sphet (version 1.5)

spreg: GM estimation of a Cliff-Ord type model with Heteroskedastic Innovations

Description

Multi step GM/IV estimation of a linear Cliff and Ord -type of model of the form:

$$y=\lambda W y + X \beta + u$$ $$u=\rho W u + e$$ with $$e ~ N(0,\sigma^2_i)$$

The model allows for spatial lag in the dependent variable and disturbances. The innovations in the disturbance process are assumed heteroskedastic of an unknown form.

Usage

spreg(formula, data=list(), listw, listw2=NULL, endog = NULL, instruments= NULL, 
lag.instr = FALSE, initial.value=0.2, 
model = c("sarar", "lag", "error", "ivhac", "ols"), het = FALSE, verbose=FALSE, 
na.action = na.fail,  HAC = FALSE, 
distance = NULL, type=c("Epanechnikov","Triangular","Bisquare","Parzen", "QS","TH"), 
bandwidth="variable" , step1.c = FALSE, control = list())

Value

A list object of class sphetcoefficientsGeneralized Spatial two stage least squares coefficient estimates of $\delta$ and GM estimator for $\rho$.varvariance-covariance matrix of the estimated coefficientss2GS2SLS residuals varianceresidualsGS2SLS residualsyhatdifference between GS2SLS residuals and response variablecallthe call used to create this objectmodelthe model matrix of datamethod'gs2slshac'

Details

The procedure consists of two steps alternating GM and IV estimators. Each step consists of sub-steps. In step one $\delta = [\beta',\lambda]'$ is estimated by 2SLS. The 2SLS residuals are first employed to obtain an consistent GM estimator of $\rho$.

In step two, the spatial Cochrane-Orcutt transformed model is estimated by 2SLS. This corresponds to a GS2SLS procedure. The GS2SLS residuals are used to obtain a consistent and efficient GM estimator for $\rho$.

The initial value for the optimization in step 1b is taken to be initial.value. The initial value for the optimization of step 2b is the optimal parameter of step 1b.

Internally, the object of class listw is transformed into a Matrix using the function listw2dgCMatrix.

For the HAC estimator (Kelejian and Prucha, 2007), there are four possibilities:

• A model with only Wy
• A model with Wy and additional endogenous
• Only additional endogenous (with no Wy)
• No additional endogenous variables

Furthermore, 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$z \leq 0.5$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 $H=[X,WX,W^2X^2]$.

References

Arraiz, I. and Drukker, M.D. and Kelejian, H.H. and Prucha, I.R. (2010) A spatial Cliff-Ord-type Model with Heteroskedastic Innovations: Small and Large Sample Results, Journal of Regional Sciences, 50, pages 592--614.

Drukker, D.M. and Egger, P. and Prucha, I.R. (2013) On Two-step Estimation of a Spatial Auto regressive Model with Autoregressive Disturbances and Endogenous Regressors, Econometric Review, 32, pages 686--733.

Kelejian, H.H. and Prucha, I.R. (2010) Specification and Estimation of Spatial Autoregressive Models with Autoregressive and Heteroskedastic Disturbances, Journal of Econometrics, 157, pages 53--67.

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

stslshac

Examples

library(spdep)
data(columbus)
listw<-nb2listw(col.gal.nb)
res<- spreg(CRIME~HOVAL + INC, data=columbus , listw= listw,   het = TRUE, verbose = FALSE)
summary(res)