## 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. The included endogenous variables are income and cigs.

3. In equation (1) what are the included exogenous variables?
4. The included exogenous variables are educ, age and white. Ok, as a technical matter age2, as well, since it enters age in nonlinear form, but for Ec 3503 you don't need to include this in your answer.

5. In equation (1) what are the excluded exogenous variables?
6. Cigpric and restaurn are the excluded exogenous variables.

7. Using the order condition are the coefficients of equation (1) identifiable? Yes How do you know? The number of excluded exogenous variables exceeds the number of endgoenous variables included on the RHS.
For the purposes of the following questions assume that cigpric is exogenous.
1. In equation (2) what are the included endogenous variables?
2. The included endogenous variables are income and cigs.

3. For equation (2) what are the included exogenous variables?
4. Cigpric and restaurn are the included exogenous variables.

5. For equation (2) what are the excluded exogenous variables?
6. white is the only excluded exogenous variable.

7. Using the order condition are the coefficients of equation (2) identifiable? YesHow do you know? The number of excluded exogenous variables exceeds the number of endgoenous variables included on the RHS.
8. Suppose that cigpric is endogenous. Is the second equation identifiable under this circumstance? No. How do you know? Now the number of endogenous variables on the RHS exceeds the number of exogenous variables excluded.
9. Derive the reduced form equation for log(income). Assume cigpric to be exogenous.
10. In a more complete answer one would express the pi terms as functions of the structural coefficients.

11. Derive the reduced form equation for cigs. Assume cigpric to be exogenous.
12. In a more complete answer one would express the delta terms as functions of the structural coefficients.

13. Estimate the coefficients of the reduced form equation for log(income).

1. What can you say about the effect of age on log(income)? After accounting for the simultaneity of cigs and income, an additional year of age will result in an increase in log(income) of .059-2*(.000651)*age. So, the effect is age dependent with diminishing marginal returns to an extra year. To get the effect on income just move the decimals two places to the right and call it %.
2. What can you say about the effect of educ on log(income)? After accounting for the simulataneity of cigs and income, an additional year of income will result in an increase in log(income) of .058, or an increase in income of 5.8%.
14. Estimate the coefficients of the reduced form equation for cigs.

1. What can you say about the effect of age on cigs? After accounting for the simultaneity of cigs and income, an additional year of age will increase cigarette consumpton by 0.8-2(.009631)age. The effect is age dependent; with diminishing marginal returns.
2. What can you say about the effect of educ on cigs? After accounting for the simultaneity of cigs and income, an additional year of educ will reduce cigarette consumpton by .451.
15. 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? educ, age, age2, white,cigpric, restaurn
2. What can you say about the effect of age on log(income) in the structural equation? For a given level of cigarette consumption, an additional year of age will increase log(income) by .09-2(.001020)age. The effect is age dependent with diminishing marginal returns.
3. Why does the educ coefficient estimate differ from that of part 12.b? The answer in 12.b is the effect after accounting for the effect of age on cigarette consumption, whereas the answer in 14.b depends on the endogeneity of cigs.
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