---

title: “Determinants of Production Costs in Turkey’s Plastic Packaging Sector” subtitle: “Econometric Analysis: 2013:09 – 2024:12” author: “Ömer Faruk Yılmaz - 20210201025” date: today format: html: toc: true toc-depth: 3 toc-title: “Table of Contents” number-sections: true theme: cosmo embed-resources: true code-fold: true code-summary: “Show Code” lang: en execute: warning: false message: false echo: true —

pci <- read_excel(paste0(path, "ufe_plastik.xlsx")) |>
  rename_with(tolower) |>
  select(1, 2) |>
  setNames(c("date", "pci")) |>
  mutate(date = as.Date(paste0(date, "-01")),
         pci  = as.numeric(pci)) |>
  filter(!is.na(pci))

New names:
• `` -> `...3`

Warning: There was 1 warning in `mutate()`.
ℹ In argument: `pci = as.numeric(pci)`.
Caused by warning:
! NAs introduced by coercion

head(pci)

# A tibble: 6 × 2
  date         pci
  <date>     <dbl>
1 2003-01-01  97.1
2 2003-02-01  98.2
3 2003-03-01  99.6
4 2003-04-01 101. 
5 2003-05-01 100. 
6 2003-06-01  98.9

brent <- read_excel(paste0(path, "MCOILBRENTEU.xlsx"), sheet = "Monthly") |>
  rename(date = observation_date, brent = MCOILBRENTEU) |>
  mutate(date  = as.Date(date),
         brent = as.numeric(brent)) |>
  filter(!is.na(brent))

head(brent)

# A tibble: 6 × 2
  date       brent
  <date>     <dbl>
1 1987-05-01  18.6
2 1987-06-01  18.9
3 1987-07-01  19.9
4 1987-08-01  19.0
5 1987-09-01  18.3
6 1987-10-01  18.8

kur <- read_excel(paste0(path, "EVDS_15-04-2026.xlsx")) |>
  select(date = Tarih, kur = TP_DK_USD_A_YTL) |>
  mutate(date = as.Date(date, format = "%d-%m-%Y"),
         kur  = as.numeric(kur)) |>
  filter(!is.na(kur)) |>
  mutate(date = as.Date(format(date, "%Y-%m-01"))) |>
  group_by(date) |>
  summarise(kur = mean(kur, na.rm = TRUE), .groups = "drop")

Warning: Expecting numeric in B8511 / R8511C2: got '(USD) ABD Doları (Döviz
Alış)-Düzey'

Warning: Expecting numeric in B8514 / R8514C2: got 'Veri Kaynağı'

Warning: Expecting logical in C8514 / R8514C3: got 'TCMB'

Warning: Expecting numeric in B8515 / R8515C2: got 'Etiketler'

Warning: Expecting logical in C8515 / R8515C3: got 'Kurlar, Döviz, Kurları,
Günlük'

New names:
• `` -> `...3`

head(kur)

# A tibble: 6 × 2
  date         kur
  <date>     <dbl>
1 2003-01-01  1.66
2 2003-02-01  1.62
3 2003-03-01  1.66
4 2003-04-01  1.63
5 2003-05-01  1.49
6 2003-06-01  1.42

enrj <- read_excel(paste0(path, "enrj.xlsx")) |>
  select(date = 1, enrj = TP_TUFE1YI_T118) |>
  mutate(date = as.Date(paste0(date, "-01")),
         enrj = as.numeric(enrj)) |>
  filter(!is.na(enrj))

New names:
• `` -> `...3`

Warning: There was 1 warning in `mutate()`.
ℹ In argument: `enrj = as.numeric(enrj)`.
Caused by warning:
! NAs introduced by coercion

head(enrj)

# A tibble: 6 × 2
  date        enrj
  <date>     <dbl>
1 2003-01-01  103.
2 2003-02-01  104.
3 2003-03-01  104.
4 2003-04-01  103.
5 2003-05-01  103.
6 2003-06-01  103.

kko <- read_excel(paste0(path, "sanayikapasitekullanım.xlsx"), sheet = "EVDS") |>
  select(date = Tarih, kko = TP_KKO_MA) |>
  mutate(date = as.Date(paste0(date, "-01")),
         kko  = as.numeric(kko)) |>
  filter(!is.na(kko))

New names:
• `` -> `...3`

Warning: There was 1 warning in `mutate()`.
ℹ In argument: `kko = as.numeric(kko)`.
Caused by warning:
! NAs introduced by coercion

head(kko)

# A tibble: 6 × 2
  date         kko
  <date>     <dbl>
1 2013-01-01  75.7
2 2013-02-01  74.6
3 2013-03-01  75.7
4 2013-04-01  75.6
5 2013-05-01  76.8
6 2013-06-01  77.1

imp_raw  <- read_excel(paste0(path, "kaucuk_bfe.xls"), col_names = FALSE)

New names:
• `` -> `...1`
• `` -> `...2`
• `` -> `...3`
• `` -> `...4`
• `` -> `...5`
• `` -> `...6`

yil_vec  <- as.numeric(imp_raw[[2]])
yil_dolu <- zoo::na.locf(
  ifelse(!is.na(yil_vec) & nchar(as.character(yil_vec)) == 4, yil_vec, NA),
  na.rm = FALSE)

imp_bfe <- tibble(
  yil     = as.numeric(yil_dolu),
  ay_str  = as.character(imp_raw[[4]]),
  imp_bfe = as.numeric(imp_raw[[6]])
) |>
  filter(!is.na(yil), !is.na(imp_bfe), nchar(ay_str) >= 2) |>
  mutate(ay   = as.integer(substr(ay_str, 1, 2)),
         date = as.Date(paste0(yil, "-", sprintf("%02d", ay), "-01"))) |>
  select(date, imp_bfe)

Warning in eval_tidy(xs[[j]], mask): NAs introduced by coercion

head(imp_bfe)

# A tibble: 6 × 2
  date       imp_bfe
  <date>       <dbl>
1 2013-01-01    166.
2 2013-02-01    165.
3 2013-03-01    163.
4 2013-04-01    165.
5 2013-05-01    161.
6 2013-06-01    157.

df_clean <- pci |>
  inner_join(brent,   by = "date") |>
  inner_join(kur,     by = "date") |>
  inner_join(enrj,    by = "date") |>
  inner_join(kko,     by = "date") |>
  inner_join(imp_bfe, by = "date") |>
  filter(date >= as.Date("2013-09-01"),
         date <= as.Date("2024-12-01")) |>
  arrange(date)

cat("Observations:", nrow(df_clean), "\n")

Observations: 136 

cat("Period:", format(min(df_clean$date), "%Y-%m"),
    "to", format(max(df_clean$date), "%Y-%m"), "\n")

Period: 2013-09 to 2024-12 

print(colSums(is.na(df_clean)))

   date     pci   brent     kur    enrj     kko imp_bfe 
      0       0       0       0       0       0       0 

theme_ts <- theme_minimal(base_size = 10) +
  theme(
    plot.title       = element_text(face = "bold", size = 10),
    axis.text.x      = element_text(angle = 45, hjust = 1, size = 8),
    panel.grid.minor = element_blank()
  )

p1 <- ggplot(df_clean, aes(x = date, y = pci)) +
  geom_line(color = "#2E75B6", linewidth = 0.8) +
  scale_x_date(date_breaks = "1 year", date_labels = "%Y") +
  labs(title = "Plastic & Rubber Producer Price Index (PCI)",
       x = "", y = "Index (2003=100)") + theme_ts

p2 <- ggplot(df_clean, aes(x = date, y = brent)) +
  geom_line(color = "#C00000", linewidth = 0.8) +
  scale_x_date(date_breaks = "1 year", date_labels = "%Y") +
  labs(title = "Brent Crude Oil Price",
       x = "", y = "USD/barrel") + theme_ts

p3 <- ggplot(df_clean, aes(x = date, y = kur)) +
  geom_line(color = "#70AD47", linewidth = 0.8) +
  scale_x_date(date_breaks = "1 year", date_labels = "%Y") +
  labs(title = "USD/TRY Exchange Rate",
       x = "", y = "TRY per USD") + theme_ts

p4 <- ggplot(df_clean, aes(x = date, y = enrj)) +
  geom_line(color = "#ED7D31", linewidth = 0.8) +
  scale_x_date(date_breaks = "1 year", date_labels = "%Y") +
  labs(title = "Energy Producer Price Index (NACE D)",
       x = "", y = "Index (2003=100)") + theme_ts

p5 <- ggplot(df_clean, aes(x = date, y = kko)) +
  geom_line(color = "#7030A0", linewidth = 0.8) +
  scale_x_date(date_breaks = "1 year", date_labels = "%Y") +
  labs(title = "General Manufacturing Capacity Utilization Rate",
       x = "", y = "%") + theme_ts

p6 <- ggplot(df_clean, aes(x = date, y = imp_bfe)) +
  geom_line(color = "#00B0F0", linewidth = 0.8) +
  scale_x_date(date_breaks = "1 year", date_labels = "%Y") +
  labs(title = "Rubber/Polymer Import Unit Value Index (2015=100)",
       x = "", y = "Index (2015=100)") + theme_ts

(p1 / p2 / p3 / p4 / p5 / p6) +
  plot_annotation(
    title    = "Figure 1: Time Series of All Model Variables",
    subtitle = "Source: TCMB EVDS, FRED, TÜİK | Period: 2013:09 – 2024:12",
    theme    = theme(
      plot.title    = element_text(size = 13, face = "bold", hjust = 0.5),
      plot.subtitle = element_text(size = 9, hjust = 0.5, color = "grey50")
    )
  )

Figure 1

# Log dönüşümü
df_log <- df_clean |>
  mutate(
    ln_pci     = log(pci),
    ln_brent   = log(brent),
    ln_kur     = log(kur),
    ln_enrj    = log(enrj),
    ln_imp_bfe = log(imp_bfe)
    # kko yüzde değişken, log alınmadı
  )

# Descriptive statistics tablosu
df_log |>
  select(ln_pci, ln_brent, ln_kur, ln_enrj, kko, ln_imp_bfe) |>
  pivot_longer(everything(), names_to = "Variable") |>
  group_by(Variable) |>
  summarise(
    N       = n(),
    Mean    = round(mean(value, na.rm=TRUE), 4),
    Std.Dev = round(sd(value, na.rm=TRUE), 4),
    Min     = round(min(value, na.rm=TRUE), 4),
    Median  = round(median(value, na.rm=TRUE), 4),
    Max     = round(max(value, na.rm=TRUE), 4)
  ) |>
  kbl(booktabs=TRUE, caption="Descriptive Statistics (Log-transformed Variables)") |>
  kable_styling(bootstrap_options=c("striped","hover"), full_width=FALSE)

Descriptive Statistics (Log-transformed Variables)

Variable	N	Mean	Std.Dev	Min	Median	Max
kko	136	76.2801	2.4118	61.9000	76.6000	79.5000
ln_brent	136	4.2009	0.3363	2.9113	4.2313	4.8098
ln_enrj	136	6.2483	0.9920	5.2513	5.9596	8.3255
ln_imp_bfe	136	4.6496	0.1460	4.3334	4.6284	4.9586
ln_kur	136	1.8746	0.8831	0.6883	1.7458	3.5526
ln_pci	136	6.2509	0.8228	5.3073	6.0674	7.9291

library(tseries)

degiskenler <- c("ln_pci","ln_brent","ln_kur","ln_enrj","kko","ln_imp_bfe")

adf_sonuc <- map_dfr(degiskenler, function(v) {
  seri      <- df_log[[v]]
  adf_duz   <- adf.test(na.omit(seri))
  adf_fark  <- adf.test(na.omit(diff(seri)))
  tibble(
    Variable        = v,
    `ADF Level`     = round(adf_duz$statistic, 3),
    `p (Level)`     = round(adf_duz$p.value, 3),
    `ADF 1st Diff`  = round(adf_fark$statistic, 3),
    `p (1st Diff)`  = round(adf_fark$p.value, 3),
    Integration     = ifelse(adf_duz$p.value < 0.05, "I(0)", "I(1)")
  )
})

Warning in adf.test(na.omit(diff(seri))): p-value smaller than printed p-value
Warning in adf.test(na.omit(diff(seri))): p-value smaller than printed p-value
Warning in adf.test(na.omit(diff(seri))): p-value smaller than printed p-value
Warning in adf.test(na.omit(diff(seri))): p-value smaller than printed p-value

adf_sonuc |>
  kbl(booktabs=TRUE, caption="ADF Unit Root Test Results") |>
  kable_styling(bootstrap_options=c("striped","hover"), full_width=FALSE) |>
  column_spec(6, background = ifelse(adf_sonuc$Integration=="I(0)","#d5f5e3","#fdebd0"))

ADF Unit Root Test Results

Variable	ADF Level	p (Level)	ADF 1st Diff	p (1st Diff)	Integration
ln_pci	-1.577	0.753	-3.597	0.036	I(1)
ln_brent	-2.745	0.267	-5.104	0.010	I(1)
ln_kur	-1.642	0.725	-4.849	0.010	I(1)
ln_enrj	-2.425	0.400	-3.714	0.026	I(1)
kko	-3.136	0.104	-6.034	0.010	I(1)
ln_imp_bfe	-3.227	0.086	-4.336	0.010	I(1)

par(mfrow=c(3,2), mar=c(4,4,3,1))

acf(df_log$ln_pci,     main="ACF: ln PCI",     lag.max=24, col="#2E75B6")
acf(df_log$ln_brent,   main="ACF: ln BRENT",   lag.max=24, col="#C00000")
acf(df_log$ln_kur,     main="ACF: ln KUR",     lag.max=24, col="#70AD47")
acf(df_log$ln_enrj,    main="ACF: ln ENRJ",    lag.max=24, col="#ED7D31")
acf(df_log$kko,        main="ACF: KKO",        lag.max=24, col="#7030A0")
acf(df_log$ln_imp_bfe, main="ACF: ln IMP_BFE", lag.max=24, col="#00B0F0")

Figure 2

lb_sonuc <- map_dfr(degiskenler, function(v) {
  test <- Box.test(df_log[[v]], lag=12, type="Ljung-Box")
  tibble(
    Variable    = v,
    `Chi-sq`    = round(test$statistic, 3),
    `p-value`   = round(test$p.value, 4),
    Result      = ifelse(test$p.value < 0.05,
                         "Autocorrelation present",
                         "No autocorrelation")
  )
})

lb_sonuc |>
  kbl(booktabs=TRUE, caption="Ljung-Box Autocorrelation Test (lag=12)") |>
  kable_styling(bootstrap_options=c("striped","hover"), full_width=FALSE)

Ljung-Box Autocorrelation Test (lag=12)

Variable	Chi-sq	p-value	Result
ln_pci	1267.721	0	Autocorrelation present
ln_brent	596.579	0	Autocorrelation present
ln_kur	1265.231	0	Autocorrelation present
ln_enrj	1291.030	0	Autocorrelation present
kko	195.869	0	Autocorrelation present
ln_imp_bfe	639.718	0	Autocorrelation present

library(lmtest)
library(sandwich)

# Adım 1: OLS regresyon
ols <- lm(ln_pci ~ ln_brent + ln_kur + ln_enrj + kko + ln_imp_bfe,
          data = df_log)

# Adım 2: Residual'ları al
residuals_ols <- residuals(ols)

# Adım 3: Residual'lara ADF testi (Engle-Granger)
eg_test <- adf.test(residuals_ols)

cat("=== Engle-Granger Cointegration Test ===\n")

=== Engle-Granger Cointegration Test ===

cat("ADF Statistic:", round(eg_test$statistic, 4), "\n")

ADF Statistic: -1.8913 

cat("p-value:", round(eg_test$p.value, 4), "\n")

p-value: 0.6217 

cat("Sonuç:", ifelse(eg_test$p.value < 0.05,
                    "Residuals stationary → Cointegration EXISTS",
                    "Residuals non-stationary → No cointegration"), "\n")

Sonuç: Residuals non-stationary → No cointegration 

# Adım 4: OLS sonuçları
summary(ols)

Call:
lm(formula = ln_pci ~ ln_brent + ln_kur + ln_enrj + kko + ln_imp_bfe, 
    data = df_log)

Residuals:
      Min        1Q    Median        3Q       Max 
-0.135859 -0.036190 -0.001304  0.034829  0.121729 

Coefficients:
              Estimate Std. Error t value Pr(>|t|)    
(Intercept)  2.9680681  0.2350276  12.629  < 2e-16 ***
ln_brent     0.0510733  0.0257346   1.985 0.049293 *  
ln_kur       0.8251377  0.0207413  39.782  < 2e-16 ***
ln_enrj      0.0890617  0.0191931   4.640 8.38e-06 ***
kko         -0.0008231  0.0021823  -0.377 0.706661    
ln_imp_bfe   0.2210385  0.0573360   3.855 0.000181 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.0565 on 130 degrees of freedom
Multiple R-squared:  0.9955,    Adjusted R-squared:  0.9953 
F-statistic:  5700 on 5 and 130 DF,  p-value: < 2.2e-16

library(vars)

Loading required package: MASS

Attaching package: 'MASS'

The following object is masked from 'package:patchwork':

    area

The following object is masked from 'package:dplyr':

    select

Loading required package: strucchange

Attaching package: 'strucchange'

The following object is masked from 'package:stringr':

    boundary

Loading required package: urca

# VAR - VECTOR AUTOREGRESSION MODELİ
# Engle-Granger eşbütünleşme bulunamadığı için (p=0.6217)
# VAR modeli uygulanıyor. Tüm değişkenler I(1) olduğu için
# birinci farkları alınarak VAR tahmin edilecek.


# Adım 1: Birinci farkları al
df_var <- df_log |>
  mutate(
    d_ln_pci     = c(NA, diff(ln_pci)),
    d_ln_brent   = c(NA, diff(ln_brent)),
    d_ln_kur     = c(NA, diff(ln_kur)),
    d_ln_enrj    = c(NA, diff(ln_enrj)),
    d_kko        = c(NA, diff(kko)),
    d_ln_imp_bfe = c(NA, diff(ln_imp_bfe))
  ) |>
  filter(!is.na(d_ln_pci))

# Adım 2: VAR için matris oluştur (dplyr::select ile çakışma önlendi)
var_data <- df_var |>
  dplyr::select(d_ln_pci, d_ln_brent, d_ln_kur,
                d_ln_enrj, d_kko, d_ln_imp_bfe) |>
  as.matrix()

# Adım 3: Optimal lag seçimi (AIC kriterine göre)
lag_select <- VARselect(var_data, lag.max = 12, type = "const")
cat("=== Optimal Lag Seçimi ===\n")

=== Optimal Lag Seçimi ===

print(lag_select$selection)

AIC(n)  HQ(n)  SC(n) FPE(n) 
     1      1      1      1 

optimal_lag <- lag_select$selection["AIC(n)"]
cat("\nSeçilen lag (AIC):", optimal_lag, "\n")

Seçilen lag (AIC): 1 

# Adım 4: VAR modeli tahmin et
var_model <- VAR(var_data, p = optimal_lag, type = "const")
summary(var_model)

VAR Estimation Results:
========================= 
Endogenous variables: d_ln_pci, d_ln_brent, d_ln_kur, d_ln_enrj, d_kko, d_ln_imp_bfe 
Deterministic variables: const 
Sample size: 134 
Log Likelihood: 1047.457 
Roots of the characteristic polynomial:
0.5857 0.5857 0.4142 0.4142 0.2818 0.1426
Call:
VAR(y = var_data, p = optimal_lag, type = "const")


Estimation results for equation d_ln_pci: 
========================================= 
d_ln_pci = d_ln_pci.l1 + d_ln_brent.l1 + d_ln_kur.l1 + d_ln_enrj.l1 + d_kko.l1 + d_ln_imp_bfe.l1 + const 

                 Estimate Std. Error t value Pr(>|t|)    
d_ln_pci.l1      0.456520   0.104372   4.374 2.52e-05 ***
d_ln_brent.l1   -0.002049   0.014332  -0.143 0.886517    
d_ln_kur.l1      0.182903   0.054082   3.382 0.000957 ***
d_ln_enrj.l1    -0.024444   0.021225  -1.152 0.251624    
d_kko.l1         0.001456   0.001088   1.338 0.183226    
d_ln_imp_bfe.l1  0.085304   0.049320   1.730 0.086128 .  
const            0.007292   0.001978   3.688 0.000334 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1


Residual standard error: 0.01716 on 127 degrees of freedom
Multiple R-Squared: 0.5351, Adjusted R-squared: 0.5131 
F-statistic: 24.36 on 6 and 127 DF,  p-value: < 2.2e-16 


Estimation results for equation d_ln_brent: 
=========================================== 
d_ln_brent = d_ln_pci.l1 + d_ln_brent.l1 + d_ln_kur.l1 + d_ln_enrj.l1 + d_kko.l1 + d_ln_imp_bfe.l1 + const 

                 Estimate Std. Error t value Pr(>|t|)    
d_ln_pci.l1      0.081696   0.638607   0.128    0.898    
d_ln_brent.l1    0.462550   0.087691   5.275 5.55e-07 ***
d_ln_kur.l1      0.315477   0.330905   0.953    0.342    
d_ln_enrj.l1     0.002159   0.129868   0.017    0.987    
d_kko.l1        -0.036039   0.006655  -5.415 2.95e-07 ***
d_ln_imp_bfe.l1  0.099139   0.301766   0.329    0.743    
const           -0.010150   0.012100  -0.839    0.403    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1


Residual standard error: 0.105 on 127 degrees of freedom
Multiple R-Squared: 0.2623, Adjusted R-squared: 0.2274 
F-statistic: 7.525 on 6 and 127 DF,  p-value: 6.473e-07 


Estimation results for equation d_ln_kur: 
========================================= 
d_ln_kur = d_ln_pci.l1 + d_ln_brent.l1 + d_ln_kur.l1 + d_ln_enrj.l1 + d_kko.l1 + d_ln_imp_bfe.l1 + const 

                 Estimate Std. Error t value Pr(>|t|)    
d_ln_pci.l1     -0.413611   0.247799  -1.669 0.097553 .  
d_ln_brent.l1   -0.029435   0.034027  -0.865 0.388641    
d_ln_kur.l1      0.580249   0.128402   4.519  1.4e-05 ***
d_ln_enrj.l1    -0.029059   0.050393  -0.577 0.565191    
d_kko.l1         0.003009   0.002582   1.165 0.246095    
d_ln_imp_bfe.l1  0.159792   0.117094   1.365 0.174779    
const            0.017854   0.004695   3.803 0.000221 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1


Residual standard error: 0.04075 on 127 degrees of freedom
Multiple R-Squared: 0.1979, Adjusted R-squared:  0.16 
F-statistic: 5.223 on 6 and 127 DF,  p-value: 7.755e-05 


Estimation results for equation d_ln_enrj: 
========================================== 
d_ln_enrj = d_ln_pci.l1 + d_ln_brent.l1 + d_ln_kur.l1 + d_ln_enrj.l1 + d_kko.l1 + d_ln_imp_bfe.l1 + const 

                  Estimate Std. Error t value Pr(>|t|)  
d_ln_pci.l1      1.0769923  0.4286592   2.512   0.0132 *
d_ln_brent.l1    0.0098845  0.0588619   0.168   0.8669  
d_ln_kur.l1      0.0954126  0.2221175   0.430   0.6682  
d_ln_enrj.l1     0.1395619  0.0871727   1.601   0.1119  
d_kko.l1        -0.0004281  0.0044673  -0.096   0.9238  
d_ln_imp_bfe.l1  0.0061906  0.2025576   0.031   0.9757  
const           -0.0076589  0.0081219  -0.943   0.3475  
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1


Residual standard error: 0.07048 on 127 degrees of freedom
Multiple R-Squared: 0.2128, Adjusted R-squared: 0.1756 
F-statistic: 5.722 on 6 and 127 DF,  p-value: 2.703e-05 


Estimation results for equation d_kko: 
====================================== 
d_kko = d_ln_pci.l1 + d_ln_brent.l1 + d_ln_kur.l1 + d_ln_enrj.l1 + d_kko.l1 + d_ln_imp_bfe.l1 + const 

                 Estimate Std. Error t value Pr(>|t|)    
d_ln_pci.l1     -10.97992    8.16091  -1.345   0.1809    
d_ln_brent.l1     7.26647    1.12063   6.484  1.8e-09 ***
d_ln_kur.l1       2.29294    4.22872   0.542   0.5886    
d_ln_enrj.l1     -0.92770    1.65962  -0.559   0.5772    
d_kko.l1         -0.21971    0.08505  -2.583   0.0109 *  
d_ln_imp_bfe.l1  -1.69826    3.85634  -0.440   0.6604    
const             0.18428    0.15463   1.192   0.2356    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1


Residual standard error: 1.342 on 127 degrees of freedom
Multiple R-Squared: 0.2616, Adjusted R-squared: 0.2267 
F-statistic: 7.499 on 6 and 127 DF,  p-value: 6.836e-07 


Estimation results for equation d_ln_imp_bfe: 
============================================= 
d_ln_imp_bfe = d_ln_pci.l1 + d_ln_brent.l1 + d_ln_kur.l1 + d_ln_enrj.l1 + d_kko.l1 + d_ln_imp_bfe.l1 + const 

                  Estimate Std. Error t value Pr(>|t|)   
d_ln_pci.l1      0.2751314  0.1859478   1.480  0.14145   
d_ln_brent.l1    0.0215394  0.0255337   0.844  0.40050   
d_ln_kur.l1      0.0191429  0.0963522   0.199  0.84283   
d_ln_enrj.l1    -0.0495073  0.0378146  -1.309  0.19283   
d_kko.l1         0.0002676  0.0019378   0.138  0.89038   
d_ln_imp_bfe.l1  0.2702951  0.0878674   3.076  0.00257 **
const           -0.0060511  0.0035232  -1.718  0.08832 . 
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1


Residual standard error: 0.03058 on 127 degrees of freedom
Multiple R-Squared: 0.139,  Adjusted R-squared: 0.09831 
F-statistic: 3.417 on 6 and 127 DF,  p-value: 0.003688 



Covariance matrix of residuals:
               d_ln_pci d_ln_brent   d_ln_kur  d_ln_enrj      d_kko
d_ln_pci      2.945e-04  7.832e-05  0.0005990  0.0002317  0.0019736
d_ln_brent    7.832e-05  1.103e-02 -0.0001900 -0.0001953  0.0480211
d_ln_kur      5.990e-04 -1.900e-04  0.0016602  0.0007029  0.0022070
d_ln_enrj     2.317e-04 -1.953e-04  0.0007029  0.0049679 -0.0003812
d_kko         1.974e-03  4.802e-02  0.0022070 -0.0003812  1.8006513
d_ln_imp_bfe -2.251e-06 -1.883e-04 -0.0001427  0.0001136  0.0003364
             d_ln_imp_bfe
d_ln_pci       -2.251e-06
d_ln_brent     -1.883e-04
d_ln_kur       -1.427e-04
d_ln_enrj       1.136e-04
d_kko           3.364e-04
d_ln_imp_bfe    9.348e-04

Correlation matrix of residuals:
              d_ln_pci d_ln_brent d_ln_kur d_ln_enrj     d_kko d_ln_imp_bfe
d_ln_pci      1.000000    0.04346  0.85657  0.191579  0.085701    -0.004289
d_ln_brent    0.043461    1.00000 -0.04441 -0.026393  0.340806    -0.058665
d_ln_kur      0.856566   -0.04441  1.00000  0.244768  0.040365    -0.114545
d_ln_enrj     0.191579   -0.02639  0.24477  1.000000 -0.004031     0.052707
d_kko         0.085701    0.34081  0.04036 -0.004031  1.000000     0.008200
d_ln_imp_bfe -0.004289   -0.05867 -0.11454  0.052707  0.008200     1.000000