Dear R users
I get different F-statistic results for a "within" model, when using
"time" or "twoways" effects in plm() [1] and when manually specifying
the time control dummies [2].
[1] vignette("plm")
[2] http://cran.r-project.org/doc/contrib/Farnsworth-EconometricsInR.pdf
Well, the question is incomplete in a way. An F-statistic is always
associated with testing a model against some restricted version of that
model. And which restricted model is reasonable might vary with your
application.
You used:
data("Grunfeld", package = "AER")
library("plm")
gr <- subset(Grunfeld, firm %in% c("General Electric", "General Motors", "IBM"))
pgr <- plm.data(gr, index = c("firm", "year"))
and then considered
gr_fe <- plm(invest ~ value + capital, data = pgr, model = "within",
effect = "individual")
which you correctly pointed out is equivalent to
gr_lm <- lm(invest ~ 0 + value + capital + firm, data = pgr)
The difference between the two is that in "gr_fe" the model knows that the
parameters of interest are "value" and "capital" and that the
firm-specific intercepts are nuisance parameters (or at least of less
importance than value/capital).
In "gr_lm" however, the fitted model does not know about that. It just
knows that you forced out the intercept (and doesn't check that a
firm-specific intercept is in fact included).
Hence, when saying summary() different models with "no effects" are
assumed. For gr_fe the model without effects just omits value/capital but
keeps the firm-specific interecepts. For gr_lm not even the intercept is
kept in the model. Thus:
gr_fe_null <- lm(invest ~ 0 + firm, data = pgr)
gr_lm_null <- lm(invest ~ 0, data = pgr)
Then, comparing the full model (gr_lm) against the different null models
yields:
R> anova(gr_fe_null, gr_lm)
Analysis of Variance Table
Model 1: invest ~ 0 + firm
Model 2: invest ~ 0 + value + capital + firm
Res.Df RSS Df Sum of Sq F Pr(>F)
1 57 1888946
2 55 243985 2 1644961 185.41 < 2.2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
R> anova(gr_lm_null, gr_lm)
Analysis of Variance Table
Model 1: invest ~ 0
Model 2: invest ~ 0 + value + capital + firm
Res.Df RSS Df Sum of Sq F Pr(>F)
1 60 9553385
2 55 243985 5 9309400 419.71 < 2.2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
In the first case, plm(..., effect="individual"), F-statistic: 185.407
and in the second F-statistic: 420, while all other regression
coefficients and standard errors are the same. Which F-statistic
should be considered?
It depends what you want to test. But I doubt that the one reported in
summary(gr_lm) tests a useful hypothesis/alternative.
Best,
Z
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