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01_Analysis_Norway.R
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01_Analysis_Norway.R
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# ---------------------------------------------------------------------------- #
# #
# R code for the article: "A note on synthetic data for replication purposes #
# in agricultural economics" #
# #
# Authors: Stefan Wimmer and Robert Finger #
# #
# Corresponding author: Stefan Wimmer ([email protected]) #
# #
# Citation: Wimmer, S., Finger, R. (2023). "A note on synthetic data for #
# replication purposes in agricultural economics." Journal of Agricultural #
# Economics. #
# #
# The program stores all tables and figures based on the Norwegian dairy #
# production data presented in the article in the subfolders 'Tables/Norway' #
# and 'Figures/Norway'. The data are automatically downloaded from the #
# internet. The script was successfully run with R version 4.2.0. #
# #
# ---------------------------------------------------------------------------- #
# Content:
# 0) Preparation (working directory, packages, data, colours)
# 1) Generation of synthetic data
# 2) Descriptive statistics
# 3) Estimation of production function
# 4) Estimation of production frontier
# 5) Data envelopment analysis
# -------------------- #
#### 0. Preparation ####
# -------------------- #
# Set working directory
my.wd <- getwd() # NOTE: getwd() can be replaced with any working directory
setwd(my.wd)
# Create subfolders for tables and figures
dir.create(file.path("Tables"))
dir.create(file.path("Tables", "Norway"))
dir.create(file.path("Figures"))
dir.create(file.path("Figures", "Norway"))
# Install missing packages
list.of.packages <- c("dplyr", "broom", "haven", "frontier", "Benchmarking",
"dotwhisker", "ggplot2", "ggpubr", "synthpop",
"stargazer")
new.packages <- list.of.packages[!(list.of.packages %in%
installed.packages()[,"Package"])]
if(length(new.packages)) install.packages(new.packages)
# Load packages
library(dplyr) # for data management
library(broom) # data preparation
library(haven) # imports .dta files
library(frontier) # efficiency analysis
library(Benchmarking) # DEA analysis
library(dotwhisker) # coefficient plots
library(ggplot2) # plots
library(ggpubr) # to merge plots
library(synthpop) # creates synthetic data
library(stargazer) # for descriptive statistics
# Load Norwegian dairy data
temp <- tempfile()
download.file("https://sites.google.com/site/sfbook2014/home/for-stata-v12-v13-v14/sfbook_data_12.zip",temp)
dat <- read_dta(unz(temp, "norway.dta"))
head(dat)
# Define colour palettes
cbPalette <- c("#8c510a", "#d8b365", "#f6e8c3", "#c7eae5", "#5ab4ac", "#01665e")
bwPalette <- c("#252525", "#636363", "#969696", "#bdbdbd", "#d9d9d9", "#f7f7f7")
# ------------------------------------- #
#### 1. Generation of synthetic data ####
# ------------------------------------- #
# Set seed for replication
my.seed <- 1234
# Define original data set
dat_orig <- as.data.frame(dat[c("y1", "x1", "x2", "x3", "x4", "x5", "x6")])
# ------------------------------------- #
##### 1.a Synthetic data using CART #####
# ------------------------------------- #
# Generate five synthetic data sets (cart)
dat_synt <- syn(dat_orig, method = "cart", m = 5, visit.sequence =
c("y1", "x1", "x2", "x3", "x4",
"x5", "x6"),
seed = my.seed,
smoothing = list(y1 = "density",
x1 = "density",
x2 = "density",
x3 = "density",
x4 = "density",
x5 = "density",
x6 = "density"))
# Store synthetic data in data frames
dat_syn1 <- as.data.frame(dat_synt$syn[[1]])
dat_syn2 <- as.data.frame(dat_synt$syn[[2]])
dat_syn3 <- as.data.frame(dat_synt$syn[[3]])
dat_syn4 <- as.data.frame(dat_synt$syn[[4]])
dat_syn5 <- as.data.frame(dat_synt$syn[[5]])
# ----------------------------------------- #
##### 1.b Synthetic data using NORMRANK #####
# ----------------------------------------- #
# Generate five synthetic data sets (normrank)
dat_synt <- syn(dat_orig, method = "parametric", m = 5, visit.sequence =
c("y1", "x1", "x2", "x3", "x4",
"x5", "x6"),
seed = my.seed,
smoothing = list(y1 = "density",
x1 = "density",
x2 = "density",
x3 = "density",
x4 = "density",
x5 = "density",
x6 = "density"))
# Store synthetic data in data frames
dat_syn6 <- as.data.frame(dat_synt$syn[[1]])
dat_syn7 <- as.data.frame(dat_synt$syn[[2]])
dat_syn8 <- as.data.frame(dat_synt$syn[[3]])
dat_syn9 <- as.data.frame(dat_synt$syn[[4]])
dat_syn10 <- as.data.frame(dat_synt$syn[[5]])
# ------------------------------- #
#### 2. Descriptive statistics ####
# ------------------------------- #
# Original data
stargazer::stargazer(dat_orig,
digits=2,
title="Descriptive statistics for the Norwegian sample (original)",
nobs = FALSE,
omit.summary.stat = c("p25", "p75"),
covariate.labels=c("Milk", "Land", "Labor",
"Feed","Material",
"Cattle","Capital"),
type = "text",
style = "ajps",
out = "Tables/Norway/TabA1a.descr_orig.txt")
# One synthetic data: CART
stargazer::stargazer(dat_syn1,
digits=2,
title="Descriptive statistics for the Norwegian sample (CART)",
nobs = FALSE,
omit.summary.stat = c("p25", "p75"),
covariate.labels=c("Milk", "Land", "Labor",
"Feed","Material",
"Cattle","Capital"),
type = "text",
style = "ajps",
out = "Tables/Norway/TabA1b.descr_cart.txt")
# One synthetic data: NORMRANK
stargazer::stargazer(dat_syn6,
digits=2,
title="Descriptive statistics for the Norwegian sample (NORMRANK)",
nobs = FALSE,
omit.summary.stat = c("p25", "p75"),
covariate.labels=c("Milk", "Land", "Labor",
"Feed","Material",
"Cattle","Capital"),
type = "text",
style = "ajps",
out = "Tables/Norway/TabA1c.descr_normrank.txt")
# -------------------------------------------- #
#### 3. Estimation of production function ####
# -------------------------------------------- #
# Define Cobb-Douglas functional form
fn.CD <- log(y1) ~ log(x1) + log(x2) +
log(x3) + log(x4) + log(x5) + log(x6)
# Define (de-meaned) translog functional form
fn.TL <- log(y1) ~ log(x1/mean(x1)) + log(x2/mean(x2)) + log(x3/mean(x3)) +
log(x4/mean(x4)) + log(x5/mean(x5)) + log(x6/mean(x6)) +
I(0.5*log(x1/mean(x1))*log(x1/mean(x1))) + I(log(x1/mean(x1))*log(x2/mean(x2))) +
I(log(x1/mean(x1))*log(x3/mean(x3))) + I(log(x1/mean(x1))*log(x4/mean(x4))) +
I(log(x1/mean(x1))*log(x5/mean(x5))) + I(log(x1/mean(x1))*log(x6/mean(x6))) +
I(0.5*log(x2/mean(x2))*log(x2/mean(x2))) + I(log(x2/mean(x2))*log(x3/mean(x3))) +
I(log(x2/mean(x2))*log(x4/mean(x4))) + I(log(x2/mean(x2))*log(x5/mean(x5))) +
I(log(x2/mean(x2))*log(x6/mean(x6))) + I(0.5*log(x3/mean(x3))*log(x3/mean(x3))) +
I(log(x3/mean(x3))*log(x4/mean(x4))) + I(log(x3/mean(x3))*log(x5/mean(x5))) +
I(log(x3/mean(x3))*log(x6/mean(x6))) + I(0.5*log(x4/mean(x4))*log(x4/mean(x4))) +
I(log(x4/mean(x4))*log(x5/mean(x5))) + I(log(x4/mean(x4))*log(x6/mean(x6))) +
I(0.5*log(x5/mean(x5))*log(x5/mean(x5))) + I(log(x5/mean(x5))*log(x6/mean(x6))) +
I(0.5*log(x6/mean(x6))*log(x6/mean(x6)))
# ---------------------------------------------#
##### 3a. Cobb Douglas Production Function #####
# ---------------------------------------------#
# Original data
prod.orig <- tidy(lm(fn.CD, data = dat_orig))
prod.orig <- prod.orig %>% mutate(model = "Original data")
# CART:
# Synthetic data 1
prod.syn1 <- tidy(lm(fn.CD, data = dat_syn1))
prod.syn1 <- prod.syn1 %>% mutate(model = "Synthetic data 1")
# Synthetic data 2
prod.syn2 <- tidy(lm(fn.CD, data = dat_syn2))
prod.syn2 <- prod.syn2 %>% mutate(model = "Synthetic data 2")
# Synthetic data 3
prod.syn3 <- tidy(lm(fn.CD, data = dat_syn3))
prod.syn3 <- prod.syn3 %>% mutate(model = "Synthetic data 3")
# Synthetic data 4
prod.syn4 <- tidy(lm(fn.CD, data = dat_syn4))
prod.syn4 <- prod.syn4 %>% mutate(model = "Synthetic data 4")
# Synthetic data 5
prod.syn5 <- tidy(lm(fn.CD, data = dat_syn5))
prod.syn5 <- prod.syn5 %>% mutate(model = "Synthetic data 5")
# NORMRANK:
# Synthetic data 6
prod.syn6 <- tidy(lm(fn.CD, data = dat_syn6))
prod.syn6 <- prod.syn6 %>% mutate(model = "Synthetic data 6")
# Synthetic data 7
prod.syn7 <- tidy(lm(fn.CD, data = dat_syn7))
prod.syn7 <- prod.syn7 %>% mutate(model = "Synthetic data 7")
# Synthetic data 8
prod.syn8 <- tidy(lm(fn.CD, data = dat_syn8))
prod.syn8 <- prod.syn8 %>% mutate(model = "Synthetic data 8")
# Synthetic data 9
prod.syn9 <- tidy(lm(fn.CD, data = dat_syn9))
prod.syn9 <- prod.syn9 %>% mutate(model = "Synthetic data 9")
# Synthetic data 10
prod.syn10 <- tidy(lm(fn.CD, data = dat_syn10))
prod.syn10 <- prod.syn10 %>% mutate(model = "Synthetic data 10")
# --------------------------------------------------------------------- #
# Figure 1. Parameter estimates of the Cobb-Douglas production function #
# with 95% confidence intervals #
# --------------------------------------------------------------------- #
# Combine all models
models_cart <- bind_rows(prod.orig, prod.syn1, prod.syn2, prod.syn3,
prod.syn4, prod.syn5)
models_normrank <- bind_rows(prod.orig, prod.syn6, prod.syn7, prod.syn8,
prod.syn9, prod.syn10)
# Make plot for CART
elast_CD_prod_cart <- dwplot(models_cart,
show_intercept = FALSE,
ci = .95,
vars_order = c("log(x1)", "log(x2)", "log(x3)",
"log(x4)", "log(x5)", "log(x6)"),
model_order = c("Original data",
"Synthetic data 1",
"Synthetic data 2",
"Synthetic data 3",
"Synthetic data 4",
"Synthetic data 5")) %>%
relabel_predictors(
c("log(x1)" = "Land",
"log(x2)" = "Labor",
"log(x3)" = "Feed",
"log(x4)" = "Material",
"log(x5)" = "Cattle",
"log(x6)" = "Capital")) +
theme_light(base_family="Times") +
xlab("Estimated elasticities with 95% CIs") +
ylab("") +
ggtitle("CART method") +
theme(
plot.title = element_text(size=10, hjust = 0.5),
legend.position = "bottom",
legend.background = element_rect(colour = "white"),
legend.title = element_blank()) +
scale_x_continuous(breaks = seq(0, 0.3, by = 0.1), limits=c(-0.0001,0.35)) +
scale_colour_manual(values=cbPalette)
# Make plot for NORMRANK
elast_CD_prod_normrank <- dwplot(models_normrank,
show_intercept = FALSE,
ci = .95,
vars_order = c("log(x1)", "log(x2)", "log(x3)",
"log(x4)", "log(x5)", "log(x6)"),
model_order = c("Original data",
"Synthetic data 6",
"Synthetic data 7",
"Synthetic data 8",
"Synthetic data 9",
"Synthetic data 10")) %>%
relabel_predictors(
c("log(x1)" = "Land",
"log(x2)" = "Labor",
"log(x3)" = "Feed",
"log(x4)" = "Material",
"log(x5)" = "Cattle",
"log(x6)" = "Capital")
) +
theme_light(base_family="Times") +
xlab("Estimated elasticities with 95% CIs") + ylab("") +
ggtitle("NORMRANK method") +
theme(
plot.title = element_text(size=10, hjust = 0.5),
legend.position = "bottom",
legend.background = element_rect(colour = "white"),
legend.title = element_blank()) +
scale_x_continuous(breaks = seq(0, 0.3, by = 0.1), limits=c(-0.0001,0.35)) +
scale_colour_manual(values=cbPalette)
# Save plots
elast_CD_prod <- ggarrange(elast_CD_prod_cart, elast_CD_prod_normrank,
ncol = 2, nrow = 1)
ggsave("Figures/Norway/Fig1.elast_CD_prod.png", elast_CD_prod,
width = 24, height = 11, units = "cm")
# Same figures in black and white for journal
# Make plot for CART
elast_CD_prod_cart <- dwplot(models_cart,
dot_args = list(aes(shape = model)),
dodge_size = .6,
show_intercept = FALSE,
ci = .95,
vars_order = c("log(x1)", "log(x2)", "log(x3)",
"log(x4)", "log(x5)", "log(x6)"),
model_order = c("Original data",
"Synthetic data 1",
"Synthetic data 2",
"Synthetic data 3",
"Synthetic data 4",
"Synthetic data 5")) %>%
relabel_predictors( c("log(x1)" = "Land",
"log(x2)" = "Labor",
"log(x3)" = "Feed",
"log(x4)" = "Material",
"log(x5)" = "Cattle",
"log(x6)" = "Capital")) +
theme_bw() +
xlab("Estimated elasticities with 95% CIs") +
ylab("") +
ggtitle("CART method") +
theme(
plot.title = element_text(size=10, hjust = 0.5),
legend.position = "bottom",
legend.background = element_rect(colour = "white"),
legend.title = element_blank(),
## remove the vertical grid lines
panel.grid.minor.y = element_blank() ,
panel.grid.major.y = element_blank() ,
# set the horizontal lines
panel.grid.minor.x = element_line( size=.05, color="lightgrey" ),
panel.grid.major.x = element_line( size=.05, color="lightgrey" )) +
scale_x_continuous(breaks = seq(0, 0.3, by = 0.1), limits=c(-0.0001,0.35)) +
scale_colour_grey(name = "Model",
start = .3, end = .3, # Same colour for all models
breaks = c("Original data",
"Synthetic data 1",
"Synthetic data 2",
"Synthetic data 3",
"Synthetic data 4",
"Synthetic data 5"),
labels = c("Original data",
"Synthetic data 1",
"Synthetic data 2",
"Synthetic data 3",
"Synthetic data 4",
"Synthetic data 5")) +
scale_shape_manual(name = "Model", # Different shapes for models
values = c(16, 0, 1, 2, 5, 6),
breaks = c("Original data",
"Synthetic data 1",
"Synthetic data 2",
"Synthetic data 3",
"Synthetic data 4",
"Synthetic data 5"),
labels = c("Original data",
"Synthetic data 1",
"Synthetic data 2",
"Synthetic data 3",
"Synthetic data 4",
"Synthetic data 5")) +
guides(
shape = guide_legend("Model"),
colour = guide_legend("Model")
) # Combine the legends for shape and colour
# Make plot for NORMRANK
elast_CD_prod_normrank <- dwplot(models_normrank,
dot_args = list(aes(shape = model)),
dodge_size = .6,
show_intercept = FALSE,
ci = .95,
vars_order = c("log(x1)", "log(x2)", "log(x3)",
"log(x4)", "log(x5)", "log(x6)"),
model_order = c("Original data",
"Synthetic data 6",
"Synthetic data 7",
"Synthetic data 8",
"Synthetic data 9",
"Synthetic data 10")) %>%
relabel_predictors( c("log(x1)" = "Land",
"log(x2)" = "Labor",
"log(x3)" = "Feed",
"log(x4)" = "Material",
"log(x5)" = "Cattle",
"log(x6)" = "Capital")) +
theme_bw() +
xlab("Estimated elasticities with 95% CIs") +
ylab("") +
ggtitle("NORMRANK method") +
theme(
plot.title = element_text(size=10, hjust = 0.5),
legend.position = "bottom",
legend.background = element_rect(colour = "white"),
legend.title = element_blank(),
# remove the vertical grid lines
panel.grid.minor.y = element_blank() ,
panel.grid.major.y = element_blank() ,
# set the horizontal lines
panel.grid.minor.x = element_line( size=.05, color="lightgrey" ),
panel.grid.major.x = element_line( size=.05, color="lightgrey" )) +
scale_x_continuous(breaks = seq(0, 0.3, by = 0.1), limits=c(-0.0001,0.35)) +
scale_colour_grey(name = "Model",
start = .3, end = .3, # Same colour for all models
breaks = c("Original data",
"Synthetic data 6",
"Synthetic data 7",
"Synthetic data 8",
"Synthetic data 9",
"Synthetic data 10"),
labels = c("Original data",
"Synthetic data 6",
"Synthetic data 7",
"Synthetic data 8",
"Synthetic data 9",
"Synthetic data 10")) +
scale_shape_manual(name = "Model", # Different shapes for models
values = c(16, 0, 1, 2, 5, 6),
breaks = c("Original data",
"Synthetic data 6",
"Synthetic data 7",
"Synthetic data 8",
"Synthetic data 9",
"Synthetic data 10"),
labels = c("Original data",
"Synthetic data 6",
"Synthetic data 7",
"Synthetic data 8",
"Synthetic data 9",
"Synthetic data 10")) +
guides(
shape = guide_legend("Model"),
colour = guide_legend("Model")
) # Combine the legends for shape and colour
# Save plots
elast_CD_prod <- ggarrange(elast_CD_prod_cart, elast_CD_prod_normrank,
ncol = 2, nrow = 1)
ggsave("Figures/Norway/Fig1.elast_CD_prod_bw.png", elast_CD_prod,
width = 24, height = 11, units = "cm")
# -----------------------------------------#
##### 3b. Translog Production Function #####
# -----------------------------------------#
# Create functions to estimate production function and calculate elasticities
prod_tl <- function(data) {
prod <- lm(fn.TL, data = data)
coef <- prod$coefficients
el_land <- coef["log(x1/mean(x1))"] +
coef["I(0.5 * log(x1/mean(x1)) * log(x1/mean(x1)))"]*log(data$x1/mean(data$x1)) +
coef["I(log(x1/mean(x1)) * log(x2/mean(x2)))"]*log(data$x2/mean(data$x2)) +
coef["I(log(x1/mean(x1)) * log(x3/mean(x3)))"]*log(data$x3/mean(data$x3)) +
coef["I(log(x1/mean(x1)) * log(x4/mean(x4)))"]*log(data$x4/mean(data$x4)) +
coef["I(log(x1/mean(x1)) * log(x5/mean(x5)))"]*log(data$x5/mean(data$x5)) +
coef["I(log(x1/mean(x1)) * log(x6/mean(x6)))"]*log(data$x6/mean(data$x6))
el_labor <- coef["log(x2/mean(x2))"] +
coef["I(log(x1/mean(x1)) * log(x2/mean(x2)))"]*log(data$x1/mean(data$x1)) +
coef["I(0.5 * log(x2/mean(x2)) * log(x2/mean(x2)))"]*log(data$x2/mean(data$x2)) +
coef["I(log(x2/mean(x2)) * log(x3/mean(x3)))"]*log(data$x3/mean(data$x3)) +
coef["I(log(x2/mean(x2)) * log(x4/mean(x4)))"]*log(data$x4/mean(data$x4)) +
coef["I(log(x2/mean(x2)) * log(x5/mean(x5)))"]*log(data$x5/mean(data$x5)) +
coef["I(log(x2/mean(x2)) * log(x6/mean(x6)))"]*log(data$x6/mean(data$x6))
el_feed <- coef["log(x3/mean(x3))"] +
coef["I(log(x1/mean(x1)) * log(x3/mean(x3)))"]*log(data$x1/mean(data$x1)) +
coef["I(log(x2/mean(x2)) * log(x3/mean(x3)))"]*log(data$x2/mean(data$x2)) +
coef["I(0.5 * log(x3/mean(x3)) * log(x3/mean(x3)))"]*log(data$x3/mean(data$x3)) +
coef["I(log(x3/mean(x3)) * log(x4/mean(x4)))"]*log(data$x4/mean(data$x4)) +
coef["I(log(x3/mean(x3)) * log(x5/mean(x5)))"]*log(data$x5/mean(data$x5)) +
coef["I(log(x3/mean(x3)) * log(x6/mean(x6)))"]*log(data$x6/mean(data$x6))
el_material <- coef["log(x4/mean(x4))"] +
coef["I(log(x1/mean(x1)) * log(x4/mean(x4)))"]*log(data$x1/mean(data$x1)) +
coef["I(log(x2/mean(x2)) * log(x4/mean(x4)))"]*log(data$x2/mean(data$x2)) +
coef["I(log(x3/mean(x3)) * log(x4/mean(x4)))"]*log(data$x3/mean(data$x3)) +
coef["I(0.5 * log(x4/mean(x4)) * log(x4/mean(x4)))"]*log(data$x4/mean(data$x4)) +
coef["I(log(x4/mean(x4)) * log(x5/mean(x5)))"]*log(data$x5/mean(data$x5)) +
coef["I(log(x4/mean(x4)) * log(x6/mean(x6)))"]*log(data$x6/mean(data$x6))
el_cattle <- coef["log(x5/mean(x5))"] +
coef["I(log(x1/mean(x1)) * log(x5/mean(x5)))"]*log(data$x1/mean(data$x1)) +
coef["I(log(x2/mean(x2)) * log(x5/mean(x5)))"]*log(data$x2/mean(data$x2)) +
coef["I(log(x3/mean(x3)) * log(x5/mean(x5)))"]*log(data$x3/mean(data$x3)) +
coef["I(log(x4/mean(x4)) * log(x5/mean(x5)))"]*log(data$x4/mean(data$x4)) +
coef["I(0.5 * log(x5/mean(x5)) * log(x5/mean(x5)))"]*log(data$x5/mean(data$x5)) +
coef["I(log(x5/mean(x5)) * log(x6/mean(x6)))"]*log(data$x6/mean(data$x6))
el_capital <- coef["log(x6/mean(x6))"] +
coef["I(log(x1/mean(x1)) * log(x6/mean(x6)))"]*log(data$x1/mean(data$x1)) +
coef["I(log(x2/mean(x2)) * log(x6/mean(x6)))"]*log(data$x2/mean(data$x2)) +
coef["I(log(x3/mean(x3)) * log(x6/mean(x6)))"]*log(data$x3/mean(data$x3)) +
coef["I(log(x4/mean(x4)) * log(x6/mean(x6)))"]*log(data$x4/mean(data$x4)) +
coef["I(log(x5/mean(x5)) * log(x6/mean(x6)))"]*log(data$x5/mean(data$x5)) +
coef["I(0.5 * log(x6/mean(x6)) * log(x6/mean(x6)))"]*log(data$x6/mean(data$x6))
result <- list()
result$elast <- cbind(el_land, el_labor, el_feed, el_material, el_cattle, el_capital)
result$model <- tidy(prod)
return(result)
}
# Estimate TL prod and calculate elasticities
# Original data
prod <- prod_tl(dat_orig)
prod.orig <- prod$model[c(1:7),] %>%
mutate(model = "Original data") # adds model label
dat_orig <- cbind(dat_orig,prod$elast)
# Synthetic data 1
prod <- prod_tl(dat_syn1)
prod.syn1 <- prod$model[c(1:7),] %>%
mutate(model = "Synthetic data 1")
dat_syn1 <- cbind(dat_syn1,prod$elast)
# Synthetic data 2
prod <- prod_tl(dat_syn2)
prod.syn2 <- prod$model[c(1:7),] %>%
mutate(model = "Synthetic data 2")
dat_syn2 <- cbind(dat_syn2,prod$elast)
# Synthetic data 3
prod <- prod_tl(dat_syn3)
prod.syn3 <- prod$model[c(1:7),] %>%
mutate(model = "Synthetic data 3")
dat_syn3 <- cbind(dat_syn3,prod$elast)
# Synthetic data 4
prod <- prod_tl(dat_syn4)
prod.syn4 <- prod$model[c(1:7),] %>%
mutate(model = "Synthetic data 4")
dat_syn4 <- cbind(dat_syn4,prod$elast)
# Synthetic data 5
prod <- prod_tl(dat_syn5)
prod.syn5 <- prod$model[c(1:7),] %>%
mutate(model = "Synthetic data 5")
dat_syn5 <- cbind(dat_syn5,prod$elast)
# Synthetic data 6
prod <- prod_tl(dat_syn6)
prod.syn6 <- prod$model[c(1:7),] %>%
mutate(model = "Synthetic data 6")
dat_syn6 <- cbind(dat_syn6,prod$elast)
# Synthetic data 7
prod <- prod_tl(dat_syn7)
prod.syn7 <- prod$model[c(1:7),] %>%
mutate(model = "Synthetic data 7")
dat_syn7 <- cbind(dat_syn7,prod$elast)
# Synthetic data 8
prod <- prod_tl(dat_syn8)
prod.syn8 <- prod$model[c(1:7),] %>%
mutate(model = "Synthetic data 8")
dat_syn8 <- cbind(dat_syn8,prod$elast)
# Synthetic data 9
prod <- prod_tl(dat_syn9)
prod.syn9 <- prod$model[c(1:7),] %>%
mutate(model = "Synthetic data 9")
dat_syn9 <- cbind(dat_syn9,prod$elast)
# Synthetic data 10
prod <- prod_tl(dat_syn10)
prod.syn10 <- prod$model[c(1:7),] %>%
mutate(model = "Synthetic data 10")
dat_syn10 <- cbind(dat_syn10,prod$elast)
# ---------------------------------------------------------------------- #
# Figure A.2. First-order parameter estimates of the Translog production #
# function with 95% confidence intervals #
# ---------------------------------------------------------------------- #
# Combine all models
models_cart <- bind_rows(prod.orig, prod.syn1, prod.syn2, prod.syn3,
prod.syn4, prod.syn5)
models_normrank <- bind_rows(prod.orig, prod.syn6, prod.syn7, prod.syn8,
prod.syn9, prod.syn10)
# Make plot for CART
elast_TL_prod_cart <- dwplot(models_cart,
show_intercept = FALSE,
ci = .95,
vars_order = c("log(x1/mean(x1))", "log(x2/mean(x2))",
"log(x3/mean(x3))", "log(x4/mean(x4))",
"log(x5/mean(x5))", "log(x6/mean(x6))"),
model_order = c("Original data",
"Synthetic data 1",
"Synthetic data 2",
"Synthetic data 3",
"Synthetic data 4",
"Synthetic data 5")) %>%
relabel_predictors(
c("log(x1/mean(x1))" = "Land",
"log(x2/mean(x2))" = "Labor",
"log(x3/mean(x3))" = "Feed",
"log(x4/mean(x4))" = "Material",
"log(x5/mean(x5))" = "Cattle",
"log(x6/mean(x6))" = "Capital")) +
theme_light(base_family="Times") +
xlab("Estimated elasticities with 95% CIs") +
ylab("") +
ggtitle("CART method") +
theme(
plot.title = element_text(size=10, hjust = 0.5),
legend.position = "bottom",
legend.background = element_rect(colour = "white"),
legend.title = element_blank() ) +
scale_x_continuous(breaks = seq(0, 0.4, by = 0.1), limits=c(-0.025,0.4)) +
scale_colour_manual(values=cbPalette)
# Make plot for NORMRANK
elast_TL_prod_normrank <- dwplot(models_normrank,
show_intercept = FALSE,
ci = .95,
vars_order = c("log(x1/mean(x1))", "log(x2/mean(x2))",
"log(x3/mean(x3))", "log(x4/mean(x4))",
"log(x5/mean(x5))", "log(x6/mean(x6))"),
model_order = c("Original data",
"Synthetic data 6",
"Synthetic data 7",
"Synthetic data 8",
"Synthetic data 9",
"Synthetic data 10")) %>%
relabel_predictors(
c("log(x1/mean(x1))" = "Land",
"log(x2/mean(x2))" = "Labor",
"log(x3/mean(x3))" = "Feed",
"log(x4/mean(x4))" = "Material",
"log(x5/mean(x5))" = "Cattle",
"log(x6/mean(x6))" = "Capital")) +
theme_light(base_family="Times") +
xlab("Estimated elasticities with 95% CIs") +
ylab("") +
ggtitle("NORMRANK method") +
theme(
plot.title = element_text(size=10, hjust = 0.5),
legend.position = "bottom",
legend.background = element_rect(colour = "white"),
legend.title = element_blank()) +
scale_x_continuous(breaks = seq(0, 0.4, by = 0.1), limits=c(-0.025,0.4)) +
scale_colour_manual(values=cbPalette)
# Save plots
elast_TL_prod <- ggarrange(elast_TL_prod_cart, elast_TL_prod_normrank,
ncol = 2, nrow = 1)
ggsave("Figures/Norway/FigA2.elast_TL_prod.png", elast_TL_prod,
width = 23, height = 11, units = "cm")
# --------------------------------------------------------------------- #
# Figure A.3. Distribution of farm-level elasticities obtained from the #
# Translog production function #
# --------------------------------------------------------------------- #
# Make data frame with elasticities from all datasets (original and synthetic)
# Land
nr_obs <- length(dat_orig$el_land)
el_land <- data.frame(matrix(ncol = 2, nrow = 11*nr_obs))
colnames(el_land) <- c("el", "data")
el_land$data <- c(rep("Original data", nr_obs),rep("Synthetic data 1", nr_obs),
rep("Synthetic data 2", nr_obs),rep("Synthetic data 3", nr_obs),
rep("Synthetic data 4", nr_obs),rep("Synthetic data 5", nr_obs),
rep("Synthetic data 6", nr_obs),rep("Synthetic data 7", nr_obs),
rep("Synthetic data 8", nr_obs),rep("Synthetic data 9", nr_obs),
rep("Synthetic data 10", nr_obs))
el_land$el <- c(dat_orig$el_land,dat_syn1$el_land,dat_syn2$el_land,
dat_syn3$el_land,dat_syn4$el_land,dat_syn5$el_land,
dat_syn6$el_land,dat_syn7$el_land,dat_syn8$el_land,
dat_syn9$el_land,dat_syn10$el_land)
el_land$inp <- "Land"
# Labor
el_labor <- data.frame(matrix(ncol = 2, nrow = 11*nr_obs))
colnames(el_labor) <- c("el", "data")
el_labor$data <- c(rep("Original data", nr_obs),rep("Synthetic data 1", nr_obs),
rep("Synthetic data 2", nr_obs),rep("Synthetic data 3", nr_obs),
rep("Synthetic data 4", nr_obs),rep("Synthetic data 5", nr_obs),
rep("Synthetic data 6", nr_obs),rep("Synthetic data 7", nr_obs),
rep("Synthetic data 8", nr_obs),rep("Synthetic data 9", nr_obs),
rep("Synthetic data 10", nr_obs))
el_labor$el <- c(dat_orig$el_labor,dat_syn1$el_labor,dat_syn2$el_labor,
dat_syn3$el_labor,dat_syn4$el_labor,dat_syn5$el_labor,
dat_syn6$el_labor,dat_syn7$el_labor,dat_syn8$el_labor,
dat_syn9$el_labor,dat_syn10$el_labor)
el_labor$inp <- "Labor"
# Feed
el_feed <- data.frame(matrix(ncol = 2, nrow = 11*nr_obs))
colnames(el_feed) <- c("el", "data")
el_feed$data <- c(rep("Original data", nr_obs),rep("Synthetic data 1", nr_obs),
rep("Synthetic data 2", nr_obs),rep("Synthetic data 3", nr_obs),
rep("Synthetic data 4", nr_obs),rep("Synthetic data 5", nr_obs),
rep("Synthetic data 6", nr_obs),rep("Synthetic data 7", nr_obs),
rep("Synthetic data 8", nr_obs),rep("Synthetic data 9", nr_obs),
rep("Synthetic data 10", nr_obs))
el_feed$el <- c(dat_orig$el_feed,dat_syn1$el_feed,dat_syn2$el_feed,
dat_syn3$el_feed,dat_syn4$el_feed,dat_syn5$el_feed,
dat_syn6$el_feed,dat_syn7$el_feed,dat_syn8$el_feed,
dat_syn9$el_feed,dat_syn10$el_feed)
el_feed$inp <- "Feed"
# Material
el_material <- data.frame(matrix(ncol = 2, nrow = 11*nr_obs))
colnames(el_material) <- c("el", "data")
el_material$data <- c(rep("Original data", nr_obs),rep("Synthetic data 1", nr_obs),
rep("Synthetic data 2", nr_obs),rep("Synthetic data 3", nr_obs),
rep("Synthetic data 4", nr_obs),rep("Synthetic data 5", nr_obs),
rep("Synthetic data 6", nr_obs),rep("Synthetic data 7", nr_obs),
rep("Synthetic data 8", nr_obs),rep("Synthetic data 9", nr_obs),
rep("Synthetic data 10", nr_obs))
el_material$el <- c(dat_orig$el_material,dat_syn1$el_material,dat_syn2$el_material,
dat_syn3$el_material,dat_syn4$el_material,dat_syn5$el_material,
dat_syn6$el_material,dat_syn7$el_material,dat_syn8$el_material,
dat_syn9$el_material,dat_syn10$el_material)
el_material$inp <- "Material"
# Cattle
el_cattle <- data.frame(matrix(ncol = 2, nrow = 11*nr_obs))
colnames(el_cattle) <- c("el", "data")
el_cattle$data <- c(rep("Original data", nr_obs),rep("Synthetic data 1", nr_obs),
rep("Synthetic data 2", nr_obs),rep("Synthetic data 3", nr_obs),
rep("Synthetic data 4", nr_obs),rep("Synthetic data 5", nr_obs),
rep("Synthetic data 6", nr_obs),rep("Synthetic data 7", nr_obs),
rep("Synthetic data 8", nr_obs),rep("Synthetic data 9", nr_obs),
rep("Synthetic data 10", nr_obs))
el_cattle$el <- c(dat_orig$el_cattle,dat_syn1$el_cattle,dat_syn2$el_cattle,
dat_syn3$el_cattle,dat_syn4$el_cattle,dat_syn5$el_cattle,
dat_syn6$el_cattle,dat_syn7$el_cattle,dat_syn8$el_cattle,
dat_syn9$el_cattle,dat_syn10$el_cattle)
el_cattle$inp <- "Cattle"
# Capital
el_capital <- data.frame(matrix(ncol = 2, nrow = 11*nr_obs))
colnames(el_capital) <- c("el", "data")
el_capital$data <- c(rep("Original data", nr_obs),rep("Synthetic data 1", nr_obs),
rep("Synthetic data 2", nr_obs),rep("Synthetic data 3", nr_obs),
rep("Synthetic data 4", nr_obs),rep("Synthetic data 5", nr_obs),
rep("Synthetic data 6", nr_obs),rep("Synthetic data 7", nr_obs),
rep("Synthetic data 8", nr_obs),rep("Synthetic data 9", nr_obs),
rep("Synthetic data 10", nr_obs))
el_capital$el <- c(dat_orig$el_capital,dat_syn1$el_capital,dat_syn2$el_capital,
dat_syn3$el_capital,dat_syn4$el_capital,dat_syn5$el_capital,
dat_syn6$el_capital,dat_syn7$el_capital,dat_syn8$el_capital,
dat_syn9$el_capital,dat_syn10$el_capital)
el_capital$inp <- "Capital"
# All
el_prod <- rbind(el_land,el_labor,el_feed,el_material,el_cattle,el_capital)
el_prod_cart <- el_prod %>% # for CART plot
filter(data == "Original data" | data == "Synthetic data 1" |
data == "Synthetic data 2" | data == "Synthetic data 3" |
data == "Synthetic data 4" | data == "Synthetic data 5")
el_prod_normrank <- el_prod %>% # for NORMRANK plot
filter(data == "Original data" | data == "Synthetic data 6" |
data == "Synthetic data 7" | data == "Synthetic data 8" |
data == "Synthetic data 9" | data == "Synthetic data 10")
# Make sure data are plotted in right order
el_prod_cart$inp <- factor(el_prod_cart$inp,
levels=c("Land","Labor","Feed","Material",
"Cattle","Capital"))
el_prod_cart$data <- factor(el_prod_cart$data,
levels=c("Synthetic data 10",
"Synthetic data 9",
"Synthetic data 8",
"Synthetic data 7",
"Synthetic data 6",
"Synthetic data 5",
"Synthetic data 4",
"Synthetic data 3",
"Synthetic data 2",
"Synthetic data 1",
"Original data"))
el_prod_normrank$inp <- factor(el_prod_normrank$inp,
levels=c("Land","Labor","Feed","Material",
"Cattle","Capital"))
el_prod_normrank$data <- factor(el_prod_normrank$data,
levels=c("Synthetic data 10",
"Synthetic data 9",
"Synthetic data 8",
"Synthetic data 7",
"Synthetic data 6",
"Synthetic data 5",
"Synthetic data 4",
"Synthetic data 3",
"Synthetic data 2",
"Synthetic data 1",
"Original data"))
# Make plot for CART
elast_TL_fl_prod_cart <- ggplot(el_prod_cart, aes(x=data, y=el, fill=data)) +
geom_violin(size=0.2) +
theme_light() +
theme(
plot.title = element_text(size=10, hjust = 0.5),
legend.position="bottom",
legend.background = element_rect(colour = "white"),
legend.title = element_blank(),
axis.text.y=element_blank()
) +
coord_flip() + # To switch X and Y axes
xlab("") +
ylab("Elasticity") +
ggtitle("CART method") +
facet_wrap(~ inp) +
scale_y_continuous(breaks = seq(-0.3, 0.6, by = 0.3), limits=c(-0.5,0.6)) +
scale_fill_manual(values=cbPalette)
# Make plot for NORMRANK
elast_TL_fl_prod_normrank <- ggplot(el_prod_normrank, aes(x=data, y=el, fill=data)) +
geom_violin(size=0.2) +
theme_light() +
theme(
plot.title = element_text(size=10, hjust = 0.5),
legend.position="bottom",
legend.background = element_rect(colour = "white"),
legend.title = element_blank(),
axis.text.y=element_blank()
) +
coord_flip() + # To switch X and Y axes
xlab("") +
ylab("Elasticity") +
ggtitle("NORMRANK method") +
facet_wrap(~ inp) +
scale_y_continuous(breaks = seq(-0.3, 0.6, by = 0.3), limits=c(-0.5,0.6)) +
scale_fill_manual(values=cbPalette)
# Save plots
elast_TL_fl_prod <- ggarrange(elast_TL_fl_prod_cart,
elast_TL_fl_prod_normrank, ncol = 2, nrow = 1)
ggsave("Figures/Norway/FigA3.elast_TL_fl_prod.png", elast_TL_fl_prod,
width = 23, height = 11, units = "cm")
# -------------------------------------------- #
#### 4. Estimation of production frontier ####
# -------------------------------------------- #
# --------------------------------------------- #
##### 4.a Cobb-Douglas Production Frontier #####
# --------------------------------------------- #
# Create functions to estimate production frontier
front_cd <- function(data) {
front <- frontier::sfa(fn.CD, data = data)
result <- list()
# Store TE scores
result$te <- frontier::efficiencies(front, asInData=TRUE)
# prepare for coefficient plot
front <- summary(front)
front <- as_tibble(front$mleParam)
front$term <- c("Intercept", "Land", "Labor", "Feed", "Material",
"Cattle", "Capital", "Sigma2", "Gamma")
front <- front %>%
select(term, everything()) #re-order variables
names(front) <- names(prod.orig)[c(1:5)]
result$estimates <- front
return(result)
}
# Original data
front <- front_cd(dat_orig)
front.orig <- front$estimates
front.orig$model <- "Original data"
te_orig <- front$te
# Synthetic data 1
front <- front_cd(dat_syn1)
front.syn1 <- front$estimates
front.syn1$model <- "Synthetic data 1"
te_syn1 <- front$te
# Synthetic data 2
front <- front_cd(dat_syn2)
front.syn2 <- front$estimates
front.syn2$model <- "Synthetic data 2"
te_syn2 <- front$te
# Synthetic data 3
front <- front_cd(dat_syn3)
front.syn3 <- front$estimates
front.syn3$model <- "Synthetic data 3"
te_syn3 <- front$te
# Synthetic data 4
front <- front_cd(dat_syn4)
front.syn4 <- front$estimates
front.syn4$model <- "Synthetic data 4"
te_syn4 <- front$te
# Synthetic data 5
front <- front_cd(dat_syn5)
front.syn5 <- front$estimates
front.syn5$model <- "Synthetic data 5"
te_syn5 <- front$te
# Synthetic data 6
front <- front_cd(dat_syn6)
front.syn6 <- front$estimates
front.syn6$model <- "Synthetic data 6"
te_syn6 <- front$te
# Synthetic data 7
front <- front_cd(dat_syn7)
front.syn7 <- front$estimates
front.syn7$model <- "Synthetic data 7"
te_syn7 <- front$te
# Synthetic data 8
front <- front_cd(dat_syn8)
front.syn8 <- front$estimates
front.syn8$model <- "Synthetic data 8"
te_syn8 <- front$te
# Synthetic data 9
front <- front_cd(dat_syn9)
front.syn9 <- front$estimates
front.syn9$model <- "Synthetic data 9"
te_syn9 <- front$te
# Synthetic data 10
front <- front_cd(dat_syn10)
front.syn10 <- front$estimates
front.syn10$model <- "Synthetic data 10"
te_syn10 <- front$te
# ----------------------------------------------------------------------- #
# Figure A.4. Parameter estimates of the Cobb-Douglas production frontier #
# with 95% confidence intervals #
# ----------------------------------------------------------------------- #
# Combine all models
models_cart <- bind_rows(front.orig, front.syn1, front.syn2, front.syn3,
front.syn4, front.syn5)
models_normrank <- bind_rows(front.orig, front.syn6, front.syn7, front.syn8,
front.syn9, front.syn10)
# Make plot for CART
elast_CD_front_cart <- dwplot(models_cart,
show_intercept = FALSE,
ci = .95,
vars_order = c("Land", "Labor", "Feed",
"Material", "Cattle", "Capital"),
model_order = c("Original data",
"Synthetic data 1",
"Synthetic data 2",
"Synthetic data 3",
"Synthetic data 4",
"Synthetic data 5")) +
theme_light(base_family="Times") +
xlab("Estimated elasticities with 95% CIs") +
ylab("") +
ggtitle("CART method") +
theme(
plot.title = element_text(size=10, hjust = 0.5),
legend.position = "bottom",
legend.background = element_rect(colour = "white"),
legend.title = element_blank()
) +
scale_x_continuous(breaks = seq(0, 0.3, by = 0.1), limits=c(-0.015,0.32)) +
scale_colour_manual(values=cbPalette)