Model \(y = \rho W y + X\beta + u\), \(u = \lambda W_2 u + e\)
(Kelejian and Prucha 1998), as spatialreg::gstsls: 2SLS of y on
(Wy, X) with instruments X, WX, \(W^2X\) (lags of the non-intercept
columns); \(\lambda\) from the generalised moments of those residuals
on \(W_2\); then 2SLS of \(y - \lambda W_2 y\) on
\((Wy - \lambda W_2 Wy, X - \lambda W_2 X)\) with the same
instruments. Covariance \(s^2 (Z_p'Z_p)^{-1}\), \(s^2 = e'e/df\)
(df = n unless sig2n_k), or the HC0 / HC1 sandwich.
Usage
GS2SLSSAC(
y,
X,
W,
W2 = NULL,
robust = NULL,
sig2n_k = FALSE,
interval = c(-0.999, 0.999)
)
Arguments
- y
Response.
- X
Design matrix; a leading column of ones is the intercept.
- W
Weights of the spatial lag.
- W2
Weights of the error process (default W).
- robust
NULL, "HC0" or "HC1".
- sig2n_k
Divide by \(n - k\).
- interval
Search interval for \(\lambda\).
Value
List with rho, lambda, sigma2_gm,
coefficients (rho first), se, cov, s2,
residuals.
References
Kelejian, H. H. and Prucha, I. R. (1998). A generalized
spatial two-stage least squares procedure for estimating a spatial
autoregressive model with autoregressive disturbances. Journal of Real
Estate Finance and Economics 17, 99-121.
Examples
W <- 1 * (abs(outer(1:8, 1:8, "-")) == 1)
W <- W / rowSums(W)
X <- cbind(1, c(.1, .6, .2, .9, .3, .5, .8, .4))
GS2SLSSAC(c(1, 2.2, 1.4, 3.1, .9, 2, 2.6, 1.1), X, W)$rho
#> [1] -0.5612591
