bp.norm = fit[, base_pay/mean(base_pay), by = Year]
base.pay.sim = bp_sim(bp.norm$V1, n.sim)
# c. Hierarchy with Inter-Firm Pay Dispersion (HF)  -----------------------------------------------------
mod = model(a = a,
b = b,
base_emp_vec = base.sim,
emp_vec = firm.sim,
base_pay_vec = base.pay.sim,
r_vec = r.sim,
sigma = sigma,
firm_size = T
)
top = top_k(mod[,1], mod[,2], 5000)
fast_mean(top)/fast_mean(firm.sim)
top = top_k(mod[,1], mod[,2], 500)
fast_mean(top)/fast_mean(firm.sim)
source('~/Desktop/Empirical Research/Income Distribution/Gini Ratio/Hierarchical Levels/Compustat_exec_space/Model.R')
runtime/100
hist(model)
source('~/Desktop/Empirical Research/Income Distribution/Gini Ratio/Hierarchical Levels/Compustat_exec_space/Model.R')
hist(model)
source('~/Desktop/Empirical Research/Income Distribution/Gini Ratio/Hierarchical Levels/Compustat_exec_space/Model.R')
hist(model)
hist(log(model))
runtime
370/60
# a. Get Model Parameters for current bootstrap values of a, b, and sigma -----------------------
s = boot_span(s.empirical$Level, s.empirical$Span)
a = s[1]
b = s[2]
sigma = boot_sigma(g.empirical)
# base level employment for each compustat firm
base.compustat =  base_fit(a, b, compustat$EMP)
fit = data.table(
compustat,
fit_model(a, b, base.compustat, compustat$EMP,
compustat$ratio, compustat$mean.pay.empirical, error.tol)
)
fit = fit[ceo_error < error.tol]
# b. Get Simulation Parameters --------------------------------------------
# simulated firm size distribution
firm.sim = rpld(n.sim, 1, alpha, ordered = F, xmax = 2.3*10^6, discrete_max = 2.3*10^6)
# simulated firm base
base.sim =  base_fit(a, b, firm.sim)
# simulated pay scaling
r.sim = r_sim(fit$EMP, fit$r, firm.sim)
#simulated base pay
bp.norm = fit[, base_pay/mean(base_pay), by = Year]
base.pay.sim = bp_sim(bp.norm$V1, n.sim)
# c. Hierarchy with Inter-Firm Pay Dispersion (HF)  -----------------------------------------------------
mod = model(a = a,
b = b,
base_emp_vec = base.sim,
emp_vec = firm.sim,
base_pay_vec = base.pay.sim,
r_vec = r.sim,
sigma = sigma,
firm_size = T
)
top = top_k(mod[,1], mod[,2], 10000)
exec_firm_ratio =  fast_mean(top)/fast_mean(firm.sim)
mod = model(a = a,
b = b,
base_emp_vec = base.sim,
emp_vec = firm.sim,
base_pay_vec = base.pay.sim,
r_vec = r.sim,
sigma = sigma,
firm_size = T,
hierarchy = T
)
top = top_k(mod[,1], mod[,2], 10000)
exec_firm_ratio =  fast_mean(top)/fast_mean(firm.sim)
View(mod)
head(mod)
head(mod)
mod = data.table(mod[, 2:3])
mod = model(a = a,
b = b,
base_emp_vec = base.sim,
emp_vec = firm.sim,
base_pay_vec = base.pay.sim,
r_vec = r.sim,
sigma = sigma,
firm_size = T,
hierarchy = T
)
top = top_k(mod[,1], mod[,2], 10000)
exec_firm_ratio =  fast_mean(top)/fast_mean(firm.sim)
mod = data.table(mod[, c(1,3)] )
g.between = mod[,  fast_mean(pay), by = h_level      ]
View(g.between)
plot(g.between)
plot(g.between, log = "y")
# simulated firm size distribution
firm.sim = rpld(n.sim, 1, alpha, ordered = F, xmax = 2.3*10^6, discrete_max = 2.3*10^6)
# simulated firm base
base.sim =  base_fit(a, b, firm.sim)
# simulated pay scaling
r.sim = r_sim(fit$EMP, fit$r, firm.sim)
#simulated base pay
bp.norm = fit[, base_pay/mean(base_pay), by = Year]
base.pay.sim = bp_sim(bp.norm$V1, n.sim)
# c. Hierarchy with Inter-Firm Pay Dispersion (HF)  -----------------------------------------------------
mod = model(a = a,
b = b,
base_emp_vec = base.sim,
emp_vec = firm.sim,
base_pay_vec = base.pay.sim,
r_vec = r.sim,
sigma = sigma,
firm_size = T,
hierarchy = T
)
top = top_k(mod[,1], mod[,2], 10000)
exec_firm_ratio =  fast_mean(top)/fast_mean(firm.sim)
mod = data.table(mod[, c(1,3)] )
g.between = mod[,  fast_mean(pay), by = h_level      ]
plot(g.between, log = "y")
g.between = fastgini( mod[,  fast_mean(pay), by = h_level      ][,2],
corr = T            )
mod[,  fast_mean(pay), by = h_level      ]
mod[,  fast_mean(pay), by = h_level      ][,2]
h_mean = mod[,  fast_mean(pay), by = h_level ]
g_between = fastgini(h_mean$V1, corr = T)
g_within =  mod[,  fastgini(pay, corr = T), by = h_level      ][,2]
g_within = mean(g_within$V1)
fastgini(mod$pay)
packages = c( 'data.table', 'doSNOW',
'foreach', 'hmod', 'magrittr',
'Rcpp', 'readr',  'RcppZiggurat',
'rstudioapi',  'snow', 'tcltk')
lapply(packages, require, character.only = TRUE)
# 1. Model Variables ---------------------------------------------------------------
# number of bootsrap iterations
n.iteration = 100
# number of cores for parallel computing
n.core = 8
# CEO pay ratio error tolerance (Model error as absolute percentage of empirical value)
error.tol = 0.05
# Firm size distribution
alpha = 2.01 # power law exponent
n.sim = 10^6 # number of firms
# 2. Import Data -------------------------------------------------------------
#  compustat Sample
dir = dirname(getActiveDocumentContext()$path)
workspace = gsub("Compustat_exec_space", "/Empirical/Exec Compensation", dir)
setwd(workspace)
compustat = fread("CEO Results.csv")
# Case Study Results
workspace = gsub("Compustat_exec_space", "/Empirical/Case Studies", dir)
setwd(workspace)
case.data = fread("Case Results.csv")
# g = vector of hierarchical level gini indexes
g.empirical = na.omit(case.data$Gini[case.data$Gini > 0])
# s = data table of non-NA span of control data
s.empirical = data.table(Level = case.data$Level, Span = case.data$span)
s.empirical =   subset(s.empirical, is.na(s.empirical$Span) == F)
# a. Get Model Parameters for current bootstrap values of a, b, and sigma -----------------------
s = boot_span(s.empirical$Level, s.empirical$Span)
a = s[1]
b = s[2]
sigma = boot_sigma(g.empirical)
# base level employment for each compustat firm
base.compustat =  base_fit(a, b, compustat$EMP)
fit = data.table(
compustat,
fit_model(a, b, base.compustat, compustat$EMP,
compustat$ratio, compustat$mean.pay.empirical, error.tol)
)
fit = fit[ceo_error < error.tol]
# b. Get Simulation Parameters --------------------------------------------
# simulated firm size distribution
firm.sim = rpld(n.sim, 1, alpha, ordered = F, xmax = 2.3*10^6, discrete_max = 2.3*10^6)
# simulated firm base
base.sim =  base_fit(a, b, firm.sim)
# simulated pay scaling
r.sim = r_sim_2(fit$EMP, fit$r, firm.sim)
#simulated base pay
bp.norm = fit[, base_pay/mean(base_pay), by = Year]
base.pay.sim = bp_sim(bp.norm$V1, n.sim)
# c. Hierarchy with Inter-Firm Pay Dispersion (HF)  -----------------------------------------------------
mod = model(a = a,
b = b,
base_emp_vec = base.sim,
emp_vec = firm.sim,
base_pay_vec = base.pay.sim,
r_vec = r.sim,
sigma = sigma,
firm_size = T,
hierarchy = T
)
top = top_k(mod[,1], mod[,2], 10000)
exec_firm_ratio =  fast_mean(top)/fast_mean(firm.sim)
mod = data.table(mod[, c(1,3)] )
fastgini(mod$pay)
mod = data.table(mod[, c(1,3)] )
h_mean = mod[,  fast_mean(pay), by = h_level ]
g_between = fastgini(h_mean$V1, corr = T)
g_within =  mod[,  fastgini(pay, corr = T), by = h_level      ][,2]
g_within = mean(g_within$V1)
mod = model(a = a,
b = b,
base_emp_vec = base.sim,
emp_vec = firm.sim,
base_pay_vec = base.pay.sim,
r_vec = r.sim,
sigma = sigma,
firm_size = T,
hierarchy = T
)
top = top_k(mod[,1], mod[,2], 10000)
exec_firm_ratio =  fast_mean(top)/fast_mean(firm.sim)
mod = data.table(mod[, c(1,3)] )
h_mean = mod[,  fast_mean(pay), by = h_level ]
g_between = fastgini(h_mean$V1, corr = T)
g_within =  mod[,  fastgini(pay, corr = T), by = h_level      ][,2]
g_within = mean(g_within$V1)
g_within =  mod[,  fastgini(pay, corr = T), by = h_level      ][,2]
View(g_within)
library(hmod)
g_within =  mod[,  fastgini(pay, corr = T), by = h_level      ][,2]
g_within = mean(g_within$V1)
fastgini(mod$pay)
g_ratio = g_between/g_within
cbind(exec_firm_ratio, g_ratio)
r.sim = (r.sim -1) * runif(1, 0.9, 1.1) +1
hist(r.sim)
source('~/Desktop/Empirical Research/Income Distribution/Gini Ratio/Hierarchical Levels/Compustat_exec_space/Model.R')
source('~/Desktop/Empirical Research/Income Distribution/Gini Ratio/Hierarchical Levels/Compustat_exec_space/Model.R')
View(model)
source('~/Desktop/Empirical Research/Income Distribution/Gini Ratio/Hierarchical Levels/Compustat_exec_space/Model.R')
plot(model)
plot(model, log = "x")
source('~/Desktop/Empirical Research/Income Distribution/Gini Ratio/Hierarchical Levels/Compustat_exec_space/Model.R')
plot(model, log = "x")
median(base.pay.sim)
# a. Get Model Parameters for current bootstrap values of a, b, and sigma -----------------------
s = boot_span(s.empirical$Level, s.empirical$Span)
a = s[1]
b = s[2]
sigma = boot_sigma(g.empirical)
# base level employment for each compustat firm
base.compustat =  base_fit(a, b, compustat$EMP)
fit = data.table(
compustat,
fit_model(a, b, base.compustat, compustat$EMP,
compustat$ratio, compustat$mean.pay.empirical, error.tol)
)
fit = fit[ceo_error < error.tol]
# b. Get Simulation Parameters --------------------------------------------
# simulated firm size distribution
firm.sim = rpld(n.sim, 1, alpha, ordered = F, xmax = 2.3*10^6, discrete_max = 2.3*10^6)
# simulated firm base
base.sim =  base_fit(a, b, firm.sim)
# simulated pay scaling
r.sim = r_sim_2(fit$EMP, fit$r, firm.sim)
#simulated base pay
bp.norm = fit[, base_pay/mean(base_pay), by = Year]
base.pay.sim = bp_sim(bp.norm$V1, n.sim)
r.sim = (r.sim -1) * runif(1, 0.1, 1.5) +1
median(base.pay.sim)
test = base.pay.sim- - median(base.pay.sim)
test = base.pay.sim -    (base.pay.sim- - median(base.pay.sim))
test = base.pay.sim -    (base.pay.sim - median(base.pay.sim))
hist(test)
test = base.pay.sim -    runif(1)*(base.pay.sim - median(base.pay.sim))
test = base.pay.sim -    runif(1)*(base.pay.sim - median(base.pay.sim))
fastgini(test)
test = base.pay.sim -    runif(1)*(base.pay.sim - median(base.pay.sim))
fastgini(test)
test = base.pay.sim -    runif(1)*(base.pay.sim - median(base.pay.sim))
fastgini(test)
test = base.pay.sim -    runif(1)*(base.pay.sim - median(base.pay.sim))
fastgini(test)
source('~/Desktop/Empirical Research/Income Distribution/Gini Ratio/Hierarchical Levels/Compustat_exec_space/Model.R')
lm(model)
View(model)
lm(model[,1] ~ model[,2])
r = lm(log(model[,1]) ~ model[,2])
summary(r)
sigma
source('~/Desktop/Empirical Research/Income Distribution/Gini Ratio/Hierarchical Levels/Compustat_exec_space/Model.R')
summary(r)
source('~/Desktop/Empirical Research/Income Distribution/Gini Ratio/Hierarchical Levels/Compustat_exec_space/Model.R')
source('~/Desktop/Empirical Research/Income Distribution/Gini Ratio/Hierarchical Levels/Compustat_exec_space/Model.R')
source('~/Desktop/Empirical Research/Income Distribution/Gini Ratio/Hierarchical Levels/Compustat_exec_space/Model.R')
plot(model, log = "x")
View(model)
plot(model)
plot(data.frame(model), log = "x")
model = data.table(model)
fwrite(model, "exec_firm_ratio_results.csv")
workspace = paste(dir, "/Results", sep = "")
setwd(workspace)
fwrite(model, "exec_firm_ratio_results.csv")
setwd("~/Desktop/Empirical Research/Income Distribution/Gini Ratio/Hierarchical Levels/Compustat_exec_space")
workspace = paste(dir, "/Results", sep = "")
setwd(workspace)
workspace
setwd(""/home/blair/Desktop/Empirical Research/Income Distribution/Gini Ratio/Hierarchical Levels/Compustat_exec_space/Results"")
setwd("/home/blair/Desktop/Empirical Research/Income Distribution/Gini Ratio/Hierarchical Levels/Compustat_exec_space/Results")
mod = fread("exec_firm_ratio_results.csv")
source('~/Desktop/Empirical Research/Plots/K Income/Exec_firm_space.R')
p
scale_color_gradientn(colors = rainbow(8))
source('~/Desktop/Empirical Research/Plots/K Income/Exec_firm_space.R')
p
source('~/Desktop/Empirical Research/Plots/K Income/Exec_firm_space.R')
p
source('~/Desktop/Empirical Research/Plots/K Income/Exec_firm_space.R')
p
source('~/Desktop/Empirical Research/Income Distribution/Gini Ratio/Hierarchical Levels/Compustat_exec_space/Model.R')
runtime/1000
setwd("/home/blair/Desktop/Empirical Research/Income Distribution/Gini Ratio/Hierarchical Levels/Compustat_exec_space/Results")
mod = fread("exec_firm_ratio_results.csv")
p = ggplot() +
geom_point(data = mod, aes(x = exec_firm_ratio, y = g_ratio, col = alpha)) +
scale_x_log10() +
scale_color_gradientn(colors = rainbow(8))
p
runtime/60
source('~/Desktop/Empirical Research/Income Distribution/Gini Ratio/Hierarchical Levels/Compustat_exec_space/Model.R')
source('~/Desktop/Empirical Research/Plots/K Income/Exec_firm_space.R')
p
p = ggplot() +
geom_point(data = mod, aes(x = exec_firm_ratio, y = g_ratio, col = alpha), size = 0.7) +
scale_x_log10() +
scale_color_gradientn(colors = rainbow(8))
p
source('~/Desktop/Empirical Research/Income Distribution/Gini Ratio/Hierarchical Levels/Compustat_exec_space/Model.R')
source('~/Desktop/Empirical Research/Income Distribution/Gini Ratio/Hierarchical Levels/Compustat_exec_space/Model.R')
source('~/Desktop/Empirical Research/Income Distribution/Gini Ratio/Hierarchical Levels/Compustat_exec_space/Model.R')
setwd("/home/blair/Desktop/Empirical Research/Income Distribution/Gini Ratio/Hierarchical Levels/Compustat_exec_space/Results")
mod = fread("exec_firm_ratio_results.csv")
p = ggplot() +
geom_point(data = mod, aes(x = exec_firm_ratio, y = g_ratio, col = alpha), size = 0.7) +
scale_x_log10() +
scale_color_gradientn(colors = rainbow(8))
p
g = ggplot() +
geom_point(data = mod, aes(x = exec_firm, y = g_ratio, col = ave.firm), size = 0.7) +
scale_x_log10() +
scale_color_gradientn(colors = rainbow(8))
g
source('~/Desktop/Empirical Research/Plots/K Income/Exec_firm_space.R')
p
g
g = ggplot() +
geom_point(data = mod, aes(x = exec_firm, y = g_ratio, col = ave.firm), size = 0.7) +
scale_x_log10() +
scale_color_gradientn(colors = rainbow(8), trans = "log")
g
lm(log(mod$exec_firm_ratio) ~ mod$g_ratio)
r = lm(log(mod$exec_firm_ratio) ~ mod$g_ratio)
summary(r)
summary(r)$r.squared
r = lm(log(mod$ave.firm) ~ mod$g_ratio)
summary(r)$r.squared
r = lm(log(mod$exec_firm) ~ mod$g_ratio)
summary(r)$r.squared
runtime/5000
source('~/Desktop/Empirical Research/Plots/K Income/Exec_firm_space.R')
source('~/Desktop/Empirical Research/Plots/K Income/Exec_firm_space.R')
p
runtime
1531/60
source('~/Desktop/Empirical Research/Income Distribution/Gini Ratio/Hierarchical Levels/Compustat_exec_space/Model.R')
setwd("/home/blair/Desktop/Empirical Research/Income Distribution/Gini Ratio/Hierarchical Levels/Compustat_exec_space/Results")
mod = fread("exec_firm_ratio_results.csv")
p = ggplot() +
geom_point(data = mod, aes(x = exec_firm_ratio, y = alpha, col = g_ratio), size = 0.7) +
scale_x_log10() +
scale_color_gradientn(colors = rainbow(8))
p
p = ggplot() +
geom_point(data = mod, aes(x = exec_firm_ratio, y = g_ratio, col = alpha), size = 0.7) +
scale_x_log10() +
scale_color_gradientn(colors = rainbow(8))
p
source('~/Desktop/Empirical Research/Income Distribution/Gini Ratio/Hierarchical Levels/Compustat_exec_space/Model.R')
source('~/Desktop/Empirical Research/Plots/K Income/Exec_firm_space.R')
p
p
p = ggplot() +
geom_point(data = mod, aes(x = exec_firm_ratio, y = alpha, col = g_ratio), size = 0.7) +
scale_x_log10() +
scale_color_gradientn(colors = rainbow(8))
p
p = ggplot() +
geom_point(data = mod, aes(x = exec_firm_ratio, y = alpha, col = g_ratio), size = 0.7) +
scale_x_log10() +
scale_color_gradientn(colors = rainbow(8), trans = "log")
p
p = ggplot() +
geom_point(data = mod, aes(x = exec_firm_ratio, y = alpha, col = g_ratio), size = 0.7) +
scale_x_log10() +
scale_color_gradientn(colors = rainbow(8), trans = "sqrt")
p
p = ggplot() +
geom_point(data = mod, aes(x = exec_firm_ratio, y = alpha, col = g_ratio), size = 0.7) +
scale_x_log10() +
scale_color_gradientn(colors = rainbow(8))
p
p = ggplot() +
geom_point(data = mod, aes(x = exec_firm_ratio, y = alpha, col = 1/g_ratio), size = 0.7) +
scale_x_log10() +
scale_color_gradientn(colors = rainbow(8))
p
p = ggplot() +
geom_point(data = mod, aes(x = exec_firm_ratio, y = alpha, col = 1/g_ratio), size = 0.7) +
scale_x_log10() +
scale_color_gradientn(colors = rainbow(8), trans = "log")
p
p = ggplot() +
geom_point(data = mod, aes(x = exec_firm_ratio, y = alpha, col = g_ratio), size = 0.7) +
scale_x_log10() +
scale_color_gradientn(colors = rainbow(8))
p
p = ggplot() +
geom_point(data = mod, aes(x = exec_firm_ratio, y = alpha, col = g_ratio), size = 0.7) +
scale_x_log10() +
scale_color_gradientn(colors = rainbow(8), max = 6)
p = ggplot() +
geom_point(data = mod, aes(x = exec_firm_ratio, y = alpha, col = g_ratio), size = 0.7) +
scale_x_log10() +
scale_color_gradientn(colors = rainbow(8), limits=c(0, 6))
p
p = ggplot() +
geom_point(data = mod, aes(x = exec_firm_ratio, y = alpha, col = g_ratio), size = 0.7) +
scale_x_log10() +
scale_color_gradientn(colors = rainbow(8), limits=c(0, 5))
p
p = ggplot() +
geom_point(data = mod, aes(x = exec_firm_ratio, y = alpha, col = g_ratio), size = 0.7) +
scale_x_log10() +
scale_color_gradientn(colors = rainbow(8), limits=c(0, 4))
p
p
p = ggplot() +
geom_point(data = mod, aes(x = exec_firm, y = alpha, col = g_ratio), size = 0.7) +
scale_x_log10() +
scale_color_gradientn(colors = rainbow(8), limits=c(0, 4))
p
setwd("/home/blair/Desktop/Empirical Research/Income Distribution/Gini Ratio/Hierarchical Levels/Compustat_exec_space/Results")
mod = fread("exec_firm_ratio_results.csv")
p = ggplot() +
geom_point(data = mod, aes(x = exec_firm, y = ave.firm, col = g_ratio), size = 0.7) +
scale_x_log10() +
scale_color_gradientn(colors = rainbow(8), limits=c(0, 4))
p
p = ggplot() +
geom_point(data = mod, aes(x = exec_firm, y = ave.firm, col = g_ratio), size = 0.7) +
scale_x_log10() +
scale_y_log10() +
scale_color_gradientn(colors = rainbow(8), limits=c(0, 4))
p
p = ggplot() +
geom_point(data = mod, aes(x = exec_firm, y = alpha, col = g_ratio), size = 0.7) +
scale_x_log10() +
scale_color_gradientn(colors = rainbow(8), limits=c(0, 4))
p
p
mod = fread("exec_firm_ratio_results.csv")
mod = subset(mod, mod$g_ratio < 4)
p = ggplot() +
geom_point(data = mod, aes(x = exec_firm, y = alpha, col = g_ratio), size = 0.7) +
scale_x_log10() +
scale_color_gradientn(colors = rainbow(8), limits=c(0, 4))
p
p = ggplot() +
geom_point(data = mod, aes(x = exec_firm, y = alpha, col = g_ratio), size = 0.7) +
scale_x_log10() +
scale_color_gradientn(colors = rainbow(8))
p
source('~/Desktop/Empirical Research/Income Distribution/Gini Ratio/Hierarchical Levels/Compustat_exec_space/Model.R')
stopCluster(cl)
stopCluster(cl)
source('~/Desktop/Empirical Research/Income Distribution/Gini Ratio/Hierarchical Levels/Compustat_exec_space/Model.R')
source('~/Desktop/Empirical Research/Plots/K Income/Exec_firm_space.R')
p
setwd("/home/blair/Desktop/Empirical Research/Income Distribution/Gini Ratio/Hierarchical Levels/Empirical/Exec Compensation")
compustat = fread("CEO Results.csv")
packages = c( 'data.table', 'doSNOW',
'foreach', 'hmod', 'magrittr',
'Rcpp', 'readr',  'RcppZiggurat',
'rstudioapi',  'snow', 'tcltk')
lapply(packages, require, character.only = TRUE)
# 1. Model Variables ---------------------------------------------------------------
# number of bootsrap iterations
n.iteration = 100000
# number of cores for parallel computing
n.core = 8
# CEO pay ratio error tolerance (Model error as absolute percentage of empirical value)
error.tol = 0.05
# Firm size distribution
#alpha = 2.01 # power law exponent
n.sim = 10^7 # number of firms
# 2. Import Data -------------------------------------------------------------
#  compustat Sample
setwd("/home/blair/Desktop/Empirical Research/Income Distribution/Gini Ratio/Hierarchical Levels/Empirical/Exec Compensation")
compustat = fread("CEO Results.csv")
# Case Study Results
setwd("/home/blair/Desktop/Empirical Research/Income Distribution/Gini Ratio/Hierarchical Levels/Empirical/Case Studies")
case.data = fread("Case Results.csv")
# g = vector of hierarchical level gini indexes
g.empirical = na.omit(case.data$Gini[case.data$Gini > 0])
# s = data table of non-NA span of control data
s.empirical = data.table(Level = case.data$Level, Span = case.data$span)
s.empirical =   subset(s.empirical, is.na(s.empirical$Span) == F)
library(here)
source('~/Desktop/Empirical Research/Income Distribution/Gini Ratio/Hierarchical Levels/Paper 2 Models/Emperical Data/Case Studies/Case Study Workbook.R')
