This function reports unbalancedness measures for panel data as defined in Ahrens and Pincus (1981) and Baltagi et al. (2001) .
punbalancedness(x, ...)
# S3 method for class 'pdata.frame'
punbalancedness(x, ...)
# S3 method for class 'data.frame'
punbalancedness(x, index = NULL, ...)
# S3 method for class 'panelmodel'
punbalancedness(x, ...)a panelmodel, a data.frame, or a pdata.frame object,
further arguments.
only relevant for data.frame interface, for details
see pdata.frame(),
A named numeric containing either two or three entries, depending on the panel structure inputted:
For the two-dimensional panel structure, the entries are called
gamma and nu,
For a nested panel structure, the entries are called c1, c2,
c3.
punbalancedness returns measures for the unbalancedness of a
panel data set.
For two-dimensional data:
The two measures of
Ahrens and Pincus (1981)
are calculated, called
"gamma" (\(\gamma\)) and "nu" (\(\nu\)).
If the panel data are balanced, both measures equal 1. The more
"unbalanced" the panel data, the lower the measures (but > 0). The
upper and lower bounds as given in Ahrens and Pincus (1981)
are:
\(0 < \gamma, \nu \le 1\), and for \(\nu\) more precisely
\(\frac{1}{n} < \nu \le 1\), with \(n\) being
the number of individuals (as in pdim(x)$nT$n).
For nested panel data (meaning including a grouping variable):
The extension of the above measures by
Baltagi et al. (2001)
, p. 368, are
calculated:
c1: measure of subgroup (individual) unbalancedness,
c2: measure of time unbalancedness,
c3: measure of group unbalancedness due to each group size.
Values are 1 if the data are balanced and become smaller as the data become more unbalanced.
An application of the measure "gamma" is found in e. g. Baltagi et al. (2001) , pp. 488-491, and Baltagi and Chang (1994) , pp. 78–87, where it is used to measure the unbalancedness of various unbalanced data sets used for Monte Carlo simulation studies. Measures c1, c2, c3 are used for similar purposes in Baltagi et al. (2001) .
In the two-dimensional case, punbalancedness uses output of
pdim() to calculate the two unbalancedness measures, so inputs to
punbalancedness can be whatever pdim works on. pdim returns
detailed information about the number of individuals and time
observations (see pdim()).
Calling punbalancedness on an estimated panelmodel object
and on the corresponding (p)data.frame used for this
estimation does not necessarily yield the same result (true
also for pdim). When called on an estimated panelmodel, the
number of observations (individual, time) actually used for
model estimation are taken into account. When called on a
(p)data.frame, the rows in the (p)data.frame are
considered, disregarding any NA values in the dependent or
independent variable(s) which would be dropped during model
estimation.
Ahrens H, Pincus R (1981). “On Two Measures of Unbalancedness in a One-Way Model and Their Relation to Efficiency.” Biometrical Journal, 23(3), 227-235. doi:10.1002/bimj.4710230302 .
Baltagi BH, Chang YJ (1994). “Incomplete panels: a comparative study of alternative estimators for the unbalanced one-way error component regression model.” Journal of Econometrics, 62, 67-89.
Baltagi BH, Song SH, Jung BC (2001). “The unbalanced nested error component regression model.” Journal of Econometrics, 101, 357-381.
Baltagi BH, Song SH, Jung BC (2002). “A comparative study of alternative estimators for the unbalanced two-way error component regression model.” The Econometrics Journal, 5(2), 480–493. ISSN 13684221, 1368423X.
# Grunfeld is a balanced panel, Hedonic is an unbalanced panel
data(list=c("Grunfeld", "Hedonic"), package="plm")
# Grunfeld has individual and time index in first two columns
punbalancedness(Grunfeld) # c(1,1) indicates balanced panel
#> gamma nu
#> 1 1
pdim(Grunfeld)$balanced # TRUE
#> [1] TRUE
# Hedonic has individual index in column "townid" (in last column)
punbalancedness(Hedonic, index="townid") # c(0.472, 0.519)
#> gamma nu
#> 0.4715336 0.5188292
pdim(Hedonic, index="townid")$balanced # FALSE
#> [1] FALSE
# punbalancedness on estimated models
plm_mod_pool <- plm(inv ~ value + capital, data = Grunfeld)
punbalancedness(plm_mod_pool)
#> gamma nu
#> 1 1
plm_mod_fe <- plm(inv ~ value + capital, data = Grunfeld[1:99, ], model = "within")
punbalancedness(plm_mod_fe)
#> gamma nu
#> 0.9995791 0.9995920
# replicate results for panel data design no. 1 in Ahrens/Pincus (1981), p. 234
ind_d1 <- c(1,1,1,2,2,2,3,3,3,3,3,4,4,4,4,4,4,4,5,5,5,5,5,5,5)
time_d1 <- c(1,2,3,1,2,3,1,2,3,4,5,1,2,3,4,5,6,7,1,2,3,4,5,6,7)
df_d1 <- data.frame(individual = ind_d1, time = time_d1)
punbalancedness(df_d1) # c(0.868, 0.887)
#> gamma nu
#> 0.8677686 0.8865248
# example for a nested panel structure with a third index variable
# specifying a group (states are grouped by region) and without grouping
data("Produc", package = "plm")
punbalancedness(Produc, index = c("state", "year", "region"))
#> c1 c2 c3
#> 0.8760816 1.0000000 0.8760816
punbalancedness(Produc, index = c("state", "year"))
#> gamma nu
#> 1 1