Questions -

Q1. Explain what simultaneous equation bias and what effect it has on the estimates using OLS.

Q2. Explain how Two-Stage-Least-Squares works and what its advantages and disadvantages are.

Q3. Suppose that, for a given state in the United States, you wish to use annual time series data to estimate the effect of the state-level minimum wage on the employment of those 18 to 25 years old (EMP). A simple model is:

gEMP_t = β= + β₁gMIN_t + β₂gPOP_t + β₃gGDP_t + β₄gGDP_t + u_t (1)

where MIN_t is the minimum wage, in real dollars, POP_t is the population from 18 to 25 years old, GSP_t is gross state product, and GDP_t is U.S. gross domestic product. The g prex indicates the growth rate from year t1 to year t, which would typically be approximated by the difference in the logs.

a. If we are worried that the state chooses its minimum wage partly based on unobserved (to us) factors that affect youth employment, what is the problem with OLS estimation?

b. Let USMIN_t be the U.S. minimum wage, which is also measured in real terms. Do you think USMIN_t is uncorrelated with u_t?

c. By law, any states minimum wage must be at least as large as the U.S. minimum. Explain why this makes gUSMIN_t a potential IV candidate for gMIN_t.

d. Explain how we can test the joint significance of variables gMIN_t and gGDP_t in (1).

Q4. A researcher is interested in the effect of military service on human capital. He collects data from a random sample of 4000 workers aged 40 and runs the OLS regression Y_i = β₀ + β₁X_i + u_i, where Y_i is the worker's earnings and X_t is a binary variable that is equal to 1 if the person served in the military and is equal to 0 otherwise.

a. Explain why the OLS estimates are likely to be unreliable. (Hint: Which variables are omitted from the regression? Are they correlated with military service?)

b. During the Vietnam War there was a draft, where priority for the draft was determined by a national lottery (Birthdates were randomly selected and ordered 1 through 365. Those with birthdates ordered first were drafted before those with birthdates ordered second, and so forth.) Explain how the lottery might be used as an instrument to estimate the effect of military service on earnings.