Spatial simultaneous autoregressive SAC model estimation by GMM

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Description

An implementation of Kelejian and Prucha's generalised moments estimator for the autoregressive parameter in a spatial model with a spatially lagged dependent variable.

Usage

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gstsls(formula, data = list(), listw, listw2 = NULL, na.action = na.fail, 
    zero.policy = NULL, pars, scaleU=FALSE, control = list(), 
    verbose=NULL, method="nlminb", robust=FALSE, legacy=FALSE, W2X=TRUE) 

Arguments

formula

a symbolic description of the model to be fit. The details of model specification are given for lm()

data

an optional data frame containing the variables in the model. By default the variables are taken from the environment which the function is called.

listw

a listw object created for example by nb2listw

listw2

a listw object created for example by nb2listw, if not given, set to the same spatial weights as the listw argument

na.action

a function (default na.fail), can also be na.omit or na.exclude with consequences for residuals and fitted values - in these cases the weights list will be subsetted to remove NAs in the data. It may be necessary to set zero.policy to TRUE because this subsetting may create no-neighbour observations. Note that only weights lists created without using the glist argument to nb2listw may be subsetted.

zero.policy

default NULL, use global option value; if TRUE assign zero to the lagged value of zones without neighbours, if FALSE (default) assign NA - causing GMerrorsar() to terminate with an error

pars

starting values for lambda and sigma squared for GMM optimisation, if missing (default), approximated from initial 2sls model as the autocorrelation coefficient corrected for weights style and model sigma squared

scaleU

Default FALSE: scale the OLS residuals before computing the moment matrices; only used if the pars argument is missing

control

A list of control parameters. See details in optim or nlminb

verbose

default NULL, use global option value; if TRUE, reports function values during optimization.

method

default nlminb, or optionally a method passed to optim to use an alternative optimizer

robust

see stsls

legacy

see stsls

W2X

see stsls

Details

When the control list is set with care, the function will converge to values close to the ML estimator without requiring computation of the Jacobian, the most resource-intensive part of ML estimation.

Value

A list object of class gmsar

lambda

simultaneous autoregressive error coefficient

coefficients

GMM coefficient estimates (including the spatial autocorrelation coefficient)

rest.se

GMM coefficient standard errors

s2

GMM residual variance

SSE

sum of squared GMM errors

parameters

number of parameters estimated

lm.model

NULL

call

the call used to create this object

residuals

GMM residuals

lm.target

NULL

fitted.values

Difference between residuals and response variable

formula

model formula

aliased

NULL

zero.policy

zero.policy for this model

LL

NULL

vv

list of internal bigG and litg components for testing optimisation surface

optres

object returned by optimizer

pars

start parameter values for optimisation

Hcov

NULL

na.action

(possibly) named vector of excluded or omitted observations if non-default na.action argument used

Author(s)

Gianfranco Piras and Roger Bivand

References

Kelejian, H. H., and Prucha, I. R., 1999. A Generalized Moments Estimator for the Autoregressive Parameter in a Spatial Model. International Economic Review, 40, pp. 509–533; Cressie, N. A. C. 1993 Statistics for spatial data, Wiley, New York.

Roger Bivand, Gianfranco Piras (2015). Comparing Implementations of Estimation Methods for Spatial Econometrics. Journal of Statistical Software, 63(18), 1-36. http://www.jstatsoft.org/v63/i18/.

See Also

optim, nlminb, GMerrorsar, GMargminImage

Examples

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data(oldcol)
COL.errW.GM <- gstsls(CRIME ~ INC + HOVAL, data=COL.OLD, nb2listw(COL.nb, style="W"))
summary(COL.errW.GM)
aa <- GMargminImage(COL.errW.GM)
levs <- quantile(aa$z, seq(0, 1, 1/12))
image(aa, breaks=levs, xlab="lambda", ylab="s2")
points(COL.errW.GM$lambda, COL.errW.GM$s2, pch=3, lwd=2)
contour(aa, levels=signif(levs, 4), add=TRUE)
COL.errW.GM <- gstsls(CRIME ~ INC + HOVAL, data=COL.OLD, nb2listw(COL.nb, style="W"), scaleU=TRUE)
summary(COL.errW.GM)
listw <- nb2listw(COL.nb)
W <- as(listw, "CsparseMatrix")
trMat <- trW(W, type="mult")
impacts(COL.errW.GM, tr=trMat)

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