Non-parametric heteroskedasticity and autocorrelation consistent (HAC) estimator of the variance-covariance (VC) for a vector of sample moments within a spatial context. The disturbance vector is generated as follows: $$ u = R \epsilon $$ where \(R\) is a non-stochastic matrix.
stslshac(formula, data = list(), listw,
na.action = na.fail, zero.policy = NULL, HAC = TRUE,
distance = NULL, type = "Epanechnikov",
bandwidth = "variable", W2X = TRUE)a description of the model to be fit
an object of class data.frame. An optional data frame containing the variables in the model.
an object of class listw created for example by nb2listw
a function which indicates what should happen when the data contains missing values. See lm for details.
See lagsarlm for details
if FALSE traditional standard errors are provided.
an object of class distance created for example by read.gwt2dist
The object contains the specification of the distance measure
to be employed in the estimation of the VC matrix. See Details.
One of c("Epanechnikov","Triangular","Bisquare","Parzen", "QS","TH").
The type of Kernel to be used. See Details.
"variable" (default) - or numeric when a fixed bandwidth is specified by the user.
default TRUE. if FALSE only WX are used as instruments in the spatial two stage least squares.
A list object of class sphet
Spatial two stage least squares coefficient estimates
variance-covariance matrix of the estimated coefficients
S2sls residulas variance
S2sls residuals
difference between residuals and response variable
the call used to create this object
the model matrix of data
the kernel employed in the estimation
the type of bandwidth
's2slshac'
The default sets the bandwith for each observation to the maximum distance for that observation (i.e. the max of each element of the list of distances).
Six different kernel functions are implemented:
'Epanechnikov': \(K(z) = 1-z^2\)
'Rectangular': \(K(z) = 1\)
'Triangular': \(K(z) = 1-z\)
'Bisquare': \(K(z) = (1-z^2)^2\)
'Parzen': \(K(z) = 1-6z^2+6 |z|^3\) if \(z \leq 0.5\) and
\( K(z) = 2(1-|z|)^3\) if \(0.5 < z \leq 1\)
'TH' (Tukey - Hanning): \( K(z) = \frac{1+ \cos(\pi z)}{2}\)
'QS' (Quadratic Spectral): \(K(z) = \frac{25}{12\pi^2z^2}
(\frac{\sin(6\pi z)/5)}{6\pi z/5} - \cos(6\pi z)/5)\)).
If the kernel type is not one of the six implemented, the function will terminate with an error message. The spatial two stage least square estimator is based on the matrix of instruments \(H=[X,WX,W^2X^2]\).
Kelejian, H.H. and Prucha, I.R. (2007) HAC estimation in a spatial framework, Journal of Econometrics, 140, pages 131--154.
Kelejian, H.H. and Prucha, I.R. (1999) A Generalized Moments Estimator for the Autoregressive Parameter in a Spatial Model, International Economic Review, 40, pages 509--533.
Kelejian, H.H. and Prucha, I.R. (1998) A Generalized Spatial Two Stage Least Square Procedure for Estimating a Spatial Autoregressive Model with Autoregressive Disturbances, Journal of Real Estate Finance and Economics, 17, pages 99--121.
# NOT RUN {
library(spdep)
data(columbus)
listw <- nb2listw(col.gal.nb)
data(coldis)
res <- stslshac(CRIME ~ HOVAL + INC, data = columbus, listw = listw,
distance = coldis, type = 'Triangular')
summary(res)
# }
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