Microeconometrics Using Stata
Transcription
1 Microeconometrics Using Stata Revised Edition A. COLIN CAMERON Department of Economics University of California Davis, CA PRAVIN K. TRIVEDI Department of Economics Indiana University Bloomington, IN A Stata Press Publication StataCorp LP College Station, Texas
2 Copyright c , by StataCorp LP All rights reserved. First edition Revised edition Published by Stata Press, Lakeway Drive, College Station, Texas Typeset in L A TEX2ε Printed in the United States of America ISBN ISBN No part of this book may be reproduced, stored in a retrieval system, or transcribed, in any form or by any means electronic, mechanical, photocopy, recording, or otherwise without the prior written permission of StataCorp LP. Stata is a registered trademark of StataCorp LP. L A TEX2ε is a trademark of the American Mathematical Society.
3 Contents List of tables xxxv List of figures xxxvii Preface to the Revised Edition xxxix Preface to the First Edition xli 1 Stata basics Interactive use Documentation Stata manuals Additional Stata resources The help command The search, findit, and hsearch commands Command syntax and operators Basic command syntax Example: The summarize command Example: The regress command Factor variables Abbreviations, case sensitivity, and wildcards Arithmetic, relational, and logical operators Error messages Do-files and log files Writing a do-file Running do-files Log files A three-step process
4 vi Contents Comments and long lines Different implementations of Stata Scalars and matrices Scalars Matrices Using results from Stata commands Using results from the r-class command summarize Using results from the e-class command regress Global and local macros Global macros Local macros Scalar or macro? Looping commands The foreach loop The forvalues loop The while loop The continue command Some useful commands Template do-file User-written commands Stata resources Exercises Data management and graphics Introduction Types of data Text or ASCII data Internal numeric data String data Formats for displaying numeric data
5 Contents vii Inputting data General principles Inputting data already in Stata format Inputting data from the keyboard Inputting nontext data Inputting text data from a spreadsheet Inputting text data in free format Inputting text data in fixed format Dictionary files Common pitfalls Data management PSID example Naming and labeling variables Viewing data Using original documentation Missing values Imputing missing data Transforming data (generate, replace, egen, recode) The generate and replace commands The egen command The recode command The by prefix Indicator variables Set of indicator variables Interactions Demeaning Saving data Selecting the sample Manipulating datasets Ordering observations and variables
6 viii Contents Preserving and restoring a dataset Wide and long forms for a dataset Merging datasets Appending datasets Graphical display of data Stata graph commands Example graph commands Saving and exporting graphs Learning how to use graph commands Box-and-whisker plot Histogram Kernel density plot Twoway scatterplots and fitted lines Lowess, kernel, local linear, and nearest-neighbor regression Multiple scatterplots Stata resources Exercises Linear regression basics Introduction Data and data summary Data description Variable description Summary statistics More-detailed summary statistics Tables for data Statistical tests Data plots Regression in levels and logs Basic regression theory OLS regression and matrix algebra
7 Contents ix Properties of the OLS estimator Heteroskedasticity-robust standard errors Cluster robust standard errors Regression in logs Basic regression analysis Correlations The regress command Hypothesis tests Tables of output from several regressions Even better tables of regression output Factor variables for categorical variables and interactions Specification analysis Specification tests and model diagnostics Residual diagnostic plots Influential observations Specification tests Test of omitted variables Test of the Box Cox model Test of the functional form of the conditional mean Heteroskedasticity test Omnibus test Tests have power in more than one direction Prediction In-sample prediction MEs and elasticities Prediction in logs: The retransformation problem Prediction exercise Sampling weights Weights Weighted mean
8 x Contents Weighted regression Weighted prediction and MEs OLS using Mata Stata resources Exercises Simulation Introduction Pseudorandom-number generators: Introduction Uniform random-number generation Draws from normal Draws from t, chi-squared, F, gamma, and beta Draws from binomial, Poisson, and negative binomial Independent (but not identically distributed) draws from binomial Independent (but not identically distributed) draws from Poisson Histograms and density plots Distribution of the sample mean Stata program The simulate command Central limit theorem simulation The postfile command Alternative central limit theorem simulation Pseudorandom-number generators: Further details Inverse-probability transformation Direct transformation Other methods Draws from truncated normal Draws from multivariate normal Direct draws from multivariate normal Transformation using Cholesky decomposition
9 Contents xi Draws using Markov chain Monte Carlo method Computing integrals Quadrature Monte Carlo integration Monte Carlo integration using different S Simulation for regression: Introduction Simulation example: OLS with χ 2 errors Interpreting simulation output Unbiasedness of estimator Standard errors t statistic Test size Number of simulations Variations Different sample size and number of simulations Test power Different error distributions Estimator inconsistency Simulation with endogenous regressors Stata resources Exercises GLS regression Introduction GLS and FGLS regression GLS for heteroskedastic errors GLS and FGLS Weighted least squares and robust standard errors Leading examples Modeling heteroskedastic data Simulated dataset
10 xii Contents OLS estimation Detecting heteroskedasticity FGLS estimation WLS estimation System of linear regressions SUR model The sureg command Application to two categories of expenditures Robust standard errors Testing cross-equation constraints Imposing cross-equation constraints Survey data: Weighting, clustering, and stratification Survey design Survey mean estimation Survey linear regression Stata resources Exercises Linear instrumental-variables regression Introduction IV estimation Basic IV theory Model setup IV estimators: IV, 2SLS, and GMM Instrument validity and relevance Robust standard-error estimates IV example The ivregress command Medical expenditures with one endogenous regressor Available instruments IV estimation of an exactly identified model
11 Contents xiii IV estimation of an overidentified model Testing for regressor endogeneity Tests of overidentifying restrictions IV estimation with a binary endogenous regressor Weak instruments Finite-sample properties of IV estimators Weak instruments Diagnostics for weak instruments Formal tests for weak instruments The estat firststage command Just-identified model Overidentified model More than one endogenous regressor Sensitivity to choice of instruments Better inference with weak instruments Conditional tests and confidence intervals LIML estimator Jackknife IV estimator Comparison of 2SLS, LIML, JIVE, and GMM SLS systems estimation Stata resources Exercises Quantile regression Introduction QR Conditional quantiles Computation of QR estimates and standard errors The qreg, bsqreg, and sqreg commands QR for medical expenditures data Data summary
12 xiv Contents QR estimates Interpretation of conditional quantile coefficients Retransformation Comparison of estimates at different quantiles Heteroskedasticity test Hypothesis tests Graphical display of coefficients over quantiles QR for generated heteroskedastic data Simulated dataset QR estimates QR for count data Quantile count regression The qcount command Summary of doctor visits data Results from QCR Stata resources Exercises Linear panel-data models: Basics Introduction Panel-data methods overview Some basic considerations Some basic panel models Individual-effects model Fixed-effects model Random-effects model Pooled model or population-averaged model Two-way effects model Mixed linear models Cluster robust inference The xtreg command
13 Contents xv Stata linear panel-data commands Panel-data summary Data description and summary statistics Panel-data organization Panel-data description Within and between variation Time-series plots for each individual Overall scatterplot Within scatterplot Pooled OLS regression with cluster robust standard errors Time-series autocorrelations for panel data Error correlation in the RE model Pooled or population-averaged estimators Pooled OLS estimator Pooled FGLS estimator or population-averaged estimator The xtreg, pa command Application of the xtreg, pa command Within estimator Within estimator The xtreg, fe command Application of the xtreg, fe command Least-squares dummy-variables regression Between estimator Between estimator Application of the xtreg, be command RE estimator RE estimator The xtreg, re command Application of the xtreg, re command
14 xvi Contents Comparison of estimators Estimates of variance components Within and between R-squared Estimator comparison Fixed effects versus random effects Hausman test for fixed effects The hausman command Robust Hausman test Prediction First-difference estimator First-difference estimator Strict and weak exogeneity Long panels Long-panel dataset Pooled OLS and PFGLS The xtpcse and xtgls commands Application of the xtgls, xtpcse, and xtscc commands Separate regressions FE and RE models Unit roots and cointegration Panel-data management Wide-form data Convert wide form to long form Convert long form to wide form An alternative wide-form data Stata resources Exercises Linear panel-data models: Extensions Introduction Panel IV estimation
15 Contents xvii Panel IV The xtivreg command Application of the xtivreg command Panel IV extensions Hausman Taylor estimator Hausman Taylor estimator The xthtaylor command Application of the xthtaylor command Arellano Bond estimator Dynamic model IV estimation in the FD model The xtabond command Arellano Bond estimator: Pure time series Arellano Bond estimator: Additional regressors Specification tests The xtdpdsys command The xtdpd command Mixed linear models Mixed linear model The xtmixed command Random-intercept model Cluster robust standard errors Random-slopes model Random-coefficients model Two-way random-effects model Clustered data Clustered dataset Clustered data using nonpanel commands Clustered data using panel commands Hierarchical linear models
16 xviii Contents Stata resources Exercises Nonlinear regression methods Introduction Nonlinear example: Doctor visits Data description Poisson model description Nonlinear regression methods MLE The poisson command Postestimation commands NLS The nl command GLM The glm command The gmm command Other estimators Different estimates of the VCE General framework The vce() option Application of the vce() option Default estimate of the VCE Robust estimate of the VCE Cluster robust estimate of the VCE Heteroskedasticity- and autocorrelation-consistent estimate of the VCE Bootstrap standard errors Statistical inference Prediction The predict and predictnl commands
17 Contents xix Application of predict and predictnl Out-of-sample prediction Prediction at a specified value of one of the regressors Prediction at a specified value of all the regressors Prediction of other quantities The margins command for prediction Marginal effects Calculus and finite-difference methods MEs estimates AME, MEM, and MER Elasticities and semielasticities Simple interpretations of coefficients in single-index models The margins command for marginal effects MEM: Marginal effect at mean Comparison of calculus and finite-difference methods MER: Marginal effect at representative value AME: Average marginal effect Elasticities and semielasticities AME computed manually Polynomial regressors Interacted regressors Complex interactions and nonlinearities Model diagnostics Goodness-of-fit measures Information criteria for model comparison Residuals Model-specification tests Stata resources Exercises Nonlinear optimization methods Introduction
18 xx Contents Newton Raphson method NR method NR method for Poisson Poisson NR example using Mata Core Mata code for Poisson NR iterations Complete Stata and Mata code for Poisson NR iterations Gradient methods Maximization options Gradient methods Messages during iterations Stopping criteria Multiple maximums Numerical derivatives The ml command: lf method The ml command The lf method Poisson example: Single-index model Negative binomial example: Two-index model NLS example: Nonlikelihood model Checking the program Program debugging using ml check and ml trace Getting the program to run Checking the data Multicollinearity and near collinearity Multiple optimums Checking parameter estimation Checking standard-error estimation The ml command: d0, d1, d2, lf0, lf1, and lf2 methods Evaluator functions The d0 method
19 Contents xxi The d1 method The lf1 method with the robust estimate of the VCE The d2 and lf2 methods The Mata optimize() function Type d and gf evaluators Optimize functions Poisson example Evaluator program for Poisson MLE The optimize() function for Poisson MLE Generalized method of moments Definition Nonlinear IV example GMM using the Mata optimize() function Stata resources Exercises Testing methods Introduction Critical values and p-values Standard normal compared with Student s t Chi-squared compared with F Plotting densities Computing p-values and critical values Which distributions does Stata use? Wald tests and confidence intervals Wald test of linear hypotheses The test command Test single coefficient Test several hypotheses Test of overall significance Test calculated from retrieved coefficients and VCE
20 xxii Contents One-sided Wald tests Wald test of nonlinear hypotheses (delta method) The testnl command Wald confidence intervals The lincom command The nlcom command (delta method) Asymmetric confidence intervals Likelihood-ratio tests Likelihood-ratio tests The lrtest command Direct computation of LR tests Lagrange multiplier test (or score test) LM tests The estat command LM test by auxiliary regression Test size and power Simulation DGP: OLS with chi-squared errors Test size Test power Asymptotic test power Specification tests Moment-based tests Information matrix test Chi-squared goodness-of-fit test Overidentifying restrictions test Hausman test Other tests Stata resources Exercises
21 Contents xxiii 13 Bootstrap methods Introduction Bootstrap methods Bootstrap estimate of standard error Bootstrap methods Asymptotic refinement Use the bootstrap with caution Bootstrap pairs using the vce(bootstrap) option Bootstrap-pairs method to estimate VCE The vce(bootstrap) option Bootstrap standard-errors example How many bootstraps? Clustered bootstraps Bootstrap confidence intervals The postestimation estat bootstrap command Bootstrap confidence-intervals example Bootstrap estimate of bias Bootstrap pairs using the bootstrap command The bootstrap command Bootstrap parameter estimate from a Stata estimation command Bootstrap standard error from a Stata estimation command Bootstrap standard error from a user-written estimation command Bootstrap two-step estimator Bootstrap Hausman test Bootstrap standard error of the coefficient of variation Bootstraps with asymptotic refinement Percentile-t method Percentile-t Wald test Percentile-t Wald confidence interval
22 xxiv Contents Bootstrap pairs using bsample and simulate The bsample command The bsample command with simulate Bootstrap Monte Carlo exercise Alternative resampling schemes Bootstrap pairs Parametric bootstrap Residual bootstrap Wild bootstrap Subsampling The jackknife Jackknife method The vce(jackknife) option and the jackknife command Stata resources Exercises Binary outcome models Introduction Some parametric models Basic model Logit, probit, linear probability, and clog-log models Estimation Latent-variable interpretation and identification ML estimation The logit and probit commands Robust estimate of the VCE OLS estimation of LPM Example Data description Logit regression Comparison of binary models and parameter estimates
23 Contents xxv Hypothesis and specification tests Wald tests Likelihood-ratio tests Additional model-specification tests Lagrange multiplier test of generalized logit Heteroskedastic probit regression Model comparison Goodness of fit and prediction Pseudo-R 2 measure Comparing predicted probabilities with sample frequencies Comparing predicted outcomes with actual outcomes The predict command for fitted probabilities The prvalue command for fitted probabilities Marginal effects Marginal effect at a representative value (MER) Marginal effect at the mean (MEM) Average marginal effect (AME) The prchange command Endogenous regressors Example Model assumptions Structural-model approach The ivprobit command Maximum likelihood estimates Two-step sequential estimates IVs approach Grouped data Estimation with aggregate data Grouped-data application Stata resources
24 xxvi Contents Exercises Multinomial models Introduction Multinomial models overview Probabilities and MEs Maximum likelihood estimation Case-specific and alternative-specific regressors Additive random-utility model Stata multinomial model commands Multinomial example: Choice of fishing mode Data description Case-specific regressors Alternative-specific regressors Multinomial logit model The mlogit command Application of the mlogit command Coefficient interpretation Predicted probabilities MEs Conditional logit model Creating long-form data from wide-form data The asclogit command The clogit command Application of the asclogit command Relationship to multinomial logit model Coefficient interpretation Predicted probabilities MEs
25 Contents xxvii Nested logit model Relaxing the independence of irrelevant alternatives assumption NL model The nlogit command Model estimates Predicted probabilities MEs Comparison of logit models Multinomial probit model MNP The mprobit command Maximum simulated likelihood The asmprobit command Application of the asmprobit command Predicted probabilities and MEs Random-parameters logit Random-parameters logit The mixlogit command Data preparation for mixlogit Application of the mixlogit command Ordered outcome models Data summary Ordered outcomes Application of the ologit command Predicted probabilities MEs Other ordered models Multivariate outcomes Bivariate probit
26 xxviii Contents Nonlinear SUR Stata resources Exercises Tobit and selection models Introduction Tobit model Regression with censored data Tobit model setup Unknown censoring point Tobit estimation ML estimation in Stata Tobit model example Data summary Tobit analysis Prediction after tobit Marginal effects Left-truncated, left-censored, and right-truncated examples Left-censored case computed directly Marginal impact on probabilities The ivtobit command Additional commands for censored regression Tobit for lognormal data Data example Setting the censoring point for data in logs Results Two-limit tobit Model diagnostics Tests of normality and homoskedasticity Generalized residuals and scores Test of normality
27 Contents xxix Test of homoskedasticity Next step? Two-part model in logs Model structure Part 1 specification Part 2 of the two-part model Selection model Model structure and assumptions ML estimation of the sample-selection model Estimation without exclusion restrictions Two-step estimation Estimation with exclusion restrictions Prediction from models with outcome in logs Predictions from tobit Predictions from two-part model Predictions from selection model Stata resources Exercises Count-data models Introduction Features of count data Generated Poisson data Overdispersion and negative binomial data Modeling strategies Estimation methods Empirical example Data summary Poisson model Poisson model results Robust estimate of VCE for Poisson MLE
28 xxx Contents Test of overdispersion Coefficient interpretation and marginal effects NB2 model NB2 model results Fitted probabilities for Poisson and NB2 models The countfit command The prvalue command Discussion Generalized NB model Nonlinear least-squares estimation Hurdle model Variants of the hurdle model Application of the hurdle model Finite-mixture models FMM specification Simulated FMM sample with comparisons ML estimation of the FMM The fmm command Application: Poisson finite-mixture model Interpretation Comparing marginal effects Application: NB finite-mixture model Model selection Cautionary note Empirical example Zero-inflated data Models for zero-inflated data Results for the NB2 model The prcounts command Results for ZINB
29 Contents xxxi Model comparison The countfit command Model comparison using countfit Models with endogenous regressors Structural-model approach Model and assumptions Two-step estimation Application Nonlinear IV method Stata resources Exercises Nonlinear panel models Introduction Nonlinear panel-data overview Some basic nonlinear panel models FE models RE models Pooled models or population-averaged models Comparison of models Dynamic models Stata nonlinear panel commands Nonlinear panel-data example Data description and summary statistics Panel-data organization Within and between variation FE or RE model for these data? Binary outcome models Panel summary of the dependent variable Pooled logit estimator The xtlogit command
30 xxxii Contents The xtgee command PA logit estimator RE logit estimator FE logit estimator Panel logit estimator comparison Prediction and marginal effects Mixed-effects logit estimator Tobit model Panel summary of the dependent variable RE tobit model Generalized tobit models Parametric nonlinear panel models Count-data models The xtpoisson command Panel summary of the dependent variable Pooled Poisson estimator PA Poisson estimator RE Poisson estimators FE Poisson estimator Panel Poisson estimators comparison Negative binomial estimators Stata resources Exercises A Programming in Stata A.1 Stata matrix commands A Stata matrix overview A Stata matrix input and output Matrix input by hand Matrix input from Stata estimation results A Stata matrix subscripts and combining matrices
31 Contents xxxiii A Matrix operators A Matrix functions A Matrix accumulation commands A OLS using Stata matrix commands A.2 Programs A Simple programs (no arguments or access to results) A Modifying a program A Programs with positional arguments A Temporary variables A Programs with named positional arguments A Storing and retrieving program results A Programs with arguments using standard Stata syntax A Ado-files A.3 Program debugging A Some simple tips A Error messages and return code A Trace B Mata B.1 How to run Mata B Mata commands in Mata B Mata commands in Stata B Stata commands in Mata B Interactive versus batch use B Mata help B.2 Mata matrix commands B Mata matrix input Matrix input by hand Identity matrices, unit vectors, and matrices of constants Matrix input from Stata data Matrix input from Stata matrix
32 xxxiv Contents Stata interface functions B Mata matrix operators Element-by-element operators B Mata functions Scalar and matrix functions Matrix inversion B Mata cross products B Mata matrix subscripts and combining matrices B Transferring Mata data and matrices to Stata Creating Stata matrices from Mata matrices Creating Stata data from a Mata vector B.3 Programming in Mata B Declarations B Mata program B Mata program with results output to Stata B Stata program that calls a Mata program B Using Mata in ado-files Glossary of abbreviations References Author index Subject index
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34 Preface to the Revised Edition Microeconometrics Using Stata, published in December , was written for Stata The book incorporated version additions to Stata , most notably, the new random-number generators. In this revised edition, we present other additions to Stata 10 that appear for the first time in Stata With few exceptions, we present these additions in a way that reproduces the results given in the first edition. First, we introduce the new construct of factor variables. These provide a simple way to specify models with sets of indicator variables formed from a categorical variable and to specify models with interactions. Factor variables replace the xi prefix command. See especially section and the end of section Second, we describe the new margins command for prediction and for computation of marginal effects in regression models. The margins command with options including the dydx() option replaces the Stata mfx command and the user-written margeff command. Additionally, the margins command when used in conjunction with factor variables can simplify computation of marginal effects in models with interactions. See sections and , especially subsections and Throughout this revised edition, notably, in chapters 14 17, we replace mfx and margeff with the margins command. In the first edition, we most often calculated the marginal effect at the mean (MEM), rather than the average marginal effect (AME), because the mfx command did not compute the AME. The new margins command can compute both the MEM and the AME. In this revised edition, we have endeavored to replicate the results given in the first edition. For that reason, we continue to most frequently calculate the MEM, though in practice, the AME is usually preferred. Third, we describe the new gmm command for generalized method of moments and nonlinear instrumental-variables estimation. See sections and Fourth, we present some minor changes that need to be made to the existing ml command when the d1 and d2 methods are used. These changes arise because the ml command is now a front-end to the new Mata moptimize() function. We also present the newlf0,lf1, andlf2 methods. See section The Mataoptimize() v evaluator has been renamed to gf evaluator; see section
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