Purpose

The purpose of this script is to show the steps and decisions taken to complete PS4 for ECON 8100.

library(dplyr)
library(tidyverse)
library(data.table)
library(ggplot2)
library(kableExtra)
library(xtable)
library(AER)
library(haven)
library(stargazer)

# Load the STATA data

data <- read_dta("medicarePS.dta")

data <- data %>%
  mutate(
    one_or_more_policies = ifelse(Ninsurance >= 1, 1, 0),
    two_or_more_policies = ifelse(Ninsurance >= 2, 1, 0),
    high_school_higher = ifelse(Education >= 2, 1, 0)
  )

avg <- data %>%
  group_by(Age) %>%
  summarize(
    avg_outcome = mean(DelayCare, na.rm = TRUE),
    avg_ninsurance = mean(Ninsurance, na.rm = TRUE),
    avg_one_or_more_policies = mean(one_or_more_policies, na.rm = TRUE),
    avg_two_or_more_policies = mean(two_or_more_policies, na.rm = TRUE),
    avg_hshigher = mean(high_school_higher, na.rm = TRUE),
    avg_minority = mean(Minority, na.rm = TRUE)
  )

Outcome

outcome_plot <- ggplot(avg, aes(x = Age, y = avg_outcome)) +
  geom_point() +
  geom_vline(xintercept = 65, linetype = "dashed", color = "red") +
  labs(
    title = "Proportion of Delay Care by Age",
    x = "Age",
    y = "Proportion of Delay Care"
  )+
  theme_minimal()

print(outcome_plot)

# export 
ggsave("outcome_plot.png", plot = outcome_plot, width = 6, height = 4, units = "in", dpi = 300)

First Stages

first_stage_1 <- ggplot(avg)  +
  geom_point(aes(x = Age, y = avg_ninsurance)) +
  geom_vline(xintercept = 65, linetype = "dashed", color = "red") +
  labs(
    title = "Number of Insurance by Age",
    x = "Age",
    y = "Average Number of Insurance Policy"
  )+
  theme_minimal()

print(first_stage_1)

# export

ggsave("first_stage_1.png", plot = first_stage_1, width = 6, height = 4, units = "in", dpi = 300)

first_stage2 <- ggplot(avg) +
  geom_point(aes(x = Age, y = avg_one_or_more_policies, color = "One or More Policies")) +
  geom_point(aes(x = Age, y = avg_two_or_more_policies, color = "Two or More Policies")) +
  geom_vline(xintercept = 65, linetype = "dashed", color = "red") +
  labs(
    title = "Insurance Policies by Age",
    x = "Age",
    y = "Proportion",
    color = ""
  ) +
  theme_minimal()

print(first_stage2)

# export

ggsave("first_stage2.png", plot = first_stage2, width = 6, height = 4, units = "in", dpi = 300)

Validity

valid_plot1 <- ggplot(avg)+
  geom_point(aes(x = Age, y = avg_hshigher, color = "High school or Higher"))+
  geom_point(aes(x = Age, y = avg_minority, color = "Minority"))+
  geom_vline(xintercept = 65, linetype = "dashed", color = "red") +
  labs(
    title = "Covariates by Age",
    x = "Age",
    y = "Proportion",
    color = ""
  ) +
  theme_minimal()

print(valid_plot1)

# export

ggsave("valid_plot1.png", plot = valid_plot1, width = 6, height = 4, units = "in", dpi = 300)

2SLS

data_2sls <- data %>%
  mutate(
    Z = ifelse(Age >= 65, 1, 0),        # Indicator for age >= 65
    AgeZ = Age * Z                     # Interaction term
  )

# Triangular Kernel Function 
triangular_kernel <- function(distance, bandwidth) {
  weight <- 1 - abs(distance / bandwidth)
  weight[weight < 0] <- 0
  return(weight)
}

# Compute weights
threshold <- 65
bandwidth <- 5
data_2sls <- data_2sls %>%
  mutate(
    distance = Age - threshold,
    kernel_weight = triangular_kernel(distance, bandwidth)
  )

data_2sls <- data_2sls %>%
  filter(Age >= 60 & Age <= 70)

model <- ivreg(DelayCare ~ Ninsurance + Age + AgeZ | Z + Age + AgeZ, 
               data = data_2sls, 
               weights = kernel_weight)

summary(model, robust = TRUE)

## 
## Call:
## ivreg(formula = DelayCare ~ Ninsurance + Age + AgeZ | Z + Age + 
##     AgeZ, data = data_2sls, weights = kernel_weight)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.14529 -0.06163 -0.03621 -0.01874  0.96012 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  0.3673161  0.0945004   3.887 0.000102 ***
## Ninsurance  -0.0527078  0.0795669  -0.662 0.507699    
## Age         -0.0037655  0.0023980  -1.570 0.116369    
## AgeZ         0.0003498  0.0006307   0.555 0.579196    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.177 on 29660 degrees of freedom
## Multiple R-Squared: 0.02028, Adjusted R-squared: -0.03198 
## Wald test: 24.47 on 3 and 29660 DF,  p-value: 8.305e-16

# export to Latex

stargazer(model, type = "latex", title = "2SLS Regression Results", 
          align = TRUE, digits =3, out = "2SLS_results.tex")

## 
## % Table created by stargazer v.5.2.3 by Marek Hlavac, Social Policy Institute. E-mail: marek.hlavac at gmail.com
## % Date and time: Fri, Dec 06, 2024 - 11:55:29 AM
## % Requires LaTeX packages: dcolumn 
## \begin{table}[!htbp] \centering 
##   \caption{2SLS Regression Results} 
##   \label{} 
## \begin{tabular}{@{\extracolsep{5pt}}lD{.}{.}{-3} } 
## \\[-1.8ex]\hline 
## \hline \\[-1.8ex] 
##  & \multicolumn{1}{c}{\textit{Dependent variable:}} \\ 
## \cline{2-2} 
## \\[-1.8ex] & \multicolumn{1}{c}{DelayCare} \\ 
## \hline \\[-1.8ex] 
##  Ninsurance & -0.053 \\ 
##   & (0.080) \\ 
##   & \\ 
##  Age & -0.004 \\ 
##   & (0.002) \\ 
##   & \\ 
##  AgeZ & 0.0003 \\ 
##   & (0.001) \\ 
##   & \\ 
##  Constant & 0.367^{***} \\ 
##   & (0.095) \\ 
##   & \\ 
## \hline \\[-1.8ex] 
## Observations & \multicolumn{1}{c}{29,664} \\ 
## R$^{2}$ & \multicolumn{1}{c}{0.020} \\ 
## Adjusted R$^{2}$ & \multicolumn{1}{c}{-0.032} \\ 
## Residual Std. Error & \multicolumn{1}{c}{0.177 (df = 29660)} \\ 
## \hline 
## \hline \\[-1.8ex] 
## \textit{Note:}  & \multicolumn{1}{r}{$^{*}$p$<$0.1; $^{**}$p$<$0.05; $^{***}$p$<$0.01} \\ 
## \end{tabular} 
## \end{table}

Changing h

# Triangular kernel function
triangular_kernel <- function(distance, bandwidth) {
  weight <- 1 - abs(distance / bandwidth)
  weight[weight < 0] <- 0
  return(weight)
}

# Update kernel weights for h = 3
data_h3 <- data_2sls %>%
  mutate(
    kernel_weight_h3 = triangular_kernel(distance, 3)
  ) %>%
  filter(abs(distance) <= 3)  # Filter for the bandwidth

# Update kernel weights for h = 7
data_h7 <- data_2sls %>%
  mutate(
    kernel_weight_h7 = triangular_kernel(distance, 7)
  ) %>%
  filter(abs(distance) <= 7)  # Filter for the bandwidth

# 2SLS regression for h = 3
model_h3 <- ivreg(DelayCare ~ Ninsurance + Age + AgeZ | Z + Age + AgeZ, 
                  data = data_h3, 
                  weights = kernel_weight_h3)





# 2SLS regression for h = 7
model_h7 <- ivreg(DelayCare ~ Ninsurance + Age + AgeZ | Z + Age + AgeZ, 
                  data = data_h7, 
                  weights = kernel_weight_h7)

stargazer(model_h3, model_h7, 
          type = "latex", 
          title = "2SLS Regression Results for Different Bandwidths", 
          align = TRUE, 
          digits = 3, 
          column.labels = c("H = 3", "H = 7"), 
          out = "2SLS_combined_results.tex")

## 
## % Table created by stargazer v.5.2.3 by Marek Hlavac, Social Policy Institute. E-mail: marek.hlavac at gmail.com
## % Date and time: Fri, Dec 06, 2024 - 11:55:30 AM
## % Requires LaTeX packages: dcolumn 
## \begin{table}[!htbp] \centering 
##   \caption{2SLS Regression Results for Different Bandwidths} 
##   \label{} 
## \begin{tabular}{@{\extracolsep{5pt}}lD{.}{.}{-3} D{.}{.}{-3} } 
## \\[-1.8ex]\hline 
## \hline \\[-1.8ex] 
##  & \multicolumn{2}{c}{\textit{Dependent variable:}} \\ 
## \cline{2-3} 
## \\[-1.8ex] & \multicolumn{2}{c}{DelayCare} \\ 
##  & \multicolumn{1}{c}{H = 3} & \multicolumn{1}{c}{H = 7} \\ 
## \\[-1.8ex] & \multicolumn{1}{c}{(1)} & \multicolumn{1}{c}{(2)}\\ 
## \hline \\[-1.8ex] 
##  Ninsurance & -0.105 & -0.106 \\ 
##   & (0.081) & (0.091) \\ 
##   & & \\ 
##  Age & -0.002 & -0.002 \\ 
##   & (0.005) & (0.002) \\ 
##   & & \\ 
##  AgeZ & 0.001 & 0.001 \\ 
##   & (0.001) & (0.001) \\ 
##   & & \\ 
##  Constant & 0.313 & 0.323^{***} \\ 
##   & (0.238) & (0.069) \\ 
##   & & \\ 
## \hline \\[-1.8ex] 
## Observations & \multicolumn{1}{c}{17,246} & \multicolumn{1}{c}{31,243} \\ 
## R$^{2}$ & \multicolumn{1}{c}{0.007} & \multicolumn{1}{c}{0.018} \\ 
## Adjusted R$^{2}$ & \multicolumn{1}{c}{-0.082} & \multicolumn{1}{c}{0.018} \\ 
## Residual Std. Error & \multicolumn{1}{c}{0.181 (df = 17242)} & \multicolumn{1}{c}{0.197 (df = 31239)} \\ 
## \hline 
## \hline \\[-1.8ex] 
## \textit{Note:}  & \multicolumn{2}{r}{$^{*}$p$<$0.1; $^{**}$p$<$0.05; $^{***}$p$<$0.01} \\ 
## \end{tabular} 
## \end{table}

Replicate Figure 2 in Caetano, Caetano, Escanciano (2023)

avg_white<- data %>%
  filter(Minority==0) %>%
  group_by(Age) %>%
  summarize(
    avg_outcome = mean(DelayCare, na.rm = TRUE),
    avg_ninsurance = mean(Ninsurance, na.rm = TRUE),
    avg_one_or_more_policies = mean(one_or_more_policies, na.rm = TRUE),
    avg_two_or_more_policies = mean(two_or_more_policies, na.rm = TRUE)
  )

cce_fig2a <- ggplot(avg_white) +
  geom_point(aes(x = Age, y = avg_one_or_more_policies, color = "One or More Policies")) +
  geom_point(aes(x = Age, y = avg_two_or_more_policies, color = "Two or More Policies")) +
  geom_vline(xintercept = 65, linetype = "dashed", color = "red") +
  labs(
    title = "White",
    x = "Age",
    y = "Proportion",
    color = ""
  ) +
  theme_minimal()

print(cce_fig2a)

# export

ggsave("cce_fig2a.png", plot = cce_fig2a, width = 6, height = 4, units = "in", dpi = 300)

avg_minor<- data %>%
  filter(Minority==1) %>%
  group_by(Age) %>%
  summarize(
    avg_outcome = mean(DelayCare, na.rm = TRUE),
    avg_ninsurance = mean(Ninsurance, na.rm = TRUE),
    avg_one_or_more_policies = mean(one_or_more_policies, na.rm = TRUE),
    avg_two_or_more_policies = mean(two_or_more_policies, na.rm = TRUE)
  )

cce_fig2b <- ggplot(avg_minor) +
  geom_point(aes(x = Age, y = avg_one_or_more_policies, color = "One or More Policies")) +
  geom_point(aes(x = Age, y = avg_two_or_more_policies, color = "Two or More Policies")) +
  geom_vline(xintercept = 65, linetype = "dashed", color = "red") +
  labs(
    title = "Minority",
    x = "Age",
    y = "Proportion",
    color = ""
  ) +
  theme_minimal()

print(cce_fig2b)

# export

ggsave("cce_fig2b.png", plot = cce_fig2b, width = 6, height = 4, units = "in", dpi = 300)

outcome_minor <- ggplot(avg_minor) +
  geom_point(aes(x = Age, y = avg_outcome)) +
  geom_vline(xintercept = 65, linetype = "dashed", color = "red") +
  labs(
    title = "Minority",
    x = "Age",
    y = "Proportion of Delay Care",
    color = ""
  ) +
  theme_minimal()

print(outcome_minor)

# export

ggsave("outcome_minor.png", plot = outcome_minor, width = 6, height = 4, units = "in", dpi = 300)

outcome_white <- ggplot(avg_white) +
  geom_point(aes(x = Age, y = avg_outcome)) +
  geom_vline(xintercept = 65, linetype = "dashed", color = "red") +
  labs(
    title = "White",
    x = "Age",
    y = "Proportion of Delay Care",
    color = ""
  ) +
  theme_minimal()

print(outcome_white)

# export

ggsave("outcome_white.png", plot = outcome_white, width = 6, height = 4, units = "in", dpi = 300)

data <- data %>% 
 mutate(Z = ifelse(Age >= 65, 1, 0),
    AgeMin = Age * Minority,          # Interaction between age and minority status
    AgeZ = Age * Z,                   # Interaction between age and Z
    MinZ = Minority * Z,              # Interaction between minority and Z
    AgeMinZ = Age * Minority * Z,    # Interaction between age, minority, and Z
    Oneins = one_or_more_policies,
    Twoins = two_or_more_policies
  )

# Define the triangular kernel function
triangular_kernel <- function(distance, bandwidth) {
  weight <- 1 - abs(distance / bandwidth)
  weight[weight < 0] <- 0
  return(weight)
}

# Calculate distance from the threshold and restrict observations
bandwidth <- 5
data <- data %>%
  mutate(
    distance = Age - 65,  # Distance from the threshold (age 65)
    kernel_weight = triangular_kernel(distance, bandwidth)
  ) %>%
  filter(abs(distance) <= bandwidth)  # Restrict to the bandwidth

# 2SLS regression
model_2sls_update <- ivreg(
  DelayCare ~ Oneins + Twoins + Age + AgeZ + Minority + MinZ + AgeMin + AgeMinZ |
    Z + MinZ + Age + AgeZ + Minority + AgeMin + AgeMinZ,
  data = data,
  weights = kernel_weight
)

# Summary with robust standard errors
summary(model_2sls_update, robust = TRUE)

## 
## Call:
## ivreg(formula = DelayCare ~ Oneins + Twoins + Age + AgeZ + Minority + 
##     MinZ + AgeMin + AgeMinZ | Z + MinZ + Age + AgeZ + Minority + 
##     AgeMin + AgeMinZ, data = data, weights = kernel_weight)
## 
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -0.230606 -0.111919 -0.034683  0.002359  1.351753 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)  
## (Intercept) -0.197892   0.388638  -0.509   0.6106  
## Oneins       0.516990   0.338698   1.526   0.1269  
## Twoins      -0.195697   0.140815  -1.390   0.1646  
## Age         -0.002919   0.003308  -0.882   0.3776  
## AgeZ         0.001049   0.001021   1.027   0.3044  
## Minority     0.008962   0.247767   0.036   0.9711  
## MinZ        -0.121250   0.055348  -2.191   0.0285 *
## AgeMin       0.001506   0.003574   0.421   0.6735  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.2201 on 29656 degrees of freedom
## Multiple R-Squared: -0.5145, Adjusted R-squared: -0.5955 
## Wald test: 10.74 on 7 and 29656 DF,  p-value: 1.36e-13

#
stargazer(model_2sls_update, type = "latex", title = "2SLS Regression Results", 
          align = TRUE, digits =3, out = "2SLS_results_update.tex")

## 
## % Table created by stargazer v.5.2.3 by Marek Hlavac, Social Policy Institute. E-mail: marek.hlavac at gmail.com
## % Date and time: Fri, Dec 06, 2024 - 11:55:33 AM
## % Requires LaTeX packages: dcolumn 
## \begin{table}[!htbp] \centering 
##   \caption{2SLS Regression Results} 
##   \label{} 
## \begin{tabular}{@{\extracolsep{5pt}}lD{.}{.}{-3} } 
## \\[-1.8ex]\hline 
## \hline \\[-1.8ex] 
##  & \multicolumn{1}{c}{\textit{Dependent variable:}} \\ 
## \cline{2-2} 
## \\[-1.8ex] & \multicolumn{1}{c}{DelayCare} \\ 
## \hline \\[-1.8ex] 
##  Oneins & 0.517 \\ 
##   & (0.339) \\ 
##   & \\ 
##  Twoins & -0.196 \\ 
##   & (0.141) \\ 
##   & \\ 
##  Age & -0.003 \\ 
##   & (0.003) \\ 
##   & \\ 
##  AgeZ & 0.001 \\ 
##   & (0.001) \\ 
##   & \\ 
##  Minority & 0.009 \\ 
##   & (0.248) \\ 
##   & \\ 
##  MinZ & -0.121^{**} \\ 
##   & (0.055) \\ 
##   & \\ 
##  AgeMin & 0.002 \\ 
##   & (0.004) \\ 
##   & \\ 
##  AgeMinZ &  \\ 
##   &  \\ 
##   & \\ 
##  Constant & -0.198 \\ 
##   & (0.389) \\ 
##   & \\ 
## \hline \\[-1.8ex] 
## Observations & \multicolumn{1}{c}{29,664} \\ 
## R$^{2}$ & \multicolumn{1}{c}{-0.515} \\ 
## Adjusted R$^{2}$ & \multicolumn{1}{c}{-0.596} \\ 
## Residual Std. Error & \multicolumn{1}{c}{0.220 (df = 29656)} \\ 
## \hline 
## \hline \\[-1.8ex] 
## \textit{Note:}  & \multicolumn{1}{r}{$^{*}$p$<$0.1; $^{**}$p$<$0.05; $^{***}$p$<$0.01} \\ 
## \end{tabular} 
## \end{table}

data <- data %>%
  mutate(
    Q1 = ifelse(Minority == 0 & Education == 2, 1, 0),  # White High School
    Q2 = ifelse(Minority == 0 & Education == 3, 1, 0),     # White College
    Q3 = ifelse(Minority == 1 & Education == 3, 1, 0),  # Minority High School
    Q4 = ifelse(Minority == 1 & Education == 2, 1, 0)      # Minority College
  )

# Create interaction variables
data <- data %>%
  mutate(
    AgeQ1 = Age * Q1,
    AgeQ2 = Age * Q2,
    AgeQ3 = Age * Q3,
    AgeQ4 = Age * Q4,
    AgeZ = Age * Z,
    Q1Z = Q1 * Z,
    Q2Z = Q2 * Z,
    Q3Z = Q3 * Z,
    Q4Z = Q4 * Z,
    AgeQ1Z = Age * Q1 * Z,
    AgeQ2Z = Age * Q2 * Z,
    AgeQ3Z = Age * Q3 * Z,
    AgeQ4Z = Age * Q4 * Z
  )

# Define triangular kernel and restrict observations
bandwidth <- 5
data <- data %>%
  mutate(
    distance = Age - 65,  # Distance from the threshold
    kernel_weight = triangular_kernel(distance, bandwidth)
  ) %>%
  filter(abs(distance) <= bandwidth)  # Filter within bandwidth

# Run 2SLS regression
model_2sls_last <- ivreg(
  DelayCare ~ Oneins + Twoins + Age + AgeZ + Q1 + Q2 + Q3 + Q4 + AgeQ1 + AgeQ2 + AgeQ3 + AgeQ4 + AgeQ1Z + AgeQ2Z + AgeQ3Z + AgeQ4Z |
    Z + Q1Z + Q2Z + Q3Z + Q4Z + AgeZ + AgeQ1Z + AgeQ2Z + AgeQ3Z + AgeQ4Z,
  data = data,
  weights = kernel_weight
)
# Summary with robust standard errors
summary(model_2sls_last, robust = TRUE)

## 
## Call:
## ivreg(formula = DelayCare ~ Oneins + Twoins + Age + AgeZ + Q1 + 
##     Q2 + Q3 + Q4 + AgeQ1 + AgeQ2 + AgeQ3 + AgeQ4 + AgeQ1Z + AgeQ2Z + 
##     AgeQ3Z + AgeQ4Z | Z + Q1Z + Q2Z + Q3Z + Q4Z + AgeZ + AgeQ1Z + 
##     AgeQ2Z + AgeQ3Z + AgeQ4Z, data = data, weights = kernel_weight)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.43420 -0.11499  0.04829  0.15160  1.23941 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)
## (Intercept)  1.275908   1.545646   0.825    0.409
## Oneins      -1.655815   3.179767  -0.521    0.603
## Twoins       0.426839   0.682997   0.625    0.532
## Age          0.002727   0.022959   0.119    0.905
## AgeZ        -0.000523   0.002200  -0.238    0.812
## Q1           1.819503   2.869902   0.634    0.526
## Q2           1.544483   2.554145   0.605    0.545
## Q3          -0.002750   0.039953  -0.069    0.945
## Q4           0.001130   0.067207   0.017    0.987
## AgeQ1       -0.027807   0.042616  -0.653    0.514
## AgeQ2       -0.023741   0.037828  -0.628    0.530
## 
## Residual standard error: 0.336 on 29653 degrees of freedom
## Multiple R-Squared: -2.529,  Adjusted R-squared: -2.718 
## Wald test: 3.351 on 10 and 29653 DF,  p-value: 0.0002249

# Export to Latex
stargazer(model_2sls_last, type = "latex", title = "2SLS Regression Results", 
          align = TRUE, digits =3, out = "2SLS_results_last.tex")

## 
## % Table created by stargazer v.5.2.3 by Marek Hlavac, Social Policy Institute. E-mail: marek.hlavac at gmail.com
## % Date and time: Fri, Dec 06, 2024 - 11:55:34 AM
## % Requires LaTeX packages: dcolumn 
## \begin{table}[!htbp] \centering 
##   \caption{2SLS Regression Results} 
##   \label{} 
## \begin{tabular}{@{\extracolsep{5pt}}lD{.}{.}{-3} } 
## \\[-1.8ex]\hline 
## \hline \\[-1.8ex] 
##  & \multicolumn{1}{c}{\textit{Dependent variable:}} \\ 
## \cline{2-2} 
## \\[-1.8ex] & \multicolumn{1}{c}{DelayCare} \\ 
## \hline \\[-1.8ex] 
##  Oneins & -1.656 \\ 
##   & (3.180) \\ 
##   & \\ 
##  Twoins & 0.427 \\ 
##   & (0.683) \\ 
##   & \\ 
##  Age & 0.003 \\ 
##   & (0.023) \\ 
##   & \\ 
##  AgeZ & -0.001 \\ 
##   & (0.002) \\ 
##   & \\ 
##  Q1 & 1.820 \\ 
##   & (2.870) \\ 
##   & \\ 
##  Q2 & 1.544 \\ 
##   & (2.554) \\ 
##   & \\ 
##  Q3 & -0.003 \\ 
##   & (0.040) \\ 
##   & \\ 
##  Q4 & 0.001 \\ 
##   & (0.067) \\ 
##   & \\ 
##  AgeQ1 & -0.028 \\ 
##   & (0.043) \\ 
##   & \\ 
##  AgeQ2 & -0.024 \\ 
##   & (0.038) \\ 
##   & \\ 
##  AgeQ3 &  \\ 
##   &  \\ 
##   & \\ 
##  AgeQ4 &  \\ 
##   &  \\ 
##   & \\ 
##  AgeQ1Z &  \\ 
##   &  \\ 
##   & \\ 
##  AgeQ2Z &  \\ 
##   &  \\ 
##   & \\ 
##  AgeQ3Z &  \\ 
##   &  \\ 
##   & \\ 
##  AgeQ4Z &  \\ 
##   &  \\ 
##   & \\ 
##  Constant & 1.276 \\ 
##   & (1.546) \\ 
##   & \\ 
## \hline \\[-1.8ex] 
## Observations & \multicolumn{1}{c}{29,664} \\ 
## R$^{2}$ & \multicolumn{1}{c}{-2.529} \\ 
## Adjusted R$^{2}$ & \multicolumn{1}{c}{-2.718} \\ 
## Residual Std. Error & \multicolumn{1}{c}{0.336 (df = 29653)} \\ 
## \hline 
## \hline \\[-1.8ex] 
## \textit{Note:}  & \multicolumn{1}{r}{$^{*}$p$<$0.1; $^{**}$p$<$0.05; $^{***}$p$<$0.01} \\ 
## \end{tabular} 
## \end{table}

ECON 8100 HW4

Kiet Le

2024-12-05

Purpose

Outcome

First Stages

Validity

2SLS

Changing h

Replicate Figure 2 in Caetano, Caetano, Escanciano (2023)