................................... 112 4.B Appendix: The large-sample VCE for linear regression ................................. 113 5 Specifying the functional form 5.1 5.2 115 Introduction .............................................................................................. 115 Specification error ....................................................................................... 115 5.2.1 Omitting relevant variables from the model ................................. 116 Specifying dynamics in time-series regression models ............... 117 5.2.2 5.2.3 5.2.4 5.2.5 5.2.6 Graphically analyzing regression data ......................................... 117 Added-variable plots ..................................................................... 119 Including irrelevant variables in the model ................................ 121 The asymmetry of specification error .......................................... 121 Misspecification of the functional form ........................................ 122 5.2.7 Ramsey's RESET ................................................................................. 122 5.2.8 5.2.9 Specification plots ......................................................................... 124 Specification and interaction terms ............................................ 125 5.2.10 Outlier statistics and measures of leverage ................................... 126 The DFITS statistic ........................................................................ 128 The DFBETA statistic ..................................................................... 130 5.3 Endogeneity and measurement error ........................................................... 132 6 Regression with non-i.i.d. errors 6.1 133 The generalized linear regression model .................................................... 134 6.1.1 6.1.2 6.1.3 6.1.4 6.1.5 Types of deviations from i.i.d. errors ........................................... 134 The robust estimator of the VCE ................................................. 136 The cluster estimator of the VCE ................................................. 138 The Newey--West estimator of the VCE ........................................ 139 The generalized least-squares estimator ..................................... 142 The FGLS estimator ....................................................................... 143 Contents 6.2 xi Heteroskedasticity in the error distribution ............................................. 143 6.2.1 Heteroskedasticity related to scale .............................................. 144 Testing for heteroskedasticity related to scale ............................. 145 FGLS estimation ............................................................................. 147 6.2.2 Heteroskedasticity between groups of observations ................... 149 Testing for heteroskedasticity between groups of observations ... 150 FGLS estimation ............................................................................. 151 6.2.3 Heteroskedasticity in grouped data ............................................. 152 FGLS estimation ............................................................................. 153 6.3 Serial correlation in the error distribution................................................. 154 6.3.1 6.3.2 Testing for serial correlation ........................................................ 155 FGLS estimation with serial correlation ...................................... 159 161 7 Regression with indicator variables 7.1 Testing for significance of a qualitative factor ............................................ 161 7.1.1 7.1.2 Regression with one qualitative measure ................................... 162 Regression with two qualitative measures ................................... 165 Interaction effects ......................................................................... 167 7.2 Regression with qualitative and quantitative factors ................................ 168 Testing for slope differences .......................................................... 170 7.3 7.4 Seasonal adjustment with indicator variables .......................................... 174 Testing for structural stability and structural change .............................. 179 7.4.1 7.4.2 Constraints of continuity and differentiability ............................ 179 Structural change in a time-series model ................................... 183 185 8 Instrumental-variables estimators 8.1 8.2 Introduction .............................................................................................. 185 Endogeneity in economic relationships ..................................................... 185 8.3 2SLS ................................................................................................................ 188 8.4 The ivreg command ........................................................................................ 189 8.5 Identification and tests of overidentifying restrictions .............................. 190 8.6 Computing IV estimates ................................................................................ 192 xii Contents 8.7 ivreg2 and GMM estimation ........................................................................... 194 8.7.1 8.7.2 8.7.3 8.7.4 8.7.5 8.8 The GMM estimator ....................................................................... 195 GMM in a homoskedastic context ............................................... 196 GMM and heteroskedasticity-consistent standard errors . . . .... 197 GMM and clustering ..................................................................... 198 GMM and HAC standard errors ................................................... 199 Testing overidentifying restrictions in GMM .............................................. 200 8.8.1 Testing a subset of the overidentifying restrictions in GMM . .... 201 8.9 Testing for heteroskedasticity in the IV context ........................................ 205 8.10 Testing the relevance of instruments............................................................ 207 8.11 Durbin--Wu--Hausman tests for endogeneity in IV estimation .................. 211 8.A Appendix: Omitted-variables bias .................................................................... 216 8.B Appendix: Measurement error ......................................................................... 216 8.B.1 Solving errors-in-variables problems ........................................... 218 219 9 Panel-data models 9.1 FE and RE models .......................................................................................... 220 9.1.1 9.1.2 9.1.3 9.1.4 9.1.5 9.1.6 One-way FE .................................................................................... 221 Time effects and two-way FE.......................................................... 224 The between estimator ................................................................ 226 One-way RE ..................................................................................... 227 Testing the appropriateness of RE .............................................. 230 Prediction from one-way FE and RE ............................................ 231 9.2 IV models for panel data ................................................................................. 232 9.3 Dynamic panel-data models ........................................................................... 232 9.4 Seemingly unrelated regression models ......................................................... 236 9.4.1 SUR with identical regressors ...................................................... 241 9.5 Moving-window regression estimates............................................................... 242 10 Models of discrete and limited dependent variables 247 10.1 Binomial logit and probit models .................................................................. 247 10.1.1 The latent-variable approach ......................................................... 248 Contents 10.1.2 Marginal effects and predictions ....................................................... 250 Binomial probit ............................................................................... 251 Binomial logit and grouped logit .................................................... 253 10.1.3 Evaluating specification and goodness of fit .................................... 254 10.2 Ordered logit and probit models .................................................................. 256 10.3 Truncated regression and tobit models ....................................................... 259 10.3.1 Truncation ...................................................................................... 259 10.3.2 Censoring.......................................................................................... 262 10.4 Incidental truncation and sample-selection models .................................... 266 10.5 Bivariate probit and probit with selection .................................................... 271 10.5.1 Binomial probit with selection .......................................................... 272 A Getting the data into Stata 277 xiii A.1 Inputting data from ASCII text files and spreadsheets .................................. 277 A.1.1 Handling text files............................................................................ 278 Free format versus fixed format ..................................................... 278 The insheet command.................................................................... 280 A.1.2 Accessing data stored in spreadsheets ......................................... 281 A.1.3 Fixed-format data files ......................................................................... 281 A.2 Importing data from other package formats.................................................... 286 B The basics of Stata programming 289 B.1 Local and global macros .................................................................................. 290 B.1.1 B.1.2 Global macros ................................................................................ 293 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 xiv Contents B.6 The program and syntax statements............................................................ 307 B.7 Using Mata functions in Stata programs ..................................................... 313 References Author index Subject index 321 329 333