Introductory Econometrics: A Modern Approach 6th Edition by Jeffrey M Wooldridge

Exercise 2

Suppose that the idiosyncratic errors in (14.4), {uit: t = 1, 2,...,T}, are serially uncorrelated with constant variance, ?2u. Show that the correlation between adjacent differences, ?uit and ?ui,t+1, is -.5. Therefore, under the ideal FE assumptions, first differencing induces negative serial correlation of a known value.