Convenience function to compute a cluster-robust variance matrix for a linear regression, with or without instruments, where clustering occurs along one dimension. Useful for calculating a variance matrix when a regression is calculated manually.
Arguments
- u
An \(n \times 1\) vector of residuals from a linear regression.
- Z
An \(n \times k\) matrix of instruments.
- X
An \(n \times k\) matrix of covariates.
- ids
A factor of length \(n\), or something that can be coerced into one, that groups observations in
u. By default each observation belongs to its own group.- df
An optional degrees of freedom correction. Default is Stata's small sample degrees of freedom correction.
Details
This function calculates the standard robust variance matrix for a linear regression, as in Manski (1988, section 8.1.2) or White (2001, Theorem 6.3); that is, \((Z'X)^{-1} V (X'Z)^{-1}\). It is useful when a regression is calculated by hand. This generalizes the variance matrix proposed by Shiller (1991, section II) when a property sells more than twice.
This function gives the same result as vcovHC(x, type = 'sss', cluster = 'group') from the plm package.
References
Manski, C. (1988). Analog Estimation Methods in Econometrics. Chapman and Hall.
Shiller, R. J. (1991). Arithmetic repeat sales price estimators. Journal of Housing Economics, 1(1):110-126.
White, H. (2001). Asymptotic Theory for Econometricians (revised edition). Emerald Publishing.
Examples
# Makes some groups in mtcars
mtcars$clust <- letters[1:4]
# Matrices for regression
x <- model.matrix(~ cyl + disp, mtcars)
y <- matrix(mtcars$mpg)
# Regression coefficients
b <- solve(crossprod(x), crossprod(x, y))
# Residuals
r <- y - x %*% b
# Robust variance matrix
vcov <- rs_var(r, x, ids = mtcars$clust)
if (FALSE) { # \dontrun{
# Same as plm
library(plm)
mdl <- plm(mpg ~ cyl + disp, mtcars, model = "pooling", index = "clust")
vcov2 <- vcovHC(mdl, type = "sss", cluster = "group")
vcov - vcov2
} # }