What is Fama-MacBeth Regression?

Fama-Macbeth regression is a two steps procedure. In the first step, it runs cross-sectional regression at each point of time; the second step estimates the coefficient as the average of the cross-sectional regression estimates (Fama & MacBeth, 1972). https://finpko.ku.edu/myssi/FIN938/Fama%20&%20Macbeth.JPE_1973.pdf

For each time t, we run a cross-sectional regression:

\[ R_i _t=α_i+βmvalue_i_t * mvalue_i_t + βkstock_i_t *kstock_it + ϵ_i_t \] Estimate the average of the first step regression coefficient estimates

\[ β^k= 1/T \sum_{t=1}^ {T}β_k _t \]

Load the packages

require(foreign)
require(plm)
require(lmtest)

Grunfeld Investment Data of 10 firms for 20 years (1935-1954) is available at http://people.stern.nyu.edu/wgreene/Econometrics/PanelDataSets.htm

Download and import data

library(readxl)
grunfeld <- read_excel("C:/Users/HP/Downloads/grunfeld.xlsx")
View(grunfeld)
names(grunfeld)
## [1] "FIRM" "YEAR" "I"    "F"    "C"

First make a copy of dataset and rename the variables

grunfeld_copy <- grunfeld
names(grunfeld_copy) <- c("FIRM", "YEAR",  "investment", "mvalue", "kstock")
names(grunfeld_copy)
## [1] "FIRM"       "YEAR"       "investment" "mvalue"     "kstock"

Fama-MacBeth regression and summary of results

fpmg <- pmg(investment ~ mvalue + kstock, grunfeld_copy, index=c("YEAR","FIRM"))
summary(fpmg)
## Mean Groups model
## 
## Call:
## pmg(formula = investment ~ mvalue + kstock, data = grunfeld_copy, 
##     index = c("YEAR", "FIRM"))
## 
## Balanced Panel: n = 20, T = 10, N = 200
## 
## Residuals:
##     Min.  1st Qu.   Median     Mean  3rd Qu.     Max. 
## -342.804  -20.101    0.727    0.000   23.653  258.505 
## 
## Coefficients:
##                Estimate  Std. Error z-value  Pr(>|z|)    
## (Intercept) -14.7569720   7.2876699 -2.0249  0.042875 *  
## mvalue        0.1306047   0.0093422 13.9801 < 2.2e-16 ***
## kstock        0.0729576   0.0277398  2.6301  0.008537 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Total Sum of Squares: 9359900
## Residual Sum of Squares: 1205800
## Multiple R-squared: 0.87117
coeftest(fpmg)
## 
## t test of coefficients:
## 
##                Estimate  Std. Error t value  Pr(>|t|)    
## (Intercept) -14.7569720   7.2876699 -2.0249  0.044225 *  
## mvalue        0.1306047   0.0093422 13.9801 < 2.2e-16 ***
## kstock        0.0729576   0.0277398  2.6301  0.009211 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
confint(fpmg)
##                    2.5 %     97.5 %
## (Intercept) -29.04054264 -0.4734014
## mvalue        0.11229429  0.1489150
## kstock        0.01858857  0.1273265