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

### Arguments

`x` | an object of class `formula`,
`data` | a `data.frame`,
`h0` | the null hypothesis: one of "fd","fe"
`...` | further arguments to be passed on to `linearHypothesis` or to `vcovHC`

### Details

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 + δ \hat{e}_{i,t-1} + η_{i,t}. Rejecting the restriction δ = -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 δ. 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 and retrieves residuals, then estimates an AR(1) `pooling` model on them. The test statistic is obtained by applying `linearHypothesis()` to the latter model to test the relevant restriction on δ, 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, 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.

### See Also

`pdwtest`, `pbgtest`, `pwartest`

### Examples

    data(EmplUK)
    pwfdtest(log(emp) ~ log(wage) + log(capital), data = EmplUK)
    pwfdtest(log(emp) ~ log(wage) + log(capital), data = EmplUK, h0 = "fe")

[Package plm version 1.5-12 Index]