R: GM estimation of a Cliff-Ord type model with Heteroskedastic...
gstslshet
R Documentation
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=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.
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, ..., tr, R = NULL, listw = NULL,
tol = 1e-06, empirical = FALSE, Q=NULL)
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
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.
obj
A gstsls spatial regression object created by gstslshet
...
Arguments passed through to methods in the coda package
tr
A vector of traces of powers of the spatial weights matrix created using trW, for approximate impact measures; if not given, listw must be given for exact measures (for small to moderate spatial weights matrices); the traces must be for the same spatial weights as were used in fitting the spatial regression
R
If given, simulations are used to compute distributions for the impact measures, returned as mcmc objects
tol
Argument passed to mvrnorm: tolerance (relative to largest variance) for numerical lack of positive-definiteness in the coefficient covariance matrix
empirical
Argument passed to mvrnorm (default FALSE): if true, the coefficients and their covariance matrix specify the empirical not population mean and covariance matrix
Q
default NULL, else an integer number of cumulative power series impacts to calculate if tr is given
Details
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.
Value
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
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.