Загружаем библиотеки и данные:
library(dplyr)
library(plm)
library(dynlm)
library(pglm)
library(readr)
library(dplyr)
library(tidyr)
library(ggplot2)
library(GGally)
library(sandwich)
library(lmtest)
library(car)
library(broom)
library(xtable)
library(ggpubr)
library(stargazer)
library(modelsummary)
library(haven)
library(readr)
library(margins)
library(ivreg)
library(readxl)
panel_data6 <- read_excel("panel_data6.xlsx")Расчет корреляция между переменными
correlation_matrix <- cor(panel_data6)
print(correlation_matrix)## Year Id FS VOL DL
## Year 1.000000000 0.000000e+00 0.05287655 0.012307931 -0.002389351
## Id 0.000000000 1.000000e+00 -0.02335167 -0.037888465 0.044661988
## FS 0.052876553 -2.335167e-02 1.00000000 0.597827535 -0.688492288
## VOL 0.012307931 -3.788846e-02 0.59782753 1.000000000 -0.404295468
## DL -0.002389351 4.466199e-02 -0.68849229 -0.404295468 1.000000000
## Bin 0.049993012 -2.040071e-02 0.72944285 0.435067395 -0.573992470
## FS_L 0.053991540 -1.926151e-02 0.82945173 0.495024766 -0.629482233
## Age -0.032119960 -1.303681e-02 0.07044426 0.038590550 -0.071024301
## Size 0.066822316 -9.521384e-03 0.80670959 0.467552078 -0.421261053
## VOL_ebit 0.014262081 -2.250004e-03 0.01809547 0.010281789 -0.032549661
## EPU 0.773087102 1.426114e-17 0.03833615 0.023572879 -0.009226967
## R -0.948754294 -2.303481e-18 -0.04973552 -0.006200962 0.003233230
## Bin FS_L Age Size VOL_ebit
## Year 0.04999301 0.05399154 -0.03211996 0.066822316 0.014262081
## Id -0.02040071 -0.01926151 -0.01303681 -0.009521384 -0.002250004
## FS 0.72944285 0.82945173 0.07044426 0.806709592 0.018095465
## VOL 0.43506740 0.49502477 0.03859055 0.467552078 0.010281789
## DL -0.57399247 -0.62948223 -0.07102430 -0.421261053 -0.032549661
## Bin 1.00000000 0.98637119 0.07891028 0.632838418 0.053329389
## FS_L 0.98637119 1.00000000 0.07931454 0.705869182 0.047461179
## Age 0.07891028 0.07931454 1.00000000 0.015695064 0.015931936
## Size 0.63283842 0.70586918 0.01569506 1.000000000 -0.010124330
## VOL_ebit 0.05332939 0.04746118 0.01593194 -0.010124330 1.000000000
## EPU 0.05215859 0.05286706 -0.04540272 0.048248752 0.026489917
## R -0.04233416 -0.04731749 0.03121915 -0.063350099 -0.002576494
## EPU R
## Year 7.730871e-01 -9.487543e-01
## Id 1.426114e-17 -2.303481e-18
## FS 3.833615e-02 -4.973552e-02
## VOL 2.357288e-02 -6.200962e-03
## DL -9.226967e-03 3.233230e-03
## Bin 5.215859e-02 -4.233416e-02
## FS_L 5.286706e-02 -4.731749e-02
## Age -4.540272e-02 3.121915e-02
## Size 4.824875e-02 -6.335010e-02
## VOL_ebit 2.648992e-02 -2.576494e-03
## EPU 1.000000e+00 -8.273969e-01
## R -8.273969e-01 1.000000e+00Проверка 1 гипотезы Для VOL_Net_income
Модель Logit
#BIN
logit_model <- pglm(Bin ~ VOL + DL + Age + Size + EPU + R, data = panel_data6,
index = c("Id", "Year"), family = binomial(link = "logit"))
summary(logit_model)## --------------------------------------------
## Maximum Likelihood estimation
## Newton-Raphson maximisation, 5 iterations
## Return code 8: successive function values within relative tolerance limit (reltol)
## Log-Likelihood: -255.5948
## 8 free parameters
## Estimates:
## Estimate Std. error t value Pr(> t)
## (Intercept) -45.28041 6.51179 -6.954 3.56e-12 ***
## VOL 0.19940 0.02888 6.905 5.01e-12 ***
## DL -15.37166 1.83099 -8.395 < 2e-16 ***
## Age 0.09044 0.03831 2.361 0.0182 *
## Size 9.04597 0.93286 9.697 < 2e-16 ***
## EPU 1.00058 0.63899 1.566 0.1174
## R 10.63817 15.47305 0.688 0.4917
## sigma -0.49426 0.41195 -1.200 0.2302
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## --------------------------------------------Модель Probit
#BIN
probit_model <- pglm(Bin ~ VOL + DL + Age + Size + EPU + R, data = panel_data6,
index = c("Id", "Year"), family = binomial(link = "probit"))
summary(probit_model)## --------------------------------------------
## Maximum Likelihood estimation
## Newton-Raphson maximisation, 8 iterations
## Return code 8: successive function values within relative tolerance limit (reltol)
## Log-Likelihood: -252.9634
## 8 free parameters
## Estimates:
## Estimate Std. error t value Pr(> t)
## (Intercept) -24.59644 3.47577 -7.077 1.48e-12 ***
## VOL 0.10659 0.01545 6.897 5.30e-12 ***
## DL -8.46827 0.95977 -8.823 < 2e-16 ***
## Age 0.04542 0.02057 2.207 0.0273 *
## Size 4.94645 0.48376 10.225 < 2e-16 ***
## EPU 0.53978 0.34724 1.555 0.1201
## R 5.94202 8.47603 0.701 0.4833
## sigma 0.08594 0.68036 0.126 0.8995
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## --------------------------------------------##Модель Probit оказалась лучше, так как Log-Likelihood: -252.9634 > -255.5948
Посмотрим на показатели AIC
aic_log <- AIC(logit_model)
aic_prob <- AIC(probit_model)
print(aic_log)## [1] 527.1897
## attr(,"df")
## [1] 8print(aic_prob)## [1] 521.9269
## attr(,"df")
## [1] 8##Модель probit лучше, так как у нее меньше AIC
Проверка 1 гипотезы Для VOL_ebitda
Модель Logit для VOL_ebitda
#BIN
logit_model1 <- pglm(Bin ~ VOL_ebit + DL + Age + Size + EPU + R, data = panel_data6,
index = c("Id", "Year"), family = binomial(link = "logit"))
summary(logit_model1)## --------------------------------------------
## Maximum Likelihood estimation
## Newton-Raphson maximisation, 5 iterations
## Return code 1: gradient close to zero (gradtol)
## Log-Likelihood: -292.7823
## 8 free parameters
## Estimates:
## Estimate Std. error t value Pr(> t)
## (Intercept) -46.39065 6.10752 -7.596 3.06e-14 ***
## VOL_ebit 1.64396 0.76686 2.144 0.03205 *
## DL -17.13349 1.71082 -10.015 < 2e-16 ***
## Age 0.09874 0.03640 2.712 0.00668 **
## Size 9.78227 0.89981 10.871 < 2e-16 ***
## EPU 0.93693 0.60654 1.545 0.12241
## R 7.54486 14.60559 0.517 0.60545
## sigma -0.56648 0.33227 -1.705 0.08822 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## --------------------------------------------Модель Probit для VOL_ebitda
#BIN
probit_model1 <- pglm(Bin ~ VOL_ebit + DL + Age + Size + EPU + R, data = panel_data6,
index = c("Id", "Year"), family = binomial(link = "probit"))
summary(probit_model1)## --------------------------------------------
## Maximum Likelihood estimation
## Newton-Raphson maximisation, 6 iterations
## Return code 8: successive function values within relative tolerance limit (reltol)
## Log-Likelihood: -288.3954
## 8 free parameters
## Estimates:
## Estimate Std. error t value Pr(> t)
## (Intercept) -25.27786 3.29877 -7.663 1.82e-14 ***
## VOL_ebit 0.87943 0.41191 2.135 0.03276 *
## DL -9.37589 0.90124 -10.403 < 2e-16 ***
## Age 0.05303 0.01944 2.728 0.00638 **
## Size 5.35293 0.46909 11.411 < 2e-16 ***
## EPU 0.49640 0.33201 1.495 0.13488
## R 4.36320 8.01703 0.544 0.58628
## sigma 0.15551 0.34392 0.452 0.65114
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## --------------------------------------------##Модель Probit оказалась лучше, так как Log-Likelihood: -288.3954 > -292.7823
Посмотрим на показатели AIC
aic_log1 <- AIC(logit_model1)
aic_prob1 <- AIC(probit_model1)
print(aic_log1)## [1] 601.5646
## attr(,"df")
## [1] 8print(aic_prob1)## [1] 592.7907
## attr(,"df")
## [1] 8##Модель probit лучше, так как у нее меньше AIC
Сравним Probit модель для VOL_Net_income и Probit модель для VOL_ebitda
##Посмотрим на их Log-Likelihood: у VOL_Net_income = -252.9634 и VOL_ebitda = -288.3954
##Посмотрим на AIC: у VOL_Net_income = 521.9269 и VOL_ebitda = 592.7907
##В обоих случаях лучше модель Probit для VOL_Net_income
Проверка 2 гипотезы Для VOL_Net_income
Модель c фиксированными эффектами
fixed_model <- plm(FS_L ~ VOL + DL + Age + Size + EPU + R, data = panel_data6,
index = c("Id", "Year"))
summary(fixed_model)## Oneway (individual) effect Within Model
##
## Call:
## plm(formula = FS_L ~ VOL + DL + Age + Size + EPU + R, data = panel_data6,
## index = c("Id", "Year"))
##
## Balanced Panel: n = 277, T = 5, N = 1385
##
## Residuals:
## Min. 1st Qu. Median 3rd Qu. Max.
## -2.770648 -0.565818 0.063558 0.650847 2.501138
##
## Coefficients:
## Estimate Std. Error t-value Pr(>|t|)
## VOL 0.0166384 0.0035097 4.7408 2.408e-06 ***
## DL -5.9334948 0.3416567 -17.3668 < 2.2e-16 ***
## Age 0.0206435 0.0108567 1.9015 0.0575 .
## Size 3.5565094 0.1522705 23.3565 < 2.2e-16 ***
## EPU 0.2079169 0.1558772 1.3339 0.1825
## R 2.3576221 3.8977017 0.6049 0.5454
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Total Sum of Squares: 3350.5
## Residual Sum of Squares: 1239.5
## R-Squared: 0.63005
## Adj. R-Squared: 0.53538
## F-statistic: 312.801 on 6 and 1102 DF, p-value: < 2.22e-16Модель c рандомными эффектами
random_model <- plm(FS_L ~ VOL + DL + Age + Size + EPU + R, data = panel_data6,
index = c("Id", "Year"), model = "random")
summary(random_model)## Oneway (individual) effect Random Effect Model
## (Swamy-Arora's transformation)
##
## Call:
## plm(formula = FS_L ~ VOL + DL + Age + Size + EPU + R, data = panel_data6,
## model = "random", index = c("Id", "Year"))
##
## Balanced Panel: n = 277, T = 5, N = 1385
##
## Effects:
## var std.dev share
## idiosyncratic 1.125 1.061 1
## individual 0.000 0.000 0
## theta: 0
##
## Residuals:
## Min. 1st Qu. Median 3rd Qu. Max.
## -3.004432 -0.572643 0.085973 0.691253 2.428730
##
## Coefficients:
## Estimate Std. Error z-value Pr(>|z|)
## (Intercept) -13.5907036 1.3419616 -10.1275 < 2.2e-16 ***
## VOL 0.0178069 0.0030513 5.8358 5.353e-09 ***
## DL -6.0537615 0.2986816 -20.2683 < 2.2e-16 ***
## Age 0.0249392 0.0095760 2.6044 0.009205 **
## Size 3.4792210 0.1336340 26.0354 < 2.2e-16 ***
## EPU 0.2064565 0.1538730 1.3417 0.179683
## R 2.2127793 3.8468403 0.5752 0.565143
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Total Sum of Squares: 4243.2
## Residual Sum of Squares: 1511.6
## R-Squared: 0.64377
## Adj. R-Squared: 0.64222
## Chisq: 2490.3 on 6 DF, p-value: < 2.22e-16Посчитаем AIC aic2 <- AIC(fixed_model) aic22 <- AIC(random_model) print(aic2) print(aic22) У модели с фиксированными эффектами AIC лучше
Проверка 2 гипотезы Для VOL_ebitda
Модель c фиксированными эффектами
fixed_model2 <- plm(FS_L ~ VOL_ebit + DL + Age + Size + EPU + R, data = panel_data6,
index = c("Id", "Year"))
summary(fixed_model2)## Oneway (individual) effect Within Model
##
## Call:
## plm(formula = FS_L ~ VOL_ebit + DL + Age + Size + EPU + R, data = panel_data6,
## index = c("Id", "Year"))
##
## Balanced Panel: n = 277, T = 5, N = 1385
##
## Residuals:
## Min. 1st Qu. Median 3rd Qu. Max.
## -2.879216 -0.557168 0.077876 0.623760 2.694895
##
## Coefficients:
## Estimate Std. Error t-value Pr(>|t|)
## VOL_ebit 0.604961 0.213579 2.8325 0.004703 **
## DL -6.324018 0.331457 -19.0795 < 2.2e-16 ***
## Age 0.021334 0.010926 1.9527 0.051112 .
## Size 3.822555 0.143194 26.6948 < 2.2e-16 ***
## EPU 0.219095 0.156918 1.3962 0.162924
## R 2.848724 3.921000 0.7265 0.467668
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Total Sum of Squares: 3350.5
## Residual Sum of Squares: 1255.6
## R-Squared: 0.62524
## Adj. R-Squared: 0.52934
## F-statistic: 306.42 on 6 and 1102 DF, p-value: < 2.22e-16Модель c рандомными эффектами
random_model2 <- plm(FS_L ~ VOL_ebit + DL + Age + Size + EPU + R, data = panel_data6,
index = c("Id", "Year"), model = "random")
summary(random_model2)## Oneway (individual) effect Random Effect Model
## (Swamy-Arora's transformation)
##
## Call:
## plm(formula = FS_L ~ VOL_ebit + DL + Age + Size + EPU + R, data = panel_data6,
## model = "random", index = c("Id", "Year"))
##
## Balanced Panel: n = 277, T = 5, N = 1385
##
## Effects:
## var std.dev share
## idiosyncratic 1.139 1.067 1
## individual 0.000 0.000 0
## theta: 0
##
## Residuals:
## Min. 1st Qu. Median 3rd Qu. Max.
## -3.105963 -0.514824 0.084386 0.669658 2.620826
##
## Coefficients:
## Estimate Std. Error z-value Pr(>|z|)
## (Intercept) -14.8483516 1.3386657 -11.0919 < 2.2e-16 ***
## VOL_ebit 0.4457952 0.1900436 2.3458 0.018989 *
## DL -6.4732643 0.2919179 -22.1749 < 2.2e-16 ***
## Age 0.0256291 0.0096737 2.6494 0.008065 **
## Size 3.7673214 0.1260135 29.8962 < 2.2e-16 ***
## EPU 0.2255714 0.1554807 1.4508 0.146835
## R 2.8847121 3.8848064 0.7426 0.457747
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Total Sum of Squares: 4243.2
## Residual Sum of Squares: 1542.8
## R-Squared: 0.63642
## Adj. R-Squared: 0.63484
## Chisq: 2412.08 on 6 DF, p-value: < 2.22e-16Посчитаем AIC aic3 <- AIC(fixed_model2) aic33 <- AIC(random_model2) print(aic3) print(aic33) У модели с фиксированными эффектами AIC лучше
Сравним модели с фиксированными эффектами для VOL_Net_income и VOL_ebitda aic2 <- AIC(fixed_model) aic3 <- AIC(fixed_model2) print(aic2) print(aic3) У модели VOL_Net_income с фиксированными эффектами AIC лучше