help spivreg                                  also see:  spivreg postestimation
                                                         spreg                 
                                                         spmat                 
-------------------------------------------------------------------------------


Title

    spivreg -- Spatial-autoregressive model with spatial-autoregressive erros
                 and additional endogenous variables


Syntax

        spivreg depvar [varlist1] (varlist2 = [varlist_iv]) [if] [in],
              id(varname) [options]


    options                         Description
    -------------------------------------------------------------------------
    Model
    * id(varname)                   ID variable
      dlmat(name)                   spmat object used in the
                                      spatial-autoregressive term
      elmat(name)                   spmat object used in the spatial-error
                                      term
      noconstant                    suppress constant term
      heteroskedastic               use the formula for the heteroskedastic
                                      error term
      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

    spivreg estimates the parameters of a cross-sectional
    spatial-autoregressive model with spatial-autoregressive disturbances
    which is known as a SARAR model when there are additional endogenous
    regressors.

    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.

    spivreg estimates the parameters 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_spivreg_2011.pdf.


Options

        +-------+
    ----+ Model +------------------------------------------------------------

    id(varname) specifies a numeric variable that contains a unique
        identifier for each observation. This option is required.

    dlmat(name) specifies an spmat object that contains the spatial-weighting
        matrix W to be used in the spatial-autoregressive term.

    elmat(name) specifies an spmat object that contains the spatial-weighting
        matrix M to be used in the spatial-error term.

    noconstant suppresses the constant term in the model.

    heteroskedastic specifies that spivreg use an estimator that allows e to
        be heteroskedastically distributed over the observations.  By
        default, spivreg 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.

        +--------------+
    ----+ Maximization +-----------------------------------------------------

    maximize_options:  iterate(#), [no]log, trace, gradient, showstep,
        showtolerance, tolerance(#), ltolerance(#), from(init_specs); see [R]
        maximize.  These options are seldom used.


Example

    Setup
        . use pollute
        . spmat use cobj using pollute.spmat

    Estimate the SARAR parameters
        . spivreg pollution area (factories = penalties), id(id) dlmat(cobj)
            elmat(cobj)


Saved results

    spivreg 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)              spivreg
      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(insts)            instruments
      e(instd)            instrumented variables
      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.  A command for
        estimating spatial-autoregressive models with spatial autoregressive
        disturbances and additional endogenous variables.  Working paper, The
        University of Maryland, Department of Economics, 
        http://econweb.umd.edu/~prucha/Papers/WP_spivreg_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, spreg, spmap, shp2dta, mif2dta (if installed)