Instrumental Variables Regression Chapter 10 Instrumental Variables Regression

Instrumental Variables Regression (SW Chapter 10)

IV Regression with One Regressor and One Instrument (SW Section 10.1)

Terminology: endogeneity and exogeneity

Two conditions for a valid instrument

The IV Estimator, one X and one Z

Two Stage Least Squares, ctd.

Two Stage Least Squares, ctd.

The IV Estimator, one X and one Z, ctd.

The IV Estimator, one X and one Z, ctd.

Consistency of the TSLS estimator

Example #1: Supply and demand for butter

TSLS in the supply-demand example:

TSLS in the supply-demand example, ctd.

Example #2: Test scores and class size

Example #2: Test scores and class size, ctd.

Inference using TSLS

Inference using TSLS, ctd.

Example: Cigarette demand, ctd.

Cigarette demand, ctd.

STATA Example: Cigarette demand, First stage

Second stage

Combined into a single command

Summary of IV Regression with a Single X and Z

The General IV Regression Model (SW Section 10.2)

Identification

Identification, ctd.

The general IV regression model: Summary of jargon

TSLS with a single endogenous regressor

Example: Demand for cigarettes

Example: Cigarette demand, one instrument

Example: Cigarette demand, two instruments

The General Instrument Validity Assumptions

The IV Regression Assumptions

Checking Instrument Validity (SW Section 10.3)

Checking Assumption #1: Instrument Relevance

What are the consequences of weak instruments?

An example: the sampling distribution of the TSLS t-statistic with weak instruments

Why does our trusty normal approximation fail us?

Measuring the strength of instruments in practice: The first-stage F-statistic

Checking for weak instruments with a single X

What to do if you have weak instruments?

Confidence intervals with weak instruments

Estimation with weak instruments

Checking Assumption #2: Instrument Exogeneity

Testing overidentifying restrictions

Checking Instrument Validity: Summary

2. Exogeneity

Application to the Demand for Cigarettes (SW Section 10.4)

Panel data set Estimation strategy Annual cigarette consumption, average prices paid by end consumer (including tax), personal income 48 continental US states, 1985-1995 Estimation strategy Having panel data allows us to control for unobserved state-level characteristics that enter the demand for cigarettes, as long as they don’t vary over time But we still need to use IV estimation methods to handle the simultaneous causality bias that arises from the interaction of supply and demand.

Fixed-effects model of cigarette demand

The “changes” method (when T=2)

STATA: Cigarette demand

Use TSLS to estimate the demand elasticity by using the “10-year changes” specification

Check instrument relevance: compute first-stage F

Check instrument relevance: compute first-stage F

What about two instruments (cig-only tax, sales tax)?

Test the overidentifying restrictions

The correct degrees of freedom for the J-statistic is m–k:

Tabular summary of these results:

How should we interpret the J-test rejection?

The Demand for Cigarettes: Summary of Empirical Results

Assess the validity of the study

Finding IVs: Examples (SW Section 10.5)

Example: Cardiac Catheterization

Cardiac catheterization, ctd.

Cardiac catheterization, ctd.

Example: Crowding Out of Private Charitable Spending

Private charitable spending, ctd.

Private charitable spending, ctd.

Private charitable spending, ctd.

Example: School Competition

School competition, ctd.

School competition, ctd.

Summary: IV Regression (SW Section 10.6)

Some IV FAQs

Threats to internal validity of IV, ctd.