Fama MacBeth 2nd Stage

[Eric Anthony]

Hello:

I am a relatively new user of Stata.

I have calculated the firm Betas for the first stage of FAMA MACBETH and created a database in STATA. I want to perform the second stage in STATA. I have 50 companies with 240 time periods of data (Panel Data). At this point can I simply run a XTREG to estimate the coefficients and complete my second stage?

Second piece of the question -> what's my best approach to estimate proper standard errors.

Thanks for your help on this.

[William Lisowski]

Welcome to Statalist.

From what I have seen on Statalist, xtreg is not appropriate for the regression that you will be doing on your betas.

You may find the discussion in post #26 at the link below helpful. It shows how to make use of the asreg command written by Attaullah Shah a frequent contributor here (see the output of search asreg) in the regression you now seek to do. Actually, it would also have been helpful in calculating your betas, if I understand correctly. But don't read too far backward in this topic, because the poster was confused and expected one asreg command to do two stages of the analysis - calculate the betas and run the second-stage regression. It's more complicated than that.

https://www.statalist.org/forums/for...98#post1498998

To exoand on this a littler further, it appears to me that "Fama-MacBeth regression" is narrowly defined as a two-step process of (1) running a series of cross-sectional regressions and then (2) doing something further using those results that I'm not clear about. That is what asreg refers to as Fama-MacBeth regression and it is the technique used for the second stage regression you now seek to do.

However, the "Fama-MacBeth regression" technique is commonly the final stage in techniques (often including the name Fama) that begin with the estimation of firm-specific betas, and the two techniques become confused. So, beware. You are I think confusing "Fama-MacBeth regression" with the broader methodology that also bear's Fama's name.

So asreg is actually helpful for both stages of the technique you are working on, but you should understand that in the discussion from Prof. Shah's website at the link below, asreg, fmb refers to that final stage of the technique you are using.

https://fintechprofessor.com/stata-p...sion-in-stata/

[Attaullah Shah]

I shall add some explanations to the helpful reply by William Lisowski
Since you seem to be conducting tests of the asset pricing models, let me give a short intro to the Fama - MacBeth procedure in asset pricing domain.

It is actually a three-step process. We would dividend the time period in 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.

[Eric Anthony]

Gentlemen:

I sincerely appreciate your time here on this. Extremely helpful. From William's response, I read the attached posts and came away with a clarifying question which Attaullah just answered very clearly - I am all finished with steps 1 and 2 and need to perform #3 (the crux of my question), so it looks like this function will do the trick for me.

Have a great rest of the weekend. Thanks again.

Eric A

[Eric Anthony]

ASREG with Interaction Terms:

I also ran the ASREG over two time periods to test the impact of my data for an "event". I ran the ASREG regression including main effects variables and added an interaction term (variable * 1 or 0 depending on the time period). Many (but not all) of the interaction variables were "(omitted)" in this procedure. For example, I have 8 primary independent variables, then 8 interaction variables ( var *( 0 or 1) ). Of the 8 interaction terms 5 were omitted. I am curious if you had any insights here. It seems odd. I have 13k observations and 241 periods.

Best,

[Eric Anthony]

ASREG with Interaction Terms:

I also ran the ASREG over two time periods to test the impact of my data for an "event". I ran the ASREG regression including main effects variables and added an interaction term (variable * 1 or 0 depending on the time period). Many (but not all) of the interaction variables were "(omitted)" in this procedure. For example, I have 8 primary independent variables, then 8 interaction variables ( var *( 0 or 1) ). Of the 8 interaction terms 5 were omitted. I am curious if you had any insights here. It seems odd. I have 13k observations and 241 periods.

Best,

After examining this further, I am pretty sure the ASREG does not allow the model to be fun with interaction variables - is anyone able to confirm this?

My interaction term is an event period 0 = pre-event while 1= post event. I multiply this dummy by the independent variables to show the effect after the event. I use this interaction variable in addition to the main independent variable. When I do this for all my interaction variables (there are 8 ) - 5 of them are omitted.

Any confirmation of my views or other options I could use with asreg, fmb would be much appreciated.

Thank you.