# pbnftest

##### Modified BNF--Durbin--Watson Test and Baltagi--Wu's LBI Test for Panel Models

Tests for AR(1) disturbances in panel models.

- Keywords
- htest

##### Usage

`pbnftest(x, ...)`# S3 method for panelmodel
pbnftest(x, test = c("bnf", "lbi"), ...)

# S3 method for formula
pbnftest(
x,
data,
test = c("bnf", "lbi"),
model = c("pooling", "within", "random"),
...
)

##### Arguments

- x
an object of class

`"panelmodel"`

or of class`"formula"`

,- …
only relevant for formula interface: further arguments to specify the model to test (arguments passed on to plm()), e.g.

`effect`

.- test
a character indicating the test to be performed, either

`"bnf"`

or`"lbi"`

for the (modified) BNF statistic or Baltagi--Wu's LBI statistic, respectively,- data
a

`data.frame`

(only relevant for formula interface),- model
a character indicating on which type of model the test shall be performed (

`"pooling"`

,`"within"`

,`"random"`

, only relevant for formula interface),

##### Details

The default, `test = "bnf"`

, gives the (modified) BNF statistic,
the generalised Durbin-Watson statistic for panels. For balanced
and consecutive panels, the reference is
Bhargava/Franzini/Narendranathan (1982). The modified BNF is given
for unbalanced and/or non-consecutive panels (d1 in formula 16 of
BALT:WU:99;textualplm).

`test = "lbi"`

yields Baltagi--Wu's LBI statistic
BALT:WU:99plm, the locally best invariant test which
is based on the modified BNF statistic.

No specific variants of these tests are available for random effect models. As the within estimator is consistent also under the random effects assumptions, the test for random effect models is performed by taking the within residuals.

No p-values are given for the statistics as their distribution is quite difficult. BHAR:FRAN:NARE:82;textualplm supply tabulated bounds for p = 0.05 for the balanced case and consecutive case.

For large N, BHAR:FRAN:NARE:82plm suggest it is sufficient to check whether the BNF statistic is < 2 to test against positive serial correlation.

##### Value

An object of class `"htest"`

.

##### References

BALT:13plm

BALT:WU:99plm

BHAR:FRAN:NARE:82plm

##### See Also

`pdwtest()`

for the original Durbin--Watson test using
(quasi-)demeaned residuals of the panel model without taking
the panel structure into account. `pbltest()`

, `pbsytest()`

,
`pwartest()`

and `pwfdtest()`

for other serial correlation
tests for panel models.

##### Examples

```
# NOT RUN {
data("Grunfeld", package = "plm")
# formula interface, replicate Baltagi/Wu (1999), table 1, test case A:
data_A <- Grunfeld[!Grunfeld[["year"]] %in% c("1943", "1944"), ]
pbnftest(inv ~ value + capital, data = data_A, model = "within")
pbnftest(inv ~ value + capital, data = data_A, test = "lbi", model = "within")
# replicate Baltagi (2013), p. 101, table 5.1:
re <- plm(inv ~ value + capital, data = Grunfeld, model = "random")
pbnftest(re)
pbnftest(re, test = "lbi")
# }
```

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