I noticed that during the recent decade most of papers, which use Fama-MacBeth regressions compute Newey-West standard errors. I tried to find detailed description of this procedure in the books on empirical asset pricing (Campbell, Lo and MacKinlay; Cochrane; Bali, Engle, Murray), but none of them clearly decribes how to compute Newey-West standard errors in Fama-MacBeth (FM) regression.

As far as I understand, in the first step of FM procedure we run cross-sectional regression of returns on characteristics for each month: $R_i = \alpha + a_1\beta_i + a_2Ch_{1i} + a_3Ch_{2i} + ... + \epsilon_i$.

In the second step for each characteristic we find sample mean of the time series of its coefficients from step 1 and find the standard error, assuming that the coefficient estimates are normal iid. That is in time series $\{\hat{a}_{11}, \hat{a}_{12} ... \hat{a}_{1t}\}$ we find its mean $\bar{a_1}$ and its standard error as a square root of $\frac{1}{t}\sigma^2(\{\hat{a}_{11}, \hat{a}_{12} ... \hat{a}_{1t}\})$, where by $\sigma^2(X)$ I mean a variance of X.

Now we want to find Newey-West standard errors. Does it mean that now standard error (suppose 3 lags) is a square root of $\frac{1}{t}(\sigma^2(\{\hat{a}_{11}, \hat{a}_{12} ... \hat{a}_{1t}\})+\frac{4}{3}\gamma_1(\{\hat{a}_{11}, \hat{a}_{12} ... \hat{a}_{1t}\})+\frac{2}{3}\gamma_2(\{\hat{a}_{11}, \hat{a}_{12} ... \hat{a}_{1t}\}))$,

where $\gamma_1(X)$ means autocovariance of X at lag 1? I used Newey-West equation from Econometrics by Hayashi, page 409.

Is it correct?


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.