This function estimates SUR models for simple spatial panel datasets.
spsurtime is restricted, specifically, to cases where there is only one equation, G=1,
and a varying number of spatial units, N, and time periods, Tm. The SUR structure appears
in form of serial dependence among the error terms corresponding to the same spatial unit.
Note that it is assumed that all spatial units share a common pattern of serial dependence.
The user can choose between different types of spatial specifications, as described below, and the estimation algorithms allow for the introduction of linear restrictions on the \(\beta\) parameters associated to the regressors. The spatial panels with SUR structure can be estimated by maximum-likelihood methods or three-stages least squares procedures, using spatial instrumental variables.
spsurtime(Form, data, time, type = "sim", method = "ml", maxlagW = 2,
W = NULL, cov = TRUE, demean = FALSE, trace = TRUE, R = NULL,
b = NULL)An object created with the package Formula
that describes the model to be estimated. This model may contain several
responses (explained variables) and a varying number of regressors in each equation.
An object of class data.frame or a matrix.
Time variable.
Type of spatial model specification: "sim","slx", "slm",
"sem", "sdm", "sdem" or "sarar". Default = "sim".
Method of estimation for the spatial panel SUR model, either ml or 3sls. Default = ml.
Maximum spatial lag order of the regressors employed to produce spatial instruments for the spatial lags of the explained variables. Default = 2. Note that in case of type="sdm", the default value for maxlagW is set to 3 because the first lag of the regressors, \(WX_{tg}\), can not be used as spatial instruments.
A spatial weighting matrix of order (NxN), assumed to be the same for all equations and time periods.
Logical value to show the covariance matrix of the beta coefficients.
Default = TRUE.
Logical value to allow for the demeaning of panel data, sustracting the individual mean to
each spatial or cross-sectional unit. Default = FALSE.
Logical value to show intermediate results. Default = TRUE.
A row vector of order (1xpr) with the set of r linear constraints
on the beta parameters. The first restriction appears in the first p terms,
the second restriction in the next p terms and so on. Default = NULL.
A column vector of order (rx1) with the values of the linear restrictions on the
beta parameters. Default = NULL.
Output of the maximum-likelihood or three-stages least-squares estimation of the spatial panel SUR model. The final list depends of the estimation method but, typically, you will find information about:
call |
Matched call. |
type |
Type of model specified. |
betas |
Estimated coefficients for the regressors. |
deltas |
Estimated spatial coefficients. |
se_betas |
Estimated standard errors for the estimates of beta. |
se_deltas |
Estimated standard errors for the estimates of the spatial coefficients. |
cov |
Estimated covariance matrix for the estimates of beta's and spatial coefficients. |
llsur |
Value of the likelihood function at maximum-likelihood estimation.Only if method = ml. |
R2 |
Global coefficient of determination for the Tm equations, obtained as the squared of the correlation coefficient between the corresponding explained variable and its estimates. |
Sigma |
Estimated covariance matrix for the residuals of the G equations. |
Sigma_corr |
stimated correlation matrix for the residuals of the G equations. |
Sigma_inv |
Inverse of Sigma, the (GxG) covariance matrix of
the residuals of the SUR model. |
residuals |
Residuals of the model. |
df.residuals |
Degrees of freedom for the residuals. |
fitted.values |
Estimated values for the dependent variables. |
BP |
Value of the Breusch-Pagan statistic to test the null hypothesis of diagonality among the errors of the G equations. Only if method = ml. |
LMM |
Marginal Lagrange Multipliers, LM(\(\rho\)|\(\lambda\)) and LM(\(\lambda\)|\(\rho\)), to test for omitted spatial effects in the specification. Only if method = ml. |
N |
Number of cross-sections or spatial units. |
Tm |
Number of time periods. |
demean |
Logical value used for demeaning. |
W |
Spatial weighting matrix. |
Function spsurtime only admits a formula, created with Formula
and a dataset of class data.frame or matrix. That is, the data cannot be uploaded using data matrices
\(Y\) and \(X\) provided for other functions in this package.
The argument time selects the variable, in the data.frame, associated to the time
dimension in the panel dataset. Then spsurtime operates as in Anselin (1988), that is,
each cross-section is treated as if it were an equation in a SUR model, which now has Tm
'equations' and N individuals.
The SUR structure appears because there is serial dependence in the errors of each individual in
the panel. The serial dependence in the errors is not parameterized, but estimated non-parametrically
in the \(Sigma\) covariance matrix returned by the function. An important constraint to mention
is that the serial dependence assumed to be the same for all individuals in the sample. Serial dependence
among individuals is excluded from Anselin approach.
Anselin, L. (1988). Spatial econometrics: methods and models. Dordrecht, Kluwer Academic Publishers.
L<U+00F3>pez, F.A., Mur, J., and Angulo, A. (2014). Spatial model selection strategies in a SUR framework. The case of regional productivity in EU. Annals of Regional Science, 53(1), 197-220.
L<U+00F3>pez, F.A., Mart<U+00ED>nez-Ortiz, P.J., & Cegarra-Navarro, J.G. (2017). Spatial spillovers in public expenditure on a municipal level in Spain. Annals of Regional Science, 58(1), 39-65.
Mur, J., L<U+00F3>pez, F., and Herrera, M. (2010). Testing for spatial effects in seemingly unrelated regressions. Spatial Economic Analysis, 5(4), 399-440.
# NOT RUN {
####################################
######## PANEL DATA (G=1; Tm>1) ###
####################################
## Example 1:
rm(list = ls()) # Clean memory
N <- nrow(spc)
Tm <- 2
index_time <- rep(1:Tm, each = N)
index_indiv <- rep(1:N, Tm)
WAGE <- c(spc$WAGE83, spc$WAGE81)
UN <- c(spc$UN83, spc$UN80)
NMR <- c(spc$NMR83, spc$NMR80)
SMSA <- c(spc$SMSA, spc$SMSA)
pspc <- data.frame(index_indiv,index_time,WAGE,UN,NMR,SMSA)
form_pspc <- WAGE ~ UN + NMR + SMSA
# SLM by 3SLS
pspc_slm <- spsurtime(Form = form_pspc, data = pspc, W = Wspc,
time = pspc$index_time, type = "slm", method = "3sls")
summary(pspc_slm)
# }
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