Mostly Econometrics
Mostly Harmless Econometrics: An Empiricist’ Companion s
Joshua D. Angrist Massachusetts Institute of Technology Jörn-Ste¤en Pischke The London School of Economics
March 2008
ii
Contents
Preface Acknowledgments Organization of this Book xi xiii xv
I
Introduction
1
3 9 10 12 16
1 Questions about Questions 2 The Experimental Ideal 2.1 2.2 2.3 The Selection Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Random Assignment Solves the Selection Problem . . . . . . . . . . . . . . . . . . . . . . . . Regression Analysis of Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
II
The Core
19
21 22 23 26 30 36 38 38 44 47 51 51
3 Making Regression Make Sense 3.1 Regression Fundamentals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.1 3.1.2 3.1.3 3.1.4 3.2 Economic Relationships and the Conditional Expectation Function . . . . . . . . . . . Linear Regression and the CEF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Asymptotic OLS Inference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Saturated Models, Main E¤ects, and Other Regression Talk . . . . . . . . . . . . . . .
Regression and Causality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.1 3.2.2 3.2.3 The Conditional Independence Assumption . . . . . . . . . . . . . . . . . . . . . . . . The Omitted Variables Bias Formula . . . . . . . . . . . . . . . . . . . . . . . . . . . . Bad Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3
Heterogeneity and Nonlinearity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.1 Regression Meets Matching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii
iv 3.3.2 3.3.3 3.4
CONTENTS Control for Covariates Using the Propensity Score . . . . . . . . . . . . . . . . . . . .
Joshua D. Angrist Massachusetts Institute of Technology Jörn-Ste¤en Pischke The London School of Economics
March 2008
ii
Contents
Preface Acknowledgments Organization of this Book xi xiii xv
I
Introduction
1
3 9 10 12 16
1 Questions about Questions 2 The Experimental Ideal 2.1 2.2 2.3 The Selection Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Random Assignment Solves the Selection Problem . . . . . . . . . . . . . . . . . . . . . . . . Regression Analysis of Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
II
The Core
19
21 22 23 26 30 36 38 38 44 47 51 51
3 Making Regression Make Sense 3.1 Regression Fundamentals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.1 3.1.2 3.1.3 3.1.4 3.2 Economic Relationships and the Conditional Expectation Function . . . . . . . . . . . Linear Regression and the CEF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Asymptotic OLS Inference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Saturated Models, Main E¤ects, and Other Regression Talk . . . . . . . . . . . . . . .
Regression and Causality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.1 3.2.2 3.2.3 The Conditional Independence Assumption . . . . . . . . . . . . . . . . . . . . . . . . The Omitted Variables Bias Formula . . . . . . . . . . . . . . . . . . . . . . . . . . . . Bad Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3
Heterogeneity and Nonlinearity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.1 Regression Meets Matching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii
iv 3.3.2 3.3.3 3.4
CONTENTS Control for Covariates Using the Propensity Score . . . . . . . . . . . . . . . . . . . .
References: REFERENCES Ananat, Elizabeth, and Guy Michaels (2008): “The E¤ect of Marital Breakup on the Income Distribution of Women with Children,” Journal of Human Resources, forthcoming