spsurtime: Estimation of SUR models for simple spatial panels (G=1).
In spsur: Spatial Seemingly Unrelated Regression Models
spsurtime R Documentation
Estimation of SUR models for simple spatial panels (G=1).
Description
This function estimates SUR models for simple spatial
panel datasets.
spsurtime is restricted, specifically, to cases where
there is only one equation, G=1, and a varying number of spatial
units, N, and time periods, Tm. The SUR structure appears
in form of serial dependence among the error terms corresponding to the
same spatial unit.
Note that it is assumed that all spatial units share a common pattern
of serial dependence.
The user can choose between different types of spatial specifications,
as described below, and the estimation algorithms allow for the
introduction of linear restrictions on the β parameters
associated to the regressors. The spatial panels with SUR structure
can be estimated by maximum-likelihood methods or three-stages least
squares procedures, using spatial instrumental variables.
Usage
spsurtime (formula, data, time, na.action,
listw = NULL, type = "sim", Durbin = NULL,
method = "eigen", fit_method = "ml", maxlagW = NULL,
zero.policy = NULL, interval = NULL, trs = NULL,
R = NULL, b = NULL, demean = FALSE, control = list() )
Arguments
formula
An object type Formula
similar to objects created with the package Formula
describing the equations to be estimated in the model.
This model may contain several responses (explained
variables) and a varying number of regressors in each equation.
data
An object of class data.frame or a matrix.
time
Time variable.
na.action
A function (default options("na.action")),
can also be na.omit or na.exclude with consequences
for residuals and fitted values. It may be necessary to set
zero.policy to TRUE because this subsetting may
create no-neighbour observations.
listw
A listw object created for example by
nb2listw from spatialreg package; if
nb2listw not given, set to
the same spatial weights as the listw argument. It can
also be a spatial weighting matrix of order (NxN) instead of
a listw object. Default = NULL.
type
Type of spatial model specification: "sim",
"slx", "slm", "sem", "sdm",
"sdem", "sarar" or "gnm". Default = "sim".
Durbin
If a formula object and model is type "sdm", "sdem"
or "slx" the subset of explanatory variables to lag for each equation.
method
Similar to the corresponding parameter of
lagsarlm function in spatialreg package.
"eigen" (default) - the Jacobian is computed as the product of
(1 - rho*eigenvalue) using eigenw, and
"spam" or "Matrix_J" for strictly symmetric weights lists of
styles "B" and "C", or made symmetric by similarity
(Ord, 1975, Appendix C) if possible for styles "W" and "S",
using code from the spam or Matrix packages to calculate the
determinant; "Matrix" and "spam_update" provide updating Cholesky
decomposition methods; "LU" provides an alternative sparse matrix
decomposition approach. In addition, there are "Chebyshev" and
Monte Carlo "MC" approximate log-determinant methods;
the Smirnov/Anselin (2009) trace approximation is available
as "moments". Three methods: "SE_classic", "SE_whichMin",
and "SE_interp" are provided experimentally, the first to
attempt to emulate the behaviour of Spatial Econometrics
toolbox ML fitting functions. All use grids of log determinant
values, and the latter two attempt to ameliorate some features
of "SE_classic".
fit_method
Method of estimation for the spatial panel SUR model,
either ml or 3sls. Default = ml.
maxlagW
Maximum spatial lag order of the regressors employed to
produce spatial instruments for the spatial lags of the explained
variables. Default = 2. Note that in case of type = "sdm", the
default value for maxlagW is set to 3 because the first lag of
the regressors, WX_{tg}, can not be used as spatial instruments.
zero.policy
Similar to the corresponding parameter of
lagsarlm function in spatialreg package.
If TRUE assign zero to the lagged value of zones without
neighbours, if FALSE assign NA - causing
spsurml() to terminate with an error. Default = NULL.
interval
Search interval for autoregressive parameter.
Default = NULL.
trs
Either NULL or vector of powered spatial weights
matrix traces output by trW. Default = NULL.
R
A row vector of order (1xpr) with the set of
r linear constraints on the beta parameters. The
first restriction appears in the first p terms,
the second restriction in the next p terms and so on.
Default = NULL.
b
A column vector of order (rx1) with the values of
the linear restrictions on the beta parameters.
Default = NULL.
demean
Logical value to allow for the demeaning of panel data. In this case,
spsurml subtracts the individual mean to each spatial
or cross-sectional unit. Default = FALSE.
control
list of additional arguments.
Details
Function spsurtime only admits a formula, created with
Formula and a dataset of class data.frame
or matrix. That is, the data cannot be uploaded using data
matrices Y and X provided for other functions in
this package.
The argument time selects the variable, in the data.frame,
associated to the time dimension in the panel dataset. Then
spsurtime operates as in Anselin (1988), that is,
each cross-section is treated as if it were an equation in a SUR model,
which now has Tm 'equations' and N individuals.
The SUR structure appears because there is serial dependence in the errors
of each individual in the panel. The serial dependence in the errors is
not parameterized, but estimated non-parametrically in the Sigma
covariance matrix returned by the function. An important constraint to
mention is that the serial dependence assumed to be the same for all
individuals in the sample. Serial dependence among individuals is
excluded from Anselin approach.
Value
An spsur object with the output of the maximum-likelihood or
three-stages least-squares estimation of the spatial panel SUR model.
Author(s)
Fernando Lopez fernando.lopez@upct.es
Roman Minguez roman.minguez@uclm.es
Jesus Mur jmur@unizar.es
References
Anselin, L. (1988). Spatial econometrics: methods and models. Dordrecht,
Kluwer Academic Publishers.
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>
See Also
spsurml, spsur3sls,
wald_betas, wald_deltas,
lmtestspsur, lr_betas
Examples
####################################
######## PANEL DATA (G=1; Tm>1) ###
####################################
## Example 1:
rm(list = ls()) # Clean memory
data(spc)
lwspc <- spdep::mat2listw(Wspc, style = "W")
N <- nrow(spc)
Tm <- 2
index_time <- rep(1:Tm, each = N)
index_indiv <- rep(1:N, Tm)
WAGE <- c(spc$WAGE83, spc$WAGE81)
UN <- c(spc$UN83, spc$UN80)
NMR <- c(spc$NMR83, spc$NMR80)
SMSA <- c(spc$SMSA, spc$SMSA)
pspc <- data.frame(index_indiv, index_time, WAGE, UN,
NMR, SMSA)
form_pspc <- WAGE ~ UN + NMR + SMSA
form2_pspc <- WAGE | NMR ~ UN | UN + SMSA
# SLM
pspc_slm <- spsurtime(formula = form_pspc, data = pspc,
listw = lwspc,
time = pspc$index_time,
type = "slm", fit_method = "ml")
summary(pspc_slm)
pspc_slm2 <- spsurtime(formula = form2_pspc, data = pspc,
listw = lwspc,
time = pspc$index_time,
type = "slm", fit_method = "ml")
summary(pspc_slm2)
## VIP: The output of the whole set of the examples can be examined
## by executing demo(demo_spsurtime, package="spsur")
### Example 2:
rm(list = ls()) # Clean memory
### Read NCOVR.sf object
data(NCOVR, package="spsur")
nbncovr <- spdep::poly2nb(NCOVR.sf, queen = TRUE)
### Some regions with no links...
lwncovr <- spdep::nb2listw(nbncovr, style = "W", zero.policy = TRUE)
N <- nrow(NCOVR.sf)
Tm <- 4
index_time <- rep(1:Tm, each = N)
index_indiv <- rep(1:N, Tm)
pHR <- c(NCOVR.sf$HR60, NCOVR.sf$HR70, NCOVR.sf$HR80, NCOVR.sf$HR90)
pPS <- c(NCOVR.sf$PS60, NCOVR.sf$PS70, NCOVR.sf$PS80, NCOVR.sf$PS90)
pUE <- c(NCOVR.sf$UE60, NCOVR.sf$UE70, NCOVR.sf$UE80, NCOVR.sf$UE90)
pNCOVR <- data.frame(indiv = index_indiv, time = index_time,
HR = pHR, PS = pPS, UE = pUE)
form_pHR <- HR ~ PS + UE
## SIM
pHR_sim <- spsurtime(formula = form_pHR, data = pNCOVR,
time = pNCOVR$time, type = "sim", fit_method = "ml")
summary(pHR_sim)
## SLM by 3SLS.
pHR_slm <- spsurtime(formula = form_pHR, data = pNCOVR, listw = lwncovr,
time = pNCOVR$time, type = "slm",
fit_method = "3sls")
summary(pHR_slm)
############################# Wald tests about betas in spatio-temporal models
### H0: equal betas for PS in equations 1, 3 and 4.
R <- matrix(0, nrow = 2, ncol = 12)
## nrow = number of restrictions
## ncol = number of beta parameters
R[1, 2] <- 1; R[1, 8] <- -1 # PS beta coefficient in equations 1 equal to 3
R[2, 2] <- 1; R[2, 11] <- -1 # PS beta coefficient in equations 1 equal to 4
b <- matrix(0, nrow=2, ncol=1)
wald_betas(pHR_sim , R = R , b = b) # SIM model
wald_betas(pHR_slm , R = R , b = b) # SLM model
############################# Wald tests about spatial-parameters in
############################# spatio-temporal models
### H0: equal rhos in slm model for equations 1 and 2.
R2 <- matrix(0, nrow = 1, ncol = 4)
R2[1, 1] <- 1; R2[1, 2] <- -1
b2 <- matrix(0, nrow = 1, ncol = 1)
wald_deltas(pHR_slm, R = R2, b = b2)
spsur documentation built on Oct. 30, 2022, 1:06 a.m.
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| spsurtime | R Documentation |
Estimation of SUR models for simple spatial panels (G=1).
Description
This function estimates SUR models for simple spatial
panel datasets.
spsurtime is restricted, specifically, to cases where
there is only one equation, G=1, and a varying number of spatial
units, N, and time periods, Tm. The SUR structure appears
in form of serial dependence among the error terms corresponding to the
same spatial unit.
Note that it is assumed that all spatial units share a common pattern
of serial dependence.
The user can choose between different types of spatial specifications, as described below, and the estimation algorithms allow for the introduction of linear restrictions on the β parameters associated to the regressors. The spatial panels with SUR structure can be estimated by maximum-likelihood methods or three-stages least squares procedures, using spatial instrumental variables.
Usage
spsurtime (formula, data, time, na.action,
listw = NULL, type = "sim", Durbin = NULL,
method = "eigen", fit_method = "ml", maxlagW = NULL,
zero.policy = NULL, interval = NULL, trs = NULL,
R = NULL, b = NULL, demean = FALSE, control = list() )
Arguments
formula |
An object type |
data |
An object of class data.frame or a matrix. |
time |
Time variable. |
na.action |
A function (default |
listw |
A |
type |
Type of spatial model specification: "sim", "slx", "slm", "sem", "sdm", "sdem", "sarar" or "gnm". Default = "sim". |
Durbin |
If a formula object and model is type "sdm", "sdem" or "slx" the subset of explanatory variables to lag for each equation. |
method |
Similar to the corresponding parameter of
|
fit_method |
Method of estimation for the spatial panel SUR model, either ml or 3sls. Default = ml. |
maxlagW |
Maximum spatial lag order of the regressors employed to
produce spatial instruments for the spatial lags of the explained
variables. Default = 2. Note that in case of |
zero.policy |
Similar to the corresponding parameter of
|
interval |
Search interval for autoregressive parameter.
Default = |
trs |
Either |
R |
A row vector of order (1xpr) with the set of
r linear constraints on the beta parameters. The
first restriction appears in the first p terms,
the second restriction in the next p terms and so on.
Default = |
b |
A column vector of order (rx1) with the values of
the linear restrictions on the beta parameters.
Default = |
demean |
Logical value to allow for the demeaning of panel data. In this case,
|
control |
list of additional arguments. |
Details
Function spsurtime only admits a formula, created with
Formula and a dataset of class data.frame
or matrix. That is, the data cannot be uploaded using data
matrices Y and X provided for other functions in
this package.
The argument time selects the variable, in the data.frame,
associated to the time dimension in the panel dataset. Then
spsurtime operates as in Anselin (1988), that is,
each cross-section is treated as if it were an equation in a SUR model,
which now has Tm 'equations' and N individuals.
The SUR structure appears because there is serial dependence in the errors
of each individual in the panel. The serial dependence in the errors is
not parameterized, but estimated non-parametrically in the Sigma
covariance matrix returned by the function. An important constraint to
mention is that the serial dependence assumed to be the same for all
individuals in the sample. Serial dependence among individuals is
excluded from Anselin approach.
Value
An spsur object with the output of the maximum-likelihood or
three-stages least-squares estimation of the spatial panel SUR model.
Author(s)
| Fernando Lopez | fernando.lopez@upct.es |
| Roman Minguez | roman.minguez@uclm.es |
| Jesus Mur | jmur@unizar.es |
References
Anselin, L. (1988). Spatial econometrics: methods and models. Dordrecht, Kluwer Academic Publishers.
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>
See Also
spsurml, spsur3sls,
wald_betas, wald_deltas,
lmtestspsur, lr_betas
Examples
####################################
######## PANEL DATA (G=1; Tm>1) ###
####################################
## Example 1:
rm(list = ls()) # Clean memory
data(spc)
lwspc <- spdep::mat2listw(Wspc, style = "W")
N <- nrow(spc)
Tm <- 2
index_time <- rep(1:Tm, each = N)
index_indiv <- rep(1:N, Tm)
WAGE <- c(spc$WAGE83, spc$WAGE81)
UN <- c(spc$UN83, spc$UN80)
NMR <- c(spc$NMR83, spc$NMR80)
SMSA <- c(spc$SMSA, spc$SMSA)
pspc <- data.frame(index_indiv, index_time, WAGE, UN,
NMR, SMSA)
form_pspc <- WAGE ~ UN + NMR + SMSA
form2_pspc <- WAGE | NMR ~ UN | UN + SMSA
# SLM
pspc_slm <- spsurtime(formula = form_pspc, data = pspc,
listw = lwspc,
time = pspc$index_time,
type = "slm", fit_method = "ml")
summary(pspc_slm)
pspc_slm2 <- spsurtime(formula = form2_pspc, data = pspc,
listw = lwspc,
time = pspc$index_time,
type = "slm", fit_method = "ml")
summary(pspc_slm2)
## VIP: The output of the whole set of the examples can be examined
## by executing demo(demo_spsurtime, package="spsur")
### Example 2:
rm(list = ls()) # Clean memory
### Read NCOVR.sf object
data(NCOVR, package="spsur")
nbncovr <- spdep::poly2nb(NCOVR.sf, queen = TRUE)
### Some regions with no links...
lwncovr <- spdep::nb2listw(nbncovr, style = "W", zero.policy = TRUE)
N <- nrow(NCOVR.sf)
Tm <- 4
index_time <- rep(1:Tm, each = N)
index_indiv <- rep(1:N, Tm)
pHR <- c(NCOVR.sf$HR60, NCOVR.sf$HR70, NCOVR.sf$HR80, NCOVR.sf$HR90)
pPS <- c(NCOVR.sf$PS60, NCOVR.sf$PS70, NCOVR.sf$PS80, NCOVR.sf$PS90)
pUE <- c(NCOVR.sf$UE60, NCOVR.sf$UE70, NCOVR.sf$UE80, NCOVR.sf$UE90)
pNCOVR <- data.frame(indiv = index_indiv, time = index_time,
HR = pHR, PS = pPS, UE = pUE)
form_pHR <- HR ~ PS + UE
## SIM
pHR_sim <- spsurtime(formula = form_pHR, data = pNCOVR,
time = pNCOVR$time, type = "sim", fit_method = "ml")
summary(pHR_sim)
## SLM by 3SLS.
pHR_slm <- spsurtime(formula = form_pHR, data = pNCOVR, listw = lwncovr,
time = pNCOVR$time, type = "slm",
fit_method = "3sls")
summary(pHR_slm)
############################# Wald tests about betas in spatio-temporal models
### H0: equal betas for PS in equations 1, 3 and 4.
R <- matrix(0, nrow = 2, ncol = 12)
## nrow = number of restrictions
## ncol = number of beta parameters
R[1, 2] <- 1; R[1, 8] <- -1 # PS beta coefficient in equations 1 equal to 3
R[2, 2] <- 1; R[2, 11] <- -1 # PS beta coefficient in equations 1 equal to 4
b <- matrix(0, nrow=2, ncol=1)
wald_betas(pHR_sim , R = R , b = b) # SIM model
wald_betas(pHR_slm , R = R , b = b) # SLM model
############################# Wald tests about spatial-parameters in
############################# spatio-temporal models
### H0: equal rhos in slm model for equations 1 and 2.
R2 <- matrix(0, nrow = 1, ncol = 4)
R2[1, 1] <- 1; R2[1, 2] <- -1
b2 <- matrix(0, nrow = 1, ncol = 1)
wald_deltas(pHR_slm, R = R2, b = b2)
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