Newey-West standard errors with Mean Groups/Fama-MacBeth estimator

Question

I'm trying to get Newey-West standard errors to work with the output of pmg() (Mean Groups/Fama-MacBeth estimator) from the plm package.

Following the example from here:

require(foreign)
require(plm)
require(lmtest)
test <- read.dta("http://www.kellogg.northwestern.edu/faculty/petersen/htm/papers/se/test_data.dta")

fpmg <- pmg(y~x, test, index=c("firmid", "year")) # Time index in second position, unlike the example

I can use coeftest directly just fine to get the Fama-MacBeth standard errors:

# Regular “Fama-MacBeth” standard errors
coeftest(fpmg)

# t test of coefficients:
#   
#             Estimate Std. Error t value Pr(>|t|)    
# (Intercept) 0.032470   0.071671   0.453   0.6505    
# x           0.969212   0.034782  27.866   <2e-16 ***
# ---
# Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

However, trying to use the Newey-West estimators fails:

# Newey-West standard-errors
coeftest(fpmg, vcov = NeweyWest(fpmg, lag=3))

# Error in UseMethod("estfun") : 
#   no applicable method for 'estfun' applied to an object of class "c('pmg', 'panelmodel')"

This seems like a shortcoming in the plm package. Do you know a way to make this work? Should I code my own estfun for pmg objects? Code a Newey-West estimator from scratch? Or should I bypass the plm package altogether?

Answer 1

Currently this is impossible with plm package.

However, you could just create them yourself.

Suppose you have:

fpmg <- pmg(y~x, test, index = c('year', 'firmid'))
fpmg.coefficients <- fpmg$coefficients
# (Intercept)            x 
#  0.03127797   1.03558610 

coeftest(fpmg)
#             Estimate Std. Error t value Pr(>|t|)    
# (Intercept) 0.031278   0.023356  1.3392   0.1806    
# x           1.035586   0.033342 31.0599   <2e-16 ***

Then you can simply create the estimators yourself like in:

the.years <- unique(test$year)
a.formula <- y ~ x


first.step <-  lapply(the.years, function(a.year) {
                temp.data <- test[test$year == a.year, ]
                an.lm <- lm(a.formula, data = temp.data)
                the.coefficients <- an.lm$coef
                the.results <- as.data.frame(cbind(a.year, t(the.coefficients)))
                the.results
                }) 

first.step.df <- do.call('rbind', first.step)

second.step.coefficients <- apply(first.step.df[, -1], 2, mean)
second.step.coefficients
# (Intercept)           x 
#  0.03127797  1.03558610 

identical(fpmg.coefficients, second.step.coefficients)
# [1] TRUE

Check that they are identical both ways just in case. Last, you can obtain the Newey-West (1987) with one lag adjusted t-statistics for the means with:

library(sandwich)
second.step.NW.sigma.sq <- apply(first.step.df[, -1], 2, 
                             function(x) sqrt(NeweyWest(lm(x ~ 1), 
                               lag = 1, prewhite = FALSE)['(Intercept)',       
                                 '(Intercept)']))
second.step.NW.sigma.sq
#  (Intercept)            x 
#   0.02438398   0.02859447
t.statistics.NW.lag.1 <- second.step.coefficients / second.step.NW.sigma.sq

t.statistics.NW.lag.1
# (Intercept)           x 
#    1.282726   36.216301

Update

In my answer, I had only included the "manual" calculation of the t-statistic, because it is computationally faster. A more generic solution is to calculcate the Newey-West corrected t-statistics and their p-values with the coeftest() function of the lmtest package.

coeftest(lm(first.step.df$'(Intercept)' ~ 1), vcov = NeweyWest(lm(first.step.df$'(Intercept)' ~ 1), lag = 1, prewhite = FALSE))
# t test of coefficients:
#             Estimate Std. Error t value Pr(>|t|)
# (Intercept) 0.031278   0.024384  1.2827   0.2316
coeftest(lm(first.step.df$x ~ 1), vcov = NeweyWest(lm(first.step.df$x ~ 1), lag = 1, prewhite = FALSE))
# t test of coefficients:
#             Estimate Std. Error t value  Pr(>|t|)    
# (Intercept) 1.035586   0.028594  36.216 4.619e-11 ***

Answer 2

I think we can use tidyverse to do Newey–West adjustment, since base R methods are too verbose. 3 or 4 years ago, tidyverse was immature, but today we can relatively perfect use tidyverse. Here is the tidyverse method. Besides, broom package is used in my answer.

# test data:
set.seed(1234)
a <- tibble(
            year = rep(1:20, each = 100),
            firmid = rep(1:100, times = 20),
            x1 = rnorm(2000),
            x2 = rnorm(2000),
            y = 2 + 3 * x1 - 2 * x2 + rnorm(1)
           )

Newey-West adjustment:

a.formula <- formula("y ~ x1+x2")
lag <- 1

regco <- a %>% 
   group_by(year) %>%
   group_modify(~tidy(lm(a.formula, data = .x))) %>% 
   select(year,term,estimate) %>% 
   pivot_wider(names_from = term,
               values_from = estimate) %>% 
   ungroup() %>% 
   select(x1, x2, `(Intercept)`) %>% 
   map(
       ~coeftest(
                 lm(.x ~ 1), 
                 vcov = NeweyWest(
                                  lm(.x ~ 1), 
                                  lag = lag, 
                                  prewhite = FALSE
                                 )
                )
      )