Suppose you are interested in whether prison guards’ pensions are inflatedby collective bargaining agreements. You get data on the generosity of prison guards’pensions yit and whether or not they are covered by a collective bargaining agreementxit for all 50 states (indexed by i) over several years (indexed by t). Your basic modelof interest can be written:
yit = β0 + β1xit + εit.
(a) Why might xit be correlated with εit?

(b) Suppose the source of endogeneity is that the error term εit is actually composedof a state-specific “generosity effect” αi that dose not change over thime (that is,some states tend to be persistently more generous with their prison guards thanothers), so εit = αi+uit. Also, more generous states (with high values of αi) tend tobargain collectively more frequently than other states, but Cov(uit, xit) = 0. Showthat running a regression on the first-differenced data will result in a consistentestimator.

(Show steps answer reasoning to how you got your answer please)