sphet (version 1.5)

gstslshet: 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

gstslshet(formula, data=list(), listw, na.action=na.fail, 
zero.policy=NULL,initial.value=0.2, abs.tol=1e-20, 
rel.tol=1e-10, eps=1e-5, inverse=T,sarar=T)
## S3 method for class 'gstsls':
impacts(obj, \dots, tr, R = NULL, listw = NULL,
tol = 1e-06, empirical = FALSE, Q=NULL)

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'WWald test for both $\rho$ and $\lambda$ are zero

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 initial (consistent but not efficient) GM estimator of $\rho$ and then a consistent and efficient estimator (involving the variance-covariance matrix of the limiting distribution of the normalized sample moments). 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 in step 1c is the optimal parameter of step 1b. Finally, the initial value for the optimization of step 2b is the optimal parameter of step 1c.

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

The expression of the estimated variance covariance matrix of the limiting distribution of the normalized sample moments based on 2SLS residuals involves the inversion of $I-\rho W'$. When inverse is FALSE, the inverse is calculated using the approximation $I +\rho W' + \rho^2 W'^2 + ...+ \rho^n W'^n$. The powers considered depend on a condition. The function will keep adding terms until the absolute value of the sum of all elements of the matrix $\rho^i W^i$ is greater than a fixed $\epsilon$ (eps). By default eps is set to 1e-5.

References

Arraiz, I. and Drukker, M.D. and Kelejian, H.H. and Prucha, I.R. (2007) A spatial Cliff-Ord-type Model with Heteroskedastic Innovations: Small and Large Sample Results, Department of Economics, University of Maryland'

Kelejian, H.H. and Prucha, I.R. (2007) Specification and Estimation of Spatial Autoregressive Models with Autoregressive and Heteroskedastic Disturbances, Journal of Econometrics, forthcoming.

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<-gstslshet(CRIME~HOVAL + INC, data=columbus, listw=listw)
summary(res)