Newey–West Standard Errors for Fama–MacBeth Regressions
Summary
The document outlines the two-step Fama–MacBeth procedure: estimate cross-sectional return regressions each month, then average each coefficient’s time series. It describes the usual standard error as the sample standard deviation of those monthly estimates divided by the square root of the number of periods, under an independent and identically distributed assumption.
The author asks whether a proposed Newey–West adjustment is correct, using lagged autocovariances with weights for a three-lag example. The text does not include an answer or establish that the proposed formula is correct. It is useful as a statement of the inference problem and a candidate adjustment, but readers would need an external derivation to confirm lag conventions, finite-sample choices, and the precise covariance estimator.
Key ideas
- Fama–MacBeth estimation averages coefficients from repeated cross-sectional regressions over time.
- The conventional second-step standard error treats the coefficient series as independent and identically distributed.
- The author proposes adding weighted lagged autocovariances to account for serial dependence.
- The document poses the formula as a question and does not verify its correctness.
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# Newey-West standard errors in Fama-MacBeth regressions
# Newey-West standard errors in Fama-MacBeth regressions
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?Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.