R: Measures for Unbalancedness of Panel Data

punbalancedness {plm} | R Documentation

## Measures for Unbalancedness of Panel Data

### Description

This function reports two unbalancedness measures for panel data as defined in Ahrens/Pincus (1981).

### Usage

    punbalancedness(x, ...)
    ## S3 method for class 'panelmodel'
    punbalancedness(x, ...)
    ## S3 method for class 'data.frame'
    punbalancedness(x, index = NULL, ...)
    ## S3 method for class 'pdata.frame'
    punbalancedness(x, ...)

### Arguments

`x` | a `panelmodel`, a `data.frame`, or a `pdata.frame` object,
`index` | only relevant for `data.frame` interface, for details see `pdata.frame`,
`...` | further arguments.

### Details

`punbalancedness` returns two measures for the unbalancedness of a panel data set (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/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`).

An application of the first measure ("gamma") is found in e. g. Baltagi/Song/Jung (2002), pp. 488-491, and Baltagi/Chang (1994), pp. 78–87, where it is used to measure the unbalancedness of various unbalanced data sets used for Monte Carlo simulation studies.

There exists also an extension of unbalancedness measures to nested panel structures as developed in Baltagi/Song/Jung (2001), p. 368, but these are not implemented in `punbalancedness` as of now.

`punbalancedness` uses output of `pdim` to calculate the unbalancedness measures, so inputs to `punbalancedness` can be whatever `pdim` works on. `pdim` returns a logical whether a panel data set is balanced or not and detailed information about the number of individuals and time observations (see `pdim`).

### Value

A numeric vector containing two entries (in this order):

`gamma` | unbalancedness measure "gamma" (γ) (as called by the Greek letter in Ahrens/Pincus (1981), p. 228),
`nu` | unbalancedness measure "nu" (ν) (as called by the Greek letter in Ahrens/Pincus (1981), p. 228).

### Note

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.

### Author(s)

Kevin Tappe

### References

Ahrens, H.; Pincus, R. (1981), “On two measures of unbalancedness in a one-way model and their relation to efficiency”, Biometrical Journal, 23(3), pp. 227–235.

Baltagi, Badi H.; Chang, Young-Jae (1994), “Incomplete panels: A comparative study of alternative estimators for the unbalanced one-way error component regression model”, Journal of Econometrics, 62(2), pp. 67–89.

Baltagi, Badi H.; Song, Seuck Heun; Jung, Byoung Cheol (2001), “The unbalanced nested error component regression model”, Journal of Econometrics, 101(2), pp. 357–381.

Baltagi, Badi H.; Song, Seuck H.; Jung, Byoung C. (2002), “A comparative study of alternative estimators for the unbalanced two-way error component regression model”, Econometrics Journal, 5(2), pp. 480–493.

### See Also

`nobs`, `pdim`, `pdata.frame`

### Examples

    # 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)

[Package plm version 1.6-5 Index]