gstslshet: GM estimation of a Cliff-Ord type model with Heteroskedastic...
In sphet: Estimation of Spatial Autoregressive Models with and without Heteroskedastic Innovations

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

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

y=λ W y + X β + u

u=ρ W u + e

with

e ~ N(0,σ^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.

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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)

`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
`initial.value`	The initial value for ρ. It can be either numeric (default is 0.2) or set to `'SAR'`, in which case the optimization will start from the estimated coefficient of a regression of the 2SLS residuals over their spatial lag (i.e. a spatial AR model)
`abs.tol`	Absolute tolerance. See nlminb for details.
`rel.tol`	Relative tolerance. See nlminb for details.
`eps`	Tolerance level for the approximation. See Details.
`inverse`	`TRUE`. If `FALSE`, an appoximated inverse is calculated. See Details.
`sarar`	`TRUE`. If `FALSE`, a spatial error model is estimated.

The procedure consists of two steps alternating GM and IV estimators. Each step consists of sub-steps. In step one δ = [β',λ]' is estimated by 2SLS. The 2SLS residuals are first employed to obtain an initial (consistent but not efficient) GM estimator of ρ 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 ρ.

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-ρ W'. When inverse is FALSE, the inverse is calculated using the approximation I +ρ W' + ρ^2 W'^2 + ...+ ρ^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 ρ^i W^i is greater than a fixed ε (eps). By default eps is set to 1e-5.

A list object of class sphet

`coefficients`	Generalized Spatial two stage least squares coefficient estimates of δ and GM estimator for ρ.
`var`	variance-covariance matrix of the estimated coefficients
`s2`	GS2SLS residuals variance
`residuals`	GS2SLS residuals
`yhat`	difference between GS2SLS residuals and response variable
`call`	the call used to create this object
`model`	the model matrix of data
`method`	`'gs2slshac'`
`W`	Wald test for both ρ and λ are zero

Gianfranco Piras gpiras@mac.com

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.

stslshac

data(columbus, package = "spdep")
listw <- spdep::nb2listw(col.gal.nb)
res <- gstslshet(CRIME ~ HOVAL + INC, data = columbus, listw = listw)
summary(res)