Card and Krueger (1994) “Minimum Wages and Employment: A Case Study of the Fast-Food Industry in New Jersey and Pennsylvania”
a. What is the causal link the paper is trying to reveal? The relationship between the minimum wage and employment in the fast-food business is the causal link that this research seeks to identify. The authors are explicitly attempting to ascertain the impact of a minimum wage rise on employment numbers in the fast-food sector. Using a difference-in-difference methodology, they compare the changes in employment in New Jersey, where the minimum wage was raised, to the changes in jobs in Pennsylvania, where the minimum wage was left unchanged, to establish a causal link between the minimum wage and employment.
b. What would be the ideal experiment to test this causal link? A randomized controlled trial would be the best experiment to determine whether the minimum wage has any bearing on employment (RCT). An RCT would randomly assign participants, in this example fast food companies, to either a treatment group where the minimum wage is raised or a control group where the minimum wage stays the same. The experiment may control for any unmeasured variables that may affect employment levels by randomly assigning firms to the treatment and control groups. This enables a plausible causal estimate of the impact of the minimum wage on employment.
c. What is the identification strategy? In this study, a difference-in-difference technique was adopted as the identification tool. The difference-in-difference approach compares changes in the outcome in the treatment group (New Jersey, where the minimum wage was increased) to changes in the outcome in the control group in order to estimate the impact of a policy change (in this case, the increase in the minimum wage) on an outcome of interest (in this case, employment levels). To account for any time-invariant unobserved factors that might have an impact on employment levels, such as regional economic conditions that are similar in New Jersey and Pennsylvania, the authors utilize the difference-in-difference technique. The authors are able to pinpoint the impact of the minimum wage hike on employment levels by contrasting the changes in employment in New Jersey to the changes in employment in Pennsylvania. The risk of omitted variable bias, which can lead to inaccurate estimates when attempting to evaluate the impact of a policy change using observational data, is lessened by employing this technique.
d. What are the assumptions / threats to this identification strategy? Assumptions: 1) Parallel trends assumption: It is expected that, in the absence of the treatment, the treatment and control groups would have seen similar trends in the outcome of interest. 2) No spillovers: It is presumed that the treatment impact only affects the treatment group and does not affect the control group
Threats: 1) Selection bias: The control group may differ significantly from the treatment group in ways that the available covariates do not capture. 2) Omitted variable bias: Unobserved factors that are related to both the treatment and the outcome may affect the results.
a. Load the data from Card and Krueger
library(tidyverse)
# load dataset into memory
MyData <- read.csv("/Users/godwinnutsugah/Dropbox/AAEE-UGA/AAEC 8610/HW/HW05/CardKrueger1994_fastfood.csv", header = TRUE, fileEncoding = "UTF-8")b. Verify that the data is correct
# Create labels for the values of state variable 0=PA and 1=NJ
labels <- c("PA", "NJ")
MyData$state <- factor(MyData$state, levels = 0:1, labels = labels)
# group the data by the 'group' variable, calculate the mean of the 'value' variable for each group, and summarize the results
df_summary <- MyData %>%
group_by(state) %>%
summarize(mean_bk=mean(bk), mean_kfc=mean(kfc), mean_roys=mean(roys), mean_wendys=mean(wendys))
# view the summarized data frame
df_summary## # A tibble: 2 × 5
## state mean_bk mean_kfc mean_roys mean_wendys
## <fct> <dbl> <dbl> <dbl> <dbl>
## 1 PA 0.443 0.152 0.215 0.190
## 2 NJ 0.411 0.205 0.248 0.136c. Verify that the data is correct
# Creating a variable for difference in FTE employment
MyData <- MyData %>%
mutate(wage_df = emptot2 - emptot)
# Run a linear regression model with the first difference variables
model1 <- lm(wage_df ~ state, data = MyData)
library(stargazer)
stargazer(model1, type="text",
no.space=TRUE, keep.stat = c("n","rsq"),
title = "DID ESTIMATES USING FD ESTIMATOR",
covariate.labels = "State(NJ=1)", dep.var.labels = "FTE EMP")##
## DID ESTIMATES USING FD ESTIMATOR
## ========================================
## Dependent variable:
## ---------------------------
## FTE EMP
## ----------------------------------------
## State(NJ=1) 2.750**
## (1.154)
## Constant -2.283**
## (1.036)
## ----------------------------------------
## Observations 384
## R2 0.015
## ========================================
## Note: *p<0.1; **p<0.05; ***p<0.01Looking ot my table, my estimate of DID estimate is 2.750 while the DID estimate in Table 3 is 2.76. These estimates are approximately equal
d. What would be the equation of a standard “difference in difference” regression? $Y_{i,t}= + D_{i} + T_{t} + (D_{i} T_{t}) + _{i,t} $ where \(\alpha\) captures the intercept the intercept \(\delta\) captures the average difference between the treated and non-treated \(\tau\) captures the Time Fixed Effects \(\gamma\) captures the treatment effect of the DID estimator
e.Compute the difference-in-differences estimator “by hand”
# Finding the mean of FTE
Mean_FTE1 <- mean(subset(MyData, state== "NJ")$emptot, na.rm = TRUE) # Mean FTE of NJ before
Mean_FTE2 <- mean(subset(MyData, state== "PA")$emptot, na.rm = TRUE) # Mean FTE of PA before
Mean_FTE3 <- mean(subset(MyData, state== "NJ")$emptot2, na.rm = TRUE) # Mean FTE of NJ after
Mean_FTE4 <- mean(subset(MyData, state== "PA")$emptot2, na.rm = TRUE) # Mean FTE of PA after
DID_est <- (Mean_FTE3- Mean_FTE4) - (Mean_FTE1-Mean_FTE2) # finding the difference in difference by hand
DID_est## [1] 2.753606The co-efficient means that the relative gain (the difference in difference of changes in employment) is 2.75 FTE employees. This that minimum wage increment in NJ resulted in an increase in total employment.