Microeconometrics using Stata, Revised Edition

A. Colin Cameron and Pravin K. Trivedi

Microeconometrics Using Stata, Revised Edition, by A. Colin Cameron and Pravin K. Trivedi, is an outstanding introduction to microeconometrics and how to do microeconometric research using Stata. Aimed at students and researchers, this book covers topics left out of microeconometrics textbooks and omitted from basic introductions to Stata. Cameron and Trivedi provide the most complete and up-to-date survey of microeconometric methods available in Stata.

The revised edition has been updated to reflect the new features available in Stata 11 that are germane to microeconomists. Instead of using mfx and the user-written margeff commands, the revised edition uses the new margins command, emphasizing both marginal effects at the means and average marginal effects. Factor variables, which allow you to specify indicator variables and interaction effects, replace the xi command. The new gmm command for generalized method of moments and nonlinear instrumental-variables estimation is presented, along with several examples. Finally, the chapter on maximum likelihood estimation incorporates the enhancements made to ml in Stata 11.

Early in the book, Cameron and Trivedi introduce simulation methods and then use them to illustrate features of the estimators and tests described in the rest of the book. While simulation methods are important tools for econometricians, they are not covered in standard textbooks. By introducing simulation methods, the authors arm students and researchers with techniques they can use in future work. Cameron and Trivedi address each topic with an in-depth Stata example, and they reference their 2005 textbook, Microeconometrics: Methods and Applications, where appropriate.

The authors also show how to use Stata’s programming features to implement methods for which Stata does not have a specific command. Although the book is not specifically about Stata programming, it does show how to solve many programming problems. These techniques are essential in applied microeconometrics because there will always be new, specialized methods beyond what has already been incorporated into a software package.

Cameron and Trivedi’s choice of topics perfectly reflects the current practice of modern microeconometrics. After introducing the reader to Stata, the authors introduce linear regression, simulation, and generalized least-squares methods. The section on cross-sectional techniques is thorough, with up-to-date treatments of instrumental-variables methods for linear models and of quantile-regression methods.

The next section of the book covers estimators for the parameters of linear panel-data models. The authors’ choice of topics is unique: after addressing the standard random-effects and fixed-effects methods, the authors also describe mixed linear models—a method used in many areas outside of econometrics.

Cameron and Trivedi not only address methods for nonlinear regression models but also show how to code new nonlinear estimators in Stata. In addition to detailing nonlinear methods, which are omitted from most econometrics textbooks, this section shows researchers and students how to easily implement new nonlinear estimators.

The authors next describe inference using analytical and bootstrap approximations to the distribution of test statistics. This section highlights Stata’s power to easily obtain bootstrap approximations, and it also introduces the basic elements of statistical inference.

Cameron and Trivedi then include an extensive section about methods for different nonlinear models. They begin by detailing methods for binary dependent variables. This section is followed by sections about multinomial models, tobit and selection models, count-data models, and nonlinear panel-data models. Two appendices about Stata programming complete the book.

The unique combination of topics, intuitive introductions to methods, and detailed illustrations of Stata examples make Microeconometrics Using Stata an invaluable, hands-on addition to the library of anyone who uses microeconometric methods.

Table of contents

List of tables

List of figures

Preface to the Revised 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, findit, and hsearch 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 Abbreviations, case sensitivity, and wildcards

1.3.5 Arithmetic, relational, and logical operators

1.3.6 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 Some useful commands

1.10 Template do-file

1.11 User-written commands

1.12 Stata resources

1.13 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

2.3.8 Dictionary files

2.3.9 Common pitfalls

2.4 Data management

2.4.1 PSID 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)

The generate and replace commands

The egen command

The recode command

The by prefix

Indicator variables

Set of indicator variables

Interactions

Demeaning

2.4.8 Saving data

2.4.9 Selecting the sample

2.5 Manipulating datasets

2.5.1 Ordering observations and variables

2.5.2 Preserving and restoring a dataset

2.5.3 Wide and long forms for a dataset

2.5.4 Merging datasets

2.5.5 Appending datasets

2.6 Graphical display of data

2.6.1 Stata graph commands

Example graph commands

Saving and exporting graphs

Learning how to use 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 Lowess, kernel, local linear, and nearest-neighbor regression

2.6.7 Multiple scatterplots

2.7 Stata 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 for data

3.2.6 Statistical tests

3.2.7 Data plots

3.3 Regression in levels and logs

3.3.1 Basic regression theory

3.3.2 OLS regression and matrix algebra

3.3.3 Properties of the OLS estimator

3.3.4 Heteroskedasticity-robust standard errors

3.3.5 Cluster–robust standard errors

3.3.6 Regression in logs

3.4 Basic regression analysis

3.4.1 Correlations

3.4.2 The regress command

3.4.3 Hypothesis tests

3.4.4 Tables of output from several regressions

3.4.5 Even better tables of regression output 3.4.6 Factor variables for categorical variables and interactions

3.5 Specification analysis

3.5.1 Specification tests and model diagnostics

3.5.2 Residual diagnostic plots

3.5.3 Influential observations

3.5.4 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

3.5.5 Tests have power in more than one direction

3.6 Prediction

3.6.1 In-sample prediction

3.6.2 MEs and elasticities

3.6.3 Prediction in logs: The retransformation problem

3.6.4 Prediction exercise

3.7 Sampling weights

3.7.1 Weights

3.7.2 Weighted mean

3.7.3 Weighted regression

3.7.4 Weighted prediction and MEs

3.8 OLS using Mata

3.9 Stata resources

3.10 Exercises

4 Simulation

4.1 Introduction

4.2 Pseudorandom-number generators: Introduction

4.2.1 Uniform random-number generation

4.2.2 Draws from normal

4.2.3 Draws from t, chi-squared, F, gamma, and beta

4.2.4 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

4.3 Distribution of the sample mean

4.3.1 Stata program

4.3.2 The simulate command

4.3.3 Central limit theorem simulation

4.3.4 The postfile command

4.3.5 Alternative central limit theorem simulation

4.4 Pseudorandom-number generators: Further details

4.4.1 Inverse-probability transformation

4.4.2 Direct transformation

4.4.3 Other methods

4.4.4 Draws from truncated normal

4.4.5 Draws from multivariate normal

Direct draws from multivariate normal

Transformation using Cholesky decomposition

4.4.6 Draws using Markov chain Monte Carlo method

4.5 Computing integrals

4.5.1 Quadrature

4.5.2 Monte Carlo integration

4.5.3 Monte Carlo integration using different S

4.6 Simulation for regression: Introduction

4.6.1 Simulation example: OLS with X² errors

4.6.2 Interpreting simulation output

Unbiasedness of estimator

Standard errors

t statistic

Test size

Number of simulations

4.6.3 Variations

Different sample size and number of simulations

Test power

Different error distributions

4.6.4 Estimator inconsistency

4.6.5 Simulation with endogenous regressors

4.7 Stata resources

4.8 Exercises

5 GLS regression

5.1 Introduction

5.2 GLS and FGLS regression

5.2.1 GLS for heteroskedastic errors

5.2.2 GLS and FGLS

5.2.3 Weighted least squares and robust standard errors

5.2.4 Leading examples

5.3 Modeling heteroskedastic data

5.3.1 Simulated dataset

5.3.2 OLS estimation

5.3.3 Detecting heteroskedasticity

5.3.4 FGLS estimation

5.3.5 WLS estimation

5.4 System of linear regressions

5.4.1 SUR model

5.4.2 The sureg command

5.4.3 Application to two categories of expenditures

5.4.4 Robust standard errors

5.4.5 Testing cross-equation constraints

5.4.6 Imposing cross-equation constraints

5.5 Survey data: Weighting, clustering, and stratification

5.5.1 Survey design

5.5.2 Survey mean estimation

5.5.3 Survey linear regression

5.6 Stata resources

5.7 Exercises

6 Linear instrumental-variables regression

6.1 Introduction

6.2 IV estimation

6.2.1 Basic IV theory

6.2.2 Model setup

6.2.3 IV estimators: IV, 2SLS, and GMM

6.2.4 Instrument validity and relevance

6.2.5 Robust standard-error estimates

6.3 IV example

6.3.1 The ivregress command

6.3.2 Medical expenditures with one endogenous regressor

6.3.3 Available instruments

6.3.4 IV estimation of an exactly identified model

6.3.5 IV estimation of an overidentified model

6.3.6 Testing for regressor endogeneity

6.3.7 Tests of overidentifying restrictions

6.3.8 IV estimation with a binary endogenous regressor

6.4 Weak instruments

6.4.1 Finite-sample properties of IV estimators

6.4.2 Weak instruments

Diagnostics for weak instruments

Formal tests for weak instruments

6.4.3 The estat firststage command

6.4.4 Just-identified model

6.4.5 Overidentified model

6.4.6 More than one endogenous regressor

6.4.7 Sensitivity to choice of instruments

6.5 Better inference with weak instruments

6.5.1 Conditional tests and confidence intervals

6.5.2 LIML estimator

6.5.3 Jackknife IV estimator

6.5.4 Comparison of 2SLS, LIML, JIVE, and GMM

6.6 3SLS systems estimation

6.7 Stata resources

6.8 Exercises

7 Quantile regression

7.1 Introduction

7.2 QR

7.2.1 Conditional quantiles

7.2.2 Computation of QR estimates and standard errors

7.2.3 The qreg, bsqreg, and sqreg commands

7.3 QR for medical expenditures data

7.3.1 Data summary

7.3.2 QR estimates

7.3.3 Interpretation of conditional quantile coefficients

7.3.4 Retransformation

7.3.5 Comparison of estimates at different quantiles

7.3.6 Heteroskedasticity test

7.3.7 Hypothesis tests

7.3.8 Graphical display of coefficients over quantiles

7.4 QR for generated heteroskedastic data

7.4.1 Simulated dataset

7.4.2 QR estimates

7.5 QR for count data

7.5.1 Quantile count regression

7.5.2 The qcount command

7.5.3 Summary of doctor visits data

7.5.4 Results from QCR

7.6 Stata resources

7.7 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

Individual-effects model

Fixed-effects model

Random-effects model

Pooled model or population-averaged model

Two-way–effects model

Mixed linear models

8.2.3 Cluster–robust inference

8.2.4 The xtreg command

8.2.5 Stata linear panel-data commands

8.3 Panel-data summary

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 population-averaged estimator

8.4.3 The xtreg, pa command

8.4.4 Application of the xtreg, pa command

8.5 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-variables regression

8.6 Between estimator

8.6.1 Between estimator

8.6.2 Application of the xtreg, be command

8.7 RE estimator

8.7.1 RE estimator

8.7.2 The xtreg, re command

8.7.3 Application of the xtreg, re command

8.8 Comparison of estimators

8.8.1 Estimates of variance components

8.8.2 Within and between R-squared

8.8.3 Estimator comparison

8.8.4 Fixed effects versus random effects

8.8.5 Hausman test for fixed effects

The hausman command

Robust Hausman test

8.8.6 Prediction

8.9 First-difference estimator

8.9.1 First-difference estimator

8.9.2 Strict and weak exogeneity

8.10 Long panels

8.10.1 Long-panel dataset

8.10.2 Pooled OLS and PFGLS

8.10.3 The xtpcse and xtgls commands

8.10.4 Application of the xtgls, xtpcse, and xtscc commands

8.10.5 Separate regressions

8.10.6 FE and RE models

8.10.7 Unit roots and cointegration

8.11 Panel-data management

8.11.1 Wide-form data

8.11.2 Convert wide form to long form

8.11.3 Convert long form to wide form

8.11.4 An alternative to wide-form data

8.12 Stata resources

8.13 Exercises

9 Linear panel-data models: Extensions

9.1 Introduction

9.2 Panel IV 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

9.5 Mixed linear models

9.5.1 Mixed linear model

9.5.2 The xtmixed command

9.5.3 Random-intercept model

9.5.4 Cluster–robust standard errors

9.5.5 Random-slopes model

9.5.6 Random-coefficients model

9.5.7 Two-way random-effects model

9.6 Clustered data

9.6.1 Clustered dataset

9.6.2 Clustered data using nonpanel commands

9.6.3 Clustered data using panel commands

9.6.4 Hierarchical linear models

9.7 Stata resources

9.8 Exercises

10 Nonlinear regression methods

10.1 Introduction

10.2 Nonlinear example: Doctor visits

10.2.1 Data description

10.2.2 Poisson model description

10.3 Nonlinear regression methods

10.3.1 MLE

10.3.2 The poisson command

10.3.3 Postestimation commands

10.3.4 NLS

10.3.5 The nl command

10.3.6 GLM

10.3.7 The glm command

10.3.8 Other estimators

10.4 Different estimates of the VCE

10.4.1 General framework

10.4.2 The vce() option

10.4.3 Application of the vce() option

10.4.4 Default estimate of the VCE

10.4.5 Robust estimate of the VCE

10.4.6 Cluster–robust estimate of the VCE

10.4.7 Heteroskedasticity- and autocorrelation-consistent estimate of the VCE

10.4.8 Bootstrap standard errors

10.4.9 Statistical inference

10.5 Prediction

10.5.1 The predict and predictnl commands

10.5.2 Application of predict and predictnl

10.5.3 Out-of-sample prediction

10.5.4 Prediction at a specified value of one of the regressors

10.5.5 Prediction at a specified value of all the regressors

10.5.6 Prediction of other quantities

          10.5.7 The margins command for prediction

10.6 Marginal effects

10.6.1 Calculus and finite-difference methods

10.6.2 MEs estimates AME, MEM, and MER

10.6.3 Elasticities and semielasticities

10.6.4 Simple interpretations of coefficients in single-index models

10.6.5 The margins command for marginal effects

10.6.6 MEM: Marginal effect at mean

Comparison of calculus and finite-difference methods

10.6.7 MER: Marginal effect at representative value

10.6.8 AME: Average marginal effect

10.6.9 Elasticities and semielasticities

10.6.10 AME computed manually

10.6.11 Polynomial regressors

10.6.12 Interacted regressors

10.6.13 Complex interactions and nonlinearities

10.7 Model diagnostics

10.7.1 Goodness-of-fit measures

10.7.2 Information criteria for model comparison

10.7.3 Residuals

10.7.4 Model-specification tests

10.8 Stata resources

10.9 Exercises

11 Nonlinear optimization methods

11.1 Introduction

11.2 Newton–Raphson method

11.2.1 NR method

11.2.2 NR method for Poisson

11.2.3 Poisson NR example using Mata

Core Mata code for Poisson NR iterations

Complete Stata and Mata code for Poisson NR iterations

11.3 Gradient methods

11.3.1 Maximization options

11.3.2 Gradient methods

11.3.3 Messages during iterations

11.3.4 Stopping criteria

11.3.5 Multiple maximums

11.3.6 Numerical derivatives

11.4 The ml command: lf method

11.4.1 The ml command

11.4.2 The lf method

11.4.3 Poisson example: Single-index model

11.4.4 Negative binomial example: Two-index model

11.4.5 NLS example: Nonlikelihood model

11.5 Checking the program

11.5.1 Program debugging using ml check and ml trace

11.5.2 Getting the program to run

11.5.3 Checking the data

11.5.4 Multicollinearity and near collinearity

11.5.5 Multiple optimums

11.5.6 Checking parameter estimation

11.5.7 Checking standard-error estimation

11.6 The ml command: d0, d1, d2, lf0, lf1, and lf2 methods 

11.6.1 Evaluator functions

11.6.2 The d0 method

11.6.3 The d1 method

11.6.4 The lf1 method with the robust estimate of the VCE 

11.6.5 The d2 and lf2 methods

11.7 The Mata optimize() function

11.7.1 Type d and gf evaluators

11.7.2 Optimize functions

11.7.3 Poisson example

Evaluator program for Poisson MLE

The optimize() function for Poisson MLE

11.8 Generalized method of moments

11.8.1 Definition

11.8.2 Nonlinear IV example

11.8.3 GMM using the Mata optimize() function

11.9 Stata resources

11.10 Exercises

12 Testing methods

12.1 Introduction

12.2 Critical values and p-values

12.2.1 Standard normal compared with Student's t

12.2.2 Chi-squared compared with F

12.2.3 Plotting densities

12.2.4 Computing p-values and critical values

12.2.5 Which distributions does Stata use?

12.3 Wald tests and confidence intervals

12.3.1 Wald test of linear hypotheses

12.3.2 The test command

Test single coefficient

Test several hypotheses

Test of overall significance

Test calculated from retrieved coefficients and VCE

12.3.3 One-sided Wald tests

12.3.4 Wald test of nonlinear hypotheses (delta method)

12.3.5 The testnl command

12.3.6 Wald confidence intervals

12.3.7 The lincom command

12.3.8 The nlcom command (delta method)

12.3.9 Asymmetric confidence intervals

12.4 Likelihood-ratio tests

12.4.1 Likelihood-ratio tests

12.4.2 The lrtest command

12.4.3 Direct computation of LR tests

12.5 Lagrange multiplier test (or score test)

12.5.1 LM tests

12.5.2 The estat command

12.5.3 LM test by auxiliary regression

12.6 Test size and power

12.6.1 Simulation DGP: OLS with chi-squared errors

12.6.2 Test size

12.6.3 Test power

12.6.4 Asymptotic test power

12.7 Specification tests

12.7.1 Moment-based tests

12.7.2 Information matrix test

12.7.3 Chi-squared goodness-of-fit test

12.7.4 Overidentifying restrictions test

12.7.5 Hausman test

12.7.6 Other tests

12.8 Stata resources

12.9 Exercises

13 Bootstrap methods

13.1 Introduction

13.2 Bootstrap methods

13.2.1 Bootstrap estimate of standard error

13.2.2 Bootstrap methods

13.2.3 Asymptotic refinement

13.2.4 Use the bootstrap with caution

13.3 Bootstrap pairs using the vce(bootstrap) option

13.3.1 Bootstrap-pairs method to estimate VCE

13.3.2 The vce(bootstrap) option

13.3.3 Bootstrap standard-errors example

13.3.4 How many bootstraps?

13.3.5 Clustered bootstraps

13.3.6 Bootstrap confidence intervals

13.3.7 The postestimation estat bootstrap command

13.3.8 Bootstrap confidence-intervals example

13.3.9 Bootstrap estimate of bias

13.4 Bootstrap pairs using the bootstrap command

13.4.1 The bootstrap command

13.4.2 Bootstrap parameter estimate from a Stata estimation command

13.4.3 Bootstrap standard error from a Stata estimation command

13.4.4 Bootstrap standard error from a user-written estimation command

13.4.5 Bootstrap two-step estimator

13.4.6 Bootstrap Hausman test

13.4.7 Bootstrap standard error of the coefficient of variation

13.5 Bootstraps with asymptotic refinement

13.5.1 Percentile-t method

13.5.2 Percentile-t Wald test

13.5.3 Percentile-t Wald confidence interval

13.6 Bootstrap pairs using bsample and simulate

13.6.1 The bsample command

13.6.2 The bsample command with simulate

13.6.3 Bootstrap Monte Carlo exercise

13.7 Alternative resampling schemes

13.7.1 Bootstrap pairs

13.7.2 Parametric bootstrap

13.7.3 Residual bootstrap

13.7.4 Wild bootstrap

13.7.5 Subsampling

13.8 The jackknife

13.8.1 Jackknife method

13.8.2 The vce(jackknife) option and the jackknife command

13.9 Stata resources

13.10 Exercises

14 Binary outcome models

14.1 Introduction

14.2 Some parametric models

14.2.1 Basic model

14.2.2 Logit, probit, linear probability, and clog-log models

14.3 Estimation

14.3.1 Latent-variable interpretation and identification

14.3.2 ML estimation

14.3.3 The logit and probit commands

14.3.4 Robust estimate of the VCE

14.3.5 OLS estimation of LPM

14.4 Example

14.4.1 Data description

14.4.2 Logit regression

14.4.3 Comparison of binary models and parameter estimates

14.5 Hypothesis and specification tests

14.5.1 Wald tests

14.5.2 Likelihood-ratio tests

14.5.3 Additional model-specification tests

          Lagrange multiplier test of generalized logit

          Heteroskedastic probit regression

14.5.4 Model comparison

14.6 Goodness of fit and prediction

14.6.1 Pseudo-R² measure

14.6.2 Comparing predicted probabilities with sample frequencies

14.6.3 Comparing predicted outcomes with actual outcomes

14.6.4 The predict command for fitted probabilities

14.6.5 The prvalue command for fitted probabilities

14.7 Marginal effects

14.7.1 Marginal effect at a representative value (MER)

14.7.2 Marginal effect at the mean (MEM)

14.7.3 Average marginal effect (AME)

14.7.4 The prchange command

14.8 Endogenous regressors

14.8.1 Example

14.8.2 Model assumptions

14.8.3 Structural-model approach

The ivprobit command

Maximum likelihood estimates

Two-step sequential estimates

14.8.4 IVs approach

14.9 Grouped data

14.9.1 Estimation with aggregate data

14.9.2 Grouped-data application

14.10 Stata resources

14.11 Exercises

15 Multinomial models

15.1 Introduction

15.2 Multinomial models overview

15.2.1 Probabilities and MEs

15.2.2 Maximum likelihood estimation

15.2.3 Case-specific and alternative-specific regressors

15.2.4 Additive random-utility model

15.2.5 Stata multinomial model commands

15.3 Multinomial example: Choice of fishing mode

15.3.1 Data description

15.3.2 Case-specific regressors

15.3.3 Alternative-specific regressors

15.4 Multinomial logit model

15.4.1 The mlogit command

15.4.2 Application of the mlogit command

15.4.3 Coefficient interpretation

15.4.4 Predicted probabilities

15.4.5 MEs

15.5 Conditional logit model

15.5.1 Creating long-form data from wide-form data

15.5.2 The asclogit command

15.5.3 The clogit command

15.5.4 Application of the asclogit command

15.5.5 Relationship to multinomial logit model

15.5.6 Coefficient interpretation

15.5.7 Predicted probabilities

15.5.8 MEs

15.6 Nested logit model

15.6.1 Relaxing the independence of irrelevant alternatives assumption

15.6.2 NL model

15.6.3 The nlogit command

15.6.4 Model estimates

15.6.5 Predicted probabilities

15.6.6 MEs

15.6.7 Comparison of logit models

15.7 Multinomial probit model

15.7.1 MNP

15.7.2 The mprobit command

15.7.3 Maximum simulated likelihood

15.7.4 The asmprobit command

15.7.5 Application of the asmprobit command

15.7.6 Predicted probabilities and MEs

15.8 Random-parameters logit

15.8.1 Random-parameters logit

15.8.2 The mixlogit command

15.8.3 Data preparation for mixlogit

15.8.4 Application of the mixlogit command

15.9 Ordered outcome models

15.9.1 Data summary

15.9.2 Ordered outcomes

15.9.3 Application of the ologit command

15.9.4 Predicted probabilities

15.9.5 MEs

15.9.6 Other ordered models

15.10 Multivariate outcomes

15.10.1 Bivariate probit

15.10.2 Nonlinear SUR

15.11 Stata resources

15.12 Exercises

16 Tobit and selection models

16.1 Introduction

16.2 Tobit model

16.2.1 Regression with censored data

16.2.2 Tobit model setup

16.2.3 Unknown censoring point

16.2.4 Tobit estimation

16.2.5 ML estimation in Stata

16.3 Tobit model example

16.3.1 Data summary

16.3.2 Tobit analysis

16.3.3 Prediction after tobit

16.3.4 Marginal effects

Left-truncated, left-censored, and right-truncated examples

Left-censored case computed directly

Marginal impact on probabilities

16.3.5 The ivtobit command

16.3.6 Additional commands for censored regression

16.4 Tobit for lognormal data

16.4.1 Data example

16.4.2 Setting the censoring point for data in logs

16.4.3 Results

16.4.4 Two-limit tobit

16.4.5 Model diagnostics

16.4.6 Tests of normality and homoskedasticity

Generalized residuals and scores

Test of normality

Test of homoskedasticity

16.4.7 Next step?

16.5 Two-part model in logs

16.5.1 Model structure

16.5.2 Part 1 specification

16.5.3 Part 2 of the two-part model

16.6 Selection model

16.6.1 Model structure and assumptions

16.6.2 ML estimation of the sample-selection model

16.6.3 Estimation without exclusion restrictions

16.6.4 Two-step estimation

16.6.5 Estimation with exclusion restrictions

16.7 Prediction from models with outcome in logs

16.7.1 Predictions from tobit

16.7.2 Predictions from two-part model

16.7.3 Predictions from selection model

16.8 Stata resources

16.9 Exercises

17 Count-data models

17.1 Introduction

17.2 Features of count data

17.2.1 Generated Poisson data

17.2.2 Overdispersion and negative binomial data

17.2.3 Modeling strategies

17.2.4 Estimation methods

17.3 Empirical example 1

17.3.1 Data summary

17.3.2 Poisson model

Poisson model results

Robust estimate of VCE for Poisson MLE

Test of overdispersion

Coefficient interpretation and marginal effects

17.3.3 NB2 model

NB2 model results

Fitted probabilities for Poisson and NB2 models

The countfit command

The prvalue command

Discussion

Generalized NB model

17.3.4 Nonlinear least-squares estimation

17.3.5 Hurdle model

Variants of the hurdle model

Application of the hurdle model

17.3.6 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

17.4 Empirical example 2

17.4.1 Zero-inflated data

17.4.2 Models for zero-inflated data

17.4.3 Results for the NB2 model

The prcounts command

17.4.4 Results for ZINB

17.4.5 Model comparison

The countfit command

Model comparison using countfit

17.5 Models with endogenous regressors

17.5.1 Structural-model approach

Model and assumptions

Two-step estimation

Application

17.5.2 Nonlinear IV method

17.6 Stata resources

17.7 Exercises

18 Nonlinear panel models

18.1 Introduction

18.2 Nonlinear panel-data overview

18.2.1 Some basic nonlinear panel models

FE models

RE models

Pooled models or population-averaged models

Comparison of models

18.2.2 Dynamic models

18.2.3 Stata nonlinear panel commands

18.3 Nonlinear panel-data example

18.3.1 Data description and summary statistics

18.3.2 Panel-data organization

18.3.3 Within and between variation

18.3.4 FE or RE model for these data?

18.4 Binary outcome models

18.4.1 Panel summary of the dependent variable

18.4.2 Pooled logit estimator

18.4.3 The xtlogit command

18.4.4 The xtgee command

18.4.5 PA logit estimator

18.4.6 RE logit estimator

18.4.7 FE logit estimator

18.4.8 Panel logit estimator comparison

18.4.9 Prediction and marginal effects

18.4.10 Mixed-effects logit estimator

18.5 Tobit model

18.5.1 Panel summary of the dependent variable

18.5.2 RE tobit model

18.5.3 Generalized tobit models

18.5.4 Parametric nonlinear panel models

18.6 Count-data models

18.6.1 The xtpoisson command

18.6.2 Panel summary of the dependent variable

18.6.3 Pooled Poisson estimator

18.6.4 PA Poisson estimator

18.6.5 RE Poisson estimators

18.6.6 FE Poisson estimator

18.6.7 Panel Poisson estimators comparison

18.6.8 Negative binomial estimators

18.7 Stata resources

18.8 Exercises

A Programming in Stata

A.1 Stata matrix commands

A.1.1 Stata matrix overview

A.1.2 Stata matrix input and output

Matrix input by hand

Matrix input from Stata estimation results

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

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

Matrix input by hand

Identity matrices, unit vectors, and matrices of constants

Matrix input from Stata data

Matrix input from Stata matrix

Stata interface functions

B.2.2 Mata matrix operators

Element-by-element operators

B.2.3 Mata functions

Scalar and matrix functions

Matrix inversion

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

Creating Stata matrices from Mata matrices

Creating Stata data from a Mata vector

B.3 Programming in Mata

B.3.1 Declarations

B.3.2 Mata program

B.3.3 Mata program with results output to Stata

B.3.4 Stata program that calls a Mata program

B.3.5 Using Mata in ado-files

Glossary of abbreviations

References

Author index

Subject Index