28.3 Sample
Sample can be relative small
(Wiles, Morgan, and Rego 2012) 572 acquisition announcements, 308 disposal announcements
Can range from 71 (Markovitch and Golder 2008) to 3552 (Borah and Tellis 2014)
28.3.1 Confounders
- Avoid confounding events: earnings announcements, key executive changes, unexpected stock buybacks, changes in dividends within the two-trading day window surrounding the event, mergers and acquisitions, spin-offers, stock splits, management changes, joint ventures, unexpected dividend, IPO, debt defaults, dividend cancellations (McWilliams and Siegel 1997)
According to (Fornell et al. 2006), need to control:
one-day event period = day when Wall Street Journal publish ACSI announcement.
5 days before and after event to rule out other news (PR Newswires, Dow Jones, Business Wires)
M&A, Spin-offs, stock splits
CEO or CFO changes,
Layoffs, restructurings, earnings announcements, lawsuits
Capital IQ - Key Developments: covers almost all important events so you don’t have to search on news.
(A. Sorescu, Warren, and Ertekin 2017) examine confounding events in the short-term windows:
From RavenPack, 3982 US publicly traded firms, with all the press releases (2000-2013)
3-day window around event dates
The difference between a sample with full observations and a sample without confounded events is negligible (non-significant).
Conclusion: excluding confounded observations may be unnecessary for short-term event studies.
Biases can stem from researchers pick and choose events to exclude
As time progresses, more and more events you need to exclude which can be infeasible.
To further illustrate this point, let’s do a quick simulation exercise
In this example, we will explore three types of events:
Focal events
Correlated events (i.e., events correlated with the focal events; the presence of correlated events can follow the presence of the focal event)
Uncorrelated events (i.e., events with dates that might randomly coincide with the focal events, but are not correlated with them).
We have the ability to control the strength of correlation between focal and correlated events in this study, as well as the number of unrelated events we wish to examine.
Let’s examine the implications of including and excluding correlated and uncorrelated events on the estimates of our focal events.
# Load required libraries
library(dplyr)
library(ggplot2)
library(tidyr)
library(tidyverse)
# Parameters
n <- 100000 # Number of observations
n_focal <- round(n * 0.2) # Number of focal events
overlap_correlated <- 0.5 # Overlapping percentage between focal and correlated events
# Function to compute mean and confidence interval
mean_ci <- function(x) {
m <- mean(x)
ci <- qt(0.975, length(x)-1) * sd(x) / sqrt(length(x)) # 95% confidence interval
list(mean = m, lower = m - ci, upper = m + ci)
}
# Simulate data
set.seed(42)
data <- tibble(
date = seq.Date(from = as.Date("2010-01-01"), by = "day", length.out = n), # Date sequence
focal = rep(0, n),
correlated = rep(0, n),
ab_ret = rnorm(n)
)
# Define focal events
focal_idx <- sample(1:n, n_focal)
data$focal[focal_idx] <- 1
true_effect <- 0.25
# Adjust the ab_ret for the focal events to have a mean of true_effect
data$ab_ret[focal_idx] <- data$ab_ret[focal_idx] - mean(data$ab_ret[focal_idx]) + true_effect
# Determine the number of correlated events that overlap with focal and those that don't
n_correlated_overlap <- round(length(focal_idx) * overlap_correlated)
n_correlated_non_overlap <- n_correlated_overlap
# Sample the overlapping correlated events from the focal indices
correlated_idx <- sample(focal_idx, size = n_correlated_overlap)
# Get the remaining indices that are not part of focal
remaining_idx <- setdiff(1:n, focal_idx)
# Check to ensure that we're not attempting to sample more than the available remaining indices
if (length(remaining_idx) < n_correlated_non_overlap) {
stop("Not enough remaining indices for non-overlapping correlated events")
}
# Sample the non-overlapping correlated events from the remaining indices
correlated_non_focal_idx <- sample(remaining_idx, size = n_correlated_non_overlap)
# Combine the two to get all correlated indices
all_correlated_idx <- c(correlated_idx, correlated_non_focal_idx)
# Set the correlated events in the data
data$correlated[all_correlated_idx] <- 1
# Inflate the effect for correlated events to have a mean of
correlated_non_focal_idx <- setdiff(all_correlated_idx, focal_idx) # Fixing the selection of non-focal correlated events
data$ab_ret[correlated_non_focal_idx] <- data$ab_ret[correlated_non_focal_idx] - mean(data$ab_ret[correlated_non_focal_idx]) + 1
# Define the numbers of uncorrelated events for each scenario
num_uncorrelated <- c(5, 10, 20, 30, 40)
# Define uncorrelated events
for (num in num_uncorrelated) {
for (i in 1:num) {
data[paste0("uncorrelated_", i)] <- 0
uncorrelated_idx <- sample(1:n, round(n * 0.1))
data[uncorrelated_idx, paste0("uncorrelated_", i)] <- 1
}
}
# Define uncorrelated columns and scenarios
unc_cols <- paste0("uncorrelated_", 1:num_uncorrelated)
results <- tibble(
Scenario = c("Include Correlated", "Correlated Effects", "Exclude Correlated", "Exclude Correlated and All Uncorrelated"),
MeanEffect = c(
mean_ci(data$ab_ret[data$focal == 1])$mean,
mean_ci(data$ab_ret[data$focal == 0 | data$correlated == 1])$mean,
mean_ci(data$ab_ret[data$focal == 1 & data$correlated == 0])$mean,
mean_ci(data$ab_ret[data$focal == 1 & data$correlated == 0 & rowSums(data[, paste0("uncorrelated_", 1:num_uncorrelated)]) == 0])$mean
),
LowerCI = c(
mean_ci(data$ab_ret[data$focal == 1])$lower,
mean_ci(data$ab_ret[data$focal == 0 | data$correlated == 1])$lower,
mean_ci(data$ab_ret[data$focal == 1 & data$correlated == 0])$lower,
mean_ci(data$ab_ret[data$focal == 1 & data$correlated == 0 & rowSums(data[, paste0("uncorrelated_", 1:num_uncorrelated)]) == 0])$lower
),
UpperCI = c(
mean_ci(data$ab_ret[data$focal == 1])$upper,
mean_ci(data$ab_ret[data$focal == 0 | data$correlated == 1])$upper,
mean_ci(data$ab_ret[data$focal == 1 & data$correlated == 0])$upper,
mean_ci(data$ab_ret[data$focal == 1 & data$correlated == 0 & rowSums(data[, paste0("uncorrelated_", 1:num_uncorrelated)]) == 0])$upper
)
)
# Add the scenarios for excluding 5, 10, 20, and 50 uncorrelated
for (num in num_uncorrelated) {
unc_cols <- paste0("uncorrelated_", 1:num)
results <- results %>%
add_row(
Scenario = paste("Exclude", num, "Uncorrelated"),
MeanEffect = mean_ci(data$ab_ret[data$focal == 1 & data$correlated == 0 & rowSums(data[, unc_cols]) == 0])$mean,
LowerCI = mean_ci(data$ab_ret[data$focal == 1 & data$correlated == 0 & rowSums(data[, unc_cols]) == 0])$lower,
UpperCI = mean_ci(data$ab_ret[data$focal == 1 & data$correlated == 0 & rowSums(data[, unc_cols]) == 0])$upper
)
}
ggplot(results,
aes(
x = factor(Scenario, levels = Scenario),
y = MeanEffect,
ymin = LowerCI,
ymax = UpperCI
)) +
geom_pointrange() +
coord_flip() +
ylab("Mean Effect") +
xlab("Scenario") +
ggtitle("Mean Effect of Focal Events under Different Scenarios") +
geom_hline(yintercept = true_effect,
linetype = "dashed",
color = "red") 
As depicted in the plot, the inclusion of correlated events demonstrates minimal impact on the estimation of our focal events. Conversely, excluding these correlated events can diminish our statistical power. This is true in cases of pronounced correlation.
However, the consequences of excluding unrelated events are notably more significant. It becomes evident that by omitting around 40 unrelated events from our study, we lose the ability to accurately identify the true effects of the focal events. In reality and within research, we often rely on the Key Developments database, excluding over 150 events, a practice that can substantially impair our capacity to ascertain the authentic impact of the focal events.
This little experiment really drives home the point – you better have a darn good reason to exclude an event from your study (make it super convincing)!