Microeconometrics Using Stata, Second Edition, Volume I: Cross-Sectional and Panel Regression Models

Contents
Tables
Figures
Preface to the Second Edition
Preface to the Second Edition
Preface to the First Edition
Preface to the First Edition
1 Stata basics
	1.1 Interactive use
	1.2 Documentation
		1.2.1 Stata manuals
		1.2.2 Additional Stata resources
		1.2.3 The help command
		1.2.4 The search and net search commands
	1.3 Command syntax and operators
		1.3.1 Basic command syntax
		1.3.2 Example: The summarize command
		1.3.3 Example: The regress command
		1.3.4 Factor variables
		1.3.5 Abbreviations, case sensitivity, and wildcards
		1.3.6 Arithmetic, relational, and logical operators
		1.3.7 Error messages
	1.4 Do-files and log files
		1.4.1 Writing a do-file
		1.4.2 Running do-files
		1.4.3 Log files
		1.4.4 A three-step process
		1.4.5 Comments and long lines
		1.4.6 Different implementations of Stata
	1.5 Scalars and matrices
		1.5.1 Scalars
		1.5.2 Matrices
	1.6 Using results from Stata commands
		1.6.1 Using results from the r-class command summarize
		1.6.2 Using results from the e-class command regress
	1.7 Global and local macros
		1.7.1 Global macros
		1.7.2 Local macros
		1.7.3 Scalar or macro?
	1.8 Looping commands
		1.8.1 The foreach loop
		1.8.2 The forvalues loop
		1.8.3 The while loop
		1.8.4 The continue command
	1.9 Mata and Python in Stata
	1.10 Some useful commands
	1.11 Template do-file
	1.12 Community-contributed commands
	1.13 Additional resources
	1.14 Exercises
2 Data management and graphics
	2.1 Introduction
	2.2 Types of data
		2.2.1 Text or ASCII data
		2.2.2 Internal numeric data
		2.2.3 String data
		2.2.4 Formats for displaying numeric data
	2.3 Inputting data
		2.3.1 General principles
		2.3.2 Inputting data already in Stata format
		2.3.3 Inputting data from the keyboard
		2.3.4 Inputting nontext data
		2.3.5 Inputting text data from a spreadsheet
		2.3.6 Inputting text data in free format
		2.3.7 Inputting text data in fixed format using infix
		2.3.8 Inputting text data in fixed format using infile and a dictionary
		2.3.9 Common pitfalls
		2.3.10 Outputting data
	2.4 Data management
		2.4.1 Panel Study of Income Dynamics example
		2.4.2 Naming and labeling variables
		2.4.3 Viewing data
		2.4.4 Using original documentation
		2.4.5 Missing values
		2.4.6 Imputing missing data
		2.4.7 Transforming data (generate, replace, egen, recode)
		2.4.8 Saving and exporting data
		2.4.9 Selecting the sample
		2.4.10 Time-series data
	2.5 Manipulating datasets
		2.5.1 Ordering observations and variables
		2.5.2 Preserving and restoring a dataset
		2.5.3 Data frames
		2.5.4 Collapsing and expanding datasets
		2.5.5 Wide and long forms for a dataset
		2.5.6 Merging datasets
		2.5.7 Appending datasets
	2.6 Graphical display of data
		2.6.1 Stata graph commands
		2.6.2 Box-and-whisker plot
		2.6.3 Histogram
		2.6.4 Kernel density plot
		2.6.5 Twoway scatterplots and fitted lines
		2.6.6 Twoway scatterplots and locally fitted lines
		2.6.7 Multiple scatterplots
	2.7 Additional resources
	2.8 Exercises
3 Linear regression basics
	3.1 Introduction
	3.2 Data and data summary
		3.2.1 Data description
		3.2.2 Variable description
		3.2.3 Summary statistics
		3.2.4 More detailed summary statistics
		3.2.5 Tables of frequencies
		3.2.6 Tables of summary statistics
		3.2.7 Hypothesis tests on the population mean
		3.2.8 Data plots
	3.3 Transformation of data before regression
	3.4 Linear regression
		3.4.1 Basic regression theory
		3.4.2 OLS regression and matrix algebra
		3.4.3 Properties of the OLS estimator
		3.4.4 Default standard errors
		3.4.5 Heteroskedasticity-robust standard errors
		3.4.6 Cluster–robust standard errors
		3.4.7 Bootstrap standard errors
		3.4.8 Regression in logs
	3.5 Basic regression analysis
		3.5.1 Correlations
		3.5.2 The regress command
		3.5.3 Postestimation commands
		3.5.4 Regression subject to constraints on the parameters
		3.5.5 Hypothesis tests
		3.5.6 Tables of output from several regressions
		3.5.7 Even better tables of regression output
		3.5.8 Factor variables for categorical variables and interactions
		3.5.9 Average marginal effects
		3.5.10 Cluster–robust standard errors
		3.5.11 Bootstrap standard errors
		3.5.12 OLS regression to test mean and difference in mean
	3.6 Specification analysis
		3.6.1 Robust regression
		3.6.2 Residual diagnostic plots
		3.6.3 Influential observations
		3.6.4 Stata’s robust regression
		3.6.5 Median regression
		3.6.6 Robust and median regression example
	3.7 Specification tests
		3.7.1 Test of omitted variables
		3.7.2 Test of the functional form of the conditional mean
		3.7.3 Test of levels versus logs
		3.7.4 Heteroskedasticity test
		3.7.5 Omnibus test
		3.7.6 Tests have power in more than one direction
	3.8 Sampling weights
		3.8.1 Weights
		3.8.2 Weighted mean
		3.8.3 Weighted regression
		3.8.4 Weighted prediction and MEs
	3.9 OLS using Mata
	3.10 Additional resources
	3.11 Exercises
4 Linear regression extensions
	4.1 Introduction
	4.2 In-sample prediction
		4.2.1 The predict command
		4.2.2 In-sample prediction
		4.2.3 Prediction in logs: The retransformation problem
		4.2.4 Prediction exercise with a binary regressor
		4.2.5 Forecast actual value versus prediction of conditional mean
	4.3 Out-of-sample prediction
		4.3.1 Out-of-sample predictions
		4.3.2 Out-of-sample prediction example
	4.4 Predictive margins
		4.4.1 Predictive margins
		4.4.2 The margins command
		4.4.3 Predictive margins examples
		4.4.4 Predictive margins for a categorical factor variable
		4.4.5 Predictive margins for continuous variables
		4.4.6 Plots of predictive margins
		4.4.7 Pairwise comparisons of predictive margins
		4.4.8 Contrasts of predictive margins
	4.5 Marginal effects
		4.5.1 Calculus and finite-difference methods
		4.5.2 Average marginal effect, ME at mean, and ME at a representative value
		4.5.3 The margins, dydx() command
		4.5.4 Average marginal effects
		4.5.5 Marginal effect at mean
		4.5.6 Marginal effect at a representative value
		4.5.7 Elasticities
		4.5.8 Semielasticities
	4.6 Regression decomposition analysis
		4.6.1 Oaxaca–Blinder decomposition
		4.6.2 An empirical example
	4.7 Shapley decomposition of relative regressor importance
		4.7.1 Empirical example
	4.8 Difference-in-differences estimators
		4.8.1 Example: Estimating the effect of training on earnings
		4.8.2 Before–after comparison
		4.8.3 Treatment–control comparison
		4.8.4 Difference-in-differences estimate
	4.9 Additional resources
	4.10 Exercises
5 Simulation
	5.1 Introduction
	5.2 Pseudorandom-number generators
		5.2.1 Uniform random-number generation
		5.2.2 Draws from normal
		5.2.3 Draws from t, chi-squared, F, gamma, and beta
		5.2.4 Draws from binomial, Poisson, and negative binomial
	5.3 Distribution of the sample mean
		5.3.1 Stata program
		5.3.2 The simulate prefix
		5.3.3 Central limit theorem simulation
		5.3.4 The postfile command
		5.3.5 Alternative central limit theorem simulation
	5.4 Pseudorandom-number generators: Further details
		5.4.1 Inverse-probability transformation
		5.4.2 Direct transformation
		5.4.3 Other methods
		5.4.4 Draws from truncated normal
		5.4.5 Draws from multivariate normal
		5.4.6 Draws using Markov chain Monte Carlo method
	5.5 Computing integrals
		5.5.1 Quadrature
		5.5.2 Monte Carlo integration
		5.5.3 Monte Carlo integration using different S
		5.5.4 Halton and Hammersley sequences
	5.6 Simulation for regression: Introduction
		5.6.1 Simulation example: OLS with errors
		5.6.2 Interpreting simulation output
		5.6.3 Variations
		5.6.4 Estimator consistency or inconsistency
		5.6.5 Simulation with endogenous regressors
	5.7 Additional resources
	5.8 Exercises
6 Linear regression with correlated errors
	6.1 Introduction
	6.2 Generalized least-squares and FGLS regression
		6.2.1 GLS for heteroskedastic errors
		6.2.2 GLS and FGLS
		6.2.3 Robust standard errors for FGLS
		6.2.4 Limitations of cluster–robust inference
		6.2.5 Leading examples of FGLS
	6.3 Modeling heteroskedastic data
		6.3.1 Simulated dataset
		6.3.2 OLS estimation
		6.3.3 Detecting heteroskedasticity
		6.3.4 FGLS estimation with heteroskedastic errors
		6.3.5 Heteroskedastic-robust standard errors for the WLS estimator
	6.4 OLS for clustered data
		6.4.1 Clustered dataset
		6.4.2 OLS and cluster–robust standard errors
		6.4.3 Intracluster correlation and inflation of OLS standard errors
		6.4.4 Two-way cluster–robust standard errors for OLS
		6.4.5 Dyad–robust standard errors for OLS
		6.4.6 Cluster–robust inference with few clusters
	6.5 FGLS estimators for clustered data
		6.5.1 Defining the cluster identifier
		6.5.2 FGLS estimator for population-averaged model
		6.5.3 Cluster-specific random-effects model
		6.5.4 RE estimator
		6.5.5 Cluster–robust standard errors for the RE estimator
	6.6 Fixed-effects estimator for clustered data
		6.6.1 Cluster-specific FE model
		6.6.2 FE estimator
		6.6.3 Cluster–robust standard errors for the FE estimator
		6.6.4 Alternative methods for computing the FE estimator
		6.6.5 Correlated RE model
		6.6.6 Methods to compute two-way FE models
	6.7 Linear mixed models for clustered data
		6.7.1 Linear mixed model
		6.7.2 Linear mixed-model estimator
		6.7.3 The mixed command
		6.7.4 Random intercept model
		6.7.5 Cluster–robust standard errors for mixed estimator
		6.7.6 Random slopes model
		6.7.7 Hierarchical linear models
		6.7.8 Two-way RE model
	6.8 Systems of linear regressions
		6.8.1 Seemingly unrelated regressions model
		6.8.2 The sureg command
		6.8.3 Application to two categories of expenditures
		6.8.4 Robust standard errors for the SUR estimator
		6.8.5 Testing cross-equation constraints
		6.8.6 Imposing cross-equation constraints
		6.8.7 The suest command for seemingly unrelated equations
	6.9 Survey data: Weighting, clustering, and stratification
		6.9.1 Survey design
		6.9.2 Survey mean estimation
		6.9.3 Survey linear regression
	6.10 Additional resources
	6.11 Exercises
7 Linear instrumental-variables regression
	7.1 Introduction
	7.2 Simultaneous equations model
		7.2.1 Structural model
		7.2.2 Reduced-form model
		7.2.3 Recursive systems
		7.2.4 Generating a sample with simultaneous dependence
		7.2.5 Estimation in the simultaneous equations example
	7.3 Instrumental-variables regression
		7.3.1 Basic IV theory
		7.3.2 Model setup
		7.3.3 IV estimators: IV, 2SLS, and GMM
		7.3.4 Instrument validity and relevance
		7.3.5 Weak instruments
		7.3.6 Robust standard-error estimates
	7.4 Instrumental-variables example
		7.4.1 The ivregress command
		7.4.2 Data and data summary
		7.4.3 Available instruments
		7.4.4 IV estimation of an exactly identified model
		7.4.5 IV estimation of an overidentified model
		7.4.6 Testing for regressor endogeneity
		7.4.7 Control function estimator
		7.4.8 Tests of overidentifying restrictions
		7.4.9 IV estimation using the eregress command
		7.4.10 IV estimation with a binary endogenous regressor
		7.4.11 IV as local average treatment-effects estimator
	7.5 Weak instruments
		7.5.1 Weak instruments essentials
		7.5.2 Finite-sample properties of IV estimators
		7.5.3 A Monte Carlo example
		7.5.4 Simulation results with uncorrelated errors
		7.5.5 Simulation results with correlated errors
		7.5.6 The first-stage F statistic
		7.5.7 The first-stage F statistic and 2SLS bias
		7.5.8 Test size distortion
	7.6 Diagnostics and tests for weak instruments
		7.6.1 Pairwise correlations
		7.6.2 Partial
		7.6.3 Tests of underidentification
		7.6.4 Tests of weak instruments
		7.6.5 The estat firststage command
		7.6.6 Just-identified model
		7.6.7 The weakivtest command
		7.6.8 Overidentified model
		7.6.9 The ivreg2 command
		7.6.10 More than one endogenous regressor
		7.6.11 Sensitivity to choice of instruments
	7.7 Inference with weak instruments
		7.7.1 Tests following pretesting for weak instruments
		7.7.2 Anderson–Rubin Wald test
		7.7.3 Anderson–Rubin Wald confidence regions
		7.7.4 Tests under weak-instrument asymptotics
		7.7.5 Minimum distance-based tests and confidence regions
	7.8 Finite sample inference with weak instruments
	7.9 Other estimators
		7.9.1 LIML estimator
		7.9.2 Jackknife IV estimator
		7.9.3 Comparison of 2SLS, LIML, JIVE, and GMM
		7.9.4 Two-sample 2SLS
	7.10 Three-stage least-squares systems estimation
	7.11 Additional resources
	7.12 Exercises
8 Linear panel-data models: Basics
	8.1 Introduction
	8.2 Panel-data methods overview
		8.2.1 Some basic considerations
		8.2.2 Some basic panel models
		8.2.3 Cluster–robust inference
		8.2.4 The xtreg command
		8.2.5 Stata linear panel-data commands
	8.3 Summary of panel data
		8.3.1 Data description and summary statistics
		8.3.2 Panel-data organization
		8.3.3 Panel-data description
		8.3.4 Within and between variation
		8.3.5 Time-series plots for each individual
		8.3.6 Overall scatterplot
		8.3.7 Within scatterplot
		8.3.8 Pooled OLS regression with cluster–robust standard errors
		8.3.9 Time-series autocorrelations for panel data
		8.3.10 Error correlation in the RE model
	8.4 Pooled or population-averaged estimators
		8.4.1 Pooled OLS estimator
		8.4.2 Pooled FGLS estimator or PA estimator
		8.4.3 The xtreg, pa command
		8.4.4 Application of the xtreg, pa command
	8.5 Fixed-effects or within estimator
		8.5.1 Within estimator
		8.5.2 The xtreg, fe command
		8.5.3 Application of the xtreg, fe command
		8.5.4 Least-squares dummy-variable regression
		8.5.5 Two-way fixed effects
	8.6 Between estimator
		8.6.1 Between estimator
		8.6.2 Application of the xtreg, be command
	8.7 Random-effects estimator
		8.7.1 RE estimator
		8.7.2 The xtreg, re command
		8.7.3 Application of the xtreg, re command
		8.7.4 Correlated RE model
	8.8 Comparison of estimators
		8.8.1 Estimates of variance components
		8.8.2 Within and between
		8.8.3 Estimator comparison
		8.8.4 FE versus RE
		8.8.5 Hausman test for FE
		8.8.6 Prediction
	8.9 First-difference estimator
		8.9.1 FD estimator
		8.9.2 Strict and weak exogeneity
	8.10 Panel-data management
		8.10.1 Wide-form data
		8.10.2 Convert wide form to long form
		8.10.3 Convert long form to wide form
		8.10.4 An alternative wide-form data
	8.11 Additional resources
	8.12 Exercises
9 Linear panel-data models: Extensions
	9.1 Introduction
	9.2 Panel instrumental-variables estimation
		9.2.1 Panel IV
		9.2.2 The xtivreg command
		9.2.3 Application of the xtivreg command
		9.2.4 Panel IV extensions
	9.3 Hausman–Taylor estimator
		9.3.1 Hausman–Taylor estimator
		9.3.2 The xthtaylor command
		9.3.3 Application of the xthtaylor command
	9.4 Arellano–Bond estimator
		9.4.1 Dynamic model
		9.4.2 IV estimation in the FD model
		9.4.3 The xtabond command
		9.4.4 Arellano–Bond estimator: Pure time series
		9.4.5 Arellano–Bond estimator: Additional regressors
		9.4.6 Specification tests
		9.4.7 The xtdpdsys command
		9.4.8 The xtdpd command
		9.4.9 The xtabond2 command
		9.4.10 Dynamic systems with fixed effects
	9.5 Long panels
		9.5.1 Long-panel dataset
		9.5.2 Pooled OLS and pooled feasible GLS
		9.5.3 The xtpcse and xtgls commands
		9.5.4 Application of the xtgls, xtpcse, and xtscc commands
		9.5.5 FE and RE models
		9.5.6 Interactive effects
		9.5.7 Separate regressions
		9.5.8 Heterogeneous panels
		9.5.9 Unit roots and cointegration
	9.6 Additional resources
	9.7 Exercises
10 Introduction to nonlinear regression
	10.1 Introduction
	10.2 Binary outcome models
		10.2.1 Doctor visit example
		10.2.2 Probit and logit model definition
	10.3 Probit model
		10.3.1 The probit command
		10.3.2 Probit estimation results
		10.3.3 Standard error computation
		10.3.4 Postestimation commands
		10.3.5 Prediction
	10.4 MEs and coefficient interpretation
		10.4.1 Calculus method and finite-difference method
		10.4.2 Average marginal effect, ME at mean, and ME at a representative value
		10.4.3 AME in treatment-effects models
		10.4.4 The margins and margins, dydx commands
		10.4.5 Probit model application
		10.4.6 Simple interpretations of coefficients
		10.4.7 Comparison with linear least squares
	10.5 Logit model
	10.6 Nonlinear least squares
		10.6.1 The nl command
		10.6.2 NLS for probit model
	10.7 Other nonlinear estimators
	10.8 Additional resources
	10.9 Exercises
11 Tests of hypotheses and model specification
	11.1 Introduction
	11.2 Critical values and p-values
		11.2.1 Standard normal compared with Student’s t
		11.2.2 Chi-squared compared with F
		11.2.3 Plotting densities
		11.2.4 Computing p-values and critical values
		11.2.5 Which distributions does Stata use?
	11.3 Wald tests and confidence intervals
		11.3.1 Wald test of linear hypotheses
		11.3.2 The test and testparm commands
		11.3.3 Data example
		11.3.4 One-sided Wald tests
		11.3.5 Wald test of nonlinear hypotheses (delta method)
		11.3.6 The testnl command
		11.3.7 Forward and backward selection based on statistical significance
		11.3.8 Pretest bias
		11.3.9 Wald confidence intervals
		11.3.10 The lincom command
		11.3.11 The nlcom command (delta method)
		11.3.12 Asymmetric confidence intervals
		11.3.13 Confidence intervals from inverting a test statistic
	11.4 Likelihood-ratio tests
		11.4.1 LR test statistic
		11.4.2 The lrtest command
		11.4.3 Direct computation of LR tests
		11.4.4 Tests at the boundary
	11.5 Lagrange multiplier test (or score test)
		11.5.1 LM tests
		11.5.2 The estat commands
		11.5.3 LM test by auxiliary regression
	11.6 Multiple testing
		11.6.1 Family-wise error rate
		11.6.2 Subgroup analysis
		11.6.3 Multiple outcomes
		11.6.4 False discovery rate
		11.6.5 More powerful multiple tests
	11.7 Test size and power
		11.7.1 Simulation DGP: OLS with chi-squared errors
		11.7.2 Test size
		11.7.3 Simulation using actual data
		11.7.4 Test power
		11.7.5 Asymptotic test power
	11.8 The power onemean command for multiple regression
		11.8.1 The power onemean command
		11.8.2 Power in a regression setting using the standard normal
		11.8.3 Power in a regression setting using the t distribution
		11.8.4 Power for clustered data
		11.8.5 Confidence intervals with desired precision
	11.9 Specification tests
		11.9.1 Moment-based tests
		11.9.2 Information matrix test
		11.9.3 Chi-squared goodness-of-fit test
		11.9.4 Overidentifying restrictions test
		11.9.5 Hausman test
		11.9.6 Other tests
	11.10 Permutation tests and randomization tests
	11.11 Additional resources
	11.12 Exercises
12 Bootstrap methods
	12.1 Introduction
	12.2 Bootstrap methods
		12.2.1 Bootstrap estimate of standard error
		12.2.2 Bootstrap methods
		12.2.3 Asymptotic refinement
		12.2.4 Use the bootstrap with caution
	12.3 Bootstrap pairs using the vce(bootstrap) option
		12.3.1 Bootstrap-pairs method to estimate the variance–covariance matrix
		12.3.2 The vce(bootstrap) option
		12.3.3 Bootstrap standard-errors example
		12.3.4 How many bootstraps?
		12.3.5 Cluster pairs bootstrap
		12.3.6 Bootstrap confidence intervals
		12.3.7 The estat bootstrap postestimation command
		12.3.8 Bootstrap confidence-intervals example
		12.3.9 Bootstrap estimate of bias
	12.4 Bootstrap pairs using the bootstrap command
		12.4.1 The bootstrap prefix
		12.4.2 Bootstrap parameter estimate from a Stata estimation command
		12.4.3 Bootstrap standard error from a Stata estimation command
		12.4.4 Bootstrap standard error from a user-written estimation command
		12.4.5 Bootstrap two-step estimator
		12.4.6 Bootstrap Hausman test
		12.4.7 Bootstrap standard error of the coefficient of variation
	12.5 Percentile-t bootstraps with asymptotic refinement
		12.5.1 Percentile-t method
		12.5.2 Percentile-t Wald test
		12.5.3 Percentile-t Wald confidence interval
	12.6 Wild bootstrap with asymptotic refinement
		12.6.1 Wild cluster bootstrap
		12.6.2 The boottest command
		12.6.3 Wild cluster bootstrap example
		12.6.4 Score-based wild cluster bootstrap
		12.6.5 Wild bootstrap for IV estimation
	12.7 Bootstrap pairs using bsample and simulate
		12.7.1 The bsample command
		12.7.2 The bsample command with simulate
	12.8 Alternative resampling schemes
		12.8.1 Bootstrap pairs resampling scheme
		12.8.2 Parametric bootstrap resampling scheme
		12.8.3 Residual bootstrap resampling scheme
		12.8.4 Wild bootstrap resampling scheme
		12.8.5 Subsampling
	12.9 The jackknife
		12.9.1 Jackknife method
		12.9.2 The vce(jackknife) option and the jackknife prefix
	12.10 Additional resources
	12.11 Exercises
13 Nonlinear regression methods
	13.1 Introduction
	13.2 Nonlinear example: Doctor visits
		13.2.1 Data description
		13.2.2 Poisson model description
	13.3 Nonlinear regression methods
		13.3.1 MLE and quasi-MLE and robust standard errors
		13.3.2 The poisson command
		13.3.3 The mlexp command
		13.3.4 Postestimation commands
		13.3.5 Nonlinear least squares
		13.3.6 The nl command
		13.3.7 Generalized linear models
		13.3.8 The glm command
		13.3.9 Generalized method of moments
		13.3.10 The gmm command
		13.3.11 The gmm command for two-step estimators
		13.3.12 Other estimators
	13.4 Different estimates of the VCE
		13.4.1 General framework
		13.4.2 The vce() option
		13.4.3 Application of the vce() option
		13.4.4 Default estimate of the VCE
		13.4.5 Heteroskedastic-robust estimate of the VCE
		13.4.6 Cluster–robust estimate of the VCE
		13.4.7 Heteroskedasticity- and autocorrelation-consistent estimate of the VCE
		13.4.8 Bootstrap standard errors
		13.4.9 Statistical inference
	13.5 Prediction
		13.5.1 The predict and predictnl commands
		13.5.2 Application of predict and predictnl
		13.5.3 Out-of-sample prediction
		13.5.4 Prediction at a specified value of one of the regressors
		13.5.5 Prediction at a specified value of all the regressors
		13.5.6 Prediction of other quantities
	13.6 Predictive margins
		13.6.1 The margins command
		13.6.2 Predictive margins: Average, at specified values, and at mean
		13.6.3 Predictive margins for a categorical factor variable
	13.7 Marginal effects
		13.7.1 Calculus and finite-difference methods
		13.7.2 Average marginal effect, ME at mean, and ME at a representative value
		13.7.3 Simple interpretations of coefficients in single-index models
		13.7.4 The dydx() option of the margins command for MEs
		13.7.5 Average marginal effect
		13.7.6 Marginal effect at the mean
		13.7.7 Marginal effect at a representative value
		13.7.8 MEs with respect to a user-defined quantity
		13.7.9 Which ME to use?
		13.7.10 AME computed manually
		13.7.11 Polynomial regressors
		13.7.12 Interacted regressors
		13.7.13 Complex interactions and nonlinearities
		13.7.14 Elasticities and semielasticities
		13.7.15 Elasticities and semielasticities example
		13.7.16 Marginal treatment effects
	13.8 Model diagnostics
		13.8.1 Goodness-of-fit measures
		13.8.2 Information criteria for model comparison
		13.8.3 Residuals
		13.8.4 Model-specification tests
	13.9 Clustered data
		13.9.1 Clustered dataset
		13.9.2 Pooled or population-averaged models
		13.9.3 RE and mixed models
		13.9.4 FE model
		13.9.5 Correlated RE model
	13.10 Additional resources
	13.11 Exercises
14 Flexible regression: Finite mixtures and nonparametric
	14.1 Introduction
	14.2 Models based on finite mixtures
		14.2.1 Univariate case
		14.2.2 Regression case
		14.2.3 Regression example
		14.2.4 Modeling considerations
		14.2.5 The fmm prefix
		14.2.6 Computational considerations
	14.3 FMM example: Earnings of doctors
		14.3.1 Data and log-linear regression
		14.3.2 Two-component model estimates
		14.3.3 Predicted conditional means in each component
		14.3.4 Random draws from each fitted component
		14.3.5 Marginal effects
		14.3.6 Predicted class probabilities
		14.3.7 Predicted class posterior probabilities
		14.3.8 Model comparison and selection
		14.3.9 Tests of equal coefficients
		14.3.10 More flexible FMM models
	14.4 Global polynomials
		14.4.1 Global polynomials
		14.4.2 Fractional polynomials and orthogonal polynomials
	14.5 Regression splines
		14.5.1 Piecewise linear regression
		14.5.2 Natural or restricted cubic splines
		14.5.3 Smoothing splines
	14.6 Nonparametric regression
		14.6.1 Local regression
		14.6.2 Nearest-neighbors regression
		14.6.3 Local polynomial regression
		14.6.4 Local linear regression using lpoly and npregress kernel
		14.6.5 lowess
		14.6.6 Series estimation using npregress series
	14.7 Partially parametric regression
	14.8 Additional resources
	14.9 Exercises
15 Quantile regression
	15.1 Introduction
	15.2 Conditional quantile regression
		15.2.1 Conditional quantiles
		15.2.2 Computation of conditional QR estimates
		15.2.3 Computation of CQR standard errors
		15.2.4 The qreg, bsqreg, sqreg, and qreg2 commands
	15.3 CQR for medical expenditures data
		15.3.1 Data summary
		15.3.2 Conditional QR estimates
		15.3.3 Interpretation of conditional quantile coefficients
		15.3.4 Retransformation
		15.3.5 Comparison of estimates at different quantiles
		15.3.6 Robust variance estimation using the qreg2 command
		15.3.7 Comparison of different standard-error estimates
		15.3.8 Heteroskedasticity test based on OLS regression
		15.3.9 Test of coefficient equality across quantiles
		15.3.10 Graphical display of coefficients over quantiles
		15.3.11 Censored conditional QR
	15.4 CQR for generated heteroskedastic data
		15.4.1 Simulated dataset
		15.4.2 CQR estimates
	15.5 Quantile treatment effects for a binary treatment
	15.6 Additional resources
	15.7 Exercises
A Programming in Stata
	A.1 Stata matrix commands
		A.1.1 Stata matrix overview
		A.1.2 Stata matrix input and output
		A.1.3 Stata matrix subscripts and combining matrices
		A.1.4 Matrix operators
		A.1.5 Matrix functions
		A.1.6 Matrix accumulation commands
		A.1.7 OLS using Stata matrix commands
	A.2 Programs
		A.2.1 Simple programs (no arguments or access to results)
		A.2.2 Modifying a program
		A.2.3 Programs with positional arguments
		A.2.4 Temporary variables
		A.2.5 Programs with named positional arguments
		A.2.6 Storing and retrieving program results
		A.2.7 Programs with arguments using standard Stata syntax
		A.2.8 Ado-files
	A.3 Program debugging
		A.3.1 Some simple tips
		A.3.2 Error messages and return code
		A.3.3 Trace
	A.4 Additional resources
B Mata
	B.1 How to run Mata
		B.1.1 Mata commands in Mata
		B.1.2 Mata commands in Stata
		B.1.3 Stata commands in Mata
		B.1.4 Interactive versus batch use
		B.1.5 Mata help
	B.2 Mata matrix commands
		B.2.1 Mata matrix input
		B.2.2 Mata matrix operators
		B.2.3 Mata functions
		B.2.4 Mata cross products
		B.2.5 Mata matrix subscripts and combining matrices
		B.2.6 Transferring Mata data and matrices to Stata
	B.3 Programming in Mata
		B.3.1 Mata program
		B.3.2 Mata program with results output to Stata
		B.3.3 Stata program that calls a Mata program
		B.3.4 Using Mata in ado-files
		B.3.5 Declarations
	B.4 Additional resources
C Optimization in Mata
	C.1 Mata moptimize() function
		C.1.1 moptimize() evaluators lf, d, gf, and q
		C.1.2 moptimize() functions
		C.1.3 moptimize() methods lf, lf0, lf1, and lf2
		C.1.4 moptimize() methods d0, d1, and d2
		C.1.5 moptimize() methods gf0, gf1, and gf2
		C.1.6 moptimize() methods q0 and q1
	C.2 Mata optimize() function
		C.2.1 optimize() d and gf evaluators
		C.2.2 Optimize functions
		C.2.3 Poisson example
	C.3 Additional resources
Glossary of abbreviations
Glossary of abbreviations
References
References
Author index
Author index
Subject index
Subject index