Fama and MacBeth (1973) procedure can be used in testing asset pricing models and other areas. In this post, my primary focus is on its use in testing asset pricing models.
FMB in asset pricing models
It is actually a three-step process. We would divide the time period into three parts.
1. The first step is to find the assets/portfolios betas in the first period. Some researchers would use these betas to classify assets into portfolios.
2. The second step is to find betas of these portfolios in the second period.
3. The third step is to find the portfolio returns in the third period and test whether the betas from the second period can explain these returns? This step involves:
(i) cross-sectional regressions of the portfolio returns on the portfolio betas in each period.
(ii) averaging coefficients from the cross-sectional regressions across time. The standard errors are adjusted for cross-sectional dependence.
What does asreg do in the above process
asreg with fmb option performs step 3(i) and 3(ii).
asreg can also help in step (1) where individual betas need to be calculated for each stock. The command might look like
bys company: asreg returns market_returns if period == 1
This means that for typical asset pricing tests, the researcher has to do step (1) and (2) and arrange the data in a panel format, listing portfolio returns and betas as variables in columns. And then use asreg with fmb option, e.g.
keep if period == 3 xtset company month asreg returns betas, fmb
Where else FMB regression can be used?
Fama and MacBeth (1973) procedure (i.e step 3(i) and (ii)) is also used in areas other than testing the asset pricing models. You can see one example in my paper, Table 3, column 8, page 264
Shah, Attaullah & Shah, Hamid Ali & Smith, Jason M. & Labianca, Giuseppe (Joe), 2017. “Judicial efficiency and capital structure: An international study,” Journal of Corporate Finance, Elsevier, vol. 44(C), pages 255-274.