within_intercept function

Overall Intercept for Within Models Along its Standard Error

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

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,

Returns

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()).

Details

The (somewhat artificial) intercept for within models (fixed effects models) was made popular by Stata of StataCorp \insertCite @see @GOUL:13plm, EViews of IHS, and gretl \insertCite @see @GRETL:2021, p. 200-201, listing 23.1plm, see for treatment in the literature, e.g., \insertCite GREE:12;textualplm, 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.

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"))

References

\insertAllCited

See Also

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

Author(s)

Kevin Tappe