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1 Instrumental Variables Regression (SW Chapter 12)
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2 Two Conditions for Valid Instrument
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3 Estimation 1 of via 2SLS
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4 IV Regression, Graphically
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5 IV Regression, Algebraically
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6 Example #1: Supply and demand
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7 So we need a variable which shifts supply but not demand!
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8 2SLS in the supply-demand example
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9 Example #2: Test scores and class size
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10 Properties of
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12 Example: Cigarette demand
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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 ------------------------------------------------------------------------------
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14 First stage
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15 Second stage
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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”!
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17 The General IV Regression Model
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18 Identification of
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19 The General IV Regression Model
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20 2SLS with a 1 endogenous X
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21 Example: Demand for cigarettes
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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
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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?
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