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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) = Prob > F = R-squared = Root MSE = | Robust lpackpc | Coef. Std. Err. t P>|t| [95% Conf. Interval] lravgprs | _cons |

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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: Y X Z. ivregress 2sls lpackpc (lravgprs = rtaxso), vce(robust); Instrumental variables (2SLS) regression Number of obs = 48 Wald chi2(1) = Prob > chi2 = R-squared = Root MSE = | Robust lpackpc | Coef. Std. Err. z P>|z| [95% Conf. Interval] lravgprs | _cons | 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) = Prob > chi2 = R-squared = Root MSE = | Robust lpackpc | Coef. Std. Err. z P>|z| [95% Conf. Interval] lravgprs | lperinc | _cons | 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) = Prob > chi2 = R-squared = Root MSE = | Robust lpackpc | Coef. Std. Err. z P>|z| [95% Conf. Interval] lravgprs | lperinc | _cons | 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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