Perform Pesaran CD test

Source: man/performPesaranTest.Rd · Help: ?performPesaranTest

Checks for cross-sectional dependence in panel residuals.

Usage

performPesaranTest(model, data = NULL, id, time)

Arguments

model

an object of class lm, the pooled lm() of the panel.

data

The data frame model was fitted to, holding the panel identifiers named by id and time, or NULL, the default. The residuals and weights are read from the fit itself, and id and time from the rows of data that hold the observations of the fit. Without data they are read from the model frame of model, which holds them only when they are variables of the model under their own names (id, not factor(id)); identifiers the model does not use need data. Since 0.16.0, data that are given are matched to the observations of the fit: rows with row names of their own by name, in any order; rows that only number themselves (a tibble, a data.table, a data frame whose row names were reset) by the row numbers of the fit, or in the order of the fit when they hold one row per observation. The rows the fit dropped may be there or not. Data whose rows cannot be shown to hold the observations of the fit are refused; see test_results.

id

individual identifier column.

time

time column. Each pair of id and time must hold one observation of the fit: since 0.16.0 a pair that holds more is refused. The units need not be observed at the same periods (Details).

Value

An object of class htest.

Details

The statistic averages pairwise correlation coefficients of the residuals and is standardized to follow a normal distribution under the null of independence. On a balanced panel of \(N\) units observed at the same \(T\) periods it is

\[ \mathrm{CD} = \sqrt{\frac{2T}{N(N - 1)}} \sum_{i < j} \hat{\rho}_{ij}, \]

where \(\hat{\rho}_{ij}\) is the correlation of the residuals of units \(i\) and \(j\). On an unbalanced panel, whose units are not all observed at the same periods, it is computed, since 0.16.0, from the periods each pair of units shares (Pesaran 2004, Section 9, equation 31), as plm::pcdtest(test = "cd") computes it:

\[ \mathrm{CD} = \sqrt{\frac{1}{P}} \sum_{i < j} \sqrt{T_{ij}}\, \hat{\rho}_{ij}, \]

where \(T_{ij}\) is the number of periods at which units \(i\) and \(j\) are both observed, \(\hat{\rho}_{ij}\) the correlation of their residuals over those periods, each centred at its mean over them, and \(P\) the number of pairs that share at least two periods, the pairs of the sum: \(N(N - 1)/2\) when every pair does. On a balanced panel, where \(T_{ij} = T\), the two are the same statistic. A pair that shares fewer than two periods has no correlation and is left out, with a warning, as plm::pcdtest() leaves it out, and a panel in which no pair shares two periods is refused. A correlation that is not defined, the residuals of a unit constant over the periods of a pair, adds nothing to the sum and the pair stays in the count, as on a balanced panel, with a warning; plm::pcdtest() returns NA there, so the statistic is that of plm::pcdtest() except where a correlation is undefined. Pesaran (2004) states its standard normal limit under the null of independence for \(T_i > k + 1\) and \(T_{ij} > 3\), with \(N\) large, \(T_i\) being the number of periods of unit \(i\) and \(k\) the number of regressors of its own regression.

Supported models

It accepts an lm and a glm with the Gaussian family and the identity link, unweighted or with positive weights, a fitWLS() fit and, since 0.16.0, a rank-deficient fit, which it tests on the estimable part of its design: it gives the value of the same model fitted without the aliased columns. It refuses a glm of another family or link, a survey::svyglm() fit, a fit with a zero weight, a coefficient that is not finite for another reason, and data that lack rows or variables of the fit. The model is a pooled lm of the panel, with the units and the periods as columns of data; a plm::plm() fit is not an lm and is refused. Since 0.16.0 a pair of id and time that holds two observations of the fit is refused. An unbalanced panel, as that of a fit that dropped some rows of some units, is tested since 0.16.0, from the periods each pair of units shares (Details), and gives the value of plm::pcdtest(test = "cd") on the residuals of the fit, except where a correlation is undefined (Details): before, the test stopped on it, or, when the number of periods of a unit divided that of the panel, returned a wrong value computed on its residuals recycled over the periods it lacks. A fit with na.action = na.exclude is tested since 0.17.0 as the same fit with na.omit, on the observations it kept, its panel balanced or not: before, it was read by position, its residuals padded with NA at the rows it dropped, against the rows of data, which had to be in the order of the fit, and an unbalanced panel of those rows was refused. Which model each test accepts, and why, is set out in test_results, under Supported models.

References

Pesaran, M. H. (2004). General diagnostic tests for cross section dependence in panels. CESifo Working Paper 1229 (also Cambridge Working Papers in Economics 0435). Section 9, “CD tests in the case of unbalanced panels”, equation 31.

Pesaran, M. H. (2015). Testing weak cross-sectional dependence in large panels. Econometric Reviews 34(6-10), 1089–1117. doi:10.1080/07474938.2014.956623.

Croissant, Y. and Millo, G. (2008). Panel data econometrics in R: the plm package. Journal of Statistical Software 27(2), 1–43. doi:10.18637/jss.v027.i02. The statistic of an unbalanced panel is that of plm::pcdtest(test = "cd") (plm 2.6-6), whose help page says its tests are “suitable also for unbalanced panels”.

Examples

 df <- data.frame(id = rep(1:3, each = 5), time = rep(1:5, 3), x = runif(15), y = rnorm(15))
 m <- lm(y ~ x, data = df)
 performPesaranTest(m, df, "id", "time")