...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 . ....
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