Title: Econometric Models for Spatial Panel Data
Version: 1.6-5
Date: 2023-12-11
Description: ML and GM estimation and diagnostic testing of econometric models for spatial panel data.
Depends: R (≥ 2.12.0)
Imports: plm, maxLik, MASS, bdsmatrix, nlme, Matrix, spam, methods, spatialreg (≥ 1.2-1), spdep (≥ 1.2-1), stringr
License: GPL-2
LazyLoad: yes
NeedsCompilation: no
Packaged: 2023-12-11 15:00:43 UTC; root
Author: Giovanni Millo [aut, cre], Gianfranco Piras [aut], Roger Bivand ORCID iD [ctb]
Maintainer: Giovanni Millo <giovanni.millo@deams.units.it>
Repository: CRAN
Date/Publication: 2023-12-20 16:20:05 UTC

Insurance consumption across Italian provinces, 1998-2002

Description

A panel of 103 observations

number of observations : 515

observation : provinces

country : Italy

Usage

data(Insurance)

Format

A dataframe containing :

code

the province code according to Istat

year

the year of observation

ppcd

real per capita premiums in 2000 euros, non-life insurance excluding mandatory motor third-party liability

rgdp

real per-capita GDP

bank

real per-capita bank deposits

den

population density per square Km

rirs

real interest rate on lending to families and small enterprises

agen

density of insurance agencies per 1000 inhabitants

school

share of people with second grade schooling or more

vaagr

share of value added, agriculture

fam

average number of family members

inef

judicial inefficiency index: average years to settle first degree of civil case

trust

survey result to the question "do you trust others?"

dXX

year dummies

NorthWest

macroregional dummy

NorthEast

macroregional dummy

Centre

macroregional dummy

South

macroregional dummy

Islands

macroregional dummy (Sicily and Sardinia)

Author(s)

Giovanni Millo

Source

Giovanni Millo and Gaetano Carmeci, (2011) “Non-life insurance consumption in Italy: a sub-regional panel data analysis”, Journal of Geographical Systems, 13:273–298.

Production of Rice in India

Description

yearly observations of 171 farms

number of observations : 1026

country : Indonesia

economic topic : producer behavior

econometrics topic : error component

Usage

data(RiceFarms)

Format

A dataframe containing :

id

the farm identifier

time

the growing season

size

the total area cultivated with rice, measured in hectares

status

land status, on of 'owner' (non sharecroppers, owner operators or leasholders or both), 'share' (sharecroppers), 'mixed' (mixed of the two previous status)

varieties

one of 'trad' (traditional varieties), 'high' (high yielding varieties) and 'mixed' (mixed varieties)

bimas

bIMAS is an intensification program ; one of 'no' (non-bimas famer), 'yes' (bimas farmer) or 'mixed' (part but not all of farmer's land was registered to be in the bimas program)

seed

seed in kilogram

urea

urea in kilogram

phosphate

phosphate in kilogram

pesticide

pesticide cost in Rupiah

pseed

price of seed in Rupiah per kg

purea

price of urea in Rupiah per kg

pphosph

price of phosphate in Rupiah per kg

hiredlabor

hired labor in hours

famlabor

family labor in hours

totlabor

total labor (excluding harvest labor)

wage

labor wage in Rupiah per hour

goutput

gross output of rice in kg

noutput

net output, gross output minus harvesting cost (paid in terms of rice)

price

price of rough rice in Rupiah per Kg

region

one of 'wargabinangun', 'langan', 'gunungwangi', 'malausma', 'sukaambit', 'ciwangi'

Source

Journal of Applied Econometrics Data Archive.

References

Qu Feng and William C. Horrace, (2012) “Alternative Measures of Technical Efficiency: Skew, Bias and Scale”, Journal of Applied Econometrics, forthcoming.

Horrace, W.C. and P. Schmidt (1996) “Confidence statements for efficiency estimates from stochastic frontier models”, Journal of Productivity Analysis, 7, 257–282.

Baltagi, Song, Jung and Koh LM test for spatial panels

Description

Baltagi, Song, Jung and Koh joint or conditional LM test for spatial error correlation or serial correlation sub spatial, serial correlation and random effects in panel models

Usage

bsjktest(x,...)
## S3 method for class 'formula'
bsjktest(x, data, index=NULL, listw,
test=c("C.1","C.2","C.3","J"), ...)

Arguments

x

an object of class formula

data

a data.frame or pdata.frame containing the variables in the model

index

either NULL (default) or a character vector to identify the indexes among the columns of the data.frame

listw

either a matrix or a listw representing the spatial structure

test

one of c("C.1","C.2","C.3","J"), the test to be performed.

...

additional arguments to be passed

Value

an object of class htest

Author(s)

Giovanni Millo

References

Baltagi, B.H., Song, S.H., Jung B. and Koh, W. (2007) Testing panel data regression models with spatial and serial error correlation. Journal of Econometrics, 140, 5-51.

See Also

bsktest

Examples

data(Produc, package="plm")
data(usaww)
fm <- log(gsp)~log(pcap)+log(pc)+log(emp)+unemp
bsjktest(fm, data=Produc, listw = usaww, test="C.1")

Baltagi, Song and Koh LM test for spatial panels

Description

Baltagi, Song and Koh marginal or conditional LM test for spatial error correlation or random effects in panel models

Usage

bsktest(x,...)
## S3 method for class 'formula'
bsktest(x, data, index=NULL, listw,
test=c("LMH","LM1","LM2","CLMlambda","CLMmu"), 
standardize=FALSE, method = "eigen", ...)

Arguments

x

a formula

data

a data.frame or pdata.frame containing the variables in the model

index

either NULL (default) or a character vector to identify the indexes among the columns of the data.frame

listw

a listw representing the spatial structure

test

one of c("LMH","LM1","LM2","CLMlambda","CLMmu"), the test to be performed

standardize

whether to standardize the test statistic or not (applies only to LM1 and LM2)

method

select a method for ML in "CLMmu". the default is "eigen"

...

additional arguments to be passed

Value

an object of class htest

Author(s)

Gianfranco Piras

References

Baltagi, B.H., Song, S.H. and Koh, W. (2003) Testing panel data regression models with spatial error correlation. Journal of Econometrics, 117, 123–150.

Millo, G., Piras, G. (2012) splm: Spatial Panel Data Models in R. Journal of Statistical Software, 47(1), 1–38. URL http://www.jstatsoft.org/v47/i01/.

See Also

sphtest

Examples

data(Produc, package="plm")
data(usaww)
fm <- log(gsp)~log(pcap)+log(pc)+log(emp)+unemp
bsktest(fm,data=Produc, listw = spdep::mat2listw(usaww),
  test="LM1")

method for extracting fixed effects

Description

Methods used for extracting fixed effects from objects of class splm where type is one of "fixed effects lag" or "fixed effects error"

Usage

## S3 method for class 'splm'
effects(object,...)

Arguments

object

an object of class 'splm'

...

additional arguments to be passed over

Details

If the argument object is not of class splm the function will terminate with an error.

If the argument object is of class splm but type is not one of "fixed effects lag" or "fixed effects error", the function will terminate with an error.

Value

An object of class effects.splm

res

a list whose elements are various type of fixed effects and the intercept (when present)

Author(s)

Gianfranco Piras

References

Elhorst, J.P. (2003) Specification and estimation of spatial panel data models, International Regional Science Review, 26, pages 244–268.

Elhorst, J.P. (2009) Spatial panel data models, In Fischer, M.M. and Getis, A. (eds), Handbook of Applied Spatial Analysis Springer, Berlin.

See Also

spml summary.effects.splm

Examples

data(Produc, package = "plm")
data(usaww)
fm <- log(gsp) ~ log(pcap) + log(pc) + log(emp) + unemp
err <- spml(fm, data = Produc, listw = spdep::mat2listw(usaww), model="within")
summary(err)
eff <- effects(err) 
print(eff)

Spatial weights matrix - Italian provinces

Description

Spatial weights matrix of the 103 Italian provinces as in 1992-2005.

Usage

data(itaww)

Format

A matrix with elements different from zero if province i and j are neighbors. Weights are row-standardized. Messina and Reggio Calabria, divided by the Messina Strait, are considered neighbours.

Author(s)

Giovanni Millo

Interface between Matrix class objects and weights list

Description

Interface between Matrix class objects and weights list

Usage

listw2dgCMatrix(listw, zero.policy = NULL)

Arguments

listw

a listw object created for example by spdep::nb2listw

zero.policy

See lagsarlm for details

Value

Matrix class object: a sparse Matrix

Author(s)

Gianfranco Piras

Examples

data(columbus, package="spdep")
listw<-spdep::nb2listw(col.gal.nb)
spW<-listw2dgCMatrix(listw)

print method for class splm

Description

Method to print objects of class summary.splm and splm

Usage

## S3 method for class 'splm'
print(x, digits = max(3,getOption("digits") -3), ...)

Arguments

x

an object of class splm

digits

minimal number of significant digits, see print.default

...

additional arguments to be passed

Details

The summary function summary.splm returns an objects of class 'splm' organized in a coefficient matrix.

Also a matrix for the error components, or the spatial coefficients will be generated depending on the estimated model.

Author(s)

Giovanni Millo, Gianfranco Piras

See Also

spml, spgm

Examples

data(Produc, package = "plm") 
data(usaww)
spremod<-spml(log(gsp)~log(pcap)+log(pc)+log(emp)+unemp, data=Produc,
listw = spdep::mat2listw(usaww), model="random", lag=TRUE, spatial.error="none")
summary(spremod)

Spatial weights matrix of Indonesian rice farms

Description

Spatial weights matrix of the 171 farms in the Indonesian Rice Farming example. Farms in the same village (out of six) are considered contiguous.

Usage

data(riceww)

Format

A matrix with elements different from zero if farms i and j are neighbors. Farms are considered neighbors if in the same village. Weights are row-standardized.

Author(s)

Giovanni Millo, data provided by Yves Croissant

Randomization-based test of spatial dependence for panel models

Description

Randomization-based test of spatial dependence for panel models, robust to global dependence induced by common factors and to persistence (serial correlation) in the data

Usage

rwtest(x, ...)
## S3 method for class 'formula'
rwtest(x, data, w, index = NULL, model = NULL,
                         replications = 99, seed=NULL, order=1,
                         mc=1, test = c("rho", "cd", "sclm"),
                         alternative=c("twosided", "onesided",
                                       "symmetric"), ...)
## S3 method for class 'panelmodel'
rwtest(x, w, replications = 99, seed=NULL,
                         order=1, mc=1,
                         test = c("rho", "cd", "sclm"),
                         alternative=c("twosided", "onesided",
                                       "symmetric"), ...)
## S3 method for class 'pseries'
rwtest(x, w, replications = 99, seed=NULL,
                         order=1, mc=1,
                         test = c("rho", "cd", "sclm"),
                         alternative=c("twosided", "onesided",
                                       "symmetric"), ...)

Arguments

x

an object of class formula, panelmodel, or pseries (depending on the respective interface) describing the model to be tested

data

a data.frame

w

a n x n matrix describing proximity between individuals, with w_ij = a where a is any number such that as.logical(a)==TRUE, if i,j are neighbours, 0 or any number b such that as.logical(b)==FALSE elsewhere. Only the lower triangluar part (without diagonal) of w after coercing by as.logical() is evaluated for neighbouring information (but w can be symmetric). See also Details and Examples.

index

an optional numerical index, in case data has to be formatted by plm.data

model

an optional character string indicating which type of model to estimate; if left to NULL, the original heterogeneous specification of Pesaran is used

replications

the number of Monte Carlo randomizations of the neighbourhood matrix (default: 99),

seed

the optional random seed,

order

the order of neighbourhood to test for,

mc

the number of parallel threads to execute; defaults to 1 (serial execution); is limited to the number of execution cores actually available, and depends on operating system support.

test

the type of test statistic to be returned. One of

  • "rho" for the average correlation coefficient,

  • "cd" for Pesaran's CD statistic, or

  • "sclm" for the scaled version of Breusch and Pagan's LM statistic,

alternative

the alternative hypothesis for the test, defaulting to (asymmetric) twosided,

...

further arguments to be passed on to plm, such as e.g. effect or random.method

Details

This test is meant as a generalization of Pesaran's spatial dependence test "CD(p)" for robustness against global dependence (perhaps of the factor type) and persistence in the data, both of which the original test does not tolerate.

The procedure can be applied to model residuals as well as to individual pseries. See the comments in pcdtest as for the different methods.

Space is defined supplying a proximity matrix (elements coercible to logical) with argument w which provides information on whether any pair of individuals are neighbours or not. If order=1, only first-order neighbouring pairs will be used in computing the test; else, w will be transformed in the neighbourhood matrix of the appropriate order. The matrix need not be binary, so commonly used “row–standardized” matrices can be employed as well. nb objects from spdep must instead be transformed into matrices by spdep's function nb2mat before using.

Notice that the "rho" and "cd" tests are permutationally equivalent.

The test is suitable also for unbalanced panels.

The test on a pseries is the same as a test on a pooled regression model of that variable on a constant, i.e. rwtest(some_pseries) is equivalent to rwtest(plm(some_var ~ 1, data = some_pdata.frame, model = "pooling") and also equivalent to rwtest(some_var ~ 1, data = some_data), where some_var is the variable name in the data which corresponds to some_pseries.

Value

An object of class "htest".

Author(s)

Giovanni Millo

References

Millo, G. (2016), A simple randomization test for spatial dependence in the presence of common factors and serial correlation, (unpublished), xx(x), pp. xxx–xxx. Pesaran, M.H. (2004), General Diagnostic Tests for Cross Section Dependence in Panels, CESifo Working Paper 1229. Pesaran, M.H. (2015), Testing Weak Cross–Sectional Dependence in Large Panels, Econometric Reviews, 34(6-10), pp. 1089–1117.

Examples

data(Produc, package = "plm")
data(usaww)
fm <- log(gsp) ~ log(pcap) + log(pc) + log(emp) + unemp
## test on heterogeneous model (separate time series regressions)
rwtest(fm, data = Produc, w=usaww, index = c("state", "year"))

## test on two-way fixed effects homogeneous model
rwtest(fm, data = Produc, w=usaww, index = c("state", "year"),
       model = "within", effect = "twoways")

## test on panelmodel object
library(plm)
g <- plm(fm, data = Produc)
rwtest(g, w=usaww)

## test on pseries, higher-order neighbourhood
pprod <- pdata.frame(Produc)
rwtest(pprod$gsp, w=usaww, order=3)

Spatial lag operator

Description

Spatial lagging method for vectors or pseries objects.

Usage

## S3 method for class 'pseries'
slag(x, listw, maxlag, ...)
## Default S3 method:
slag(x, listw, maxlag, index, ...)

Arguments

x

an object of class pseries

listw

an object of class listw

maxlag

the spatial lag order (including lower)

index

the default method needs a well-specified index

...

additional arguments to be passed

Value

a pseries

Author(s)

Giovanni Millo

Examples

data(Produc, package="plm")
data(usaww)
usalw <- spdep::mat2listw(usaww)
fm <- log(gsp)~log(pcap)+log(pc)+log(emp)+unemp+slag(log(pcap),
  listw=usalw)
slxmod <- spreml(fm, data=Produc, w = usaww,
  model="pooling", lag=FALSE, errors="ols")

Locally robust panel Lagrange Multiplier tests for spatial dependence

Description

Locally robust LM tests for spatial lag (error) correlation sub spatial error (lag) correlation in panel models

Usage

slmtest(x,...)
## S3 method for class 'formula'
slmtest(formula, data, listw, model="pooling",
 test=c("lme","lml","rlme","rlml"), index=NULL, ...)
## S3 method for class 'plm'
slmtest(x, listw,
 test=c("lme","lml","rlme","rlml"), ...)

Arguments

formula

an object of class formula

data

a data.frame or pdata.frame containing the variables in the model

x

an object of class plm

listw

either a matrix or a listw representing the spatial structure

model

a character value specifying the transformation to be applied to the data.

test

one of c("lme","lml","rlme","rlml"), the test to be performed.

index

either NULL (default) or a character vector to identify the indexes among the columns of the data.frame

...

additional arguments to be passed

Details

This tests are panel versions of the locally robust LM tests of Anselin et al. (1996), based on a pooling assumption: i.e., they do not allow for any kind of individual effect. Therefore it is advisable to employ a within transformation whenever individual effects cannot be ruled out.

It must be kept in mind that these locally robust procedures have been designed for situations in which the "other" effect is not of substantial magnitude, and can behave suboptimally otherwise.

Four tests are available to be chosen through the test argument: "lml" for "LM lag" and, respectively, "lme" for "LM error" are the standard, non-robust versions, obtained simply pooling the cross-sectional versions; "rlml" and "rlme" are, respectively, the locally robust test for lag, allowing for a spatial error; and for error, allowing for a spatial lag.

The model argument, specified according to the standards of plm, is passed on internally and employed to determine the panel data transformation to be applied before calculating the test. Defaults to "pooling" (no transformation).

Value

an object of class htest

Author(s)

Giovanni Millo

References

Anselin, L., Bera, A.K., Florax, R. and Yoon, M.J. (1996) Simple diagnostic tests for spatial dependence. Regional Science and Urban Economics, 26(1), 77-104. Elhorst, J.P. (2014) Spatial Panel data Models, in Spatial Econometrics (Springer) 37-93.

Examples

data(Produc, package="plm")
data(usaww)
fm <- log(gsp)~log(pcap)+log(pc)+log(emp)+unemp
## robust LM test for spatial error sub spatial lag
## model on original data, pooling hypothesis
slmtest(fm, data=Produc, listw = usaww, test="rlme")
## model on within-transformed (time-demeaned) data,
## eliminates individual effects
slmtest(fm, data=Produc, listw = usaww, test="rlme",
  model="within")

GM estimation of spatial panel data models

Description

GM estimation of panel data models with spatially correlated errors components of the form:

y_N(t) = \lambda W y + X_N(t) \beta + u_N(t)

u_N(t) = \rho W_N u_N(t) + \epsilon(t)

\epsilon_N = (e_T \otimes I_N ) \mu_N + \nu_N

where \rho, and the variance components \sigma^2_\mu and \sigma^2_\nu are estimated by GM, and the model coefficients by a Feasible GLS estimator. The model can also include additional (other than the spatial lag) endogenous variables.

Usage

spgm(formula, data=list(), index=NULL, listw = NULL, listw2 = NULL, Durbin = FALSE,
         model = c("within", "random"), lag = FALSE, spatial.error = TRUE,
         moments = c("initial", "weights", "fullweights"), endog = NULL, 
         instruments = NULL, lag.instruments = FALSE, verbose = FALSE, 
         method = c("w2sls", "b2sls", "g2sls", "ec2sls"), control = list(), 
         optim.method = "nlminb",  pars = NULL)

Arguments

formula

a description of the model to be fit. The details of model specification are given for lm

data

an object of class data.frame or pdata.frame. An optional data frame containing the variables in the model. When the obect is a data.frame, the first two columns may contain the indexes. See index

index

if not NULL (default), a character vector to identify the indexes among the columns of the data.frame

listw

an object of class listw, matrix, or Matrix

.

listw2

an object of class listw, matrix, or Matrix. Only if both lag and spatial.error are both TRUE

Durbin

default FALSE. If TRUE all the regressors are also spatially lagged. If it is a formula (Durbin = ~ xi + x2), only the variables specified in the formula are lagged.

model

One of "within" or "random". The assumption made on the individual effects

lag

if TRUE a spatial lag of the dependent variable is added to the regression equation

spatial.error

a logic vector. If TRUE the spatial autoregressive error term is added to the model and an estimate for \rho is produced

moments

"initial" (default) defines the set of GM estimator to be used. Alternatives are "weights" and "fullweights" (See Details)

endog

additional endogenous variables. Default NULL. If not NULL should be specified as a formula with no dependent variable (endog = ~ x1 + x2). Note the ~ before the expression.

instruments

external instruments. Default NULL. If not NULL should be specified as a formula with no dependent variable (instruments = ~ x1 + x2). Note the ~ before the expression.

lag.instruments

should the external instruments be spatially lagged?

verbose

default fALSE, If TRUE reports function values during optimization

method

One of "w2sls", "b2sls", "g2sls", "ec2sls". (See Details)

control

a list of control parameters for the optimization

optim.method

default set to "nlminb". or optionally a method passed to optim to use an alternative optimizer.

pars

initial values of the parameter rho and sigmav. The default for rho is to start from a regression of the spatially lagged residuals on the residuals (depending on the model). for sigmav the starting value is the variance of the residuals (again this depends on the model).

Details

The function is a very general interface to estimate various nested specifications of the general model including additional endogenous variables described above. When both spatial.error and lag are FALSE the model reduces to a panel data model with an additional endogeneous variable. The function then uses ivsplm to perform the Instrumental Variables and two-stage least squares for panel data model. method = "w2sls" corresponds to the fixed effects estimator, method = "b2sls" to the between effects model, method = "g2sls" to the GLS random effects model, and method = "ec2sls" to the Baltagi's EC2SLS.

When spatial.error is TRUE and lag is FALSE the model is one with spatially autocorrelated error components. If effects is "random", the Kapoor et al. (2007) GM estimator is performed and the residuals in the first step come from an OLS regression. When moments is "initial", the initial estimator is calculated. This first set of GM estimators is based only on a subset of the moments conditions and assigns equal weigths to each of them. When moments is "fullweights", the second set of GM estimators is calculated. This estimator is based on the full set of moments conditions. It also involves the expression for the variance covariance matrix of the sample moments calculated under the assumption of normally distributed innovations. The calculation of the trace terms in the expression of the variance covariance matrix of the sample moments uses codes from the Matrix package. When moments is"weights", the third set of GM estimator is used. This is motivated by computational issues. The procedure is analogous to the second one but uses a simplified expression for the variance covariance matrix of the sample moments. If effects is "fixed", the initial estimator is a within estimator and the moments conditions of Kapoor et al. (2007) are modified accordingly.

Finally, when both spatial.error and lag are TRUE the complete model is estimated (with or without additional endogenous variables). OLS residuals are no longer consistent because of the spatially lagged dependent variable. If effects is "random", two initial estimators are computed: a within two-stage least squares and a between two stage least squares. The two sets of corresponding residuals are used in the spatial generalized moments estimator (GM) where the moments conditions of Kapoor et al. (2007) are again modified accordingly. If effects is "fixed", the initial estimator is a within two stage least squares estimator and the moments conditions of Kapoor et al. (2007) are modified accordingly.

Note that for the random effects models, \sigma^2_\mu is not reported. \sigma^2_1 is reported instead. However, a value for \sigma^2_\mu can easily be obtained from:

\sigma^2_1 = \sigma^2_\nu + T \sigma^2_\mu

The function also produces an estimate for \theta which is a function of the variance components.

Value

An object of class "splm".

coefficients

GLS coefficients estimate of the model parameters

vcov

the variance covariance matrix of the estimated coefficients

residuals

the GLS residuals

fitted.values

difference between response variable and residuals

sigma2

GLS residuals variance

type

'a description of the model estimated'

rho

a vector including the spatial parameter and the variance components (see Details)

model

the matrix of the data used

call

the call used to create the object

Author(s)

Gianfranco Piras

References

Kapoor, M., Kelejian, H.H. and Prucha, I.R. (2007) Panel data model with spatially correlated error components, Journal of Econometrics, 140, pages 97–130.

Mutl, J., and Pfaffermayr, M. (2011) The Hausman test in a Cliff and Ord panel model, Econometrics Journal, 14, pages 48–76.

Kelejian, H.H. and Prucha, I.R. (1999) A Generalized Moments Estimator for the Autoregressive Parameter in a Spatial Model, International Economic Review, 40, pages 509–533.

Kelejian, H.H. and Prucha, I.R. (1999) A Generalized Spatial Two Stage Least Square Procedure for Estimating a Spatial Autoregressive Model with Autoregressive Disturbances, Journal of Real Estate Finance and Economics, 17, pages 99–121.

Millo, G., Piras, G. (2012) splm: Spatial Panel Data Models in R. Journal of Statistical Software, 47(1), 1–38. URL http://www.jstatsoft.org/v47/i01/.

Examples

library(splm)
library(plm)
data(Produc)
data(usaww)
########SPATIAL LAG MODEL######
#no space no endog: error use plm
## Not run: GM_lag_b2sls <- spgm(log(gsp) ~ log(pcap) + log(pc) + unemp, data=Produc,
                     lag = FALSE, spatial.error = FALSE, method = "b2sls",
                     listw = usaww)
## End(Not run)
#no space but endog 
GM_b2sls_e <- spgm(log(gsp) ~  log(pc) + unemp, data=Produc,
                       lag = FALSE, spatial.error = FALSE, endog = ~ log(pcap),
                       method = "b2sls",
                       instruments = ~log(hwy), listw = usaww)
summary(GM_b2sls_e)
GM_g2sls_e <- spgm(log(gsp) ~  log(pc) + unemp, data=Produc,
                   lag = FALSE, spatial.error = FALSE, endog = ~ log(pcap),
                   method = "g2sls",
                   instruments = ~log(hwy), listw = usaww)
summary(GM_g2sls_e)
GM_ec2sls_e <- spgm(log(gsp) ~  log(pc) + unemp, data=Produc,
                   lag = FALSE, spatial.error = FALSE, endog = ~ log(pcap),
                   method = "ec2sls",
                   instruments = ~log(hwy), listw = usaww)
summary(GM_ec2sls_e)
GM_w2sls_e <- spgm(log(gsp) ~  log(pc) + unemp, data=Produc,
                   lag = FALSE, spatial.error = FALSE, endog = ~ log(pcap),
                   method = "w2sls",
                   instruments = ~log(hwy), listw = usaww)
summary(GM_w2sls_e)
#SPATIAL LAG MODEL 
GM_lag_b2sls <- spgm(log(gsp) ~ log(pcap) + log(pc) + unemp, data=Produc,
           lag = TRUE, spatial.error = FALSE, method = "b2sls",
           listw = usaww)
summary(GM_lag_b2sls)
GM_lag_g2sls <- spgm(log(gsp) ~ log(pcap) + log(pc) + unemp, data=Produc,
           lag = TRUE, spatial.error = FALSE, method = "g2sls",
           listw = usaww)
summary(GM_lag_g2sls)
GM_lag_ec2sls <- spgm(log(gsp) ~ log(pcap) + log(pc) + unemp, data=Produc,
           lag = TRUE, spatial.error = FALSE, method = "ec2sls",
           listw = usaww)
summary(GM_lag_ec2sls)
GM_lag_w2sls <- spgm(log(gsp) ~ log(pcap) + log(pc) + unemp, data=Produc,
           lag = TRUE, spatial.error = FALSE,
           listw = usaww, method = "w2sls")
summary(GM_lag_w2sls)
#endogenous
GM_lag_b2sls_e <- spgm(log(gsp) ~  log(pc) + unemp, data=Produc,
                  lag = TRUE,
                  spatial.error = FALSE, endog = ~ log(pcap),
                  method = "b2sls",
                  instruments = ~log(hwy), listw = usaww)
summary(GM_lag_b2sls_e)
GM_lag_g2sls_e <- spgm(log(gsp) ~  log(pc) + unemp, data=Produc,
                       lag = TRUE,
                       spatial.error = FALSE, endog = ~ log(pcap),
                       method = "g2sls",
                       instruments = ~log(hwy), listw = usaww)
summary(GM_lag_g2sls_e)
GM_lag_ec2sls_e <- spgm(log(gsp) ~  log(pc) + unemp, data=Produc,
                       lag = TRUE,
                       spatial.error = FALSE, endog = ~ log(pcap),
                       method = "ec2sls",
                       instruments = ~log(hwy), listw = usaww)
summary(GM_lag_ec2sls_e)
GM_lag_w2sls_e <- spgm(log(gsp) ~  log(pc) + unemp, data=Produc,
                       lag = TRUE,
                       spatial.error = FALSE, endog = ~ log(pcap),
                       method = "w2sls",
                       instruments = ~log(hwy), listw = usaww)
summary(GM_lag_w2sls_e)

########SPATIAL ERROR MODEL######
GM_error_within <- spgm(log(gsp) ~ log(pcap) + log(pc) + unemp, data=Produc,
                     lag = FALSE, spatial.error = TRUE, model = "within",
                     listw = usaww)
summary(GM_error_within)
GM_error_random <- spgm(log(gsp) ~ log(pcap) + log(pc) + unemp, data=Produc,
                        lag = FALSE, spatial.error = TRUE, model = "random",
                        listw = usaww)
summary(GM_error_random)
GM_error_within_fw <- spgm(log(gsp) ~ log(pcap) + log(pc) + unemp, data=Produc,
                        lag = FALSE, spatial.error = TRUE, model = "within",
                        listw = usaww, moments = "fullweights")
summary(GM_error_within_fw)
GM_error_random_w <- spgm(log(gsp) ~ log(pcap) + log(pc) + unemp, data=Produc,
                        lag = FALSE, spatial.error = TRUE, model = "random",
                        listw = usaww, moments = "fullweights")
summary(GM_error_random_w)
#endogenous
GM_error_within_e <- spgm(log(gsp) ~  log(pc) + unemp, data=Produc,
                        lag = FALSE,
                        spatial.error = TRUE, endog = ~ log(pcap),
                        model = "within",
                        instruments = ~log(hwy), listw = usaww)
summary(GM_error_within_e)
GM_error_random_e <- spgm(log(gsp) ~  log(pc) + unemp, data=Produc,
                       lag = FALSE,
                       spatial.error = TRUE, endog = ~ log(pcap),
                       model = "random",
                       instruments = ~log(hwy), listw = usaww)
summary(GM_error_random_e)

########SARAR MODEL######
GM_sarar_within <- spgm(log(gsp) ~ log(pcap) + log(pc) + unemp, data=Produc,
                        lag = TRUE, spatial.error = TRUE, model = "within",
                        listw = usaww)
summary(GM_sarar_within)
GM_sarar_random <- spgm(log(gsp) ~ log(pcap) + log(pc) + unemp, data=Produc,
                        lag = TRUE, spatial.error = TRUE, model = "random",
                        listw = usaww)
summary(GM_sarar_random)
GM_sarar_within_fw <- spgm(log(gsp) ~ log(pcap) + log(pc) + unemp, data=Produc,
                           lag = TRUE, spatial.error = TRUE, model = "within",
                           listw = usaww, moments = "fullweights")
summary(GM_sarar_within_fw)
GM_sarar_random_fw <- spgm(log(gsp) ~ log(pcap) + log(pc) + unemp, data=Produc,
                          lag = TRUE, spatial.error = TRUE, model = "random",
                          listw = usaww, moments = "fullweights")
summary(GM_sarar_random_fw)
#endogenous
GM_sarar_within_e <- spgm(log(gsp) ~  log(pc) + unemp, data=Produc,
                          lag = TRUE,
                          spatial.error = TRUE, endog = ~ log(pcap),
                          model = "within",
                          instruments = ~log(hwy), listw = usaww)
summary(GM_sarar_within_e)
GM_sarar_random_e <- spgm(log(gsp) ~  log(pc) + unemp, data=Produc,
                          lag = TRUE,
                          spatial.error = TRUE, endog = ~ log(pcap),
                          model = "random",
                          instruments = ~log(hwy), listw = usaww)
summary(GM_sarar_random_e)

Hausman test for spatial panel data models

Description

Hausman specification test for spatial panel data models

Usage

sphtest(x, ...)
## S3 method for class 'formula'
sphtest(x, data, index = NULL, listw,
      spatial.model = c("lag", "error", "sarar"),
      method = c("ML", "GM"), errors = c("KKP", "BSK"),...)
## S3 method for class 'splm'
sphtest(x, x2, ...)

Arguments

x

an object of class formula or splm

x2

an object of class splm

data

an object of class data.frame or pdata.frame. An optional data frame containing the variables in the model. When the obect is a data.frame, the first two columns may contain the indexes. See index

index

if not NULL (default), a character vector to identify the indexes among the columns of the data.frame

listw

an object of class listw created for example by spdep::nb2listw

spatial.model

one of c("lag","error","sarar"), the model to be estimated (only lag, only error, both lag and error dependence)

method

one of c("ML","GM")

errors

one of c("BSK","KPP"). When method is "ML" defines the specification of the innovations

...

additional arguments to be passed

Value

an object of class htest

Author(s)

Gianfranco Piras

References

Millo, G., Piras, G. (2012) splm: Spatial Panel Data Models in R. Journal of Statistical Software, 47(1), 1–38. URL http://www.jstatsoft.org/v47/i01/.

See Also

spgm

Examples

data(Produc, package="plm")
data(usaww)
fm <- log(gsp)~log(pcap)+log(pc)+log(emp)+unemp
test1<-sphtest(fm,data=Produc, listw = spdep::mat2listw(usaww),
                spatial.model = "error", method="GM")
test1
mod1<- spgm(fm, data=Produc, listw = usaww, model = "random",
             spatial.error = TRUE, moments="fullweights")
mod2<- spgm(fm, data=Produc, listw = usaww, model = "within",
             spatial.error = TRUE)
test2<-sphtest(mod1, mod2)
test2

Spatial Panel Model by Maximum Likelihood

Description

Maximum likelihood (ML) estimation of spatial panel models, possibly with fixed or random effects.

Usage

spml(formula, data, index=NULL, listw, listw2=listw, na.action,
                 model=c("within","random","pooling"),
                 effect=c("individual","time","twoways"),
                 lag=FALSE, spatial.error=c("b","kkp","none"),
                 ...)
## S3 method for class 'splm_ML'
impacts(obj, listw = NULL,
                         time = NULL, ...,
                         tr = NULL, R = 200,
                         type = "mult",
                         empirical = FALSE, Q = NULL)
## S3 method for class 'splm_GM'
impacts(obj, ..., tr=NULL, 
                            R=NULL, listw=NULL,
                            type = "mult",
                            time = NULL,
                            evalues=NULL, tol=1e-6, 
                            empirical=FALSE, Q=NULL, 
                            KPformula = FALSE, prt = TRUE)

Arguments

formula

a symbolic description of the model to be estimated

data

an object of class data.frame or pdata.frame. A data frame containing the variables in the model. When the object is a data.frame, the first two columns shall contain the indexes, unless otherwise specified. See index

index

if not NULL (default), a character vector to identify the indexes among the columns of the data.frame

listw

an object of class listw or a matrix. It represents the spatial weights to be used in estimation.

listw2

an object of class listw or a matrix. Second of set spatial weights for estimation, if different from the first (e.g., in a 'sarar' model).

na.action

see spdep for more details.

model

one of c("within", "random", "pooling").

effect

one of c("individual","time","twoways"); the effects introduced in the model.

lag

default=FALSE. If TRUE, a spatial lag of the dependent variable is added.

spatial.error

one of c("b","kkp","none"). The type of spatial error in the specification, if any. See details.

...

additional argument to pass over to other functions

obj

fitted model object

time

??time??

tr

A vector of traces of powers of the spatial weights matrix created using 'trW', for approximate impact measures

R

If given, simulations are used to compute distributions for the impact measures, returned as 'mcmc' objects

type

Either "mult" (default) for powering a sparse matrix (with moderate or larger N, the matrix becomes dense, and may lead to swapping), or "MC" for Monte Carlo simulation of the traces (the first two simulated traces are replaced by their analytical equivalents), or "moments" to use the looping space saving algorithm proposed by Smirnov and Anselin (2009) - for "moments", 'W' must be symmetric, for row-standardised weights through a similarity transformation

empirical

Argument passed to 'mvrnorm' (default FALSE)

Q

default NULL, else an integer number of cumulative power series impacts to calculate if 'tr' is given

evalues

vector of eigenvalues of spatial weights matrix for impacts calculations

tol

Argument passed to 'mvrnorm'

KPformula

not yet implemented

prt

not yet implemented

Details

The models are estimated by two-step Maximum Likelihood. Further optional parameters to be passed on to the estimator may be: pvar: if TRUE the pvar function is called hess: if TRUE use numerical Hessian instead of GLS for the standard errors of the estimates quiet: if FALSE report function and parameters values during optimization initval: one of c("zeros", "estimate"), the initial values for the parameters. If "zeros" a vector of zeros is used. if "estimate" the initial values are retreived from the estimation of the nested specifications. Alternatively, a numeric vector can be specified. x.tol: Tolerance. See nlminb for details. rel.tol: Relative tolerance. See nlminb for details.

Value

An object of class "splm".

coefficients

coefficients estimate of the model parameters

arcoef

the coefficient for the spatial lag on y

errcomp

the estimates of the error variance components

vcov

the asymptotic variance covariance matrix of the estimated coefficients

vcov.arcoef

the asymptotic variance of the estimated spatial lag parameter

vcov.errcomp

the asymptotic variance covariance matrix of the estimated error covariance parameters

type

'random effects ML'

residuals

the model residuals

fitted.values

the fitted values, calculated as \hat{y}=X \hat{\beta}

sigma2

GLS residuals variance

model

the matrix of the data used

call

the call used to create the object

logLik

the value of the log likelihood function at the optimum

errors

the value of the errors argument

Author(s)

Giovanni Millo

References

Baltagi, B.H., Song, S.H., Jung B. and Koh, W. (2007) Testing panel data regression models with spatial and serial error correlation. Journal of Econometrics, 140, 5-51.

Millo, G., Piras, G. (2012) splm: Spatial Panel Data Models in R. Journal of Statistical Software, 47(1), 1–38. URL http://www.jstatsoft.org/v47/i01/.

See Also

spgm

Examples

data(Produc, package = "plm")
data(usaww)
fm <- log(gsp) ~ log(pcap) + log(pc) + log(emp) + unemp
## the two standard specifications (SEM and SAR) one with FE
## and the other with RE:
## fixed effects panel with spatial errors
fespaterr <- spml(fm, data = Produc, listw = spdep::mat2listw(usaww),
                   model="within", spatial.error="b", Hess = FALSE)
summary(fespaterr)
## random effects panel with spatial lag
respatlag <- spml(fm, data = Produc, listw = spdep::mat2listw(usaww),
                   model="random", spatial.error="none", lag=TRUE)
summary(respatlag)
## calculate impact measures
#impac1 <- impacts.splm(respatlag, listw = spdep::mat2listw(usaww, #style = "W"), time = 17)
#summary(impac1, zstats=TRUE, short=TRUE)

Spatial Panel Model with Random Effects by Maximum Likelihood

Description

Maximum likelihood (ML) estimation of spatial panel models with random effects and serial error correlation.

Usage

spreml(formula, data, index = NULL, w, w2=w, lag = FALSE,
          errors = c("semsrre", "semsr", "srre", "semre",
                     "re", "sr", "sem","ols", "sem2srre",
                     "sem2re", "semgre"),
          pvar = FALSE, hess = FALSE, quiet = TRUE,
          initval = c("zeros", "estimate"),
          x.tol = 1.5e-18, rel.tol = 1e-15, ...)

Arguments

formula

a symbolic description of the model to be estimated

data

an object of class data.frame or pdata.frame. A data frame containing the variables in the model. When the object is a data.frame, the first two columns shall contain the indexes, unless otherwise specified. See index

index

if not NULL (default), a character vector to identify the indexes among the columns of the data.frame

w

an object of class listw or a matrix. It represents the spatial weights to be used in estimation.

w2

an object of class listw or a matrix. Second set of spatial weights for estimation, if different from the first (e.g., in a 'sarar' model).

lag

default=FALSE. If TRUE, a spatial lag of the dependent variable is added.

errors

Specifies the error covariance structure. See details.

pvar

legacy parameter here only for compatibility.

hess

default=FALSE. If TRUE estimate the covariance for beta_hat by numerical Hessian instead of GLS at optimal values.

quiet

default=TRUE. If FALSE, report function and parameters values during optimization.

initval

one of c("zeros", "estimate"), the initial values for the parameters. If "zeros" a vector of zeros is used. if "estimate" the initial values are retreived from the estimation of the nested specifications. Alternatively, a numeric vector can be specified.

x.tol

control parameter for tolerance. See nlminb for details.

rel.tol

control parameter for relative tolerance. See nlminb for details.

...

additional arguments to pass over to other functions, e.g. method.

Details

Second-level wrapper for estimation of random effects models with serial and spatial correlation. The specifications without serial correlation (no "sr" in errors) can be called through spml, the extended ones only through spreml. The models are estimated by two-step Maximum Likelihood. Abbreviations in errors correspond to: "sem" Anselin-Baltagi type spatial autoregressive error: if present, random effects are not spatially correlated; "sem2" Kapoor, Kelejian and Prucha-type spatial autoregressive error model with spatially correlated random effects; "sr" serially correlated remainder errors; "re" random effects; "ols" spherical errors (usually combined with lag=T). The optimization method can be passed on as optional parameter. Default is "nlminb"; all constrained optimization methods from maxLik are allowed ("BFGS", "NM", "SANN") but the latter two are still experimental.

Value

An object of class "splm".

coefficients

coefficients estimate of the model parameters

arcoef

the coefficient for the spatial lag on y

errcomp

the estimates of the error variance components

vcov

the asymptotic variance covariance matrix of the estimated coefficients

vcov.arcoef

the asymptotic variance of the estimated spatial lag parameter

vcov.errcomp

the asymptotic variance covariance matrix of the estimated error covariance parameters

type

'random effects ML'

residuals

the model residuals

fitted.values

the fitted values, calculated as \hat{y}=X \hat{\beta}

sigma2

GLS residuals variance

model

the matrix of the data used

call

the call used to create the object

logLik

the value of the log likelihood function at the optimum

errors

the value of the errors argument

Author(s)

Giovanni Millo

References

Millo, G. (2014) Maximum likelihood estimation of spatially and serially correlated panels with random effects. Computational Statistics and Data Analysis, 71, 914–933.

See Also

spml

Examples

data(Produc, package = "plm")
data(usaww)
fm <- log(gsp) ~ log(pcap) + log(pc) + log(emp) + unemp
## random effects panel with spatial lag and serial error correlation
## optimization method set to "BFGS"
sarsrmod <- spreml(fm, data = Produc, w = usaww, errors="sr", lag=TRUE,
                    method="BFGS")
summary(sarsrmod)

summary method for class splm

Description

Method for summarizing the results of objects of class 'splm'

Usage


## S3 method for class 'splm'
summary(object,...)

Arguments

object

an object of class 'splm'

...

additional arguments to be passed

Details

The summary function summary.splm returns an objects of class 'splm' organized in a coefficient matrix.

Also a matrix for the error components, or the spatial coefficients will be generated depending on the estimated model.

When the 'splm' is produced by the function 'spsegm', the summary will be generated looping over the number of equations in the system.

Value

An object of class 'summary.splm'

Author(s)

Giovanni Millo, Gianfranco Piras

See Also

spml, spgm

Examples

data(Produc, package = "plm") 
data(usaww)
GM <- spgm(log(gsp)~log(pcap)+log(pc)+log(emp)+unemp, data=Produc,
            listw=usaww, moments = "fullweights", spatial.error = TRUE)
summary(GM)

Spatial weights matrix - US states

Description

Spatial weights matrix of the 48 continental US States based on the queen contiguity criterium.

Usage

data(usaww)

Format

A matrix with elements different from zero if state i and j are neighbors. Weights are row standardized. According to the queen contiguity criterium, Arizona and Colorado are considered neighbours.

Author(s)

Giovanni Millo

Covariance extractor method for splm objects

Description

Covariance extractor method for splm objects. Seldom used as such but needed, e.g., for interoperability with testing functions in lmtest and car.

Usage

## S3 method for class 'splm'
vcov(object, ...)

Arguments

object

an object of class splm

...

additional arguments to be passed; currently not used

Value

a covariance matrix of beta coefficients

Author(s)

Giovanni Millo

References

Zeileis, A. (2006) Object-Oriented Computation of Sandwich Estimators. Journal of Statistical Software, 16(9), 1-16.

Examples

## not run:
## data(Produc, package="plm")
## data(usaww)
## fm <- log(gsp)~log(pcap)+log(pc)+log(emp)+unemp
## sarremod <- spml(fm, data=Produc, listw = spdep::mat2listw(usaww),
##  model="random", lag=TRUE, spatial.error="none")
## ## compact representation of betas
## library(lmtest)
## coeftest(sarremod)
## ## linear hypothesis test
## library(car)
## lht(sarremod, "log(pcap)=log(pc)")