spsur-package: Spatial Seemingly Unrelated Regression Models.
In spsur: Spatial Seemingly Unrelated Regression Models
spsur-package 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:
Datasets with a single equation G=1, for different time
periods Tm>1 and a certain number of spatial units in the
cross-sectional dimension, N. This is what we call
spatial panel datasets. In this case, the SUR structure appears
in form of (intra) serial dependence in the errors of each spatial unit.
Datasets with a several equations G>1, different time
periods Tm>1 and a certain number of spatial units, N.
The SUR structure appears, as usual, because the errors
of the spatial units for different equations are contemporaneously
correlated.
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:
-
SUR-SIM: SUR model without spatial effects
y_{tg} = X_{tg} β_{g} + ε_{tg}
-
SUR-SLX: SUR model with spatial lags of the regresors
y_{tg} = X_{tg} β_{g} +
WX_{tg} θ_{g} + ε_{tg}
-
SUR-SLM: SUR model with spatial lags of the endogenous
y_{tg} = ρ_{g} Wy_{tg} + X_{tg} β_{g} +
ε_{tg}
-
SUR-SEM: SUR model with spatial errors
y_{tg} = X_{tg} β_{g} + u_{tg}
u_{tg} = λ_{g} Wu_{tg} + ε_{tg}
-
SUR-SDM: SUR model with spatial lags of the endogenous
variable and of the regressors or Spatial Durbin model
y_{tg} = ρ_{g} Wy_{tg} + X_{tg} β_{g} +
WX_{tg} θ_{g} + ε_{tg}
-
SUR-SDEM: SUR model with spatial errors and spatial
lags of the endogenous variable and of the regressors
y_{tg} = X_{tg} β_{g} + WX_{tg} θ_{g} + u_{tg}
u_{tg} = λ_{g} W u_{tg} + ε_{tg}
-
SUR-SARAR: Spatial lag model with spatial errors
y_{tg} = ρ_{g} Wy_{tg} + X_{tg} β_{g} +
u_{tg}
u_{tg} = λ_{g} W u_{tg} + ε_{tg}
-
SUR-GNM: SUR model with spatial lags of the explained
variables, regressors and spatial errors
y_{tg} = ρ_{g} Wy_{tg} + X_{tg} β_{g} +
WX_{tg} θ_{g} + u_{tg}
u_{tg} = λ_{g} W u_{tg} + ε_{tg}
where y_{tg}, u_{tg} and ε_{tg} are
(Nx1) vectors; X_{tg} is a matrix of regressors of
order (NxP); ρ_{g} and λ_{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:
-
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(ρ|λ) tests for omitted
spatial lags in a model specified with spatial errors (SUR-SEM;
SUR-SDEM). The LM(λ|ρ) tests for omitted
spatial error in a model specified with spatial lags
of the explained variable (SUR-SLM; SUR-SDM).
-
Coefficients stability tests
spsur includes two functions designed to test for linear
restrictions on the β coefficients of the models and on
the spatial coefficients (ρs and λs 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
The spc dataset (Spatial Phillips-Curve) is a
classical dataset taken from Anselin (1988, p. 203), of small
dimensions.
The NCOVR dataset comprises Homicides and a list of
selected socio-economic variables for continental U.S. counties
in four decennial census years: 1960, 1970, 1980 and 1990.
It is freely available from
https://geodacenter.github.io/data-and-lab/ncovr/.
NCOVR is a typical spatial panel dataset (G=1).
The spain.covid dataset comprises Within and Exit mobility index
together with the weeklly incidence COVID-19 at Spain provinces from
February 21 to May 21 2020.
https://www.mitma.gob.es/ministerio/covid-19/evolucion-movilidad-big-data
Author(s)
Fernando Lopez fernando.lopez@upct.es
Roman Minguez roman.minguez@uclm.es
Jesus Mur jmur@unizar.es
References
Breusch T, Pagan A (1980). The Lagrange multiplier test
and its applications to model specification in econometrics.
Review of Economic Studies 47: 239-254.
LeSage, J., and Pace, R. K. (2009). Introduction to
spatial econometrics. Chapman and Hall/CRC.
Lopez, 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.
<doi:10.1007/s00168-014-0624-2>
Lopez, F.A., Martinez-Ortiz, P.J., and Cegarra-Navarro, J.G.
(2017). Spatial spillovers in public expenditure on a municipal
level in Spain. Annals of Regional Science, 58(1), 39-65.
<doi:10.1007/s00168-016-0780-7>
Minguez, R., Lopez, F.A. and Mur, J. (2022).
spsur: An R Package for Dealing with Spatial
Seemingly Unrelated Regression Models.
Journal of Statistical Software,
104(11), 1–43.
<doi:10.18637/jss.v104.i11>
Mur, J., Lopez, F., and Herrera, M. (2010). Testing for spatial
effects in seemingly unrelated regressions. Spatial Economic
Analysis, 5(4), 399-440.
<doi:10.1080/17421772.2010.516443>
spsur documentation built on Oct. 30, 2022, 1:06 a.m.
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| spsur-package | 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:
Datasets with a single equation G=1, for different time periods Tm>1 and a certain number of spatial units in the cross-sectional dimension, N. This is what we call spatial panel datasets. In this case, the SUR structure appears in form of (intra) serial dependence in the errors of each spatial unit.
Datasets with a several equations G>1, different time periods Tm>1 and a certain number of spatial units, N. The SUR structure appears, as usual, because the errors of the spatial units for different equations are contemporaneously correlated.
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:
-
SUR-SIM: SUR model without spatial effects
y_{tg} = X_{tg} β_{g} + ε_{tg}
-
SUR-SLX: SUR model with spatial lags of the regresors
y_{tg} = X_{tg} β_{g} + WX_{tg} θ_{g} + ε_{tg}
-
SUR-SLM: SUR model with spatial lags of the endogenous
y_{tg} = ρ_{g} Wy_{tg} + X_{tg} β_{g} + ε_{tg}
-
SUR-SEM: SUR model with spatial errors
y_{tg} = X_{tg} β_{g} + u_{tg}
u_{tg} = λ_{g} Wu_{tg} + ε_{tg}
-
SUR-SDM: SUR model with spatial lags of the endogenous variable and of the regressors or Spatial Durbin model
y_{tg} = ρ_{g} Wy_{tg} + X_{tg} β_{g} + WX_{tg} θ_{g} + ε_{tg}
-
SUR-SDEM: SUR model with spatial errors and spatial lags of the endogenous variable and of the regressors
y_{tg} = X_{tg} β_{g} + WX_{tg} θ_{g} + u_{tg}
u_{tg} = λ_{g} W u_{tg} + ε_{tg}
-
SUR-SARAR: Spatial lag model with spatial errors
y_{tg} = ρ_{g} Wy_{tg} + X_{tg} β_{g} + u_{tg}
u_{tg} = λ_{g} W u_{tg} + ε_{tg}
-
SUR-GNM: SUR model with spatial lags of the explained variables, regressors and spatial errors
y_{tg} = ρ_{g} Wy_{tg} + X_{tg} β_{g} + WX_{tg} θ_{g} + u_{tg}
u_{tg} = λ_{g} W u_{tg} + ε_{tg}
where y_{tg}, u_{tg} and ε_{tg} are (Nx1) vectors; X_{tg} is a matrix of regressors of order (NxP); ρ_{g} and λ_{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:
-
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 byspsurml. In particular, the LM(ρ|λ) tests for omitted spatial lags in a model specified with spatial errors (SUR-SEM; SUR-SDEM). The LM(λ|ρ) tests for omitted spatial error in a model specified with spatial lags of the explained variable (SUR-SLM; SUR-SDM). -
Coefficients stability tests
spsur includes two functions designed to test for linear restrictions on the β coefficients of the models and on the spatial coefficients (ρs and λs terms). The function for the first case iswald_betasandwald_deltasthat 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
The spc dataset (Spatial Phillips-Curve) is a classical dataset taken from Anselin (1988, p. 203), of small dimensions.
The NCOVR dataset comprises Homicides and a list of selected socio-economic variables for continental U.S. counties in four decennial census years: 1960, 1970, 1980 and 1990. It is freely available from https://geodacenter.github.io/data-and-lab/ncovr/. NCOVR is a typical spatial panel dataset (G=1).
The spain.covid dataset comprises Within and Exit mobility index together with the weeklly incidence COVID-19 at Spain provinces from February 21 to May 21 2020. https://www.mitma.gob.es/ministerio/covid-19/evolucion-movilidad-big-data
Author(s)
| Fernando Lopez | fernando.lopez@upct.es |
| Roman Minguez | roman.minguez@uclm.es |
| Jesus Mur | jmur@unizar.es |
References
Breusch T, Pagan A (1980). The Lagrange multiplier test and its applications to model specification in econometrics. Review of Economic Studies 47: 239-254.
LeSage, J., and Pace, R. K. (2009). Introduction to spatial econometrics. Chapman and Hall/CRC.
Lopez, 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. <doi:10.1007/s00168-014-0624-2>
Lopez, F.A., Martinez-Ortiz, P.J., and Cegarra-Navarro, J.G. (2017). Spatial spillovers in public expenditure on a municipal level in Spain. Annals of Regional Science, 58(1), 39-65. <doi:10.1007/s00168-016-0780-7>
Minguez, R., Lopez, F.A. and Mur, J. (2022). spsur: An R Package for Dealing with Spatial Seemingly Unrelated Regression Models. Journal of Statistical Software, 104(11), 1–43. <doi:10.18637/jss.v104.i11>
Mur, J., Lopez, F., and Herrera, M. (2010). Testing for spatial effects in seemingly unrelated regressions. Spatial Economic Analysis, 5(4), 399-440. <doi:10.1080/17421772.2010.516443>
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