the impact of New Jersey’s minimum’s wage rise on employment growth at stores in New Jersey and Pennsylvania.
What would be the ideal experiment to test this causal link? For the ideal experiment, all subjects have to be comparable and there is no spillovers. Comparison of employment at stores in New Jersey and the other state such as Pennsylvania before and after the New Jersey’s minimum’s wage rise. If two states are perfectly same except for the minimum’s wage rise and no migration between the states, then it would be the ideal experiment.
What is the identification strategy? Difference in Difference is used as the identification strategy. Regression adjusted models are also used to incorporate other sources of variation in employment growth such as differences across chains.
What are the assumptions/threats to this identification strategy? As I mentioned in part b, if the comparability is violated and spillover effects exist, then it would be threats to the identification strategy. New Jersey and Pennsylvania cannot be the same in many ways.Thus it would be possible that they are not comparable. In addition, because of the minimum wage rise, residents of Pennsylvania might move to New Jersey and the industry where had been suffered from low labor supply could hire new labor force. Thus, employment reduce may not appear.
f <- read.csv("C:/Users/ho643/OneDrive - University of Georgia/UGA/2023 Spring/AAEC8610 Adv Quant Meth Econ/HW/HW5/CardKrueger1994_fastfood.csv")
head(f)## id state emptot emptot2 demp chain bk kfc roys wendys wage_st wage_st2
## 1 46 0 40.50 24.0 -16.50 1 1 0 0 0 NA 4.30
## 2 49 0 13.75 11.5 -2.25 2 0 1 0 0 NA 4.45
## 3 506 0 8.50 10.5 2.00 2 0 1 0 0 NA 5.00
## 4 56 0 34.00 20.0 -14.00 4 0 0 0 1 5.0 5.25
## 5 61 0 24.00 35.5 11.50 4 0 0 0 1 5.5 4.75
## 6 62 0 20.50 NA NA 4 0 0 0 1 5.0 NA#install.packages("dplyr")
library(dplyr) ##
## Attaching package: 'dplyr'## The following objects are masked from 'package:stats':
##
## filter, lag## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, union# Distributiuon of Stores
f$state[f$state == 0]<-'PA'
f$state[f$state == 1]<-'NJ'
f %>%
group_by(state) %>%
summarize(
BurgerKing = round(sum(bk)/sum(bk, wendys, roys, kfc) * 100,1),
KFC = round(sum(kfc)/sum(bk, wendys, roys, kfc)* 100,1),
RoyRogers = round(sum(roys)/sum(bk, wendys, roys, kfc)* 100,1),
Wendys = round(sum(wendys)/sum(bk, wendys, roys, kfc)* 100,1),
FTE_W1 = round(mean(emptot, na.rm = TRUE), 1),
FTE_W2 = round(mean(emptot2, na.rm = TRUE),1)) ## # A tibble: 2 x 7
## state BurgerKing KFC RoyRogers Wendys FTE_W1 FTE_W2
## <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 NJ 41.1 20.5 24.8 13.6 20.4 21
## 2 PA 44.3 15.2 21.5 19 23.3 21.2# Use OLS to obtain DID
library(stargazer)##
## Please cite as:## Hlavac, Marek (2022). stargazer: Well-Formatted Regression and Summary Statistics Tables.## R package version 5.2.3. https://CRAN.R-project.org/package=stargazerreg1 <- lm(demp ~state, data=f)
stargazer(reg1, dep.var.labels = "NJ - PA",type = "text")##
## ===============================================
## Dependent variable:
## ---------------------------
## NJ - PA
## -----------------------------------------------
## statePA -2.750**
## (1.154)
##
## Constant 0.467
## (0.510)
##
## -----------------------------------------------
## Observations 384
## R2 0.015
## Adjusted R2 0.012
## Residual Std. Error 8.968 (df = 382)
## F Statistic 5.675** (df = 1; 382)
## ===============================================
## Note: *p<0.1; **p<0.05; ***p<0.01A standard DID equation would be
\(Y_ {it} = \beta_{0} + \beta_{1}States_{i} + \beta_{2} Post_{t} + \beta_{3} States_{i}*Post_{t} + e_{it}\)
,where \(Y_ {it}\) is the outcome variable of states t and period t, \(States_{i}\) is the treatment variable, and \(Post_{t}\) is the dummy variable whether is post intervention or not.
#Get the numbers from the table
PA_before <- 23.33
PA_Post <- 21.17
NJ_before <- 20.44
NJ_Post <- 21.03
#Compute the difference-in-differences estimator by hand
DID <- NJ_Post - PA_Post - (NJ_before - PA_before)
DID## [1] 2.75I’ve got DID estimator by hand calculation, which is 2.75. It is ATE by definition and it would be interpreted as the estimator of employment after the minimum wage rise in NJ state compared to PA state before the rise.
#reshape the data to long
f <-f[!duplicated(f$id), ]
f$state[f$state == 'PA']<-0
f$state[f$state == 'NJ']<-1
f_long <- reshape(f, varying=c("emptot","wage_st", "emptot2","wage_st2"),
v.names=c("emptot","wage_st"),
timevar = "post",
times=c("0", "1"),
idvar = c("id"),
direction = "long")
#create DID term
f_long$post<-as.numeric(f_long$post)
f_long$state<-as.numeric(f_long$state)
f_long$state_post <- f_long$state * f_long$post
#run the regression
reg2 <- lm(demp ~ state + post + state_post, data = f_long)
stargazer(reg2, title="Differnce in Difference", dep.var.labels = "NJ - PA",type = "text")##
## Differnce in Difference
## ===============================================
## Dependent variable:
## ---------------------------
## NJ - PA
## -----------------------------------------------
## state 2.743**
## (1.156)
##
## post -0.000
## (1.466)
##
## state_post 0.000
## (1.635)
##
## Constant -2.283**
## (1.037)
##
## -----------------------------------------------
## Observations 766
## R2 0.015
## Adjusted R2 0.011
## Residual Std. Error 8.979 (df = 762)
## F Statistic 3.754** (df = 3; 762)
## ===============================================
## Note: *p<0.1; **p<0.05; ***p<0.01we can see the DID estimator is 0.000 even though it is not significant. When we just compare NJ and PA state, there is significance difference in employment between these two states. However, DID did not show any significance difference between those states and post and pre intervention. Thus, we can conclude that the minimum wage rise did not affect the employment in NJ state.