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04a_TFP for EU_A-DEA_crs.R
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04a_TFP for EU_A-DEA_crs.R
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# --------------------------------------- #
# #
# This program estimates the additive TFP #
# index under CRS using shadow prices as #
# weights for the EU country-level data #
# #
# --------------------------------------- #
# Open packages
library(tidyverse) #for data manipulation
library(reshape2) #to reshape the data
library(tikzDevice) #to save ggplot object in latex format
library(ggpubr) #to combine plots
library(kableExtra) # to convert data frames to Latex
# More packages (productivity decomposition)
library(doFuture) #for DEA
library(progressr) #for DEA
library(lpSolveAPI) #for DEA
library(plm) #for DEA (The source codes rely on "is.pbalanced)
# Load the required source codes
source('R_aux/aux_lowe.R')
source('R_aux/auxiliaries.R')
source('R_aux/lowe.R')
# Set path to Latex compiler if figures should be stored in Latex format
options("tikzLatex"='C:/Program Files/MiKTeX/miktex/bin/x64/pdflatex.exe')
# Load the EU country-level data
load("R_output/EUdata.Rda")
# Order data by country
EUdata <- EUdata[order(EUdata$country),]
# ------------------------------------ #
#### Estimation of reference prices ####
# ------------------------------------ #
# Estimation of each observations' shadow prices
# Input and output vectors
XREF <- t(as.matrix(EUdata[, c("x_capital", "x_land","x_labor","x_interm")]))
YREF <- t(as.matrix(EUdata[, c("q_animals", "q_crops", "q_other")]))
# Output distance function
outShad <- foreach(dmu = 1:dim(EUdata)[1], .combine = rbind) %do%
{
DO.shdu(XOBS = XREF[, dmu], YOBS = YREF[, dmu], XREF = XREF,
YREF = YREF, rts = "crs")
}
# Input distance function
inpShad <- foreach(dmu = 1:dim(EUdata)[1], .combine = rbind) %do%
{
DI.shdu(XOBS = XREF[, dmu], YOBS = YREF[, dmu], XREF = XREF,
YREF = YREF, rts = "crs")
}
# Use mean shadow prices as reference prices
# Compute means
meanY <- apply(outShad, 2, FUN = function(x) mean(x))
meanX <- apply(inpShad, 2, FUN = function(x) mean(x))
# Add reference prices to data frame
EUdata$p0_animals <- meanY[1]
EUdata$p0_crops <- meanY[2]
EUdata$p0_other <- meanY[3]
EUdata$w0_capital <- meanX[1]
EUdata$w0_land <- meanX[2]
EUdata$w0_labor <- meanX[3]
EUdata$w0_interm <- meanX[4]
# -------------------------------------------- #
#### Calculate and decompose TFP under CRS ####
# -------------------------------------------- #
# Subsets for each region
Cluster1 <- subset(EUdata, country == "BEL" |
country == "FRA" |
country == "GBR"|
country == "IRL"|
country == "NLD")
Cluster2 <- subset(EUdata,country == "EST" |
country == "FIN" |
country == "LTU" |
country == "LVA" |
country == "SWE")
Cluster3 <- subset(EUdata, country == "AUT" |
country == "CZE" |
country == "DEU" |
country == "DNK" |
country == "HUN" |
country == "LUX" |
country == "POL" |
country == "ROU" |
country == "SVN" |
country == "SVK")
Cluster4 <- subset(EUdata, country == "ESP" |
country == "GRC" |
country == "ITA" |
country == "MLT" |
country == "PRT")
# Note: We use the code from the Lowe index but use the above estimated
# shadow prices to obtain the additive TFP index with shadow prices
# as weights.
#Cluster1
ADEA_cluster1 <- lowe(data = Cluster1, id.var = "country", time.var = "year",
x.vars = c("x_capital", "x_land","x_labor","x_interm"),
y.vars = c("q_animals", "q_crops", "q_other"),
w.vars = c("w0_capital", "w0_land","w0_labor","w0_interm"),
p.vars = c("p0_animals", "p0_crops", "p0_other"),
tech.change = T, tech.reg = T, rts = "crs",
orientation = "out", cores = 8, scaled = F,
window = c(3), by.year = 1)
#Cluster2
ADEA_cluster2 <- lowe(data = Cluster2, id.var = "country", time.var = "year",
x.vars = c("x_capital", "x_land","x_labor","x_interm"),
y.vars = c("q_animals", "q_crops", "q_other"),
w.vars = c("w0_capital", "w0_land","w0_labor","w0_interm"),
p.vars = c("p0_animals", "p0_crops", "p0_other"),
tech.change = T, tech.reg = T, rts = "crs",
orientation = "out", cores = 8, scaled = F,
window = c(3), by.year = 1)
#Cluster3
ADEA_cluster3 <- lowe(data = Cluster3, id.var = "country", time.var = "year",
x.vars = c("x_capital", "x_land","x_labor","x_interm"),
y.vars = c("q_animals", "q_crops", "q_other"),
w.vars = c("w0_capital", "w0_land","w0_labor","w0_interm"),
p.vars = c("p0_animals", "p0_crops", "p0_other"),
tech.change = T, tech.reg = T, rts = "crs",
orientation = "out", cores = 8, scaled = F,
window = c(3), by.year = 1)
#Cluster4
ADEA_cluster4 <- lowe(data = Cluster4, id.var = "country", time.var = "year",
x.vars = c("x_capital", "x_land","x_labor","x_interm"),
y.vars = c("q_animals", "q_crops", "q_other"),
w.vars = c("w0_capital", "w0_land","w0_labor","w0_interm"),
p.vars = c("p0_animals", "p0_crops", "p0_other"),
tech.change = T, tech.reg = T, rts = "crs",
orientation = "out", cores = 8, scaled = F,
window = c(3), by.year = 1)
# Join the results
ADEA.level_crs <- rbind(ADEA_cluster1$Levels, ADEA_cluster2$Levels,
ADEA_cluster3$Levels, ADEA_cluster4$Levels)
# Order results by country
ADEA.level_crs <- ADEA.level_crs[order(ADEA.level_crs$country),]
# Normalize with Base = AUT 2000
ADEA.level_crs_norm <- ADEA.level_crs %>%
mutate_each(funs(./.[1]), setdiff(names(.), c("country","year")))
# ---------------------------------------------------- #
#### Replicate tables 2 and 3 from O'Donnell (2012) ####
# ---------------------------------------------------- #
# Prepare data for the tables
data_tables <- data.frame(matrix(ncol = 22, nrow = 25))
colnames(data_tables) <- c("country", "TFP2000", "TFP2019", "DTFP",
"MP2000", "MP2019", "DMP",
"TFPE2000", "TFPE2019", "DTFPE",
"OTE2000", "OTE2019", "DOTE",
"OSE2000", "OSE2019", "DOSE",
"OME2000", "OME2019", "DOME",
"OSME2000", "OSME2019", "DOSME")
data_tables$country <- (unique(EUdata$country))
# TOTAL FACTOR PRODUCTIVITY
# TFP2000
data_tables$TFP2000 <- ADEA.level_crs$TFP[ADEA.level_crs$year==2000]
# TFP2019
data_tables$TFP2019 <- ADEA.level_crs$TFP[ADEA.level_crs$year==2019]
# DTFP
data_tables$DTFP <- (data_tables$TFP2019 / data_tables$TFP2000)
# MAXIMM TOTAL FACTOR PRODUCTIVITY
# MP2000
data_tables$MP2000 <- ADEA.level_crs$MP[ADEA.level_crs$year==2000]
# MP2019
data_tables$MP2019 <- ADEA.level_crs$MP[ADEA.level_crs$year==2019]
# DMP
data_tables$DMP <- (data_tables$MP2019 / data_tables$MP2000)
# TFP EFFICIENCY
# TFPE2000
data_tables$TFPE2000 <- ADEA.level_crs$TFPE[ADEA.level_crs$year==2000]
# TFPE2019
data_tables$TFPE2019 <- ADEA.level_crs$TFPE[ADEA.level_crs$year==2019]
# DTFPE
data_tables$DTFPE <- (data_tables$TFPE2019 / data_tables$TFPE2000)
# OUTPUT TECHNICAL EFFICIENCY
# OTE2000
data_tables$OTE2000 <- ADEA.level_crs$OTE[ADEA.level_crs$year==2000]
# OTE2019
data_tables$OTE2019 <- ADEA.level_crs$OTE[ADEA.level_crs$year==2019]
# DOTE
data_tables$DOTE <- (data_tables$OTE2019 / data_tables$OTE2000)
# OUTPUT SCALE EFFICIENCY
# OSE2000
data_tables$OSE2000 <- ADEA.level_crs$OSE[ADEA.level_crs$year==2000]
# OSE2019
data_tables$OSE2019 <- ADEA.level_crs$OSE[ADEA.level_crs$year==2019]
# DOSE
data_tables$DOSE <- (data_tables$OSE2019 / data_tables$OSE2000)
# OUTPUT MIX EFFICIENCY
# OME2000
data_tables$OME2000 <- ADEA.level_crs$OME[ADEA.level_crs$year==2000]
# OME2019
data_tables$OME2019 <- ADEA.level_crs$OME[ADEA.level_crs$year==2019]
# DOME
data_tables$DOME <- (data_tables$OME2019 / data_tables$OME2000)
# OUTPUT SCALE MIX EFFICIENCY
# OSME2000
data_tables$OSME2000 <- ADEA.level_crs$OSME[ADEA.level_crs$year==2000]
# OSME2019
data_tables$OSME2019 <- ADEA.level_crs$OSME[ADEA.level_crs$year==2019]
# DOSME
data_tables$DOSME <- (data_tables$OSME2019 / data_tables$OSME2000)
# Add EU25-average (geometric, because we have not used logs)
data_tables <- data_tables %>%
add_row(country="EU25",
TFP2000=NA, TFP2019=NA, DTFP=exp(mean(log(data_tables$DTFP))),
MP2000=NA, MP2019=NA, DMP=exp(mean(log(data_tables$DMP))),
TFPE2000=NA, TFPE2019=NA, DTFPE=exp(mean(log(data_tables$DTFPE))),
OTE2000=NA, OTE2019=NA, DOTE=exp(mean(log(data_tables$DOTE))),
OSE2000=NA, OSE2019=NA, DOSE=exp(mean(log(data_tables$DOSE))),
OME2000=NA, OME2019=NA, DOME=exp(mean(log(data_tables$DOME))),
OSME2000=NA, OSME2019=NA, DOSME=exp(mean(log(data_tables$DOSME))))
# Write Table: "TFP, technical change, and efficiency change in EU agriculture (2000--2019) using the A-DEA index)
# Set global option to produce latex output
options(knitr.table.format = "latex", knitr.kable.NA = '')
# Select data
data_ADEA_TFPDecomp <- subset(data_tables, select = c(1:10))
# Write table
Tab_ADEA_TFPDecomp_EU_crs <- kable(data_ADEA_TFPDecomp, booktabs = T,
digits = 2,
row.names = FALSE,
escape = FALSE,
linesep = "",
caption = "TFP, technical change, and efficiency change in EU agriculture (2000--2019) using the A-DEA index under CRS.",
label = "Tab_ADEA_TFPDecomp_EU_crs",
col.names = c('Country',
'2000', '2019', "$\\Delta$",
'2000', '2019', "$\\Delta$",
'2000', '2019', "$\\Delta$")) %>%
add_header_above(c("", "TFP" = 3, "TFP* (=OET)" = 3,
"TFPE" = 3)) %>%
row_spec(25, hline_after=T) %>%
footnote(general = "TFP is total factor productivity, TFP* is the maximum \\\\\\\\
possible TFP based on the output-oriented
environment and technology (OET) index, and TFPE is TFP efficiency.",
footnote_as_chunk = T,
threeparttable = T,
general_title = "Notes:",
escape=F) %>%
kable_styling(latex_options = c("HOLD_position")) #note: this table looks much nicer without "scale_down"
# Print Latex file
writeLines(Tab_ADEA_TFPDecomp_EU_crs, "Tables/Tab_ADEA_TFPDecomp_EU_crs.tex")
# Write Table: "Output-oriented components of efficiency change in EU agriculture (2000--2019) using the A-DEA index"
# Set global option to produce latex output
options(knitr.table.format = "latex", knitr.kable.NA = '')
# Select data
data_ADEA_TFPEDecomp <- subset(data_tables, select = c(1,8:22))
# Write table
Tab_ADEA_TFPEDecomp_EU_crs <- kable(data_ADEA_TFPEDecomp, booktabs = T,
digits = 2,
row.names = FALSE,
escape = FALSE,
linesep = "",
caption = "Output-oriented components of efficiency change in EU agriculture (2000--2019) using the A-DEA index under CRS.",
label = "Tab_ADEA_TFPEDecomp_EU_crs",
col.names = c('Country',
'2000', '2019', "$\\Delta$",
'2000', '2019', "$\\Delta$",
'2000', '2019', "$\\Delta$",
'2000', '2019', "$\\Delta$",
'2000', '2019', "$\\Delta$")) %>%
add_header_above(c("", "TFPE=OTE$\\\\times$OSME" = 3, "OTE" = 3,
"OSE" = 3, "OME" = 3,
"OSME" = 3),
escape=F) %>%
row_spec(25, hline_after=T) %>%
footnote(general = "TFPE is TFP efficiency, OTE is output-oriented technical efficiency, OSE is output-oriented scale efficiency,
OME is output-oriented mix efficiency, and OSME is output-oriented scale-mix efficiency.",
footnote_as_chunk = T,
threeparttable = T,
general_title = "Notes:",
escape=F) %>%
#kable_styling(latex_options = c("HOLD_position")) %>% #note: this table looks much nicer without "scale_down"
landscape()
# Print Latex file
writeLines(Tab_ADEA_TFPEDecomp_EU_crs, "Tables/Tab_ADEA_TFPEDecomp_EU_crs.tex")
# ------------------------------------- #
#### Create figures for EU aggregate ####
# ------------------------------------- #
# Prepare the data
# Compare every level to the country's *own* 2000 level --> obtains cumulative growth
idcountries <- unique(ADEA.level_crs$country)
ADEA.cumulative_crs <- list()
for (i in idcountries) {
ADEA.cumulative_crs[[which(i==idcountries)]] <- cbind(country = i, year=2000:2019,
sweep(ADEA.level_crs[ADEA.level_crs$country==i,-c(1:2)],MARGIN = 2,
STATS = as.numeric(ADEA.level_crs[ADEA.level_crs$country==i,-c(1:2)][1,]),FUN = "/")) # for myself: 2 refers to column
}
ADEA.cumulative_crs <- do.call(rbind, ADEA.cumulative_crs) #turns the list into a data frame
# Calculate US average using the geometric mean
ADEA.EU25_crs <- list()
for (yr in 2000:2019) {
ADEA.EU25_crs[[which(yr == 2000:2019)]] <- c(year = yr, apply(ADEA.cumulative_crs[ADEA.cumulative_crs$year==yr,-c(1:2)],2,FUN = function(x) exp(mean(log(x)))))
}
ADEA.EU25_crs <- as.data.frame(do.call(rbind, ADEA.EU25_crs)) #turns the list into a data frame
# For the efficiencies (last figure), we need arithmetic averages
ADEA.EU25_crs_eff <- ADEA.level_crs[,c("country", "year","TFPE", "OTE", "OME", "OSME")]
ADEA.EU25_crs_eff <- ADEA.EU25_crs_eff %>%
group_by(year) %>%
summarise_at(.vars = vars(TFPE,OTE,OME,OSME),
.funs = c(mean="mean"))
# --------------------------------- #
# Panel A: Components of TFP change #
# --------------------------------- #
# Note: We do not plot profitability change due to the lack of consistent prices
# Prepare data for the plot
data_plot <- ADEA.EU25_crs %>%
select("year", "TFP", "MP", "TFPE") %>%
reshape2::melt(id.vars="year")
# plot
panel_A <- ggplot() +
geom_line(data = data_plot, aes(x = year, y = value, linetype = variable)
) + labs(
x = "",
y = "",
linetype = ""
) + scale_linetype_manual(name ="",
breaks=c("TFP", "MP", "TFPE"),
labels=c("?TFP", "?TFP*", "?TFPE"),
values=c("solid", "12", "42")) +
theme_bw() +
scale_x_continuous(breaks = seq(2000, 2019, by = 2)) +
scale_y_continuous(breaks = seq(0, 1.5, by = 0.25), limits=c(0,1.6)) +
theme(axis.text.x = element_text(angle=90)) +
theme(legend.position="bottom",
legend.margin=margin(t = -0.7, unit='cm'),
legend.text=element_text(size=6))
# -------------------------- #
# Panel B: Efficiency levels #
# -------------------------- #
# Prepare data for the plot
data_plot <- ADEA.EU25_crs_eff %>%
reshape2::melt(id.vars="year")
# plot
panel_B <- ggplot() +
geom_line(data = data_plot, aes(x = year, y = value, color = variable, linetype = variable)
) + labs(
x = "",
y = "",
linetype = "") +
scale_color_manual(name ="",
breaks=c("OTE_mean", "OME_mean", "OSME_mean", "TFPE_mean"),
labels=c("OTE", "OME", "OSME", "TFPE"),
values=c("#0a0a0a","#0a0a0a","#9E9E9E","#0a0a0a")) +
scale_linetype_manual(name = "",
breaks=c("OTE_mean", "OME_mean", "OSME_mean", "TFPE_mean"),
labels=c("OTE", "OME", "OSME", "TFPE"),
values=c("solid", "42", "solid", "12")) +
theme_bw() +
#ggtitle("C") +
scale_x_continuous(breaks = seq(2000, 2019, by = 2)) +
scale_y_continuous(breaks = seq(0, 1.2, by = 0.2), limits=c(0,1.3)) +
theme(axis.text.x = element_text(angle=90)) +
theme(legend.position="bottom",
legend.margin=margin(t = -0.7, unit='cm'),
legend.text=element_text(size=6))
# -------------------------------------------------- #
# Combine panels to one figure and save as tex file #
# -------------------------------------------------- #
# Options for special characters
options(
tikzSanitizeCharacters = c('%','$','}','{','^','_','#','&','~','?'),
tikzReplacementCharacters = c('\\%','\\$','\\}','\\{','\\^{}','\\_{}',
'\\#','\\&','\\char???\\~','$\\Delta$')
)
# set filepath for latex output
tikz(file = "Figures/Fig_ADEA_EU25_crs.tex", width = 7, height = 3.5, sanitize=TRUE)
plot <- ggarrange(panel_A, panel_B,
labels = c("a", "b"),
ncol = 2, nrow = 1)
print(plot)
dev.off()