Jeffrey M. Wooldridge Econometric Analysis of Cross Section and Panel Data

Chapter 4 The Single-Equation Linear Model and OLS Estimation

Section 4.2 Asymptotic Properties of OLS

Subsection 4.2.2 Asymptotic Inference Using OLS

Assumption OLS.3: $E\left(u^{2}x^{\prime}x\right)=\sigma^{2}E\left(x^{\prime}x\right)\text{ where }\sigma^{2}\equiv E\left(u^{2}\right)$

Eq. (4.10) states $\widehat{Avar\left(\hat{\beta}\right)}=\hat{\sigma}^{2}\left(X^{\prime}X\right)^{-1}$ where $\hat{\sigma}$ is a consistent estimator of $\sigma$

I think it should be $\widehat{Avar\left(\hat{\beta}\right)}=\hat{\sigma}^{2}\left(\frac{1}{N}X^{\prime}X\right)^{-1}$

which one is correct:

$\widehat{Avar\left(\hat{\beta}\right)}=\hat{\sigma}^{2}\left(\sum_{i=1}^{N}x_{i}^{\prime}x_{i}\right)^{-1}$

$\widehat{Avar\left(\hat{\beta}\right)}=\hat{\sigma}^{2}\left(\frac{1}{N}\sum_{i=1}^{N}x_{i}^{\prime}x_{i}\right)^{-1}$?