EC 2402 - Your textbook modifies the four assumptions for the multiple regression model

1. Your textbook modifies the four assumptions for the multiple regression model by adding a new assumption. This represents an extension of the cross-sectional data case, where errors are uncorrelated across entities. The new assumption requires the errors to be uncorrelated across time, conditional on the regressors as well (cov(uit, uis Xit, Xis) = 0 for t ≠ s.). 
(a) Discuss why there might be correlation over time in the errors when you use U.S. state panel  data. Does this mean that you should not use OLS as an estimator?
(b) Now consider pairs of adjacent states such as Indiana and Michigan, Texas and Arkansas, New  York and Connecticut, etc. Is it likely that the fifth assumption will hold here, even though the  "contemporaneous" errors are correlated? If not, can you still use OLS for estimation?

2) . A study attempts to investigate the role of the various determinants of regional Canadian unemployment rates in order to get a better picture of Canadian aggregate unemployment rate  behavior. The annual data (1967-1991) is for five regions (Atlantic region, Quebec, Ontario, Prairies,  and British Columbia), and four age-gender groups (female and male, adult and young). Focusing on  young females, the authors find significant effects for the following variables: the regional relative  minimum wage rate (minimum wages divided by average hourly earnings), the regional share of youth in the labor force, the regional share of adult females in the labor force, United States activity shocks (deviations of United States GDP from trend), an indicator of the degree of monetary tightness in Canada, regional union density, and a regional index of unemployment insurance generosity. 
Explain why the authors only used region fixed effects. How would their specification have to change if they also employed time fixed effects?