prais implements the Prais-Winsten estimator for models with strictly
exogenous regressors and AR(1) serial correlation of the errors.
install.packages("prais")# install.packages("devtools")
devtools::install_github("franzmohr/prais")# Load the package
library(prais)
# Load the data
data("barium")
pw <- prais_winsten(lchnimp ~ lchempi + lgas + lrtwex + befile6 + affile6 + afdec6,
data = barium, index = "t")## Iteration 0: rho = 0
## Iteration 1: rho = 0.2708
## Iteration 2: rho = 0.291
## Iteration 3: rho = 0.293
## Iteration 4: rho = 0.2932
## Iteration 5: rho = 0.2932
## Iteration 6: rho = 0.2932
## Iteration 7: rho = 0.2932
summary(pw)##
## Call:
## prais_winsten(formula = lchnimp ~ lchempi + lgas + lrtwex + befile6 +
## affile6 + afdec6, data = barium, index = "t")
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.99386 -0.32219 0.03748 0.40226 1.50282
##
## AR(1) coefficient rho after 7 iterations: 0.2932
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -37.07582 22.77843 -1.628 0.1061
## lchempi 2.94096 0.63284 4.647 8.46e-06 ***
## lgas 1.04630 0.97734 1.071 0.2864
## lrtwex 1.13277 0.50666 2.236 0.0272 *
## befile6 -0.01648 0.31938 -0.052 0.9589
## affile6 -0.03316 0.32181 -0.103 0.9181
## afdec6 -0.57681 0.34199 -1.687 0.0942 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5733 on 124 degrees of freedom
## Multiple R-squared: 0.2021, Adjusted R-squared: 0.1635
## F-statistic: 5.235 on 6 and 124 DF, p-value: 7.764e-05
##
## Durbin-Watson statistic (original): 1.458
## Durbin-Watson statistic (transformed): 2.087
library(lmtest)
coeftest(pw, vcov. = vcovHC(pw, "HC1"))##
## t test of coefficients:
##
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -37.075825 20.897425 -1.7742 0.07849 .
## lchempi 2.940963 0.599549 4.9053 2.866e-06 ***
## lgas 1.046299 0.925151 1.1309 0.26026
## lrtwex 1.132774 0.495127 2.2878 0.02384 *
## befile6 -0.016478 0.327779 -0.0503 0.95999
## affile6 -0.033158 0.277297 -0.1196 0.90501
## afdec6 -0.576811 0.422552 -1.3651 0.17470
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Estimate a panel model, for which PCSE should be obtained.
# Example 2 in the documentation of Stata function xtpcse
# Load data
data <- haven::read_dta("http://www.stata-press.com/data/r14/grunfeld.dta")
# Estimate
x <- prais_winsten(invest ~ mvalue + kstock, data = data, index = c("company", "year"),
twostep = TRUE, panelwise = TRUE, rhoweight = "T1")
# Results
summary(x)##
## Call:
## prais_winsten(formula = invest ~ mvalue + kstock, data = data,
## index = c("company", "year"), twostep = TRUE, panelwise = TRUE,
## rhoweight = "T1")
##
## Residuals:
## Min 1Q Median 3Q Max
## -305.52 -42.61 4.15 33.23 343.52
##
## AR(1) coefficient rho after 1 iterations: 0.906
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -39.125687 26.362285 -1.484 0.139
## mvalue 0.095016 0.007683 12.367 < 2e-16 ***
## kstock 0.306005 0.036630 8.354 1.17e-14 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 42.41 on 197 degrees of freedom
## Multiple R-squared: 0.5468, Adjusted R-squared: 0.5422
## F-statistic: 118.8 on 2 and 197 DF, p-value: < 2.2e-16
##
## Durbin-Watson statistic (original): 0.2097
## Durbin-Watson statistic (transformed): 1.473
Obtain PCSE by using only those residuals from periods that are common
to all panels by setting pairwise = FALSE.
coeftest(x, vcov. = vcovPC(x, pairwise = FALSE))##
## t test of coefficients:
##
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -39.125687 30.503546 -1.2827 0.2011
## mvalue 0.095016 0.012993 7.3126 6.434e-12 ***
## kstock 0.306005 0.060372 5.0687 9.202e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Obtain PCSE by using all observations that can be matched by period
between two panels by setting pairwise = TRUE.
coeftest(x, vcov. = vcovPC(x, pairwise = TRUE))##
## t test of coefficients:
##
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -39.125687 30.503546 -1.2827 0.2011
## mvalue 0.095016 0.012993 7.3126 6.434e-12 ***
## kstock 0.306005 0.060372 5.0687 9.202e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Beck, N. L. and Katz, J. N. (1995): What to do (and not to do) with time-series cross-section data. American Political Science Review 89, 634-647.
Prais, S. J. and Winsten, C. B. (1954): Trend Estimators and Serial Correlation. Cowles Commission Discussion Paper, 383 (Chicago).
Wooldridge, J. M. (2016). Introductory Econometrics. A Modern Approach. 6th ed. Mason, OH: South-Western Cengage Learning.