# pbsytest

##### Bera, Sosa-Escudero and Yoon Locally--Robust Lagrange Multiplier Tests for Panel Models and Joint Test by Baltagi and Li

Test for residual serial correlation (or individual random effects) locally robust vs. individual random effects (serial correlation) for panel models and joint test of serial correlation and the random effect specification by Baltagi and Li.

- Keywords
- htest

##### Usage

`pbsytest(x, ...)`# S3 method for formula
pbsytest(
x,
data,
...,
test = c("ar", "re", "j"),
re.normal = if (test == "re") TRUE else NULL
)

# S3 method for panelmodel
pbsytest(
x,
test = c("ar", "re", "j"),
re.normal = if (test == "re") TRUE else NULL,
...
)

##### Arguments

- x
an object of class

`formula`

or of class`panelmodel`

,- …
further arguments.

- data
a

`data.frame`

,- test
a character string indicating which test to perform: first--order serial correlation (

`"ar"`

), random effects (`"re"`

) or joint test for either of them (`"j"`

),- re.normal
logical, only relevant for

`test = "re"`

:`TRUE`

(default) computes the one-sided`"re"`

test,`FALSE`

the two-sided test (see also Details); not relevant for other values of`test`

and, thus, should be`NULL`

,

##### Details

These Lagrange multiplier tests are robust vs. local misspecification of the alternative hypothesis, i.e. they test the null of serially uncorrelated residuals against AR(1) residuals in a pooling model, allowing for local departures from the assumption of no random effects; or they test the null of no random effects allowing for local departures from the assumption of no serial correlation in residuals. They use only the residuals of the pooled OLS model and correct for local misspecification as outlined in BERA:SOSA:YOON:01;textualplm.

For `test = "re"`

, the default (`re.normal = TRUE`

) is to compute
a one-sided test which is expected to lead to a more powerful test
(asymptotically N(0,1) distributed). Setting `re.normal = FALSE`

gives
the two-sided test (asymptotically chi-squared(2) distributed). Argument
`re.normal`

is irrelevant for all other values of `test`

.

The joint test of serial correlation and the random effect
specification (`test = "j"`

) is due to
BALT:LI:91;textualplm (also mentioned in
BALT:LI:95;textualplm, pp. 135--136) and is added
for convenience under this same function.

The unbalanced version of all tests are derived in SOSA:BERA:08;textualplm. The functions implemented are suitable for balanced as well as unbalanced panel data sets.

A concise treatment of the statistics for only balanced panels is given in BALT:13;textualplm, p. 108.

Here is an overview of how the various values of the `test`

argument relate to the literature:

`test = "ar"`

:\(RS*_{\rho}\) in Bera et al. (2001), p. 9 (balanced)

\(LM*_{\rho}\) in Baltagi (2013), p. 108 (balanced)

\(RS*_{\lambda}\) in Sosa-Escudero/Bera (2008), p. 73 (unbalanced)

`test = "re", re.normal = TRUE`

(default) (one-sided test, asymptotically N(0,1) distributed):\(RSO*_{\mu}\) in Bera et al. (2001), p. 11 (balanced)

\(RSO*_{\mu}\) in Sosa-Escudero/Bera (2008), p. 75 (unbalanced)

`test = "re", re.normal = FALSE`

(two-sided test, asymptotically chi-squared(2) distributed):\(RS*_{\mu}\) in Bera et al. (2001), p. 7 (balanced)

\(LM*_{\mu}\) in Baltagi (2013), p. 108 (balanced)

\(RS*_{\mu}\) in Sosa-Escudero/Bera (2008), p. 73 (unbalanced)

`test = "j"`

:\(RS_{\mu\rho}\) in Bera et al. (2001), p. 10 (balanced)

\(LM\) in Baltagi/Li (2001), p. 279 (balanced)

\(LM_{1}\) in Baltagi and Li (1995), pp. 135--136 (balanced)

\(LM1\) in Baltagi (2013), p. 108 (balanced)

\(RS_{\lambda\rho}\) in Sosa-Escudero/Bera (2008), p. 74 (unbalanced)

##### Value

An object of class `"htest"`

.

##### References

BERA:SOSA:YOON:01plm

BALT:13plm

BALT:LI:91plm

BALT:LI:95plm

SOSA:BERA:08plm

##### See Also

`plmtest()`

for individual and/or time random effects
tests based on a correctly specified model; `pbltest()`

,
`pbgtest()`

and `pdwtest()`

for serial correlation tests
in random effects models.

##### Examples

```
# NOT RUN {
## Bera et. al (2001), p. 13, table 1 use
## a subset of the original Grunfeld
## data which contains three errors -> construct this subset:
data("Grunfeld", package = "plm")
Grunsubset <- rbind(Grunfeld[1:80, ], Grunfeld[141:160, ])
Grunsubset[Grunsubset$firm == 2 & Grunsubset$year %in% c(1940, 1952), ][["inv"]] <- c(261.6, 645.2)
Grunsubset[Grunsubset$firm == 2 & Grunsubset$year == 1946, ][["capital"]] <- 232.6
## default is AR testing (formula interface)
pbsytest(inv ~ value + capital, data = Grunsubset, index = c("firm", "year"))
pbsytest(inv ~ value + capital, data = Grunsubset, index = c("firm", "year"), test = "re")
pbsytest(inv ~ value + capital, data = Grunsubset, index = c("firm", "year"),
test = "re", re.normal = FALSE)
pbsytest(inv ~ value + capital, data = Grunsubset, index = c("firm", "year"), test = "j")
## plm interface
mod <- plm(inv ~ value + capital, data = Grunsubset, model = "pooling")
pbsytest(mod)
# }
```

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