$14\mathrm{.}1$ Suppose that the idiosyncratic errors in $(14\mathrm{.}4),\{u_{it}$:$t=1,2,...,T\},$ are serially uncorrelated with constant variance, ${}^2.$ Show that the correlation between adjacent differences, $u_{it}$ and $u_{i,t+1},$ is $-\mathrm{.}5.$ Therefore, under the ideal FE assumptions, first differencing induces negative serial correlation of a known value.

$y_{it}={}_1{x}_{it1}+{}_2{x}_{i2}+...+{}_k{x}_{ik}+a_i+u_{i,},t=1,2,$dots,$T$