spsegm: Spatial Simultaneous Equations
In spse: Spatial Simultaneous Equations and Spatial Sur Model

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

Feasible generalized three stages least square estimator (FGS3SLS) of symultaneous systems of spatially interrelated cross sectional equations of the form:

Y = Y B + X C + \bar{Y} L + U

U = \bar{U} R + E

with Y = (y_1,…,y_m), X = (x_1,…,x_m), U = (u_1,…,u_m), \bar{Y} = (\bar{y}_1,…,\bar{y}_m) and \bar{y}_j = W y_j j=1,…,m, E = (e_1,…,e_m), \bar{U} = (\bar{u}_1,…,\bar{u}_m) and \bar{u}_j = W u_j j=1,…,m. B, C, L and R=diag_{j=1}^m (ρ_j) are matrix of parameters

1 2	spsegm(formula,data=list(), panel=FALSE,index=NULL, w, method='spatialsim', lags=NULL, errors=NULL, endogenous=NULL, zero.policy = FALSE)

`formula`	a list of objects of class `formula`
`data`	an object of class `data.frame` or `pdata.frame`.An optional data frame containing the variables in the model. An optional data frame containing the variables in the model. When the obect is a data.frame, the first two columns may contain the indexes. See index
`panel`	logical. When TRUE, the data frame is a panel data set with cross-sectional and time observations
`index`	if not NULL (default), a character vector to identify the indexes among the columns of the `data.frame`
`w`	an object of class `listw` created for example by `nb2listw` or a `matrix`
`method`	`spatialsim`
`lags`	A logical list of length equal to the number of equations. If TRUE the spatial lag of the variable is included in the equation
`errors`	A logical vector. When TRUE a spatially autocorrelated error term is included in the corresponding equation
`endogenous`	A logical list of length equal to the number of equations. If TRUE the endogenous variable is included in the equation
`zero.policy`	See `lagsarlm` for details

The function can be specified with any number of equations. The number of equations is determined through the formula object. The data can also be specified as a panel data frame. The logical argument PANEL should then be set to TRUE.

The logical list lags controls which spatial lags should be included in the equations. The logical list errors determines which equations should include an autoregressive term. The logical list endogenous determines which equations should include an autoregressive term.

An object of class "splm".

`coefficients`	FG3SLS coefficients estimate of the model parameters (for all equations)
`vcov`	the variance covariance matrix of the estimated coefficients
`type`	'spsegm'
`model`	the matrix of the data used (responses in each equation are reported first, then the explanatory variables)
`N`	the number of cross-sectional observations
`Eq`	the number of equations in the system
`k`	the number of columns of the matrix of regressors (i.e. this corresponds to the number of explanatory variables in each equation only when `spec="default"`)
`call`	the call used to create the object
`terms`	the `terms` object generated from `formula` and some optional arguments
`Xnames`	the names of the variables in the matrix of explanatory variables
`Ynames`	the names of the responses
`spec`	the argument `spec`

Gianfranco Pirasgpiras@mac.com

Kelejian, H.H. and Prucha, I.R. (2004) Estimation of Simultaneous systems of spatially interrelated cross sectional equations, Journal of Econometrics, 118, pages 27–50.

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.

spseml

data(Produc, package = "Ecdat")
data(usaww)
Produc <- Produc[Produc$year<1973, ]
eq1 <- log(gsp) ~ log(pcap) + log(pc) + log(emp) + unemp 
eq2 <- log(gsp) ~ log(pcap) + log(pc) + log(emp) + unemp 
eq3 <- log(gsp) ~ log(pcap) + log(pc) + log(emp) + unemp 
formula<-list(tp1 = eq1, tp2 = eq2, tp3=eq3)
w<-mat2listw(usaww)
se<-spsegm(formula, data=Produc, w=w, panel= TRUE,lags=list(c(TRUE,TRUE,TRUE),c(TRUE,TRUE,TRUE),c(TRUE,TRUE,TRUE)), errors=list(FALSE,TRUE,FALSE),endogenous=list(c(FALSE,TRUE,FALSE),c(TRUE,FALSE,FALSE),c(TRUE,FALSE,FALSE)))
summary(se)