Health Econometrics Using Stata 2 Partha Deb Hunter College, CUNY and NBER Edward C. Norton University of Michigan and NBER Willard G. Manning University of Chicago ® A Stata Press Publication StataCorp LLC College Station, Texas ® Copyright © 2017 StataCorp LLC All rights reserved. First edition 2017 Published by Stata Press, 4905 Lakeway Drive, College Station, Texas 77845 Typeset in LATEX 2 Printed in the United States of America 10 9 8 7 6 5 4 3 2 1 Print ISBN-10: 1-59718-228-1 Print ISBN-13: 978-1-59718-228-7 ePub ISBN-10: 1-59718-229-X ePub ISBN-13: 978-1-59718-229-4 Mobi ISBN-10: 1-59718-230-3 Mobi ISBN-13: 978-1-59718-230-0 Library of Congress Control Number: 2016960172 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. Stata, , Stata Press, Mata, , and NetCourse are registered trademarks of StataCorp LLC. Stata and Stata Press are registered trademarks with the World Intellectual Property Organization of the United Nations. 3 NetCourseNow is a trademark of StataCorp LLC. LATEX 2 is a trademark of the American Mathematical Society. 4 Dedication to Willard G. Manning, Jr. (1946– 2014) Will Manning joined the RAND Corporation in 1975, a few years after completing his PhD at Stanford. He quickly became involved in the RAND Health Insurance Experiment . Will was the lead author of the article that reported the main insurance results in the 1987 American Economic Review, one of the most cited and influential articles in health economics. He also published many seminal articles about demand for alcohol and cigarettes, the taxes of sin, and mental healthcare. In 2010, the American Society of Health Economics awarded the Victor R. Fuchs Award to Will for his lifetime contributions to the field of health economics. But perhaps his strongest influence was on empirical methods central to applied health economics research. With others at RAND, he advocated moving away from tobit and sample-selection models to deal with distributions of dependent variables that had a large mass at zero. The two- part model , in all of its forms, is now the dominant model for healthcare expenditures and use. He also understood the power and limitations of taking logarithms of skewed distributions. And woe to the author who did not deal adequately with heteroskedasticity upon retransformation. Will continued to push the field of health econometrics through the end of his career. He helped develop new methods and advocated the work of others who found better ways of modeling healthcare expenditures and use. His influence on applied health economics is deep and lasting (Konetzka 2015; Mullahy 2015) . Will had three other characteristics that we grew to appreciate, if not emulate, over the years. He was absolutely meticulous about research— data, methods, and attribution. Precision is not merely an abstract statistical concept but an essential part of all steps in a research project. Will was extraordinarily generous with his time. We know of many junior economists who were amazed and profoundly grateful that Will took the time to give detailed feedback on their article or presentation— and to explain why their standard errors were all wrong. Finally, Will was hilariously funny. We know this is a rare trait in an economist, but a little levity makes the daily give and take in search of 5 truth that much more enjoyable. We dedicate this book to our friend and colleague, Will Manning. Partha Deb and Edward C. Norton 6 Contents Tables Figures Preface Notation and typography 1 Introduction 1.1 Outline 1.2 Themes 1.3 Health econometric myths 1.4 Stata friendly 1.5 A useful way forward 2 Framework 2.1 Introduction 2.2 Potential outcomes and treatment effects 2.3 Estimating ATEs 2.3.1 A laboratory experiment 2.3.2 Randomization 2.3.3 Covariate adjustment 2.4 Regression estimates of treatment effects 2.4.1 Linear regression 2.4.2 Nonlinear regression 2.5 Incremental and marginal effects 2.6 Model selection 2.6.1 In-sample model selection 2.6.2 Cross-validation 2.7 Other issues 3 MEPS data 3.1 Introduction 3.2 Overview of all variables 3.3 Expenditure and use variables 3.4 Explanatory variables 3.5 Sample dataset 7 3.6 Stata resources 4 The linear regression model: Specification and checks 4.1 Introduction 4.2 The linear regression model 4.3 Marginal, incremental, and treatment effects 4.3.1 Marginal and incremental effects 4.3.2 Graphical representation of marginal and incremental effects 4.3.3 Treatment effects 4.4 Consequences of misspecification 4.4.1 Example: A quadratic specification 4.4.2 Example: An exponential specification 4.5 Visual checks 4.5.1 Artificial-data example of visual checks 4.5.2 MEPS example of visual checks 4.6 Statistical tests 4.6.1 Pregibon’s link test 4.6.2 Ramsey’s RESET test 4.6.3 Modified Hosmer–Lemeshow test 4.6.4 Examples 4.6.5 Model selection using AIC and BIC 4.7 Stata resources 5 Generalized linear models 5.1 Introduction 5.2 GLM framework 5.2.1 GLM assumptions 5.2.2 Parameter estimation 5.3 GLM examples 5.4 GLM predictions 5.5 GLM example with interaction term 5.6 Marginal and incremental effects 5.7 Example of marginal and incremental effects 5.8 Choice of link function and distribution family 5.8.1 AIC and BIC 5.8.2 Test for the link function 5.8.3 Modified Park test for the distribution family 5.8.4 Extended GLM 5.9 Conclusions 5.10 Stata resources 8 6 Log and Box–Cox models 6.1 Introduction 6.2 Log models 6.2.1 Log model estimation and interpretation 6.3 Retransformation from ln(y) to raw scale 6.3.1 Error retransformation and model predictions 6.3.2 Marginal and incremental effects 6.4 Comparison of log models to GLM 6.5 Box–Cox models 6.5.1 Box–Cox example 6.6 Stata resources 7 Models for continuous outcomes with mass at zero 7.1 Introduction 7.2 Two-part models 7.2.1 Expected values and marginal and incremental effects 7.3 Generalized tobit 7.3.1 Full-information maximum likelihood and limited-information maximum likelihood 7.4 Comparison of two-part and generalized tobit models 7.4.1 Examples that show similarity of marginal effects 7.5 Interpretation and marginal effects 7.5.1 Two-part model example 7.5.2 Two-part model marginal effects 7.5.3 Two-part model marginal effects example 7.5.4 Generalized tobit interpretation 7.5.5 Generalized tobit example 7.6 Single-index models that accommodate zeros 7.6.1 The tobit model 7.6.2 Why tobit is used sparingly 7.6.3 One-part models 7.7 Statistical tests 7.8 Stata resources 8 Count models 8.1 Introduction 8.2 Poisson regression 8.2.1 Poisson MLE 8.2.2 Robustness of the Poisson regression 8.2.3 Interpretation 9 8.2.4 Is Poisson too restrictive? 8.3 Negative binomial models 8.3.1 Examples of negative binomial models 8.4 Hurdle and zero-inflated count models 8.4.1 Hurdle count models 8.4.2 Zero-inflated models 8.5 Truncation and censoring 8.5.1 Truncation 8.5.2 Censoring 8.6 Model comparisons 8.6.1 Model selection 8.6.2 Cross-validation 8.7 Conclusion 8.8 Stata resources 9 Models for heterogeneous effects 9.1 Introduction 9.2 Quantile regression 9.2.1 MEPS examples 9.2.2 Extensions 9.3 Finite mixture models 9.3.1 MEPS example of healthcare expenditures 9.3.2 MEPS example of healthcare use 9.4 Nonparametric regression 9.4.1 MEPS examples 9.5 Conditional density estimator 9.6 Stata resources 10 Endogeneity 10.1 Introduction 10.2 Endogeneity in linear models 10.2.1 OLS is inconsistent 10.2.2 2SLS 10.2.3 Specification tests 10.2.4 2SRI 10.2.5 Modeling endogeneity with ERM 10.3 Endogeneity with a binary endogenous variable 10.3.1 Additional considerations 10.4 GMM 10.5 Stata resources 10