spsur (version 1.0.0.2)

spsurml: Maximum likelihood estimation of spatial SUR model.

Description

This function estimates spatial SUR models using maximum-likelihood methods. The number of equations, time periods and cross-sectional units is not restricted. The user can choose between different spatial specifications as described below. The estimation procedure allows for the introduction of linear restrictions on the \(\beta\) parameters associated to the regressors.

Usage

spsurml(Form = NULL, data = NULL, R = NULL, b = NULL, W = NULL,
  X = NULL, Y = NULL, G = NULL, N = NULL, Tm = NULL, p = NULL,
  demean = FALSE, type = "sim", cov = TRUE, control = list(tol =
  0.05, maxit = 200, trace = TRUE))

Value

Output of the maximum-likelihood estimation of the specified spatial SUR model. A list with:

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 the maximum-likelihood estimates.
R2	Coefficient of determination for each equation, obtained as the squared of the correlation coefficient between the corresponding explained variable and its estimate. spsurml also shows a global coefficient of determination obtained, in the same manner, for the set of G equations.
Sigma	Estimated covariance matrix for the residuals of the G equations.
Sigma_corr	Estimated 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.
LMM	Marginal Lagrange Multipliers, LM(\(\rho\)|\(\lambda\)) and LM(\(\lambda\)|\(\rho\)), to test for omitted spatial effects in the specification.
G	Number of equations.
N	Number of cross-sections or spatial units.
Tm	Number of time periods.
p	Number of regressors by equation (including intercepts).
demean	Logical value used for demeaning.
Y	Vector Y of the explained variables of the SUR model.
X	Matrix X of the regressors of the SUR model.

Control arguments

tol	Numerical value for the tolerance for the estimation algorithm until convergence. Default = 1e-3.
maxit	Maximum number of iterations until convergence; it must be an integer value. Default = 200.
trace	A logical value to show intermediate results during the estimation process. Default = TRUE.

Details

The list of (spatial) models that can be estimated with the spsurml function are:

• "sim": SUR model with no spatial effects $$ y_{tg} = X_{tg} \beta_{g} + \epsilon_{tg} $$

• "slx": SUR model with spatial lags of the regressors $$ y_{tg} = X_{tg} \beta_{g} + WX_{tg} \theta_{g} + \epsilon_{tg} $$

• "slm": SUR model with spatial lags of the explained variables $$y_{tg} = \lambda_{g} Wy_{tg} + X_{tg} \beta_{g} + \epsilon_{tg} $$

• "sem": SUR model with spatial errors $$ y_{tg} = X_{tg} \beta_{g} + u_{tg} $$ $$ u_{tg} = \rho_{g} Wu_{tg} + \epsilon_{tg} $$

• "sdm": SUR model of the Spatial Durbin type $$ y_{tg} = \lambda_{g} Wy_{tg} + X_{tt} \beta_{g} + WX_{tg} \theta_{g} + \epsilon_{tg} $$

• "sdem": SUR model with spatial lags of the regressors and spatial errors $$ y_{tg} = X_{tg} \beta_{g} + WX_{tg} \theta_{g} + u_{tg} $$ $$ u_{tg} = \rho_{g} W u_{tg} + \epsilon_{tg} $$

• "sarar": SUR model with spatial lags of the explained variables and spatial errors $$ y_{tg} = \lambda_{g} Wy_{tg} + X_{tg} \beta_{g} + u_{tg} $$ $$ u_{tg} = \rho_{g} W u_{tg} + \epsilon_{tg} $$

References

• 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.

• 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.

• Breusch T, Pagan A (1980) The Lagrange multiplier test and its applications to model specification in econometrics. Rev Econ Stud 47: 239-254

See Also

spsur3sls, lmtestspsur, wald_betas, lrtestspsur

Examples

# NOT RUN {
#################################################
######## CROSS SECTION DATA (G>1; Tm=1) ########
#################################################

#### Example 1: Spatial Phillips-Curve. Anselin (1988, p. 203)
## It usually requires 2-3 minutes maximum...
rm(list = ls()) # Clean memory
data(spc)
Tformula <- WAGE83 | WAGE81 ~ UN83 + NMR83 + SMSA | UN80 + NMR80 + SMSA
spcsur.sim <-spsurml(Form = Tformula, data = spc, type = "sim", W = Wspc)
summary(spcsur.sim)

## A SUR-SLX model
spcsur.slx <-spsurml(Form = Tformula, data = spc, type = "slx", W = Wspc)
summary(spcsur.slx)
# }
# NOT RUN {
## Not run:
## A SUR-SLM model
spcsur.slm <-spsurml(Form = Tformula, data = spc, type = "slm", W = Wspc)
summary(spcsur.slm)
rm(spcsur.slm) # remove
# }