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Cost_benefit_table_pooled.R
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Cost_benefit_table_pooled.R
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## ---- include=F-----------------------------------------------------------------------------------------------
rm(list = ls())
options(tinytex.verbose = TRUE)
## ----setup, include=FALSE-------------------------------------------------------------------------------------
# Loading required libraries
list.of.packages <- c("tidyverse", "haven", "here", "kableExtra")
lapply(list.of.packages, library, character.only = TRUE)
library(rootSolve)
knitr::opts_knit$set(root.dir = here())
knitr::opts_chunk$set(echo = F)
print_code <- TRUE
## ----parameters-----------------------------------------------------------------------------------------------
# Parameters (see SI Appendix, Section D for details)
gov_bonds_so <- 0.09 # Interest rate on government bonds
inflation_so <- 0.04 # Kenyan inflation rate
tax_so <- 0.16575 # Taxes as a share of GDP
unit_cost_so <- 0.42 # Unit cost of deworming (in 2018 USD) - from Evidence Action
periods_so <- 50 #Total number of periods to forecast wages
time_to_jm_so <- 10 #Time from intial period until individual join the labor force
years_of_treat_so <- 2.41 # Additional Years of Deworming Treatment for Groups 1 & 2
q_full_so <- 0.75 #Take up rates with full subsidy. From Miguel and Kremmer (2007)
q_zero_so <- 0 #Take up rates with zero subsidy. From Miguel and Kremmer (2007)
# Schooling costs
teach_sal_so <- 50000 #Monthly secondary schooling compensation (in 2017 KES) overestimated to account for benefits - news sources
teach_sal_so <- 12*teach_sal_so #Yearly secondary schooling compensation
n_students_so <- 45 #Average pupils per teacher 45
delta_ed_so <- c(-0.00176350949079451, # (Delta E) Additional direct seconday schooling increase
0.00696052250263997,
0.0258570306763183,
0.0239963665555466,
0.027301406306074,
0.0234125454594173,
0.0279278879439199,
0.00647044449446303,
0.00835739437790601)
delta_ed_so <- cbind(delta_ed_so, 1999:2007)
# Treatment effect estimates - using pooled numbers at 10, 15, 20 year horizons
lambda1_2017usdppp_so <- c(79.51465, # avg treatment effect from klps2-4 pooled (already adjusted for ppp and inflation) -- Table 1
79.51465, # avg treatment effect from klps2-4 pooled (already adjusted for ppp and inflation) - Table 1
79.51465) # avg treatment effect from klps2-4 pooled (already adjusted for ppp and inflation) - Table 1
consump_2017usdppp_so <- c(0, # assume 0 treatment effect at 10 years
305.108, # avg treatment effect from klps3-4 pooled (already adjusted for ppp and inflation) - Table 1
305.108) # avg treatment effect from klps3-4 pooled (already adjusted for ppp and inflation) - Table 1
# Inflation and exchange rates
ex_rate_2018 <-101.30 # Exchange rate (KES per international $) - https://data.worldbank.org/indicator/PA.NUS.FCRF?locations=KE
ex_rate_2009 <- 77.352 # Exchange rate (KES per international $) - https://data.worldbank.org/indicator/PA.NUS.FCRF?locations=KE
ex_rate_2007 <- 67.318 # Exchange rate (KES per international $) - https://data.worldbank.org/indicator/PA.NUS.FCRF?locations=KE
ex_rate_2018_ppp_so <- 50.058 # KLPS4_E+_globals.do (originally from the World Bank)
ex_rate_2017_ppp_so <- 49.773 # KLPS4_E+_globals.do (originally from the World Bank)
ex_rate_2009_ppp_so <- 31.317 # KLPS4_E+_globals.do (originally from the World Bank)
ex_rate_2007_ppp_so <- 25.024 # KLPS4_E+_globals.do (originally from the World Bank)
cpi_2007_so <- 207.342 # KLPS4_E+_globals.do (originally from the Bureau of Labor Statistics)
cpi_2009_so <- 214.537 # KLPS4_E+_globals.do (originally from the Bureau of Labor Statistics)
cpi_2018_so <- 251.10 # KLPS4_E+_globals.do (originally from the Bureau of Labor Statistics)
cpi_2017_so <- 245.120 # KLPS4_E+_globals.do (originally from the Bureau of Labor Statistics)
# Research
# CALCULATIONS TO CONVERT ALL CURRENCY TO 2017 USD PPP (will need to be updated if monetary inputs are updated)
# Adjust for currency: convert all costs to USD PPP **NOTE: 1 international dollar = 1 USD (https://data.worldbank.org/indicator/PA.NUS.PRVT.PP?locations=KE-US)***
unit_cost_ppp_so <- unit_cost_so*ex_rate_2018/ex_rate_2018_ppp_so
teach_sal_ppp_so <- teach_sal_so/ex_rate_2017_ppp_so
# Adjust for inflation: convert all costs to 2017 USD
unit_cost_2017usdppp_so <- unit_cost_ppp_so*cpi_2017_so/cpi_2018_so
teach_sal_2017usdppp_so <- teach_sal_ppp_so*cpi_2017_so/cpi_2017_so # redundant, but for the sake of consistency
## ----model----------------------------------------------------------------------------------------------------
###########################
# CONSTUCTING MODEL #
###########################
npv_mo_f <- function(interest_r_var = interest_in,
n_male_var = 1/2, n_female_var = 1/2,
delta_welfare_var,
tax_var = tax_so,
cost_of_schooling_var = cost_per_student_in,
delta_ed_male_var = delta_ed_so[,1],
delta_ed_female_var = delta_ed_so[,1],
s1_var = 0, q1_var = 0, s2_var = s2_in, q2_var = q2_in,
periods_var = periods_so, years_of_treat_var = years_of_treat_so) {
ns <- c(n_male_var, n_female_var)
l_index_t <- 0:periods_var
delta_ed_s <- cbind(delta_ed_male_var, delta_ed_female_var)
delta_ed_s <- rbind(c(0,0), delta_ed_s, matrix(0,41, 2) )
###############################################################################
benef <- matrix(NA, 51,2)
for (i in 1:2){
benef[,i] <- ( 1 / (1 + interest_r_var) )^l_index_t * delta_welfare_var
}
res1 <- sum( ns * ( tax_var * apply(benef, 2, sum) -
apply( ( 1 / (1 + interest_r_var) )^l_index_t *
delta_ed_s * cost_of_schooling_var, 2, sum) )) -
sum( ( 1 / (1 + interest_r_var) )^(0:2) * (s2_var * q2_var - s1_var * q1_var) )
###############################################################################
return(res1)
}
## ----interest-rate--------------------------------------------------------------------------------------------
# - inputs: gov_bonds_so, inflation_so
# - inputs: gov_bonds_so, inflation_so
# - outputs: interest_in
interest_in_f <- function(gov_bonds_var = gov_bonds_so , inflation_var = inflation_so) {
###############################################################################
interest_in = gov_bonds_var - inflation_var
###############################################################################
return(list("interest_in" = interest_in))
}
invisible( list2env(interest_in_f(),.GlobalEnv) )
## ----costs----------------------------------------------------------------------------------------------------
# - inputs:
# - inputs:
# - outputs:
costs_f <- function(unit_cost_var = unit_cost_2017usdppp_so,
years_of_treat_var = years_of_treat_so,
q_full_var = q_full_so){
###############################################################################
s2_in <- c(rep(unit_cost_var,2), .4*unit_cost_var)
q2_in <- q_full_var
###############################################################################
return(list("s2_in" = s2_in, "q2_in" = q2_in))
}
invisible( list2env(costs_f(),.GlobalEnv) )
## ----ed-costs-------------------------------------------------------------------------------------------------
# - inputs: coverage_so, q_full_so, q_zero_so
# - outputs: saturation_in
ed_costs_in_f <- function(teach_sal_var = teach_sal_2017usdppp_so,
n_students_var = n_students_so,
delta_ed_var = delta_ed_so[,1]){
###############################################################################
cost_per_student_in <- (teach_sal_var)/ n_students_var
delta_ed_in <- delta_ed_var
###############################################################################
return(list("cost_per_student_in" = cost_per_student_in, "delta_ed_in" = delta_ed_in))
}
invisible( list2env(ed_costs_in_f(),.GlobalEnv) )
## ----delta_earnings, eval=TRUE--------------------------------------------------------------------------------
# - inputs: periods_so, lambda1_2017usdppp_so
# - outputs:
delta_welfare_in_f <- function(t_var = 0:periods_so,
welfarek1_var,
welfarek2_var,
welfarek3_var) {
###############################################################################
delta_welfare_in <- 1*(10 <= t_var & t_var < 15) * welfarek1_var +
1*(15 <= t_var & t_var < 20) * welfarek2_var +
1*(20 <= t_var & t_var < 25) * welfarek3_var
###############################################################################
return(delta_welfare_in)
}
## ----delta_earnings_p, eval=TRUE------------------------------------------------------------------------------
# - inputs: periods_so, lambda1_2017usdppp_so
# - outputs:
delta_welfare_p_in_f <- function(t_var = 0:periods_so,
welfarek1_var,
welfarek2_var,
welfarek3_var) {
###############################################################################
delta_welfare_p_in <- 1*(10 <= t_var & t_var < 15) * welfarek1_var +
1*(15 <= t_var & t_var < 20) * welfarek2_var +
1*(20 <= t_var) * welfarek3_var
###############################################################################
return(delta_welfare_p_in)
}
## ----earnings, eval=TRUE--------------------------------------------------------------------------------------
delta_earnings_in = delta_welfare_in_f(welfarek1_var = lambda1_2017usdppp_so[1],
welfarek2_var = lambda1_2017usdppp_so[2],
welfarek3_var = lambda1_2017usdppp_so[3])
delta_earnings_p_in = delta_welfare_p_in_f(welfarek1_var = lambda1_2017usdppp_so[1],
welfarek2_var = lambda1_2017usdppp_so[2],
welfarek3_var = lambda1_2017usdppp_so[3])
## ----consumption, eval=TRUE-----------------------------------------------------------------------------------
delta_consumption_in = delta_welfare_in_f(welfarek1_var = consump_2017usdppp_so[1],
welfarek2_var = consump_2017usdppp_so[2],
welfarek3_var = consump_2017usdppp_so[3])
delta_consumption_p_in = delta_welfare_p_in_f(welfarek1_var = consump_2017usdppp_so[1],
welfarek2_var = consump_2017usdppp_so[2],
welfarek3_var = consump_2017usdppp_so[3])
## ----model_cwelfare-------------------------------------------------------------------------------------------
npv_cwelfare_p_mo_f <- function(interest_r_var = interest_in,
n_male_var = 1/2, n_female_var = 1/2,
delta_welfare_var,
lambda1_male_var = lambda1_2017usdppp_so[1],
lambda1_female_var = lambda1_2017usdppp_so[2],
tax_var = tax_so,
cost_of_schooling_var = cost_per_student_in,
delta_ed_male_var = delta_ed_so[,1],
delta_ed_female_var = delta_ed_so[,1],
s1_var = 0, q1_var = 0, s2_var = s2_in, q2_var = q2_in,
periods_var = periods_so, years_of_treat_var = years_of_treat_so) {
ns <- c(n_male_var, n_female_var)
l_index_t <- 0:periods_var
delta_ed_s <- cbind(delta_ed_male_var, delta_ed_female_var)
delta_ed_s <- rbind(c(0,0), delta_ed_s, matrix(0,41, 2) )
###############################################################################
benef <- matrix(NA, 51,2)
for (i in 1:2){
benef[,i] <- ( 1 / (1 + interest_r_var) )^l_index_t * (1*(10 <= l_index_t & l_index_t < 15) * delta_welfare_var + 1*(15 <= l_index_t & l_index_t < 20) * delta_welfare_var +1*(20 <= l_index_t) * delta_welfare_var)
}
res1 <- sum( ns * ( tax_var * apply(benef, 2, sum) -
apply( ( 1 / (1 + interest_r_var) )^l_index_t *
delta_ed_s * cost_of_schooling_var, 2, sum) )) -
sum( ( 1 / (1 + interest_r_var) )^(0:2) * (s2_var * q2_var - s1_var * q1_var) )
###############################################################################
return(res1)
}
npv_cwelfare_d_mo_f <- function(interest_r_var = interest_in,
n_male_var = 1/2, n_female_var = 1/2,
delta_welfare_var,
lambda1_male_var = lambda1_2017usdppp_so[1],
lambda1_female_var = lambda1_2017usdppp_so[2],
tax_var = tax_so,
cost_of_schooling_var = cost_per_student_in,
delta_ed_male_var = delta_ed_so[,1],
delta_ed_female_var = delta_ed_so[,1],
s1_var = 0, q1_var = 0, s2_var = s2_in, q2_var = q2_in,
periods_var = periods_so, years_of_treat_var = years_of_treat_so) {
ns <- c(n_male_var, n_female_var)
l_index_t <- 0:periods_var
delta_ed_s <- cbind(delta_ed_male_var, delta_ed_female_var)
delta_ed_s <- rbind(c(0,0), delta_ed_s, matrix(0,41, 2) )
###############################################################################
benef <- matrix(NA, 51,2)
for (i in 1:2){
benef[,i] <- ( 1 / (1 + interest_r_var) )^l_index_t * (1*(10 <= l_index_t & l_index_t < 15) * delta_welfare_var + 1*(15 <= l_index_t & l_index_t < 20) * delta_welfare_var + 1*(20 <= l_index_t & l_index_t < 25) * delta_welfare_var)
}
res1 <- sum( ns * ( tax_var * apply(benef, 2, sum) -
apply( ( 1 / (1 + interest_r_var) )^l_index_t * delta_ed_s * cost_of_schooling_var, 2, sum) )
) - sum( ( 1 / (1 + interest_r_var) )^(0:2) * (s2_var * q2_var - s1_var * q1_var) )
###############################################################################
return(res1)
}
## ----table 1 results------------------------------------------------------------------------------------------
######################
# TABLE CALCULATIONS #
######################
#########
# PANEL A
#########
e_social_persist_int10 <- (multiroot(function(x) npv_cwelfare_p_mo_f(delta_welfare_var = x, tax_var = 1, interest_r_var = 0.10), 4, maxiter=1000000, positive = T))$root
e_social_persist_int05 <- (multiroot(function(x) npv_cwelfare_p_mo_f(delta_welfare_var = x, tax_var = 1, interest_r_var = 0.05), 4, maxiter=1000000, positive = T))$root
e_social_die_int10 <- (multiroot(function(x) npv_cwelfare_d_mo_f(delta_welfare_var = x, tax_var = 1, interest_r_var = 0.10), 4, maxiter=1000000, positive = T))$root
e_social_die_int05 <- (multiroot(function(x) npv_cwelfare_d_mo_f(delta_welfare_var = x, tax_var = 1, interest_r_var = 0.05), 4, maxiter=1000000, positive = T))$root
e_tax_persist_int10 <- (multiroot(function(x) npv_cwelfare_p_mo_f(delta_welfare_var = x, interest_r_var = 0.10), 4, maxiter=10000000, positive = T))$root
e_tax_persist_int05 <- (multiroot(function(x) npv_cwelfare_p_mo_f(delta_welfare_var = x, interest_r_var = 0.05), 4, maxiter=10000000, positive = T))$root
e_tax_die_int10 <- (multiroot(function(x) npv_cwelfare_d_mo_f(delta_welfare_var = x, interest_r_var = 0.10), 4, maxiter=10000000, positive = T))$root
e_tax_die_int05 <- (multiroot(function(x) npv_cwelfare_d_mo_f(delta_welfare_var = x, interest_r_var = 0.05), 4, maxiter=10000000, positive = T))$root
#########
# PANEL B
#########
# Net Present Value (2017 USD PPP)
e_npv_int05_persist <- npv_mo_f(delta_welfare_var = delta_earnings_p_in, tax_var = 1)
e_npv_int05_die <- npv_mo_f(delta_welfare_var = delta_earnings_in, tax_var = 1)
e_npv_int10_persist <- npv_mo_f(delta_welfare_var = delta_earnings_p_in, interest_r_var = 0.10, tax_var = 1)
e_npv_int10_die <- npv_mo_f(delta_welfare_var = delta_earnings_in, interest_r_var = 0.10, tax_var = 1)
# Net Present Value of tax revenue (2017 USD PPP)
e_tax_int05_persist <- npv_mo_f(delta_welfare_var = delta_earnings_p_in, interest_r_var = .05)
e_tax_int05_die <- npv_mo_f(delta_welfare_var = delta_earnings_in, interest_r_var = .05)
e_tax_int10_persist <- npv_mo_f(delta_welfare_var = delta_earnings_p_in, interest_r_var = 0.10)
e_tax_int10_die <- npv_mo_f(delta_welfare_var = delta_earnings_in, interest_r_var = 0.10)
#########
# PANEL C
#########
e_irr_social_persist <- (multiroot(function(x) npv_mo_f(interest_r_var = x, tax_var = 1, delta_welfare_var = delta_earnings_p_in), .1, maxiter=1000000, positive = T))$root
e_irr_social_die <- (multiroot(function(x) npv_mo_f(interest_r_var = x, tax_var = 1, delta_welfare_var = delta_earnings_in), .1, maxiter=10000000, positive = T))$root
e_irr_tax_persist <- (multiroot(function(x) npv_mo_f(interest_r_var = x, delta_welfare_var = delta_earnings_p_in), .1, maxiter=1000000, positive = T))$root
e_irr_tax_die <- (multiroot(function(x) npv_mo_f(interest_r_var = x, delta_welfare_var = delta_earnings_in), .1, maxiter=1000000, positive = T))$root
#########
# PANEL A
#########
c_social_persist_int10 <- (multiroot(function(x) npv_cwelfare_p_mo_f(delta_welfare_var = x, tax_var = 1, interest_r_var = 0.10), 4, maxiter=1000000, positive = T))$root
c_social_persist_int05 <- (multiroot(function(x) npv_cwelfare_p_mo_f(delta_welfare_var = x, tax_var = 1, interest_r_var = 0.05), 4, maxiter=1000000, positive = T))$root
c_social_die_int10 <- (multiroot(function(x) npv_cwelfare_d_mo_f(delta_welfare_var = x, tax_var = 1, interest_r_var = 0.10), 4, maxiter=1000000, positive = T))$root
c_social_die_int05 <- (multiroot(function(x) npv_cwelfare_d_mo_f(delta_welfare_var = x, tax_var = 1, interest_r_var = 0.05), 4, maxiter=1000000, positive = T))$root
c_tax_persist_int10 <- (multiroot(function(x) npv_cwelfare_p_mo_f(delta_welfare_var = x, interest_r_var = 0.10), 4, maxiter=1000000, positive = T))$root
c_tax_persist_int05 <- (multiroot(function(x) npv_cwelfare_p_mo_f(delta_welfare_var = x, interest_r_var = 0.05), 4, maxiter=1000000, positive = T))$root
c_tax_die_int10 <- (multiroot(function(x) npv_cwelfare_d_mo_f(delta_welfare_var = x, interest_r_var = 0.10), 4, maxiter=1000000, positive = T))$root
c_tax_die_int05 <- (multiroot(function(x) npv_cwelfare_d_mo_f(delta_welfare_var = x, interest_r_var = 0.05), 4, maxiter=1000000, positive = T))$root
#########
# PANEL B
#########
# Net Present Value (2017 USD PPP)
c_npv_int05_persist <- npv_mo_f(delta_welfare_var = delta_consumption_p_in, interest_r_var = 0.05, tax_var = 1)
c_npv_int05_die <- npv_mo_f(delta_welfare_var = delta_consumption_in, interest_r_var = 0.05, tax_var = 1)
c_npv_int10_persist <- npv_mo_f(delta_welfare_var = delta_consumption_p_in, interest_r_var = 0.10, tax_var = 1)
c_npv_int10_die <- npv_mo_f(delta_welfare_var = delta_consumption_in, interest_r_var = 0.10, tax_var = 1)
# Net Present Value of tax revenue (2017 USD PPP)
c_tax_int05_persist <- npv_mo_f(delta_welfare_var = delta_consumption_p_in, interest_r_var = 0.05)
c_tax_int05_die <- npv_mo_f(delta_welfare_var = delta_consumption_in, interest_r_var = 0.05)
c_tax_int10_persist <- npv_mo_f(delta_welfare_var = delta_consumption_p_in, interest_r_var = 0.10)
c_tax_int10_die <- npv_mo_f(delta_welfare_var = delta_consumption_in, interest_r_var = 0.10)
#########
# PANEL C
#########
c_irr_social_persist <- (multiroot(function(x) npv_mo_f(interest_r_var = x, tax_var = 1, delta_welfare_var = delta_consumption_p_in), .1, maxiter=1000000, positive = T))$root
c_irr_social_die <- (multiroot(function(x) npv_mo_f(interest_r_var = x, tax_var = 1, delta_welfare_var = delta_consumption_in), .1, maxiter=1000000, positive = T))$root
c_irr_tax_persist <- (multiroot(function(x) npv_mo_f(interest_r_var = x, delta_welfare_var = delta_consumption_p_in), .1, maxiter=1000000, positive = T))$root
c_irr_tax_die <- (multiroot(function(x) npv_mo_f(interest_r_var = x, delta_welfare_var = delta_consumption_in), .1, maxiter=1000000, positive = T))$root