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(u_it, u_is | X_it, X_is)= 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?

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The Answer of 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(u_it, u_is | X_it, X_is)= 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?

Your Textbook Modifies the Four Assumptions for the Multiple Regression