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02f_TFP for US_M-SFA_vrs and crs.R
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02f_TFP for US_M-SFA_vrs and crs.R
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# --------------------------------------- #
# #
# This program estimates the stochastic #
# multiplicative TFP index for the state- #
# level US data index for the US, under #
# both VRS and CRS #
# #
# --------------------------------------- #
# Open packages
library(fastDummies) #to greate dummy variables
library(dplyr) #for data manipulation
library(msm) #for delta method
library(ggplot2) #to create plots
library(ggthemes) #to format plots
library(gridExtra) #to arrange plots
library(reshape2) #to reshape the data
library(tikzDevice) #to save ggplot object in latex format
library(ggpubr) ## for ggarrange
library(kableExtra) # to convert data frames to Latex
# Set path to Latex compiler if figures should be stored in Latex format
options("tikzLatex"='C:/Program Files/MiKTeX/miktex/bin/x64/pdflatex.exe')
#-----------------------#
#### 0) Preparations ####
#-----------------------#
# load US production data
load("R_output/USdata.Rda")
# Create trend variable
trend <- data.frame(matrix(ncol = 2, nrow = length(unique(USdata$year))))
colnames(trend) <- c("trend","year")
trend$trend <- seq(from = 1, to = length(unique(USdata$year)))
trend$year <- seq(from = min(USdata$year), to = max(USdata$year))
USdata <- right_join(USdata, trend)
USdata$trend <- as.numeric(USdata$trend)
# For semi-decade specific time trend
USdata <- USdata %>%
mutate(semidecade = case_when(
year >= 1960 & year < 1965 ~ "sdec60s",
year >= 1965 & year < 1970 ~ "sdec65s",
year >= 1970 & year < 1975 ~ "sdec70s",
year >= 1975 & year < 1980 ~ "sdec75s",
year >= 1980 & year < 1985 ~ "sdec80s",
year >= 1985 & year < 1990 ~ "sdec85s",
year >= 1990 & year < 1995 ~ "sdec90s",
year >= 1995 & year < 2000 ~ "sdec95s",
year >= 2000 ~ "sdec00s")
)
USdata <- USdata %>%
dummy_cols(select_columns = "semidecade",remove_first_dummy=FALSE)
# State dummy variables
USdata <- USdata %>%
dummy_cols(select_columns = "state",remove_first_dummy=TRUE)
# Regional variables
USdata$region[USdata$state == "CA"|
USdata$state == "OR" |
USdata$state == "WA"] <- "Pacific"
USdata$region[USdata$state == "AZ" |
USdata$state == "CO" |
USdata$state == "ID" |
USdata$state == "MT" |
USdata$state == "NM" |
USdata$state == "NV" |
USdata$state == "UT" |
USdata$state == "WY"] <- "Mountain"
USdata$region[USdata$state == "KS" |
USdata$state == "ND" |
USdata$state == "NE" |
USdata$state == "SD"] <- "NPlains"
USdata$region[USdata$state == "OK" |
USdata$state == "TX"] <- "SPlains"
USdata$region[USdata$state == "IA" |
USdata$state == "IL" |
USdata$state == "IN" |
USdata$state == "MO" |
USdata$state == "OH"] <- "Cornbelt"
USdata$region[USdata$state == "AL" |
USdata$state == "FL" |
USdata$state == "GA" |
USdata$state == "SC"] <- "Southeast"
USdata$region[USdata$state == "CT" |
USdata$state == "DE" |
USdata$state == "MA" |
USdata$state == "MD" |
USdata$state == "ME" |
USdata$state == "NH" |
USdata$state == "NJ" |
USdata$state == "NY"|
USdata$state == "PA" |
USdata$state == "RI" |
USdata$state == "VT"] <- "Northeast"
USdata$region[USdata$state == "MI" |
USdata$state == "MN" |
USdata$state == "WI"] <- "Lake"
USdata$region[USdata$state == "KY" |
USdata$state == "NC" |
USdata$state == "TN"|
USdata$state == "VA" |
USdata$state == "WV"] <- "Appalacian"
USdata$region[USdata$state == "AR" |
USdata$state == "LA" |
USdata$state == "MS"] <- "Delta"
# ------------------------------------ #
#### 1) Compute TFP index under VRS ####
# ------------------------------------ #
# ------------------------------- #
##### 1a) Frontier estimation #####
# ------------------------------- #
sfa_string <- as.formula(paste0(c("-log(q_crops)",
paste0(c("log(q_livestock/q_crops)",
"log(q_otheroutp/q_crops)",
"log(x_capital)", "log(x_land)",
"log(x_labor)", "log(x_interm)",
"factor(state)",
"trend:factor(region):factor(semidecade)"),
collapse = " + ")),
collapse = " ~ "))
model_sfa <- sfaR::sfacross(sfa_string, S=-1, data = USdata)
summary(model_sfa)
# Estimate model as OLS to find noise component below
model_ols <- lm(sfa_string, data = USdata)
summary(model_ols)
# ------------------------------- #
##### 1b) Decompose TFP index #####
# ------------------------------- #
# Scale elasticity
scale_elas <- -model_sfa$mlParam["log(x_capital)"] + -model_sfa$mlParam["log(x_land)"] +
-model_sfa$mlParam["log(x_labor)"] + -model_sfa$mlParam["log(x_interm)"]
# Aggregate output
USdata$Qit <- USdata$q_livestock^(model_sfa$mlParam["log(q_livestock/q_crops)"]) *
USdata$q_otheroutp^(model_sfa$mlParam["log(q_otheroutp/q_crops)"]) *
USdata$q_crops^(1 - model_sfa$mlParam["log(q_livestock/q_crops)"] - model_sfa$mlParam["log(q_otheroutp/q_crops)"])
# Aggregate input
USdata$Xit <- USdata$x_capital^(-model_sfa$mlParam["log(x_capital)"]/scale_elas) *
USdata$x_land^(-model_sfa$mlParam["log(x_land)"]/scale_elas) *
USdata$x_labor^(-model_sfa$mlParam["log(x_labor)"]/scale_elas) *
USdata$x_interm^(-model_sfa$mlParam["log(x_interm)"]/scale_elas)
# Total factor productivity
USdata$TFPit <- USdata$Qit/USdata$Xit
# Output technical efficiency
USdata$OTEit <- sfaR::efficiencies(model_sfa)[, "teJLMS"]
# Noise component
USdata$NCit <- exp(log(USdata$q_crops) - as.numeric(crossprod(matrix(-model_sfa$mlParam[1:(length(model_sfa$mlParam) - 2)]),
t(model.matrix(model_ols)))) + sfaR::efficiencies(model_sfa)[, "u"]) # noise component
# Output scale component
USdata$OSEit <- USdata$x_capital^(-model_sfa$mlParam["log(x_capital)"] * (1 - 1/scale_elas)) *
USdata$x_land^(-model_sfa$mlParam["log(x_land)"] * (1 - 1/scale_elas)) *
USdata$x_labor^(-model_sfa$mlParam["log(x_labor)"] * (1 - 1/scale_elas)) *
USdata$x_interm^(-model_sfa$mlParam["log(x_interm)"] * (1 - 1/scale_elas))
# Technical change component
USdata$TCit <- exp(apply(sweep(model.matrix(~factor(state),data=USdata),MARGIN=2, STATS=c(-model_sfa$mlParam[1],-model_sfa$mlParam[stringr::str_detect(names(model_sfa$mlParam),
"state")]), FUN="*"),1, sum) +
apply(sweep(model.matrix(~-1 + trend:factor(region):factor(semidecade), data = USdata), MARGIN = 2, STATS = -model_sfa$mlParam[stringr::str_detect(names(model_sfa$mlParam),
"trend")], FUN = "*"), 1, sum)) ## technical change component
# Summarize the results
summary(USdata[c("OTEit", "NCit", "OSEit", "TCit")])
# Subset data to only contain the index components
MSFA.level_vrs <- USdata %>%
dplyr::select(year,state,Qit,Xit,TFPit,TCit,OTEit,OSEit,NCit)
# Check if they add up
MSFA.level_vrs$TFPcomp <- MSFA.level_vrs$TCit * MSFA.level_vrs$OTEit * MSFA.level_vrs$OSEit * MSFA.level_vrs$NCit
summary(MSFA.level_vrs$TFPit-MSFA.level_vrs$TFPcomp)
# Save results for comparison in "03h_TFP for US_comparison"
save(MSFA.level_vrs, file="R_output/MSFA.level_vrs.Rda")
# --------------------------------- #
##### 1c) Create results tables #####
# --------------------------------- #
# ----------------------------------------- #
# Table to summarize the regression results #
# ----------------------------------------- #
df.sfa_vrs <- data.frame(matrix(ncol = 3, nrow = 11))
x <- c("Variable", "Estimate", "Standard Error")
colnames(df.sfa_vrs) <- x
df.sfa_vrs$Variable <- c("ln(livestock/Crops)",
"ln(Other output/Crops)",
"ln(Capital)",
"ln(Land)",
"ln(Labor)",
"ln(Intermediate inputs)",
"Binary variables for states",
"Regional- and semidecade- \\\\ specific time trends",
"$\\delta$",
"$\\phi$",
"Average efficiency")
estimates <- model_sfa$mlParam
stderrs <- sqrt(diag(model_sfa$invHessian))
zvals <- estimates/stderrs
pvals <- 2*pnorm(q=abs(zvals), lower.tail=FALSE)
df.sfa_vrs[1,2] <- paste0(format(round(model_sfa$mlParam["log(q_livestock/q_crops)"],3),nsmall=3),
ifelse(pvals[2]<0.01,"***",
ifelse(pvals[2]<0.05,"**",
ifelse(pvals[2]<0.1,"*",""))))
df.sfa_vrs[1,3] <- paste0("(",format(round(stderrs[2],3),nsmall=3),")")
df.sfa_vrs[2,2] <- paste0(format(round(model_sfa$mlParam["log(q_otheroutp/q_crops)"],3),nsmall=3),
ifelse(pvals[3]<0.01,"***",
ifelse(pvals[3]<0.05,"**",
ifelse(pvals[3]<0.1,"*",""))))
df.sfa_vrs[2,3] <- paste0("(",format(round(stderrs[3],3),nsmall=3),")")
df.sfa_vrs[3,2] <- paste0(format(round(model_sfa$mlParam["log(x_capital)"],3),nsmall=3),
ifelse(pvals[4]<0.01,"***",
ifelse(pvals[4]<0.05,"**",
ifelse(pvals[4]<0.1,"*",""))))
df.sfa_vrs[3,3] <- paste0("(",format(round(stderrs[4],3),nsmall=3),")")
df.sfa_vrs[4,2] <- paste0(format(round(model_sfa$mlParam["log(x_land)"],3),nsmall=3),
ifelse(pvals[5]<0.01,"***",
ifelse(pvals[5]<0.05,"**",
ifelse(pvals[4]<0.1,"*",""))))
df.sfa_vrs[4,3] <- paste0("(",format(round(stderrs[5],3),nsmall=3),")")
df.sfa_vrs[5,2] <- paste0(format(round(model_sfa$mlParam["log(x_labor)"],3),nsmall=3),
ifelse(pvals[6]<0.01,"***",
ifelse(pvals[6]<0.05,"**",
ifelse(pvals[4]<0.1,"*",""))))
df.sfa_vrs[5,3] <- paste0("(",format(round(stderrs[6],3),nsmall=3),")")
df.sfa_vrs[6,2] <- paste0(format(round(model_sfa$mlParam["log(x_interm)"],3),nsmall=3),
ifelse(pvals[7]<0.01,"***",
ifelse(pvals[7]<0.05,"**",
ifelse(pvals[4]<0.1,"*",""))))
df.sfa_vrs[6,3] <- paste0("(",format(round(stderrs[7],3),nsmall=3),")")
df.sfa_vrs[7,2] <- "not reported"
df.sfa_vrs[7,3] <- ""
df.sfa_vrs[8,2] <- "not reported"
df.sfa_vrs[8,3] <- ""
df.sfa_vrs[9,2] <- paste0(format(round(model_sfa$mlParam["Zu_(Intercept)"],3),nsmall=3),
ifelse(pvals[145]<0.01,"***",
ifelse(pvals[145]<0.05,"**",
ifelse(pvals[145]<0.1,"*",""))))
df.sfa_vrs[9,3] <- paste0("(",format(round(stderrs[145],3),nsmall=3),")")
df.sfa_vrs[10,2] <- paste0(format(round(model_sfa$mlParam["Zv_(Intercept)"],3),nsmall=3),
ifelse(pvals[146]<0.01,"***",
ifelse(pvals[146]<0.05,"**",
ifelse(pvals[146]<0.1,"*",""))))
df.sfa_vrs[10,3] <- paste0("(",format(round(stderrs[146],3),nsmall=3),")")
df.sfa_vrs[11,2] <- "0.942"
df.sfa_vrs[11,3] <- ""
# Set global option to produce latex output
options(knitr.table.format = "latex")
# Create table
Tab_sfa_vrs <- kable(df.sfa_vrs, booktabs = T,
row.names = FALSE,
escape = FALSE,
linesep = "",
caption = "Coefficient estimates of the Cobb-Douglas distance function for US agriculture (1960-2004) under VRS.",
label = "Tab_sfa_vrs",
col.names = c('Variable', 'Estimate',
'St. Err.')) %>%
footnote(general = "Dependent variable is -ln(crops). Estimation is based on 2160 observations. $exp(\\\\delta)$ is
the variance of the one-sided error term $u_{it}$ and $exp(\\\\phi)$ is the variance of the two-sided
error term $\\\\nu_{it}$ in equation (\\\\ref{eq:CD_frontier}).",
footnote_as_chunk = T,
threeparttable = T,
general_title = "Note:",
escape=F) %>%
kable_styling(latex_options = c("HOLD_position"))
# Print Latex file
writeLines(Tab_sfa_vrs, "Tables/Tab_sfa_vrs.tex")
# ---------------------------------- #
#### Create table for the results ####
# ---------------------------------- #
# Prepare data for the tables
data_MSFA_vrs <- data.frame(matrix(ncol = 16, nrow = 48))
colnames(data_MSFA_vrs) <- c("state",
"TFP1960", "TFP2004", "DTFP",
"MP1960", "MP2004", "DMP",
"OTE1960", "OTE2004", "DOTE",
"OSE1960", "OSE2004", "DOSE",
"SNI1960", "SNI2004", "DSNI")
data_MSFA_vrs$state <- rep(c("AL","AR","AZ","CA","CO","CT","DE","FL",
"GA","IA","ID","IL","IN","KS","KY","LA",
"MA","MD","ME","MI","MN","MO","MS","MT",
"NC","ND","NE","NH","NJ","NM","NV","NY",
"OH","OK","OR","PA","RI","SC","SD","TN",
"TX","UT","VA","VT","WA","WI","WV","WY"))
# TOTAL FACTOR PRODUCTIVITY
# TFP1960
data_MSFA_vrs$TFP1960 <- MSFA.level_vrs$TFPit[MSFA.level_vrs$year==1960]
# TFP2004
data_MSFA_vrs$TFP2004 <- MSFA.level_vrs$TFPit[MSFA.level_vrs$year==2004]
# DTFP
data_MSFA_vrs$DTFP <- (data_MSFA_vrs$TFP2004 / data_MSFA_vrs$TFP1960)
# TECHNICAL CHANGE
# MP1960
data_MSFA_vrs$MP1960 <- MSFA.level_vrs$TCit[MSFA.level_vrs$year==1960]
# MP2004
data_MSFA_vrs$MP2004 <- MSFA.level_vrs$TCit[MSFA.level_vrs$year==2004]
# DMP
data_MSFA_vrs$DMP <- (data_MSFA_vrs$MP2004 / data_MSFA_vrs$MP1960)
# OUTPUT TECHNICAL EFFICIENCY (OTE)
# OTE1960
data_MSFA_vrs$OTE1960 <- MSFA.level_vrs$OTEit[MSFA.level_vrs$year==1960]
# OTE2004
data_MSFA_vrs$OTE2004 <- MSFA.level_vrs$OTEit[MSFA.level_vrs$year==2004]
# DOTE
data_MSFA_vrs$DOTE <- (data_MSFA_vrs$OTE2004 / data_MSFA_vrs$OTE1960)
# OUTPUT SCALE EFFICIENCY (OSE)
# OSE1960
data_MSFA_vrs$OSE1960 <- MSFA.level_vrs$OSEit[MSFA.level_vrs$year==1960]
# OSE2004
data_MSFA_vrs$OSE2004 <- MSFA.level_vrs$OSEit[MSFA.level_vrs$year==2004]
# DOSE
data_MSFA_vrs$DOSE <- (data_MSFA_vrs$OSE2004 / data_MSFA_vrs$OSE1960)
# STATISTICAL NOISE INDEX (SNI)
# SNI1960
data_MSFA_vrs$SNI1960 <- MSFA.level_vrs$NCit[MSFA.level_vrs$year==1960]
# SNI2004
data_MSFA_vrs$SNI2004 <- MSFA.level_vrs$NCit[MSFA.level_vrs$year==2004]
# DSNI
data_MSFA_vrs$DSNI <- (data_MSFA_vrs$SNI2004 / data_MSFA_vrs$SNI1960)
# Add US-average as geometric mean
data_MSFA_vrs <- data_MSFA_vrs %>%
add_row(state="US48",
TFP1960=NA, TFP2004=NA, DTFP=exp(mean(log(data_MSFA_vrs$DTFP))),
MP1960=NA, MP2004=NA, DMP=exp(mean(log(data_MSFA_vrs$DMP))),
OTE1960=NA, OTE2004=NA, DOTE=exp(mean(log(data_MSFA_vrs$DOTE))),
OSE1960=NA, OSE2004=NA, DOSE=exp(mean(log(data_MSFA_vrs$DOSE))),
SNI1960=NA, SNI2004=NA, DSNI=exp(mean(log(data_MSFA_vrs$DSNI))))
# Save US-average for comparison in 03h_TFP for US_comparison.R
Summary_msfa_US_vrs <- list(data_MSFA_vrs$DTFP[data_MSFA_vrs$state=="US48"],
data_MSFA_vrs$DMP[data_MSFA_vrs$state=="US48"],
data_MSFA_vrs$DOTE[data_MSFA_vrs$state=="US48"] * data_MSFA_vrs$DOSE[data_MSFA_vrs$state=="US48"])
names(Summary_msfa_US_vrs) <- c("TFP", "TC", "TFPE")
save(Summary_msfa_US_vrs, file = "R_output/Summary_msfa_US_vrs.Rda")
# Write Table: "TFP decomposition for US agriculture (1960-2004) using the Global Malmquist index.
# Set global option to produce latex output
options(knitr.table.format = "latex", knitr.kable.NA = '')
# Create table
Tab_MSFA_US_TFPDecomp_vrs <- kable(data_MSFA_vrs, booktabs = T,
digits = 2,
row.names = FALSE,
escape = FALSE,
linesep = "",
caption = "TFP decomposition for US agriculture (1960--2004) using the M-SFA index under VRS.",
label = "Tab_MSFA_US_TFPDecomp_vrs",
col.names = c('State',
'1960', '2004', "$\\Delta$",
'1960', '2004', "$\\Delta$",
'1960', '2004', "$\\Delta$",
'1960', '2004', "$\\Delta$",
'1960', '2004', "$\\Delta$")) %>%
add_header_above(c("", "TFP" = 3, "TFP*" = 3, "OTE" = 3, "OSE" = 3, "SN" = 3)) %>%
row_spec(48, hline_after=T) %>%
kable_styling(font_size = 12,
latex_options = c("scale_down", "HOLD_position"))
# Print Latex file
writeLines(Tab_MSFA_US_TFPDecomp_vrs, "Tables/Tab_MSFA_US_TFPDecomp_vrs.tex")
# ------------------------------------ #
#### 2) Compute TFP index under CRS ####
# ------------------------------------ #
# ------------------------------- #
##### 2a) Frontier estimation #####
# ------------------------------- #
# Normalize dependent variable and input variables by intermediate inputs to impose CRS
sfa_string <- as.formula(paste0(c("-log(q_crops/x_interm)",
paste0(c("log(q_livestock/q_crops)",
"log(q_otheroutp/q_crops)",
"log(x_capital/x_interm)", "log(x_land/x_interm)",
"log(x_labor/x_interm)",
"factor(state)",
"trend:factor(region):factor(semidecade)"),
collapse = " + ")),
collapse = " ~ "))
model_sfa <- sfaR::sfacross(sfa_string, S=-1, data = USdata)
summary(model_sfa)
# for Delta method: mean and variance of parameters
estmean <- coef(model_sfa)
estvar <- model_sfa$invHessian #The covariance matrix of the parameters obtained from the ML estimation
# Estimate model as OLS to find noise component below
model_ols <- lm(sfa_string, data = USdata)
summary(model_ols)
# ------------------------------- #
##### 2b) Decompose TFP index #####
# ------------------------------- #
# Recover estimate for intermediate inputs
coef_interm <- -1 - estmean[4] - estmean[5] - estmean[6]
se_interm <- deltamethod (~ -1-x4-x5-x6, estmean, estvar)
z_interm <- coef_interm / se_interm
pval_interm <- 2*pnorm(q=abs(z_interm), lower.tail=FALSE)
# Scale elasticity
scale_elas <- -model_sfa$mlParam["log(x_capital/x_interm)"] + -model_sfa$mlParam["log(x_land/x_interm)"] +
-model_sfa$mlParam["log(x_labor/x_interm)"] + -coef_interm
# Aggregate output
USdata$Qit <- USdata$q_livestock^(model_sfa$mlParam["log(q_livestock/q_crops)"]) *
USdata$q_otheroutp^(model_sfa$mlParam["log(q_otheroutp/q_crops)"]) *
USdata$q_crops^(1 - model_sfa$mlParam["log(q_livestock/q_crops)"] - model_sfa$mlParam["log(q_otheroutp/q_crops)"])
# Aggregate input
USdata$Xit <- USdata$x_capital^(-model_sfa$mlParam["log(x_capital/x_interm)"]) *
USdata$x_land^(-model_sfa$mlParam["log(x_land/x_interm)"]) *
USdata$x_labor^(-model_sfa$mlParam["log(x_labor/x_interm)"]) *
USdata$x_interm^(-coef_interm)
# Total factor productivity
USdata$TFPit <- USdata$Qit/USdata$Xit
# Output technical efficiency
USdata$OTEit <- sfaR::efficiencies(model_sfa)[, "teBC"]
# Noise component
USdata$NCit <- exp(log(USdata$q_crops/USdata$x_interm) - as.numeric(crossprod(matrix(-model_sfa$mlParam[1:(length(model_sfa$mlParam) - 2)]),
t(model.matrix(model_ols)))) + sfaR::efficiencies(model_sfa)[, "u"]) # noise component
# Output scale component
USdata$OSEit <- USdata$x_capital^(-model_sfa$mlParam["log(x_capital/x_interm)"] * (1 - 1/scale_elas)) *
USdata$x_land^(-model_sfa$mlParam["log(x_land/x_interm)"] * (1 - 1/scale_elas)) *
USdata$x_labor^(-model_sfa$mlParam["log(x_labor/x_interm)"] * (1 - 1/scale_elas)) *
USdata$x_interm^(-coef_interm * (1 - 1/scale_elas))
# Technical change component
USdata$TCit <- exp(apply(sweep(model.matrix(~factor(state),data=USdata),MARGIN=2, STATS=c(-model_sfa$mlParam[1],-model_sfa$mlParam[stringr::str_detect(names(model_sfa$mlParam),
"state")]), FUN="*"),1, sum) +
apply(sweep(model.matrix(~-1 + trend:factor(region):factor(semidecade),
data = USdata), MARGIN = 2, STATS = -model_sfa$mlParam[stringr::str_detect(names(model_sfa$mlParam),
"trend")], FUN = "*"), 1, sum)) ## technical change component
# Summarize the results
summary(USdata[c("OTEit", "NCit", "OSEit", "TCit")])
# Subset data to only contain the index components
MSFA.level_crs <- USdata %>%
dplyr::select(year,state,Qit,Xit,TFPit,TCit,OTEit,OSEit,NCit)
# Save results for comparison in "03h_TFP for US_comparison"
save(MSFA.level_crs, file="R_output/MSFA.level_crs.Rda")
# --------------------------------- #
##### 2c) Create results tables #####
# --------------------------------- #
# ----------------------------------------- #
# Table to summarize the regression results #
# ----------------------------------------- #
df.sfa_crs <- data.frame(matrix(ncol = 3, nrow = 11))
colnames(df.sfa_crs) <- c("Variable", "Estimate", "Standard Error")
df.sfa_crs$Variable <- c("ln(livestock/Crops)",
"ln(Other output/Crops)",
"ln(Capital)",
"ln(Land)",
"ln(Labor)",
"ln(Intermediate inputs)",
"Binary variables for states",
"Regional- and semidecade- \\\\ specific time trends",
"$\\delta$",
"$\\phi$",
"Average efficiency")
estimates <- model_sfa$mlParam
stderrs <- sqrt(diag(model_sfa$invHessian))
zvals <- estimates/stderrs
pvals <- 2*pnorm(q=abs(zvals), lower.tail=FALSE)
df.sfa_crs[1,2] <- paste0(format(round(model_sfa$mlParam["log(q_livestock/q_crops)"],3),nsmall=3),
ifelse(pvals[2]<0.01,"***",
ifelse(pvals[2]<0.05,"**",
ifelse(pvals[2]<0.1,"*",""))))
df.sfa_crs[1,3] <- paste0("(",format(round(stderrs[2],3),nsmall=3),")")
df.sfa_crs[2,2] <- paste0(format(round(model_sfa$mlParam["log(q_otheroutp/q_crops)"],3),nsmall=3),
ifelse(pvals[3]<0.01,"***",
ifelse(pvals[3]<0.05,"**",
ifelse(pvals[3]<0.1,"*",""))))
df.sfa_crs[2,3] <- paste0("(",format(round(stderrs[3],3),nsmall=3),")")
df.sfa_crs[3,2] <- paste0(format(round(model_sfa$mlParam["log(x_capital/x_interm)"],3),nsmall=3),
ifelse(pvals[4]<0.01,"***",
ifelse(pvals[4]<0.05,"**",
ifelse(pvals[4]<0.1,"*",""))))
df.sfa_crs[3,3] <- paste0("(",format(round(stderrs[4],3),nsmall=3),")")
df.sfa_crs[4,2] <- paste0(format(round(model_sfa$mlParam["log(x_land/x_interm)"],3),nsmall=3),
ifelse(pvals[5]<0.01,"***",
ifelse(pvals[5]<0.05,"**",
ifelse(pvals[4]<0.1,"*",""))))
df.sfa_crs[4,3] <- paste0("(",format(round(stderrs[5],3),nsmall=3),")")
df.sfa_crs[5,2] <- paste0(format(round(model_sfa$mlParam["log(x_labor/x_interm)"],3),nsmall=3),
ifelse(pvals[6]<0.01,"***",
ifelse(pvals[6]<0.05,"**",
ifelse(pvals[4]<0.1,"*",""))))
df.sfa_crs[5,3] <- paste0("(",format(round(stderrs[6],3),nsmall=3),")")
df.sfa_crs[6,2] <- paste0(format(round(coef_interm,3),nsmall=3),
ifelse(pval_interm<0.01,"***",
ifelse(pval_interm[7]<0.05,"**",
ifelse(pval_interm[4]<0.1,"*",""))))
df.sfa_crs[6,3] <- paste0("(",format(round(se_interm,3),nsmall=3),")")
df.sfa_crs[7,2] <- "not reported"
df.sfa_crs[7,3] <- ""
df.sfa_crs[8,2] <- "not reported"
df.sfa_crs[8,3] <- ""
df.sfa_crs[9,2] <- paste0(format(round(model_sfa$mlParam["Zu_(Intercept)"],3),nsmall=3),
ifelse(pvals[144]<0.01,"***",
ifelse(pvals[144]<0.05,"**",
ifelse(pvals[144]<0.1,"*",""))))
df.sfa_crs[9,3] <- paste0("(",format(round(stderrs[144],3),nsmall=3),")")
df.sfa_crs[10,2] <- paste0(format(round(model_sfa$mlParam["Zv_(Intercept)"],3),nsmall=3),
ifelse(pvals[145]<0.01,"***",
ifelse(pvals[145]<0.05,"**",
ifelse(pvals[145]<0.1,"*",""))))
df.sfa_crs[10,3] <- paste0("(",format(round(stderrs[145],3),nsmall=3),")")
df.sfa_crs[11,2] <- "0.942"
df.sfa_crs[11,3] <- ""
# Set global option to produce latex output
options(knitr.table.format = "latex")
# Create table
Tab_sfa_crs <- kable(df.sfa_crs, booktabs = T,
row.names = FALSE,
escape = FALSE,
linesep = "",
caption = "Coefficient estimates of the Cobb-Douglas distance function for US agriculture (1960-2004) under CRS.",
label = "Tab_sfa_crs",
col.names = c('Variable', 'Estimate',
'St. Err.')) %>%
footnote(general = "Dependent variable is -ln(crops). Estimation is based on 2160 observations. $exp(\\\\delta)$ is
the variance of the one-sided error term $u_{it}$ and $exp(\\\\phi)$ is the variance of the two-sided
error term $\\\\nu_{it}$ in equation (\\\\ref{eq:CD_frontier}). The dependent variable and the input variables
have been normalized by intermediate inputs to impose constant returns to scale. The standard
error of this numeraire has been obtained using the Delta method.",
footnote_as_chunk = T,
threeparttable = T,
general_title = "Note:",
escape=F) %>%
kable_styling(latex_options = c("HOLD_position"))
# Print Latex file
writeLines(Tab_sfa_crs, "Tables/Tab_sfa_crs.tex")
# ---------------------------------- #
#### Create table for the results ####
# ---------------------------------- #
# Prepare data for the tables
data_MSFA_crs <- data.frame(matrix(ncol = 16, nrow = 48))
colnames(data_MSFA_crs) <- c("state",
"TFP1960", "TFP2004", "DTFP",
"MP1960", "MP2004", "DMP",
"OTE1960", "OTE2004", "DOTE",
"OSE1960", "OSE2004", "DOSE",
"SNI1960", "SNI2004", "DSNI")
data_MSFA_crs$state <- rep(c("AL","AR","AZ","CA","CO","CT","DE","FL",
"GA","IA","ID","IL","IN","KS","KY","LA",
"MA","MD","ME","MI","MN","MO","MS","MT",
"NC","ND","NE","NH","NJ","NM","NV","NY",
"OH","OK","OR","PA","RI","SC","SD","TN",
"TX","UT","VA","VT","WA","WI","WV","WY"))
# TOTAL FACTOR PRODUCTIVITY
# TFP1960
data_MSFA_crs$TFP1960 <- MSFA.level_crs$TFPit[MSFA.level_crs$year==1960]
# TFP2004
data_MSFA_crs$TFP2004 <- MSFA.level_crs$TFPit[MSFA.level_crs$year==2004]
# DTFP
data_MSFA_crs$DTFP <- (data_MSFA_crs$TFP2004 / data_MSFA_crs$TFP1960)
# TECHNICAL CHANGE
# MP1960
data_MSFA_crs$MP1960 <- MSFA.level_crs$TCit[MSFA.level_crs$year==1960]
# MP2004
data_MSFA_crs$MP2004 <- MSFA.level_crs$TCit[MSFA.level_crs$year==2004]
# DMP
data_MSFA_crs$DMP <- (data_MSFA_crs$MP2004 / data_MSFA_crs$MP1960)
# OUTPUT TECHNICAL EFFICIENCY (OTE)
# OTE1960
data_MSFA_crs$OTE1960 <- MSFA.level_crs$OTEit[MSFA.level_crs$year==1960]
# OTE2004
data_MSFA_crs$OTE2004 <- MSFA.level_crs$OTEit[MSFA.level_crs$year==2004]
# DOTE
data_MSFA_crs$DOTE <- (data_MSFA_crs$OTE2004 / data_MSFA_crs$OTE1960)
# OUTPUT SCALE EFFICIENCY (OSE)
# OSE1960
data_MSFA_crs$OSE1960 <- MSFA.level_crs$OSEit[MSFA.level_crs$year==1960]
# OSE2004
data_MSFA_crs$OSE2004 <- MSFA.level_crs$OSEit[MSFA.level_crs$year==2004]
# DOSE
data_MSFA_crs$DOSE <- (data_MSFA_crs$OSE2004 / data_MSFA_crs$OSE1960)
# STATISTICAL NOISE INDEX (SNI)
# SNI1960
data_MSFA_crs$SNI1960 <- MSFA.level_crs$NCit[MSFA.level_crs$year==1960]
# SNI2004
data_MSFA_crs$SNI2004 <- MSFA.level_crs$NCit[MSFA.level_crs$year==2004]
# DSNI
data_MSFA_crs$DSNI <- (data_MSFA_crs$SNI2004 / data_MSFA_crs$SNI1960)
# Add US-average as geometric mean
data_MSFA_crs <- data_MSFA_crs %>%
add_row(state="US48",
TFP1960=NA, TFP2004=NA, DTFP=exp(mean(log(data_MSFA_crs$DTFP))),
MP1960=NA, MP2004=NA, DMP=exp(mean(log(data_MSFA_crs$DMP))),
OTE1960=NA, OTE2004=NA, DOTE=exp(mean(log(data_MSFA_crs$DOTE))),
OSE1960=NA, OSE2004=NA, DOSE=exp(mean(log(data_MSFA_crs$DOSE))),
SNI1960=NA, SNI2004=NA, DSNI=exp(mean(log(data_MSFA_crs$DSNI))))
# Save US-average for comparison in 03h_TFP for US_comparison.R
Summary_msfa_US_crs <- list(data_MSFA_crs$DTFP[data_MSFA_crs$state=="US48"],
data_MSFA_crs$DMP[data_MSFA_crs$state=="US48"],
data_MSFA_crs$DOTE[data_MSFA_crs$state=="US48"] * data_MSFA_crs$DOSE[data_MSFA_crs$state=="US48"])
names(Summary_msfa_US_crs) <- c("TFP", "TC", "TFPE")
save(Summary_msfa_US_crs, file = "R_output/Summary_msfa_US_crs.Rda")
# Write Table: "TFP decomposition for US agriculture (1960-2004) using the Global Malmquist index.
# Set global option to produce latex output
options(knitr.table.format = "latex", knitr.kable.NA = '')
# Create table
Tab_MSFA_US_TFPDecomp_crs <- kable(data_MSFA_crs, booktabs = T,
digits = 2,
row.names = FALSE,
escape = FALSE,
linesep = "",
caption = "TFP decomposition for US agriculture (1960--2004) using the M-SFA index under CRS.",
label = "Tab_MSFA_US_TFPDecomp_crs",
col.names = c('State',
'1960', '2004', "$\\Delta$",
'1960', '2004', "$\\Delta$",
'1960', '2004', "$\\Delta$",
'1960', '2004', "$\\Delta$",
'1960', '2004', "$\\Delta$")) %>%
add_header_above(c("", "TFP" = 3, "TFP*" = 3, "OTE" = 3, "OSE" = 3, "SN" = 3)) %>%
row_spec(48, hline_after=T) %>%
kable_styling(font_size = 12,
latex_options = c("scale_down", "HOLD_position"))
# Print Latex file
writeLines(Tab_MSFA_US_TFPDecomp_crs, "Tables/Tab_MSFA_US_TFPDecomp_crs.tex")