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05a_EstSim_main.R
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05a_EstSim_main.R
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#-------------------------------------------------------#
# #
# This program estimates first- and second-stage #
# regressions and simulates the outcomes for the #
# 2018-drought, for the main model. #
# #
# Note: The farm-level data are confidential and cannot #
# be loaded (line 17). The results at the sample mean #
# are saved in line 477 and the figure in Section 5 #
# can be created. #
# #
#-------------------------------------------------------#
library(dplyr)
library(systemfit)
library(ggplot2)
load("rOutput/farm_ready.Rda")
#-----------------------------------------------------------#
#### 1) Prepare the weather variables for the simulation ####
#-----------------------------------------------------------#
# Load simulated weather
load("rOutput/sim2018.Rda")
# Load LTA weather and weather in 2018
load("rOutput/df_weather_lta.Rda")
load("rOutput/df_weather_2018.Rda")
# Add observed weather to simulated weather
sim2018$gdd_obs <- c(df_weather_lta$gdd, df_weather_2018$gdd, rep(df_weather_lta$gdd,10))
sim2018$prec_obs <- c(df_weather_lta$prec, df_weather_2018$prec, rep(df_weather_lta$prec,10))
sim2018$gddHigh_obs <- c(df_weather_lta$gddHigh, df_weather_2018$gddHigh, rep(df_weather_lta$gddHigh,10))
sim2018$dd_obs <- c(df_weather_lta$dd, df_weather_2018$dd, rep(df_weather_lta$dd,10))
# Add interactions between observed and experienced weather
sim2018$gdd_obs_1to3 <- sim2018$gdd_obs * sim2018$gdd_1to3
sim2018$prec_obs_1to3 <- sim2018$prec_obs * sim2018$prec_1to3
sim2018$gddHigh_obs_1to3 <- sim2018$gddHigh_obs * sim2018$gddHigh_1to3
sim2018$dd_obs_1to3 <- sim2018$dd_obs * sim2018$dd_1to3
sim2018$gdd_obs_4to10 <- sim2018$gdd_obs * sim2018$gdd_4to10
sim2018$prec_obs_4to10 <- sim2018$prec_obs * sim2018$prec_4to10
sim2018$gddHigh_obs_4to10 <- sim2018$gddHigh_obs * sim2018$gddHigh_4to10
sim2018$dd_obs_4to10 <- sim2018$dd_obs * sim2018$dd_4to10
# Add time indicator for simulation
sim2018$t <- c(-1:10)
#----------------------------------#
#### 2) Run probit regressions #####
#----------------------------------#
#Define probit regressions
cereal.eq <- iCereals ~ np_cereals + np_protein + np_oilseed + np_roots + np_corn + nw_fert +
k_land + k_labor + k_capital + trend + trend2 +
lsh_cereals + lsh_protein + lsh_oilseed + lsh_roots +
gdd_1to3 + prec_1to3 + gddHigh_1to3 + dd_1to3 +
gdd_4to10 + prec_4to10 + gddHigh_4to10 + dd_4to10 +
np_cereals_fm + np_protein_fm + np_oilseed_fm + np_roots_fm + np_corn_fm + nw_fert_fm +
k_land_fm + k_labor_fm + k_capital_fm + trend_fm + trend2_fm +
lsh_cereals_fm + lsh_protein_fm + lsh_oilseed_fm + lsh_roots_fm +
gdd_1to3_fm + prec_1to3_fm + gddHigh_1to3_fm + dd_1to3_fm +
gdd_4to10_fm + prec_4to10_fm + gddHigh_4to10_fm + dd_4to10_fm
protein.eq <- iProtein ~ np_cereals + np_protein + np_oilseed + np_roots + np_corn + nw_fert +
k_land + k_labor + k_capital + trend + trend2 +
lsh_cereals + lsh_protein + lsh_oilseed + lsh_roots +
gdd_1to3 + prec_1to3 + gddHigh_1to3 + dd_1to3 +
gdd_4to10 + prec_4to10 + gddHigh_4to10 + dd_4to10 +
np_cereals_fm + np_protein_fm + np_oilseed_fm + np_roots_fm + np_corn_fm + nw_fert_fm +
k_land_fm + k_labor_fm + k_capital_fm + trend_fm + trend2_fm +
lsh_cereals_fm + lsh_protein_fm + lsh_oilseed_fm + lsh_roots_fm +
gdd_1to3_fm + prec_1to3_fm + gddHigh_1to3_fm + dd_1to3_fm +
gdd_4to10_fm + prec_4to10_fm + gddHigh_4to10_fm + dd_4to10_fm
oilseed.eq <- iOilseed ~ np_cereals + np_protein + np_oilseed + np_roots + np_corn + nw_fert +
k_land + k_labor + k_capital + trend + trend2 +
lsh_cereals + lsh_protein + lsh_oilseed + lsh_roots +
gdd_1to3 + prec_1to3 + gddHigh_1to3 + dd_1to3 +
gdd_4to10 + prec_4to10 + gddHigh_4to10 + dd_4to10 +
np_cereals_fm + np_protein_fm + np_oilseed_fm + np_roots_fm + np_corn_fm + nw_fert_fm +
k_land_fm + k_labor_fm + k_capital_fm + trend_fm + trend2_fm +
lsh_cereals_fm + lsh_protein_fm + lsh_oilseed_fm + lsh_roots_fm +
gdd_1to3_fm + prec_1to3_fm + gddHigh_1to3_fm + dd_1to3_fm +
gdd_4to10_fm + prec_4to10_fm + gddHigh_4to10_fm + dd_4to10_fm
roots.eq <- iRoots ~ np_cereals + np_protein + np_oilseed + np_roots + np_corn + nw_fert +
k_land + k_labor + k_capital + trend + trend2 +
lsh_cereals + lsh_protein + lsh_oilseed + lsh_roots +
gdd_1to3 + prec_1to3 + gddHigh_1to3 + dd_1to3 +
gdd_4to10 + prec_4to10 + gddHigh_4to10 + dd_4to10 +
np_cereals_fm + np_protein_fm + np_oilseed_fm + np_roots_fm + np_corn_fm + nw_fert_fm +
k_land_fm + k_labor_fm + k_capital_fm + trend_fm + trend2_fm +
lsh_cereals_fm + lsh_protein_fm + lsh_oilseed_fm + lsh_roots_fm +
gdd_1to3_fm + prec_1to3_fm + gddHigh_1to3_fm + dd_1to3_fm +
gdd_4to10_fm + prec_4to10_fm + gddHigh_4to10_fm + dd_4to10_fm
corn.eq <- iCorn ~ np_cereals + np_protein + np_oilseed + np_roots + np_corn + nw_fert +
k_land + k_labor + k_capital + trend + trend2 +
lsh_cereals + lsh_protein + lsh_oilseed + lsh_roots +
gdd_1to3 + prec_1to3 + gddHigh_1to3 + dd_1to3 +
gdd_4to10 + prec_4to10 + gddHigh_4to10 + dd_4to10 +
np_cereals_fm + np_protein_fm + np_oilseed_fm + np_roots_fm + np_corn_fm + nw_fert_fm +
k_land_fm + k_labor_fm + k_capital_fm + trend_fm + trend2_fm +
lsh_cereals_fm + lsh_protein_fm + lsh_oilseed_fm + lsh_roots_fm +
gdd_1to3_fm + prec_1to3_fm + gddHigh_1to3_fm + dd_1to3_fm +
gdd_4to10_fm + prec_4to10_fm + gddHigh_4to10_fm + dd_4to10_fm
#set-up the loop over crops
list_crops <- data.frame(crops=c("Cereals","Protein","Oilseed","Roots","Corn"),
probit=c("cereal.eq","protein.eq","oilseed.eq","roots.eq","corn.eq"),
abbrev=c("cer","prot","oil","roots","corn"))
n_crops <- list_crops %>% count() %>% as.numeric() # number of crops
#set-up the lists to store the results
# List for actual results
list_probit_act <- list(Cereals=list(PHI="", phi=""),
Protein=list(PHI="", phi=""),
Oilseed=list(PHI="", phi=""),
Roots= list(PHI="", phi=""),
Corn=list(PHI="", phi=""))
# List for simulated results (Note: I need t=1 to t=12 because t-1 does not work in lists)
list_probit_sim <- list(Cereals=list(PHI=list(t1="", t2="", t3="", t4="", t5="",t6="", t7="", t8="", t9="", t10="", t11="", t12=""),
phi=list(t1="", t2="", t3="", t4="", t5="",t6="", t7="", t8="", t9="", t10="", t11="", t12="")),
Protein=list(PHI=list(t1="", t2="", t3="", t4="", t5="",t6="", t7="", t8="", t9="", t10="", t11="", t12=""),
phi=list(t1="", t2="", t3="", t4="", t5="",t6="", t7="", t8="", t9="", t10="", t11="", t12="")),
Oilseed=list(PHI=list(t1="", t2="", t3="", t4="", t5="",t6="", t7="", t8="", t9="", t10="", t11="", t12=""),
phi=list(t1="", t2="", t3="", t4="", t5="",t6="", t7="", t8="", t9="", t10="", t11="", t12="")),
Roots= list(PHI=list(t1="", t2="", t3="", t4="", t5="",t6="", t7="", t8="", t9="", t10="", t11="", t12=""),
phi=list(t1="", t2="", t3="", t4="", t5="",t6="", t7="", t8="", t9="", t10="", t11="", t12="")),
Corn=list(PHI=list(t1="", t2="", t3="", t4="", t5="",t6="", t7="", t8="", t9="", t10="", t11="", t12=""),
phi=list(t1="", t2="", t3="", t4="", t5="",t6="", t7="", t8="", t9="", t10="", t11="", t12="")))
# Loop over all crops and estimate probits
for (i in 1:n_crops) {
# Probit estimation
crop.eq <- get(list_crops[i,"probit"])
iCrop <- glm(crop.eq, family = binomial(link = "probit"),
data = df_farm)
# Actual prediction
# At the farm-level
iCrop_linpred <- predict(iCrop)
# PHI
list_probit_act[[i]][[1]] <- pnorm(iCrop_linpred)
# phi
list_probit_act[[i]][[2]] <- dnorm(iCrop_linpred)
# Simulation
# Data used in probit model
X <- as_tibble(model.matrix(iCrop)) #note: with as_tibble, I retain the column names
for (t in -1:10)
{
# Simulate t = -1
X$gdd_1to3 <- sim2018$gdd_1to3[sim2018$t==t]
X$prec_1to3 <- sim2018$prec_1to3[sim2018$t==t]
X$gddHigh_1to3 <- sim2018$gddHigh_1to3[sim2018$t==t]
X$dd_1to3 <- sim2018$dd_1to3[sim2018$t==t]
X$gdd_4to10 <- sim2018$gdd_4to10[sim2018$t==t]
X$prec_4to10 <- sim2018$prec_4to10[sim2018$t==t]
X$gddHigh_4to10 <- sim2018$gddHigh_4to10[sim2018$t==t]
X$dd_4to10 <- sim2018$dd_4to10[sim2018$t==t]
# Store PHI's and phi's
list_probit_sim[[i]][[1]][[t+2]] <- as.vector ( pnorm( t( as.matrix(as.numeric(iCrop$coefficients) %*% t(as.matrix(X))) ) ) )
list_probit_sim[[i]][[2]][[t+2]] <- as.vector ( dnorm( t( as.matrix(as.numeric(iCrop$coefficients) %*% t(as.matrix(X))) ) ) )
}
}
# Append actual farm-level PHIs and phis to data set
df_farm$PHI_cereals <- as.numeric(do.call(c, list_probit_act[[1]][1]))
df_farm$PHI_protein <- as.numeric(do.call(c, list_probit_act[[2]][1]))
df_farm$PHI_oilseed <- as.numeric(do.call(c, list_probit_act[[3]][1]))
df_farm$PHI_roots <- as.numeric(do.call(c, list_probit_act[[4]][1]))
df_farm$PHI_corn <- as.numeric(do.call(c, list_probit_act[[5]][1]))
df_farm$phi_cereals <- as.numeric(do.call(c, list_probit_act[[1]][2]))
df_farm$phi_protein <- as.numeric(do.call(c, list_probit_act[[2]][2]))
df_farm$phi_oilseed <- as.numeric(do.call(c, list_probit_act[[3]][2]))
df_farm$phi_roots <- as.numeric(do.call(c, list_probit_act[[4]][2]))
df_farm$phi_corn <- as.numeric(do.call(c, list_probit_act[[5]][2]))
#--------------------------------------#
#### 3) Run structural regressions #####
#--------------------------------------#
#Define structural equations
eqQQcereals <- qq_cereals ~ PHI_cereals + I(PHI_cereals*np_cereals) + I(PHI_cereals*np_protein) + I(PHI_cereals*np_oilseed) + I(PHI_cereals*np_roots) + I(PHI_cereals*np_corn) + I(PHI_cereals*nw_fert) +
I(PHI_cereals*k_land) + I(PHI_cereals*k_labor) + I(PHI_cereals*k_capital) + I(PHI_cereals*trend) + I(PHI_cereals*trend2) +
I(PHI_cereals*gdd_obs) + I(PHI_cereals*prec_obs) + I(PHI_cereals*gddHigh_obs) + I(PHI_cereals*dd_obs) +
I(PHI_cereals*gdd_1to3) + I(PHI_cereals*prec_1to3) + I(PHI_cereals*gddHigh_1to3) + I(PHI_cereals*dd_1to3) +
I(PHI_cereals*gdd_4to10) + I(PHI_cereals*prec_4to10) + I(PHI_cereals*gddHigh_4to10) + I(PHI_cereals*dd_4to10) +
I(PHI_cereals*gdd_obs_1to3) + I(PHI_cereals*prec_obs_1to3) + I(PHI_cereals*gddHigh_obs_1to3) + I(PHI_cereals*dd_obs_1to3) +
I(PHI_cereals*gdd_obs_4to10) + I(PHI_cereals*prec_obs_4to10) + I(PHI_cereals*gddHigh_obs_4to10) + I(PHI_cereals*dd_obs_4to10) +
I(PHI_cereals*np_cereals_fm) + I(PHI_cereals*np_protein_fm) + I(PHI_cereals*np_oilseed_fm) + I(PHI_cereals*np_roots_fm) + I(PHI_cereals*np_corn_fm) + I(PHI_cereals*nw_fert_fm) +
I(PHI_cereals*k_land_fm) + I(PHI_cereals*k_labor_fm) + I(PHI_cereals*k_capital_fm) + I(PHI_cereals*trend_fm) + I(PHI_cereals*trend2_fm) +
I(PHI_cereals*gdd_obs_fm) + I(PHI_cereals*prec_obs_fm) + I(PHI_cereals*gddHigh_obs_fm) + I(PHI_cereals*dd_obs_fm) +
I(PHI_cereals*gdd_1to3_fm) + I(PHI_cereals*prec_1to3_fm) + I(PHI_cereals*gddHigh_1to3_fm) + I(PHI_cereals*dd_1to3_fm) +
I(PHI_cereals*gdd_4to10_fm) + I(PHI_cereals*prec_4to10_fm) + I(PHI_cereals*gddHigh_4to10_fm) + I(PHI_cereals*dd_4to10_fm) +
I(PHI_cereals*gdd_obs_1to3_fm) + I(PHI_cereals*prec_obs_1to3_fm) + I(PHI_cereals*gddHigh_obs_1to3_fm) + I(PHI_cereals*dd_obs_1to3_fm) +
I(PHI_cereals*gdd_obs_4to10_fm) + I(PHI_cereals*prec_obs_4to10_fm) + I(PHI_cereals*gddHigh_obs_4to10_fm) + I(PHI_cereals*dd_obs_4to10_fm) +
phi_cereals -1
eqQQprotein <- qq_protein ~ PHI_protein + I(PHI_protein*np_cereals) + I(PHI_protein*np_protein) + I(PHI_protein*np_oilseed) + I(PHI_protein*np_roots) + I(PHI_protein*np_corn) + I(PHI_protein*nw_fert) +
I(PHI_protein*k_land) + I(PHI_protein*k_labor) + I(PHI_protein*k_capital) + I(PHI_protein*trend) + I(PHI_protein*trend2) +
I(PHI_protein*gdd_obs) + I(PHI_protein*prec_obs) + I(PHI_protein*gddHigh_obs) + I(PHI_protein*dd_obs) +
I(PHI_protein*gdd_1to3) + I(PHI_protein*prec_1to3) + I(PHI_protein*gddHigh_1to3) + I(PHI_protein*dd_1to3) +
I(PHI_protein*gdd_4to10) + I(PHI_protein*prec_4to10) + I(PHI_protein*gddHigh_4to10) + I(PHI_protein*dd_4to10) +
I(PHI_protein*gdd_obs_1to3) + I(PHI_protein*prec_obs_1to3) + I(PHI_protein*gddHigh_obs_1to3) + I(PHI_protein*dd_obs_1to3) +
I(PHI_protein*gdd_obs_4to10) + I(PHI_protein*prec_obs_4to10) + I(PHI_protein*gddHigh_obs_4to10) + I(PHI_protein*dd_obs_4to10) +
I(PHI_protein*np_cereals_fm) + I(PHI_protein*np_protein_fm) + I(PHI_protein*np_oilseed_fm) + I(PHI_protein*np_roots_fm) + I(PHI_protein*np_corn_fm) + I(PHI_protein*nw_fert_fm) +
I(PHI_protein*k_land_fm) + I(PHI_protein*k_labor_fm) + I(PHI_protein*k_capital_fm) + I(PHI_protein*trend_fm) + I(PHI_protein*trend2_fm) +
I(PHI_protein*gdd_obs_fm) + I(PHI_protein*prec_obs_fm) + I(PHI_protein*gddHigh_obs_fm) + I(PHI_protein*dd_obs_fm) +
I(PHI_protein*gdd_1to3_fm) + I(PHI_protein*prec_1to3_fm) + I(PHI_protein*gddHigh_1to3_fm) + I(PHI_protein*dd_1to3_fm) +
I(PHI_protein*gdd_4to10_fm) + I(PHI_protein*prec_4to10_fm) + I(PHI_protein*gddHigh_4to10_fm) + I(PHI_protein*dd_4to10_fm) +
I(PHI_protein*gdd_obs_1to3_fm) + I(PHI_protein*prec_obs_1to3_fm) + I(PHI_protein*gddHigh_obs_1to3_fm) + I(PHI_protein*dd_obs_1to3_fm) +
I(PHI_protein*gdd_obs_4to10_fm) + I(PHI_protein*prec_obs_4to10_fm) + I(PHI_protein*gddHigh_obs_4to10_fm) + I(PHI_protein*dd_obs_4to10_fm) +
phi_protein -1
eqQQoilseed <- qq_oilseed ~ PHI_oilseed + I(PHI_oilseed*np_cereals) + I(PHI_oilseed*np_protein) + I(PHI_oilseed*np_oilseed) + I(PHI_oilseed*np_roots) + I(PHI_oilseed*np_corn) + I(PHI_oilseed*nw_fert) +
I(PHI_oilseed*k_land) + I(PHI_oilseed*k_labor) + I(PHI_oilseed*k_capital) + I(PHI_oilseed*trend) + I(PHI_oilseed*trend2) +
I(PHI_oilseed*gdd_obs) + I(PHI_oilseed*prec_obs) + I(PHI_oilseed*gddHigh_obs) + I(PHI_oilseed*dd_obs) +
I(PHI_oilseed*gdd_1to3) + I(PHI_oilseed*prec_1to3) + I(PHI_oilseed*gddHigh_1to3) + I(PHI_oilseed*dd_1to3) +
I(PHI_oilseed*gdd_4to10) + I(PHI_oilseed*prec_4to10) + I(PHI_oilseed*gddHigh_4to10) + I(PHI_oilseed*dd_4to10) +
I(PHI_oilseed*gdd_obs_1to3) + I(PHI_oilseed*prec_obs_1to3) + I(PHI_oilseed*gddHigh_obs_1to3) + I(PHI_oilseed*dd_obs_1to3) +
I(PHI_oilseed*gdd_obs_4to10) + I(PHI_oilseed*prec_obs_4to10) + I(PHI_oilseed*gddHigh_obs_4to10) + I(PHI_oilseed*dd_obs_4to10) +
I(PHI_oilseed*np_cereals_fm) + I(PHI_oilseed*np_protein_fm) + I(PHI_oilseed*np_oilseed_fm) + I(PHI_oilseed*np_roots_fm) + I(PHI_oilseed*np_corn_fm) + I(PHI_oilseed*nw_fert_fm) +
I(PHI_oilseed*k_land_fm) + I(PHI_oilseed*k_labor_fm) + I(PHI_oilseed*k_capital_fm) + I(PHI_oilseed*trend_fm) + I(PHI_oilseed*trend2_fm) +
I(PHI_oilseed*gdd_obs_fm) + I(PHI_oilseed*prec_obs_fm) + I(PHI_oilseed*gddHigh_obs_fm) + I(PHI_oilseed*dd_obs_fm) +
I(PHI_oilseed*gdd_1to3_fm) + I(PHI_oilseed*prec_1to3_fm) + I(PHI_oilseed*gddHigh_1to3_fm) + I(PHI_oilseed*dd_1to3_fm) +
I(PHI_oilseed*gdd_4to10_fm) + I(PHI_oilseed*prec_4to10_fm) + I(PHI_oilseed*gddHigh_4to10_fm) + I(PHI_oilseed*dd_4to10_fm) +
I(PHI_oilseed*gdd_obs_1to3_fm) + I(PHI_oilseed*prec_obs_1to3_fm) + I(PHI_oilseed*gddHigh_obs_1to3_fm) + I(PHI_oilseed*dd_obs_1to3_fm) +
I(PHI_oilseed*gdd_obs_4to10_fm) + I(PHI_oilseed*prec_obs_4to10_fm) + I(PHI_oilseed*gddHigh_obs_4to10_fm) + I(PHI_oilseed*dd_obs_4to10_fm) +
phi_oilseed -1
eqQQroots <- qq_roots ~ PHI_roots + I(PHI_roots*np_cereals) + I(PHI_roots*np_protein) + I(PHI_roots*np_oilseed) + I(PHI_roots*np_roots) + I(PHI_roots*np_corn) + I(PHI_roots*nw_fert) +
I(PHI_roots*k_land) + I(PHI_roots*k_labor) + I(PHI_roots*k_capital) + I(PHI_roots*trend) + I(PHI_roots*trend2) +
I(PHI_roots*gdd_obs) + I(PHI_roots*prec_obs) + I(PHI_roots*gddHigh_obs) + I(PHI_roots*dd_obs) +
I(PHI_roots*gdd_1to3) + I(PHI_roots*prec_1to3) + I(PHI_roots*gddHigh_1to3) + I(PHI_roots*dd_1to3) +
I(PHI_roots*gdd_4to10) + I(PHI_roots*prec_4to10) + I(PHI_roots*gddHigh_4to10) + I(PHI_roots*dd_4to10) +
I(PHI_roots*gdd_obs_1to3) + I(PHI_roots*prec_obs_1to3) + I(PHI_roots*gddHigh_obs_1to3) + I(PHI_roots*dd_obs_1to3) +
I(PHI_roots*gdd_obs_4to10) + I(PHI_roots*prec_obs_4to10) + I(PHI_roots*gddHigh_obs_4to10) + I(PHI_roots*dd_obs_4to10) +
I(PHI_roots*np_cereals_fm) + I(PHI_roots*np_protein_fm) + I(PHI_roots*np_oilseed_fm) + I(PHI_roots*np_roots_fm) + I(PHI_roots*np_corn_fm) + I(PHI_roots*nw_fert_fm) +
I(PHI_roots*k_land_fm) + I(PHI_roots*k_labor_fm) + I(PHI_roots*k_capital_fm) + I(PHI_roots*trend_fm) + I(PHI_roots*trend2_fm) +
I(PHI_roots*gdd_obs_fm) + I(PHI_roots*prec_obs_fm) + I(PHI_roots*gddHigh_obs_fm) + I(PHI_roots*dd_obs_fm) +
I(PHI_roots*gdd_1to3_fm) + I(PHI_roots*prec_1to3_fm) + I(PHI_roots*gddHigh_1to3_fm) + I(PHI_roots*dd_1to3_fm) +
I(PHI_roots*gdd_4to10_fm) + I(PHI_roots*prec_4to10_fm) + I(PHI_roots*gddHigh_4to10_fm) + I(PHI_roots*dd_4to10_fm) +
I(PHI_roots*gdd_obs_1to3_fm) + I(PHI_roots*prec_obs_1to3_fm) + I(PHI_roots*gddHigh_obs_1to3_fm) + I(PHI_roots*dd_obs_1to3_fm) +
I(PHI_roots*gdd_obs_4to10_fm) + I(PHI_roots*prec_obs_4to10_fm) + I(PHI_roots*gddHigh_obs_4to10_fm) + I(PHI_roots*dd_obs_4to10_fm) +
phi_roots -1
eqQQcorn <- qq_corn ~ PHI_corn + I(PHI_corn*np_cereals) + I(PHI_corn*np_protein) + I(PHI_corn*np_oilseed) + I(PHI_corn*np_roots) + I(PHI_corn*np_corn) + I(PHI_corn*nw_fert) +
I(PHI_corn*k_land) + I(PHI_corn*k_labor) + I(PHI_corn*k_capital) + I(PHI_corn*trend) + I(PHI_corn*trend2) +
I(PHI_corn*gdd_obs) + I(PHI_corn*prec_obs) + I(PHI_corn*gddHigh_obs) + I(PHI_corn*dd_obs) +
I(PHI_corn*gdd_1to3) + I(PHI_corn*prec_1to3) + I(PHI_corn*gddHigh_1to3) + I(PHI_corn*dd_1to3) +
I(PHI_corn*gdd_4to10) + I(PHI_corn*prec_4to10) + I(PHI_corn*gddHigh_4to10) + I(PHI_corn*dd_4to10) +
I(PHI_corn*gdd_obs_1to3) + I(PHI_corn*prec_obs_1to3) + I(PHI_corn*gddHigh_obs_1to3) + I(PHI_corn*dd_obs_1to3) +
I(PHI_corn*gdd_obs_4to10) + I(PHI_corn*prec_obs_4to10) + I(PHI_corn*gddHigh_obs_4to10) + I(PHI_corn*dd_obs_4to10) +
I(PHI_corn*np_cereals_fm) + I(PHI_corn*np_protein_fm) + I(PHI_corn*np_oilseed_fm) + I(PHI_corn*np_roots_fm) + I(PHI_corn*np_corn_fm) + I(PHI_corn*nw_fert_fm) +
I(PHI_corn*k_land_fm) + I(PHI_corn*k_labor_fm) + I(PHI_corn*k_capital_fm) + I(PHI_corn*trend_fm) + I(PHI_corn*trend2_fm) +
I(PHI_corn*gdd_obs_fm) + I(PHI_corn*prec_obs_fm) + I(PHI_corn*gddHigh_obs_fm) + I(PHI_corn*dd_obs_fm) +
I(PHI_corn*gdd_1to3_fm) + I(PHI_corn*prec_1to3_fm) + I(PHI_corn*gddHigh_1to3_fm) + I(PHI_corn*dd_1to3_fm) +
I(PHI_corn*gdd_4to10_fm) + I(PHI_corn*prec_4to10_fm) + I(PHI_corn*gddHigh_4to10_fm) + I(PHI_corn*dd_4to10_fm) +
I(PHI_corn*gdd_obs_1to3_fm) + I(PHI_corn*prec_obs_1to3_fm) + I(PHI_corn*gddHigh_obs_1to3_fm) + I(PHI_corn*dd_obs_1to3_fm) +
I(PHI_corn*gdd_obs_4to10_fm) + I(PHI_corn*prec_obs_4to10_fm) + I(PHI_corn*gddHigh_obs_4to10_fm) + I(PHI_corn*dd_obs_4to10_fm) +
phi_corn -1
eqNXfert <- nx_fert ~ np_cereals + np_protein + np_oilseed + np_roots + np_corn + nw_fert +
k_land + k_labor + k_capital + trend + trend2 +
gdd_obs + prec_obs + gddHigh_obs + dd_obs +
gdd_1to3 + prec_1to3 + gddHigh_1to3 + dd_1to3 +
gdd_4to10 + prec_4to10 + gddHigh_4to10 + dd_4to10 +
gdd_obs_1to3 + prec_obs_1to3 + gddHigh_obs_1to3 + dd_obs_1to3 +
gdd_obs_4to10 + prec_obs_4to10 + gddHigh_obs_4to10 + dd_obs_4to10 +
np_cereals_fm + np_protein_fm + np_oilseed_fm + np_roots_fm + np_corn_fm + nw_fert_fm +
k_land_fm + k_labor_fm + k_capital_fm + trend_fm + trend2_fm +
gdd_obs_fm + prec_obs_fm + gddHigh_obs_fm + dd_obs_fm +
gdd_1to3_fm + prec_1to3_fm + gddHigh_1to3_fm + dd_1to3_fm +
gdd_4to10_fm + prec_4to10_fm + gddHigh_4to10_fm + dd_4to10_fm +
gdd_obs_1to3_fm + prec_obs_1to3_fm + gddHigh_obs_1to3_fm + dd_obs_1to3_fm +
gdd_obs_4to10_fm + prec_obs_4to10_fm + gddHigh_obs_4to10_fm + dd_obs_4to10_fm
system <- list( QQcereals = eqQQcereals,
QQprotein = eqQQprotein,
QQoilseed = eqQQoilseed,
QQroots = eqQQroots,
QQcorn = eqQQcorn,
NXfert = eqNXfert)
## restrictions
restrict <- c( "QQcereals_I(PHI_cereals * np_protein) - QQprotein_I(PHI_protein * np_cereals) = 0",
"QQcereals_I(PHI_cereals * np_oilseed) - QQoilseed_I(PHI_oilseed * np_cereals) = 0",
"QQcereals_I(PHI_cereals * np_roots) - QQroots_I(PHI_roots * np_cereals) = 0",
"QQcereals_I(PHI_cereals * np_corn) - QQcorn_I(PHI_corn * np_cereals) = 0",
"QQcereals_I(PHI_cereals * nw_fert) - NXfert_np_cereals = 0",
"QQprotein_I(PHI_protein * np_oilseed) - QQoilseed_I(PHI_oilseed * np_protein) = 0",
"QQprotein_I(PHI_protein * np_roots) - QQroots_I(PHI_roots * np_protein) = 0",
"QQprotein_I(PHI_protein * np_corn) - QQcorn_I(PHI_corn * np_protein) = 0",
"QQprotein_I(PHI_protein * nw_fert) - NXfert_np_protein = 0",
"QQoilseed_I(PHI_oilseed * np_roots) - QQroots_I(PHI_roots * np_oilseed) = 0",
"QQoilseed_I(PHI_oilseed * np_corn) - QQcorn_I(PHI_corn * np_oilseed) = 0",
"QQoilseed_I(PHI_oilseed * nw_fert) - NXfert_np_oilseed = 0",
"QQroots_I(PHI_roots * np_corn) - QQcorn_I(PHI_corn * np_roots) = 0",
"QQroots_I(PHI_roots * nw_fert) - NXfert_np_roots = 0",
"QQcorn_I(PHI_corn * nw_fert) - NXfert_np_corn = 0")
## Regression with iterated SUR estimation
model_linear <- systemfit( formula = system, method = "SUR",
data = df_farm, restrict.matrix = restrict,
maxit = 100 )
# Calculate MAE (to compare with out-of-sample prediction)
predicted_outcomes <- predict(model_linear)
caret::postResample(df_farm$qq_cereals,predicted_outcomes$QQcereals.pred)
caret::postResample(df_farm$qq_protein,predicted_outcomes$QQprotein.pred)
caret::postResample(df_farm$qq_oilseed,predicted_outcomes$QQoilseed.pred)
caret::postResample(df_farm$qq_roots,predicted_outcomes$QQroots.pred)
caret::postResample(df_farm$qq_corn,predicted_outcomes$QQcorn.pred)
caret::postResample(df_farm$x_fert,-predicted_outcomes$NXfert.pred)
# Extract data used in this estimation for simulation later
dat_str_cereals <- as_tibble(model.matrix(model_linear)[grep('^QQcereals', rownames(model.matrix(model_linear))),]) %>%
mutate_at(vars(c(1:dim(.)[2])), funs(./df_farm$PHI_cereals)) %>%
select(where(~ any(. != 0)))
dat_str_protein <- as_tibble(model.matrix(model_linear)[grep('^QQprotein', rownames(model.matrix(model_linear))),]) %>%
mutate_at(vars(c(1:dim(.)[2])), funs(./df_farm$PHI_protein)) %>%
select(where(~ any(. != 0)))
dat_str_oilseed <- as_tibble(model.matrix(model_linear)[grep('^QQoilseed', rownames(model.matrix(model_linear))),]) %>%
mutate_at(vars(c(1:dim(.)[2])), funs(./df_farm$PHI_oilseed)) %>%
select(where(~ any(. != 0)))
dat_str_roots <- as_tibble(model.matrix(model_linear)[grep('^QQroots', rownames(model.matrix(model_linear))),]) %>%
mutate_at(vars(c(1:dim(.)[2])), funs(./df_farm$PHI_roots)) %>%
select(where(~ any(. != 0)))
dat_str_corn <- as_tibble(model.matrix(model_linear)[grep('^QQcorn', rownames(model.matrix(model_linear))),]) %>%
mutate_at(vars(c(1:dim(.)[2])), funs(./df_farm$PHI_corn)) %>%
select(where(~ any(. != 0)))
dat_str_fert <- as_tibble(model.matrix(model_linear)[grep('^NXfert', rownames(model.matrix(model_linear))),]) %>%
select(where(~ any(. != 0)))
# ------------------------------------ #
#### 4) Simulation of drought shock ####
# ------------------------------------ #
#set-up the loop over crops
list_outcome <- data.frame(outcome=c("cereals","protein","oilseed","roots","corn", "fert"),
sur=c("QQcereals","QQprotein","QQoilseed","QQroots","QQcorn", "NXfert"))
n_outcomes <- list_outcome %>% count() %>% as.numeric() # number of crops
#set-up the lists to store the results
list_simresults <- list(Cereals=list(t1="", t2="", t3="", t4="", t5="",t6="", t7="", t8="", t9="", t10="", t11="", t12=""),
Protein=list(t1="", t2="", t3="", t4="", t5="",t6="", t7="", t8="", t9="", t10="", t11="", t12=""),
Oilseed=list(t1="", t2="", t3="", t4="", t5="",t6="", t7="", t8="", t9="", t10="", t11="", t12=""),
Roots=list(t1="", t2="", t3="", t4="", t5="",t6="", t7="", t8="", t9="", t10="", t11="", t12=""),
Corn=list(t1="", t2="", t3="", t4="", t5="",t6="", t7="", t8="", t9="", t10="", t11="", t12=""),
Fertilizer=list(t1="", t2="", t3="", t4="", t5="",t6="", t7="", t8="", t9="", t10="", t11="", t12=""))
# Loop over all outcomes and estimate probits
for (i in 1:n_outcomes) {
# Get data
X <- as_tibble(get(paste0("dat_str_", list_outcome[i,"outcome"])))
# "Clean" variable names
names(X) <- c("const","np_cereals","np_protein","np_oilseed","np_roots","np_corn","nw_fert",
"k_land","k_labor","k_capital","trend","trend2",
"gdd_obs","prec_obs","gddHigh_obs","dd_obs",
"gdd_1to3","prec_1to3","gddHigh_1to3","dd_1to3",
"gdd_4to10","prec_4to10","gddHigh_4to10","dd_4to10",
"gdd_obs_1to3","prec_obs_1to3","gddHigh_obs_1to3","dd_obs_1to3",
"gdd_obs_4to10","prec_obs_4to10","gddHigh_obs_4to10","dd_obs_4to10",
"np_cereals_fm","np_protein_fm","np_oilseed_fm","np_roots_fm","np_corn_fm","nw_fert_fm",
"k_land_fm","k_labor_fm","k_capital_fm","trend_fm","trend2_fm",
"gdd_obs_fm","prec_obs_fm","gddHigh_obs_fm","dd_obs_fm",
"gdd_1to3_fm","prec_1to3_fm","gddHigh_1to3_fm","dd_1to3_fm",
"gdd_4to10_fm","prec_4to10_fm","gddHigh_4to10_fm","dd_4to10_fm",
"gdd_obs_1to3_fm","prec_obs_1to3_fm","gddHigh_obs_1to3_fm","dd_obs_1to3_fm",
"gdd_obs_4to10_fm","prec_obs_4to10_fm","gddHigh_obs_4to10_fm","dd_obs_4to10_fm",
"phi")
# Simulate the outcome
for (t in -1:10) {
X_sim <- X
# Replace the weather variables for the simulation
X_sim$gdd_obs <- sim2018$gdd_obs[sim2018$t==t]
X_sim$prec_obs <- sim2018$prec_obs[sim2018$t==t]
X_sim$gddHigh_obs <- sim2018$gddHigh_obs[sim2018$t==t]
X_sim$dd_obs <- sim2018$dd_obs[sim2018$t==t]
X_sim$gdd_1to3 <- sim2018$gdd_1to3[sim2018$t==t]
X_sim$prec_1to3 <- sim2018$prec_1to3[sim2018$t==t]
X_sim$gddHigh_1to3 <- sim2018$gddHigh_1to3[sim2018$t==t]
X_sim$dd_1to3 <- sim2018$dd_1to3[sim2018$t==t]
X_sim$gdd_4to10 <- sim2018$gdd_4to10[sim2018$t==t]
X_sim$prec_4to10 <- sim2018$prec_4to10[sim2018$t==t]
X_sim$gddHigh_4to10 <- sim2018$gddHigh_4to10[sim2018$t==t]
X_sim$dd_4to10 <- sim2018$dd_4to10[sim2018$t==t]
X_sim$gdd_obs_1to3 <- sim2018$gdd_obs_1to3[sim2018$t==t]
X_sim$prec_obs_1to3 <- sim2018$prec_obs_1to3[sim2018$t==t]
X_sim$gddHigh_obs_1to3 <- sim2018$gddHigh_obs_1to3[sim2018$t==t]
X_sim$dd_obs_1to3 <- sim2018$dd_obs_1to3[sim2018$t==t]
X_sim$gdd_obs_4to10 <- sim2018$gdd_obs_4to10[sim2018$t==t]
X_sim$prec_obs_4to10 <- sim2018$prec_obs_4to10[sim2018$t==t]
X_sim$gddHigh_obs_4to10 <- sim2018$gddHigh_obs_4to10[sim2018$t==t]
X_sim$dd_obs_4to10 <- sim2018$dd_obs_4to10[sim2018$t==t]
# Replace phi and PHI for all crops, but not for fert
if (list_outcome[i,"outcome"] != "fert") {
X_sim$phi <- do.call(c,list_probit_sim[[i]][[2]][t+2])
PHI <- do.call(c,list_probit_sim[[i]][[1]][t+2])
} else {
X_sim$phi <- NULL
PHI <- 1
}
# Predict output
X_sim <- as.matrix(X_sim)
C <- as.data.frame(t(coef_linear) ) %>% select(starts_with(list_outcome[i,"sur"]))
C <- t(C)
list_simresults[[i]][[t+2]] <- PHI * (X_sim %*% C)
}
}
# Calculate sample mean of simulations
simresults <- data.frame(
t = c(-1:10),
Cereals = c(mean(list_simresults$Cereals$t1), mean(list_simresults$Cereals$t2), mean(list_simresults$Cereals$t3),
mean(list_simresults$Cereals$t4), mean(list_simresults$Cereals$t5), mean(list_simresults$Cereals$t6),
mean(list_simresults$Cereals$t7), mean(list_simresults$Cereals$t8), mean(list_simresults$Cereals$t9),
mean(list_simresults$Cereals$t10), mean(list_simresults$Cereals$t11), mean(list_simresults$Cereals$t12)),
Protein = c(mean(list_simresults$Protein$t1), mean(list_simresults$Protein$t2), mean(list_simresults$Protein$t3),
mean(list_simresults$Protein$t4), mean(list_simresults$Protein$t5), mean(list_simresults$Protein$t6),
mean(list_simresults$Protein$t7), mean(list_simresults$Protein$t8), mean(list_simresults$Protein$t9),
mean(list_simresults$Protein$t10), mean(list_simresults$Protein$t11), mean(list_simresults$Protein$t12)),
Oilseed = c(mean(list_simresults$Oilseed$t1), mean(list_simresults$Oilseed$t2), mean(list_simresults$Oilseed$t3),
mean(list_simresults$Oilseed$t4), mean(list_simresults$Oilseed$t5), mean(list_simresults$Oilseed$t6),
mean(list_simresults$Oilseed$t7), mean(list_simresults$Oilseed$t8), mean(list_simresults$Oilseed$t9),
mean(list_simresults$Oilseed$t10), mean(list_simresults$Oilseed$t11), mean(list_simresults$Oilseed$t12)),
Roots = c(mean(list_simresults$Roots$t1), mean(list_simresults$Roots$t2), mean(list_simresults$Roots$t3),
mean(list_simresults$Roots$t4), mean(list_simresults$Roots$t5), mean(list_simresults$Roots$t6),
mean(list_simresults$Roots$t7), mean(list_simresults$Roots$t8), mean(list_simresults$Roots$t9),
mean(list_simresults$Roots$t10), mean(list_simresults$Roots$t11), mean(list_simresults$Roots$t12)),
Corn = c(mean(list_simresults$Corn$t1), mean(list_simresults$Corn$t2), mean(list_simresults$Corn$t3),
mean(list_simresults$Corn$t4), mean(list_simresults$Corn$t5), mean(list_simresults$Corn$t6),
mean(list_simresults$Corn$t7), mean(list_simresults$Corn$t8), mean(list_simresults$Corn$t9),
mean(list_simresults$Corn$t10), mean(list_simresults$Corn$t11), mean(list_simresults$Corn$t12)),
Fertilizer = -c(mean(list_simresults$Fertilizer$t1), mean(list_simresults$Fertilizer$t2), mean(list_simresults$Fertilizer$t3),
mean(list_simresults$Fertilizer$t4), mean(list_simresults$Fertilizer$t5), mean(list_simresults$Fertilizer$t6),
mean(list_simresults$Fertilizer$t7), mean(list_simresults$Fertilizer$t8), mean(list_simresults$Fertilizer$t9),
mean(list_simresults$Fertilizer$t10), mean(list_simresults$Fertilizer$t11), mean(list_simresults$Fertilizer$t12))
)
# Save simulation result
save(simresults, file="rOutput/simresults_main.Rda")
#----------------------------------------------#
#### 5) Plot the results at the sample mean ####
#----------------------------------------------#
# Load results
load("rOutput/simresults_main.Rda")
# Normalize the data for plotting
simresults <- simresults %>%
mutate_each(funs(./.[1]), setdiff(names(.), c("t")))
# Transform data to long data
simresults_long <- reshape2::melt(simresults, id.vars="t")
# Plot the results
Fig_main <- ggplot(simresults_long, aes(x=t, y=value, group=variable, shape=variable, color=variable)) +
geom_line()+
geom_point() +
theme_bw() +
scale_color_manual(values=c("#8c510a", "#bf812d", "#dfc27d", "#80cdc1", "#35978f", "#003c30"),
name = "",
labels = c("Cereals",
"Protein crops",
"Oilseeds",
"Root crops",
"Corn",
"Fertilizer")) +
scale_shape_manual(values=c(10,16,17,18,15,13),
name = "",
labels = c("Cereals",
"Protein crops",
"Oilseeds",
"Root crops",
"Corn",
"Fertilizer")) +
ggtitle("") +
scale_x_continuous(breaks = seq(-1, 10, by = 1),
labels = c("-1","0","1","2","3","4",
"5","6","7","8","9","10"),
name = "Periods (t) since drought shock") +
scale_y_continuous(breaks = seq(0, 1.4, by = 0.2), limits=c(0,1.52)) +
theme(text = element_text(size = 11),
legend.text=element_text(size=9),
axis.title = element_text(size = 10),
legend.margin=margin(t = -0.7, unit='cm'),
panel.grid.minor.y = element_blank(),
panel.grid.minor.x = element_blank(),
panel.grid.major.x = element_blank(),
panel.border = element_blank(),
axis.ticks = element_blank()) +
labs(
x = "",
y = "Index",
linetype = ""
) +
geom_segment(aes(x = 0, y = 0, xend = 0, yend = 1.45), linetype="dashed", color="grey") +
annotate(geom="text", x=0, y=1.52, label="Drought shock",
color="darkgrey", size=3.5)
Fig_main
# Save the plot as .png and .eps files
ggsave("Figures/Figure_3.png", Fig_main, device="png", width = 6, height = 3, units = "in", dpi=1200)
ggsave("Figures/Figure_3.eps", Fig_main, device="eps", width = 6, height = 3, units = "in", dpi=1200)