GM estimation of a CliffOrd 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
1 2 3 4 5 6 
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 
na.action 
a function which indicates what should happen when the data contains missing values. See lm for details. 
zero.policy 
See 
initial.value 
The initial value for ρ. It can be either numeric (default is 0.2) or
set to 
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 

sarar 

obj 
A gstsls spatial regression object created by 
... 
Arguments passed through to methods in the coda package 
tr 
A vector of traces of powers of the spatial weights matrix created using 
R 
If given, simulations are used to compute distributions for the impact measures, returned as 
tol 
Argument passed to 
empirical 
Argument passed to 
Q 
default NULL, else an integer number of cumulative power series impacts to calculate if 
Details
The procedure consists of two steps alternating GM and IV estimators. Each step consists of substeps. 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 variancecovariance matrix of the limiting distribution of the normalized sample moments). In step two, the spatial CochraneOrcutt 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 Iρ 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 1e5.
Value
A list object of class sphet
coefficients 
Generalized Spatial two stage least squares coefficient estimates of δ and GM estimator for ρ. 
var 
variancecovariance 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 

W 
Wald test for both ρ and λ are zero 
Author(s)
Gianfranco Piras gpiras@mac.com
References
Arraiz, I. and Drukker, M.D. and Kelejian, H.H. and Prucha, I.R. (2007) A spatial CliffOrdtype 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
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