R - Plm and lm - Fixed effects

Question

I have a balanced panel data set, df, that essentially consists in three variables, A, B and Y, that vary over time for a bunch of uniquely identified regions. I would like to run a regression that includes both regional (region in the equation below) and time (year) fixed effects. If I'm not mistaken, I can achieve this in different ways:

lm(Y ~ A + B + factor(region) + factor(year), data = df)

or

library(plm)
plm(Y ~ A + B, 
    data = df, index = c('region', 'year'), model = 'within',
    effect = 'twoways')

In the second equation I specify indices (region and year), the model type ('within', FE), and the nature of FE ('twoways', meaning that I'm including both region and time FE).

Despite I seem to be doing things correctly, I get extremely different results. The problem disappears when I do not consider time fixed effects - and use the argument effect = 'individual'. What's the deal here? Am I missing something? Are there any other R packages that allow to run the same analysis?

Results for variables A and B should be the same. The lm approach (LSDV) will give you estimates of the individual and time fixed effects and an intercept as well. — Helix123
two ideas: in the lm command specify the formula as you have, but add a -1 to the end. As pointed out above, this will remove the intercept, which plm won't add automatically. The second point: rather than factor, have you tried as.factor? — Moritz Schwarz

maccruiskeen maccruiskeen · Accepted Answer · 2017-04-26T14:26:21

Perhaps posting an example of your data would help answer the question. I am getting the same coefficients for some made up data. You can also use felm from the package lfe to do the same thing:

N <- 10000
df <- data.frame(a = rnorm(N), b = rnorm(N),
                 region = rep(1:100, each = 100), year = rep(1:100, 100))
df$y <- 2 * df$a - 1.5 * df$b + rnorm(N)


model.a <- lm(y ~ a + b + factor(year) + factor(region), data = df)
summary(model.a)
#  (Intercept)       -0.0522691  0.1422052   -0.368   0.7132    
#  a                  1.9982165  0.0101501  196.866   <2e-16 ***
#  b                 -1.4787359  0.0101666 -145.450   <2e-16 ***

library(plm)
pdf <- pdata.frame(df, index = c("region", "year"))

model.b <- plm(y ~ a + b, data = pdf, model = "within", effect = "twoways")
summary(model.b)

# Coefficients :
#    Estimate Std. Error t-value  Pr(>|t|)    
# a  1.998217   0.010150  196.87 < 2.2e-16 ***
# b -1.478736   0.010167 -145.45 < 2.2e-16 ***

library(lfe)

model.c <- felm(y ~ a + b | factor(region) + factor(year), data = df)
summary(model.c)

# Coefficients:
#   Estimate Std. Error t value Pr(>|t|)    
# a  1.99822    0.01015   196.9   <2e-16 ***
# b -1.47874    0.01017  -145.4   <2e-16 ***

R - Plm and lm - Fixed effects

2 Answers