Persamaan Simultan 3SLS

Berkas Analisis Persamaan Simultan 3SLS Skripsiku

Model persamaan simultan merupakan model yang terdiri dari lebih dari satu persamaan regresi yang saling memiliki keterkaitan antara satu dengan lainnya (Gujarati & Porter, 2009). Model persamaan simultan terdiri dari persamaan struktural yang dibangun atas teori ekonomi dimana variabel terikat dalam satu atau lebih persamaan pada saat yang sama merupakan variabel bebas untuk persamaan lainnya. Persamaan simultan mengindikasikan terdapat hubungan dua arah (simultan) antara variabel dependen dan independen. Model persamaan simultan melibatkan lebih dari satu variabel dependen atau endogen sehingga membutuhkan persamaan dengan jumlah sebanyak variabel endogen.

Sharing

Load Data

library(readxl)
data <- read_excel("F:/Berkas Skripsi/A. SkripsiQ/Dataset/Data_Skripsi.xlsx", 
                           sheet = "Final")
head(data,10)

## # A tibble: 10 x 12
##     Year     dLNG    dPE   dAHH   INF  dLNKURS    IR    dLNLF   dM2   dUNEM
##    <dbl>    <dbl>  <dbl>  <dbl> <dbl>    <dbl> <dbl>    <dbl> <dbl>   <dbl>
##  1  2000 NA       NA     NA      9.35 NA       14.5  NA       NA    NA     
##  2  2001 -0.0411  -1.28   0.265 12.6  -0.198   17.6   0.00780 -4.75  0     
##  3  2002 -0.184    0.85   0.284 10.0   0.0971  12.9  -0.00103 -7.11  0.520 
##  4  2003 -0.122    0.29   0.310  5.06  0.0821   8.31  0.0109   3.18  0.0600
##  5  2004  0.172    0.25   0.338  6.4  -0.0413   7.43  0.0152   1.21  0.640 
##  6  2005  0.0641   0.66   0.365 17.1  -0.0822  12.8  -0.00451  7.19  0.640 
##  7  2006 -0.137   -0.190  0.383  6.6   0.0578   9.75  0.0155  -1.39 -0.390 
##  8  2007  0.00192  0.84   0.388  6.59  0.00200  8     0.0481   4.38  0.510 
##  9  2008 -0.0591  -0.33   0.380 11.1  -0.0592   9.25  0.0182  -4.40 -0.850 
## 10  2009 -0.0945  -1.39   0.368  2.78 -0.0688   6.5   0.0103  -1.97 -1.10  
## # ... with 2 more variables: lagINF <dbl>, dgr <dbl>

#data
awal <- read_excel("F:/Berkas Skripsi/A. SkripsiQ/Dataset/Data_Skripsi.xlsx", 
                           sheet = "New_era")
head(awal,10)

## # A tibble: 10 x 21
##     Year     G    PE   AHH   INF    KURS    IR     LF    M2  UNEM ...11    dlngg
##    <dbl> <dbl> <dbl> <dbl> <dbl>   <dbl> <dbl>  <dbl> <dbl> <dbl> <lgl>    <dbl>
##  1  2000  60.4  4.92  65.8  9.35 1.19e-4 14.5  9.93e7 16.6   6.08 NA    NA      
##  2  2001  58.0  3.64  66.0 12.6  9.75e-5 17.6  1.00e8 11.9   6.08 NA    -0.0411 
##  3  2002  48.3  4.49  66.3 10.0  1.07e-4 12.9  1.00e8  4.76  6.60 NA    -0.184  
##  4  2003  42.7  4.78  66.6  5.06 1.17e-4  8.31 1.01e8  7.94  6.66 NA    -0.122  
##  5  2004  50.7  5.03  67.0  6.4  1.12e-4  7.43 1.03e8  9.14  7.30 NA     0.172  
##  6  2005  54.1  5.69  67.3 17.1  1.03e-4 12.8  1.02e8 16.3   7.94 NA     0.0641 
##  7  2006  47.1  5.5   67.7  6.6  1.09e-4  9.75 1.04e8 14.9   7.55 NA    -0.137  
##  8  2007  47.2  6.34  68.1  6.59 1.09e-4  8    1.09e8 19.3   8.06 NA     0.00192
##  9  2008  44.5  6.01  68.5 11.1  1.03e-4  9.25 1.11e8 14.9   7.21 NA    -0.0591 
## 10  2009  40.5  4.62  68.9  2.78 9.62e-5  6.5  1.12e8 13.0   6.11 NA    -0.0945 
## # ... with 9 more variables: dpe1 <dbl>, dahh <dbl>, inf <dbl>, dlnkurs <dbl>,
## #   ir <dbl>, dlf <dbl>, dm2 <dbl>, dunem <dbl>, lagINF <dbl>

Spesifikasi Model dan Identifikasi Variabel

#Persamaan Struktural
G <- dLNG ~ dPE + dAHH + INF + IR + dLNKURS + dLNLF
PE <- dPE ~ dLNG + dAHH + dM2 + dLNLF + dLNKURS + INF
AHH <- dAHH ~ dLNG + dPE + lagINF + dUNEM + dLNLF + INF

#Identifikasi Sistem Simultan
sys <- list(G, PE, AHH)

#Variabel predetermined
instr <- ~INF + IR + dLNKURS + dLNLF + dUNEM + dM2 + lagINF

Uji Stasioner

#Uji Stasioneritas
library(tseries)
adf.test(diff(log(awal$G)),k=3)

## 
##  Augmented Dickey-Fuller Test
## 
## data:  diff(log(awal$G))
## Dickey-Fuller = -2.7988, Lag order = 3, p-value = 0.2681
## alternative hypothesis: stationary

#di Eviews --> merupakan trend and intercept dengan AKAIKE -> kurang bervariasi -> pakai Eviews aja

Persamaan Regresi Tereduksi (Reduced Form)

Globalisasi Ekonomi Tereduksi

rf_g <- lm(dLNG ~ INF + IR + dLNKURS + dLNLF + dUNEM + dM2 + lagINF
           ,data=data)
summary(rf_g)

## 
## Call:
## lm(formula = dLNG ~ INF + IR + dLNKURS + dLNLF + dUNEM + dM2 + 
##     lagINF, data = data)
## 
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -0.051115 -0.019206 -0.010046  0.006732  0.121241 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)  
## (Intercept)  0.075707   0.055617   1.361   0.2007  
## INF          0.004394   0.007006   0.627   0.5433  
## IR          -0.011029   0.009666  -1.141   0.2781  
## dLNKURS     -0.462383   0.164821  -2.805   0.0171 *
## dLNLF        0.350738   1.326335   0.264   0.7963  
## dUNEM        0.047286   0.026183   1.806   0.0983 .
## dM2          0.006038   0.004626   1.305   0.2185  
## lagINF      -0.006526   0.004639  -1.407   0.1871  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.05253 on 11 degrees of freedom
##   (1 observation deleted due to missingness)
## Multiple R-squared:  0.7361, Adjusted R-squared:  0.5682 
## F-statistic: 4.383 on 7 and 11 DF,  p-value: 0.01479

res_rf_g = residuals(rf_g)
res_rf_g=data.frame(res_rf_g)
fit_rf_g = fitted.values(rf_g)

#Uji Asumsi Klasik

#normalitas -> ga terpenuhi
library(nortest)
lillie.test(res_rf_g$res_rf_g)

## 
##  Lilliefors (Kolmogorov-Smirnov) normality test
## 
## data:  res_rf_g$res_rf_g
## D = 0.20004, p-value = 0.04393

#Homoskedastisitas
library(nortsTest)
arch.test(res_rf_g$res_rf_g,arch = c("box","Lm"),alpha = 0.05,lag.max = 3)

## 
##  Box-Ljung test
## 
## data:  y^2
## X-squared = 0.61774, df = 3, p-value = 0.8924
## alternative hypothesis: y is heteroscedastic

#Non-Autokorelasi
library(lmtest)
dwtest(rf_g)

## 
##  Durbin-Watson test
## 
## data:  rf_g
## DW = 2.457, p-value = 0.7306
## alternative hypothesis: true autocorrelation is greater than 0

#non multikol
library(car)
vif(rf_g)

##      INF       IR  dLNKURS    dLNLF    dUNEM      dM2   lagINF 
## 4.865387 6.638818 1.289722 1.548669 1.355334 1.603372 2.054128

Pertumbuhan Ekonomi Tereduksi

rf_pe <- lm(dPE ~ INF + IR + dLNKURS + dLNLF + dUNEM + dM2 + lagINF
           ,data=data)
summary(rf_pe)

## 
## Call:
## lm(formula = dPE ~ INF + IR + dLNKURS + dLNLF + dUNEM + dM2 + 
##     lagINF, data = data)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.19928 -0.14602 -0.03913  0.05547  0.46740 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  0.284602   0.261427   1.089 0.299586    
## INF          0.093461   0.032931   2.838 0.016139 *  
## IR          -0.057903   0.045432  -1.274 0.228754    
## dLNKURS      6.548807   0.774735   8.453 3.85e-06 ***
## dLNLF        9.931700   6.234386   1.593 0.139456    
## dUNEM        0.580723   0.123070   4.719 0.000631 ***
## dM2         -0.004453   0.021744  -0.205 0.841490    
## lagINF      -0.049375   0.021803  -2.265 0.044734 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.2469 on 11 degrees of freedom
##   (1 observation deleted due to missingness)
## Multiple R-squared:  0.9248, Adjusted R-squared:  0.877 
## F-statistic: 19.33 on 7 and 11 DF,  p-value: 2.355e-05

res_rf_pe = residuals(rf_pe)
fit_rf_pe = fitted.values(rf_pe)

#Uji Asumsi Klasik

#Normalitas
library(nortest)
lillie.test(res_rf_pe)

## 
##  Lilliefors (Kolmogorov-Smirnov) normality test
## 
## data:  res_rf_pe
## D = 0.16427, p-value = 0.1943

#Homoskedastisitas
library(nortsTest)
arch.test(res_rf_pe,arch = c("box","Lm"),alpha = 0.05,lag.max = 3)

## 
##  Box-Ljung test
## 
## data:  y^2
## X-squared = 0.81816, df = 3, p-value = 0.8451
## alternative hypothesis: y is heteroscedastic

#Non-autokorelasi
dwtest(rf_pe)

## 
##  Durbin-Watson test
## 
## data:  rf_pe
## DW = 2.3591, p-value = 0.6553
## alternative hypothesis: true autocorrelation is greater than 0

#non multikol
library(car)
vif(rf_pe)

##      INF       IR  dLNKURS    dLNLF    dUNEM      dM2   lagINF 
## 4.865387 6.638818 1.289722 1.548669 1.355334 1.603372 2.054128

Angka harapan hidup tereduksi

rf_ahh <- lm(dAHH ~ INF + IR + dLNKURS + dLNLF + dUNEM + dM2 + lagINF
           ,data=data)
summary(rf_ahh)

## 
## Call:
## lm(formula = dAHH ~ INF + IR + dLNKURS + dLNLF + dUNEM + dM2 + 
##     lagINF, data = data)
## 
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -0.074408 -0.016423  0.004651  0.021885  0.050060 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  0.214577   0.044868   4.782 0.000569 ***
## INF          0.014091   0.005652   2.493 0.029866 *  
## IR          -0.012305   0.007797  -1.578 0.142847    
## dLNKURS     -0.008103   0.132966  -0.061 0.952499    
## dLNLF        1.708806   1.069996   1.597 0.138567    
## dUNEM       -0.018424   0.021122  -0.872 0.401702    
## dM2          0.004287   0.003732   1.149 0.275001    
## lagINF       0.010858   0.003742   2.902 0.014402 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.04238 on 11 degrees of freedom
##   (1 observation deleted due to missingness)
## Multiple R-squared:  0.6247, Adjusted R-squared:  0.3859 
## F-statistic: 2.616 on 7 and 11 DF,  p-value: 0.07466

res_rf_ahh = residuals(rf_ahh)
fit_rf_ahh = fitted.values(rf_ahh)

#Uji Asumsi Klasik

#Normalitas
lillie.test(res_rf_ahh)

## 
##  Lilliefors (Kolmogorov-Smirnov) normality test
## 
## data:  res_rf_ahh
## D = 0.15621, p-value = 0.2571

#Homoskedastisitas
library(nortsTest)
arch.test(res_rf_ahh,arch = c("box","Lm"),alpha = 0.05,lag.max = 3)

## 
##  Box-Ljung test
## 
## data:  y^2
## X-squared = 0.76724, df = 3, p-value = 0.8573
## alternative hypothesis: y is heteroscedastic

#non-autokorelasi -> ga terpenuhi
dwtest(rf_ahh)

## 
##  Durbin-Watson test
## 
## data:  rf_ahh
## DW = 1.2823, p-value = 0.01931
## alternative hypothesis: true autocorrelation is greater than 0

dwtest(rf_ahh,exact = TRUE,alternative = "two.sided",iterations = 1)

## 
##  Durbin-Watson test
## 
## data:  rf_ahh
## DW = 1.2823, p-value = 0.03729
## alternative hypothesis: true autocorrelation is not 0

#non multikol
library(car)
vif(rf_ahh)

##      INF       IR  dLNKURS    dLNLF    dUNEM      dM2   lagINF 
## 4.865387 6.638818 1.289722 1.548669 1.355334 1.603372 2.054128

Uji Endogenitas dan Simultanitas Pindyx | Gujarati

fit_rf_g=data.frame(fit_rf_g)
fit_rf_ahh=data.frame(fit_rf_ahh)
fit_rf_pe=data.frame(fit_rf_pe)
fit = data.frame(fit_rf_g,fit_rf_pe,fit_rf_ahh)
residual = data.frame(res_rf_g,res_rf_pe,res_rf_ahh)

#Penyatuan dataset
library(openxlsx)
library(expss)
#Import data
#write.xlsx(fit,file = "fitted_rf.xlsx")
#write.xlsx(residual,file = "res_rf.xlsx")

#Endogenitas 1
endogen <- read_excel("F:/Berkas Skripsi/A. SkripsiQ/Dataset/Pengolahan Data/New/fitted_rf.xlsx")
end_g <- lm(dLNG ~ dPE + dAHH + INF + IR + dLNKURS + dLNLF + res_rf_pe + res_rf_ahh
           ,data=endogen)
summary(end_g)

## 
## Call:
## lm(formula = dLNG ~ dPE + dAHH + INF + IR + dLNKURS + dLNLF + 
##     res_rf_pe + res_rf_ahh, data = endogen)
## 
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -0.065445 -0.032363 -0.002963  0.022121  0.083343 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)  
## (Intercept)  0.008443   0.134544   0.063   0.9512  
## dPE          0.117435   0.049717   2.362   0.0398 *
## dAHH         0.180417   0.513174   0.352   0.7325  
## INF         -0.003588   0.011991  -0.299   0.7709  
## IR          -0.010409   0.008604  -1.210   0.2542  
## dLNKURS     -1.215746   0.389387  -3.122   0.0108 *
## dLNLF       -0.688878   1.840174  -0.374   0.7160  
## res_rf_pe   -0.187643   0.083895  -2.237   0.0493 *
## res_rf_ahh   0.261717   0.646821   0.405   0.6943  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.05451 on 10 degrees of freedom
##   (1 observation deleted due to missingness)
## Multiple R-squared:  0.7417, Adjusted R-squared:  0.535 
## F-statistic: 3.588 on 8 and 10 DF,  p-value: 0.03135

end_pe<-lm(dPE ~ dLNG + dAHH + dM2 + dLNLF + dLNKURS + INF + res_rf_g+res_rf_ahh,
           data=endogen)
summary(end_pe)

## 
## Call:
## lm(formula = dPE ~ dLNG + dAHH + dM2 + dLNLF + dLNKURS + INF + 
##     res_rf_g + res_rf_ahh, data = endogen)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.34374 -0.14591  0.02324  0.14504  0.56830 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  0.22401    0.70301   0.319  0.75656    
## dLNG         7.01697    2.26961   3.092  0.01141 *  
## dAHH        -2.08507    2.74811  -0.759  0.46552    
## dM2         -0.03643    0.04122  -0.884  0.39759    
## dLNLF        9.95646    8.52191   1.168  0.26977    
## dLNKURS      9.92969    1.36171   7.292 2.63e-05 ***
## INF          0.10036    0.02703   3.714  0.00402 ** 
## res_rf_g    -8.67058    2.86558  -3.026  0.01277 *  
## res_rf_ahh   3.70456    3.50065   1.058  0.31483    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.2908 on 10 degrees of freedom
##   (1 observation deleted due to missingness)
## Multiple R-squared:  0.9052, Adjusted R-squared:  0.8294 
## F-statistic: 11.94 on 8 and 10 DF,  p-value: 0.0003349

end_ahh <- lm(dAHH ~ fit_rf_g + fit_rf_pe + lagINF + dUNEM + dLNLF + INF + res_rf_g+res_rf_pe,
              data=endogen)
summary(end_ahh)

## 
## Call:
## lm(formula = dAHH ~ fit_rf_g + fit_rf_pe + lagINF + dUNEM + dLNLF + 
##     INF + res_rf_g + res_rf_pe, data = endogen)
## 
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -0.064525 -0.017248  0.008513  0.018252  0.048394 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)   
## (Intercept)  0.138592   0.044405   3.121  0.01085 * 
## fit_rf_g     0.788294   0.318045   2.479  0.03262 * 
## fit_rf_pe    0.054498   0.021663   2.516  0.03061 * 
## lagINF       0.018597   0.005506   3.378  0.00703 **
## dUNEM       -0.087968   0.029750  -2.957  0.01436 * 
## dLNLF        0.878745   1.091291   0.805  0.43941   
## INF          0.005239   0.003165   1.655  0.12889   
## res_rf_g     0.300872   0.242962   1.238  0.24387   
## res_rf_pe    0.046790   0.051689   0.905  0.38664   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.04077 on 10 degrees of freedom
##   (1 observation deleted due to missingness)
## Multiple R-squared:  0.6842, Adjusted R-squared:  0.4315 
## F-statistic: 2.708 on 8 and 10 DF,  p-value: 0.07118

exo_pe <- end_pe<-lm(dPE ~ dLNG + dAHH + dM2 + dLNLF + dLNKURS + INF + fit_rf_g+fit_rf_ahh,
           data=endogen)
summary(exo_pe)

## 
## Call:
## lm(formula = dPE ~ dLNG + dAHH + dM2 + dLNLF + dLNKURS + INF + 
##     fit_rf_g + fit_rf_ahh, data = endogen)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.34374 -0.14591  0.02324  0.14504  0.56830 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  0.22401    0.70301   0.319  0.75656    
## dLNG        -1.65361    1.74941  -0.945  0.36681    
## dAHH         1.61949    2.16851   0.747  0.47237    
## dM2         -0.03643    0.04122  -0.884  0.39759    
## dLNLF        9.95646    8.52191   1.168  0.26977    
## dLNKURS      9.92969    1.36171   7.292 2.63e-05 ***
## INF          0.10036    0.02703   3.714  0.00402 ** 
## fit_rf_g     8.67058    2.86558   3.026  0.01277 *  
## fit_rf_ahh  -3.70456    3.50065  -1.058  0.31483    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.2908 on 10 degrees of freedom
##   (1 observation deleted due to missingness)
## Multiple R-squared:  0.9052, Adjusted R-squared:  0.8294 
## F-statistic: 11.94 on 8 and 10 DF,  p-value: 0.0003349

Pendugaan 2SLS dan DWH Simultanitas Test

#Pendugaan secara sistem antara 2SLS dan 3SLS
library(systemfit)
ive3_sem <- systemfit(sys, inst=instr, method="3SLS",data=data)
ive2_sem <- systemfit(sys, inst=instr, method="2SLS", data=data)
summary(ive2_sem)

## 
## systemfit results 
## method: 2SLS 
## 
##         N DF     SSR detRCov   OLS-R2 McElroy-R2
## system 57 36 3.00318       0 0.669528   0.929483
## 
##      N DF      SSR      MSE     RMSE       R2   Adj R2
## eq1 19 12 0.052728 0.004394 0.066287 0.541544 0.312315
## eq2 19 12 2.926860 0.243905 0.493867 0.671872 0.507808
## eq3 19 12 0.023589 0.001966 0.044337 0.551889 0.327834
## 
## The covariance matrix of the residuals
##             eq1        eq2         eq3
## eq1  0.00439401 -0.0303649 -0.00155122
## eq2 -0.03036493  0.2439050  0.01185086
## eq3 -0.00155122  0.0118509  0.00196573
## 
## The correlations of the residuals
##           eq1       eq2       eq3
## eq1  1.000000 -0.927537 -0.527815
## eq2 -0.927537  1.000000  0.541225
## eq3 -0.527815  0.541225  1.000000
## 
## 
## 2SLS estimates for 'eq1' (equation 1)
## Model Formula: dLNG ~ dPE + dAHH + INF + IR + dLNKURS + dLNLF
## Instruments: ~INF + IR + dLNKURS + dLNLF + dUNEM + dM2 + lagINF
## 
##                Estimate  Std. Error  t value Pr(>|t|)  
## (Intercept)  0.00844298  0.16361491  0.05160 0.959694  
## dPE          0.11743538  0.06045867  1.94241 0.075925 .
## dAHH         0.18041656  0.62405285  0.28910 0.777435  
## INF         -0.00358823  0.01458193 -0.24607 0.809784  
## IR          -0.01040891  0.01046339 -0.99479 0.339474  
## dLNKURS     -1.21574583  0.47352073 -2.56746 0.024661 *
## dLNLF       -0.68887850  2.23777325 -0.30784 0.763481  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.066287 on 12 degrees of freedom
## Number of observations: 19 Degrees of Freedom: 12 
## SSR: 0.052728 MSE: 0.004394 Root MSE: 0.066287 
## Multiple R-Squared: 0.541544 Adjusted R-Squared: 0.312315 
## 
## 
## 2SLS estimates for 'eq2' (equation 2)
## Model Formula: dPE ~ dLNG + dAHH + dM2 + dLNLF + dLNKURS + INF
## Instruments: ~INF + IR + dLNKURS + dLNLF + dUNEM + dM2 + lagINF
## 
##               Estimate Std. Error  t value  Pr(>|t|)   
## (Intercept)  0.2240078  1.1940808  0.18760 0.8543261   
## dLNG         7.0169740  3.8549688  1.82024 0.0937391 . 
## dAHH        -2.0850699  4.6676981 -0.44670 0.6630451   
## dM2         -0.0364295  0.0700160 -0.52030 0.6123176   
## dLNLF        9.9564599 14.4745839  0.68786 0.5046214   
## dLNKURS      9.9296946  2.3128876  4.29320 0.0010444 **
## INF          0.1003648  0.0459041  2.18640 0.0493251 * 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.493867 on 12 degrees of freedom
## Number of observations: 19 Degrees of Freedom: 12 
## SSR: 2.92686 MSE: 0.243905 Root MSE: 0.493867 
## Multiple R-Squared: 0.671872 Adjusted R-Squared: 0.507808 
## 
## 
## 2SLS estimates for 'eq3' (equation 3)
## Model Formula: dAHH ~ dLNG + dPE + lagINF + dUNEM + dLNLF + INF
## Instruments: ~INF + IR + dLNKURS + dLNLF + dUNEM + dM2 + lagINF
## 
##                Estimate  Std. Error  t value  Pr(>|t|)   
## (Intercept)  0.13859182  0.04828406  2.87034 0.0140808 * 
## dLNG         0.78829352  0.34582847  2.27944 0.0417208 * 
## dPE          0.05449763  0.02355540  2.31359 0.0392200 * 
## lagINF       0.01859708  0.00598708  3.10620 0.0090847 **
## dUNEM       -0.08796790  0.03234845 -2.71938 0.0186290 * 
## dLNLF        0.87874451  1.18662361  0.74054 0.4732129   
## INF          0.00523894  0.00344168  1.52220 0.1538647   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.044337 on 12 degrees of freedom
## Number of observations: 19 Degrees of Freedom: 12 
## SSR: 0.023589 MSE: 0.001966 Root MSE: 0.044337 
## Multiple R-Squared: 0.551889 Adjusted R-Squared: 0.327834

summary(ive3_sem)

## 
## systemfit results 
## method: 3SLS 
## 
##         N DF     SSR detRCov   OLS-R2 McElroy-R2
## system 57 36 2.65516       0 0.707823   0.988629
## 
##      N DF      SSR      MSE     RMSE       R2   Adj R2
## eq1 19 12 0.065603 0.005467 0.073938 0.429603 0.144404
## eq2 19 12 2.564186 0.213682 0.462258 0.712531 0.568797
## eq3 19 12 0.025374 0.002115 0.045984 0.517971 0.276956
## 
## The covariance matrix of the residuals used for estimation
##             eq1        eq2         eq3
## eq1  0.00439401 -0.0303649 -0.00155122
## eq2 -0.03036493  0.2439050  0.01185086
## eq3 -0.00155122  0.0118509  0.00196573
## 
## The covariance matrix of the residuals
##             eq1        eq2         eq3
## eq1  0.00546690 -0.0338072 -0.00210962
## eq2 -0.03380724  0.2136821  0.01356296
## eq3 -0.00210962  0.0135630  0.00211452
## 
## The correlations of the residuals
##           eq1       eq2       eq3
## eq1  1.000000 -0.989134 -0.620480
## eq2 -0.989134  1.000000  0.638064
## eq3 -0.620480  0.638064  1.000000
## 
## 
## 3SLS estimates for 'eq1' (equation 1)
## Model Formula: dLNG ~ dPE + dAHH + INF + IR + dLNKURS + dLNLF
## Instruments: ~INF + IR + dLNKURS + dLNLF + dUNEM + dM2 + lagINF
## 
##                Estimate  Std. Error  t value   Pr(>|t|)    
## (Intercept) -0.06715600  0.13157372 -0.51041 0.61902548    
## dPE          0.15308848  0.03614169  4.23579 0.00115607 ** 
## dAHH         0.45487658  0.50200169  0.90613 0.38270336    
## INF         -0.01306865  0.00793165 -1.64766 0.12533848    
## IR          -0.00313454  0.00552198 -0.56765 0.58073923    
## dLNKURS     -1.45715921  0.33088621 -4.40381 0.00085963 ***
## dLNLF       -1.47362512  1.94613674 -0.75721 0.46353620    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.073938 on 12 degrees of freedom
## Number of observations: 19 Degrees of Freedom: 12 
## SSR: 0.065603 MSE: 0.005467 Root MSE: 0.073938 
## Multiple R-Squared: 0.429603 Adjusted R-Squared: 0.144404 
## 
## 
## 3SLS estimates for 'eq2' (equation 2)
## Model Formula: dPE ~ dLNG + dAHH + dM2 + dLNLF + dLNKURS + INF
## Instruments: ~INF + IR + dLNKURS + dLNLF + dUNEM + dM2 + lagINF
## 
##               Estimate Std. Error  t value   Pr(>|t|)    
## (Intercept)  0.7065334  0.9987472  0.70742 0.49281626    
## dLNG         5.5406346  3.1280894  1.77125 0.10188977    
## dAHH        -3.8401960  3.9461280 -0.97316 0.34968485    
## dM2          0.0106790  0.0335750  0.31806 0.75590298    
## dLNLF       11.2248179 14.2028422  0.79032 0.44467796    
## dLNKURS      9.0644578  1.9986172  4.53536 0.00068332 ***
## INF          0.1028293  0.0455048  2.25975 0.04323061 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.462258 on 12 degrees of freedom
## Number of observations: 19 Degrees of Freedom: 12 
## SSR: 2.564186 MSE: 0.213682 Root MSE: 0.462258 
## Multiple R-Squared: 0.712531 Adjusted R-Squared: 0.568797 
## 
## 
## 3SLS estimates for 'eq3' (equation 3)
## Model Formula: dAHH ~ dLNG + dPE + lagINF + dUNEM + dLNLF + INF
## Instruments: ~INF + IR + dLNKURS + dLNLF + dUNEM + dM2 + lagINF
## 
##                Estimate  Std. Error  t value  Pr(>|t|)   
## (Intercept)  0.14073978  0.04824596  2.91713 0.0129089 * 
## dLNG         0.82760343  0.34208535  2.41929 0.0323594 * 
## dPE          0.05664100  0.02348772  2.41152 0.0328219 * 
## lagINF       0.01812902  0.00590769  3.06872 0.0097400 **
## dUNEM       -0.09955531  0.03091475 -3.22032 0.0073501 **
## dLNLF        0.75136245  1.18276774  0.63526 0.5371858   
## INF          0.00562158  0.00339744  1.65465 0.1238942   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.045984 on 12 degrees of freedom
## Number of observations: 19 Degrees of Freedom: 12 
## SSR: 0.025374 MSE: 0.002115 Root MSE: 0.045984 
## Multiple R-Squared: 0.517971 Adjusted R-Squared: 0.276956

#Pendugaan 2SLS dan DWH Simultanitas test
library(AER)
a=ivreg(dLNG ~ dPE + dAHH + INF + IR + dLNKURS + dLNLF|INF + IR + dLNKURS + dLNLF + dUNEM + dM2 + lagINF, data=data)
b=ivreg(dPE ~ dLNG + dAHH + dM2 + dLNLF + dLNKURS + INF|INF + IR + dLNKURS + dLNLF + dUNEM + dM2 + lagINF, data=data)
c=ivreg(dAHH ~ dLNG + dPE + lagINF + dUNEM + dLNLF + INF|INF + IR + dLNKURS + dLNLF + dUNEM + dM2 + lagINF, data=data)
summary(a,diagnostics=TRUE)

## 
## Call:
## ivreg(formula = dLNG ~ dPE + dAHH + INF + IR + dLNKURS + dLNLF | 
##     INF + IR + dLNKURS + dLNLF + dUNEM + dM2 + lagINF, data = data)
## 
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -0.112591 -0.025327 -0.004994  0.013418  0.133839 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)  
## (Intercept)  0.008443   0.163615   0.052   0.9597  
## dPE          0.117435   0.060459   1.942   0.0759 .
## dAHH         0.180417   0.624053   0.289   0.7774  
## INF         -0.003588   0.014582  -0.246   0.8098  
## IR          -0.010409   0.010463  -0.995   0.3395  
## dLNKURS     -1.215746   0.473521  -2.567   0.0247 *
## dLNLF       -0.688878   2.237773  -0.308   0.7635  
## 
## Diagnostic tests:
##                         df1 df2 statistic p-value   
## Weak instruments (dPE)    3  11    11.547 0.00101 **
## Weak instruments (dAHH)   3  11     3.679 0.04688 * 
## Wu-Hausman                2  10     2.933 0.09946 . 
## Sargan                    1  NA     1.908 0.16718   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.06629 on 12 degrees of freedom
## Multiple R-Squared: 0.5415,  Adjusted R-squared: 0.3123 
## Wald test:  3.01 on 6 and 12 DF,  p-value: 0.0493

summary(b,diagnostics=TRUE)

## 
## Call:
## ivreg(formula = dPE ~ dLNG + dAHH + dM2 + dLNLF + dLNKURS + INF | 
##     INF + IR + dLNKURS + dLNLF + dUNEM + dM2 + lagINF, data = data)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.81612 -0.21131  0.01341  0.20779  0.99467 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)   
## (Intercept)  0.22401    1.19408   0.188  0.85433   
## dLNG         7.01697    3.85497   1.820  0.09374 . 
## dAHH        -2.08507    4.66770  -0.447  0.66305   
## dM2         -0.03643    0.07002  -0.520  0.61232   
## dLNLF        9.95646   14.47458   0.688  0.50462   
## dLNKURS      9.92969    2.31289   4.293  0.00104 **
## INF          0.10036    0.04590   2.186  0.04933 * 
## 
## Diagnostic tests:
##                         df1 df2 statistic p-value  
## Weak instruments (dLNG)   3  11     3.345  0.0595 .
## Weak instruments (dAHH)   3  11     3.506  0.0530 .
## Wu-Hausman                2  10     6.573  0.0151 *
## Sargan                    1  NA     1.755  0.1853  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4939 on 12 degrees of freedom
## Multiple R-Squared: 0.6719,  Adjusted R-squared: 0.5078 
## Wald test: 5.452 on 6 and 12 DF,  p-value: 0.006214

summary(c, vcov = sandwich, diagnostics = TRUE)

## 
## Call:
## ivreg(formula = dAHH ~ dLNG + dPE + lagINF + dUNEM + dLNLF + 
##     INF | INF + IR + dLNKURS + dLNLF + dUNEM + dM2 + lagINF, 
##     data = data)
## 
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -0.060764 -0.031197  0.004543  0.030326  0.056333 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  0.138592   0.039443   3.514 0.004273 ** 
## dLNG         0.788294   0.207869   3.792 0.002566 ** 
## dPE          0.054498   0.011287   4.828 0.000413 ***
## lagINF       0.018597   0.004547   4.090 0.001500 ** 
## dUNEM       -0.087968   0.020394  -4.313 0.001008 ** 
## dLNLF        0.878745   1.002561   0.877 0.397965    
## INF          0.005239   0.002327   2.252 0.043872 *  
## 
## Diagnostic tests:
##                         df1 df2 statistic  p-value    
## Weak instruments (dLNG)   3  11    28.171 1.84e-05 ***
## Weak instruments (dPE)    3  11    69.388 1.97e-07 ***
## Wu-Hausman                2  10     2.526    0.129    
## Sargan                    1  NA     0.007    0.931    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.04434 on 12 degrees of freedom
## Multiple R-Squared: 0.5519,  Adjusted R-squared: 0.3278 
## Wald test: 7.798 on 6 and 12 DF,  p-value: 0.00138

summary(c,diagnostics = TRUE)

## 
## Call:
## ivreg(formula = dAHH ~ dLNG + dPE + lagINF + dUNEM + dLNLF + 
##     INF | INF + IR + dLNKURS + dLNLF + dUNEM + dM2 + lagINF, 
##     data = data)
## 
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -0.060764 -0.031197  0.004543  0.030326  0.056333 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)   
## (Intercept)  0.138592   0.048284   2.870  0.01408 * 
## dLNG         0.788294   0.345828   2.279  0.04172 * 
## dPE          0.054498   0.023555   2.314  0.03922 * 
## lagINF       0.018597   0.005987   3.106  0.00908 **
## dUNEM       -0.087968   0.032348  -2.719  0.01863 * 
## dLNLF        0.878745   1.186624   0.741  0.47321   
## INF          0.005239   0.003442   1.522  0.15386   
## 
## Diagnostic tests:
##                         df1 df2 statistic  p-value    
## Weak instruments (dLNG)   3  11     3.159   0.0682 .  
## Weak instruments (dPE)    3  11    30.817 1.19e-05 ***
## Wu-Hausman                2  10     0.784   0.4828    
## Sargan                    1  NA     0.007   0.9310    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.04434 on 12 degrees of freedom
## Multiple R-Squared: 0.5519,  Adjusted R-squared: 0.3278 
## Wald test: 2.788 on 6 and 12 DF,  p-value: 0.06172

Uji Perbandingan Konsistensi 2SLS dan 3SLS

Uji = hausman.systemfit(ive2_sem,ive3_sem)
Uji

## 
##  Hausman specification test for consistency of the 3SLS estimation
## 
## data:  data
## Hausman = 2.2861, df = 21, p-value = 1

Uji$qVar

##                 eq1_(Intercept)       eq1_dPE      eq1_dAHH       eq1_INF
## eq1_(Intercept)    9.458196e-03 -4.695149e-03 -0.0359416808  1.189979e-03
## eq1_dPE           -4.695149e-03  2.349029e-03  0.0179670036 -5.910211e-04
## eq1_dAHH          -3.594168e-02  1.796700e-02  0.1374362617 -4.524058e-03
## eq1_INF            1.189979e-03 -5.910211e-04 -0.0045240579  1.497216e-04
## eq1_IR            -8.597216e-04  4.228437e-04  0.0032401114 -1.081004e-04
## eq1_dLNKURS        3.265420e-02 -1.640116e-02 -0.1253955728  4.111539e-03
## eq1_dLNLF          1.064270e-01 -5.347509e-02 -0.4088290921  1.340071e-02
## eq2_(Intercept)    1.018178e-01 -5.660271e-03 -0.3775823207  1.141456e-03
## eq2_dLNG           3.707192e-02  7.778871e-02  0.2928711184 -1.191403e-03
## eq2_dAHH          -3.343964e-01  4.048538e-02  1.6110907567 -1.117167e-02
## eq2_dM2           -4.964906e-04 -4.634552e-04 -0.0012835308 -1.866106e-05
## eq2_dLNLF         -6.454208e-02 -1.792986e-01 -2.5819727099  4.450211e-02
## eq2_dLNKURS        7.129689e-02  3.074617e-02 -0.1165064460  2.809077e-03
## eq2_INF            1.195547e-03 -2.754667e-04 -0.0122853490  2.501573e-04
## eq3_(Intercept)    2.945135e-03  1.022441e-04 -0.0075309879 -1.577946e-05
## eq3_dLNG          -1.454777e-02  3.399676e-03  0.0767357856 -6.279713e-04
## eq3_dPE           -5.774182e-04  1.974804e-04  0.0033534861 -1.671148e-05
## eq3_lagINF        -3.265248e-04  2.630648e-05  0.0014497734 -1.130227e-05
## eq3_dUNEM          1.372737e-03 -1.289593e-04 -0.0063853958  4.064865e-05
## eq3_dLNLF         -2.132937e-02 -7.826039e-03 -0.0491074841  1.630130e-03
## eq3_INF           -5.342045e-05 -1.553972e-05 -0.0001530601  9.035726e-06
##                        eq1_IR   eq1_dLNKURS    eq1_dLNLF eq2_(Intercept)
## eq1_(Intercept) -8.597216e-04  3.265420e-02  0.106426973    0.1018178197
## eq1_dPE          4.228437e-04 -1.640116e-02 -0.053475086   -0.0056602708
## eq1_dAHH         3.240111e-03 -1.253956e-01 -0.408829092   -0.3775823207
## eq1_INF         -1.081004e-04  4.111539e-03  0.013400714    0.0011414564
## eq1_IR           7.899030e-05 -2.927095e-03 -0.009535684    0.0012396250
## eq1_dLNKURS     -2.927095e-03  1.147362e-01  0.374160925    0.0961853738
## eq1_dLNLF       -9.535684e-03  3.741609e-01  1.220180890    0.1794691848
## eq2_(Intercept)  1.239625e-03  9.618537e-02  0.179469185    0.4283329425
## eq2_dLNG        -1.219635e-02 -5.711876e-01 -2.299843568   -1.4623023560
## eq2_dAHH        -7.273985e-03 -5.261642e-01 -3.095464348   -1.6292345263
## eq2_dM2          1.086381e-04  3.403740e-03  0.014373557    0.0401578655
## eq2_dLNLF        2.610749e-02  1.572648e+00 24.705188703    1.6874631843
## eq2_dLNKURS     -5.085286e-03  5.750198e-02 -0.657827877   -0.7617878411
## eq2_INF          4.059330e-05  5.113128e-03  0.048416504    0.0035628539
## eq3_(Intercept) -1.569633e-05  2.968406e-04 -0.016163682   -0.0211571472
## eq3_dLNG        -4.214653e-04 -3.824773e-02 -0.177864310    0.1424576949
## eq3_dPE         -2.634772e-05 -1.768085e-04 -0.009262779    0.0065061928
## eq3_lagINF      -2.524781e-06 -3.281965e-04 -0.002460247    0.0026596505
## eq3_dUNEM        2.414804e-05  1.156443e-03  0.011604052   -0.0124721380
## eq3_dLNLF        1.051914e-03  4.454235e-02  1.122652486    0.0804263056
## eq3_INF          1.563350e-06  9.214276e-05  0.001892016    0.0002961082
##                     eq2_dLNG     eq2_dAHH       eq2_dM2   eq2_dLNLF
## eq1_(Intercept)  0.037071924 -0.334396398 -4.964906e-04 -0.06454208
## eq1_dPE          0.077788711  0.040485379 -4.634552e-04 -0.17929862
## eq1_dAHH         0.292871118  1.611090757 -1.283531e-03 -2.58197271
## eq1_INF         -0.001191403 -0.011171674 -1.866106e-05  0.04450211
## eq1_IR          -0.012196352 -0.007273985  1.086381e-04  0.02610749
## eq1_dLNKURS     -0.571187637 -0.526164186  3.403740e-03  1.57264765
## eq1_dLNLF       -2.299843568 -3.095464348  1.437356e-02 24.70518870
## eq2_(Intercept) -1.462302356 -1.629234526  4.015787e-02  1.68746318
## eq2_dLNG         5.075841108  5.601355099 -1.361819e-01 -6.07033001
## eq2_dAHH         5.601355099  6.215480071 -1.523178e-01 -6.56376253
## eq2_dM2         -0.136181852 -0.152317776  3.774958e-03  0.15482203
## eq2_dLNLF       -6.070330005 -6.563762530  1.548220e-01  7.79285077
## eq2_dLNKURS      2.597239799  2.895962426 -7.145836e-02 -2.98835292
## eq2_INF         -0.012921067 -0.013907494  3.257446e-04  0.01683975
## eq3_(Intercept) -0.011228957  0.054214500  8.496032e-05  0.12529672
## eq3_dLNG        -0.324538949 -0.651339752  2.120849e-03  1.34456470
## eq3_dPE         -0.019852484 -0.030348324  1.389386e-04  0.07142182
## eq3_lagINF      -0.002221536 -0.011324743  1.319031e-05  0.01821344
## eq3_dUNEM        0.015325078  0.053854175 -1.105667e-04 -0.09312371
## eq3_dLNLF        0.785434567  0.560317090 -5.415944e-03 -8.60297571
## eq3_INF          0.001363695  0.001367373 -8.763080e-06 -0.01418180
##                   eq2_dLNKURS       eq2_INF eq3_(Intercept)      eq3_dLNG
## eq1_(Intercept)  0.0712968932  1.195547e-03    2.945135e-03 -1.454777e-02
## eq1_dPE          0.0307461708 -2.754667e-04    1.022441e-04  3.399676e-03
## eq1_dAHH        -0.1165064460 -1.228535e-02   -7.530988e-03  7.673579e-02
## eq1_INF          0.0028090772  2.501573e-04   -1.577946e-05 -6.279713e-04
## eq1_IR          -0.0050852863  4.059330e-05   -1.569633e-05 -4.214653e-04
## eq1_dLNKURS      0.0575019766  5.113128e-03    2.968406e-04 -3.824773e-02
## eq1_dLNLF       -0.6578278772  4.841650e-02   -1.616368e-02 -1.778643e-01
## eq2_(Intercept) -0.7617878411  3.562854e-03   -2.115715e-02  1.424577e-01
## eq2_dLNG         2.5972397990 -1.292107e-02   -1.122896e-02 -3.245389e-01
## eq2_dAHH         2.8959624255 -1.390749e-02    5.421450e-02 -6.513398e-01
## eq2_dM2         -0.0714583573  3.257446e-04    8.496032e-05  2.120849e-03
## eq2_dLNLF       -2.9883529242  1.683975e-02    1.252967e-01  1.344565e+00
## eq2_dLNKURS      1.3549784986 -6.305195e-03   -1.258716e-02 -2.807511e-02
## eq2_INF         -0.0063051949  3.650052e-05    1.450429e-04  4.926140e-03
## eq3_(Intercept) -0.0125871628  1.450429e-04    3.677895e-06 -7.333284e-06
## eq3_dLNG        -0.0280751091  4.926140e-03   -7.333284e-06  2.574941e-03
## eq3_dPE         -0.0177279787  1.480923e-04    1.207008e-06  8.207772e-05
## eq3_lagINF       0.0001600303  8.246812e-05   -1.571765e-06  2.955657e-05
## eq3_dUNEM        0.0046606393 -3.689745e-04   -1.812819e-05 -2.259879e-05
## eq3_dLNLF        0.4148362121 -1.330449e-02   -9.988440e-05 -3.856202e-03
## eq3_INF          0.0007077983 -6.726774e-05    9.714841e-07 -1.278674e-05
##                       eq3_dPE    eq3_lagINF     eq3_dUNEM     eq3_dLNLF
## eq1_(Intercept) -5.774182e-04 -3.265248e-04  1.372737e-03 -2.132937e-02
## eq1_dPE          1.974804e-04  2.630648e-05 -1.289593e-04 -7.826039e-03
## eq1_dAHH         3.353486e-03  1.449773e-03 -6.385396e-03 -4.910748e-02
## eq1_INF         -1.671148e-05 -1.130227e-05  4.064865e-05  1.630130e-03
## eq1_IR          -2.634772e-05 -2.524781e-06  2.414804e-05  1.051914e-03
## eq1_dLNKURS     -1.768085e-04 -3.281965e-04  1.156443e-03  4.454235e-02
## eq1_dLNLF       -9.262779e-03 -2.460247e-03  1.160405e-02  1.122652e+00
## eq2_(Intercept)  6.506193e-03  2.659650e-03 -1.247214e-02  8.042631e-02
## eq2_dLNG        -1.985248e-02 -2.221536e-03  1.532508e-02  7.854346e-01
## eq2_dAHH        -3.034832e-02 -1.132474e-02  5.385418e-02  5.603171e-01
## eq2_dM2          1.389386e-04  1.319031e-05 -1.105667e-04 -5.415944e-03
## eq2_dLNLF        7.142182e-02  1.821344e-02 -9.312371e-02 -8.602976e+00
## eq2_dLNKURS     -1.772798e-02  1.600303e-04  4.660639e-03  4.148362e-01
## eq2_INF          1.480923e-04  8.246812e-05 -3.689745e-04 -1.330449e-02
## eq3_(Intercept)  1.207008e-06 -1.571765e-06 -1.812819e-05 -9.988440e-05
## eq3_dLNG         8.207772e-05  2.955657e-05 -2.259879e-05 -3.856202e-03
## eq3_dPE          3.183895e-06  3.560634e-07 -7.887713e-06 -1.665971e-04
## eq3_lagINF       3.560634e-07  9.443841e-07  7.140920e-06  8.344767e-07
## eq3_dUNEM       -7.887713e-06  7.140920e-06  9.070097e-05  5.853728e-04
## eq3_dLNLF       -1.665971e-04  8.344767e-07  5.853728e-04  9.136061e-03
## eq3_INF         -3.919372e-08 -5.271378e-07 -4.539468e-06 -9.198434e-06
##                       eq3_INF
## eq1_(Intercept) -5.342045e-05
## eq1_dPE         -1.553972e-05
## eq1_dAHH        -1.530601e-04
## eq1_INF          9.035726e-06
## eq1_IR           1.563350e-06
## eq1_dLNKURS      9.214276e-05
## eq1_dLNLF        1.892016e-03
## eq2_(Intercept)  2.961082e-04
## eq2_dLNG         1.363695e-03
## eq2_dAHH         1.367373e-03
## eq2_dM2         -8.763080e-06
## eq2_dLNLF       -1.418180e-02
## eq2_dLNKURS      7.077983e-04
## eq2_INF         -6.726774e-05
## eq3_(Intercept)  9.714841e-07
## eq3_dLNG        -1.278674e-05
## eq3_dPE         -3.919372e-08
## eq3_lagINF      -5.271378e-07
## eq3_dUNEM       -4.539468e-06
## eq3_dLNLF       -9.198434e-06
## eq3_INF          3.025864e-07

Uji$statistic

##          [,1]
## [1,] 2.286074
## attr(,"names")
## [1] "Hausman"

#Perhitungan manual p-value
a=1-pchisq(Uji$statistic,Uji$parameter)
print(a)

##           [,1]
## [1,] 0.9999999

Asumsi Residual 3SLS

Multivariate Normal

#Multivariate Normal
ty = data.frame(residuals(ive3_sem))

#Uji Henze Zirkler MVN
library(mvnTest)
HZ.test(ty[2:20,],qqplot = TRUE)

##             Henze-Zirkler test for Multivariate Normality 
## 
##   data : ty[2:20, ] 
## 
##   HZ              : 0.8254725 
##   p-value         : 0.04898418 
## 
##   Result  : Data are not multivariate normal (sig.level = 0.05)

#Uji Mshapiro Wilk
library(mvnormtest)
mshapiro.test(t(ty[2:20,]))

## 
##  Shapiro-Wilk normality test
## 
## data:  Z
## W = 0.76475, p-value = 0.0003672

library(nortest)
lillie.test(ty$eq3)

## 
##  Lilliefors (Kolmogorov-Smirnov) normality test
## 
## data:  ty$eq3
## D = 0.11335, p-value = 0.7507

ks.test(ty$eq3,"pnorm")

## 
##  Exact one-sample Kolmogorov-Smirnov test
## 
## data:  ty$eq3
## D = 0.47767, p-value = 0.0001659
## alternative hypothesis: two-sided

shapiro.test(ty$eq3)

## 
##  Shapiro-Wilk normality test
## 
## data:  ty$eq3
## W = 0.95555, p-value = 0.4883

library(caret)
library(MASS)
library(klaR)
library(MVN)
library(biotools)
library(candisc)
library(DFA.CANCOR)
nm.mardia.test <- mvn(ty[2:20,], mvnTest = "mardia",
                      multivariateOutlierMethod = "adj",showNewData = F)

##Deteksi Multikolinearitas

#Panel of correlations
panel.corr <- function(x, y){
    usr <- par("usr"); on.exit(par(usr))
    par(usr = c(0, 1, 0, 1))
    r <- round(cor(x, y), digits=3)
    txt <- paste0("Corr: ", r)
    text(0.5, 0.5, txt, cex = 1)
}

#Panel of histograms
panel.hist <- function(x, ...){
    usr <- par("usr"); on.exit(par(usr))
    par(usr = c(usr[1:2], 0, 1.5) )
    h <- hist(x, plot = FALSE)
    breaks <- h$breaks
    len <- length(breaks)
    y <- h$counts/max(h$counts)
    rect(breaks[-len], 0, breaks[-1], y, col = "lightblue")
}

#Panel of scatterplots
panel.scat <- function(x, y){
  points(x,y, pch = 19, cex = 1, col = rainbow(2))
  lines(stats::lowess(x,y))
}

#Plot
pairs(awal[, c(2:10)],  
      lower.panel = panel.scat,
      upper.panel = panel.corr,
      diag.panel = panel.hist,
      labels = c("G","Pe","AHH",
                 "INF","Kurs","IR","LF","M2","Unem"),
      gap = 0.5, 
      main = "Scatterplot Variabel Penelitian")

##Variabel Transformasi

## Menggunakan chart.Correlation()
library(PerformanceAnalytics)

chart.Correlation(data[,c(2:11)],
                  histogram = TRUE, # tambahkan histogram pada diagonal
                  pch = 1,method = "pearson") # jenis point = 1

Contoh Demand and Supply Theory

data( "Kmenta" )
eqDemand <- consump ~ price + income
eqSupply <- consump ~ price + farmPrice + trend
inst <- ~ income + farmPrice + trend
system <- list( demand = eqDemand, supply = eqSupply )

## perform the estimations
fit2sls <- systemfit( system, "2SLS", inst = inst, data = Kmenta )
fit3sls <- systemfit( system, "3SLS", inst = inst, data = Kmenta )

## perform the Hausman test
h <- hausman.systemfit( fit2sls, fit3sls )
print( h )

## 
##  Hausman specification test for consistency of the 3SLS estimation
## 
## data:  Kmenta
## Hausman = 2.5357, df = 7, p-value = 0.9244

summary(fit2sls)

## 
## systemfit results 
## method: 2SLS 
## 
##         N DF     SSR detRCov   OLS-R2 McElroy-R2
## system 40 33 162.362 4.36424 0.697214   0.548127
## 
##         N DF     SSR     MSE    RMSE       R2   Adj R2
## demand 20 17 65.7291 3.86642 1.96632 0.754847 0.726005
## supply 20 16 96.6332 6.03958 2.45756 0.639582 0.572004
## 
## The covariance matrix of the residuals
##         demand  supply
## demand 3.86642 4.35744
## supply 4.35744 6.03958
## 
## The correlations of the residuals
##          demand   supply
## demand 1.000000 0.901724
## supply 0.901724 1.000000
## 
## 
## 2SLS estimates for 'demand' (equation 1)
## Model Formula: consump ~ price + income
## Instruments: ~income + farmPrice + trend
## 
##               Estimate Std. Error  t value   Pr(>|t|)    
## (Intercept) 94.6333039  7.9208383 11.94738 1.0762e-09 ***
## price       -0.2435565  0.0964843 -2.52431   0.021832 *  
## income       0.3139918  0.0469437  6.68869 3.8109e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.966321 on 17 degrees of freedom
## Number of observations: 20 Degrees of Freedom: 17 
## SSR: 65.729088 MSE: 3.866417 Root MSE: 1.966321 
## Multiple R-Squared: 0.754847 Adjusted R-Squared: 0.726005 
## 
## 
## 2SLS estimates for 'supply' (equation 2)
## Model Formula: consump ~ price + farmPrice + trend
## Instruments: ~income + farmPrice + trend
## 
##               Estimate Std. Error t value   Pr(>|t|)    
## (Intercept) 49.5324417 12.0105264 4.12409 0.00079536 ***
## price        0.2400758  0.0999339 2.40235 0.02878451 *  
## farmPrice    0.2556057  0.0472501 5.40964 5.7854e-05 ***
## trend        0.2529242  0.0996551 2.53800 0.02192877 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 2.457555 on 16 degrees of freedom
## Number of observations: 20 Degrees of Freedom: 16 
## SSR: 96.633244 MSE: 6.039578 Root MSE: 2.457555 
## Multiple R-Squared: 0.639582 Adjusted R-Squared: 0.572004

summary(fit3sls)

## 
## systemfit results 
## method: 3SLS 
## 
##         N DF     SSR detRCov   OLS-R2 McElroy-R2
## system 40 33 173.643  1.0332 0.676177   0.786468
## 
##         N DF      SSR     MSE    RMSE       R2   Adj R2
## demand 20 17  65.7291 3.86642 1.96632 0.754847 0.726005
## supply 20 16 107.9138 6.74461 2.59704 0.597508 0.522041
## 
## The covariance matrix of the residuals used for estimation
##         demand  supply
## demand 3.86642 4.35744
## supply 4.35744 6.03958
## 
## The covariance matrix of the residuals
##         demand  supply
## demand 3.86642 5.00443
## supply 5.00443 6.74461
## 
## The correlations of the residuals
##         demand  supply
## demand 1.00000 0.97999
## supply 0.97999 1.00000
## 
## 
## 3SLS estimates for 'demand' (equation 1)
## Model Formula: consump ~ price + income
## Instruments: ~income + farmPrice + trend
## 
##               Estimate Std. Error  t value   Pr(>|t|)    
## (Intercept) 94.6333039  7.9208383 11.94738 1.0762e-09 ***
## price       -0.2435565  0.0964843 -2.52431   0.021832 *  
## income       0.3139918  0.0469437  6.68869 3.8109e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.966321 on 17 degrees of freedom
## Number of observations: 20 Degrees of Freedom: 17 
## SSR: 65.729088 MSE: 3.866417 Root MSE: 1.966321 
## Multiple R-Squared: 0.754847 Adjusted R-Squared: 0.726005 
## 
## 
## 3SLS estimates for 'supply' (equation 2)
## Model Formula: consump ~ price + farmPrice + trend
## Instruments: ~income + farmPrice + trend
## 
##               Estimate Std. Error t value   Pr(>|t|)    
## (Intercept) 52.1972042 11.8933720 4.38876 0.00045780 ***
## price        0.2285892  0.0996732 2.29339 0.03570648 *  
## farmPrice    0.2281580  0.0439938 5.18614 9.0087e-05 ***
## trend        0.3611384  0.0728894 4.95461 0.00014343 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 2.597039 on 16 degrees of freedom
## Number of observations: 20 Degrees of Freedom: 16 
## SSR: 107.913821 MSE: 6.744614 Root MSE: 2.597039 
## Multiple R-Squared: 0.597508 Adjusted R-Squared: 0.522041