Using Panel data: Difference-in-Differences Impact of Minimum Wages

This a replication of the results obtained in the paper by Card and Krueger (1994), it should be noted that Card was awarded the Nobel Price in part due to this paper.

Card

Part 1: Reading the paper

Looking at the paper: 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.

What is the causal link the paper is trying to reveal?
Does an augment of the minimum wage affect the level of employment? The idea behind this question comes from the fact that in a competitive market, workers are paid according to their marginal productivity. In this context, imposing a minimum wage would only generate higher levels of unemployment.

What would be the ideal experiment to test this causal link?
The ideal experiment would be to have two firms that are completely identical (in particular they hire the same kind of workers for the same positions) and use the same system to determine the amount of workers and the wage level. And impose minimum wages to one and not the other to observe what decisions they take.

What is the identification strategy?
They are going to use a natural experiment. Two neighbor states, New Jersey and Pensylvania, used to have the same minimum wage $4.25. However New Jersey decided to raise their minimum wage to $5.05, while Philadelphia kept it at its original level. Assuming this states are comparable, they will measure the different behaviors

What are the assumptions / threats to this identification strategy?
The preoblems are that there might be other situations going on that might affect the the outcome (employment levels) that are not related with this policies. Maybe there was a shift in the taste for fast food in New Jersey that did not happen in Pennsylvania. Maybe there was a change in the levels of education of a specific cohort that happen in one state and not in the other. Many situations could be affecting the results.

Part 2: Replication Analysis

Load data from Card and Krueger AER 1994

Verify that the data is correct Reproduce the % of Burger King, KFC, Roys, and Wendys, as well as the FTE means in the 2 waves.

Q2 <- my_data_HW5 %>% 
  group_by(chain) %>% 
  summarise(
    count = n(),
    percentage = count/410,
    FTE_mean_t1 = mean(emptot, na.rm=TRUE),
    FTE_mean_t2 = mean(emptot2, na.rm=TRUE))
    
Q2[,1]<-c("Burguer King", "KFC", "Roys", "Wendys")

Q2 %>%
  kbl() %>%
  kable_styling(bootstrap_options = c("striped", "hover", "condensed", "responsive"))
chain count percentage FTE_mean_t1 FTE_mean_t2
Burguer King 171 0.4170732 23.62073 24.17922
KFC 80 0.1951220 12.47152 13.61875
Roys 99 0.2414634 22.54592 20.67368
Wendys 60 0.1463415 22.61404 23.09545

Use OLS to obtain their Diff-in-diff estimator (almost – you won’t get it exactly)

Q3 <-lm(demp ~ state, data = my_data_HW5)
stargazer(Q3, title="Table 3 - Difference NJ-PA", align=TRUE,  type='html')
Table 3 - Difference NJ-PA
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<0.01

We can observe that the obtained value 2.75 is almost the same as the one that they get on the paper (2.76).

What would be the equation of a standard “difference in difference” regression?

\[\Delta Y_i = \alpha +\beta D_i + \tau T_t + \gamma (D_i T_t) + \varepsilon_{i,t}\]

Where:
* The variable \(\Delta Y_i\) is the difference in the outcome (the difference in the employment level).
* The variable \(T_t\) is the time fixed effect, in this case \(\{0,1\}\) to represent before and after the policy.
* The variable \(D_i\) is the state fixed effect, in this case \(\{0,1\}\) to represent Pennsylvania or New Jersey.
* The variable \(D_i T_t\) is the treatment, it will be one for the cases in which the local is located in New Jersey and the policy has been implemented.
* The variable \(D_i\) is an indicator function that represents the treatment. In this case it will be 1 if the observation refers to New Jersey after the policy has been implemented.