Reference no: EM132412205

Question 1 - Instrumental Variables

The purpose of this exercise is to compare the estimates and standard errors obtained by correctly using 2SLS with those obtained using inappropriate procedures. Use the data file WAGE2.wf1.

(i) Use a 2SLS routine to estimate the equation:

log(wage) = β₀ + β₁educ + β₂exper + β₃tenure + β₄black + u

where sibs is IV for educ. Report the results in the usual form.

(ii) Now manually carry out 2SLS. That is, first regress educ on sibs, exper, tenure and black and obtain the fitted values, (educ)^{^}_i, i=1,2,3... Then, run the second stage regression of log(wage) on (educ)^{^}_i, exper, tenure and black. Verify that the coefficients are identical to those obtained in part (i), but that the standard errors are somewhat different. The standard errors obtained from the second stage regression when manually carrying out 2SLS are generally inappropriate.

(iii) Now use the following two-step procedure, which generally yields inconsistent parameter estimates of the coefficients, and not just inconsistent standard errors. In step one, regress educ on sibs only and obtain fitted values, say (educ)^~_i. (NOTE: this is an incorrect first stage regression). Then, in the second step, run the regression of log(wage) on (educ)^~_i, exper, tenure and black. How does the estimate from this incorrect, two-step procedure compare with the correct 2SLS estimate of the return to education?

Question 2 - Instrumental Variables

Use the data set smoke.wf1. A model to estimate the effects of smoking on annual income (perhaps through lost work days due to illness) is

log(income) = β₀ + β₁cigs + β₂educ + β₃age + β₄age² = u₁ (1)

where cigs is the number of cigarettes smoked per day on average.

(i) Briefly explain why the regression coefficient β₁ on cigs in Equation (1) may be biased in the current context.

(ii) How do you interpret β₁?

(iii) To reflect the fact that cigarette consumption might be jointly determined with income, a demand for cigarettes equation is

cigs = γ₀ + γ₁ log(income) + γ₂ edu + γ₃ age + γ₄ age² + γ₅ log(cigprice) + γ₆restaurn + u₂ (2)

cigpric is the price of a pack of cigarettes (in cents), and restaurn is a binary variable equal to unity if the person lives in a state with restaurant smoking restrictions. Assuming these are exogenous to the individual, what signs would you expect for γ₅ and γ₆.

(iv) Under what assumption is the income equation from part an identified?

(v) Estimate the income equation by OLS and discuss the estimate of β₁?

(vi) Estimate the reduced form for cigs. (Recall that this entails regressing cigs on all exogenous variables). Are log(cigpric) and restaurn significant in the reduced form?

(vii) Now, estimate the income equation by 2SLS. Discuss how the estimate of β₁ compares with the OLS estimates.

(viii) Do you think that cigarette prices and restaurant smoking restrictions are exogenous in the income equation?

Question 3: Instrumental Variables

Use the data set in fish.wf1, which comes from Graddy (1995), to do this exercise. We will use is to estimate a demand function for fish.

i. Assume that the demand equation can be written in equilibrium for each time period as:

log(totqty_t) = α₁log(avgprc_t) + β₁₀ + β₁₁mon + β₁₂tues_t + β₁₃wed_t + β₁₄wed_t + u_t

So demand is allowed to differ across days of the week. Treating the price variable as endogenous, what additional information do we need to consistently estimate the demand-equation parameters?

ii. The variables wave_2t and wave_3t are measures of ocean wave heights over the past several days. What two assumptions do we need to make in order to use wave 2 and wave 3 as IV for log(avgprc_t) in estimating the demand equation?

iii. Regress log(avgprc) on the day-of-the-week dummies and the two wave measures. Are wave2 and wave3 jointly significant? What is the p-value of the test?

iv. Now, estimate the demand equation by 2SLS. What is the 95% confidence interval for the price elasticity of demand? Is the estimated elasticity reasonable?

v. Obtain the 2SLS residuals, u^{^}_t1. Add a single lag, u^{^}_t1-1,1 in estimating the demand equation by 2SLS. Remember, use u^{^}_t1-1,1 as its own instrument. Is there evidence of AR(1) serial correlation in the demand equation errors?

vi. Given that the supply equation evidently depends on the wave variables, what two assumptions would we need to make in order to estimate the price elasticity of supply?

vii. In the reduced form equation for log(avgprct), are the day-of-the-week dummies jointly significant? What do you conclude about being able to estimate the supply equation?