Description Usage Arguments Details Value Author(s) References See Also Examples

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

1 2 3 4 5 |

`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.

1 2 3 4 5 6 7 8 9 10 11 12 13 | ```
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")
``` |

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