4 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
gEMPt 5 b0 1 b1gMINt 1 b2gPOPt 1 b3gGSPt 1 b4gGDPt 1 ut,
where MINt is the minimum wage, in real dollars, POPt is the population from 18 to 25 years old, GSPt is gross state product, and GDPt is U.S. gross domestic product. The g prefix indicates the growth rate from year t 2 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 unob- served (to us) factors that affect youth employment, what is the problem with OLS estimation?
(ii) Let USMINt be the U.S. minimum wage, which is also measured in real terms. Do you think gUSMINt is uncorrelated with ut?
(iii) By law, any state’s minimum wage must be at least as large as the U.S. minimum. Explain why this makes gUSMINt a potential IV candidate for gMINt.