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10b_Bootstrap_nonlinear.R
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10b_Bootstrap_nonlinear.R
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#------------------------------------------------------#
# #
# This program estimates the model with nonlinearities #
# in weather with bootstrapped standard errors. #
# #
# Note: The bootstrap program (Section 1: Bootstrap #
# program) cannot be run because farm-level data are #
# confidential. The results of the bootstrap are #
# stored in lines 924 and 939, allowing to #
# create the tables in Section 2 (Presentation of #
# results). #
# #
#------------------------------------------------------#
# load packages
library(dplyr)
library(writexl)
library(systemfit)
library(doFuture)
library(doRNG)
# load data
load("rOutput/farm_ready.Rda")
#----------------------------#
#### 1) Bootstrap program ####
#----------------------------#
my.boot <- function(data, nrep, cluster, nCores, actual) {
# Set up the bootstrap
B <- nrep #Number of draws
registerDoFuture() # Initialize parallel computing
plan(multisession, workers = nCores) # Define parallel computing plan with number of cores
res <- foreach(1:B, .combine = rbind) %dorng% {
if (actual==FALSE) {
cluster_id <- unique(cluster)
sb_ID <- sample(cluster_id, replace = TRUE) # For clustering at farm-level, select "ID_farm". Otherwise, select "ID_nuts2"
data_boot <- list()
for (j in 1:length(sb_ID)) {
data_boot[[j]] <- df_farm[which(cluster == sb_ID[j]), ]
}
data_boot <- do.call(rbind, data_boot)
} else if (actual==TRUE) {
data_boot <- df_farm
}
tryCatch( { # in case there is an optimization error in one of the draws:
# -------------------- #
# START OF ESTIMATIONS #
# -------------------- #
library(dplyr)
#calculate sample mean for elasticity evaluation
dat_sm <- dplyr::summarise_all(data_boot, mean)
#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 + gdd2_1to3 + prec_1to3 + prec2_1to3 + gddHigh_1to3 + dd_1to3 +
gdd_4to10 + gdd2_4to10 + prec_4to10 + prec2_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 + gdd2_1to3_fm + prec_1to3_fm + prec2_1to3_fm + gddHigh_1to3_fm + dd_1to3_fm +
gdd_4to10_fm + gdd2_4to10_fm + prec_4to10_fm + prec2_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 + gdd2_1to3 + prec_1to3 + prec2_1to3 + gddHigh_1to3 + dd_1to3 +
gdd_4to10 + gdd2_4to10 + prec_4to10 + prec2_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 + gdd2_1to3_fm + prec_1to3_fm + prec2_1to3_fm + gddHigh_1to3_fm + dd_1to3_fm +
gdd_4to10_fm + gdd2_4to10_fm + prec_4to10_fm + prec2_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 + gdd2_1to3 + prec_1to3 + prec2_1to3 + gddHigh_1to3 + dd_1to3 +
gdd_4to10 + gdd2_4to10 + prec_4to10 + prec2_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 + gdd2_1to3_fm + prec_1to3_fm + prec2_1to3_fm + gddHigh_1to3_fm + dd_1to3_fm +
gdd_4to10_fm + gdd2_4to10_fm + prec_4to10_fm + prec2_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 + gdd2_1to3 + prec_1to3 + prec2_1to3 + gddHigh_1to3 + dd_1to3 +
gdd_4to10 + gdd2_4to10 + prec_4to10 + prec2_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 + gdd2_1to3_fm + prec_1to3_fm + prec2_1to3_fm + gddHigh_1to3_fm + dd_1to3_fm +
gdd_4to10_fm + gdd2_4to10_fm + prec_4to10_fm + prec2_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 + gdd2_1to3 + prec_1to3 + prec2_1to3 + gddHigh_1to3 + dd_1to3 +
gdd_4to10 + gdd2_4to10 + prec_4to10 + prec2_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 + gdd2_1to3_fm + prec_1to3_fm + prec2_1to3_fm + gddHigh_1to3_fm + dd_1to3_fm +
gdd_4to10_fm + gdd2_4to10_fm + prec_4to10_fm + prec2_4to10_fm + gddHigh_4to10_fm + dd_4to10_fm
#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*gdd2_obs) + I(PHI_cereals*prec_obs) + I(PHI_cereals*prec2_obs) + I(PHI_cereals*gddHigh_obs) + I(PHI_cereals*dd_obs) + # Compared to the baseline model, I have nonlinearities here
I(PHI_cereals*gdd_1to3) + I(PHI_cereals*gdd2_1to3) + I(PHI_cereals*prec_1to3) + I(PHI_cereals*prec2_1to3) + I(PHI_cereals*gddHigh_1to3) + I(PHI_cereals*dd_1to3) + # Compared to the baseline model, I have nonlinearities here
I(PHI_cereals*gdd_4to10) + I(PHI_cereals*gdd2_4to10) + I(PHI_cereals*prec_4to10) + I(PHI_cereals*prec2_4to10) + I(PHI_cereals*gddHigh_4to10) + I(PHI_cereals*dd_4to10) + # Compared to the baseline model, I have nonlinearities here
I(PHI_cereals*gdd_obs_1to3) + I(PHI_cereals*prec_obs_1to3) + I(PHI_cereals*gddHigh_obs_1to3) + I(PHI_cereals*dd_obs_1to3) + # Weather-climate Interactions as in the baseline model
I(PHI_cereals*gdd_obs_4to10) + I(PHI_cereals*prec_obs_4to10) + I(PHI_cereals*gddHigh_obs_4to10) + I(PHI_cereals*dd_obs_4to10) + # Weather-climate Interactions as in the baseline model
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*gdd2_obs_fm) + I(PHI_cereals*prec_obs_fm) + I(PHI_cereals*prec2_obs_fm) + I(PHI_cereals*gddHigh_obs_fm) + I(PHI_cereals*dd_obs_fm) + # Nonlinearities also here
I(PHI_cereals*gdd_1to3_fm) + I(PHI_cereals*gdd2_1to3_fm) + I(PHI_cereals*prec_1to3_fm) + I(PHI_cereals*prec2_1to3_fm) + I(PHI_cereals*gddHigh_1to3_fm) + I(PHI_cereals*dd_1to3_fm) + # Nonlinearities also here
I(PHI_cereals*gdd_4to10_fm) + I(PHI_cereals*gdd2_4to10_fm) + I(PHI_cereals*prec_4to10_fm) + I(PHI_cereals*prec2_4to10_fm) + I(PHI_cereals*gddHigh_4to10_fm) + I(PHI_cereals*dd_4to10_fm) + # Nonlinearities also here
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) + # Weather-climate Interactions as in the baseline model
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) + # Weather-climate Interactions as in the baseline model
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*gdd2_obs) + I(PHI_protein*prec_obs) + I(PHI_protein*prec2_obs) + I(PHI_protein*gddHigh_obs) + I(PHI_protein*dd_obs) +
I(PHI_protein*gdd_1to3) + I(PHI_protein*gdd2_1to3) + I(PHI_protein*prec_1to3) + I(PHI_protein*prec2_1to3) + I(PHI_protein*gddHigh_1to3) + I(PHI_protein*dd_1to3) +
I(PHI_protein*gdd_4to10) + I(PHI_protein*gdd2_4to10) + I(PHI_protein*prec_4to10) + I(PHI_protein*prec2_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*gdd2_obs_fm) + I(PHI_protein*prec_obs_fm) + I(PHI_protein*prec2_obs_fm) + I(PHI_protein*gddHigh_obs_fm) + I(PHI_protein*dd_obs_fm) +
I(PHI_protein*gdd_1to3_fm) + I(PHI_protein*gdd2_1to3_fm) + I(PHI_protein*prec_1to3_fm) + I(PHI_protein*prec2_1to3_fm) + I(PHI_protein*gddHigh_1to3_fm) + I(PHI_protein*dd_1to3_fm) +
I(PHI_protein*gdd_4to10_fm) + I(PHI_protein*gdd2_4to10_fm) + I(PHI_protein*prec_4to10_fm) + I(PHI_protein*prec2_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*gdd2_obs) + I(PHI_oilseed*prec_obs) + I(PHI_oilseed*prec2_obs) + I(PHI_oilseed*gddHigh_obs) + I(PHI_oilseed*dd_obs) +
I(PHI_oilseed*gdd_1to3) + I(PHI_oilseed*gdd2_1to3) + I(PHI_oilseed*prec_1to3) + I(PHI_oilseed*prec2_1to3) + I(PHI_oilseed*gddHigh_1to3) + I(PHI_oilseed*dd_1to3) +
I(PHI_oilseed*gdd_4to10) + I(PHI_oilseed*gdd2_4to10) + I(PHI_oilseed*prec_4to10) + I(PHI_oilseed*prec2_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*gdd2_obs_fm) + I(PHI_oilseed*prec_obs_fm) + I(PHI_oilseed*prec2_obs_fm) + I(PHI_oilseed*gddHigh_obs_fm) + I(PHI_oilseed*dd_obs_fm) +
I(PHI_oilseed*gdd_1to3_fm) + I(PHI_oilseed*gdd2_1to3_fm) + I(PHI_oilseed*prec_1to3_fm) + I(PHI_oilseed*prec2_1to3_fm) + I(PHI_oilseed*gddHigh_1to3_fm) + I(PHI_oilseed*dd_1to3_fm) +
I(PHI_oilseed*gdd_4to10_fm) + I(PHI_oilseed*gdd2_4to10_fm) + I(PHI_oilseed*prec_4to10_fm) + I(PHI_oilseed*prec2_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*gdd2_obs) + I(PHI_roots*prec_obs) + I(PHI_roots*prec2_obs) + I(PHI_roots*gddHigh_obs) + I(PHI_roots*dd_obs) +
I(PHI_roots*gdd_1to3) + I(PHI_roots*gdd2_1to3) + I(PHI_roots*prec_1to3) + I(PHI_roots*prec2_1to3) + I(PHI_roots*gddHigh_1to3) + I(PHI_roots*dd_1to3) +
I(PHI_roots*gdd_4to10) + I(PHI_roots*gdd2_4to10) + I(PHI_roots*prec_4to10) + I(PHI_roots*prec2_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*gdd2_obs_fm) + I(PHI_roots*prec_obs_fm) + I(PHI_roots*prec2_obs_fm) + I(PHI_roots*gddHigh_obs_fm) + I(PHI_roots*dd_obs_fm) +
I(PHI_roots*gdd_1to3_fm) + I(PHI_roots*gdd2_1to3_fm) + I(PHI_roots*prec_1to3_fm) + I(PHI_roots*prec2_1to3_fm) + I(PHI_roots*gddHigh_1to3_fm) + I(PHI_roots*dd_1to3_fm) +
I(PHI_roots*gdd_4to10_fm) + I(PHI_roots*gdd2_4to10_fm) + I(PHI_roots*prec_4to10_fm) + I(PHI_roots*prec2_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*gdd2_obs) + I(PHI_corn*prec_obs) + I(PHI_corn*prec2_obs) + I(PHI_corn*gddHigh_obs) + I(PHI_corn*dd_obs) +
I(PHI_corn*gdd_1to3) + I(PHI_corn*gdd2_1to3) + I(PHI_corn*prec_1to3) + I(PHI_corn*prec2_1to3) + I(PHI_corn*gddHigh_1to3) + I(PHI_corn*dd_1to3) +
I(PHI_corn*gdd_4to10) + I(PHI_corn*gdd2_4to10) + I(PHI_corn*prec_4to10) + I(PHI_corn*prec2_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*gdd2_obs_fm) + I(PHI_corn*prec_obs_fm) + I(PHI_corn*prec2_obs_fm) + I(PHI_corn*gddHigh_obs_fm) + I(PHI_corn*dd_obs_fm) +
I(PHI_corn*gdd_1to3_fm) + I(PHI_corn*gdd2_1to3_fm) + I(PHI_corn*prec_1to3_fm) + I(PHI_corn*prec2_1to3_fm) + I(PHI_corn*gddHigh_1to3_fm) + I(PHI_corn*dd_1to3_fm) +
I(PHI_corn*gdd_4to10_fm) + I(PHI_corn*gdd2_4to10_fm) + I(PHI_corn*prec_4to10_fm) + I(PHI_corn*prec2_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 + gdd2_obs + prec_obs + prec2_obs + gddHigh_obs + dd_obs +
gdd_1to3 + gdd2_1to3 + prec_1to3 + prec2_1to3 + gddHigh_1to3 + dd_1to3 +
gdd_4to10 + gdd2_4to10 + prec_4to10 + prec2_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 + gdd2_obs_fm + prec_obs_fm + prec2_obs_fm + gddHigh_obs_fm + dd_obs_fm +
gdd_1to3_fm + gdd2_1to3_fm + prec_1to3_fm + prec2_1to3_fm + gddHigh_1to3_fm + dd_1to3_fm +
gdd_4to10_fm + gdd2_4to10_fm + prec_4to10_fm + prec2_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
# Define system of equations
system <- list( QQcereals = eqQQcereals,
QQprotein = eqQQprotein,
QQoilseed = eqQQoilseed,
QQroots = eqQQroots,
QQcorn = eqQQcorn,
NXfert = eqNXfert)
# Define 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")
#----------------------------------#
#### Step 1: Probit regressions ####
#----------------------------------#
# Obtain data mean for probit-variables (same for all probit regressions)
iCrop <- glm(cereal.eq, family = binomial(link = "probit"),
data = data_boot)
dat_prob <- dplyr::as_tibble(model.matrix(iCrop))
dat_sm_prob <- dat_prob %>%
dplyr::summarise_all(mean)
#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
# Create list where the results will be stored
list_probit_act <- list(Cereals=list(linpred_sm="", PHI="", PHI_sm="", phi="", phi_sm="", probit_me=""),
Protein=list(linpred_sm="", PHI="", PHI_sm="", phi="", phi_sm="", probit_me=""),
Oilseed=list(linpred_sm="", PHI="", PHI_sm="", phi="", phi_sm="", probit_me=""),
Roots= list(linpred_sm="", PHI="", PHI_sm="", phi="", phi_sm="", probit_me=""),
Corn=list(linpred_sm="", PHI="", PHI_sm="", phi="", phi_sm="", probit_me=""))
# 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 = data_boot)
# Linear prediction at the sample mean (=linpred_sm)
list_probit_act[[i]][[1]] <- iCrop_linpred_sm <- crossprod(matrix(iCrop$coefficients),
t(dat_sm_prob))
# PHI at the farm-level
list_probit_act[[i]][[2]] <- pnorm(predict(iCrop)) #note: predict(iCrop) is iCrop_linpred
# PHI at the sample mean
list_probit_act[[i]][[3]] <- pnorm(iCrop_linpred_sm)
# phi at the farm-level
list_probit_act[[i]][[4]] <- dnorm(predict(iCrop)) #note: predict(iCrop) is iCrop_linpred
# phi at the sample mean
list_probit_act[[i]][[5]] <- dnorm(iCrop_linpred_sm)
# Probit coefficients
if (i == 1) {
coef_iCereals <- iCrop$coefficients
} else if (i == 2) {
coef_iProtein <- iCrop$coefficients
} else if (i == 3) {
coef_iOilseed <- iCrop$coefficients
} else if (i == 4) {
coef_iRoots <- iCrop$coefficients
} else if (i == 5) {
coef_iCorn <- iCrop$coefficients
}
# Marginal effects (iCrop_me)
list_probit_act[[i]][[6]] <- dnorm(iCrop_linpred_sm)*coef(iCrop) #note: dnorm(iCrop_linpred_sm) is phi_crop_sm
}
# Restore the results estimated in the loop
# Probit linear prediction at the sample mean (for elasticity evaluation)
iCereals_linpred_sm <- as.numeric(do.call(c, list_probit_act[[1]][1]))
iProtein_linpred_sm <- as.numeric(do.call(c, list_probit_act[[2]][1]))
iOilseed_linpred_sm <- as.numeric(do.call(c, list_probit_act[[3]][1]))
iRoots_linpred_sm <- as.numeric(do.call(c, list_probit_act[[4]][1]))
iCorn_linpred_sm <- as.numeric(do.call(c, list_probit_act[[5]][1]))
# PHIs at the farm-level (for estimation of second stage)
data_boot$PHI_cereals <- as.numeric(do.call(c, list_probit_act[[1]][2]))
data_boot$PHI_protein <- as.numeric(do.call(c, list_probit_act[[2]][2]))
data_boot$PHI_oilseed <- as.numeric(do.call(c, list_probit_act[[3]][2]))
data_boot$PHI_roots <- as.numeric(do.call(c, list_probit_act[[4]][2]))
data_boot$PHI_corn <- as.numeric(do.call(c, list_probit_act[[5]][2]))
# PHIs at the sample mean (for elasticity evaluation)
PHI_cereals_sm <- as.numeric(do.call(c, list_probit_act[[1]][3]))
PHI_protein_sm <- as.numeric(do.call(c, list_probit_act[[2]][3]))
PHI_oilseed_sm <- as.numeric(do.call(c, list_probit_act[[3]][3]))
PHI_roots_sm <- as.numeric(do.call(c, list_probit_act[[4]][3]))
PHI_corn_sm <- as.numeric(do.call(c, list_probit_act[[5]][3]))
# phis at the farm-level (for estimation of second stage)
data_boot$phi_cereals <- as.numeric(do.call(c, list_probit_act[[1]][4]))
data_boot$phi_protein <- as.numeric(do.call(c, list_probit_act[[2]][4]))
data_boot$phi_oilseed <- as.numeric(do.call(c, list_probit_act[[3]][4]))
data_boot$phi_roots <- as.numeric(do.call(c, list_probit_act[[4]][4]))
data_boot$phi_corn <- as.numeric(do.call(c, list_probit_act[[5]][4]))
# phis at the sample mean (for elasticity evaluation)
phi_cereals_sm <- as.numeric(do.call(c, list_probit_act[[1]][5]))
phi_protein_sm <- as.numeric(do.call(c, list_probit_act[[2]][5]))
phi_oilseed_sm <- as.numeric(do.call(c, list_probit_act[[3]][5]))
phi_roots_sm <- as.numeric(do.call(c, list_probit_act[[4]][5]))
phi_corn_sm <- as.numeric(do.call(c, list_probit_act[[5]][5]))
# Probit marginal effects (for results presentation)
iCereals_me <- as.numeric(do.call(c, list_probit_act[[1]][6]))
iProtein_me <- as.numeric(do.call(c, list_probit_act[[2]][6]))
iOilseed_me <- as.numeric(do.call(c, list_probit_act[[3]][6]))
iRoots_me <- as.numeric(do.call(c, list_probit_act[[4]][6]))
iCorn_me <- as.numeric(do.call(c, list_probit_act[[5]][6]))
#----------------------------------------#
#### Step 2: Run Structural equations ####
#----------------------------------------#
## Regression with iterated SUR estimation
model_nonlinear <- systemfit::systemfit( formula = system, method = "SUR",
data = data_boot, restrict.matrix = restrict,
maxit = 100 )
coef_nonlinear <- coef(model_nonlinear)
# "x times \beta" (needed for elasticities)
qx_pred <- predict(model_nonlinear)
qq_cereals_pred_b <- mean(qx_pred$QQcereals.pred) - model_nonlinear$coefficients["QQcereals_phi_cereals"]*mean(data_boot$phi_cereals)
qq_cereals_pred <- (qq_cereals_pred_b) / mean(data_boot$PHI_cereals)
qq_protein_pred_b <- mean(qx_pred$QQprotein.pred) - model_nonlinear$coefficients["QQprotein_phi_protein"]*mean(data_boot$phi_protein)
qq_protein_pred <- (qq_protein_pred_b) / mean(data_boot$PHI_protein)
qq_oilseed_pred_b <- mean(qx_pred$QQoilseed.pred) - model_nonlinear$coefficients["QQoilseed_phi_oilseed"]*mean(data_boot$phi_oilseed)
qq_oilseed_pred <- (qq_oilseed_pred_b) / mean(data_boot$PHI_oilseed)
qq_roots_pred_b <- mean(qx_pred$QQroots.pred) - model_nonlinear$coefficients["QQroots_phi_roots"]*mean(data_boot$phi_roots)
qq_roots_pred <- (qq_roots_pred_b) / mean(data_boot$PHI_roots)
qq_corn_pred_b <- mean(qx_pred$QQcorn.pred) - model_nonlinear$coefficients["QQcorn_phi_corn"]*mean(data_boot$phi_corn)
qq_corn_pred <- (qq_corn_pred_b) / mean(data_boot$PHI_corn)
nx_fert_pred <- mean(qx_pred$NXfert.pred)
# -------------------------------- #
#### Compute price elasticities ####
# ---------------------------------#
#set-up a data frame to store the results
elast_prices <- data.frame("Variables"=c("P Cereals", "P Protein", "P Oilseed", "P Roots", "P Corn", "W Fertilizer", "W Others"),
"Q Cereals"=rep(NA,7),
"Q Protein"=rep(NA,7),
"Q Oilseed"=rep(NA,7),
"Q Roots"=rep(NA,7),
"Q Corn"=rep(NA,7),
"X Fertilizer"=rep(NA,7),
"X Others"=rep(NA,7))
# ------------------------------ #
# Price elasticities for outputs #
# ------------------------------ #
#set-up the loop over crops
list_qcrops <- data.frame(crops=c("cereals","protein","oilseed","roots","corn"),
probit=c("iCereals","iProtein","iOilseed","iRoots","iCorn"),
struct=c("QQcereals","QQprotein", "QQoilseed", "QQroots", "QQcorn"))
n_qcrops <- list_qcrops %>% count() %>% as.numeric() # number of crops
list_prices <- data.frame(prices=c("np_cereals", "np_protein", "np_oilseed", "np_roots", "np_corn", "nw_fert"),
endswith=c("np_cereals)", "np_protein)", "np_oilseed)", "np_roots)", "np_corn)", "nw_fert)"))
n_prices <- list_prices %>% count() %>% as.numeric()
# Loop over all crops
for (i in 1:n_qcrops) {
coefs_struct_crop <- dplyr::as_tibble(t(coef_nonlinear)) %>% select(starts_with(list_qcrops[i,"struct"]))
coefs_probit_crop <- dplyr::as_tibble(t(get(paste0("coef_",list_qcrops[i,"probit"]))))
coef_phi_struct <- coefs_struct_crop %>% select(ends_with(paste0("phi_",list_qcrops[i,"crops"]), ignore.case = FALSE)) # phi_cereals etc.
PHI <- get(paste0("PHI_",list_qcrops[i,"crops"],"_sm"))
phi <- get(paste0("phi_",list_qcrops[i,"crops"],"_sm"))
linpred <- get(paste0(list_qcrops[i,"probit"],"_linpred_sm"))
pred <- get(paste0("qq_",list_qcrops[i,"crops"],"_pred"))
mean_quantity <- dat_sm %>% select(paste0("qq_",list_qcrops[i,"crops"]))
for (j in 1:n_prices) {
coef_probit_p <- coefs_probit_crop %>% select(list_prices[j,"prices"])
coef_struct_p <- coefs_struct_crop %>% select(ends_with(list_prices[j,"endswith"]))
mean_price <- dat_sm %>% select(list_prices[j,"prices"])
elast_prices[j,1+i] <- (PHI * coef_struct_p + phi * pred * coef_probit_p -
coef_phi_struct * linpred * coef_probit_p * phi ) * (mean_price / mean_quantity )
}
# Price elasticity for numeraire adds up to 0
elast_prices[j+1,1+i] <- 0 - elast_prices[1,1+i] - elast_prices[2,1+i] - elast_prices[3,1+i] - elast_prices[4,1+i] - elast_prices[5,1+i] - elast_prices[6,1+i]
}
# ----------------------------- #
# Price elasticities for inputs #
# ----------------------------- #
# Fertilizer demand (note: There is no selection equation for fertilizer --> use regular derivative)
coef_fert <- dplyr::as_tibble(t(coef_nonlinear)) %>% select(starts_with("NXfert"))
for (j in 1:n_prices) {
coef_struct_p <- coef_fert %>% select(ends_with(list_prices[j,"prices"]))
mean_price <- dat_sm %>% select(list_prices[j,"prices"])
elast_prices[j,7] <- coef_struct_p * (mean_price/dat_sm$nx_fert)
}
elast_prices[j+1,7] <- 0 - elast_prices[1,7] - elast_prices[2,7] - elast_prices[3,7] - elast_prices[4,7] - elast_prices[5,7] - elast_prices[6,7]
# Other input demand
list_prices <- data.frame(prices=c("np_cereals", "np_protein", "np_oilseed", "np_roots", "np_corn", "nw_fert"),
endswith=c("np_cereals)", "np_protein)", "np_oilseed)", "np_roots)", "np_corn)", "nw_fert)"),
quantities=c("qq_cereals", "qq_protein", "qq_oilseed", "qq_roots", "qq_corn", "x_fert")) # Note: Here I use x_fert instead of nx_fert so that I do not have to add a negative sign to X.Others_W.Fert
n_prices <- list_prices %>% count() %>% as.numeric()
for (j in 1:n_prices) {
elast_sum <- sum(elast_prices[1:n_prices,j+1]) # sum of all elasticities except for w_others
mean_quantity <- dat_sm %>% select(list_prices[j,"quantities"])
mean_price <- dat_sm %>% select(list_prices[j,"prices"])
elast_prices[j,8] <- (mean_quantity * mean_price) / dat_sm$x_otherinp *
(elast_sum)
}
elast_prices[j+1,8] <- 0 - elast_prices[1,8] - elast_prices[2,8] - elast_prices[3,8] - elast_prices[4,8] - elast_prices[5,8] - elast_prices[6,8]
# ------------------------------------- #
# Store price elasticities in bootstrap #
# --------------------------------------#
#q_cer
el_qcer_pcer <- c('el_qcer_pcer' = as.numeric(elast_prices[1,2]))
el_qcer_pprot <- c('el_qcer_pprot' = as.numeric(elast_prices[2,2]))
el_qcer_poil <- c('el_qcer_poil' = as.numeric(elast_prices[3,2]))
el_qcer_proots <- c('el_qcer_proots' = as.numeric(elast_prices[4,2]))
el_qcer_pcorn <- c('el_qcer_pcorn' = as.numeric(elast_prices[5,2]))
el_qcer_wfert <- c('el_qcer_wfert' = as.numeric(elast_prices[6,2]))
el_qcer_wotherinp <- c('el_qcer_wotherinp' = as.numeric(elast_prices[7,2]))
#q_prot
el_qprot_pcer <- c('el_qprot_pcer' = as.numeric(elast_prices[1,3]))
el_qprot_pprot <- c('el_qprot_pprot' = as.numeric(elast_prices[2,3]))
el_qprot_poil <- c('el_qprot_poil' = as.numeric(elast_prices[3,3]))
el_qprot_proots <- c('el_qprot_proots' = as.numeric(elast_prices[4,3]))
el_qprot_pcorn <- c('el_qprot_pcorn' = as.numeric(elast_prices[5,3]))
el_qprot_wfert <- c('el_qprot_wfert' = as.numeric(elast_prices[6,3]))
el_qprot_wotherinp <- c('el_qprot_wotherinp' = as.numeric(elast_prices[7,3]))
#q_oil
el_qoil_pcer <- c('el_qoil_pcer' = as.numeric(elast_prices[1,4]))
el_qoil_pprot <- c('el_qoil_pprot' = as.numeric(elast_prices[2,4]))
el_qoil_poil <- c('el_qoil_poil' = as.numeric(elast_prices[3,4]))
el_qoil_proots <- c('el_qoil_proots' = as.numeric(elast_prices[4,4]))
el_qoil_pcorn <- c('el_qoil_pcorn' = as.numeric(elast_prices[5,4]))
el_qoil_wfert <- c('el_qoil_wfert' = as.numeric(elast_prices[6,4]))
el_qoil_wotherinp <- c('el_qoil_wotherinp' = as.numeric(elast_prices[7,4]))
#qroots
el_qroots_pcer <- c('el_qroots_pcer' = as.numeric(elast_prices[1,5]))
el_qroots_pprot <- c('el_qroots_pprot' = as.numeric(elast_prices[2,5]))
el_qroots_poil <- c('el_qroots_poil' = as.numeric(elast_prices[3,5]))
el_qroots_proots <- c('el_qroots_proots' = as.numeric(elast_prices[4,5]))
el_qroots_pcorn <- c('el_qroots_pcorn' = as.numeric(elast_prices[5,5]))
el_qroots_wfert <- c('el_qroots_wfert' = as.numeric(elast_prices[6,5]))
el_qroots_wotherinp <- c('el_qroots_wotherinp' = as.numeric(elast_prices[7,5]))
#qcorn
el_qcorn_pcer <- c('el_qcorn_pcer' = as.numeric(elast_prices[1,6]))
el_qcorn_pprot <- c('el_qcorn_pprot' = as.numeric(elast_prices[2,6]))
el_qcorn_poil <- c('el_qcorn_poil' = as.numeric(elast_prices[3,6]))
el_qcorn_proots <- c('el_qcorn_proots' = as.numeric(elast_prices[4,6]))
el_qcorn_pcorn <- c('el_qcorn_pcorn' = as.numeric(elast_prices[5,6]))
el_qcorn_wfert <- c('el_qcorn_wfert' = as.numeric(elast_prices[6,6]))
el_qcorn_wotherinp <- c('el_qcorn_wotherinp' = as.numeric(elast_prices[7,6]))
#xfert
el_xfert_pcer <- c('el_xfert_pcer' = as.numeric(elast_prices[1,7]))
el_xfert_pprot <- c('el_xfert_pprot' = as.numeric(elast_prices[2,7]))
el_xfert_poil <- c('el_xfert_poils' = as.numeric(elast_prices[3,7]))
el_xfert_proots <- c('el_xfert_proots' = as.numeric(elast_prices[4,7]))
el_xfert_pcorn <- c('el_xfert_pcorn' = as.numeric(elast_prices[5,7]))
el_xfert_wfert <- c('el_xfert_wfert' = as.numeric(elast_prices[6,7]))
el_xfert_wotherinp <- c('el_xfert_woth' = as.numeric(elast_prices[7,7]))
#xother
el_xotherinp_pcer <- c('el_xotherinp_pcer' = as.numeric(elast_prices[1,8]))
el_xotherinp_pprot <- c('el_xotherinp_pprot' = as.numeric(elast_prices[2,8]))
el_xotherinp_poil <- c('el_xotherinp_poil' = as.numeric(elast_prices[3,8]))
el_xotherinp_proots <- c('el_xotherinp_proots' = as.numeric(elast_prices[4,8]))
el_xotherinp_pcorn <- c('el_xotherinp_pcorn' = as.numeric(elast_prices[5,8]))
el_xotherinp_wfert <- c('el_xotherinp_wfert' = as.numeric(elast_prices[6,8]))
el_xotherinp_wotherinp <- c('el_xotherinp_wotherinp' = as.numeric(elast_prices[7,8]))
# ---------------------------------- #
#### Compute weather elasticities ####
# ---------------------------------- #
# ------------------------------ #
# Weather elasticities for crops #
# ------------------------------ #
#set-up a data frame to store the results
elast_weather <- data.frame("Variables"=c("GDD_obs", "PREC_obs", "GDDHigh_obs", "DD_obs", "GDD_past", "PREC_past", "GDDHigh_past", "DD_past"),
"Q Cereals"=rep(NA,8),
"Q Protein"=rep(NA,8),
"Q Oilseed"=rep(NA,8),
"Q Roots"=rep(NA,8),
"Q Corn"=rep(NA,8),
"X Fertilizer"=rep(NA,8))
# Weather vars
list_weather <- data.frame(weather_obs= c("gdd_obs","prec_obs","gddHigh_obs","dd_obs"),
weather2_obs = c("gdd2_obs", "prec2_obs", NA, NA),
weather_1to3= c("gdd_1to3","prec_1to3","gddHigh_1to3","dd_1to3"),
weather2_1to3 = c("gdd2_1to3", "prec2_1to3", NA, NA),
weather_4to10=c("gdd_4to10","prec_4to10","gddHigh_4to10","dd_4to10"),
weather2_4to10 = c("gdd2_4to10", "prec2_4to10", NA, NA),
weather_obs_1to3 = c("gdd_obs_1to3","prec_obs_1to3","gddHigh_obs_1to3","dd_obs_1to3"),
weather_obs_4to10 = c("gdd_obs_4to10","prec_obs_4to10","gddHigh_obs_4to10","dd_obs_4to10"),
weather_obs_endwith= c("* gdd_obs)","* prec_obs)","* gddHigh_obs)","* dd_obs)"),
weather2_obs_endwith = c("* gdd2_obs)", "* prec2_obs)", NA, NA),
weather_1to3_endwith= c("* gdd_1to3)","* prec_1to3)","* gddHigh_1to3)","* dd_1to3)"),
weather2_1to3_endwith = c("* gdd2_1to3)", "* prec2_1to3)", NA, NA),
weather_4to10_endwith=c("* gdd_4to10)","* prec_4to10)","* gddHigh_4to10)","* dd_4to10)"),
weather2_4to10_endwith = c("* gdd2_4to10)", "* prec2_4to10)", NA, NA),
weather_obs_1to3_endwith = c("* gdd_obs_1to3)","* prec_obs_1to3)","* gddHigh_obs_1to3)","* dd_obs_1to3)"),
weather_obs_4to10_endwith = c("* gdd_obs_4to10)","* prec_obs_4to10)","* gddHigh_obs_4to10)","* dd_obs_4to10)"))
n_weather <- list_weather %>% count() %>% as.numeric()
# Loop over all crops
for (i in 1:n_qcrops) {
coefs_struct_crop <- dplyr::as_tibble(t(coef_nonlinear)) %>% select(starts_with(list_qcrops[i,"struct"]))
coefs_probit_crop <- dplyr::as_tibble(t(get(paste0("coef_",list_qcrops[i,"probit"]))))
coef_phi_struct <- coefs_struct_crop %>% select(ends_with(paste0("phi_",list_qcrops[i,"crops"]), ignore.case = FALSE)) # phi_cereals etc.
PHI <- get(paste0("PHI_",list_qcrops[i,"crops"],"_sm"))
phi <- get(paste0("phi_",list_qcrops[i,"crops"],"_sm"))
linpred <- get(paste0(list_qcrops[i,"probit"],"_linpred_sm"))
pred <- get(paste0("qq_",list_qcrops[i,"crops"],"_pred"))
mean_quantity <- dat_sm %>% select(paste0("qq_",list_qcrops[i,"crops"]))
# Loop over all weather variables
for (j in 1:n_weather) {
# Weather-squared terms
coef_probit_weather2_1to3 <- as.numeric(ifelse(j<3,coefs_probit_crop %>% select(list_weather[j,"weather2_1to3"]),0)) #squared terms only for gdd and prec
coef_probit_weather2_4to10 <- as.numeric(ifelse(j<3,coefs_probit_crop %>% select(list_weather[j,"weather2_4to10"]),0))
coef_struct_weather2_obs <- as.numeric(ifelse(j<3,coefs_struct_crop %>% select(ends_with(list_weather[j,"weather2_obs_endwith"])),0)) #squared terms only for gdd and prec
coef_struct_weather2_1to3 <- as.numeric(ifelse(j<3,coefs_struct_crop %>% select(ends_with(list_weather[j,"weather2_1to3_endwith"])),0))
coef_struct_weather2_4to10 <- as.numeric(ifelse(j<3,coefs_struct_crop %>% select(ends_with(list_weather[j,"weather2_4to10_endwith"])),0))
# Weather-interaction terms
coef_struct_weather_obs_1to3 <- coefs_struct_crop %>% select(ends_with(list_weather[j,"weather_obs_1to3_endwith"]))
coef_struct_weather_obs_4to10 <- coefs_struct_crop %>% select(ends_with(list_weather[j,"weather_obs_4to10_endwith"]))
# Mean weather for derivatives
mean_weather_obs <- dat_sm %>% select(list_weather[j,"weather_obs"])
mean_weather_1to3 <- dat_sm %>% select(list_weather[j,"weather_1to3"])
mean_weather_4to10 <- dat_sm %>% select(list_weather[j,"weather_4to10"])
# Observed weather (note: observed weather only affects structural equations, not crop selection; also note that PHI_* is treated like a constant term )
coef_struct_weather <- coefs_struct_crop %>% select(ends_with(list_weather[j,"weather_obs_endwith"]))
elast_weather[j,i+1] <- PHI * (coef_struct_weather + coef_struct_weather_obs_1to3*mean_weather_1to3 + coef_struct_weather_obs_4to10*mean_weather_4to10 + 2*coef_struct_weather2_obs*mean_weather_obs) * (1/mean_quantity)
# Weather_1to3
coef_probit_weather <- coefs_probit_crop %>% select(list_weather[j,"weather_1to3"])
coef_struct_weather <- coefs_struct_crop %>% select(ends_with(list_weather[j,"weather_1to3_endwith"]))
elast_weather_1to3 <- (PHI * (coef_struct_weather + coef_struct_weather_obs_1to3*mean_weather_obs + 2*coef_struct_weather2_1to3*mean_weather_1to3) + phi * pred *
(coef_probit_weather + 2*coef_probit_weather2_1to3*mean_weather_1to3) -
coef_phi_struct * linpred * (coef_probit_weather + 2*coef_probit_weather2_1to3*mean_weather_1to3) * phi) * (1 / mean_quantity )
# Weather_4to10
coef_probit_weather <- coefs_probit_crop %>% select(list_weather[j,"weather_4to10"])
coef_struct_weather <- coefs_struct_crop %>% select(ends_with(list_weather[j,"weather_4to10_endwith"]))
elast_weather_4to10 <- (PHI * (coef_struct_weather + coef_struct_weather_obs_4to10*mean_weather_obs + 2*coef_struct_weather2_4to10*mean_weather_4to10) + phi * pred *
(coef_probit_weather + 2*coef_probit_weather2_4to10*mean_weather_4to10) -
coef_phi_struct * linpred * (coef_probit_weather + 2*coef_probit_weather2_4to10*mean_weather_4to10) * phi) * (1 / mean_quantity )
# Weather_past
elast_weather[j+4,i+1] <- elast_weather_1to3 + elast_weather_4to10
}
}
# ----------------------------------- #
# Weather elasticities for fertilizer #
# ----------------------------------- #
# Weather vars
list_weather <- data.frame(weather_obs= c("gdd_obs","prec_obs","gddHigh_obs","dd_obs"),
weather2_obs = c("gdd2_obs", "prec2_obs", NA, NA),
weather_1to3= c("gdd_1to3","prec_1to3","gddHigh_1to3","dd_1to3"),
weather2_1to3 = c("gdd2_1to3", "prec2_1to3", NA, NA),
weather_4to10=c("gdd_4to10","prec_4to10","gddHigh_4to10","dd_4to10"),
weather2_4to10 = c("gdd2_4to10", "prec2_4to10", NA, NA),
weather_obs_1to3 = c("gdd_obs_1to3","prec_obs_1to3","gddHigh_obs_1to3","dd_obs_1to3"),
weather_obs_4to10 = c("gdd_obs_4to10","prec_obs_4to10","gddHigh_obs_4to10","dd_obs_4to10"),
weather_obs_endwith= c("_gdd_obs","_prec_obs","_gddHigh_obs","_dd_obs"),
weather2_obs_endwith = c("_gdd2_obs", "_prec2_obs", NA, NA),
weather_1to3_endwith= c("_gdd_1to3","_prec_1to3","_gddHigh_1to3","_dd_1to3"),
weather2_1to3_endwith = c("_gdd2_1to3", "_prec2_1to3", NA, NA),
weather_4to10_endwith=c("_gdd_4to10","_prec_4to10","_gddHigh_4to10","_dd_4to10"),
weather2_4to10_endwith = c("_gdd2_4to10", "_prec2_4to10", NA, NA),
weather_obs_1to3_endwith = c("_gdd_obs_1to3","_prec_obs_1to3","_gddHigh_obs_1to3","_dd_obs_1to3"),
weather_obs_4to10_endwith = c("_gdd_obs_4to10","_prec_obs_4to10","_gddHigh_obs_4to10","_dd_obs_4to10"))
n_weather <- list_weather %>% count() %>% as.numeric()
coefs_fert <- dplyr::as_tibble(t(coef_nonlinear)) %>% select(starts_with("NXfert"))
# Loop over all weather variables
for (j in 1:n_weather) {
# Weather-squared terms
coef_fert_weather2_obs <- as.numeric(ifelse(j<3,coefs_fert %>% select(ends_with(list_weather[j,"weather2_obs_endwith"])),0)) #squared terms only for gdd and prec
coef_fert_weather2_1to3 <- as.numeric(ifelse(j<3,coefs_fert %>% select(ends_with(list_weather[j,"weather2_1to3_endwith"])),0))
coef_fert_weather2_4to10 <- as.numeric(ifelse(j<3,coefs_fert %>% select(ends_with(list_weather[j,"weather2_4to10_endwith"])),0))
# Weather-interaction terms
coef_fert_weather_obs_1to3 <- coefs_fert %>% select(ends_with(list_weather[j,"weather_obs_1to3_endwith"]))
coef_fert_weather_obs_4to10 <- coefs_fert %>% select(ends_with(list_weather[j,"weather_obs_4to10_endwith"]))
# Mean weather for derivatives
mean_weather_obs <- dat_sm %>% select(list_weather[j,"weather_obs"])
mean_weather_1to3 <- dat_sm %>% select(list_weather[j,"weather_1to3"])
mean_weather_4to10 <- dat_sm %>% select(list_weather[j,"weather_4to10"])
# Observed weather (note: observed weather only affects structural equations, not crop selection; also note that PHI_* is treated like a constant term )
coef_fert_weather <- coefs_fert %>% select(ends_with(list_weather[j,"weather_obs_endwith"]))
elast_weather[j,7] <- (coef_fert_weather + coef_fert_weather_obs_1to3*mean_weather_1to3 + coef_fert_weather_obs_4to10*mean_weather_4to10 + 2*coef_fert_weather2_obs*mean_weather_obs) * (1/dat_sm$nx_fert)
# Weather_1to3
coef_fert_weather <- coefs_fert %>% select(ends_with(list_weather[j,"weather_1to3_endwith"]))
elast_weather_1to3 <- (coef_fert_weather + coef_fert_weather_obs_1to3*mean_weather_obs + 2*coef_fert_weather2_1to3*mean_weather_1to3) * (1/dat_sm$nx_fert)
# Weather_4to10
coef_fert_weather <- coefs_fert %>% select(ends_with(list_weather[j,"weather_4to10_endwith"]))
elast_weather_4to10 <- (coef_fert_weather + coef_fert_weather_obs_4to10*mean_weather_obs + 2*coef_fert_weather2_4to10*mean_weather_4to10) * (1/dat_sm$nx_fert)
# Weather_past
elast_weather[j+4,7] <- elast_weather_1to3 + elast_weather_4to10
}
# --------------------------------------- #
# Store weather elasticities in bootstrap #
# ----------------------------------------#
# Rescale results to obtain the units days, mm, days, days
elast_weather[,2:7] <- elast_weather[,2:7]*100
#qcer
# obs
sel_qcer_gdd_obs <- c('sel_qcer_gdd_obs' = as.numeric(elast_weather[1,2]))
sel_qcer_prec_obs <- c('sel_qcer_prec_obs' = as.numeric(elast_weather[2,2]))
sel_qcer_gddHigh_obs <- c('sel_qcer_gddHigh_obs' = as.numeric(elast_weather[3,2]))
sel_qcer_dd_obs <- c('sel_qcer_dd_obs' = as.numeric(elast_weather[4,2]))
#past
sel_qcer_gdd_past <- c('sel_qcer_gdd_past' = as.numeric(elast_weather[5,2]))
sel_qcer_prec_past <- c('sel_qcer_prec_past' = as.numeric(elast_weather[6,2]))
sel_qcer_gddHigh_past <- c('sel_qcer_gddHigh_past' = as.numeric(elast_weather[7,2]))
sel_qcer_dd_past <- c('sel_qcer_dd_past' = as.numeric(elast_weather[8,2]))
#qprot
# obs
sel_qprot_gdd_obs <- c('sel_qprot_gdd_obs' = as.numeric(elast_weather[1,3]))
sel_qprot_prec_obs <- c('sel_qprot_prec_obs' = as.numeric(elast_weather[2,3]))
sel_qprot_gddHigh_obs <- c('sel_qprot_gddHigh_obs' = as.numeric(elast_weather[3,3]))
sel_qprot_dd_obs <- c('sel_qprot_dd_obs' = as.numeric(elast_weather[4,3]))
#past
sel_qprot_gdd_past <- c('sel_qprot_gdd_past' = as.numeric(elast_weather[5,3]))
sel_qprot_prec_past <- c('sel_qprot_prec_past' = as.numeric(elast_weather[6,3]))
sel_qprot_gddHigh_past <- c('sel_qprot_gddHigh_past' = as.numeric(elast_weather[7,3]))
sel_qprot_dd_past <- c('sel_qprot_dd_past' = as.numeric(elast_weather[8,3]))
#qoil
# obs
sel_qoil_gdd_obs <- c('sel_qoil_gdd_obs' = as.numeric(elast_weather[1,4]))
sel_qoil_prec_obs <- c('sel_qoil_prec_obs' = as.numeric(elast_weather[2,4]))
sel_qoil_gddHigh_obs <- c('sel_qoil_gddHigh_obs' = as.numeric(elast_weather[3,4]))
sel_qoil_dd_obs <- c('sel_qoil_dd_obs' = as.numeric(elast_weather[4,4]))
#past
sel_qoil_gdd_past <- c('sel_qoil_gdd_past' = as.numeric(elast_weather[5,4]))
sel_qoil_prec_past <- c('sel_qoil_prec_past' = as.numeric(elast_weather[6,4]))
sel_qoil_gddHigh_past <- c('sel_qoil_gddHigh_past' = as.numeric(elast_weather[7,4]))
sel_qoil_dd_past <- c('sel_qoil_dd_past' = as.numeric(elast_weather[8,4]))
#qroots
# obs
sel_qroots_gdd_obs <- c('sel_qroots_gdd_obs' = as.numeric(elast_weather[1,5]))
sel_qroots_prec_obs <- c('sel_qroots_prec_obs' = as.numeric(elast_weather[2,5]))
sel_qroots_gddHigh_obs <- c('sel_qroots_gddHigh_obs' = as.numeric(elast_weather[3,5]))
sel_qroots_dd_obs <- c('sel_qroots_dd_obs' = as.numeric(elast_weather[4,5]))
#past
sel_qroots_gdd_past <- c('sel_qroots_gdd_past' = as.numeric(elast_weather[5,5]))
sel_qroots_prec_past <- c('sel_qroots_prec_past' = as.numeric(elast_weather[6,5]))
sel_qroots_gddHigh_past <- c('sel_qroots_gddHigh_past' = as.numeric(elast_weather[7,5]))
sel_qroots_dd_past <- c('sel_qroots_dd_past' = as.numeric(elast_weather[8,5]))
#corn
# obs
sel_qcorn_gdd_obs <- c('sel_qcorn_gdd_obs' = as.numeric(elast_weather[1,6]))
sel_qcorn_prec_obs <- c('sel_qcorn_prec_obs' = as.numeric(elast_weather[2,6]))
sel_qcorn_gddHigh_obs <- c('sel_qcorn_gddHigh_obs' = as.numeric(elast_weather[3,6]))
sel_qcorn_dd_obs <- c('sel_qcorn_dd_obs' = as.numeric(elast_weather[4,6]))
#past
sel_qcorn_gdd_past <- c('sel_qcorn_gdd_past' = as.numeric(elast_weather[5,6]))
sel_qcorn_prec_past <- c('sel_qcorn_prec_past' = as.numeric(elast_weather[6,6]))
sel_qcorn_gddHigh_past <- c('sel_qcorn_gddHigh_past' = as.numeric(elast_weather[7,6]))
sel_qcorn_dd_past <- c('sel_qcorn_dd_past' = as.numeric(elast_weather[8,6]))
#xfert
# obs
sel_xfert_gdd_obs <- c('sel_xfert_gdd_obs' = as.numeric(elast_weather[1,7]))
sel_xfert_prec_obs <- c('sel_xfert_prec_obs' = as.numeric(elast_weather[2,7]))
sel_xfert_gddHigh_obs <- c('sel_xfert_gddHigh_obs' = as.numeric(elast_weather[3,7]))
sel_xfert_dd_obs <- c('sel_xfert_dd_obs' = as.numeric(elast_weather[4,7]))
#past
sel_xfert_gdd_past <- c('sel_xfert_gdd_past' = as.numeric(elast_weather[5,7]))
sel_xfert_prec_past <- c('sel_xfert_prec_past' = as.numeric(elast_weather[6,7]))
sel_xfert_gddHigh_past <- c('sel_xfert_gddHigh_past' = as.numeric(elast_weather[7,7]))
sel_xfert_dd_past <- c('sel_xfert_dd_past' = as.numeric(elast_weather[8,7]))
# ------------------------------- #
#### Store results of interest ####
# ------------------------------- #
result <- c(coef_iCereals, # Probit coefficients
coef_iProtein,
coef_iOilseed,
coef_iRoots,
coef_iCorn,
iCereals_me, # Probit marginal effects
iProtein_me,
iOilseed_me,
iRoots_me,
iCorn_me,
model_nonlinear$coefficients, #structural coefficients
el_qcer_pcer, #price elasticities
el_qcer_pprot,
el_qcer_poil,
el_qcer_proots,
el_qcer_pcorn,
el_qcer_wfert,
el_qcer_wotherinp,
el_qprot_pcer,
el_qprot_pprot,
el_qprot_poil,
el_qprot_proots,
el_qprot_pcorn,
el_qprot_wfert,
el_qprot_wotherinp,
el_qoil_pcer,
el_qoil_pprot,
el_qoil_poil,
el_qoil_proots,
el_qoil_pcorn,
el_qoil_wfert,
el_qoil_wotherinp,
el_qroots_pcer,
el_qroots_pprot,
el_qroots_poil,
el_qroots_proots,
el_qroots_pcorn,
el_qroots_wfert,
el_qroots_wotherinp,
el_qcorn_pcer,
el_qcorn_pprot,
el_qcorn_poil,
el_qcorn_proots,
el_qcorn_pcorn,
el_qcorn_wfert,
el_qcorn_wotherinp,
el_xfert_pcer,
el_xfert_pprot,
el_xfert_poil,
el_xfert_proots,
el_xfert_pcorn,
el_xfert_wfert,
el_xfert_wotherinp,
el_xotherinp_pcer,
el_xotherinp_pprot,
el_xotherinp_poil,
el_xotherinp_proots,
el_xotherinp_pcorn,
el_xotherinp_wfert,
el_xotherinp_wotherinp,
sel_qcer_gdd_obs, #weather elasticities
sel_qcer_prec_obs,
sel_qcer_gddHigh_obs,
sel_qcer_dd_obs,
sel_qprot_gdd_obs,
sel_qprot_prec_obs,
sel_qprot_gddHigh_obs,
sel_qprot_dd_obs,
sel_qoil_gdd_obs,
sel_qoil_prec_obs,
sel_qoil_gddHigh_obs,
sel_qoil_dd_obs,
sel_qroots_gdd_obs,
sel_qroots_prec_obs,
sel_qroots_gddHigh_obs,
sel_qroots_dd_obs,
sel_qcorn_gdd_obs,
sel_qcorn_prec_obs,
sel_qcorn_gddHigh_obs,
sel_qcorn_dd_obs,
sel_xfert_gdd_obs,
sel_xfert_prec_obs,
sel_xfert_gddHigh_obs,
sel_xfert_dd_obs,
sel_qcer_gdd_past,
sel_qcer_prec_past,
sel_qcer_gddHigh_past,
sel_qcer_dd_past,
sel_qprot_gdd_past,
sel_qprot_prec_past,
sel_qprot_gddHigh_past,
sel_qprot_dd_past,
sel_qoil_gdd_past,
sel_qoil_prec_past,
sel_qoil_gddHigh_past,
sel_qoil_dd_past,
sel_qroots_gdd_past,
sel_qroots_prec_past,
sel_qroots_gddHigh_past,
sel_qroots_dd_past,
sel_qcorn_gdd_past,
sel_qcorn_prec_past,
sel_qcorn_gddHigh_past,
sel_qcorn_dd_past,
sel_xfert_gdd_past,
sel_xfert_prec_past,
sel_xfert_gddHigh_past,
sel_xfert_dd_past)
result
}, error=function(err) {rep(NA,1102)} ) # insert NA's if there is an optimization error
}
}
#-------------------------------------------#
#### Obtain and store the actual results ####
#-------------------------------------------#
# run one draw with the original data
system.time(boot_actresults <- my.boot(data=df_farm, nrep=1, cluster=df_farm$key, nCores=1, actual=TRUE))
# save actual result
save(boot_actresults, file="rOutput/bootresults_nonlinear_actual.Rda")
boot_actresults <- NULL
#------------------------------------------------#
#### Run bootstrap: Cluster at the farm-level ####
#------------------------------------------------#
# find number of cores
nCores <- parallel::detectCores() -1
# run the bootstrap
set.seed(1234)
system.time(boot_results <- my.boot(data=df_farm, nrep=1000, cluster=df_farm$key, nCores=nCores, actual=FALSE))
# save
save(boot_results, file="rOutput/bootresults_nonlinear.Rda")
boot_results <- NULL
#----------------------------------#
#### 2) Presentation of results ####
#----------------------------------#
load("rOutput/bootresults_nonlinear.Rda")
load("rOutput/bootresults_nonlinear_actual.Rda")
# Turn matrix into data frame
boot_results <- as.data.frame(boot_results)
summary(boot_results$sel_qcer_gdd_obs)
# --------------------------------- #
# Create list with original results #
# --------------------------------- #
names(boot_results)
boot_summary <- data.frame("Variable"=c(names(boot_results)),
"Original"=boot_actresults)
# ------------------------ #
# Add confidence intervals #
# ------------------------ #
# Confidence intervals
CIs <- t(sapply(boot_results,function(i) quantile(i,c(0.025, 0.975), na.rm=TRUE)))
CIs <- as.data.frame(CIs)
colnames(CIs) <- c("L95","U95")
# Add CIs to boot_summary
boot_summary <- cbind(boot_summary, CIs)
# Organize
coef_iCereals <- boot_summary[c(1:55),]
coef_iProtein <- boot_summary[c(56:110),]
coef_iOilseed <- boot_summary[c(111:165),]
coef_iRoots <- boot_summary[c(166:220),]
coef_iCorn <- boot_summary[c(221:275),]
iCereals_me <- boot_summary[c(276:330),]
iProtein_me <- boot_summary[c(331:385),]
iOilseed_me <- boot_summary[c(386:440),]
iRoots_me <- boot_summary[c(441:495),]
iCorn_me <- boot_summary[c(496:550),]
qqCereals <- boot_summary[(startsWith(x = boot_summary$Variable, prefix = "QQcereals_")),]
qqProtein <- boot_summary[(startsWith(x = boot_summary$Variable, prefix = "QQprotein_")),]
qqOilseed <- boot_summary[(startsWith(x = boot_summary$Variable, prefix = "QQoilseed_")),]
qqRoots <- boot_summary[(startsWith(x = boot_summary$Variable, prefix = "QQroots_")),]
qqCorn <- boot_summary[(startsWith(x = boot_summary$Variable, prefix = "QQcorn_")),]
nxFert <- boot_summary[(startsWith(x = boot_summary$Variable, prefix = "NXfert_")),]
PriceElast_cereals <- boot_summary[(startsWith(x = boot_summary$Variable, prefix = "el_qcer_")),]
PriceElast_protein <- boot_summary[(startsWith(x = boot_summary$Variable, prefix = "el_qprot_")),]
PriceElast_oilseed <- boot_summary[(startsWith(x = boot_summary$Variable, prefix = "el_qoil_")),]
PriceElast_roots <- boot_summary[(startsWith(x = boot_summary$Variable, prefix = "el_qroots_")),]
PriceElast_corn <- boot_summary[(startsWith(x = boot_summary$Variable, prefix = "el_qcorn_")),]