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 ---------------------------------------------------------------------------------

If we wished 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 |

**Fama-MacBeth Two-Step procedure (Newey SE)**

invest | Coef. | St.Err. | t-value | p-value | [95% Co | Interval] | Sig |
---|---|---|---|---|---|---|---|

mvalue | 0.131 | 0.015 | 8.70 | 0 | 0.099 | 0.162 | *** |

kstock | 0.073 | 0.038 | 1.95 | 0.068 | -0.006 | 0.152 | * |

cons | -14.757 | 8.395 | -1.76 | 0.097 | -32.469 | 2.955 | * |

Mean dependent var | SD dependent var | 216.875 | |||||

R-squared | Number of obs | 200.000 | |||||

F-test | Prob > F | 0.000 | |||||

Notes: *** p<.01, ** p<.05, * p<.1 |

## Paid help for FMB regression

The Fama and Macbeth regression are extensively used in testing asset pricing models. As discussed in this post, the typical use is to divide the sample period in several periods, make portfolios, find their betas in the first period, make portfolios on those beta-rankings, find returns in the subsequent periods, and regression those returns on the portfolio betas. These steps are usually computationally extensive and hard to understand. We offer a paid help in such cases. We also provide help if a researcher has a unique research design and wants to apply the FMB regression. See this page for pricing options and other details.

## More on FMB regression

Fama McBeth regression with Shanken correction

FMB regression – what, how and where

haraAugust 1, 2022 at 11:49 pmHi Mr. Attaullah Shah. thanks for your useful code. I have a question. how can I change the confidence level in this code? I want to run this code with 1% and 10% confidence level. I would appreciate if you help me.

ricardoNovember 9, 2022 at 5:28 amHello,

Thank you again for this package. It really useful indeed.

I want to store the e(F) test in a variable by ID. I am doing a fmb regressions by ID, and trying to access the scalar values from the results to create a new variable.

But I am struggling with the syntax. I hope you can help me with this one.

Thank you