stslshac: Spatial two stages least square with HAC standard errors
In sphet: Estimation of Spatial Autoregressive Models with and without Heteroskedastic Innovations

Description Usage Arguments Details Value Author(s) References See Also Examples

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 ε

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)

`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 `listw` created for example by `nb2listw`
`na.action`	a function which indicates what should happen when the data contains missing values. See lm for details.
`zero.policy`	See `lagsarlm` for details
`HAC`	if FALSE traditional standard errors are provided.
`distance`	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.
`type`	One of `c("Epanechnikov","Triangular","Bisquare","Parzen", "QS","TH")`. The type of Kernel to be used. See Details.
`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.

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 ≤q 0.5 and K(z) = 2(1-|z|)^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].

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`	`'s2slshac'`

Gianfranco Piras gpiras@mac.com

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.

gstslshet, distance, distance

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)