Introductory Econometrics 4th Edition by Jeffrey Wooldridge

Exercise 16

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 = 0 + 1 gMIN t + 2 gPOP t + 3 gGSP t + 4 gGDP t + u t ,
where MIN is the minimum wage, in real dollars, POP 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 prefix indicates the growth rate from year t - 1 to year t, which would typically be approximated by the difference in the logs.
(i) 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
(ii) Let USMIN t be the U.S. minimum wage, which is also measured in real terms. Do you think gUSMIN t is uncorrelated with u t
(iii) By law, any state's 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.