Fama and MacBeth (1973) Fastest regression in Stata

The Fama-McBeth (1973) regression is a two-step procedure . The first step involves estimation of N cross-sectional regressions and the second step involves T time-series averages of the coefficients of the N-cross-sectional regressions. The standard errors are adjusted for cross-sectional dependence. This is generally an acceptable solution when there is a large number of cross-sectional units and a relatively small time series for each cross-sectional unit. However, if both cross-sectional and time-series dependencies are suspected in the data set, then Newey-West consistent standard errors can be an acceptable solution.

 

Estimation Procedure


The Fama-McBeth (FMB) can be easily estimated in Stata using asreg package.  Consider the following three steps for estimation of FMB regression in Stata.

1.  Arrange the data as panel data and use xtset command to tell Stata about it.

2.  Install asreg from ssc with this line of code:

ssc install asreg

3. Apply asreg command with fmb option

 

An Example


We shall use the grunfeld dataset in our example. Let’s download it first:

webuse grunfeld

This data is already xtset, with the following command:

xtset company year

Assume that we want to estimate a FMB regression where the dependent variable is invest and independent variables are mvalue and kstock. Just like regress command, asreg uses the first variable as dependent variable and rest of the variables as independent variables. Using the grunfeld data, asreg command for FMB regression is given below:

asreg invest mvalue kstock, fmb

 

 Fama-MacBeth (1973) Two-Step procedure Number of obs = 200  Num. time periods = 20
                                                            F( 2, 19)         = 195.04
                                                            Prob > F          = 0.0000
                                                            avg. R-squared    = 0.8369
 ------------------------------------------------------------------------------
        |            Fama-MacBeth
 invest | Coef.      Std. Err.     t         P>|t|   [95% Conf. Interval]
 -------------+----------------------------------------------------------------
 mvalue | .1306047      .0093422   13.98     0.000   .1110512   .1501581
 kstock | .0729575      .0277398   2.63      0.016   .0148975   .1310176
 _cons  | -14.75697     7.287669  -2.02      0.057   -30.01024   .496295
 ------------------------------------------------------------------------------

 

 

Newey-West standard errors


If Newey-West standard errors are required for the second stage regression, we can use the option newey(integer).  The integer value specifies the number of lags for estimation of Newey-West consistent standard errors. Please note that without using option newey, asreg estimates normal standard errors of OLS. This option accepts only integers, for example newey(1) or newey(4) are acceptable, but newey(1.5) or newey(2.3) are not. So if we were to use two lags with the Newey-West error for the above command, we shall type;

asreg invest mvalue kstock, fmb newey(2)
Fama-MacBeth Two-Step procedure (Newey SE)            Number of obs     = 200
(Newey-West adj. Std. Err. using lags(2))             Num. time periods = 20
                                                      F( 2, 19)         = 39.73
                                                      Prob > F          = 0.0000
                                                      avg. R-squared    = 0.8369
---------------------------------------------------------------------------------
        |            Newey-FMB
 invest | Coef.      Std. Err. t       P>|t|     [95% Conf. Interval]
-------------+-------------------------------------------------------------------
 mvalue | .1306047  .0150138   8.70    0.000    .0991804   .1620289
 kstock | .0729575  .0375046   1.95    0.067    -.0055406   .1514557
 _cons  | -14.75697  8.394982  -1.76   0.095    -32.32787   2.813928
---------------------------------------------------------------------------------

 


For some reasons, if we wish to display the first stage N – cross-sectional regressions of the FMB procedure, we can use the option first. And if we wish to save the first stage results to a file, we can use the option save(filename). Therefore, commands for these options will look like:

asreg invest mvalue kstock, fmb newey(2) first

asreg invest mvalue kstock, fmb newey(2) first save(FirstStage)

                               First stage Fama-McBeth regression results

_TimeVar _obs _R2 _b_mva~e _b_kstock _Cons
1935 10 .865262 .1024979 -.0019948 .3560334
1936 10 .6963937 .0837074 -.0536413 15.21895
1937 10 .6637627 .0765138 .2177224 -3.386471
1938 10 .7055773 .0680178 .2691146 -17.5819
1939 10 .8266015 .0655219 .1986646 -21.15423
1940 10 .8392551 .095399 .2022906 -27.04707
1941 10 .8562148 .1147638 .177465 -16.51949
1942 10 .857307 .1428251 .071024 -17.61828
1943 10 .842064 .1186095 .1054119 -22.7638
1944 10 .875515 .1181642 .0722072 -15.82815
1945 10 .9067973 .1084709 .0502208 -10.51968
1946 10 .8947517 .1379482 .0054134 -5.990657
1947 10 .8912394 .163927 -.0037072 -3.732489
1948 10 .7888235 .1786673 -.0425555 8.53881
1949 10 .8632568 .1615962 -.0369651 5.178286
1950 10 .8577138 .1762168 -.0220956 -12.17468
1951 10 .873773 .1831405 -.1120569 26.13816
1952 10 .8461224 .1989208 -.067495 7.29284
1953 10 .8892606 .1826739 .0987533 -50.15255
1954 10 .8984501 .1345116 .3313746 -133.3931

 

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