R: Overall Intercept for Within Models Along its Standard Error

within_intercept {plm} | R Documentation

## Overall Intercept for Within Models Along its Standard Error

### Description

This function gives an overall intercept for within models and its accompanying standard error

### Usage

    within_intercept(object, ...)
    ## S3 method for class 'plm'
    within_intercept(object, vcov = NULL, ...)

### Arguments

`object` | object of class `plm` which must be a within model (fixed effects model),
`vcov` | if not `NULL` (default), a function to calculate a user defined variance–covariance matrix (function for robust vcov),
`...` | further arguments (currently none).

### Details

The (somewhat artificial) intercept for within models (fixed effects models) was made popular by Stata of StataCorp (see Gould (2013)) and later also adopted by Gretl (see Cottrell/Lucchetti (2016), p. 160-161 (example 18.1)), see for treatment in the literature, e.g. Greene (2012), Ch. 11.4.4, p. 364. It can be considered an overall intercept in the within model framework and is the weighted mean of fixed effects (see Examples for the relationship).

`within_intercept` estimates a new model which is computationally more demanding than just taking the weighted mean. However, with `within_intercept` one also gets the associated standard error and it is possible to get an overall intercept for twoway fixed effect models.

Users can set argument `vcov` to a function to calculate a specific (robust) variance–covariance matrix and get the respective (robust) standard error for the overall intercept, e.g. the function `vcovHC`, see examples for usage. Note: The argument `vcov` must be a function, not a matrix, because the model to calculate the overall intercept for the within model is different from the within model itself.

### Value

A named `numeric` vector of length one: The overall intercept for the estimated within model along attribute "se" which contains the standard error for the intercept.

### Author(s)

Kevin Tappe

### References

Cottrell, A./Lucchetti, R., Gretl User's Guide, http://gretl.sourceforge.net/gretl-help/gretl-guide.pdf.

Gould, W. (2013), “How can there be an intercept in the fixed-effects model estimated by xtreg, fe?”, http://www.stata.com/support/faqs/statistics/intercept-in-fixed-effects-model/.

Greene, W. H. (2012), Econometric Analysis, 7th ed., Prentice Hall, Ch. 11.4.4.

### See Also

`fixef` to extract the fixed effects of a within model.

### Examples

    # estimate within model (unbalanced data)
    data("Hedonic", package = "plm")
    mod_fe <- plm(mv ~ age + crim, data = Hedonic, index = "townid")
    overallint <- within_intercept(mod_fe)
    attr(overallint, "se") # standard error

    # overall intercept is the weighted mean of fixed effects in the one-way case
    weighted.mean(fixef(mod_fe), as.numeric(table(index(mod_fe)[[1]])))

    # relationship of type="dmean", "level" and within_intercept in the one-way case
    data("Grunfeld", package = "plm")
    gi <- plm(inv ~ value + capital, data = Grunfeld, model = "within")
    fx_level <- fixef(gi, type = "level")
    fx_dmean <- fixef(gi, type = "dmean")
    overallint <- within_intercept(gi)
    all.equal(overallint + fx_dmean, fx_level, check.attributes = FALSE) # TRUE

    # overall intercept with robust standard error
    within_intercept(gi, vcov = function(x) vcovHC(x, method="arellano", type="HC0"))

[Package plm version 1.6-5 Index]