Ec1123 Section 7 Instrumental Variables - Harvard University

Ec1123 Section 7 Instrumental Variables

Andrea Passalacqua

Harvard University andreapassalacqua@g.harvard.edu

November 16th, 2017

Andrea Passalacqua (Harvard)

Ec1123 Section 7 Instrumental Variables

November 16th, 2017 1 / 28

Outline

1 Simultaneous Causality 2 Instrumental Variable Regression: Introduction

Conditions 3 IV: Examples 4 Two-Stage Least Squares 5 Testing the Validity of Instruments

Andrea Passalacqua (Harvard)

Ec1123 Section 7 Instrumental Variables

November 16th, 2017 2 / 28

Simultaneous causality: What is that?

Yi = 0 + 1Xi + 2W1i + 3W2i + ui

Simultaneous causality arises when X - Y and X - Y

OLS will fail because conditional mean independence (CMI) is violated. Recall CMI: E [u|X , W1, W2] = E [u|W1, W2] ? conditional on Z1 and Z2, X is as good as randomly assigned

However, it is not as "fixable" as OVB (ie. when E [u|X ] = 0) since adding controls won't address the fact that X - Y

Andrea Passalacqua (Harvard)

Ec1123 Section 7 Instrumental Variables

November 16th, 2017 3 / 28

Examples of simultaneous causality

QUANTITYi = 0 + 1PRICEi + ui

Changes in price affect quantities supplied and demanded Changes in quantity supplied and demanded affect price Price and quantity are jointly determined by a set of simultaneous equations (ie. the demand and supply curve)

Other examples: Democracy and growth Parental involvement and child's performance in school Police and crime

Andrea Passalacqua (Harvard)

Ec1123 Section 7 Instrumental Variables

November 16th, 2017 4 / 28

Outline

1 Simultaneous Causality 2 Instrumental Variable Regression: Introduction

Conditions 3 IV: Examples 4 Two-Stage Least Squares 5 Testing the Validity of Instruments

Andrea Passalacqua (Harvard)

Ec1123 Section 7 Instrumental Variables

November 16th, 2017 5 / 28

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