In the following example, we shall use asreg that can be installed from SSC by typing the following line in Stata command window
ssc install asreg
The problem
Let’s say that we wish to report different regression statistics from Fama and MacBeth (1973) regression such the standard errors of variables. Using the fmb option, asreg can efficiently estimate FMB regression. Further, it reports the regression coefficients of the first stage regression when option first is used with the option fmb. However, it does not report other regression statistics.
The solution
The good news is that we can still find different regression components using asreg. Since the first stage regression of the FMB procedure is the cross-sectional regression, we can use the bysort period prefix with asreg.
An example
Let us use the grunfeld data and estimate the FMB regression in the usual manner.
webuse grunfeld, clear
asreg invest mvalue kstock, fmb first
First stage Fama-McBeth regression results
+------------------------------------------------------------+
| _TimeVar _obs _R2 _b_mva~e _b_kst~k _Cons |
|------------------------------------------------------------|
| 1935 10 .865262 .102498 -.001995 .356033 |
| 1936 10 .696394 .083707 -.053641 15.2189 |
| 1937 10 .663763 .076514 .217722 -3.38647 |
| 1938 10 .705577 .068018 .269115 -17.5819 |
| 1939 10 .826602 .065522 .198665 -21.1542 |
| 1940 10 .839255 .095399 .202291 -27.0471 |
| 1941 10 .856215 .114764 .177465 -16.5195 |
| 1942 10 .857307 .142825 .071024 -17.6183 |
| 1943 10 .842064 .11861 .105412 -22.7638 |
| 1944 10 .875515 .118164 .072207 -15.8281 |
| 1945 10 .906797 .108471 .050221 -10.5197 |
| 1946 10 .894752 .137948 .005413 -5.99066 |
| 1947 10 .891239 .163927 -.003707 -3.73249 |
| 1948 10 .788823 .178667 -.042556 8.53881 |
| 1949 10 .863257 .161596 -.036965 5.17829 |
| 1950 10 .857714 .176217 -.022096 -12.1747 |
| 1951 10 .873773 .183141 -.112057 26.1382 |
| 1952 10 .846122 .198921 -.067495 7.29284 |
| 1953 10 .889261 .182674 .098753 -50.1525 |
| 1954 10 .89845 .134512 .331375 -133.393 |
|------------------------------------------------------------|
|Mean 1944.5 10 .83690 .130605 .07295 -14.757 |
+------------------------------------------------------------+
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
------------------------------------------------------------------------------
An alternate way to first-stage
bys year: asreg invest mvalue kstock, se
bys year: keep if _n == _N
list _*
+-------------------------------------------------------------------------------------------------------------+
| year _Nobs _R2 _adjR2 _b_mvalue _b_kstock _b_cons _se_mv~e _se_ks~k _se_cons |
|-------------------------------------------------------------------------------------------------------------|
| 1935 10 .86526202 .82676546 .10249786 -.00199479 .35603339 .0157931 .2148591 23.82794 |
| 1936 10 .69639369 .60964903 .08370736 -.05364126 15.218946 .0211982 .4125528 49.72796 |
| 1937 10 .6637627 .56769491 .0765138 .21772236 -3.3864706 .0218952 .4745161 62.14382 |
| 1938 10 .70557727 .62145649 .06801777 .26911462 -17.581903 .0220019 .2076121 33.62243 |
| 1939 10 .82660153 .77705911 .06552194 .19866456 -21.154227 .0131751 .1563955 29.10151 |
|-------------------------------------------------------------------------------------------------------------|
| 1940 10 .83925512 .79332801 .095399 .20229056 -27.047068 .0171077 .2206074 42.49812 |
| 1941 10 .85621485 .81513338 .11476375 .17746501 -16.519486 .0197202 .2338307 47.43406 |
| 1942 10 .85730699 .81653756 .14282513 .07102405 -17.618283 .0246973 .1966943 43.85369 |
| 1943 10 .84206394 .79693935 .11860951 .10541193 -22.763795 .0207092 .1887016 46.8604 |
| 1944 10 .87551498 .83994783 .11816422 .07220719 -15.828145 .0169881 .1537212 41.84578 |
|-------------------------------------------------------------------------------------------------------------|
| 1945 10 .90679731 .88016797 .1084709 .05022083 -10.519677 .0133214 .1254533 35.10524 |
| 1946 10 .89475165 .8646807 .13794817 .00541339 -5.9906571 .018637 .1600683 45.73243 |
| 1947 10 .89123943 .86016498 .16392696 -.00370721 -3.7324894 .0280743 .1285463 37.80575 |
| 1948 10 .7888235 .72848735 .1786673 -.04255555 8.5388099 .0463983 .1661775 52.39133 |
| 1949 10 .86325678 .82418728 .16159617 -.03696511 5.1782863 .0346516 .1268614 41.07802 |
|-------------------------------------------------------------------------------------------------------------|
| 1950 10 .85771384 .81706065 .17621675 -.02209565 -12.17468 .0393216 .1361792 46.6222 |
| 1951 10 .87377295 .83770808 .18314051 -.11205694 26.138157 .0358898 .1486738 53.00348 |
| 1952 10 .84612242 .80215739 .19892081 -.06749499 7.2928402 .052286 .1906835 67.84544 |
| 1953 10 .88926056 .85762072 .18267385 .09875335 -50.152546 .058579 .2164437 77.91569 |
| 1954 10 .89845005 .86943578 .13451162 .33137459 -133.39308 .0704524 .1932826 76.18067 |
+-------------------------------------------------------------------------------------------------------------+
Explanation
In the above lines of code, we estimated a yearly cross-sectional regression with the option se to report the standard errors. Then we retained just one observation per year and deleted duplicates. The results are the same as reported by the option first in the fmb regression, with the only difference that we have now additional regression statistics.
Thank you for the all explanation anf efforts. I have a question . Is the “b_kstock” , which shown on the table “First stage Fama-McBeth regression results”, means Beta of the stock ? And, are the coefficients of the variables at Fama&Macbeth two-ways results risk factors?