Title
spreg -- Spatial-autoregressive model with spatial-autoregressive disturbances
Syntax
spreg estimator depvar [indepvars] [if] [in], id(varname) [options]
estimator description ------------------------------------------------------------------------- ml maximum likelihood (ML) gs2sls generalized spatial two-stage least squares (GS2SLS) -------------------------------------------------------------------------
options Description ------------------------------------------------------------------------- Model * id(varname) ID variable dlmat(name[, eig]) spmat object used in the spatial-autoregressive term elmat(name[, eig]) spmat object used in the spatial-error term noconstant suppress constant term
ML estimator gridsearch(#) search for initial values constraints(constraints) apply specified linear constraints
GS2SLS estimator heteroskedastic use the estimator that allows for heteroskedastic disturbance terms impower(q) use q powers of matrix W in forming the instrument matrix H; default is 2
Maximization maximize_options control the maximization process; seldom used ------------------------------------------------------------------------- * Required
Description
spreg estimates the parameters of a cross-sectional spatial-autoregressive model with spatial-autoregressive disturbances which is known as a SARAR model.
A SARAR model includes a weighted average of the dependent variable, known as a spatial lag, as a right-hand-side variable and it allows the disturbance term to depend on a weighted average of the disturbances corresponding to other units. The weights may differ for each observation and are frequently inversely related to the distance from the current observation. These weights must be stored in a spatial-weighting matrix created by spmat.
spreg estimates the parameters by either maximum likelihood (ML) or by generalized spatial two-stage least squares (GS2SLS).
You can download Drukker, Prucha, and Raciborski (2011), which documents this command, from http://econweb.umd.edu/~prucha/Papers/WP_spreg_2011.pdf.
Options
+-------+ ----+ Model +------------------------------------------------------------
id(varname) specifies a numeric variable that contains a unique identifier for each observation.
dlmat(name[, eig]) specifies an spmat object that contains the spatial-weighting matrix W to be used in the spatial-autoregressive term. eig forces the calculation of the eigenvalues of W, even if the spmat object contains them. The eig option is only allowed with the ml estimator.
elmat(name[, eig]) specifies an spmat object that contains the spatial-weighting matrix M to be used in the spatial-error term. eig forces the calculation of the eigenvalues of {bf:M, even if the spmat object contains them. The eig option is only allowed with the ml estimator.
noconstant suppresses the constant term in the model.
+----+ ----+ ML +---------------------------------------------------------------
gridsearch(#) specifies the fineness of the grid used in searching for the initial values of the parameters lambda and rho in the concentrated log likelihood. The allowed range is [0.001,0.1] with 0.1 being the default.
constraints(constraints); see [R] estimation options.
maximize_options: difficult, technique(algorithm_spec), iterate(#), [no]log, trace, gradient, showstep, hessian, showtolerance, tolerance(#), ltolerance(#), nrtolerance(#), nonrtolerance, from(init_specs); see [R] maximize. These options are seldom used. from() takes precedence over gridsearch().
+--------+ ----+ GS2SLS +-----------------------------------------------------------
heteroskedastic specifies that spreg use an estimator that allows e to be heteroskedastically distributed over the observations. By default, spreg uses an estimator that assumes homoskedasticity.
impower(q) specifies how many powers of the matrix W to include in calculating the instrument matrix H. Integers in the set {2, 3, ..., floor(sqrt(cols(W)))} are allowed, with q = 2 being the default.
maximize_options: iterate(#), [no]log, trace, gradient, showstep, showtolerance, tolerance(#), ltolerance(#); see [R] maximize. These options are seldom used. from(init_specs) is also allowed, but because rho is the only parameter in the optimization problem, the initial value should be specified as from(#).
Example
Setup . use pollute, clear . spmat use cobj using pollute.spmat, replace
Estimate the SARAR parameters by ML . spreg ml pollution factories area, id(id) dlmat(cobj) elmat(cobj)
Estimate the SARAR parameters by GS2SLS . spreg gs2sls pollution factories area, id(id) dlmat(cobj) elmat(cobj)
Saved results
spreg ml saves the following in e():
Scalars e(N) number of observations e(k) number of parameters e(df_m) model degrees of freedom e(rank) rank of e(V) e(iterations) number of ML iterations e(converged) 1 if converged, 0 otherwise e(ll) log likelihood e(chi2) chi-squared statistic e(p) significance
Macros e(cmdline) command as typed e(cmd) spreg e(estimator) ml e(model) sarar, sar, sare, or lr e(title) title in estimation output e(depvar) name of dependent variable e(indeps) names of independent variables e(constant) noconstant or hasconstant e(idvar) name of ID variable e(dlmat) name of spmat object in dlmat() e(elmat) name of spmat object in elmat() e(chi2type) type of model chi-squared test e(vce) oim e(user) name of likelihood-evaluator program e(crittype) type of optimization e(technique) maximization technique e(predict) program used to implement predict e(estat_cmd) program used to implement estat e(properties) b V
Matrices e(b) coefficient vector e(V) variance-covariance matrix of the estimators e(Cns) constraints matrix e(ilog) iteration log e(gradient) gradient vector
Functions e(sample) marks estimation sample
spreg gs2sls saves the following in e():
Scalars e(N) number of observations e(k) number of parameters e(rho_2sls) initial estimate of rho e(iterations) number of GMM iterations e(iterations_2sls) number of 2SLS iterations e(converged) 1 if GMM stage converged, 0 otherwise e(converged_2sls) 1 if 2SLS stage converged, 0 otherwise
Macros e(cmdline) command as typed e(cmd) spreg e(estimator) gs2sls e(model) sarar, sar, sare, or lr e(het) heteroskedastic or homoskedastic e(title) title in estimation output e(depvar) name of dependent variable e(indeps) names of independent variables e(exogr) exogenous regressors e(constant) noconstant or hasconstant e(H_omitted) names of omitted instruments in H e(idvar) name of ID variable e(dlmat) name of spmat object in dlmat() e(elmat) name of spmat object in elmat() e(predict) program used to implement predict e(estat_cmd) program used to implement estat e(properties) b V
Matrices e(b) coefficient vector e(V) variance-covariance matrix of the estimators e(delta_2sls) initial estimate of lambda and b
Functions e(sample) marks estimation sample
References
Drukker, D. M., I. R. Prucha, and R. Raciborski. 2011. Maximum-likelihood and generalized spatial two-stage least-squares estimators for a spatial-autoregressive model with spatial-autoregressive disturbances. Working paper, University of Maryland, Department of Economics, http://econweb.umd.edu/~prucha/Papers/WP_spreg_2011.pdf.
Authors
David Drukker, StataCorp, College Station, TX. ddrukker@stata.com.
Ingmar Prucha, Department of Economics, University of Maryland, College Park, MD. prucha@econ.umd.edu.
Rafal Raciborski, StataCorp, College Station, TX. rraciborski@stata.com.
Acknowledgment
We gratefully acknowledge financial support from the National Institute of Health through the SBIR grant R43 AG027622 and R44 AG027622.
Also see
Online: spmat, spivreg, spmap, shp2dta, mif2dta (if installed)