A, Kết nối data
library(readxl)
setwd("d:/DATA2021/ThuySan.VECM/data5.5.21")
solieu <-read_excel("data.ca.5.5.21.xlsx")
congthuc1 <-LnGDP ~ LnFEX + LnLAB + REER + LnOPEN + LnFDI
congthuc3 <-LnFGDP ~ LnFEX + LnLAB + REER + LnOPEN + LnFDI
lm(data=solieu,congthuc1) -> hoiquy1
library(dynlm)
## Loading required package: zoo
##
## Attaching package: 'zoo'
## The following objects are masked from 'package:base':
##
## as.Date, as.Date.numeric
hoiquy2 <-dynlm(data=solieu,congthuc1)
summary(hoiquy1)
##
## Call:
## lm(formula = congthuc1, data = solieu)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.210940 -0.058072 0.003733 0.039472 0.269841
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 23.35330 4.89950 4.766 9.14e-06 ***
## LnFEX 0.40039 0.06716 5.962 7.86e-08 ***
## LnLAB -2.96920 0.63490 -4.677 1.28e-05 ***
## REER -1.00061 0.53801 -1.860 0.06688 .
## LnOPEN 0.53708 0.08649 6.210 2.81e-08 ***
## LnFDI 0.13661 0.04067 3.359 0.00124 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.09556 on 74 degrees of freedom
## Multiple R-squared: 0.9455, Adjusted R-squared: 0.9418
## F-statistic: 256.6 on 5 and 74 DF, p-value: < 2.2e-16
summary(hoiquy2)
##
## Time series regression with "numeric" data:
## Start = 1, End = 80
##
## Call:
## dynlm(formula = congthuc1, data = solieu)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.210940 -0.058072 0.003733 0.039472 0.269841
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 23.35330 4.89950 4.766 9.14e-06 ***
## LnFEX 0.40039 0.06716 5.962 7.86e-08 ***
## LnLAB -2.96920 0.63490 -4.677 1.28e-05 ***
## REER -1.00061 0.53801 -1.860 0.06688 .
## LnOPEN 0.53708 0.08649 6.210 2.81e-08 ***
## LnFDI 0.13661 0.04067 3.359 0.00124 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.09556 on 74 degrees of freedom
## Multiple R-squared: 0.9455, Adjusted R-squared: 0.9418
## F-statistic: 256.6 on 5 and 74 DF, p-value: < 2.2e-16
B, Kiểm định
1. The Breusch-Pagan Test
library(lmtest)
bptest(hoiquy1)
##
## studentized Breusch-Pagan test
##
## data: hoiquy1
## BP = 11.791, df = 5, p-value = 0.03776
bptest(hoiquy2)
##
## studentized Breusch-Pagan test
##
## data: hoiquy2
## BP = 11.791, df = 5, p-value = 0.03776
library("skedastic") # Không hỗ trợ dynlm
## Warning: package 'skedastic' was built under R version 4.0.5
breusch_pagan(hoiquy1)
## # A tibble: 1 x 5
## statistic p.value parameter method alternative
## <dbl> <dbl> <dbl> <chr> <chr>
## 1 11.8 0.0378 5 Koenker (studentised) greater
library(car)
## Loading required package: carData
ncvTest(hoiquy1)
## Non-constant Variance Score Test
## Variance formula: ~ fitted.values
## Chisquare = 14.97445, Df = 1, p = 0.00010898
library("olsrr")
## Warning: package 'olsrr' was built under R version 4.0.5
##
## Attaching package: 'olsrr'
## The following object is masked from 'package:datasets':
##
## rivers
ols_test_breusch_pagan(hoiquy1)
##
## Breusch Pagan Test for Heteroskedasticity
## -----------------------------------------
## Ho: the variance is constant
## Ha: the variance is not constant
##
## Data
## ---------------------------------
## Response : LnGDP
## Variables: fitted values of LnGDP
##
## Test Summary
## -------------------------------
## DF = 1
## Chi2 = 14.97445
## Prob > Chi2 = 0.0001089765
ols_test_breusch_pagan(hoiquy1, rhs = TRUE, multiple = TRUE)
##
## Breusch Pagan Test for Heteroskedasticity
## -----------------------------------------
## Ho: the variance is constant
## Ha: the variance is not constant
##
## Data
## ----------------------------------------
## Response : LnGDP
## Variables: LnFEX LnLAB REER LnOPEN LnFDI
##
## Test Summary (Unadjusted p values)
## ---------------------------------------------------
## Variable chi2 df p
## ---------------------------------------------------
## LnFEX 13.05466741 1 0.0003025296
## LnLAB 10.40351041 1 0.0012577598
## REER 0.05259098 1 0.8186145835
## LnOPEN 12.48558439 1 0.0004101044
## LnFDI 8.83139845 1 0.0029609140
## ---------------------------------------------------
## simultaneous 16.12819970 5 0.0064874316
## ---------------------------------------------------
2. Goldfeld-Quandt Test
gqtest(hoiquy2)
##
## Goldfeld-Quandt test
##
## data: hoiquy2
## GQ = 2.8686, df1 = 34, df2 = 34, p-value = 0.001423
## alternative hypothesis: variance increases from segment 1 to 2
goldfeld_quandt(hoiquy1)
## # A tibble: 1 x 5
## statistic p.value parameter method alternative
## <dbl> <dbl> <int> <chr> <chr>
## 1 17.5 0.00000000619 20 Goldfeld-Quandt F Test greater
3. Vẽ đồ thị
hetplot(hoiquy1)
4. White test
white_lm(hoiquy1)
## # A tibble: 1 x 5
## statistic p.value parameter method alternative
## <dbl> <dbl> <dbl> <chr> <chr>
## 1 20.2 0.0271 10 White's Test greater
library(tseries)
## Registered S3 method overwritten by 'quantmod':
## method from
## as.zoo.data.frame zoo
C, Khác phục
1. Khắc phục Box-Cox transformation
library(caret)
## Warning: package 'caret' was built under R version 4.0.5
## Loading required package: lattice
## Loading required package: ggplot2
head(solieu)
## # A tibble: 6 x 9
## STT QUY LnGDP LnFGDP LnFEX LnLAB REER LnOPEN LnFDI
## <dbl> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 1 2000q1 12.3 7.20 19.5 10.6 0.996 22.6 10.3
## 2 2 2000q2 12.6 7.46 19.8 10.6 1.00 22.7 10.6
## 3 3 2000q3 12.5 7.39 19.7 10.6 1.01 22.7 10.5
## 4 4 2000q4 12.7 7.59 19.9 10.6 1.01 22.9 10.7
## 5 5 2001q1 12.4 7.32 19.7 10.6 0.993 22.6 10.5
## 6 6 2001q2 12.6 7.55 20.0 10.6 0.999 22.8 10.7
bienchon <-solieu[,3]
bieny <-data.frame(bienchon)
preProcess(bieny, method=c("BoxCox")) -> biendoi
biendoi
## Created from 80 samples and 1 variables
##
## Pre-processing:
## - Box-Cox transformation (1)
## - ignored (0)
##
## Lambda estimates for Box-Cox transformation:
## -0.3
bienphuthuoc <- predict(biendoi,bieny) # thực hiện box-cox dữ liệu
head(bienphuthuoc)
## LnGDP
## 1 1.764175
## 2 1.773697
## 3 1.771170
## 4 1.778657
## 5 1.766982
## 6 1.775728
solieu2 <-cbind(solieu,bienphuthuoc)
head(solieu2)
## STT QUY LnGDP LnFGDP LnFEX LnLAB REER LnOPEN LnFDI
## 1 1 2000q1 12.32272 7.204922 19.51234 10.55482 0.9962832 22.62871 10.34393
## 2 2 2000q2 12.57529 7.457496 19.76492 10.56007 0.9997200 22.73124 10.59650
## 3 3 2000q3 12.50762 7.389821 19.69724 10.56939 1.0071360 22.71304 10.52882
## 4 4 2000q4 12.70953 7.591730 19.89915 10.55959 1.0072360 22.87906 10.73074
## 5 5 2001q1 12.39648 7.320969 19.72526 10.58206 0.9931406 22.57954 10.45481
## 6 6 2001q2 12.63004 7.554526 19.95881 10.58733 0.9989467 22.81070 10.68836
## LnGDP
## 1 1.764175
## 2 1.773697
## 3 1.771170
## 4 1.778657
## 5 1.766982
## 6 1.775728
library(tidyverse)
## -- Attaching packages ---------------------------------------------------------------------------------------------------------- tidyverse 1.3.0 --
## v tibble 3.0.1 v dplyr 1.0.0
## v tidyr 1.1.0 v stringr 1.4.0
## v readr 1.3.1 v forcats 0.5.0
## v purrr 0.3.4
## -- Conflicts ------------------------------------------------------------------------------------------------------------- tidyverse_conflicts() --
## x dplyr::filter() masks stats::filter()
## x dplyr::lag() masks stats::lag()
## x purrr::lift() masks caret::lift()
## x dplyr::recode() masks car::recode()
## x purrr::some() masks car::some()
solieu3 <- solieu2 %>% select(1,2,4,5,6,7,8,9,10 )
head(solieu3)
## STT QUY LnFGDP LnFEX LnLAB REER LnOPEN LnFDI LnGDP
## 1 1 2000q1 7.204922 19.51234 10.55482 0.9962832 22.62871 10.34393 1.764175
## 2 2 2000q2 7.457496 19.76492 10.56007 0.9997200 22.73124 10.59650 1.773697
## 3 3 2000q3 7.389821 19.69724 10.56939 1.0071360 22.71304 10.52882 1.771170
## 4 4 2000q4 7.591730 19.89915 10.55959 1.0072360 22.87906 10.73074 1.778657
## 5 5 2001q1 7.320969 19.72526 10.58206 0.9931406 22.57954 10.45481 1.766982
## 6 6 2001q2 7.554526 19.95881 10.58733 0.9989467 22.81070 10.68836 1.775728
hoiquy3 <-lm(data=solieu3,congthuc1)
summary(hoiquy3)
##
## Call:
## lm(formula = congthuc1, data = solieu3)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.0074671 -0.0019219 0.0001459 0.0014695 0.0086881
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.142708 0.165537 12.944 < 2e-16 ***
## LnFEX 0.014001 0.002269 6.171 3.30e-08 ***
## LnLAB -0.103910 0.021451 -4.844 6.80e-06 ***
## REER -0.029255 0.018177 -1.609 0.111785
## LnOPEN 0.018810 0.002922 6.437 1.08e-08 ***
## LnFDI 0.005002 0.001374 3.640 0.000502 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.003229 on 74 degrees of freedom
## Multiple R-squared: 0.9496, Adjusted R-squared: 0.9462
## F-statistic: 278.6 on 5 and 74 DF, p-value: < 2.2e-16
bptest(hoiquy3)
##
## studentized Breusch-Pagan test
##
## data: hoiquy3
## BP = 10.565, df = 5, p-value = 0.06071
### Cách 2 #################################################################
bienchon2 <- BoxCoxTrans(solieu$LnGDP)
bienchon2
## Box-Cox Transformation
##
## 80 data points used to estimate Lambda
##
## Input data summary:
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 12.32 12.84 13.13 13.14 13.43 14.01
##
## Largest/Smallest: 1.14
## Sample Skewness: 0.0712
##
## Estimated Lambda: -0.3
solieu4 <- cbind(solieu, LnGDP2 = predict(bienchon2, solieu$LnGDP))
head(solieu4)
## STT QUY LnGDP LnFGDP LnFEX LnLAB REER LnOPEN LnFDI
## 1 1 2000q1 12.32272 7.204922 19.51234 10.55482 0.9962832 22.62871 10.34393
## 2 2 2000q2 12.57529 7.457496 19.76492 10.56007 0.9997200 22.73124 10.59650
## 3 3 2000q3 12.50762 7.389821 19.69724 10.56939 1.0071360 22.71304 10.52882
## 4 4 2000q4 12.70953 7.591730 19.89915 10.55959 1.0072360 22.87906 10.73074
## 5 5 2001q1 12.39648 7.320969 19.72526 10.58206 0.9931406 22.57954 10.45481
## 6 6 2001q2 12.63004 7.554526 19.95881 10.58733 0.9989467 22.81070 10.68836
## LnGDP2
## 1 1.764175
## 2 1.773697
## 3 1.771170
## 4 1.778657
## 5 1.766982
## 6 1.775728
congthuc4 <-LnGDP2 ~ LnFEX + LnLAB + REER + LnOPEN + LnFDI
hoiquy4 <-dynlm(data=solieu4,congthuc4)
summary(hoiquy4)
##
## Time series regression with "numeric" data:
## Start = 1, End = 80
##
## Call:
## dynlm(formula = congthuc4, data = solieu4)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.0074671 -0.0019219 0.0001459 0.0014695 0.0086881
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.142708 0.165537 12.944 < 2e-16 ***
## LnFEX 0.014001 0.002269 6.171 3.30e-08 ***
## LnLAB -0.103910 0.021451 -4.844 6.80e-06 ***
## REER -0.029255 0.018177 -1.609 0.111785
## LnOPEN 0.018810 0.002922 6.437 1.08e-08 ***
## LnFDI 0.005002 0.001374 3.640 0.000502 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.003229 on 74 degrees of freedom
## Multiple R-squared: 0.9496, Adjusted R-squared: 0.9462
## F-statistic: 278.6 on 5 and 74 DF, p-value: < 2.2e-16
bptest(hoiquy4)
##
## studentized Breusch-Pagan test
##
## data: hoiquy4
## BP = 10.565, df = 5, p-value = 0.06071
2. khắc phục bằng robust
summary(hoiquy1)
##
## Call:
## lm(formula = congthuc1, data = solieu)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.210940 -0.058072 0.003733 0.039472 0.269841
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 23.35330 4.89950 4.766 9.14e-06 ***
## LnFEX 0.40039 0.06716 5.962 7.86e-08 ***
## LnLAB -2.96920 0.63490 -4.677 1.28e-05 ***
## REER -1.00061 0.53801 -1.860 0.06688 .
## LnOPEN 0.53708 0.08649 6.210 2.81e-08 ***
## LnFDI 0.13661 0.04067 3.359 0.00124 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.09556 on 74 degrees of freedom
## Multiple R-squared: 0.9455, Adjusted R-squared: 0.9418
## F-statistic: 256.6 on 5 and 74 DF, p-value: < 2.2e-16
summary(hoiquy1, robust=T)
##
## Call:
## lm(formula = congthuc1, data = solieu)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.210940 -0.058072 0.003733 0.039472 0.269841
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 23.35330 4.89950 4.766 9.14e-06 ***
## LnFEX 0.40039 0.06716 5.962 7.86e-08 ***
## LnLAB -2.96920 0.63490 -4.677 1.28e-05 ***
## REER -1.00061 0.53801 -1.860 0.06688 .
## LnOPEN 0.53708 0.08649 6.210 2.81e-08 ***
## LnFDI 0.13661 0.04067 3.359 0.00124 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.09556 on 74 degrees of freedom
## Multiple R-squared: 0.9455, Adjusted R-squared: 0.9418
## F-statistic: 256.6 on 5 and 74 DF, p-value: < 2.2e-16
library(car)
cov1 <- hccm(hoiquy1, type="hc1")
cov1
## (Intercept) LnFEX LnLAB REER LnOPEN
## (Intercept) 13.7880633 -0.116129774 -1.72876101 0.427427298 0.233685284
## LnFEX -0.1161298 0.005632093 0.00886418 -0.005583130 -0.002824423
## LnLAB -1.7287610 0.008864180 0.22706023 -0.075715962 -0.028978684
## REER 0.4274273 -0.005583130 -0.07571596 0.250218844 0.011091491
## LnOPEN 0.2336853 -0.002824423 -0.02897868 0.011091491 0.004576206
## LnFDI 0.1012366 -0.001863764 -0.01086540 -0.001899852 0.001307476
## LnFDI
## (Intercept) 0.101236556
## LnFEX -0.001863764
## LnLAB -0.010865404
## REER -0.001899852
## LnOPEN 0.001307476
## LnFDI 0.002163586
LnGDP.HC1 <- coeftest(hoiquy1, vcov.=cov1)
LnGDP.HC1
##
## t test of coefficients:
##
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 23.353300 3.713228 6.2892 2.013e-08 ***
## LnFEX 0.400395 0.075047 5.3352 1.001e-06 ***
## LnLAB -2.969203 0.476508 -6.2312 2.567e-08 ***
## REER -1.000614 0.500219 -2.0004 0.049132 *
## LnOPEN 0.537083 0.067648 7.9394 1.686e-11 ***
## LnFDI 0.136611 0.046514 2.9370 0.004416 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
3. khắc phục bằng sandwich
library(sandwich)
vcovHC(hoiquy1)
## (Intercept) LnFEX LnLAB REER LnOPEN
## (Intercept) 15.3632332 -0.134615834 -1.91582601 0.441320957 0.261040666
## LnFEX -0.1346158 0.006355764 0.01041341 -0.005616570 -0.003244032
## LnLAB -1.9158260 0.010413415 0.25038317 -0.079780326 -0.032175479
## REER 0.4413210 -0.005616570 -0.07978033 0.274083077 0.011749735
## LnOPEN 0.2610407 -0.003244032 -0.03217548 0.011749735 0.005120680
## LnFDI 0.1141484 -0.002121524 -0.01217130 -0.002780107 0.001475815
## LnFDI
## (Intercept) 0.114148447
## LnFEX -0.002121524
## LnLAB -0.012171302
## REER -0.002780107
## LnOPEN 0.001475815
## LnFDI 0.002455086
vcovHC(hoiquy2)
## (Intercept) LnFEX LnLAB REER LnOPEN
## (Intercept) 15.3632332 -0.134615834 -1.91582601 0.441320957 0.261040666
## LnFEX -0.1346158 0.006355764 0.01041341 -0.005616570 -0.003244032
## LnLAB -1.9158260 0.010413415 0.25038317 -0.079780326 -0.032175479
## REER 0.4413210 -0.005616570 -0.07978033 0.274083077 0.011749735
## LnOPEN 0.2610407 -0.003244032 -0.03217548 0.011749735 0.005120680
## LnFDI 0.1141484 -0.002121524 -0.01217130 -0.002780107 0.001475815
## LnFDI
## (Intercept) 0.114148447
## LnFEX -0.002121524
## LnLAB -0.012171302
## REER -0.002780107
## LnOPEN 0.001475815
## LnFDI 0.002455086
coeftest(hoiquy1, vcov = vcovHC(hoiquy1, type = "HC1"))
##
## t test of coefficients:
##
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 23.353300 3.713228 6.2892 2.013e-08 ***
## LnFEX 0.400395 0.075047 5.3352 1.001e-06 ***
## LnLAB -2.969203 0.476508 -6.2312 2.567e-08 ***
## REER -1.000614 0.500219 -2.0004 0.049132 *
## LnOPEN 0.537083 0.067648 7.9394 1.686e-11 ***
## LnFDI 0.136611 0.046514 2.9370 0.004416 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
coeftest(hoiquy1, vcov = vcovHC(hoiquy1, type = "HC2"))
##
## t test of coefficients:
##
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 23.353300 3.740536 6.2433 2.440e-08 ***
## LnFEX 0.400395 0.075845 5.2791 1.251e-06 ***
## LnLAB -2.969203 0.478765 -6.2018 2.902e-08 ***
## REER -1.000614 0.501729 -1.9943 0.049800 *
## LnOPEN 0.537083 0.068219 7.8729 2.252e-11 ***
## LnFDI 0.136611 0.047074 2.9021 0.004881 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
coeftest(hoiquy1, vcov = vcovHC(hoiquy1, type = "HC3"))
##
## t test of coefficients:
##
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 23.353300 3.919596 5.9581 7.992e-08 ***
## LnFEX 0.400395 0.079723 5.0223 3.425e-06 ***
## LnLAB -2.969203 0.500383 -5.9339 8.833e-08 ***
## REER -1.000614 0.523529 -1.9113 0.059841 .
## LnOPEN 0.537083 0.071559 7.5055 1.110e-10 ***
## LnFDI 0.136611 0.049549 2.7571 0.007341 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
coeftest(hoiquy1, vcov = vcovHC(hoiquy1, type = "HC4"))
##
## t test of coefficients:
##
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 23.353300 3.794109 6.1551 3.527e-08 ***
## LnFEX 0.400395 0.077144 5.1903 1.777e-06 ***
## LnLAB -2.969203 0.484092 -6.1336 3.859e-08 ***
## REER -1.000614 0.506806 -1.9744 0.052074 .
## LnOPEN 0.537083 0.069250 7.7557 3.748e-11 ***
## LnFDI 0.136611 0.047979 2.8473 0.005703 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
D, Giải pháp
d1. Robust Standard Error (Heteroskedasticity-consistent standard errors)
vcovHC(hoiquy1, type = 'HC')
## (Intercept) LnFEX LnLAB REER LnOPEN
## (Intercept) 12.75395854 -0.107420041 -1.599103936 0.395370250 0.216158887
## LnFEX -0.10742004 0.005209686 0.008199366 -0.005164395 -0.002612591
## LnLAB -1.59910394 0.008199366 0.210030711 -0.070037265 -0.026805283
## REER 0.39537025 -0.005164395 -0.070037265 0.231452431 0.010259629
## LnOPEN 0.21615889 -0.002612591 -0.026805283 0.010259629 0.004232990
## LnFDI 0.09364381 -0.001723981 -0.010050499 -0.001757363 0.001209415
## LnFDI
## (Intercept) 0.093643814
## LnFEX -0.001723981
## LnLAB -0.010050499
## REER -0.001757363
## LnOPEN 0.001209415
## LnFDI 0.002001317
coeftest(hoiquy1, vcov = vcovHC(hoiquy1, type = "HC1"))
##
## t test of coefficients:
##
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 23.353300 3.713228 6.2892 2.013e-08 ***
## LnFEX 0.400395 0.075047 5.3352 1.001e-06 ***
## LnLAB -2.969203 0.476508 -6.2312 2.567e-08 ***
## REER -1.000614 0.500219 -2.0004 0.049132 *
## LnOPEN 0.537083 0.067648 7.9394 1.686e-11 ***
## LnFDI 0.136611 0.046514 2.9370 0.004416 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
d2. Feasible GLS (FGLS)
fgls <- lm(congthuc1, data = solieu, weights = 1/hoiquy1$fitted.values^2)
summary(fgls)
##
## Call:
## lm(formula = congthuc1, data = solieu, weights = 1/hoiquy1$fitted.values^2)
##
## Weighted Residuals:
## Min 1Q Median 3Q Max
## -0.0162096 -0.0041682 0.0002274 0.0029887 0.0197952
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 23.25310 4.74814 4.897 5.55e-06 ***
## LnFEX 0.40036 0.06634 6.035 5.81e-08 ***
## LnLAB -2.95468 0.61552 -4.800 8.04e-06 ***
## REER -0.98182 0.52661 -1.864 0.06623 .
## LnOPEN 0.53439 0.08402 6.360 1.49e-08 ***
## LnFDI 0.13575 0.04083 3.324 0.00138 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.007149 on 74 degrees of freedom
## Multiple R-squared: 0.9475, Adjusted R-squared: 0.944
## F-statistic: 267.3 on 5 and 74 DF, p-value: < 2.2e-16
vcov(fgls)
## (Intercept) LnFEX LnLAB REER LnOPEN
## (Intercept) 22.5448231 -0.120047962 -2.886118286 0.981459258 0.3761833716
## LnFEX -0.1200480 0.004400907 0.011272805 -0.009065692 -0.0029335778
## LnLAB -2.8861183 0.011272805 0.378865846 -0.150377699 -0.0483803847
## REER 0.9814593 -0.009065692 -0.150377699 0.277315613 0.0235673297
## LnOPEN 0.3761834 -0.002933578 -0.048380385 0.023567330 0.0070595694
## LnFDI 0.0811786 -0.001030762 -0.009174869 -0.002570730 0.0009340571
## LnFDI
## (Intercept) 0.0811785981
## LnFEX -0.0010307620
## LnLAB -0.0091748688
## REER -0.0025707304
## LnOPEN 0.0009340571
## LnFDI 0.0016673445
bptest(fgls)
##
## studentized Breusch-Pagan test
##
## data: fgls
## BP = 11.791, df = 5, p-value = 0.03776
