pwfdtest {plm} | R Documentation |
Wooldridge first–difference–based test for AR(1) errors in levels or first–differenced panel models
Description
First–differencing–based test of serial correlation for (the idiosyncratic component of) the errors in either levels or first–differenced panel models.
Usage
pwfdtest(x, ...)
## S3 method for class 'formula'
pwfdtest(x, data, ..., h0 = c("fd", "fe"))
## S3 method for class 'panelmodel'
pwfdtest(x, ..., h0 = c("fd", "fe"))
Arguments
x |
an object of class |
... |
further arguments to be passed on to |
data |
a |
h0 |
the null hypothesis: one of |
Details
As Wooldridge (2010), Sec. 10.6.3 observes, if the
idiosyncratic errors in the model in levels are uncorrelated (which
we label hypothesis "fe"
), then the errors of the model in first
differences (FD) must be serially correlated with
cor(\hat{e}_{it}, \hat{e}_{is}) = -0.5
for each t,s
. If
on the contrary the levels model's errors are a random walk, then
there must be no serial correlation in the FD errors (hypothesis
"fd"
). Both the fixed effects (FE) and the first–differenced
(FD) estimators remain consistent under either assumption, but the
relative efficiency changes: FE is more efficient under "fe"
, FD
under "fd"
.
Wooldridge (ibid.) suggests basing a test for either hypothesis on
a pooled regression of FD residuals on their first lag:
\hat{e}_{i,t}=\alpha + \rho \hat{e}_{i,t-1} +
\eta_{i,t}
. Rejecting the restriction \rho = -0.5
makes us
conclude against the null of no serial correlation in errors of the
levels equation ("fe"
). The null hypothesis of no serial
correlation in differenced errors ("fd"
) is tested in a similar
way, but based on the zero restriction on \rho
(\rho =
0
). Rejecting "fe"
favours the use of the first–differences
estimator and the contrary, although it is possible that both be
rejected.
pwfdtest
estimates the fd
model (or takes an fd
model as
input for the panelmodel interface) and retrieves its residuals,
then estimates an AR(1) pooling
model on them. The test statistic
is obtained by applying a F test to the latter model to test the
relevant restriction on \rho
, setting the covariance matrix
to vcovHC
with the option method="arellano"
to control for
serial correlation.
Unlike the pbgtest
and pdwtest
, this test does not rely on
large–T asymptotics and has therefore good properties in ”short”
panels. Furthermore, it is robust to general
heteroskedasticity. The "fe"
version can be used to test for
error autocorrelation regardless of whether the maintained
specification has fixed or random effects
(see Drukker 2003).
Value
An object of class "htest"
.
Author(s)
Giovanni Millo
References
Drukker DM (2003). “Testing for Serial Correlation in Linear Panel–Data Models.” The Stata Journal, 3(2), 168-177.
Wooldridge JM (2002). Econometric Analysis of Cross–Section and Panel Data. MIT Press. Sec. 10.6.3, pp. 282–283.
Wooldridge JM (2010). Econometric Analysis of Cross–Section and Panel Data, 2nd edition. MIT Press. Sec. 10.6.3, pp. 319–320
See Also
pdwtest
, pbgtest
, pwartest
,
Examples
data("EmplUK" , package = "plm")
pwfdtest(log(emp) ~ log(wage) + log(capital), data = EmplUK)
pwfdtest(log(emp) ~ log(wage) + log(capital), data = EmplUK, h0 = "fe")
# pass argument 'type' to vcovHC used in test
pwfdtest(log(emp) ~ log(wage) + log(capital), data = EmplUK, type = "HC3", h0 = "fe")
# same with panelmodel interface
mod <- plm(log(emp) ~ log(wage) + log(capital), data = EmplUK, model = "fd")
pwfdtest(mod)
pwfdtest(mod, h0 = "fe")
pwfdtest(mod, type = "HC3", h0 = "fe")