## Simultaneous Equations Homework

The data set for this homework is smoke.wf1. There is also a file containing variable descriptions. It is believed that income and smoking are jointly determined. Smoking can have an adverse effect on one's income from lost days of work due to illness or lost productivity while ducking outside the workplace to catch an illicit smoke. On the other hand, the stress and pressure of earning a higher income may result in one lighting up more often. To caputre these effects we posit the following two equation structural model model.

(1)

(2)

1. In equation (1) what are the included endogenous variables?
2. In equation (1) what are the included exogenous variables?
3. In equation (1) what are the excluded exogenous variables?
4. Using the order condition are the coefficients of equation (1) identifiable? How do you know?
For the purposes of the following questions assume that cigpric is exogenous.
1. In equation (2) what are the included endogenous variables?
2. For equation (2) what are the included exogenous variables?
3. For equation (2) what are the excluded exogenous variables?
4. Using the order condition are the coefficients of equation (2) identifiable? How do you know?
5. Suppose that cigpric is endogenous. Is the second equation identifiable under this circumstance? How do you know?
6. Derive the reduced form equation for log(income). Assume cigpric to be exogenous.
7. Derive the reduced form equation for cigs. Assume cigpric to be exogenous.
8. Estimate the coefficients of the reduced form equation for log(income).
1. What can you say about the effect of age on log(income)?
2. What can you say about the effect of educ on log(income)?
9. Estimate the coefficients of the reduced form equation for cigs.
1. What can you say about the effect of age on cigs?
2. What can you say about the effect of educ on cigs?
10. Use Two Stage Least Squares (2SLS) to estimate the coefficients of structural equation (1).
1. What are the exogenous variables to be used as instruments?
2. What can you say about the effect of age on log(income) in the structural equation?
3. Why does the educ coefficient estimate differ from that of part 12.b?