Download and go over this seminal paper by David Card and Alan Krueger. Card and Krueger (1994) Minimum Wages and Employment: A Case Study of the Fast-Food Industry in New Jersey and Pennsylvania AER 84(4): 772-793. Be careful: They released a 2000 follow up with the exact same title followed by “:Reply”. We want the original, not the follow-up.
Briefly answer these questions:
The causal effect of the minimum wage increase on the employment.
The idea experiment would be that we randomly assign two groups of people with identity characteristics and backgrounds. Then we assign one group of people as treatment group where every person are offered at a higher minimum wage to work. Then the other group of people is control group where each person are offered at the original minimum wage at the same industry. Then we compare the employment between these two groups of people.
The author uses the difference in difference (DID) method to analyze the data from survey conducted by telephone to 410 fast-food stores in New Jersey and eastern Pennsylvania from the Burger King, KFC, Wendy’s and Roy Rogers chains before and after the minimum wage rise. The author chooses two waves of the survey time: the first wave is a month before minimum wage increase; the second is 8 months after the increase. Then the author uses the DID to get the minimum wage increase effect on employment.
fast-food restaurants’ employment can represent the whole employment: The authors thinks that fast-food restaurants is “leading employer of low-wage workers”; it complies with the minimum-wage regulations and response to the rise in minimum wage; and it is reliable measurement to employment; and it easy to build the frame.
no anticipation effect: with or without the rise of the minimum wage, it will not affect the workers in New Jersey before they are actually treated with higher minimum wage.
parallel trend assumption: without the rise of the minimum wage, the difference employment between New Jersey and eastern Pennsylvania remain the same.
library(tidyverse)
fastfood <-read.csv("hw5/CardKrueger1994_fastfood.csv",header=TRUE)
head(fastfood)## 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# the % of Burger King, KFC, Roys, and Wendys
library(dplyr)
d <- fastfood %>% group_by(state) %>% summarize(Burger_King =sum(bk),
KFC = sum(kfc),
Roys = sum(roys),
Wendys = sum(wendys), )
d <- as.matrix(d)
d <- d[,-1]
rownames(d) <- c( "eastern Pennsylvania", "New Jersey")
(d/rowSums(d) *100)## Burger_King KFC Roys Wendys
## eastern Pennsylvania 44.30380 15.18987 21.51899 18.98734
## New Jersey 41.08761 20.54381 24.77341 13.59517# the FTE means in the 2 waves
d1 <- fastfood %>% group_by(state) %>% summarize(First_Wave=mean(emptot,na.rm=TRUE),Second_Wave=mean(emptot2,na.rm=TRUE))
d1 <- as.matrix(d1)
d1 <- d1[,-1]
rownames(d1) <- c( "eastern Pennsylvania", "New Jersey")
d1## First_Wave Second_Wave
## eastern Pennsylvania 23.33117 21.16558
## New Jersey 20.43941 21.02743g <- lm(demp~state,data = fastfood)
library(stargazer)
stargazer(g,
type="text",
title = "Table 3")##
## Table 3
## ===============================================
## Dependent variable:
## ---------------------------
## demp
## -----------------------------------------------
## state 2.750**
## (1.154)
##
## Constant -2.283**
## (1.036)
##
## -----------------------------------------------
## 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<0.01The results (2.75) from the OLS is similar to the results (2.76) in DID from the paper.
\[ y_{it} = \beta_0 + \beta_1 state_i + \beta_2 D_t + \beta_3 state_i \times D_t + \epsilon_{it}\] Where the dummy variable \(D_t\) represents the treatment in each period t, which is 0 when the wage doesn’t increase and 1 when the wage increases.
I calculate the difference-in-differences estimator
library(knitr)
did <- data.frame(
Name = c("PA", "NJ","Diff"),
FTE_before = c(23.33,20.44,-2.89),
FTE_after = c(21.17,21.03,-0.14),
Diff = c(-2.28,0.23,2.75)
)
kable(did,caption = "DID calculation")| Name | FTE_before | FTE_after | Diff |
|---|---|---|---|
| PA | 23.33 | 21.17 | -2.28 |
| NJ | 20.44 | 21.03 | 0.23 |
| Diff | -2.89 | -0.14 | 2.75 |
Then I calculate the DID estimator as below \[ \begin{aligned} & A T T=\left(Y_{1, i, \text { after }}\left|D=1-Y_{1, i, a \text { after }}\right| D=0\right)-\left(Y_{i, \text { before }}\left|D=1-Y_{i, \text { before }}\right| D=0\right)=-0.14 -(-2.89) =2.75 \\ & \text { or }: \\ & A T T=\left(Y_{1, i, \text { after }}\left|D=1-Y_{i, \text { before }}\right| D=1\right)-\left(Y_{1, i, a \text { fter }}\left|D=0-Y_{i, \text { before }}\right| D=0\right)=0.23 -(-2.28)=2.75 \end{aligned} \]
The DID estimator here shows the difference in how two cities (PA and NJ) changed after increasing minimum wage.
# transfer the wide data into long
library(reshape2)
fastfood2 <- reshape(fastfood,
idvar= c("id","state"),
sep= "",
timevar = "D",
direction = "long",
varying = rbind(c("emptot","emptot2"),
c("wage_st","wage_st2")) )
# regression
g2 <- lm(emptot ~ state * D ,data = fastfood2)
summary(g2)##
## Call:
## lm(formula = emptot ~ state * D, data = fastfood2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -21.166 -6.439 -1.027 4.473 64.561
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 25.497 2.397 10.638 <2e-16 ***
## state -5.645 2.669 -2.115 0.0347 *
## D -2.166 1.516 -1.429 0.1535
## state:D 2.754 1.688 1.631 0.1033
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 9.406 on 790 degrees of freedom
## (26 observations deleted due to missingness)
## Multiple R-squared: 0.007401, Adjusted R-squared: 0.003632
## F-statistic: 1.964 on 3 and 790 DF, p-value: 0.118library(stargazer)
stargazer(g2,
type="text")##
## ===============================================
## Dependent variable:
## ---------------------------
## emptot
## -----------------------------------------------
## state -5.645**
## (2.669)
##
## D -2.166
## (1.516)
##
## state:D 2.754
## (1.688)
##
## Constant 25.497***
## (2.397)
##
## -----------------------------------------------
## Observations 794
## R2 0.007
## Adjusted R2 0.004
## Residual Std. Error 9.406 (df = 790)
## F Statistic 1.964 (df = 3; 790)
## ===============================================
## Note: *p<0.1; **p<0.05; ***p<0.01