空间面板数据分析--R的splm包

空间面板数据分析——R 的splm 包

（任建辉，暨南大学）

The package provides methods for fitting spatial panel data by maximum likelihood and GM.

安装R 软件及其编辑器Rstudio

网址：

下载好Rstudio 以后，操作都可以Rstudio 中完成了，包括命令的编写、命令运行、图形展示，最方便的要数查看数据了。

R 界面

Rstudio 界面，形如

matlab

下面进入正题，了解splm 包中的数据、命令及结果展示。所有命令都写在编辑窗口（studio 左上区域），可以单独的运行每行命令，也可选取一段一起执行，点run 按钮。

1、首先，安装splm 包并导入，命令如下:

intall.packages(“splm ”) ，选择最近的下载点

library(splm)

> library(splm)

载入需要的程辑包：MASS

载入需要的程辑包：nlme

载入需要的程辑包：spdep

载入需要的程辑包：sp

载入需要的程辑包：Matrix

载入需要的程辑包：plm

载入需要的程辑包：bdsmatrix

载入程辑包：‘bdsmatrix’

下列对象被屏蔽了from ‘package:base’:

backsolve

载入需要的程辑包：Formula

载入需要的程辑包：sandwich

载入需要的程辑包：zoo

载入程辑包：‘zoo’

下列对象被屏蔽了from ‘package:base’:

as.Date, as.Date.numeric

载入需要的程辑包：spam

载入需要的程辑包：grid Spam version 0.40-0 (2013-09-11) is loaded. Type 'help( Spam)' or 'demo( spam)' for a short introduction and overview of this package. Help for individual functions is also obtained by adding the

suffix '.spam' to the function name, e.g. 'help( chol.spam)'.

载入程辑包：‘spam’

下列对象被屏蔽了from ‘package:bdsmatrix’:

backsolve

下列对象被屏蔽了from ‘package:base’:

backsolve, forwardsolve

载入需要的程辑包：ibdreg

载入需要的程辑包：car

载入需要的程辑包：lmtest

载入需要的程辑包：Ecdat

载入程辑包：‘Ecdat’

下列对象被屏蔽了from ‘package:car’:

Mroz

下列对象被屏蔽了from ‘package:nlme’:

Gasoline

下列对象被屏蔽了from ‘package:MASS’:

SP500

下列对象被屏蔽了from ‘package:datasets’:

Orange

载入需要的程辑包：maxLik

载入需要的程辑包：miscTools Please cite the 'maxLik' package as: Henningsen, Arne and Toomet, Ott (2011). maxLik: A package for maximum likelihood estimation in R. Computational Statistics 26(3), 443-458. DOI 10.1007/s00180-010-0217-1. If you have questions, suggestions, or comments regarding the 'maxLik' package, please use a forum or 'tracker' at maxLik's R-Forge site: https://r-forge.r-project.org/projects/maxlik/ Warning message:

程辑包‘Matrix’是用R 版本3.0.3 来建造的

注意：在导入splm 时，如果发现还有其他配套的包没有安装，需要先安装。

2、接着，查看数据及结构，命令如下：

data(Produc,package=”Ecdat ”)

View(Produc)

3、引入空间权重矩阵（spatial weights matrix），命令如下

data(usaww)

Views(usaww)

4、空间面板数据的广义矩估计，命令spgm

listw=usaww, moments=”fullweights ”, spatial.error=TRUE)

summary(GM)

> GM

+ listw=usaww,moments="fullweights",spatial.error=TRUE)

> summary(GM)

Spatial panel fixed effects GM model Call: spgm(formula = log(gsp) ~ log(pcap) + log(pc) + log(emp) + unemp, data = Produc, listw = usaww, spatial.error = TRUE, moments = "fullweights") Residuals: Min. 1st Qu. Median 3rd Qu. Max.

-0.14000 -0.01950 -0.00316 0.01530 0.16800 Estimated spatial coefficient, variance components and theta: Estimate rho 0.3277625

sigma^2_v 0.0012179 Coefficients: Estimate Std. Error t-value Pr(>|t|) log(pcap) -0.0022435 0.0262646 -0.0854 0.9319295 log(pc) 0.2414979 0.0235826 10.2405

Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

5、空间面板极大似然估计，命令spml

## fixed effects panel with spatial errors

Fespaterr

spatial.error=”b ”,hess=FALSE)

summary(Fespaterr)

> fm

> Fespaterr

> summary(Fespaterr)

Spatial panel fixed effects error model Call: spml(formula = fm, data = Produc, listw = mat2listw(usaww), model = "within", spatial.error = "b", hess = FALSE) Residuals: Min. 1st Qu. Median 3rd Qu. Max.

-0.1250 -0.0238 -0.0035 0.0171 0.1880 Coefficients: Estimate Std. Error t-value Pr(>|t|) rho 0.5574013 0.0329554 16.9138

S ignif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

##random effects panal with spatial lag

Respatlag

spatial.error=”none ”,lag=TRUE)

summary(Respatlag)

> Respatlag

> summary(Respatlag)

Spatial panel random effects ML model Call: spreml(formula = formula, data = data, index = index, w = listw2mat(listw), w2 = listw2mat(listw2), lag = lag, errors = errors, cl = cl) Residuals: Min. 1st Qu. Median Mean 3rd Qu. Max.

1.38 1.57 1.70 1.70 1.80 2.13 Error variance parameters: Estimate Std. Error t-value Pr(>|t|)

phi 21.3175 8.3017 2.5678 0.01023 *

Spatial autoregressive coefficient:

Estimate Std. Error t-value Pr(>|t|)

lambda 0.161615 0.029099 5.554 2.793e-08 *** Coefficients: Estimate Std. Error t-value Pr(>|t|) (Intercept) 1.65814995 0.15071855 11.0016

S ignif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

6、伴有随机效应和序列误差相关的空间面板模型的极大似然估计，命令speml

##random effects panel with spatial lag and serial error correlation

##optimization method set to “BFGS “

Sarsrmod

summary(Sarsrmod)

> Sarsrmod summary(Sarsrmod)

Spatial panel random effects ML model Call: spreml(formula = fm, data = Produc, w = usaww, lag = TRUE, errors = "sr", method = "BFGS") Residuals: Min. 1st Qu. Median Mean 3rd Qu. Max.

2.66 3.02 3.18 3.18 3.31 3.77 Error variance parameters: Estimate Std. Error t-value Pr(>|t|)

psi 0.99726353 0.00082138 1214.1 |t|)

lambda 0.302942 0.030376 9.973 |t|) (Intercept) 1.23670293 0.22777554 5.4295 5.652e-08 ***

log(pcap) 0.08257977 0.03617371 2.2829 0.02244 *

log(pc) 0.01509919 0.01977324 0.7636 0.44510 log(emp) 0.73882021 0.02934144 25.1801

Signi f. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

7、模型检验

（1）bsjktest ，Baltigi,Song,Jung, and Koh LM test for spatial panels

> bsjktest(fm, data=Produc, listw = usaww, test="C.1")

data: log(gsp) ~ log(pcap) + log(pc) + log(emp) + unemp LM = 0.2617, df = 1, p-value = 0.609 alternative hypothesis: spatial dependence in error terms, sub RE and serial corr.

Baltagi, Song, Jung and Koh C.1 conditional test （2）bsktest ，Baltigi,Song and Koh LM test for spatial panels

> bsktest(fm,data=Produc, listw = mat2listw(usaww),

+ test="LM1", standardize=TRUE)

data: log(gsp) ~ log(pcap) + log(pc) + log(emp) + unemp SLM1 = 0.083, p-value = 0.9338

alternative hypothesis: Random effects

Baltagi, Song and Koh SLM1 marginal test （3）Covariance extractor method for splm objects

> sarremod

> library(lmtest)

> coeftest(sarremod)

z test of coefficients: Estimate Std. Error z value Pr(>|z|) (Intercept) 1.65814995 0.15071855 11.0016

log(emp) 0.67081075 0.02642113 25.3892

unemp -0.00579716 0.00089175 -6.5009 7.984e-11 *** ---

Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

> library(car)

> lht(sarremod,"log(pcap)=log(pc)")

Linear hypothesis test Hypothesis:

log(pcap) - log(pc) = 0 Model 1: restricted model Model 2: function (x, ...)

UseMethod("formula") Df Chisq Pr(>Chisq) 1 2 1 36.268 1.719e-09 *** ---

Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

(更多详情请查看splm 的help 文档以及文后列的参考文献)

参考文献

1.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

2.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

3.Millo,G.,Piras,G.(2012) splm:Spatial Panel Data Models in R. Journal of Statistical Software,47(1),1-38.URL

4.Elhorst, J.P (2003) Specification and estimation of spatial panel data models, International

Regional Science Review,26,pages 244-268

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

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

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

8.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

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

10.Kelejian,H.H. and Prucha,I.R.(1999) A Generalied Moments Estimator for the Autoregressive Parameter in a Spatial Model, International Economic Reviews,40, pages509-533

11. Kelejian,H.H. and Prucha,I.R.(1999) A Generalied Spatial Two Stage Least Square Procedure for Estimating a Spatial Autoregressive Model with Autoregressive Disturbances,Journal of Real Estate Finance and Economics,17,pages99-122

12.Millo,G.(2013) Maximum likelihood estimation of spatially and serially correlated panel with random effects. Computational Statistics and Data Analysis, forthcoming.

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