# pwartest

##### Wooldridge Test for AR(1) Errors in FE Panel Models

Test of serial correlation for (the idiosyncratic component of) the errors in fixed--effects panel models.

- Keywords
- htest

##### Usage

`pwartest(x, ...)`# S3 method for formula
pwartest(x, data, ...)

# S3 method for panelmodel
pwartest(x, ...)

##### Arguments

- x
an object of class

`formula`

or of class`panelmodel`

,- …
further arguments to be passed on to

`vcovHC`

(see Details and Examples).- data
a

`data.frame`

,

##### Details

As WOOL:10;textualplm, Sec. 10.5.4 observes, under the null of no serial correlation in the errors, the residuals of a FE model must be negatively serially correlated, with \(cor(\hat{u}_{it}, \hat{u}_{is})=-1/(T-1)\) for each \(t,s\). He suggests basing a test for this null hypothesis on a pooled regression of FE residuals on their first lag: \(\hat{u}_{i,t} = \alpha + \delta \hat{u}_{i,t-1} + \eta_{i,t}\). Rejecting the restriction \(\delta = -1/(T-1)\) makes us conclude against the original null of no serial correlation.

`pwartest`

estimates the `within`

model and retrieves 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
above restriction on \(\delta\), 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.

##### Value

An object of class `"htest"`

.

##### References

WOOL:02plm

WOOL:10plm

##### See Also

##### Examples

```
# NOT RUN {
data("EmplUK", package = "plm")
pwartest(log(emp) ~ log(wage) + log(capital), data = EmplUK)
# pass argument 'type' to vcovHC used in test
pwartest(log(emp) ~ log(wage) + log(capital), data = EmplUK, type = "HC3")
# }
```

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