pwfdtest {plm} | R Documentation |
First–differencing–based test of serial correlation for (the idiosyncratic component of) the errors in either levels or first–differenced panel models.
pwfdtest(x, ...) ## S3 method for class 'panelmodel' pwfdtest(x, ..., h0 = c("fd", "fe")) ## S3 method for class 'formula' pwfdtest(x, data, ..., h0 = c("fd", "fe"))
x |
an object of class |
data |
a |
h0 |
the null hypothesis: one of |
... |
further arguments to be passed on to |
As Wooldridge (2003/2010, 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}=α + ρ \hat{e}_{i,t-1} + η_{i,t}. Rejecting the
restriction ρ = -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 ρ (ρ = 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 ρ,
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)).
An object of class "htest"
.
Giovanni Millo
Drukker, D.M. (2003) Testing for serial correlation in linear panel–data models, The Stata Journal, 3(2), pp. 168–177.
Wooldridge, J.M. (2003) Econometric Analysis of Cross Section and Panel Data, MIT Press, Sec. 10.6.3, pp. 282–283.
Wooldridge, J.M. (2010) Econometric Analysis of Cross Section and Panel Data, 2nd ed., MIT Press, Sec. 10.6.3, pp. 319–320.
pdwtest
, pbgtest
, pwartest
,
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")