# 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 ε

where R is a non-stochastic matrix.

### Usage

 1 2 3 stslshac(formula, data=list(),listw,na.action=na.fail,zero.policy=NULL, HAC=TRUE, distance=NULL,type=c("Epanechnikov","Triangular","Bisquare","Parzen", "QS","TH"), 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 listw created for example by nb2listw 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. 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 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) = 1-z^2

• '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].

### 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 's2slshac'

### 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.

gstslshet, distance, distance
 1 2 3 4 5 6 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)