# 1 Instrumental Variables Regression (SW Chapter 12)

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1 Instrumental Variables Regression (SW Chapter 12)

2 Two Conditions for Valid Instrument

3 Estimation  1 of via 2SLS

4 IV Regression, Graphically

5 IV Regression, Algebraically

6 Example #1: Supply and demand

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

8 2SLS in the supply-demand example

9 Example #2: Test scores and class size

10 Properties of

11

12 Example: Cigarette demand

13 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 ------------------------------------------------------------------------------

14 First stage

15 Second stage

16 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”!

17 The General IV Regression Model

18 Identification of

19 The General IV Regression Model

20 2SLS with a 1 endogenous X

21 Example: Demand for cigarettes

22 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: lravgprs Instruments: lperinc rtaxso

23 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: lravgprs Instruments: lperinc rtaxso rtaxs Differences when multiple instruments? Normal or inferior good? Luxury good or not? Elastic or inelastic?