General estimator useful for testing the within specification
piest(formula, data, subset, na.action, index = NULL, robust = TRUE, ...)
# S3 method for class 'piest'
print(x, ...)
# S3 method for class 'piest'
summary(object, ...)
# S3 method for class 'summary.piest'
print(
x,
digits = max(3, getOption("digits") - 2),
width = getOption("width"),
subset = NULL,
...
)a symbolic description for the model to be estimated,
a data.frame,
see lm(),
see lm(),
the indexes,
logical, if FALSE, the error is assumed to be spherical,
if TRUE, a robust estimation of the covariance matrix is computed,
further arguments.
an object of class "piest" and of class "summary.piest"
for the print method of summary for piest objects,
number of digits for printed output,
the maximum length of the lines in the printed output,
An object of class "piest".
The Chamberlain method consists in using the covariates of all the periods as regressors. It allows to test the within specification.
Chamberlain G (1982). “Multivariate regression models for panel data.” Journal of Econometrics, 18, 5–46.
data("RiceFarms", package = "plm")
pirice <- piest(log(goutput) ~ log(seed) + log(totlabor) + log(size), RiceFarms, index = "id")
summary(pirice)
#> Estimate Std. Error z-value Pr(>|z|)
#> log(seed) 0.1096449 0.0157087 6.9799 2.954e-12 ***
#> log(totlabor) 0.2261224 0.0168539 13.4166 < 2.2e-16 ***
#> log(size) 0.6575833 0.0226042 29.0912 < 2.2e-16 ***
#> log(seed).1 0.1168747 0.0282226 4.1412 3.455e-05 ***
#> log(totlabor).1 0.0440505 0.0352284 1.2504 0.2111448
#> log(size).1 -0.2315263 0.0451630 -5.1265 2.952e-07 ***
#> log(seed).2 -0.0190152 0.0119321 -1.5936 0.1110215
#> log(totlabor).2 -0.0261597 0.0290088 -0.9018 0.3671718
#> log(size).2 0.0314256 0.0233416 1.3463 0.1781949
#> log(seed).3 -0.0687868 0.0247259 -2.7820 0.0054030 **
#> log(totlabor).3 0.1221667 0.0294784 4.1443 3.409e-05 ***
#> log(size).3 0.0487253 0.0238871 2.0398 0.0413683 *
#> log(seed).4 0.0132149 0.0285666 0.4626 0.6436509
#> log(totlabor).4 0.0526304 0.0272371 1.9323 0.0533221 .
#> log(size).4 -0.0046384 0.0443225 -0.1047 0.9166526
#> log(seed).5 -0.1105456 0.0291603 -3.7910 0.0001501 ***
#> log(totlabor).5 -0.2277151 0.0390801 -5.8269 5.647e-09 ***
#> log(size).5 0.2376872 0.0437637 5.4311 5.599e-08 ***
#> log(seed).6 0.2556306 0.0364290 7.0172 2.263e-12 ***
#> log(totlabor).6 0.1535560 0.0354287 4.3342 1.463e-05 ***
#> log(size).6 -0.3550436 0.0422203 -8.4093 < 2.2e-16 ***
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
#> Chamberlain's pi test
#>
#> data: log(goutput) ~ log(seed) + log(totlabor) + log(size)
#> chisq = 113.72, df = 87, p-value = 0.02882
#> alternative hypothesis: within specification does not apply
#>