within_intercept {plm}

Overall Intercept for Within Models Along its Standard Error

Description

This function gives an overall intercept for within models and its accompanying standard error or an within model with the overall intercept

Usage

within_intercept(object, ...)

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

Arguments

object

object of class plm which must be a within model (fixed effects model),

...

further arguments (currently none).

vcov

if not NULL (default), a function to calculate a user defined variance–covariance matrix (function for robust vcov), only used if return.model = FALSE,

return.model

a logical to indicate whether only the overall intercept (FALSE is default) or a full model object (TRUE) is to be returned,

Details

The (somewhat artificial) intercept for within models (fixed effects models) was made popular by Stata of StataCorp (see Gould 2013), EViews of IHS, and gretl (see Cottrell and Lucchetti 2021, p. 200-201, listing 23.1), 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 two-way 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.

If argument return.model = TRUE is set, the full model object is returned, while in the default case only the intercept is returned.

Value

Depending on argument return.model: If FALSE (default), a named numeric of length one: The overall intercept for the estimated within model along attribute "se" which contains the standard error for the intercept. If return.model = TRUE, the full model object, a within model with the overall intercept (NB: the model identifies itself as a pooling model, e.g., in summary()).

Author(s)

Kevin Tappe

References

Cottrell A, Lucchetti R (2021). “Gretl User’s Guide.” https://gretl.sourceforge.net/.

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

Greene WH (2012). Econometric Analysis, 7th edition. Prentice Hall.

See Also

fixef() to extract the fixed effects of a within model.

Examples

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), pdim(mod_fe)$Tint$Ti)

### relationship of type="dmean", "level" and within_intercept
## one-way balanced 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
## two-ways unbalanced case
gtw_u <- plm(inv ~ value + capital, data = Grunfeld[-200, ], effect = "twoways")
int_tw_u <- within_intercept(gtw_u)
fx_dmean_tw_i_u <- fixef(gtw_u, type = "dmean", effect = "individual")[index(gtw_u)[[1L]]]
fx_dmean_tw_t_u <- fixef(gtw_u, type = "dmean", effect = "time")[index(gtw_u)[[2L]]]
fx_level_tw_u <- as.numeric(fixef(gtw_u, "twoways", "level"))
fx_level_tw_u2 <- int_tw_u + fx_dmean_tw_i_u + fx_dmean_tw_t_u
all.equal(fx_level_tw_u, fx_level_tw_u2, check.attributes = FALSE) # TRUE

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

## have a model returned
mod_fe_int <- within_intercept(gi, return.model = TRUE)
summary(mod_fe_int)
# replicates Stata's robust standard errors exactly as model is with intercept
summary(mod_fe_int, vcov = function(x) vcovHC(x, type = "sss"))