# pwfdtest

##### Wooldridge first--difference--based test for AR(1) errors in levels or first--differenced panel models

First--differencing--based test of serial correlation for (the idiosyncratic component of) the errors in either levels or first--differenced panel models.

- Keywords
- htest

##### Usage

`pwfdtest(x, ...)`# S3 method for formula
pwfdtest(x, data, ..., h0 = c("fd", "fe"))

# S3 method for panelmodel
pwfdtest(x, ..., h0 = c("fd", "fe"))

##### Arguments

- x
an object of class

`formula`

or a`"fd"`

-model (plm object),- …
further arguments to be passed on to

`vcovHC`

(see Details and Examples).- data
a

`data.frame`

,- h0
the null hypothesis: one of

`"fd"`

,`"fe"`

,

##### Details

As WOOL:10;textualplm, 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 @DRUK:03plm.

##### Value

An object of class `"htest"`

.

##### References

DRUK:03plm

WOOL:02plm Sec. 10.6.3, pp. 282--283.

WOOL:10plm Sec. 10.6.3, pp. 319--320

##### See Also

`pdwtest`

, `pbgtest`

, `pwartest`

,

##### Examples

```
# NOT RUN {
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")
# }
```

*Documentation reproduced from package plm, version 2.2-5, License: GPL (>= 2)*