Microeconometrics Using Stata Volume II: Nonlinear Models and Causal Inference Methods Second Edition A. COLIN CAMERON Department of Economics University of California, Davis, CA and School of Economics University of Sydney, Sydney, Australia PRAVIN K. TRIVEDI School of Economics University of Queensland, Brisbane, Australia and Department of Economics Indiana University, Bloomington, IN ® A Stata Press Publication StataCorp LLC College Station, Texas ® Copyright © 2009, 2010, 2022 by StataCorp LLC All rights reserved. First edition 2009 Revised edition 2010 Second edition 2022 Published by Stata Press, 4905 Lakeway Drive, College Station, Texas 77845 Typeset in LaTeX2e Printed in the United States of America 10 9 8 7 6 5 4 3 2 1 Print ISBN-10: 1-59718-359-8 (volumes I and II) Print ISBN-10: 1-59718-361-X (volume I) Print ISBN-10: 1-59718-362-8 (volume II) Print ISBN-13: 978-1-59718-359-8 (volumes I and II) Print ISBN-13: 978-1-59718-361-1 (volume I) Print ISBN-13: 978-1-59718-362-8 (volume II) ePub ISBN-10: 1-59718-360-1 (volumes I and II) ePub ISBN-10: 1-59718-363-6 (volumes I) ePub ISBN-10: 1-59718-364-4 (volumes II) ePub ISBN-13: 978-1-59718-360-4 (volumes I and II) ePub ISBN-13: 978-1-59718-363-5 (volumes I) ePub ISBN-13: 978-1-59718-364-2 (volumes II) Library of Congress Control Number: 2022938057 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 LLC. 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Contents 16 Nonlinear optimization methods 16.1 Introduction 16.2 Newton–Raphson method 16.3 Gradient methods 16.4 Overview of ml, moptimize(), and optimize() 16.5 The ml command: lf method 16.6 Checking the program 16.7 The ml command: lf0–lf2, d0–d2, and gf0 methods 16.8 Nonlinear instrumental-variables (GMM) example 16.9 Additional resources 16.10 Exercises 17 Binary outcome models 17.1 Introduction 17.2 Some parametric models 17.3 Estimation 17.4 Example 17.5 Goodness of fit and prediction 17.6 Marginal effects 17.7 Clustered data 17.8 Additional models 17.9 Endogenous regressors 17.10 Grouped and fractional data 17.11 Additional resources 17.12 Exercises 18 Multinomial models 18.1 Introduction 18.2 Multinomial models overview 18.3 Multinomial example: Choice of fishing mode 18.4 Multinomial logit model 18.5 Alternative-specific conditional logit model 18.6 Nested logit model 18.7 Multinomial probit model 18.8 Alternative-specific random-parameters logit 18.9 Ordered outcome models 18.10 Clustered data 18.11 Multivariate outcomes 18.12 Additional resources 18.13 Exercises 19 Tobit and selection models 19.1 Introduction 19.2 Tobit model 19.3 Tobit model example 19.4 Tobit for lognormal data 19.5 Two-part model in logs 19.6 Selection models 19.7 Nonnormal models of selection 19.8 Prediction from models with outcome in logs 19.9 Endogenous regressors 19.10 Missing data 19.11 Panel attrition 19.12 Additional resources 19.13 Exercises 20 Count-data models 20.1 Introduction 20.2 Modeling strategies for count data 20.3 Poisson and negative binomial models 20.4 Hurdle model 20.5 Finite-mixture models 20.6 Zero-inflated models 20.7 Endogenous regressors 20.8 Clustered data 20.9 Quantile regression for count data 20.10 Additional resources 20.11 Exercises 21 Survival analysis for duration data 21.1 Introduction 21.2 Data and data summary 21.3 Survivor and hazard functions 21.4 Semiparametric regression model 21.5 Fully parametric regression models 21.6 Multiple-records data 21.7 Discrete-time hazards logit model 21.8 Time-varying regressors 21.9 Clustered data 21.10 Additional resources 21.11 Exercises 22 Nonlinear panel models 22.1 Introduction 22.2 Nonlinear panel-data overview 22.3 Nonlinear panel-data example 22.4 Binary outcome and ordered outcome models 22.5 Tobit and interval-data models 22.6 Count-data models 22.7 Panel quantile regression 22.8 Endogenous regressors in nonlinear panel models 22.9 Additional resources 22.10 Exercises 23 Parametric models for heterogeneity and endogeneity 23.1 Introduction 23.2 Finite mixtures and unobserved heterogeneity 23.3 Empirical examples of FMMs 23.4 Nonlinear mixed-effects models 23.5 Linear structural equation models 23.6 Generalized structural equation models 23.7 ERM commands for endogeneity and selection 23.8 Additional resources 23.9 Exercises 24 Randomized control trials and exogenous treatment effects 24.1 Introduction 24.2 Potential outcomes 24.3 Randomized control trials 24.4 Regression in an RCT 24.5 Treatment evaluation with exogenous treatment 24.6 Treatment evaluation methods and estimators 24.7 Stata commands for treatment evaluation 24.8 Oregon Health Insurance Experiment example 24.9 Treatment-effect estimates using the OHIE data 24.10 Multilevel treatment effects 24.11 Conditional quantile TEs 24.12 Additional resources 24.13 Exercises 25 Endogenous treatment effects 25.1 Introduction 25.2 Parametric methods for endogenous treatment 25.3 ERM commands for endogenous treatment 25.4 ET commands for binary endogenous treatment 25.5 The LATE estimator for heterogeneous effects 25.6 Difference-in-differences and synthetic control 25.7 Regression discontinuity design 25.8 Conditional quantile regression with endogenous regressors 25.9 Unconditional quantiles 25.10 Additional resources 25.11 Exercises 26 Spatial regression 26.1 Introduction 26.2 Overview of spatial regression models 26.3 Geospatial data 26.4 The spatial weighting matrix 26.5 OLS regression and test for spatial correlation 26.6 Spatial dependence in the error 26.7 Spatial autocorrelation regression models 26.8 Spatial instrumental variables 26.9 Spatial panel-data models 26.10 Additional resources 26.11 Exercises 27 Semiparametric regression 27.1 Introduction 27.2 Kernel regression 27.3 Series regression 27.4 Nonparametric single regressor example 27.5 Nonparametric multiple regressor example 27.6 Partial linear model 27.7 Single-index model 27.8 Generalized additive models 27.9 Additional resources 27.10 Exercises 28 Machine learning for prediction and inference 28.1 Introduction 28.2 Measuring the predictive ability of a model 28.3 Shrinkage estimators 28.4 Prediction using lasso, ridge, and elasticnet 28.5 Dimension reduction 28.6 Machine learning methods for prediction 28.7 Prediction application 28.8 Machine learning for inference in partial linear model 28.9 Machine learning for inference in other models 28.10 Additional resources 28.11 Exercises 29 Bayesian methods: Basics 29.1 Introduction 29.2 Bayesian introductory example 29.3 Bayesian methods overview 29.4 An i.i.d. example 29.5 Linear regression 29.6 A linear regression example 29.7 Modifying the MH algorithm 29.8 RE model 29.9 Bayesian model selection 29.10 Bayesian prediction 29.11 Probit example 29.12 Additional resources 29.13 Exercises