Minimum Wage Dynamics and Unemployment Disparities: Panel Evidence from 12 EU Countries (2010–2023)
Si Tang Lin
2025-06-01
Si-Tang Lin
Loading Require Library
Import & Inspect data
#import data
eu_panel_data <- read.csv("~/Desktop/dsba/spring semester/econometrics/final project/eu_panel_data.csv")
str(eu_panel_data)## 'data.frame': 168 obs. of 9 variables:
## $ Country : chr "Belgium" "Belgium" "Belgium" "Belgium" ...
## $ Year : int 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 ...
## $ Total.Unemployment.Rate : num 8.3 7.2 7.6 8.4 8.5 8.5 7.8 7.1 6 5.4 ...
## $ Monthly.Minimum.Wage..euro. : chr "1,388" "1,430" "1,458" "1,502" ...
## $ Real.GDP.Growth.Rate : num 100 102 102 102 104 ...
## $ Inflation.Rate..HICP. : num 92.1 95.2 97.7 98.9 99.4 ...
## $ Education.Expenditure....of.GDP. : num 6 6.2 6.2 6.3 6.3 6.3 6.3 6.2 6.2 6.1 ...
## $ Social.Protection.Expenditure..million.euro.: chr "101,947.70" "107,535.07" "109,573.14" "113,134.35" ...
## $ Labor.Force.Participation.Rate : num 54.1 53.2 53.2 53.6 53.5 ...Data Cleaning
#change the data to numerical type
eu_panel_data <- eu_panel_data %>%
mutate(
Monthly.Minimum.Wage..euro. = as.numeric(gsub(",", "", Monthly.Minimum.Wage..euro.)),
Social.Protection.Expenditure..million.euro. = as.numeric(gsub(",", "", Social.Protection.Expenditure..million.euro.))
)
#change names of variable
eu_panel_data <- eu_panel_data %>%rename(Unemployment_Rate=Total.Unemployment.Rate)
eu_panel_data <- eu_panel_data %>%rename(Minimum_wage=Monthly.Minimum.Wage..euro.)
eu_panel_data <- eu_panel_data %>%rename(GDP=Real.GDP.Growth.Rate)
eu_panel_data <- eu_panel_data %>%rename(Inflation=Inflation.Rate..HICP.)
eu_panel_data <- eu_panel_data %>%rename(Edu_exp=Education.Expenditure....of.GDP.)
eu_panel_data <- eu_panel_data %>%rename(Siopo_exp=Social.Protection.Expenditure..million.euro.)
eu_panel_data <- eu_panel_data %>%rename(LF_partic=Labor.Force.Participation.Rate)
#Clean data
model_vars <- c("Unemployment_Rate", "Minimum_wage", "GDP", "Inflation", "Edu_exp", "Siopo_exp","LF_partic")
complete_panel <- eu_panel_data[complete.cases(eu_panel_data[, model_vars]), ]Variable Description
# Variable explanation
#**Unemployment Rate**: Share of the labor force aged 15–74 that is jobless, actively seeking work, and available to start within two weeks.
#**Minimum Wage**: Statutory minimum remuneration set by law or national agreement, usually expressed monthly.
#**GDP Growth Rate**: Annual percentage change in real GDP.
#**Inflation Rate**: Year-over-year percentage change in the Harmonised Index of Consumer Prices (HICP).
#**Education Expenditure**: Public spending on education as a percentage of GDP, including school operations and support to households.
#**Social Protection Expenditure**: Government expenditure on social welfare programs, such as pensions, healthcare, and unemployment benefits (% of GDP).
#**Labor Force Participation**: Percentage of the population aged 15–64 that is either employed or actively looking for work.
# This is a unbalanced panel
## Germany officially introduced a national wide minimum wage system for the first time in 2015. Therefore, the missing data on Germany's minimum wage for the years prior to 2015 is not a random omission, but a structural absence reflecting historical economic policy.
## Greece has a missing value for social protection expenditure in 2023, possibly due to reporting delays or data unavailability from official sources.
## Thus, instead of 168 datasize, we have 6 missing variables in our dataset. 162 will further proceed in our research.Data Visualization
# Visualize of variables
library(DescTools)##
## Attaching package: 'DescTools'## The following object is masked from 'package:car':
##
## RecodeDesc(eu_panel_data)## ──────────────────────────────────────────────────────────────────────────────
## Describe eu_panel_data (data.frame):
##
## data frame: 168 obs. of 9 variables
## 162 complete cases (96.4%)
##
## Nr Class ColName NAs Levels
## 1 chr Country .
## 2 int Year .
## 3 num Unemployment_Rate .
## 4 num Minimum_wage 5 (3.0%)
## 5 num GDP .
## 6 num Inflation .
## 7 num Edu_exp .
## 8 num Siopo_exp 1 (0.6%)
## 9 num LF_partic .
##
##
## ──────────────────────────────────────────────────────────────────────────────
## 1 - Country (character)
##
## length n NAs unique levels dupes
## 168 168 0 12 12 y
## 100.0% 0.0%
##
## level freq perc cumfreq cumperc
## 1 Belgium 14 8.3% 14 8.3%
## 2 Croatia 14 8.3% 28 16.7%
## 3 Czechia 14 8.3% 42 25.0%
## 4 France 14 8.3% 56 33.3%
## 5 Germany 14 8.3% 70 41.7%
## 6 Greece 14 8.3% 84 50.0%
## 7 Hungary 14 8.3% 98 58.3%
## 8 Netherlands 14 8.3% 112 66.7%
## 9 Poland 14 8.3% 126 75.0%
## 10 Portugal 14 8.3% 140 83.3%
## 11 Slovakia 14 8.3% 154 91.7%
## 12 Spain 14 8.3% 168 100.0%
## ──────────────────────────────────────────────────────────────────────────────
## 2 - Year (integer)
##
## length n NAs unique 0s mean meanCI'
## 168 168 0 14 0 2'016.50 2'015.88
## 100.0% 0.0% 0.0% 2'017.12
##
## .05 .10 .25 median .75 .90 .95
## 2'010.00 2'011.00 2'013.00 2'016.50 2'020.00 2'022.00 2'023.00
##
## range sd vcoef mad IQR skew kurt
## 13.00 4.04 0.00 5.19 7.00 0.00 -1.23
##
## lowest : 2'010 (12), 2'011 (12), 2'012 (12), 2'013 (12), 2'014 (12)
## highest: 2'019 (12), 2'020 (12), 2'021 (12), 2'022 (12), 2'023 (12)
##
## ' 95%-CI (classic)
## ──────────────────────────────────────────────────────────────────────────────
## 3 - Unemployment_Rate (numeric)
##
## length n NAs unique 0s mean meanCI'
## 168 168 0 102 0 9.296 8.414
## 100.0% 0.0% 0.0% 10.178
##
## .05 .10 .25 median .75 .90 .95
## 2.970 3.400 5.100 7.400 12.275 17.300 21.890
##
## range sd vcoef mad IQR skew kurt
## 25.500 5.788 0.623 4.818 7.175 1.207 0.933
##
## lowest : 2.0, 2.2 (2), 2.6 (2), 2.8 (2), 2.9 (2)
## highest: 24.8, 24.9, 26.1, 26.5, 27.5
##
## ' 95%-CI (classic)
## ──────────────────────────────────────────────────────────────────────────────
## 4 - Minimum_wage (numeric)
##
## length n NAs unique 0s mean meanCI'
## 168 163 5 133 0 878.15 801.62
## 97.0% 3.0% 0.0% 954.69
##
## .05 .10 .25 median .75 .90 .95
## 317.30 339.40 461.00 700.00 1'444.50 1'562.60 1'662.90
##
## range sd vcoef mad IQR skew kurt
## 1'732.00 494.83 0.56 472.95 983.50 0.56 -1.21
##
## lowest : 265.0, 287.0, 307.0, 308.0, 310.0 (2)
## highest: 1'741.0, 1'750.0, 1'955.0, 1'965.0, 1'997.0
##
## ' 95%-CI (classic)
## ──────────────────────────────────────────────────────────────────────────────
## 5 - GDP (numeric)
##
## length n NAs unique 0s mean meanCI'
## 168 168 0 157 0 108.8113 106.7237
## 100.0% 0.0% 0.0% 110.8989
##
## .05 .10 .25 median .75 .90 .95
## 85.2285 95.4363 100.3780 106.6860 115.6348 126.0570 134.1301
##
## range sd vcoef mad IQR skew kurt
## 77.2730 13.7055 0.1260 9.9127 15.2568 0.6302 1.0739
##
## lowest : 78.07, 80.738, 81.166, 81.192, 81.377
## highest: 140.463, 140.542, 147.219, 154.956, 155.343
##
## ' 95%-CI (classic)
## ──────────────────────────────────────────────────────────────────────────────
## 6 - Inflation (numeric)
##
## length n NAs unique 0s mean meanCI'
## 168 168 0 147 0 104.8731 103.2179
## 100.0% 0.0% 0.0% 106.5283
##
## .05 .10 .25 median .75 .90 .95
## 93.0640 95.3550 99.5150 101.2850 106.5700 118.9980 126.6355
##
## range sd vcoef mad IQR skew kurt
## 71.1200 10.8669 0.1036 4.2254 7.0550 2.1521 5.8222
##
## lowest : 89.47, 91.69, 92.05, 92.09, 92.55
## highest: 137.22, 138.79, 143.5, 147.9, 160.59
##
## ' 95%-CI (classic)
## ──────────────────────────────────────────────────────────────────────────────
## 7 - Edu_exp (numeric)
##
## length n NAs unique 0s mean meanCI'
## 168 168 0 27 0 4.857 4.755
## 100.0% 0.0% 0.0% 4.958
##
## .05 .10 .25 median .75 .90 .95
## 3.935 4.100 4.300 4.800 5.300 5.630 6.200
##
## range sd vcoef mad IQR skew kurt
## 3.000 0.665 0.137 0.741 1.000 0.577 -0.268
##
## lowest : 3.7, 3.8, 3.9 (7), 4.0 (6), 4.1 (10)
## highest: 6.1 (2), 6.2 (6), 6.3 (5), 6.5, 6.7
##
## heap(?): remarkable frequency (9.5%) for the mode(s) (= 5)
##
## ' 95%-CI (classic)
## ──────────────────────────────────────────────────────────────────────────────
## 8 - Siopo_exp (numeric)
##
## length n NAs unique 0s mean'
## 168 167 1 = n 0 215'625.83
## 99.4% 0.6% 0.0%
##
## .05 .10 .25 median .75 .90
## 11'189.35 13'806.52 30'106.00 69'336.31 259'208.64 748'134.89
##
## range sd vcoef mad IQR skew
## 1'188'340.62 296'062.73 1.37 82'050.78 229'102.65 1.68
##
## meanCI
## 170'393.25
## 260'858.41
##
## .95
## 873'700.03
##
## kurt
## 1.58
##
## lowest : 9'158.79, 9'222.77, 9'296.36, 9'300.86, 9'375.08
## highest: 1'001'380.08, 1'071'830.54, 1'108'092.13, 1'137'580.91, 1'197'499.41
##
## ' 95%-CI (classic)
## ──────────────────────────────────────────────────────────────────────────────
## 9 - LF_partic (numeric)
##
## length n NAs unique 0s mean meanCI'
## 168 168 0 167 0 57.37587 56.76996
## 100.0% 0.0% 0.0% 57.98179
##
## .05 .10 .25 median .75 .90 .95
## 51.33455 51.66350 54.15550 57.92200 59.87475 61.48880 64.47730
##
## range sd vcoef mad IQR skew kurt
## 18.20200 3.97794 0.06933 3.40701 5.71925 0.17414 -0.39621
##
## lowest : 50.344, 50.489, 50.677, 50.771, 50.841
## highest: 64.963, 65.006, 66.987, 67.899, 68.546
##
## ' 95%-CI (classic)
# correlation matrix
num_data <- eu_panel_data[, c("Unemployment_Rate", "Minimum_wage", "GDP",
"Inflation", "Edu_exp", "Siopo_exp", "LF_partic")]
corr_matrix <- cor(num_data, use = "complete.obs")
corrplot(corr_matrix, method = "color", type = "upper",
addCoef.col = "black", tl.cex = 0.8, number.cex = 0.7)
Unemployment Rate is strongly negatively correlated with GDP and moderately negatively with Labor Force Participation, while positively correlated with Inflation. Minimum Wage shows a strong positive correlation with Social Protection Expenditure and a moderate positive correlation with Education Expenditure.
# Minimum wages and unemployment
panel_plot_data <- eu_panel_data %>%
mutate(Unemployment_Rate_scaled = Unemployment_Rate * 100) %>%
select(Country, Year, Minimum_wage, Unemployment_Rate_scaled) %>%
pivot_longer(cols = c(Minimum_wage, Unemployment_Rate_scaled),
names_to = "Indicator", values_to = "Value")
ggplot(panel_plot_data, aes(x = Year, y = Value, color = Indicator)) +
geom_line(linewidth = 1) +
facet_wrap(~ Country, scales = "free_y") +
scale_color_manual(
values = c("Minimum_wage" = "steelblue", "Unemployment_Rate_scaled" = "darkred"),
labels = c("Minimum Wage", "Unemployment Rate (×100)")
) +
labs(
title = "Minimum Wage vs. Unemployment Rate by Country",
x = "Year", y = NULL, color = "Indicator"
) +
theme_minimal()
In most countries, rising minimum wages are associated with a declining unemployment rate. However, further examination is needed to determine whether this relationship is causal or consistent across different contexts.
Model Building
#Panel Model- Base model
re_base<-plm(Unemployment_Rate~Minimum_wage+GDP+Inflation+Edu_exp+Siopo_exp+LF_partic, data=complete_panel, index=c("Country", "Year"), model="random")
summary(re_base)## Oneway (individual) effect Random Effect Model
## (Swamy-Arora's transformation)
##
## Call:
## plm(formula = Unemployment_Rate ~ Minimum_wage + GDP + Inflation +
## Edu_exp + Siopo_exp + LF_partic, data = complete_panel, model = "random",
## index = c("Country", "Year"))
##
## Unbalanced Panel: n = 12, T = 9-14, N = 162
##
## Effects:
## var std.dev share
## idiosyncratic 3.450 1.858 0.293
## individual 8.336 2.887 0.707
## theta:
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.7903 0.8305 0.8305 0.8278 0.8305 0.8305
##
## Residuals:
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## -5.7206 -1.2474 -0.2280 0.0083 1.0124 6.7696
##
## Coefficients:
## Estimate Std. Error z-value Pr(>|z|)
## (Intercept) 16.1602854388 7.0512711382 2.2918 0.02192 *
## Minimum_wage -0.0087569729 0.0019481442 -4.4950 0.000006956 ***
## GDP -0.2854710161 0.0287128966 -9.9423 < 0.00000000000000022 ***
## Inflation 0.1144802426 0.0266515718 4.2954 0.000017435 ***
## Edu_exp 0.2091720188 0.5081880033 0.4116 0.68063
## Siopo_exp 0.0000057978 0.0000032427 1.7880 0.07378 .
## LF_partic 0.3100815537 0.1364887896 2.2718 0.02310 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Total Sum of Squares: 1668.7
## Residual Sum of Squares: 608.49
## R-Squared: 0.63537
## Adj. R-Squared: 0.62125
## Chisq: 271.11 on 6 DF, p-value: < 0.000000000000000222To investigate whether the impact of minimum wage policies varies under different macroeconomic conditions, we introduce interaction terms between minimum wage and key structural variables.
#Panel Model- Interact model+macro interaction
complete_panel <- complete_panel %>%
mutate(
MW_GDP = Minimum_wage * GDP,
MW_Inflation = Minimum_wage * Inflation)
re_macro_interact<-plm(Unemployment_Rate~Minimum_wage+GDP+Inflation+Edu_exp+Siopo_exp+LF_partic+MW_GDP+MW_Inflation, data=complete_panel, index=c("Country", "Year"), model="random")
summary(re_macro_interact)## Oneway (individual) effect Random Effect Model
## (Swamy-Arora's transformation)
##
## Call:
## plm(formula = Unemployment_Rate ~ Minimum_wage + GDP + Inflation +
## Edu_exp + Siopo_exp + LF_partic + MW_GDP + MW_Inflation,
## data = complete_panel, model = "random", index = c("Country",
## "Year"))
##
## Unbalanced Panel: n = 12, T = 9-14, N = 162
##
## Effects:
## var std.dev share
## idiosyncratic 3.076 1.754 0.254
## individual 9.029 3.005 0.746
## theta:
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.8090 0.8459 0.8459 0.8434 0.8459 0.8459
##
## Residuals:
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## -5.1737 -1.1826 -0.1559 0.0072 0.8907 6.5791
##
## Coefficients:
## Estimate Std. Error z-value Pr(>|z|)
## (Intercept) 26.2981457431 7.6465281002 3.4392 0.0005834 ***
## Minimum_wage -0.0271606590 0.0056603034 -4.7984 0.000001599016033 ***
## GDP -0.4210319181 0.0606689280 -6.9398 0.000000000003926 ***
## Inflation 0.1478052684 0.0491084466 3.0098 0.0026144 **
## Edu_exp 0.4693989562 0.4976556459 0.9432 0.3455682
## Siopo_exp 0.0000053150 0.0000033177 1.6020 0.1091448
## LF_partic 0.3210388192 0.1348249162 2.3812 0.0172585 *
## MW_GDP 0.0002425235 0.0000836708 2.8985 0.0037490 **
## MW_Inflation -0.0000833362 0.0000605175 -1.3771 0.1684940
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Total Sum of Squares: 1648.5
## Residual Sum of Squares: 550.29
## R-Squared: 0.66619
## Adj. R-Squared: 0.64873
## Chisq: 306.27 on 8 DF, p-value: < 0.000000000000000222Specifically, we construct interactions with GDP per capita and inflation to explore potential moderation effects. These interactions aim to capture heterogeneous policy effects across countries with differing economic capacities and price dynamics.
Panel Model
Ordinary Least Squares
# OLS Model
ols<- lm(Unemployment_Rate~Minimum_wage+GDP+Inflation+Edu_exp+Siopo_exp+LF_partic, data=complete_panel)Fixed Effect
#Panel Data-Fixed Effect
fixed<-plm(Unemployment_Rate~Minimum_wage+GDP+Inflation+Edu_exp+Siopo_exp+LF_partic, data=complete_panel, index=c("Country", "Year"), model="within")Random Effect
#Panel Data-Random Effect
random<-plm(Unemployment_Rate~Minimum_wage+GDP+Inflation+Edu_exp+Siopo_exp+LF_partic, data=complete_panel, index=c("Country", "Year"), model="random")F-test for individual effects
# F-test for individual effects (pFtest)
pFtest(fixed, ols)##
## F test for individual effects
##
## data: Unemployment_Rate ~ Minimum_wage + GDP + Inflation + Edu_exp + ...
## F = 40.562, df1 = 11, df2 = 144, p-value < 0.00000000000000022
## alternative hypothesis: significant effects# H₀: All individual (country-specific) effects are equal to zero — the Pooled OLS model is appropriate.
# H₁: At least one individual effect is non-zero — the Fixed Effects model is preferred.
# The p-value is below the significance level, so we reject the null hypothesis.
# This suggests that the Fixed Effects model is more appropriate for our data.Hausman Test
#Hausman test
phtest(fixed, random)##
## Hausman Test
##
## data: Unemployment_Rate ~ Minimum_wage + GDP + Inflation + Edu_exp + ...
## chisq = 12.234, df = 6, p-value = 0.05695
## alternative hypothesis: one model is inconsistent# H₀: The Random Effects model is consistent and efficient (difference in coefficients is not systematic).
# H₁: The Fixed Effects model is consistent, but Random Effects is not (difference in coefficients is systematic).
# The p-value is larger than 5%, so we failed to reject the null hypothesis.
# Therefore, the Random Effects model is preferred in this case.
print("Random Effect is prefered in this case")## [1] "Random Effect is prefered in this case"General to Specific
# general to specific
model_general <- plm(Unemployment_Rate~Minimum_wage+GDP+Inflation+Edu_exp+Siopo_exp+LF_partic, data=complete_panel, index=c("Country", "Year"), model="random")
summary(model_general)## Oneway (individual) effect Random Effect Model
## (Swamy-Arora's transformation)
##
## Call:
## plm(formula = Unemployment_Rate ~ Minimum_wage + GDP + Inflation +
## Edu_exp + Siopo_exp + LF_partic, data = complete_panel, model = "random",
## index = c("Country", "Year"))
##
## Unbalanced Panel: n = 12, T = 9-14, N = 162
##
## Effects:
## var std.dev share
## idiosyncratic 3.450 1.858 0.293
## individual 8.336 2.887 0.707
## theta:
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.7903 0.8305 0.8305 0.8278 0.8305 0.8305
##
## Residuals:
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## -5.7206 -1.2474 -0.2280 0.0083 1.0124 6.7696
##
## Coefficients:
## Estimate Std. Error z-value Pr(>|z|)
## (Intercept) 16.1602854388 7.0512711382 2.2918 0.02192 *
## Minimum_wage -0.0087569729 0.0019481442 -4.4950 0.000006956 ***
## GDP -0.2854710161 0.0287128966 -9.9423 < 0.00000000000000022 ***
## Inflation 0.1144802426 0.0266515718 4.2954 0.000017435 ***
## Edu_exp 0.2091720188 0.5081880033 0.4116 0.68063
## Siopo_exp 0.0000057978 0.0000032427 1.7880 0.07378 .
## LF_partic 0.3100815537 0.1364887896 2.2718 0.02310 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Total Sum of Squares: 1668.7
## Residual Sum of Squares: 608.49
## R-Squared: 0.63537
## Adj. R-Squared: 0.62125
## Chisq: 271.11 on 6 DF, p-value: < 0.000000000000000222model_specific <- plm(Unemployment_Rate~Minimum_wage+GDP+Inflation+Siopo_exp+LF_partic, data=complete_panel, index=c("Country", "Year"), model="random")
waldtest(model_general, model_specific)## Wald test
##
## Model 1: Unemployment_Rate ~ Minimum_wage + GDP + Inflation + Edu_exp +
## Siopo_exp + LF_partic
## Model 2: Unemployment_Rate ~ Minimum_wage + GDP + Inflation + Siopo_exp +
## LF_partic
## Res.Df Df Chisq Pr(>Chisq)
## 1 155
## 2 156 -1 0.1694 0.6806# This implies that Edu_exp can be removed from the model.
# Further steps are needed to continue the general-to-specific model reduction.##drop variabe 'Edu_exp'
gets_1<- plm(Unemployment_Rate~Minimum_wage+GDP+Inflation+Siopo_exp+LF_partic, data=complete_panel, index=c("Country", "Year"), model="random")
summary(gets_1)## Oneway (individual) effect Random Effect Model
## (Swamy-Arora's transformation)
##
## Call:
## plm(formula = Unemployment_Rate ~ Minimum_wage + GDP + Inflation +
## Siopo_exp + LF_partic, data = complete_panel, model = "random",
## index = c("Country", "Year"))
##
## Unbalanced Panel: n = 12, T = 9-14, N = 162
##
## Effects:
## var std.dev share
## idiosyncratic 3.433 1.853 0.208
## individual 13.040 3.611 0.792
## theta:
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.8314 0.8641 0.8641 0.8619 0.8641 0.8641
##
## Residuals:
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## -5.9032 -1.1828 -0.2104 0.0079 1.0300 6.6300
##
## Coefficients:
## Estimate Std. Error z-value Pr(>|z|)
## (Intercept) 14.6435249400 6.9972190251 2.0928 0.03637 *
## Minimum_wage -0.0098957434 0.0020938387 -4.7261 0.000002288 ***
## GDP -0.2801566820 0.0279457977 -10.0250 < 0.00000000000000022 ***
## Inflation 0.1169115925 0.0267423014 4.3718 0.000012323 ***
## Siopo_exp 0.0000070535 0.0000035209 2.0033 0.04515 *
## LF_partic 0.3526142318 0.1401769591 2.5155 0.01189 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Total Sum of Squares: 1626.8
## Residual Sum of Squares: 577.15
## R-Squared: 0.64523
## Adj. R-Squared: 0.63386
## Chisq: 284.43 on 5 DF, p-value: < 0.000000000000000222stargazer(model_general,model_specific,gets_1,type="text")##
## =============================================
## Dependent variable:
## --------------------------------
## Unemployment_Rate
## (1) (2) (3)
## ---------------------------------------------
## Minimum_wage -0.009*** -0.010*** -0.010***
## (0.002) (0.002) (0.002)
##
## GDP -0.285*** -0.280*** -0.280***
## (0.029) (0.028) (0.028)
##
## Inflation 0.114*** 0.117*** 0.117***
## (0.027) (0.027) (0.027)
##
## Edu_exp 0.209
## (0.508)
##
## Siopo_exp 0.00001* 0.00001** 0.00001**
## (0.00000) (0.00000) (0.00000)
##
## LF_partic 0.310** 0.353** 0.353**
## (0.136) (0.140) (0.140)
##
## Constant 16.160** 14.644** 14.644**
## (7.051) (6.997) (6.997)
##
## ---------------------------------------------
## Observations 162 162 162
## R2 0.635 0.645 0.645
## Adjusted R2 0.621 0.634 0.634
## F Statistic 271.110*** 284.430*** 284.430***
## =============================================
## Note: *p<0.1; **p<0.05; ***p<0.01# All explanatory variables are statistically significant at this stage,
# thus concluding the general-to-specific modeling procedure.
# No evidence suggests that we have incorrectly retained irrelevant variables,
# reducing the risk of Type I errors in variable selection.Edu_exp was removed from the final model specification.
Diagnostic Test
Breusch-Godfrey/Wooldridge test for serial correlation in panel data.
#Testing for serial correlation
pbgtest(gets_1)##
## Breusch-Godfrey/Wooldridge test for serial correlation in panel models
##
## data: Unemployment_Rate ~ Minimum_wage + GDP + Inflation + Siopo_exp + ...
## chisq = 95.51, df = 9, p-value < 0.00000000000000022
## alternative hypothesis: serial correlation in idiosyncratic errorsThis indicates strong evidence of serial correlation in the idiosyncratic errors (p < 0.00000000000000022). Robust standard errors are required.
# Testing for heteroskedasticity
bptest(Unemployment_Rate~Minimum_wage+GDP+Inflation+Siopo_exp+LF_partic, data=complete_panel, studentize=TRUE)##
## studentized Breusch-Pagan test
##
## data: Unemployment_Rate ~ Minimum_wage + GDP + Inflation + Siopo_exp + LF_partic
## BP = 24.194, df = 5, p-value = 0.0001992The model residuals exhibit heteroskedasticity.
Robust standard errors are thus required for valid inference
# Robust standard error
coeftest(gets_1, vcov = vcovHC(random, method = "arellano", type = "HC1", cluster = "group"))##
## t test of coefficients:
##
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 14.6435249400 9.8286120213 1.4899 0.13827
## Minimum_wage -0.0098957434 0.0031241513 -3.1675 0.00185 **
## GDP -0.2801566820 0.0583478798 -4.8015 0.000003662 ***
## Inflation 0.1169115925 0.0277011045 4.2205 0.000041244 ***
## Siopo_exp 0.0000070535 0.0000042368 1.6648 0.09795 .
## LF_partic 0.3526142318 0.2218706672 1.5893 0.11402
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Parameter interpretation (based on robust standard errors)
We can conclude that:
- A one-unit increase in Minimum Wage is associated with a 0.0098% decrease in the Unemployment Rate, holding other variables constant.
- A one-unit increase in GDP growth is associated with a 0.2801 percentage decrease in the Unemployment Rate
- A one-unit increase in the Inflation Rate is associated with a 0.1169 percentage increase in the Unemployment Rate.
- An increase of one million euros in Social Protection Expenditure is associated with a 0.000007% increase in the Unemployment Rate.
- Labor Force Participation Rate have no effect with the Unemployment Rate.