stslshac {sphet} | R Documentation |
Spatial two stages least square with HAC standard errors
Description
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.
Usage
stslshac(formula, data = list(), listw,
na.action = na.fail, zero.policy = NULL, HAC = TRUE,
distance = NULL, type = "Epanechnikov",
bandwidth = "variable", W2X = TRUE)
Arguments
formula |
a description of the model to be fit |
data |
an object of class data.frame. An optional data frame containing the variables in the model. |
listw |
an object of class |
na.action |
a function which indicates what should happen when the data contains missing values. See lm for details. |
zero.policy |
See |
HAC |
if FALSE traditional standard errors are provided. |
distance |
an object of class |
type |
One of |
bandwidth |
"variable" (default) - or numeric when a fixed bandwidth is specified by the user. |
W2X |
default TRUE. if FALSE only WX are used as instruments in the spatial two stage least squares. |
Details
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
ifz \leq 0.5
andK(z) = 2(1-|z|)^3
if0.5 < 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]
.
Value
A list object of class sphet
coefficients |
Spatial two stage least squares coefficient estimates |
vcmat |
variance-covariance matrix of the estimated coefficients |
s2 |
S2sls residulas variance |
residuals |
S2sls residuals |
yhat |
difference between residuals and response variable |
call |
the call used to create this object |
model |
the model matrix of data |
type |
the kernel employed in the estimation |
bandwidth |
the type of bandwidth |
method |
|
Author(s)
Gianfranco Piras gpiras@mac.com
References
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.
See Also
Examples
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)