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11a_EstSim_restricted.R
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11a_EstSim_restricted.R
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#-------------------------------------------------------#
# #
# This program estimates first- and second-stage #
# regressions and simulates the outcomes for the #
# 2018-drought, for the model with curvature imposed. #
# #
# Note: The farm-level data are confidential and cannot #
# be loaded (line 17). The results at the sample mean #
# are saved in line 1234 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_1030, df_weather_2018$gdd_1030, rep(df_weather_lta$gdd_1030,10))
sim2018$prec_obs <- c(df_weather_lta$prec, df_weather_2018$prec, rep(df_weather_lta$prec,10))
sim2018$gddHigh_obs <- c(df_weather_lta$gdd_30, df_weather_2018$gdd_30, rep(df_weather_lta$gdd_30,10))
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
#-------------------------------------------------#
# Estimate and store probit results for all crops #
#-------------------------------------------------#
#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 #####
#--------------------------------------#
#De-mean the data so the regression can converge
vars <- c("qq_cereals", "qq_protein", "qq_oilseed", "qq_roots", "qq_corn", "x_fert", "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",
"PHI_cereals", "phi_cereals", "PHI_protein", "phi_protein", "PHI_oilseed", "phi_oilseed", "PHI_roots", "phi_roots", "PHI_corn", "phi_corn")
temp_fn <- function(x) x/mean(x)
df_farm_dem <- df_farm %>% mutate(across(vars, temp_fn))
#Define structural equations
eqns <-
list(qq_cereals ~ (b1*PHI_cereals +
(c11*c11)*np_cereals*PHI_cereals +
(c11*c12)*np_protein*PHI_cereals +
(c11*c13)*np_oilseed*PHI_cereals +
(c11*c14)*np_roots*PHI_cereals +
(c11*c15)*np_corn*PHI_cereals +
(c11*c16)*nw_fert*PHI_cereals +
k11*k_land*PHI_cereals +
k12*k_labor*PHI_cereals +
k13*k_capital*PHI_cereals +
t1*trend*PHI_cereals +
tsq1*trend2*PHI_cereals +
w11*gdd_obs*PHI_cereals +
w12*prec_obs*PHI_cereals +
w13*gddHigh_obs*PHI_cereals +
w14*dd_obs*PHI_cereals +
w15*gdd_1to3*PHI_cereals +
w16*prec_1to3*PHI_cereals +
w17*gddHigh_1to3*PHI_cereals +
w18*dd_1to3*PHI_cereals +
w19*gdd_4to10*PHI_cereals +
w110*prec_4to10*PHI_cereals +
w111*gddHigh_4to10*PHI_cereals +
w112*dd_4to10*PHI_cereals +
m11*np_cereals_fm*PHI_cereals +
m12*np_protein_fm*PHI_cereals +
m13*np_oilseed_fm*PHI_cereals +
m14*np_roots_fm*PHI_cereals +
m15*np_corn_fm*PHI_cereals +
m16*nw_fert_fm*PHI_cereals +
m17*k_land_fm*PHI_cereals +
m18*k_labor_fm*PHI_cereals +
m19*k_capital_fm*PHI_cereals +
t1_fm*trend_fm*PHI_cereals +
tsq1_fm*trend2_fm*PHI_cereals +
w11_fm*gdd_obs_fm*PHI_cereals +
w12_fm*prec_obs_fm*PHI_cereals +
w13_fm*gddHigh_obs_fm*PHI_cereals +
w14_fm*dd_obs_fm*PHI_cereals +
w15_fm*gdd_1to3_fm*PHI_cereals +
w16_fm*prec_1to3_fm*PHI_cereals +
w17_fm*gddHigh_1to3_fm*PHI_cereals +
w18_fm*dd_1to3_fm*PHI_cereals +
w19_fm*gdd_4to10_fm*PHI_cereals +
w110_fm*prec_4to10_fm*PHI_cereals +
w111_fm*gddHigh_4to10_fm*PHI_cereals +
w112_fm*dd_4to10_fm*PHI_cereals) +
phi11*phi_cereals,
qq_protein ~ (b2*PHI_protein +
(c12*c11)*np_cereals*PHI_protein +
(c12*c12+c22*c22)*np_protein*PHI_protein +
(c12*c13+c22*c23)*np_oilseed*PHI_protein +
(c12*c14+c22*c24)*np_roots*PHI_protein +
(c12*c15+c22*c25)*np_corn*PHI_protein +
(c12*c16+c22*c26)*nw_fert*PHI_protein +
k21*k_land*PHI_protein +
k22*k_labor*PHI_protein +
k23*k_capital*PHI_protein +
t2*trend*PHI_protein +
tsq2*trend2*PHI_protein +
w21*gdd_obs*PHI_protein +
w22*prec_obs*PHI_protein +
w23*gddHigh_obs*PHI_protein +
w24*dd_obs*PHI_protein +
w25*gdd_1to3*PHI_protein +
w26*prec_1to3*PHI_protein +
w27*gddHigh_1to3*PHI_protein +
w28*dd_1to3*PHI_protein +
w29*gdd_4to10*PHI_protein +
w210*prec_4to10*PHI_protein +
w211*gddHigh_4to10*PHI_protein +
w212*dd_4to10*PHI_protein +
m21*np_cereals_fm*PHI_protein +
m22*np_protein_fm*PHI_protein +
m23*np_oilseed_fm*PHI_protein +
m24*np_roots_fm*PHI_protein +
m25*np_corn_fm*PHI_protein +
m26*nw_fert_fm*PHI_protein +
m27*k_land_fm*PHI_protein +
m28*k_labor_fm*PHI_protein +
m29*k_capital_fm*PHI_protein +
t2_fm*trend_fm*PHI_protein +
tsq2_fm*trend2_fm*PHI_protein +
w21_fm*gdd_obs_fm*PHI_protein +
w22_fm*prec_obs_fm*PHI_protein +
w23_fm*gddHigh_obs_fm*PHI_protein +
w24_fm*dd_obs_fm*PHI_protein +
w25_fm*gdd_1to3_fm*PHI_protein +
w26_fm*prec_1to3_fm*PHI_protein +
w27_fm*gddHigh_1to3_fm*PHI_protein +
w28_fm*dd_1to3_fm*PHI_protein +
w29_fm*gdd_4to10_fm*PHI_protein +
w210_fm*prec_4to10_fm*PHI_protein +
w211_fm*gddHigh_4to10_fm*PHI_protein +
w212_fm*dd_4to10_fm*PHI_protein) +
phi22*phi_protein,
qq_oilseed ~ (b3*PHI_oilseed +
(c13*c11)*np_cereals*PHI_oilseed +
(c13*c12+c23*c22)*np_protein*PHI_oilseed +
(c13*c13+c23*c23+c33*c33)*np_oilseed*PHI_oilseed +
(c13*c14+c23*c24+c33*c34)*np_roots*PHI_oilseed +
(c13*c15+c23*c25+c33*c35)*np_corn*PHI_oilseed +
(c13*c16+c23*c26+c33*c36)*nw_fert*PHI_oilseed +
k31*k_land*PHI_oilseed +
k32*k_labor*PHI_oilseed +
k33*k_capital*PHI_oilseed +
t3*trend*PHI_oilseed +
tsq3*trend2*PHI_oilseed +
w31*gdd_obs*PHI_oilseed +
w32*prec_obs*PHI_oilseed +
w33*gddHigh_obs*PHI_oilseed +
w34*dd_obs*PHI_oilseed +
w35*gdd_1to3*PHI_oilseed +
w36*prec_1to3*PHI_oilseed +
w37*gddHigh_1to3*PHI_oilseed +
w38*dd_1to3*PHI_oilseed +
w39*gdd_4to10*PHI_oilseed +
w310*prec_4to10*PHI_oilseed +
w311*gddHigh_4to10*PHI_oilseed +
w312*dd_4to10*PHI_oilseed +
m31*np_cereals_fm*PHI_oilseed +
m32*np_protein_fm*PHI_oilseed +
m33*np_oilseed_fm*PHI_oilseed +
m34*np_roots_fm*PHI_oilseed +
m35*np_corn_fm*PHI_oilseed +
m36*nw_fert_fm*PHI_oilseed +
m37*k_land_fm*PHI_oilseed +
m38*k_labor_fm*PHI_oilseed +
m39*k_capital_fm*PHI_oilseed +
t3_fm*trend_fm*PHI_oilseed +
tsq3_fm*trend2_fm*PHI_oilseed +
w31_fm*gdd_obs_fm*PHI_oilseed +
w32_fm*prec_obs_fm*PHI_oilseed +
w33_fm*gddHigh_obs_fm*PHI_oilseed +
w34_fm*dd_obs_fm*PHI_oilseed +
w35_fm*gdd_1to3_fm*PHI_oilseed +
w36_fm*prec_1to3_fm*PHI_oilseed +
w37_fm*gddHigh_1to3_fm*PHI_oilseed +
w38_fm*dd_1to3_fm*PHI_oilseed +
w39_fm*gdd_4to10_fm*PHI_oilseed +
w310_fm*prec_4to10_fm*PHI_oilseed +
w311_fm*gddHigh_4to10_fm*PHI_oilseed +
w312_fm*dd_4to10_fm*PHI_oilseed) +
phi33*phi_oilseed,
qq_roots ~ (b4*PHI_roots +
(c14*c11)*np_cereals*PHI_roots +
(c14*c12+c24*c22)*np_protein*PHI_roots +
(c14*c13+c24*c23+c34*c33)*np_oilseed*PHI_roots +
(c14*c14+c24*c24+c34*c34+c44*c44)*np_roots*PHI_roots +
(c14*c15+c24*c25+c34*c35+c44*c45)*np_corn*PHI_roots +
(c14*c16+c24*c26+c34*c36+c44*c46)*nw_fert*PHI_roots +
k41*k_land*PHI_roots +
k42*k_labor*PHI_roots +
k43*k_capital*PHI_roots +
t4*trend*PHI_roots +
tsq4*trend2*PHI_roots +
w41*gdd_obs*PHI_roots +
w42*prec_obs*PHI_roots +
w43*gddHigh_obs*PHI_roots +
w44*dd_obs*PHI_roots +
w45*gdd_1to3*PHI_roots +
w46*prec_1to3*PHI_roots +
w47*gddHigh_1to3*PHI_roots +
w48*dd_1to3*PHI_roots +
w49*gdd_4to10*PHI_roots +
w410*prec_4to10*PHI_roots +
w411*gddHigh_4to10*PHI_roots +
w412*dd_4to10*PHI_roots +
m41*np_cereals_fm*PHI_roots +
m42*np_protein_fm*PHI_roots +
m43*np_oilseed_fm*PHI_roots +
m44*np_roots_fm*PHI_roots +
m45*np_corn_fm*PHI_roots +
m46*nw_fert_fm*PHI_roots +
m47*k_land_fm*PHI_roots +
m48*k_labor_fm*PHI_roots +
m49*k_capital_fm*PHI_roots +
t4_fm*trend_fm*PHI_roots +
tsq4_fm*trend2_fm*PHI_roots +
w41_fm*gdd_obs_fm*PHI_roots +
w42_fm*prec_obs_fm*PHI_roots +
w43_fm*gddHigh_obs_fm*PHI_roots +
w44_fm*dd_obs_fm*PHI_roots +
w45_fm*gdd_1to3_fm*PHI_roots +
w46_fm*prec_1to3_fm*PHI_roots +
w47_fm*gddHigh_1to3_fm*PHI_roots +
w48_fm*dd_1to3_fm*PHI_roots +
w49_fm*gdd_4to10_fm*PHI_roots +
w410_fm*prec_4to10_fm*PHI_roots +
w411_fm*gddHigh_4to10_fm*PHI_roots +
w412_fm*dd_4to10_fm*PHI_roots) +
phi44*phi_roots,
qq_corn ~ (b5*PHI_corn +
(c15*c11)*np_cereals*PHI_corn +
(c15*c12+c25*c22)*np_protein*PHI_corn +
(c15*c13+c25*c23+c35*c33)*np_oilseed*PHI_corn +
(c15*c14+c25*c24+c35*c34+c45*c44)*np_roots*PHI_corn +
(c15*c15+c25*c25+c35*c35+c45*c45)*np_corn*PHI_corn +
(c15*c16+c25*c26+c35*c36+c45*c46)*nw_fert*PHI_corn +
k51*k_land*PHI_corn +
k52*k_labor*PHI_corn +
k53*k_capital*PHI_corn +
t5*trend*PHI_corn +
tsq5*trend2*PHI_corn +
w51*gdd_obs*PHI_corn +
w52*prec_obs*PHI_corn +
w53*gddHigh_obs*PHI_corn +
w54*dd_obs*PHI_corn +
w55*gdd_1to3*PHI_corn +
w56*prec_1to3*PHI_corn +
w57*gddHigh_1to3*PHI_corn +
w58*dd_1to3*PHI_corn +
w59*gdd_4to10*PHI_corn +
w510*prec_4to10*PHI_corn +
w511*gddHigh_4to10*PHI_corn +
w512*dd_4to10*PHI_corn +
m51*np_cereals_fm*PHI_corn +
m52*np_protein_fm*PHI_corn +
m53*np_oilseed_fm*PHI_corn +
m54*np_roots_fm*PHI_corn +
m55*np_corn_fm*PHI_corn +
m56*nw_fert_fm*PHI_corn +
m57*k_land_fm*PHI_corn +
m58*k_labor_fm*PHI_corn +
m59*k_capital_fm*PHI_corn +
t5_fm*trend_fm*PHI_corn +
tsq5_fm*trend2_fm*PHI_corn +
w51_fm*gdd_obs_fm*PHI_corn +
w52_fm*prec_obs_fm*PHI_corn +
w53_fm*gddHigh_obs_fm*PHI_corn +
w54_fm*dd_obs_fm*PHI_corn +
w55_fm*gdd_1to3_fm*PHI_corn +
w56_fm*prec_1to3_fm*PHI_corn +
w57_fm*gddHigh_1to3_fm*PHI_corn +
w58_fm*dd_1to3_fm*PHI_corn +
w59_fm*gdd_4to10_fm*PHI_corn +
w510_fm*prec_4to10_fm*PHI_corn +
w511_fm*gddHigh_4to10_fm*PHI_corn +
w512_fm*dd_4to10_fm*PHI_corn) +
phi55*phi_corn,
nx_fert ~ b6 +
(c16*c11)*np_cereals +
(c16*c12+c26*c22)*np_protein +
(c16*c13+c26*c23+c36*c33)*np_oilseed +
(c16*c14+c26*c24+c36*c34+c46*c44)*np_roots +
(c16*c15+c26*c25+c36*c35+c46*c45)*np_corn +
(c16*c16+c26*c26+c36*c36+c46*c46)*nw_fert +
k61*k_land +
k62*k_labor +
k63*k_capital +
t6*trend +
tsq6*trend2 +
w61*gdd_obs +
w62*prec_obs +
w63*gddHigh_obs +
w64*dd_obs +
w65*gdd_1to3 +
w66*prec_1to3 +
w67*gddHigh_1to3 +
w68*dd_1to3 +
w69*gdd_4to10 +
w610*prec_4to10 +
w611*gddHigh_4to10 +
w612*dd_4to10 +
m61*np_cereals_fm +
m62*np_protein_fm +
m63*np_oilseed_fm +
m64*np_roots_fm +
m65*np_corn_fm +
m66*nw_fert_fm +
m67*k_land_fm +
m68*k_labor_fm +
m69*k_capital_fm +
t6_fm*trend_fm +
tsq6_fm*trend2_fm +
w61_fm*gdd_obs_fm +
w62_fm*prec_obs_fm +
w63_fm*gddHigh_obs_fm +
w64_fm*dd_obs_fm +
w65_fm*gdd_1to3_fm +
w66_fm*prec_1to3_fm +
w67_fm*gddHigh_1to3_fm +
w68_fm*dd_1to3_fm +
w69_fm*gdd_4to10_fm +
w610_fm*prec_4to10_fm +
w611_fm*gddHigh_4to10_fm +
w612_fm*dd_4to10_fm)
# Starting values
strtvls <- c(
b1 = 4.744e+00,
c11 = 6.026e-01,
c12 = 3.133e-02,
c13 = 2.506e-01,
c14 = 4.535e-02,
c15 = 1.821e-04,
c16 = 1.714e-01,
b2 = 2.370e+00,
c22 = 2.649e-01,
c23 = 5.500e-01,
c24 = 2.463e-01,
c25 = 6.245e-03,
c26 = -2.012e-01,
b3 = -7.524e+00,
c33 = 8.229e-01,
c34 = -2.346e-01,
c35 = -4.137e-03,
c36 = -1.313e-01,
b4 = -3.511e+00,
c44 = 1.060e-01,
c45 = -1.791e-02,
c46 = -4.182e-02,
b5 = -2.147e+01,
b6 = -1.637e+00,
k11 = 8.506e-01,
k12 = 1.971e-02,
k13 = 2.880e-02,
k21 = 4.423e-01,
k22 = -1.504e-01,
k23 = -3.305e-03,
k31 = 8.172e-01,
k32 = -1.141e-01,
k33 = -7.944e-03,
k41 = 2.216e-01,
k42 = -2.688e-02,
k43 = 9.322e-02,
k51 = -4.386e-01,
k52 = -6.078e-03,
k53 = -1.145e-01,
k61 = 9.240e-01,
k62 = 5.283e-02,
k63 = 1.645e-02,
t1 = 5.591e-01,
t2 = 7.405e-01,
t3 = 1.764e+00,
t4 = -4.822e-01,
t5 = 1.258e+00,
t6 = 1.471e+00,
tsq1 = -2.616e-01,
tsq2 = -3.847e-01,
tsq3 = -8.903e-01,
tsq4 = 4.978e-01,
tsq5 = 6.851e-03,
tsq6 = -9.430e-01,
m11 = -3.285e-01,
m12 = -4.149e-02,
m13 = 6.116e-01,
m14 = -2.290e-01,
m15 = 7.683e-04,
m16 = -1.566e+00,
m17 = 1.349e-01,
m18 = -9.083e-02,
m19 = 1.771e-01,
m21 = -3.537e-01,
m22 = 1.381e-01,
m23 = -6.508e-01,
m24 = -6.999e-01,
m25 = -8.149e-03,
m26 = -2.438e+00,
m27 = -1.030e-01,
m28 = 1.211e-01,
m29 = 1.302e-01,
m31 = 1.282e-01,
m32 = -4.534e-01,
m33 = 1.160e+00,
m34 = -4.210e-02,
m35 = 5.258e-03,
m36 = 1.193e+00,
m37 = -1.690e-01,
m38 = 9.611e-02,
m39 = 4.714e-02,
m41 = -5.264e-01,
m42 = 2.478e-01,
m43 = -3.216e-01,
m44 = 2.055e-01,
m45 = -4.556e-03,
m46 = 1.057e+00,
m47 = 2.963e-02,
m48 = 8.101e-02,
m49 = 1.212e-01,
m51 = 2.782e+00,
m52 = 2.398e-04,
m53 = -6.510e-01,
m54 = 6.485e-01,
m55 = 1.062e-02,
m56 = 4.782e+00,
m57 = 1.025e+00,
m58 = -1.659e-01,
m59 = 1.113e-01,
m61 = 3.381e-01,
m62 = -7.972e-02,
m63 = 2.413e-01,
m64 = -3.678e-03,
m65 = 1.031e-03,
m66 = -4.943e-03,
m67 = 8.042e-02,
m68 = -4.373e-02,
m69 = -1.008e-02,
w11 = -5.737e-01,
w12 = -1.041e-01,
w13 = 1.269e-02,
w14 = -4.374e-01,
w15 = -2.429e-01,
w16 = 1.799e-01,
w17 = -9.369e-03,
w18 = 3.181e-01,
w19 = -2.698e+00,
w110 = -7.678e-02,
w111 = 5.092e-02,
w112 = 5.239e-01,
w21 = -1.146e+00,
w22 = -1.995e-01,
w23 = 6.001e-02,
w24 = -9.992e-01,
w25 = -2.017e+00,
w26 = 2.651e-01,
w27 = 3.794e-02,
w28 = 4.538e-01,
w29 = -5.314e+00,
w210 = 2.795e+00,
w211 = 2.413e-01,
w212 = 1.594e+00,
w31 = -1.071e+00,
w32 = -3.907e-01,
w33 = 2.911e-02,
w34 = -7.920e-01,
w35 = -1.453e+00,
w36 = 7.968e-03,
w37 = 2.429e-02,
w38 = -5.488e-01,
w39 = -3.730e+00,
w310 = -2.264e+00,
w311 = 2.021e-02,
w312 = -3.697e+00,
w41 = 1.993e-01,
w42 = -3.278e-02,
w43 = -7.838e-02,
w44 = 1.265e-01,
w45 = 1.625e+00,
w46 = 4.335e-01,
w47 = -1.508e-01,
w48 = 1.729e-01,
w49 = 6.157e+00,
w410 = 1.079e+00,
w411 = -4.365e-01,
w412 = 3.608e-01,
w51 = -1.009e+00,
w52 = -4.142e-01,
w53 = -9.755e-02,
w54 = -7.066e-01,
w55 = -5.234e-01,
w56 = -9.629e-01,
w57 = -2.581e-01,
w58 = -2.359e+00,
w59 = -1.210e+00,
w510 = -3.034e+00,
w511 = -4.900e-01,
w512 = -1.239e+01,
w61 = -1.469e+00,
w62 = 5.296e-02,
w63 = 5.357e-02,
w64 = 1.269e+00,
w65 = -2.039e+00,
w66 = -1.499e-01,
w67 = -8.245e-02,
w68 = 4.067e-02,
w69 = -3.168e-01,
w610 = -3.940e-01,
w611 = -6.995e-02,
w612 = 2.666e-01,
phi11 = -2.183e-03,
phi22 = -4.959e-01,
phi33 = -9.127e-02,
phi44 = -2.256e-01,
phi55 = -5.720e-01,
t1_fm = -1.390e-01,
t2_fm = 4.151e-01,
t3_fm = -1.513e+00,
t4_fm = 3.726e-01,
t5_fm = 8.685e-01,
t6_fm = -5.762e-01,
tsq1_fm = -1.736e-01,
tsq2_fm = -4.534e-01,
tsq3_fm = 7.420e-01,
tsq4_fm = 1.914e-01,
tsq5_fm = -3.968e-01,
tsq6_fm = 3.613e-01,
w11_fm = -4.496e+00,
w12_fm = 8.577e-02,
w13_fm = 2.534e-01,
w14_fm = 2.011e-01,
w15_fm = 1.905e+00,
w16_fm = -6.720e-01,
w17_fm = -1.322e-02,
w18_fm = -2.990e+00,
w19_fm = 4.685e+00,
w110_fm = 3.109e-01,
w111_fm = -8.961e-02,
w112_fm = -9.329e-02,
w21_fm = -6.051e+00,
w22_fm = -2.119e+00,
w23_fm = 1.082e-01,
w24_fm = 4.192e+00,
w25_fm = 1.762e+00,
w26_fm = 6.114e-01,
w27_fm = 5.651e-01,
w28_fm = -4.839e+00,
w29_fm = 1.139e+01,
w210_fm = -7.979e-01,
w211_fm = -9.319e-01,
w212_fm = 1.838e+00,
w31_fm = -9.971e-01,
w32_fm = 2.136e+00,
w33_fm = 1.551e-01,
w34_fm = 2.807e+00,
w35_fm = 5.321e+00,
w36_fm = -8.559e-01,
w37_fm = -2.256e-01,
w38_fm = -1.902e+00,
w39_fm = 2.518e+00,
w310_fm = 2.041e+00,
w311_fm = -3.737e-01,
w312_fm = 7.639e+00,
w41_fm = -2.341e-01,
w42_fm = 6.146e-01,
w43_fm = -3.271e-02,
w44_fm = 2.645e+00,
w45_fm = -4.284e+00,
w46_fm = -1.399e+00,
w47_fm = 8.840e-02,
w48_fm = -2.255e+00,
w49_fm = -3.481e-01,
w410_fm = -1.055e+00,
w411_fm = -1.978e-01,
w412_fm = -1.842e-01,
w51_fm = 1.118e+01,
w52_fm = -3.170e-01,
w53_fm = -9.601e-01,
w54_fm = 4.075e+00,
w55_fm = -1.602e+01,
w56_fm = 1.826e+00,
w57_fm = 1.457e+00,
w58_fm = -5.088e+00,
w59_fm = 1.145e+01,
w510_fm = 4.361e+00,
w511_fm = -1.073e+00,
w512_fm = 2.578e+01,
w61_fm = -2.735e+00,
w62_fm = 1.756e+00,
w63_fm = 5.111e-02,
w64_fm = 2.907e+00,
w65_fm = 2.011e+00,
w66_fm = -1.781e+00,
w67_fm = 9.353e-02,
w68_fm = -6.691e+00,
w69_fm = 3.138e+00,
w610_fm = 1.207e+00,
w611_fm = -2.754e-02,
w612_fm = 3.767e+00)
## Regression with nonlinear SUR
system.time(model_linear <- nlsur(eqns = eqns, data = df_farm_dem, startvalues = strtvls, type = "FGNLS",
trace = TRUE, eps = 1e-03, tol = 1e-07, maxiter=1000))
# Extract data used in this estimation for simulation later
dat_str_all <- df_farm %>%
select(c(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,
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))
dat_str_cereals <- cbind(1,dat_str_all,df_farm$phi_cereals)
dat_str_protein <- cbind(1,dat_str_all,df_farm$phi_protein)
dat_str_oilseed <- cbind(1,dat_str_all,df_farm$phi_oilseed)
dat_str_roots <- cbind(1,dat_str_all,df_farm$phi_roots)
dat_str_corn <- cbind(1,dat_str_all,df_farm$phi_corn)
dat_str_fert <- cbind(1,dat_str_all)
#------------------------------------------------#
##### 3b) Restore "non-Cholesky" parameters ######
#------------------------------------------------#
coef_cereals <- c(b1=model_linear$coefficients["b1"] * mean(df_farm$qq_cereals) / mean(df_farm$PHI_cereals),
b11=model_linear$coefficients["c11"]*model_linear$coefficients["c11"] * mean(df_farm$qq_cereals) / mean(df_farm$np_cereals) / mean(df_farm$PHI_cereals),
b12=model_linear$coefficients["c11"]*model_linear$coefficients["c12"] * mean(df_farm$qq_cereals) / mean(df_farm$np_protein) / mean(df_farm$PHI_cereals),
b13=model_linear$coefficients["c11"]*model_linear$coefficients["c13"] * mean(df_farm$qq_cereals) / mean(df_farm$np_oilseed) / mean(df_farm$PHI_cereals),
b14=model_linear$coefficients["c11"]*model_linear$coefficients["c14"] * mean(df_farm$qq_cereals) / mean(df_farm$np_roots) / mean(df_farm$PHI_cereals),
b15=model_linear$coefficients["c11"]*model_linear$coefficients["c15"] * mean(df_farm$qq_cereals) / mean(df_farm$np_corn) / mean(df_farm$PHI_cereals),
b16=model_linear$coefficients["c11"]*model_linear$coefficients["c16"] * mean(df_farm$qq_cereals) / mean(df_farm$nw_fert) / mean(df_farm$PHI_cereals),
k11 <- model_linear$coefficients["k11"] * mean(df_farm$qq_cereals) / mean(df_farm$k_land) / mean(df_farm$PHI_cereals),
k12 <- model_linear$coefficients["k12"] * mean(df_farm$qq_cereals) / mean(df_farm$k_labor) / mean(df_farm$PHI_cereals),
k13 <- model_linear$coefficients["k13"] * mean(df_farm$qq_cereals) / mean(df_farm$k_capital) / mean(df_farm$PHI_cereals),
t1 <- model_linear$coefficients["t1"] * mean(df_farm$qq_cereals) / mean(df_farm$trend) / mean(df_farm$PHI_cereals),
tsq1 <- model_linear$coefficients["tsq1"] * mean(df_farm$qq_cereals) / mean(df_farm$trend2) / mean(df_farm$PHI_cereals),
w11 <- model_linear$coefficients["w11"] * mean(df_farm$qq_cereals) / mean(df_farm$gdd_obs) / mean(df_farm$PHI_cereals),
w12 <- model_linear$coefficients["w12"] * mean(df_farm$qq_cereals) / mean(df_farm$prec_obs) / mean(df_farm$PHI_cereals),
w13 <- model_linear$coefficients["w13"] * mean(df_farm$qq_cereals) / mean(df_farm$gddHigh_obs) / mean(df_farm$PHI_cereals),
w14 <- model_linear$coefficients["w14"] * mean(df_farm$qq_cereals) / mean(df_farm$dd_obs) / mean(df_farm$PHI_cereals),
w15 <- model_linear$coefficients["w15"] * mean(df_farm$qq_cereals) / mean(df_farm$gdd_1to3) / mean(df_farm$PHI_cereals),
w16 <- model_linear$coefficients["w16"] * mean(df_farm$qq_cereals) / mean(df_farm$prec_1to3) / mean(df_farm$PHI_cereals),
w17 <- model_linear$coefficients["w17"] * mean(df_farm$qq_cereals) / mean(df_farm$gddHigh_1to3) / mean(df_farm$PHI_cereals),
w18 <- model_linear$coefficients["w18"] * mean(df_farm$qq_cereals) / mean(df_farm$dd_1to3) / mean(df_farm$PHI_cereals),
w19 <- model_linear$coefficients["w19"] * mean(df_farm$qq_cereals) / mean(df_farm$gdd_4to10) / mean(df_farm$PHI_cereals),
w110 <- model_linear$coefficients["w110"] * mean(df_farm$qq_cereals) / mean(df_farm$prec_4to10) / mean(df_farm$PHI_cereals),
w111 <- model_linear$coefficients["w111"] * mean(df_farm$qq_cereals) / mean(df_farm$gddHigh_4to10) / mean(df_farm$PHI_cereals),
w112 <- model_linear$coefficients["w112"] * mean(df_farm$qq_cereals) / mean(df_farm$dd_4to10) / mean(df_farm$PHI_cereals),
m11 <- model_linear$coefficients["m11"] * mean(df_farm$qq_cereals) / mean(df_farm$np_cereals_fm) / mean(df_farm$PHI_cereals),
m12 <- model_linear$coefficients["m12"] * mean(df_farm$qq_cereals) / mean(df_farm$np_protein_fm) / mean(df_farm$PHI_cereals),
m13 <- model_linear$coefficients["m13"] * mean(df_farm$qq_cereals) / mean(df_farm$np_oilseed_fm) / mean(df_farm$PHI_cereals),
m14 <- model_linear$coefficients["m14"] * mean(df_farm$qq_cereals) / mean(df_farm$np_roots_fm) / mean(df_farm$PHI_cereals),
m15 <- model_linear$coefficients["m15"] * mean(df_farm$qq_cereals) / mean(df_farm$np_corn_fm) / mean(df_farm$PHI_cereals),
m16 <- model_linear$coefficients["m16"] * mean(df_farm$qq_cereals) / mean(df_farm$nw_fert_fm) / mean(df_farm$PHI_cereals),
m17 <- model_linear$coefficients["m17"] * mean(df_farm$qq_cereals) / mean(df_farm$k_land_fm) / mean(df_farm$PHI_cereals),
m18 <- model_linear$coefficients["m18"] * mean(df_farm$qq_cereals) / mean(df_farm$k_labor_fm) / mean(df_farm$PHI_cereals),
m19 <- model_linear$coefficients["m19"] * mean(df_farm$qq_cereals) / mean(df_farm$k_capital_fm) / mean(df_farm$PHI_cereals),
t1_fm <- model_linear$coefficients["t1_fm"] * mean(df_farm$qq_cereals) / mean(df_farm$trend_fm) / mean(df_farm$PHI_cereals),
tsq1_fm <- model_linear$coefficients["tsq1_fm"] * mean(df_farm$qq_cereals) / mean(df_farm$trend2_fm) / mean(df_farm$PHI_cereals),
w11_fm <- model_linear$coefficients["w11_fm"] * mean(df_farm$qq_cereals) / mean(df_farm$gdd_obs_fm) / mean(df_farm$PHI_cereals),
w12_fm <- model_linear$coefficients["w12_fm"] * mean(df_farm$qq_cereals) / mean(df_farm$prec_obs_fm) / mean(df_farm$PHI_cereals),
w13_fm <- model_linear$coefficients["w13_fm"] * mean(df_farm$qq_cereals) / mean(df_farm$gddHigh_obs_fm) / mean(df_farm$PHI_cereals),
w14_fm <- model_linear$coefficients["w14_fm"] * mean(df_farm$qq_cereals) / mean(df_farm$dd_obs_fm) / mean(df_farm$PHI_cereals),
w15_fm <- model_linear$coefficients["w15_fm"] * mean(df_farm$qq_cereals) / mean(df_farm$gdd_1to3_fm) / mean(df_farm$PHI_cereals),
w16_fm <- model_linear$coefficients["w16_fm"] * mean(df_farm$qq_cereals) / mean(df_farm$prec_1to3_fm) / mean(df_farm$PHI_cereals),
w17_fm <- model_linear$coefficients["w17_fm"] * mean(df_farm$qq_cereals) / mean(df_farm$gddHigh_1to3_fm) / mean(df_farm$PHI_cereals),
w18_fm <- model_linear$coefficients["w18_fm"] * mean(df_farm$qq_cereals) / mean(df_farm$dd_1to3_fm) / mean(df_farm$PHI_cereals),
w19_fm <- model_linear$coefficients["w19_fm"] * mean(df_farm$qq_cereals) / mean(df_farm$gdd_4to10_fm) / mean(df_farm$PHI_cereals),
w110_fm <- model_linear$coefficients["w110_fm"] * mean(df_farm$qq_cereals) / mean(df_farm$prec_4to10_fm) / mean(df_farm$PHI_cereals),
w111_fm <- model_linear$coefficients["w111_fm"] * mean(df_farm$qq_cereals) / mean(df_farm$gddHigh_4to10_fm) / mean(df_farm$PHI_cereals),
w112_fm <- model_linear$coefficients["w112_fm"] * mean(df_farm$qq_cereals) / mean(df_farm$dd_4to10_fm) / mean(df_farm$PHI_cereals),
phi1 <- model_linear$coefficients["phi11"] * mean(df_farm$qq_cereals) / mean(df_farm$phi_cereals))
coef_protein <- c(
b2 <- model_linear$coefficients["b2"] * mean(df_farm$qq_protein) / mean(df_farm$PHI_protein),
b21 <- (model_linear$coefficients["c12"]*model_linear$coefficients["c11"]) * mean(df_farm$qq_protein) / mean(df_farm$np_cereals) / mean(df_farm$PHI_protein),
b22 <- (model_linear$coefficients["c12"]*model_linear$coefficients["c12"]+model_linear$coefficients["c22"]*model_linear$coefficients["c22"]) * mean(df_farm$qq_protein) / mean(df_farm$np_protein) / mean(df_farm$PHI_protein),
b23 <- (model_linear$coefficients["c12"]*model_linear$coefficients["c13"]+model_linear$coefficients["c22"]*model_linear$coefficients["c23"]) * mean(df_farm$qq_protein) / mean(df_farm$np_oilseed) / mean(df_farm$PHI_protein),
b24 <- (model_linear$coefficients["c12"]*model_linear$coefficients["c14"]+model_linear$coefficients["c22"]*model_linear$coefficients["c24"]) * mean(df_farm$qq_protein) / mean(df_farm$np_roots) / mean(df_farm$PHI_protein),
b25 <- (model_linear$coefficients["c12"]*model_linear$coefficients["c15"]+model_linear$coefficients["c22"]*model_linear$coefficients["c25"]) * mean(df_farm$qq_protein) / mean(df_farm$np_corn) / mean(df_farm$PHI_protein),
b26 <- (model_linear$coefficients["c12"]*model_linear$coefficients["c16"]+model_linear$coefficients["c22"]*model_linear$coefficients["c26"]) * mean(df_farm$qq_protein) / mean(df_farm$nw_fert) / mean(df_farm$PHI_protein),
k21 <- model_linear$coefficients["k21"] * mean(df_farm$qq_protein) / mean(df_farm$k_land) / mean(df_farm$PHI_protein),
k22 <- model_linear$coefficients["k22"] * mean(df_farm$qq_protein) / mean(df_farm$k_labor) / mean(df_farm$PHI_protein),
k23 <- model_linear$coefficients["k23"] * mean(df_farm$qq_protein) / mean(df_farm$k_capital) / mean(df_farm$PHI_protein),
t2 <- model_linear$coefficients["t2"] * mean(df_farm$qq_protein) / mean(df_farm$trend) / mean(df_farm$PHI_protein),
tsq2 <- model_linear$coefficients["tsq2"] * mean(df_farm$qq_protein) / mean(df_farm$trend2) / mean(df_farm$PHI_protein),
w21 <- model_linear$coefficients["w21"] * mean(df_farm$qq_protein) / mean(df_farm$gdd_obs) / mean(df_farm$PHI_protein),
w22 <- model_linear$coefficients["w22"] * mean(df_farm$qq_protein) / mean(df_farm$prec_obs) / mean(df_farm$PHI_protein),
w23 <- model_linear$coefficients["w23"] * mean(df_farm$qq_protein) / mean(df_farm$gddHigh_obs) / mean(df_farm$PHI_protein),
w24 <- model_linear$coefficients["w24"] * mean(df_farm$qq_protein) / mean(df_farm$dd_obs) / mean(df_farm$PHI_protein),
w25 <- model_linear$coefficients["w25"] * mean(df_farm$qq_protein) / mean(df_farm$gdd_1to3) / mean(df_farm$PHI_protein),
w26 <- model_linear$coefficients["w26"] * mean(df_farm$qq_protein) / mean(df_farm$prec_1to3) / mean(df_farm$PHI_protein),
w27 <- model_linear$coefficients["w27"] * mean(df_farm$qq_protein) / mean(df_farm$gddHigh_1to3) / mean(df_farm$PHI_protein),
w28 <- model_linear$coefficients["w28"] * mean(df_farm$qq_protein) / mean(df_farm$dd_1to3) / mean(df_farm$PHI_protein),
w29 <- model_linear$coefficients["w29"] * mean(df_farm$qq_protein) / mean(df_farm$gdd_4to10) / mean(df_farm$PHI_protein),
w210 <- model_linear$coefficients["w210"] * mean(df_farm$qq_protein) / mean(df_farm$prec_4to10) / mean(df_farm$PHI_protein),
w211 <- model_linear$coefficients["w211"] * mean(df_farm$qq_protein) / mean(df_farm$gddHigh_4to10) / mean(df_farm$PHI_protein),
w212 <- model_linear$coefficients["w212"] * mean(df_farm$qq_protein) / mean(df_farm$dd_4to10) / mean(df_farm$PHI_protein),
m21 <- model_linear$coefficients["m21"] * mean(df_farm$qq_protein) / mean(df_farm$np_cereals_fm) / mean(df_farm$PHI_protein),
m22 <- model_linear$coefficients["m22"] * mean(df_farm$qq_protein) / mean(df_farm$np_protein_fm) / mean(df_farm$PHI_protein),
m23 <- model_linear$coefficients["m23"] * mean(df_farm$qq_protein) / mean(df_farm$np_oilseed_fm) / mean(df_farm$PHI_protein),
m24 <- model_linear$coefficients["m24"] * mean(df_farm$qq_protein) / mean(df_farm$np_roots_fm) / mean(df_farm$PHI_protein),
m25 <- model_linear$coefficients["m25"] * mean(df_farm$qq_protein) / mean(df_farm$np_corn_fm) / mean(df_farm$PHI_protein),
m26 <- model_linear$coefficients["m26"] * mean(df_farm$qq_protein) / mean(df_farm$nw_fert_fm) / mean(df_farm$PHI_protein),
m27 <- model_linear$coefficients["m27"] * mean(df_farm$qq_protein) / mean(df_farm$k_land_fm) / mean(df_farm$PHI_protein),
m28 <- model_linear$coefficients["m28"] * mean(df_farm$qq_protein) / mean(df_farm$k_labor_fm) / mean(df_farm$PHI_protein),
m29 <- model_linear$coefficients["m29"] * mean(df_farm$qq_protein) / mean(df_farm$k_capital_fm) / mean(df_farm$PHI_protein),
t2_fm <- model_linear$coefficients["t2_fm"] * mean(df_farm$qq_protein) / mean(df_farm$trend_fm) / mean(df_farm$PHI_protein),
tsq2_fm <- model_linear$coefficients["tsq2_fm"] * mean(df_farm$qq_protein) / mean(df_farm$trend2_fm) / mean(df_farm$PHI_protein),
w21_fm <- model_linear$coefficients["w21_fm"] * mean(df_farm$qq_protein) / mean(df_farm$gdd_obs_fm) / mean(df_farm$PHI_protein),
w22_fm <- model_linear$coefficients["w22_fm"] * mean(df_farm$qq_protein) / mean(df_farm$prec_obs_fm) / mean(df_farm$PHI_protein),
w23_fm <- model_linear$coefficients["w23_fm"] * mean(df_farm$qq_protein) / mean(df_farm$gddHigh_obs_fm) / mean(df_farm$PHI_protein),
w24_fm <- model_linear$coefficients["w24_fm"] * mean(df_farm$qq_protein) / mean(df_farm$dd_obs_fm) / mean(df_farm$PHI_protein),
w25_fm <- model_linear$coefficients["w25_fm"] * mean(df_farm$qq_protein) / mean(df_farm$gdd_1to3_fm) / mean(df_farm$PHI_protein),
w26_fm <- model_linear$coefficients["w26_fm"] * mean(df_farm$qq_protein) / mean(df_farm$prec_1to3_fm) / mean(df_farm$PHI_protein),
w27_fm <- model_linear$coefficients["w27_fm"] * mean(df_farm$qq_protein) / mean(df_farm$gddHigh_1to3_fm) / mean(df_farm$PHI_protein),
w28_fm <- model_linear$coefficients["w28_fm"] * mean(df_farm$qq_protein) / mean(df_farm$dd_1to3_fm) / mean(df_farm$PHI_protein),
w29_fm <- model_linear$coefficients["w29_fm"] * mean(df_farm$qq_protein) / mean(df_farm$gdd_4to10_fm) / mean(df_farm$PHI_protein),
w210_fm <- model_linear$coefficients["w210_fm"] * mean(df_farm$qq_protein) / mean(df_farm$prec_4to10_fm) / mean(df_farm$PHI_protein),
w211_fm <- model_linear$coefficients["w211_fm"] * mean(df_farm$qq_protein) / mean(df_farm$gddHigh_4to10_fm) / mean(df_farm$PHI_protein),
w212_fm <- model_linear$coefficients["w212_fm"] * mean(df_farm$qq_protein) / mean(df_farm$dd_4to10_fm) / mean(df_farm$PHI_protein),
phi2 <- model_linear$coefficients["phi22"] * mean(df_farm$qq_protein) / mean(df_farm$phi_protein)
)
coef_oilseed <- c(
b3 <- model_linear$coefficients["b3"] * mean(df_farm$qq_oilseed) / mean(df_farm$PHI_oilseed),
b31 <- (model_linear$coefficients["c13"]*model_linear$coefficients["c11"]) * mean(df_farm$qq_oilseed) / mean(df_farm$np_cereals) / mean(df_farm$PHI_oilseed),
b32 <- (model_linear$coefficients["c13"]*model_linear$coefficients["c12"]+model_linear$coefficients["c23"]*model_linear$coefficients["c22"]) * mean(df_farm$qq_oilseed) / mean(df_farm$np_protein) / mean(df_farm$PHI_oilseed),
b33 <- (model_linear$coefficients["c13"]*model_linear$coefficients["c13"]+model_linear$coefficients["c23"]*model_linear$coefficients["c23"]+model_linear$coefficients["c33"]*model_linear$coefficients["c33"]) * mean(df_farm$qq_oilseed) / mean(df_farm$np_oilseed) / mean(df_farm$PHI_oilseed),
b34 <- (model_linear$coefficients["c13"]*model_linear$coefficients["c14"]+model_linear$coefficients["c23"]*model_linear$coefficients["c24"]+model_linear$coefficients["c33"]*model_linear$coefficients["c34"]) * mean(df_farm$qq_oilseed) / mean(df_farm$np_roots) / mean(df_farm$PHI_oilseed),
b35 <- (model_linear$coefficients["c13"]*model_linear$coefficients["c15"]+model_linear$coefficients["c23"]*model_linear$coefficients["c25"]+model_linear$coefficients["c33"]*model_linear$coefficients["c35"]) * mean(df_farm$qq_oilseed) / mean(df_farm$np_corn) / mean(df_farm$PHI_oilseed),
b36 <- (model_linear$coefficients["c13"]*model_linear$coefficients["c16"]+model_linear$coefficients["c23"]*model_linear$coefficients["c26"]+model_linear$coefficients["c33"]*model_linear$coefficients["c36"]) * mean(df_farm$qq_oilseed) / mean(df_farm$nw_fert) / mean(df_farm$PHI_oilseed),
k31 <- model_linear$coefficients["k31"] * mean(df_farm$qq_oilseed) / mean(df_farm$k_land) / mean(df_farm$PHI_oilseed),
k32 <- model_linear$coefficients["k32"] * mean(df_farm$qq_oilseed) / mean(df_farm$k_labor) / mean(df_farm$PHI_oilseed),
k33 <- model_linear$coefficients["k33"] * mean(df_farm$qq_oilseed) / mean(df_farm$k_capital) / mean(df_farm$PHI_oilseed),
t3 <- model_linear$coefficients["t3"] * mean(df_farm$qq_oilseed) / mean(df_farm$trend) / mean(df_farm$PHI_oilseed),
tsq3 <- model_linear$coefficients["tsq3"] * mean(df_farm$qq_oilseed) / mean(df_farm$trend2) / mean(df_farm$PHI_oilseed),
w31 <- model_linear$coefficients["w31"] * mean(df_farm$qq_oilseed) / mean(df_farm$gdd_obs) / mean(df_farm$PHI_oilseed),
w32 <- model_linear$coefficients["w32"] * mean(df_farm$qq_oilseed) / mean(df_farm$prec_obs) / mean(df_farm$PHI_oilseed),
w33 <- model_linear$coefficients["w33"] * mean(df_farm$qq_oilseed) / mean(df_farm$gddHigh_obs) / mean(df_farm$PHI_oilseed),
w34 <- model_linear$coefficients["w34"] * mean(df_farm$qq_oilseed) / mean(df_farm$dd_obs) / mean(df_farm$PHI_oilseed),
w35 <- model_linear$coefficients["w35"] * mean(df_farm$qq_oilseed) / mean(df_farm$gdd_1to3) / mean(df_farm$PHI_oilseed),
w36 <- model_linear$coefficients["w36"] * mean(df_farm$qq_oilseed) / mean(df_farm$prec_1to3) / mean(df_farm$PHI_oilseed),
w37 <- model_linear$coefficients["w37"] * mean(df_farm$qq_oilseed) / mean(df_farm$gddHigh_1to3) / mean(df_farm$PHI_oilseed),
w38 <- model_linear$coefficients["w38"] * mean(df_farm$qq_oilseed) / mean(df_farm$dd_1to3) / mean(df_farm$PHI_oilseed),
w39 <- model_linear$coefficients["w39"] * mean(df_farm$qq_oilseed) / mean(df_farm$gdd_4to10) / mean(df_farm$PHI_oilseed),
w310 <- model_linear$coefficients["w310"] * mean(df_farm$qq_oilseed) / mean(df_farm$prec_4to10) / mean(df_farm$PHI_oilseed),
w311 <- model_linear$coefficients["w311"] * mean(df_farm$qq_oilseed) / mean(df_farm$gddHigh_4to10) / mean(df_farm$PHI_oilseed),
w312 <- model_linear$coefficients["w312"] * mean(df_farm$qq_oilseed) / mean(df_farm$dd_4to10) / mean(df_farm$PHI_oilseed),
m31 <- model_linear$coefficients["m31"] * mean(df_farm$qq_oilseed) / mean(df_farm$np_cereals_fm) / mean(df_farm$PHI_oilseed),
m32 <- model_linear$coefficients["m32"] * mean(df_farm$qq_oilseed) / mean(df_farm$np_protein_fm) / mean(df_farm$PHI_oilseed),
m33 <- model_linear$coefficients["m33"] * mean(df_farm$qq_oilseed) / mean(df_farm$np_oilseed_fm) / mean(df_farm$PHI_oilseed),
m34 <- model_linear$coefficients["m34"] * mean(df_farm$qq_oilseed) / mean(df_farm$np_roots_fm) / mean(df_farm$PHI_oilseed),
m35 <- model_linear$coefficients["m35"] * mean(df_farm$qq_oilseed) / mean(df_farm$np_corn_fm) / mean(df_farm$PHI_oilseed),
m36 <- model_linear$coefficients["m36"] * mean(df_farm$qq_oilseed) / mean(df_farm$nw_fert_fm) / mean(df_farm$PHI_oilseed),
m37 <- model_linear$coefficients["m37"] * mean(df_farm$qq_oilseed) / mean(df_farm$k_land_fm) / mean(df_farm$PHI_oilseed),
m38 <- model_linear$coefficients["m38"] * mean(df_farm$qq_oilseed) / mean(df_farm$k_labor_fm) / mean(df_farm$PHI_oilseed),
m39 <- model_linear$coefficients["m39"] * mean(df_farm$qq_oilseed) / mean(df_farm$k_capital_fm) / mean(df_farm$PHI_oilseed),
t3_fm <- model_linear$coefficients["t3_fm"] * mean(df_farm$qq_oilseed) / mean(df_farm$trend_fm) / mean(df_farm$PHI_oilseed),
tsq3_fm <- model_linear$coefficients["tsq3_fm"] * mean(df_farm$qq_oilseed) / mean(df_farm$trend2_fm) / mean(df_farm$PHI_oilseed),
w31_fm <- model_linear$coefficients["w31_fm"] * mean(df_farm$qq_oilseed) / mean(df_farm$gdd_obs_fm) / mean(df_farm$PHI_oilseed),
w32_fm <- model_linear$coefficients["w32_fm"] * mean(df_farm$qq_oilseed) / mean(df_farm$prec_obs_fm) / mean(df_farm$PHI_oilseed),
w33_fm <- model_linear$coefficients["w33_fm"] * mean(df_farm$qq_oilseed) / mean(df_farm$gddHigh_obs_fm) / mean(df_farm$PHI_oilseed),
w34_fm <- model_linear$coefficients["w34_fm"] * mean(df_farm$qq_oilseed) / mean(df_farm$dd_obs_fm) / mean(df_farm$PHI_oilseed),
w35_fm <- model_linear$coefficients["w35_fm"] * mean(df_farm$qq_oilseed) / mean(df_farm$gdd_1to3_fm) / mean(df_farm$PHI_oilseed),
w36_fm <- model_linear$coefficients["w36_fm"] * mean(df_farm$qq_oilseed) / mean(df_farm$prec_1to3_fm) / mean(df_farm$PHI_oilseed),
w37_fm <- model_linear$coefficients["w37_fm"] * mean(df_farm$qq_oilseed) / mean(df_farm$gddHigh_1to3_fm) / mean(df_farm$PHI_oilseed),
w38_fm <- model_linear$coefficients["w38_fm"] * mean(df_farm$qq_oilseed) / mean(df_farm$dd_1to3_fm) / mean(df_farm$PHI_oilseed),
w39_fm <- model_linear$coefficients["w39_fm"] * mean(df_farm$qq_oilseed) / mean(df_farm$gdd_4to10_fm) / mean(df_farm$PHI_oilseed),
w310_fm <- model_linear$coefficients["w310_fm"] * mean(df_farm$qq_oilseed) / mean(df_farm$prec_4to10_fm) / mean(df_farm$PHI_oilseed),
w311_fm <- model_linear$coefficients["w311_fm"] * mean(df_farm$qq_oilseed) / mean(df_farm$gddHigh_4to10_fm) / mean(df_farm$PHI_oilseed),
w312_fm <- model_linear$coefficients["w312_fm"] * mean(df_farm$qq_oilseed) / mean(df_farm$dd_4to10_fm) / mean(df_farm$PHI_oilseed),
phi3 <- model_linear$coefficients["phi33"] * mean(df_farm$qq_oilseed) / mean(df_farm$phi_oilseed)
)
coef_roots <- c(
b4 <- model_linear$coefficients["b4"] * mean(df_farm$qq_roots) / mean(df_farm$PHI_roots),
b41 <- (model_linear$coefficients["c14"]*model_linear$coefficients["c11"]) * mean(df_farm$qq_roots) / mean(df_farm$np_cereals) / mean(df_farm$PHI_roots),
b42 <- (model_linear$coefficients["c14"]*model_linear$coefficients["c12"]+model_linear$coefficients["c24"]*model_linear$coefficients["c22"]) * mean(df_farm$qq_roots) / mean(df_farm$np_protein) / mean(df_farm$PHI_roots),
b43 <- (model_linear$coefficients["c14"]*model_linear$coefficients["c13"]+model_linear$coefficients["c24"]*model_linear$coefficients["c23"]+model_linear$coefficients["c34"]*model_linear$coefficients["c33"]) * mean(df_farm$qq_roots) / mean(df_farm$np_oilseed) / mean(df_farm$PHI_roots),
b44 <- (model_linear$coefficients["c14"]*model_linear$coefficients["c14"]+model_linear$coefficients["c24"]*model_linear$coefficients["c24"]+model_linear$coefficients["c34"]*model_linear$coefficients["c34"]+model_linear$coefficients["c44"]*model_linear$coefficients["c44"]) * mean(df_farm$qq_roots) / mean(df_farm$np_roots) / mean(df_farm$PHI_roots),
b45 <- (model_linear$coefficients["c14"]*model_linear$coefficients["c15"]+model_linear$coefficients["c24"]*model_linear$coefficients["c25"]+model_linear$coefficients["c34"]*model_linear$coefficients["c35"]+model_linear$coefficients["c44"]*model_linear$coefficients["c45"]) * mean(df_farm$qq_roots) / mean(df_farm$np_corn) / mean(df_farm$PHI_roots),
b46 <- (model_linear$coefficients["c14"]*model_linear$coefficients["c16"]+model_linear$coefficients["c24"]*model_linear$coefficients["c26"]+model_linear$coefficients["c34"]*model_linear$coefficients["c36"]+model_linear$coefficients["c44"]*model_linear$coefficients["c46"]) * mean(df_farm$qq_roots) / mean(df_farm$nw_fert) / mean(df_farm$PHI_roots),
k41 <- model_linear$coefficients["k41"] * mean(df_farm$qq_roots) / mean(df_farm$k_land) / mean(df_farm$PHI_roots),
k42 <- model_linear$coefficients["k42"] * mean(df_farm$qq_roots) / mean(df_farm$k_labor) / mean(df_farm$PHI_roots),
k43 <- model_linear$coefficients["k43"] * mean(df_farm$qq_roots) / mean(df_farm$k_capital) / mean(df_farm$PHI_roots),
t4 <- model_linear$coefficients["t4"] * mean(df_farm$qq_roots) / mean(df_farm$trend) / mean(df_farm$PHI_roots),
tsq4 <- model_linear$coefficients["tsq4"] * mean(df_farm$qq_roots) / mean(df_farm$trend2) / mean(df_farm$PHI_roots),
w41 <- model_linear$coefficients["w41"] * mean(df_farm$qq_roots) / mean(df_farm$gdd_obs) / mean(df_farm$PHI_roots),
w42 <- model_linear$coefficients["w42"] * mean(df_farm$qq_roots) / mean(df_farm$prec_obs) / mean(df_farm$PHI_roots),
w43 <- model_linear$coefficients["w43"] * mean(df_farm$qq_roots) / mean(df_farm$gddHigh_obs) / mean(df_farm$PHI_roots),
w44 <- model_linear$coefficients["w44"] * mean(df_farm$qq_roots) / mean(df_farm$dd_obs) / mean(df_farm$PHI_roots),
w45 <- model_linear$coefficients["w45"] * mean(df_farm$qq_roots) / mean(df_farm$gdd_1to3) / mean(df_farm$PHI_roots),
w46 <- model_linear$coefficients["w46"] * mean(df_farm$qq_roots) / mean(df_farm$prec_1to3) / mean(df_farm$PHI_roots),
w47 <- model_linear$coefficients["w47"] * mean(df_farm$qq_roots) / mean(df_farm$gddHigh_1to3) / mean(df_farm$PHI_roots),
w48 <- model_linear$coefficients["w48"] * mean(df_farm$qq_roots) / mean(df_farm$dd_1to3) / mean(df_farm$PHI_roots),
w49 <- model_linear$coefficients["w49"] * mean(df_farm$qq_roots) / mean(df_farm$gdd_4to10) / mean(df_farm$PHI_roots),
w410 <- model_linear$coefficients["w410"] * mean(df_farm$qq_roots) / mean(df_farm$prec_4to10) / mean(df_farm$PHI_roots),
w411 <- model_linear$coefficients["w411"] * mean(df_farm$qq_roots) / mean(df_farm$gddHigh_4to10) / mean(df_farm$PHI_roots),
w412 <- model_linear$coefficients["w412"] * mean(df_farm$qq_roots) / mean(df_farm$dd_4to10) / mean(df_farm$PHI_roots),