Springer Texts in Business and Economics

Violations of the Classical Assumptions

5.1 s2 is Biased Under Heteroskedasticity. From Chap. 3 we have shown that

ei = Yi 'ols "olsXi = yi "olsxi = "ols^ Xi + (ui u/

for i = 1, 2, .., n.

The second equality substitutes aols = Y — |3olsX and the third equality substitutes yi = "xi + (ui — it). Hence,

n

Xe2 = (° ols — " x2 + X (ui — u)2 — 2 ols — ") X xi (ui — u)

i=1 i=1 i=1

n1
of.
n
i=1

B. H. Baltagi, Solutions Manual for Econometrics, Springer Texts in Business and Economics, DOI 10.1007/978-3-642-54548-1—5, © Springer-Verlag Berlin Heidelberg 2015

nb E( ±e2)
Hence, E(s2) =
1 n — 2	n1
Under homoskedasticity this reverts back to E(s2) = -2.
1
■ (" ols)
getE
n2
for b > 0.

This means that, on the average, the estimated standard error of "ojs understates the true standard error. Hence, the t-statistic reported by the regression package for Ho; " = 0 is overblown.