We compute the share of labour compensation in GDP & the depreciation rate of the capital stock for France, Italy, Spain, Germany and the Euro Area since 1995. We use the data from Feenstra, Inklaar, and Timmer (2015) available here. All the code is written in R, thanks to the R Core Team (2016) and RStudio Team (2016).

The depreciation rate of the capital stock

Step1: data for Euro Area countries

We obtain the variable labsh from the Penn World Table, for the countries that compose the Euro Area.

df <- read.dta13("https://www.rug.nl/ggdc/docs/pwt90.dta") %>%
  mutate(country=countrycode, period=as.Date(as.yearqtr(year)))%>%
  filter(year(period)>=1995 & currency_unit=="Euro" & !grepl('MNE', country))

delta<-
  df%>%
  select(country, period, value=delta)%>%
  add_column(var="delta")

Step2: Euro Area GDP-weighted average

After retrieving the data on the average depreciation rate of the capital stock for the Euro Area countries, it is possible to build the GDP-weighted average for the Eurozone. First, it is necessary to establish the weights that will be used for this purpose, using the output-side real GDP at chained PPPs (in mil. 2011US$) of each country.

gdp <- 
  df %>% 
  select(country, period, value=rgdpo)
  
EA_gdp <-
  gdp %>%
  group_by(period) %>%
  summarize(value=sum(value))

weights <-
  gdp %>%
  left_join(EA_gdp,by="period") %>%
  ungroup() %>%
  transmute(country, period, weight=value.x/value.y)

Now we apply these weights to our country data in order to build the Euro Area GDP-weighted average. The figure below shows the final series for France, Germany, Italy, Spain and the Euro Area.

delta_EA <-
  delta %>%
  left_join(weights,by=c("country","period"))

delta_EA <-
  delta_EA %>%
  transmute(period,value=value*weight) %>%
  group_by(period) %>%
  summarize(value =sum(value)) %>%
  add_column(country="EA",var="delta")

delta_4 <- 
  delta %>%
  filter(grepl('FRA|DEU|ITA|ESP', country))

delta_FIN <- 
  bind_rows(delta_4,delta_EA)

delta_FIN$country <- factor(delta_FIN$country)                  
levels(delta_FIN$country) <- listcountry

ggplot(delta_FIN,aes(period,value,colour=country))+
  geom_line()+
  scale_x_date(expand = c(0.01,0.01)) +
  theme + xlab(NULL) + ylab(NULL) + 
  theme(legend.title=element_blank()) +
  ggtitle("Depreciation rate of the capital stock")

The share of labour compensation in GDP

Step1: data for Euro Area countries

We obtain the variable delta from the Penn World Table, for the countries that compose the Euro Area.

alpha<-
  df%>%
  select(country, period, value=labsh)%>%
  add_column(var="alpha")

Step2: Euro Area GDP-weighted average

Now we apply the GDP-weights to our country data in order to build the Euro Area GDP-weighted average. The figure below shows the final series for France, Germany, Italy, Spain and the Euro Area.

alpha_EA <-
  alpha %>%
  left_join(weights,by=c("country","period"))

alpha_EA <-
  alpha_EA %>%
  transmute(period,value=value*weight) %>%
  group_by(period) %>%
  summarize(value =sum(value)) %>%
  add_column(country="EA",var="alpha")

alpha_4 <- 
  alpha %>%
  filter(grepl('FRA|DEU|ITA|ESP', country))

alpha_FIN <- 
  bind_rows(alpha_4,alpha_EA)

alpha_FIN$country <- factor(alpha_FIN$country)                  
levels(alpha_FIN$country) <- listcountry

ggplot(alpha_FIN,aes(period,value,colour=country))+
  geom_line()+
  scale_x_date(expand = c(0.01,0.01)) +
  theme + xlab(NULL) + ylab(NULL) + 
  theme(legend.title=element_blank()) +
  ggtitle("Share of labour compensation in GDP")

Steady State

We summarize the steady state values of the share of labour compensation in GDP & the average depreciation rate of the capital stock in the following table:

alpha_delta <- 
  bind_rows(alpha_FIN,delta_FIN)

ss_alpha_delta<-
  alpha_delta %>%
  group_by(var,country) %>% 
  summarize(steady_state =mean(value)) %>% 
  mutate(steady_state=round(steady_state,3)) %>% 
  spread(country, steady_state) %>%
  ungroup() 

kable(ss_alpha_delta, "html", caption = "alpha & delta steady state values") %>%
  kable_styling(bootstrap_options = c("striped", "hover", "condensed"), position = "center")
alpha & delta steady state values
var France Germany Italy Spain Euro Area
alpha 0.621 0.627 0.53 0.626 0.599
delta 0.040 0.039 0.04 0.038 0.040 
ss_alpha_delta_plot <-
  ss_alpha_delta%>%
  gather(country,value,-var)

ggplot(ss_alpha_delta_plot,aes(country, value, fill=country))+
  geom_bar(stat="identity")+
  facet_wrap(~var ,scales ="free_y",ncol = 3)+
  theme + xlab(NULL) + ylab(NULL) + 
  theme(legend.title=element_blank()) +
  ggtitle("alpha & delta steady state values")

We can download ready-to-use data for France, Germany, Italy, Spain and the Euro Area in csv format:

list_country <- list("FR"="France",
                     "DE"="Germany",
                     "IT"="Italy",
                     "ES"= "Spain",
                     "EA"="Euro Area")

alpha_delta$country <- factor(alpha_delta$country)                  
levels(alpha_delta$country)<-list_country

alpha_delta_eurodata <- 
  alpha_delta %>% 
  unite("var",c("country","var")) %>%
  mutate(period=year(period)) %>%
  spread(var,value)

write.csv(alpha_delta_eurodata,"alpha_delta_eurodata.csv",row.names = FALSE)

References

Feenstra, Robert C, Robert Inklaar, and Marcel P Timmer. 2015. “The Next Generation of the Penn World Table.” American Economic Review 105 (10): 3150–82.

R Core Team. 2016. R: A Language and Environment for Statistical Computing. Vienna, Austria: R Foundation for Statistical Computing. https://www.R-project.org.

RStudio Team. 2016. RStudio: Integrated Development Environment for R. Boston, MA: RStudio, Inc. http://www.rstudio.com/.