Instrumental Variables Regression

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Chapter 12

• Instrumental Variables Regression

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Instrumental Variables Regression (SW Chapter 12)
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IV Regression with One Regressor and One
Instrument (SW Section 12.1)
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Terminology endogeneity and exogeneity
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Two conditions for a valid instrument
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The IV Estimator, one X and one Z
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Two Stage Least Squares, ctd.
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Two Stage Least Squares, ctd.
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The IV Estimator, one X and one Z, ctd.
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The IV Estimator, one X and one Z, ctd.
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Consistency of the TSLS estimator
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Example 1 Supply and demand for butter
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TSLS in the supply-demand example
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TSLS in the supply-demand example, ctd.
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Example 2 Test scores and class size
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Example 2 Test scores and class size, ctd.
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Inference using TSLS
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Inference using TSLS, ctd.
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Example Cigarette demand, ctd.
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Cigarette demand, ctd.
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STATA Example Cigarette demand, First stage
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Second stage
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Combined into a single command
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Summary of IV Regression with a Single X and Z
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The General IV Regression Model(SW Section 12.2)
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Identification
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Identification, ctd.
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The general IV regression model Summary of
jargon
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TSLS with a single endogenous regressor
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Example Demand for cigarettes
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Example Cigarette demand, one instrument
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Example Cigarette demand, two instruments
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The General Instrument Validity Assumptions
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The IV Regression Assumptions
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Checking Instrument Validity (SW Section 12.3)
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Checking Assumption 1 Instrument Relevance
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What are the consequences of weak instruments?
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An example the sampling distribution of the TSLS
t-statistic with weak instruments
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Why does our trusty normal approximation fail us?
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Measuring the strength of instruments in
practice The first-stage F-statistic
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Checking for weak instruments with a single X
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What to do if you have weak instruments?
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Confidence intervals with weak instruments
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Estimation with weak instruments
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Checking Assumption 2 Instrument Exogeneity
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Testing overidentifying restrictions
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Checking Instrument Validity Summary
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2. Exogeneity
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Application to the Demand for Cigarettes (SW
Section 12.4)
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Panel data set

• 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 dont
  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.

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Fixed-effects model of cigarette demand
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The changes method (when T2)
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STATA Cigarette demand
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Use TSLS to estimate the demand elasticity by
using the 10-year changes specification
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Check instrument relevance compute first-stage F
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Check instrument relevance compute first-stage F
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What about two instruments (cig-only tax, sales
tax)?
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Test the overidentifying restrictions
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The correct degrees of freedom for the
J-statistic is mk
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Tabular summary of these results
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How should we interpret the J-test rejection?
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The Demand for CigarettesSummary of Empirical
Results
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Assess the validity of the study
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Finding IVs Examples (SW Section 12.5)
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Example Cardiac Catheterization
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Cardiac catheterization, ctd.
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Cardiac catheterization, ctd.
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Example Crowding Out of Private Charitable
Spending
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Private charitable spending, ctd.
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Private charitable spending, ctd.
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Private charitable spending, ctd.
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Example School Competition
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School competition, ctd.
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School competition, ctd.
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Summary IV Regression(SW Section 12.6)
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Some IV FAQs
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Threats to internal validity of IV, ctd.