prais

Overview

prais implements the Prais-Winsten estimator for models with strictly exogenous regressors and AR(1) serial correlation of the errors.

Installation

CRAN

install.packages("prais")

Development version

# install.packages("devtools")
devtools::install_github("franzmohr/prais")

Usage

# Load the package
library(prais)

# Load the data
# install.packages("wooldridge")
library(wooldridge)
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  0.03747  0.40226  1.50281 
## 
## AR(1) coefficient rho after 7 iterations: 0.2932
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -37.07770   22.77830  -1.628   0.1061    
## lchempi       2.94095    0.63284   4.647 8.46e-06 ***
## lgas          1.04638    0.97734   1.071   0.2864    
## lrtwex        1.13279    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

Robust standard errors

White’s estimator

library(lmtest)

coeftest(pw, vcov. = vcovHC(pw, "HC1"))

## 
## t test of coefficients:
## 
##               Estimate Std. Error t value  Pr(>|t|)    
## (Intercept) -37.077704  20.897126 -1.7743   0.07847 .  
## lchempi       2.940949   0.599551  4.9053 2.867e-06 ***
## lgas          1.046380   0.925137  1.1311   0.26021    
## lrtwex        1.132791   0.495130  2.2879   0.02384 *  
## befile6      -0.016479   0.327779 -0.0503   0.95998    
## affile6      -0.033156   0.277298 -0.1196   0.90502    
## afdec6       -0.576812   0.422553 -1.3651   0.17470    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Panel-corrected standard errors (PCSE)

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

References

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.