spsur-package {spsur}R Documentation

Spatial Seemingly Unrelated Regression Models.

Description

spsur offers the user a collection of functions to estimate Spatial Seemingly Unrelated Regression (SUR) models by maximum likelihood or three-stage least squares, using spatial instrumental variables. Moreover, spsur obtains a collection of misspecification tests for omitted or wrongly specified spatial structure. The user will find spatial models more popular in applied research such as the SUR-SLX, SUR-SLM, SUR-SEM, SUR-SDM, SUR-SDEM SUR-SARAR and SUR-GNM plus the spatially independent SUR, or SUR-SIM.

Details

Some functionalities that have been included in spsur package are:

1. Testing for spatial effects

The function lmtestspsur provides a collection of Lagrange Multipliers, LM, for testing different forms of spatial dependence in SUR models. They are extended versions of the well-known LM tests for omitted lags of the explained variable in the right hand side of the equation, LM-SLM, the LM tests for omitted spatial errors, LM-SEM, the join test of omitted spatial lags and spatial errors, LM-SARAR, and the robust version of the firt two Lagrange Multipliers, LM*-SLM and LM*-SEM.
These tests can be applied to models always with a SUR nature. Roughly, we may distinguish two situations:

2. Estimation of the Spatial SUR models

As indicated above, spsur package may work with a list of different spatial specifications. They are the following:

where y_{tg}, u_{tg} and \epsilon_{tg} are (Nx1) vectors; X_{tg} is a matrix of regressors of order (NxP); \rho_{g} and \lambda_{g} are parameters of spatial dependence and W is the (NxN) spatial weighting matrix.

These specifications can be estimated by maximum-likelihood methods, using the function spsurml. Moroever, the models that include spatial lags of the explained variables in the right hand side of the equations, and the errors are assumed to be spatially incorrelated (namely, the SUR-SLM and the SUR-SDM), can also be estimated using three-stage least-squares, spsur3sls, using spatial instrumental variable to correct for the problem of endogeneity present in these cases.

3. Diagnostic tests

Testing for inconsistencies or misspecifications in the results of an estimated (SUR) model should be a primary task for the user. spsur focuses, especifically, on two main question such as omitted or wrongly specified spatial structure and the existence of structural breaks or relevant restrictions in the parameters of the model. In this sense, the user will find:

  1. Marginal tests
    The Marginal Multipliers test for omitted or wrongly specified spatial structure in the equations. They are routinely part of the output of the maximum-likelihood estimation, shown by spsurml. In particular, the LM(\rho|\lambda) tests for omitted spatial lags in a model specified with spatial errors (SUR-SEM; SUR-SDEM). The LM(\lambda|\rho) tests for omitted spatial error in a model specified with spatial lags of the explained variable (SUR-SLM; SUR-SDM).

  2. Coefficients stability tests
    spsur includes two functions designed to test for linear restrictions on the \beta coefficients of the models and on the spatial coefficients (\rhos and \lambdas terms). The function for the first case is wald_betas and wald_deltas that of the second case. The user has ample flexibility to define different forms of linear restrictions, so that it is possible, for example, to test for their time constancy to identify structural breaks.

4. Marginal effects

In recent years, since the publication of LeSage and Pace (2009), it has become popular in spatial econometrics to evaluate the multiplier effects that a change in the value of a regressor, in a point in the space, has on the explained variable. spsur includes a function, impacts, that computes these effects. Specifically, impacts obtains the average, over the N spatial units and Tm time periods, of such a change on the contemporaneous value of the explained variable located in the same point as the modified variable. This is the so-called Average Direct effect. The Average Indirect effect measure the proportion of the impact that spills-over to other locations. The sum of the two effects is the Average Total effect.
These estimates are complemented with a measure of statistical significance, following the randomization approach suggested by LeSage and Pace (2009).

5. Additional functionalities

A particular feature of spsur is that the package allows to obtain simulated datasets with a SUR nature and the spatial structure decided by the user. This is the purpose of the function dgp_spsur. The function can be inserted into a more general code to solve, for example, Monte Carlo studies related to these type of models or, simply, to show some of the stylized characteristics of a SUR model with certain spatial structure.

Datasets

spsur includes three different datasets: spc, NCOVR and spain.covid. These sets are used to illustrate the capabilities of different functions. Briefly, their main characteristics are the following

Author(s)

Fernando Lopez fernando.lopez@upct.es
Roman Minguez roman.minguez@uclm.es
Jesus Mur jmur@unizar.es

References

[Package spsur version 1.0.2.5 Index]