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02_EMI-Inequality.rmd
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---
title: "EMI and inequality"
author: "David Garcia and Segun Aroyehun"
output: pdf_document
---
# 1: Cross-correlations between EMI and inequality
```{r, message=FALSE}
library(dplyr)
library(lmtest)
library(sandwich)
library(tseries)
library(ggplot2)
library(ggrepel)
library(stargazer)
library(car)
library(interactions)
library(modelsummary)
library(tibble)
library(modelsummary)
library(tibble)
library(stringr)
library(knitr)
library(kableExtra)
source("Functions.R")
output_path <- "output"
df <- read.csv("data/emi_congressw2v_prod_variables_public_laws.csv")
df_avg <- df %>% rowwise() %>% mutate(Avg_pol=mean(c(House_party.mean.diff.d1, Senate_party.mean.diff.d1), na.rm=T))
# Inequality data pre 1944 affected by high exemption levels: https://eml.berkeley.edu/~saez/pikettyqje.pdf
Ineq <- df_avg$share_ptinc_top1pct[df_avg$starting_year>=1944]
EMI <- df_avg$evidence_minus_intuition_score[df_avg$starting_year>=1944]
Pol <- df_avg$Avg_pol[df_avg$starting_year>=1944]
lagmax <- 10
lags <- seq(-1*lagmax, lagmax)
corrs <- crosscor(Ineq, EMI, lagmax)
plotdf <- data.frame(x=lags, y=corrs$corr, yminus = corrs$low, yplus= corrs$high)
ggplot(plotdf, aes(x=x, y=y)) +
geom_point()+ geom_vline(xintercept = 0, linetype="dotted")+ geom_hline(yintercept = 0, linetype="dotted")+
geom_errorbar(aes(ymin=yminus, ymax=yplus), width=.2) +
xlab(" (Inequality precedes) Lag [sessions] (EMI precedes) ")+
ylab("Correlation coefficient") + theme_bw()
ggsave(filename = file.path(output_path, "Ineqemi_corr.png"), width = 6.5, height = 3, dpi = 300)
ggsave(filename = file.path(output_path, "Ineqemi_corr.svg"), width = 6.5, height = 3, dpi = 300, device = "svg")
ggsave(filename = file.path(output_path, "Ineqemi_corr.pdf"), width = 6.5, height = 3, dpi = 300, device = "pdf")
corrs$lag[abs(corrs$corr)==max(abs(corrs$corr))]
cor.test(EMI, Ineq)
cor.test(lag(EMI,1), Ineq)
cor.test(lag(EMI,2), Ineq)
plotdf <- data.frame(x=lag(EMI,1), y=Ineq, year=df$starting_year[df$starting_year>=1944])
ggplot(plotdf, aes(x,y, label=year)) + geom_point(col="red") + geom_path(col="red") + geom_text_repel(direction="y",size=3) + geom_smooth() + xlab("EMI score (lagged one session)") + ylab("Inequality (top 1%)") + theme_bw()
ggsave(filename = file.path(output_path, 'emilag_ineq_corr_1944.png'), width = 7, height = 5, dpi = 300)
ggsave(filename = file.path(output_path, 'emilag_ineq_corr_1944.svg'), width = 7, height = 5, dpi = 300, device = "svg")
ggsave(filename = file.path(output_path, 'emilag_ineq_corr_1944.pdf'), width = 7, height = 5, dpi = 300, device = "pdf")
lagmax <- 10
lags <- seq(-1*lagmax, lagmax)
corrs <- crosscor(Ineq, Pol, lagmax)
corrs$lag[abs(corrs$corr)==max(abs(corrs$corr))]
plotdf <- data.frame(x=lags, y=corrs$corr, yminus = corrs$low, yplus= corrs$high)
ggplot(plotdf, aes(x=x, y=y)) +
geom_point()+ geom_vline(xintercept = 0, linetype="dotted")+ geom_hline(yintercept = 0, linetype="dotted")+
geom_errorbar(aes(ymin=yminus, ymax=yplus), width=.2) +
xlab(" (Inequality precedes) Lag [sessions] (Polarization precedes)")+
ylab("Correlation coefficient") + theme_bw()
ggsave(filename = file.path(output_path, "IneqPol_corr.png"), width = 6.5, height = 3, dpi = 300)
ggsave(filename = file.path(output_path, "IneqPol_corr.svg"), width = 6.5, height = 3, dpi = 300, device = "svg")
ggsave(filename = file.path(output_path, "IneqPol_corr.pdf"), width = 6.5, height = 3, dpi = 300, device = "pdf")
```
# 2: Regression model of Inequality with EMI
```{r, message=FALSE}
attach(df_avg)
EMIpre <- lag(EMI,1)
Polpre <- lag(Pol,1)
Ineqpre <- lag(Ineq,1)
model_ineq0 <- lm(Ineq ~ Ineqpre + Polpre)
model_ineq0_coefs <- coeftest(model_ineq0, vcov=vcovHAC(model_ineq0))
model_ineq0_coefs
model_ineq <- lm(Ineq ~ Ineqpre + Polpre + EMIpre)
vif(model_ineq)
model_ineq <- lm(Ineq ~ Ineqpre + Polpre * EMIpre)
interact_plot(model =model_ineq, pred = EMIpre, modx = Polpre, interval=TRUE)
ggsave(filename = file.path(output_path, "Interaction-Ineq.pdf"), width = 6.5, height = 5, dpi = 300, device = "pdf")
model_ineq_coefs <- coeftest(model_ineq, vcov=vcovHAC(model_ineq))
model_ineq_coefs
adf.test(residuals(model_ineq))
kpss.test(residuals(model_ineq))
jarque.bera.test(residuals(model_ineq))
stargazer(model_ineq0, model_ineq,type = "latex", digits = 2, df = F,
se=list(model_ineq0_coefs[,2], model_ineq_coefs[,2]),
p=list(model_ineq0_coefs[,4], model_ineq_coefs[,4]),
out="output/EMI-Ineq-LM.tex")
stargazer(model_ineq0, model_ineq, type = "text", digits = 2, df = F,
se=list(model_ineq0_coefs[,2], model_ineq_coefs[,2]),
p=list(model_ineq0_coefs[,4], model_ineq_coefs[,4]),
out="output/EMI-Ineq-LM.txt")
f_statistics <- c(
summary(model_ineq0)$fstatistic["value"],
summary(model_ineq)$fstatistic["value"]
)
f_df1 <- c(
summary(model_ineq0)$fstatistic["numdf"],
summary(model_ineq)$fstatistic["numdf"]
)
f_df2 <- c(
summary(model_ineq0)$fstatistic["dendf"],
summary(model_ineq)$fstatistic["dendf"]
)
# Extract and format F-statistic p-values in "p = ..." format
f_p_values <- c(
pf(f_statistics[1], f_df1[1], f_df2[1], lower.tail = FALSE),
pf(f_statistics[2], f_df1[2], f_df2[2], lower.tail = FALSE)
)
formatted_f_statistics <- sprintf("%.2f", f_statistics)
formatted_f_p_values <- sprintf("p=%s", format(f_p_values, scientific = TRUE, digits = 3))
# List of models
models <- list(
"INEQ" = model_ineq0,
"INEQ_INT" = model_ineq
)
# Generate LaTeX table
f <- function(x) format(x, digits = 3, nsmall = 2)
row <- tribble(~term, ~m1, ~m2,
'F Statistic', formatted_f_statistics[1], formatted_f_statistics[2],
'F Statistic p value', formatted_f_p_values[1], formatted_f_p_values[2]
)
attr(row, 'position') <- 14
modelsummary(
models,
output = "output/EMI-Ineq-LM_summary.html", # Change to "html" for HTML or "docx" for Word
estimate = "{estimate} [{conf.low}, {conf.high}]",
statistic = "p={p.value}", conf_level=0.95, fmt=f,
notes = "Values in square brackets represent 95% confidence intervals.",
add_rows=row, gof_omit="AIC|BIC|RMSE|Log.Lik.",
vcov = function(model) vcovHAC(model)
)
modelsummary(
models,
output = "output/EMI-Ineq-LM_summary.tex", # Change to "html" for HTML or "docx" for Word
estimate = "{estimate} [{conf.low}, {conf.high}]",
statistic = "p={p.value}", conf_level=0.95, fmt=f,
notes = "Values in square brackets represent 95% confidence intervals.",
add_rows=row, gof_omit="AIC|BIC|RMSE|Log.Lik.",
vcov = function(model) vcovHAC(model)
)
```
```{r, message=FALSE}
Pol8 <- lag(Pol,8)
#Alternative specification: lag 8 for polarization
model_ineq8 <- lm(Ineq ~ EMIpre + Pol8 + Ineqpre, data = df_avg)
vif(model_ineq8)
model_ineq8 <- lm(Ineq ~ EMIpre * Pol8 + Ineqpre, data = df_avg)
interact_plot(model =model_ineq8, pred = EMIpre, modx = Pol8, interval=TRUE)
ggsave(filename = file.path(output_path, "Interaction-Ineq8.pdf"), width = 6.5, height = 5, dpi = 300, device = "pdf")
model_ineq8_coefs <- coeftest(model_ineq8, vcov=vcovHAC(model_ineq8))
model_ineq8_coefs
adf.test(residuals(model_ineq8))
kpss.test(residuals(model_ineq8))
jarque.bera.test(residuals(model_ineq8))
#Alternative specification: Gini index
Gini <- df_avg$income_gini[df_avg$starting_year>=1944]
Ginipre <- lag(Gini,1)
model_gini0 <- lm(Gini ~ Ginipre)
model_gini0_coefs <- coeftest(model_gini0, vcov=vcovHAC(model_gini0))
model_gini0_coefs
model_gini <- lm(Gini ~ EMIpre + Polpre + Ginipre, data = df_avg)
vif(model_gini)
model_gini <- lm(Gini ~ EMIpre * Polpre + Ginipre, data = df_avg)
interact_plot(model =model_gini, pred = EMIpre, modx = Polpre, interval=TRUE)
ggsave(filename = file.path(output_path, "Interaction-Ineq-Gini.pdf"), width = 6.5, height = 5, dpi = 300, device = "pdf")
model_gini_coefs <- coeftest(model_gini, vcov=vcovHAC(model_gini))
model_gini_coefs
adf.test(residuals(model_gini))
kpss.test(residuals(model_gini))
jarque.bera.test(residuals(model_gini))
# Alternative specification: data since 1912
Ineq <- df_avg$share_ptinc_top1pct[df_avg$starting_year>=1912]
EMI <- df_avg$evidence_minus_intuition_score[df_avg$starting_year>=1912]
Pol <- df_avg$Avg_pol[df_avg$starting_year>=1912]
EMIpre <- lag(EMI,1)
Polpre <- lag(Pol,1)
Ineqpre <- lag(Ineq,1)
model_ineq0 <- lm(Ineq ~ Ineqpre)
model_ineq0_coefs <- coeftest(model_ineq0, vcov=vcovHAC(model_ineq0))
model_ineq0_coefs
model_ineq <- lm(Ineq ~ Ineqpre + Polpre + EMIpre)
vif(model_ineq)
model_ineq <- lm(Ineq ~ Ineqpre + Polpre * EMIpre)
interact_plot(model =model_ineq, pred = EMIpre, modx = Polpre, interval=TRUE)
ggsave(filename = file.path(output_path, "Interaction-Ineq-1912.pdf"), width = 6.5, height = 5, dpi = 300, device = "pdf")
model_ineq_coefs <- coeftest(model_ineq, vcov=vcovHAC(model_ineq))
model_ineq_coefs
adf.test(residuals(model_ineq))
kpss.test(residuals(model_ineq))
jarque.bera.test(residuals(model_ineq))
stargazer(model_gini, model_ineq, model_ineq8, type = "latex", digits = 2, df = F,
se=list(model_gini_coefs[,2], model_ineq_coefs[,2], model_ineq8_coefs[,2]),
p=list(model_gini_coefs[,4], model_ineq_coefs[,4], model_ineq8_coefs[,4]),
out="output/EMI-Ineq-extra-LM.tex")
stargazer(model_gini, model_ineq, model_ineq8, type = "text", digits = 2, df = F,
se=list(model_gini_coefs[,2], model_ineq_coefs[,2], model_ineq8_coefs[,2]),
p=list(model_gini_coefs[,4], model_ineq_coefs[,4], model_ineq8_coefs[,4]),
out="output/EMI-Ineq-extra-LM.txt")
f_statistics <- c(
summary(model_gini)$fstatistic["value"],
summary(model_ineq)$fstatistic["value"],
summary(model_ineq8)$fstatistic["value"]
)
f_df1 <- c(
summary(model_gini)$fstatistic["numdf"],
summary(model_ineq)$fstatistic["numdf"],
summary(model_ineq8)$fstatistic["numdf"]
)
f_df2 <- c(
summary(model_gini)$fstatistic["dendf"],
summary(model_ineq)$fstatistic["dendf"],
summary(model_ineq8)$fstatistic["dendf"]
)
# Extract and format F-statistic p-values in "p = ..." format
f_p_values <- c(
pf(f_statistics[1], f_df1[1], f_df2[1], lower.tail = FALSE),
pf(f_statistics[2], f_df1[2], f_df2[2], lower.tail = FALSE),
pf(f_statistics[3], f_df1[3], f_df2[3], lower.tail = FALSE)
)
formatted_f_statistics <- sprintf("%.2f", f_statistics)
formatted_f_p_values <- sprintf("p=%s", format(f_p_values, scientific = TRUE, digits = 3))
# List of models
models <- list(
"INEQ_GINI" = model_gini,
"INEQ_1912" = model_ineq,
"INEQ_1912_POL8" = model_ineq8
)
# Generate LaTeX table
f <- function(x) format(x, digits = 3, nsmall = 2)
row <- tribble(~term, ~m1, ~m2, ~m3,
'F Statistic', formatted_f_statistics[1], formatted_f_statistics[2], formatted_f_statistics[3],
'F Statistic p value', formatted_f_p_values[1], formatted_f_p_values[2], formatted_f_p_values[3]
)
attr(row, 'position') <- 22
modelsummary(
models,
output = "output/EMI-Ineq-extra-LM_summary.html", # Change to "html" for HTML or "docx" for Word
estimate = "{estimate} [{conf.low}, {conf.high}]",
statistic = "p={p.value}", conf_level=0.95, fmt=f,
notes = "Values in square brackets represent 95% confidence intervals.",
add_rows=row, gof_omit="AIC|BIC|RMSE|Log.Lik.",
vcov = function(model) vcovHAC(model)
)
modelsummary(
models,
output = "output/EMI-Ineq-extra-LM_summary.tex", # Change to "html" for HTML or "docx" for Word
estimate = "{estimate} [{conf.low}, {conf.high}]",
statistic = "p={p.value}", conf_level=0.95, fmt=f,
notes = "Values in square brackets represent 95% confidence intervals.",
add_rows=row, gof_omit="AIC|BIC|RMSE|Log.Lik.",
vcov = function(model) vcovHAC(model)
)
set.seed(1985)
library(boot)
bootf <- function(df, indices)
{
model_ineq <- lm(Ineq ~ Ineqpre + Polpre * EMIpre, data=df, subset=indices)
return(model_ineq$coefficients[4])
}
boots <- boot(df_avg, bootf, R=10000)
quantile(boots$t, p=c(0.025, 0.5, 0.975)) # to verify, we perform a bootstrapping test, hight part of CI still negative
```