rsmatrix (version 0.2.8)

rs_var: Robust variance matrix for repeat-sales indexes

Description

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.

Usage

rs_var(u, Z, X = Z, ids = seq_len(nrow(X)), df = NULL)

Value

A \(k \times k\) covariance matrix.

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) {
# Same as plm
library(plm)
mdl <- plm(mpg ~ cyl + disp, mtcars, model = "pooling", index = "clust")
vcov2 <- vcovHC(mdl, type = "sss", cluster = "group")
vcov - vcov2
}