Difference in Difference (DiD)

Card and Krueger (1994)

Card and Krueger (1994) Minimum Wages and Employment: A Case Study of the Fast-Food Industry in New Jersey and Pennsylvania, The American Economic Review, 84(4), 772-793. https://davidcard.berkeley.edu/papers/njmin-aer.pdf

Abstract of the paper: On April 1, 1992, New Jersey’s minimum wage rose from $4.25 to $5.05 per hour. To evaluate the impact of the law we surveyed 410 fast-food restaurants in New Jersey and eastern Pennsylvania before and after the rise. Comparisons of employment growth at stores in New Jersey and Pennsylvania (where the minimum wage was constant) provide simple estimates of the effect of the higher minimum wage. We also compare employment changes at stores in New Jersey that were initially paying high wages (above $5) to the changes at lower-wage stores. We find no indication that the rise in the minimum wage reduced employment.

• time=0 : February 1992

• time=1 : November 1992

• treatment=1 : NJ raised the state minimum wage from $4.25 to %5.05

• treatment=0 : PA minimum wage stays the same at $4.25

# install.packages("leaps") 
# install.packages("ivreg")
library("leaps")
library("ivreg")

data = read.table("https://hedibert.org/wp-content/uploads/2024/10/card-krueger.txt",header=TRUE)

attach(data)

pretreatment.untreated  = mean(outcome[time==0 & treatment==0])
pretreatment.treated    = mean(outcome[time==0 & treatment==1])
posttreatment.untreated = mean(outcome[time==1 & treatment==0])
posttreatment.treated   = mean(outcome[time==1 & treatment==1])

A = posttreatment.treated   - pretreatment.treated
B = posttreatment.untreated - pretreatment.untreated
effect = A-B
c(A,B,effect)

## [1]  0.4666667 -2.2833333  2.7500000

interaction = time*treatment

summary(lm(outcome~time+treatment+interaction))

## 
## Call:
## lm(formula = outcome ~ time + treatment + interaction)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -21.097  -6.472  -0.931   4.603  64.569 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   23.380      1.098  21.288   <2e-16 ***
## time          -2.283      1.553  -1.470   0.1419    
## treatment     -2.949      1.224  -2.409   0.0162 *  
## interaction    2.750      1.731   1.588   0.1126    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 9.511 on 764 degrees of freedom
## Multiple R-squared:  0.007587,   Adjusted R-squared:  0.00369 
## F-statistic: 1.947 on 3 and 764 DF,  p-value: 0.1206

plot(c(0,0),xlim=c(0,3),ylim=c(19.5,23.5),col=0,axes=FALSE,xlab="",ylab="Employment growth")
box();axis(2)
abline(v=1.5)
text(1,pretreatment.untreated,round(pretreatment.untreated,2),col=2)
text(2,posttreatment.untreated,round(posttreatment.untreated,2),col=2)
text(1,pretreatment.treated,round(pretreatment.treated,2),col=4)
text(2,posttreatment.treated,round(posttreatment.treated,2),col=4)
text(1,19.5,"Pre-treatment")
text(2,19.5,"Post-treatment")
legend("topright",legend=c("Control Group","Treated Group"),col=c(2,4),pch=16,bty="n")