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Instrumental Variables Regression (SW Chapter 12)

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Two Conditions for Valid Instrument

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Estimation 1 of via 2SLS

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IV Regression, Graphically

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IV Regression, Algebraically

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Example #1: Supply and demand

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• So we need a variable which shifts supply but not demand!

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2SLS in the supply-demand example

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Example #2: Test scores and class size

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Properties of

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Example: Cigarette demand

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Ignoring endogeneity of ln(Price) . reg lpackpc lravgprs, r;

Linear regression Number of obs = 48 F( 1, 46) = 38.86 Prob > F = 0.0000 R-squared = 0.4058 Root MSE = .18962

------------------------------------------------------------------------------ | Robust lpackpc | Coef. Std. Err. t P>|t| [95% Conf. Interval]-------------+---------------------------------------------------------------- lravgprs | -1.213057 .1945897 -6.23 0.000 -1.604746 -.8213686 _cons | 10.33892 .9348204 11.06 0.000 8.457229 12.22062------------------------------------------------------------------------------

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First stage

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Second stage

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Combined 1st & 2nd stages

Old “ivreg” command vs. “ivregress: http://www.ats.ucla.edu/stat/stata/seminars/stata10/endogenous.htm

Y X Z. ivregress 2sls lpackpc (lravgprs = rtaxso), vce(robust);

Instrumental variables (2SLS) regression Number of obs = 48 Wald chi2(1) = 12.05 Prob > chi2 = 0.0005 R-squared = 0.4011 Root MSE = .18635

------------------------------------------------------------------------------ | Robust lpackpc | Coef. Std. Err. z P>|z| [95% Conf. Interval]-------------+---------------------------------------------------------------- lravgprs | -1.083587 .3122035 -3.47 0.001 -1.695494 -.471679 _cons | 9.719876 1.496143 6.50 0.000 6.78749 12.65226------------------------------------------------------------------------------Instrumented: lravgprs This is the endogenous X Instruments: rtaxso This is the instrumental variable

• 2SLS is the estimator, as opposed to GMM or LIML

• Don’t abbreviate as “ivreg”!

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The General IV Regression Model

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Identification of

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The General IV Regression Model

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2SLS with a 1 endogenous X

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Example: Demand for cigarettes

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Example: 1 instrument

Y W X Z. ivregress 2sls lpackpc lperinc (lravgprs = rtaxso), vce(robust);

Instrumental variables (2SLS) regression Number of obs = 48 Wald chi2(2) = 17.47 Prob > chi2 = 0.0002 R-squared = 0.4189 Root MSE = .18355

------------------------------------------------------------------------------ | Robust lpackpc | Coef. Std. Err. z P>|z| [95% Conf. Interval]-------------+---------------------------------------------------------------- lravgprs | -1.143375 .3604804 -3.17 0.002 -1.849903 -.4368463 lperinc | .214515 .3018474 0.71 0.477 -.377095 .8061251 _cons | 9.430658 1.219401 7.73 0.000 7.040675 11.82064------------------------------------------------------------------------------Instrumented: lravgprsInstruments: lperinc rtaxso

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Example: 2 instruments Y W X Z1 Z2. ivregress 2sls lpackpc lperinc (lravgprs = rtaxso rtaxs), vce(robust);

Instrumental variables (2SLS) regression Number of obs = 48 Wald chi2(2) = 34.51 Prob > chi2 = 0.0000 R-squared = 0.4294 Root MSE = .18189

------------------------------------------------------------------------------ | Robust lpackpc | Coef. Std. Err. z P>|z| [95% Conf. Interval]-------------+---------------------------------------------------------------- lravgprs | -1.277424 .2416838 -5.29 0.000 -1.751115 -.8037324 lperinc | .2804045 .2458274 1.14 0.254 -.2014083 .7622174 _cons | 9.894955 .9287578 10.65 0.000 8.074623 11.71529------------------------------------------------------------------------------Instrumented: lravgprsInstruments: lperinc rtaxso rtaxs

• Differences when multiple instruments? • Normal or inferior good? Luxury good or not?• Elastic or inelastic?