Spatial two stages least square with HAC standard errors
Description
Nonparametric heteroskedasticity and autocorrelation consistent (HAC) estimator of the variancecovariance (VC) for a vector of sample moments within a spatial context. The disturbance vector is generated as follows:
u = R ε
where R is a nonstochastic matrix.
Usage
1 2 3 
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 
distance 
an object of class 
type 
One of 
na.action 
a function which indicates what should happen when the data contains missing values. See lm for details. 
zero.policy 
See 
bandwidth 
"variable" (default)  or numeric when a fixed bandwidth is specified by the user. 
HAC 
if FALSE traditional standard errors are provided. 
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) = 1z^2 
'Triangular'
: K(z) = 1z 
'Bisquare'
: K(z) = (1z^2)^2 
'Parzen'
: K(z) = 16z^2+6 z^3 if z ≤q 0.5 and K(z) = 2(1z)^3 if 0.5 < z ≤q 1 
'TH'
(Tukey  Hanning): K(z) = \frac{1+ \cos(π z)}{2} 
'QS'
(Quadratic Spectral): K(z) = \frac{25}{12π^2z^2} (\frac{\sin(6π z)/5)}{6π z/5}  \cos(6π 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 
variancecovariance 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
gstslshet
, distance
, distance
Examples
1 2 3 4 5 6 
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