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 |

Relevant articles:

## 6 Comments

## Dr. Hassan Raza

March 24, 2019at 11:25 amDear Sir,

Hope you are fine and in good health. I am one of your student from Bara-Gali workshop, I am applying Fama and Macbeth regression on Pakistan Stock exchange firms on monthly data (Data sheet attached herewith). I have some queries regarding asreg

, this code provides the second stage Fama and Macbeth results, but as I check the first stage it only shows me … (Dots) in the first process, why?

When same procedure is applied for Global market excess return, it omitted the same variable and provide results for only constant term why?

I am sorry for your precious time. Please also let me know about any coming workshop on Stata.

## Attaullah Shah

March 24, 2019at 11:35 amA bit of code was missing which I have added. The updated version can be downloaded from SSC a week or so. However, at the moment, there is a workaround and you do not need to wait for the updated version. So just add the

`save`

option to the line and it will work as expected. Bonus yet, you can the first stage regression ouptut in a file.## Dr. Hassan Raza

March 24, 2019at 11:43 amThank you so much sir. What about when I regressed against excess global premium it omitted the said variable and only report constant. Sorry for your time.

## Attaullah Shah

March 24, 2019at 11:45 amSince the FMB regression is a cross-sectional regression, estimated in each time period, therefore, the variables need to vary across entities. Your gspc_return variable seems to be constant within a given period. See the case of the first month:

and you shall see that all the values of this variable are the same within the given month, and is also the case with other months; therefore, the regression does not find any variation in the dataset to fit the model.

## Mathias

April 12, 2019at 10:37 amDear Attaullah Shah,

Is the F value in asreg Y X, fmb by(time) defined as the time-series average of the F values from the cross-sectional regressions?

Thank you for your asreg package, which is very useful to me.

Regards,

Mathias

## Attaullah Shah

April 13, 2019at 11:26 amMathiasThe F-value is directly reported from the mvreg regression that is estimated for all the cross-sectional regressions of the first stage of FMB