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1 Instrumental Variables Regression (SW Chapter 12)

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1 1 Instrumental Variables Regression (SW Chapter 12)

2 2 Two Conditions for Valid Instrument

3 3 Estimation  1 of via 2SLS

4 4 IV Regression, Graphically

5 5 IV Regression, Algebraically

6 6 Example #1: Supply and demand

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

8 8 2SLS in the supply-demand example

9 9 Example #2: Test scores and class size

10 10 Properties of

11 11

12 12 Example: Cigarette demand

13 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 |

14 14 First stage

15 15 Second stage

16 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”!

17 17 The General IV Regression Model

18 18 Identification of

19 19 The General IV Regression Model

20 20 2SLS with a 1 endogenous X

21 21 Example: Demand for cigarettes

22 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

23 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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