1. Econ 140 Lecture 241 Simultaneous Equations II Lecture 24

2. Econ 140 Lecture 242 Today’s plan More on instrumental variables Identification The Hausman test LATE and random variation in the number of kids you may have.

3. Econ 140 Lecture 243 Identification Our model was: (D): H i = a 1 + b 1 W i + u i (S): H i = a 2 +b 2 W i + c 2 X i + d 2 NK i +v i –problem: both hours and wages are endogenous Instrumental variables and identification to get around this problem If we had a model (D): H i = a 1 + b 1 W i + e 1i (S): H i = a 2 +b 2 W i + e 2i –from economic theory we’d expect b 1 0

4. Econ 140 Lecture 244 Identification (2) If we run a regression of hours on wages, we don’t know what equation from the graph is estimated: S D H W

5. Econ 140 Lecture 245 Identification (3) In order to determine which curve the regression estimates, we need to identify one of the equations Think back to the model and add one more variable to the supply equation: (D): H i = a 1 + b 1 W i + e 1i (S): H i = a 2 +b 2 W i + c 2 X 1 + e 2i –Where X 1 is age

6. Econ 140 Lecture 246 Identification (4) With each additional variable that’s not included in the other equation, we trace out another supply curve: S1S1 D H W S2S2

7. Econ 140 Lecture 247 Identification (5) Each additional variable must be a factor of one equation but not the other Example: if age is a factor of demand such that employers hire aging workers for less hours, system is no longer identified

8. Econ 140 Lecture 248 Order condition 1) “Just identified”: If we have one variable that differentiates demand from supply 2) “Over-identification”: If we have more than one variable that differentiates demand and supply Must have variables that are exogenous to the system that don’t count in both equations! L23.xls example: we identified the demand equation –over-identified: two additional variables in demand equation –wrong sign on b 1

9. Econ 140 Lecture 249 Hausman test How do we know the system was identified at all? Need to test to see if: –added variables are in fact exogenous instruments Hausman test tests for over-identification –We have an estimating equation [2nd stage of TSLS]: –First we have: X i = a 2 + b 2 Z i + v i [1st stage of TSLS] –Idea of test: look for correlation between the instruments Z i and the u i from the 2nd stage equation if there is correlation, Z i is no longer a valid instrument

10. Econ 140 Lecture 2410 Steps for the Hausman test 1) Regress errors from the second stage equation on the instrumental variables: 2) Calculate R 2 *(n-k) where k = m + 1 –test is distributed: [R 2 *(n-k)] ~  2 (m-1) –we have m-1 over-identifying variables –null hypothesis: H 0 : E(Z, u) = 0 –In this test, R 2 is: We want numerator to tend towards zero

11. Econ 140 Lecture 2411 Quick summary L24.xls –Shows how to construct Hausman test We’ve learned so far: –How to estimate given simultaneity (TSLS) –Working with instrumental variables –How to test if simultaneity still exists with the selected instruments (Hausman test)

12. Econ 140 Lecture 2412 LATE and Angrist & Evans Instrumental variables are important in economics because of local average treatment effects (LATE) Angrist and Evans –tested for the effect of having children on hours worked –looked at random instruments for a treatment and control group Number of kids and propensity to have another child –testing to see if sex of the first two affects the likelihood of having a third

13. Econ 140 Lecture 2413 LATE and Angrist & Evans (2) Random assignment of treatment and control groups –can’t determine sex of children –assumption: number of kids influences hours of work because the more kids you have, the less time time you have to work Identification comes off small part of sample: need very large sample size

14. Econ 140 Lecture 2414 LATE and Angrist & Evans (3) Estimated the following equation:H i = a 1 +b 1 X i + b 2 NK i +  I –here they identifying on the number of kids (NK i ) Why can we expect NK i to be endogenous? –Might choose combination of number of kids and hours of work, but can’t choose sex of children So Angrist and Evans used the same sex variable as the identifying variable: NK i = g 1 + g 2 X i + g 3 samesex i + v i –samesex i is a dummy variable equal to 1 if the children are the same sex and 0 otherwise –Negative result: more kids leads to less hours of work –L24.xls has a worked example