Measures for Unbalancedness of Panel Data
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, ...)
x |
a |
... |
further arguments. |
index |
only relevant for |
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" (γ) and "nu" (ν).
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 < γ, ν ≤ 1, and for ν more precisely
1/n < ν ≤ 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).
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
.
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.
Kevin Tappe
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, https://onlinelibrary.wiley.com/doi/abs/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 pdim(Grunfeld)$balanced # TRUE # Hedonic has individual index in column "townid" (in last column) punbalancedness(Hedonic, index="townid") # c(0.472, 0.519) pdim(Hedonic, index="townid")$balanced # FALSE # punbalancedness on estimated models plm_mod_pool <- plm(inv ~ value + capital, data = Grunfeld) punbalancedness(plm_mod_pool) plm_mod_fe <- plm(inv ~ value + capital, data = Grunfeld[1:99, ], model = "within") punbalancedness(plm_mod_fe) # 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) # 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")) punbalancedness(Produc, index = c("state", "year"))
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