Problem 1 You are interested in learning how labor contributes to sales in high tech com- panies. To do so, you specify the following linear regression: S; = Bo + BEL:+BAK; + BmM; +W; Where Si are total annual sales for company i, Li is quantity of labor in total hours worked, Ki is machinery and equipment used in production, M, are intermediate inputs used in production (think of raw materials), and ui is the residual, interpreted as the productivity of the company (how much "extra" sales is generated after controlling for all inputs). You are interested in B, but you are worried that the quantity of labor is correlated with productivity U;. Indeed, on average, more productive companies may be larger and will want to use more of all inputs such that E(U; L) 70. To learn about the effect of labor in production, an analyst proposes using minmum wage minwage, as an instrument for labor. Indeed, minimum wage varies based on the location of the firm, and firms facing higher minimum wage may be constrained to use less labor. L; = 0 + aminwage; + & i. What are the assumptions required for minimum wage to be a valid instru- ment? ii. If you believe that more productive firms are more likely to establish them- selves in locations with low minimum wage, what assumption() isare) violated? Why? iii. If you believe that that firms in high tech industries only hire workers at wages largely above the minimum wage, what assumption() is(are) vio- lated? Why? iv. Provide a null and an alternative hypothesis test for your beliefs in (ii). Be precise. v. Provide a null and an alternative hypothesis test for your beliefs in (iii). Be precise. a