Problem Set 5

\(\color{darkblue}{\text{QUESTION 1}}\)

nm %>%
  na.omit() %>%
  group_by(nj,d) %>%
  summarise(pre_ct= mean(fte))

(21.02743- 21.16558) - (20.43941 -23.33117)

## [1] 2.75361

Note: Subtracting (post-treatment NJ - post-treatment PA) from (pre-treatment NJ - pre-treatment PA) accounts for initial level differences between the two, given Pennsylvania had greater number of full-time employees, and hence accounts for the fact that the two states were not at the same level pre-treatment.

\(\color{darkblue}{\text{QUESTION 2}}\)

nm %>%
  lm(fte~ nj*d, data=.) %>%
  summary()

Estimate	Std.Error	t_value	P_value
2.754	1.6883	1.631	0.1033

\(\color{grey}{\text{Note: Above coeffiencts are for nj:d }}\)

The difference in the differences between pre and post treatment New Jersey and Pennsylvania employment is 2.754 FTE employees. Hence, the passing of minimum wage law in New Jersey increased full-time employment rates in the fast-food industry in NJ by 2.75 full time employees post-treatment when compared with neighbouring Pennsylvania. However, since this result is not statistically significant, it supports the null hypothesis that FTE employment was not significantly different post treatment in New Jersey. Hence, a rise in minimum wages in the state of New Jersey did not reduce employment when compared to Pennsylvania.

\(\color{darkblue}{\text{QUESTION 3}}\)

nm3 <- nm %>%
  na.replace()

nm3 %>%
  lm(fte~ nj*d, data=.) %>%
  summary()

Estimate	Std.Error	t_value	P_value
2.554	1.764	1.448	0.1481

\(\color{grey}{\text{Note: Above coeffiencts are for nj:d }}\)

Yes, the coefficient of interest did change numerically from 2.754 to 2.554, however this does not change our results from question 2 qualitatively. The interaction between NJ and post-treatment is still not statistically significant, meaning there is no evidence to suggest that FTE employment in NJ was different post-treatment when compared to pre-treatment, holding all else constant. Furthermore, the change is relatively small from 2.754 to 2.554.

\(\color{darkblue}{\text{QUESTION 4}}\)

nm4 <- nm %>%
  mutate(Time= ifelse(d=="0"," Pre-treatment","Post-treatment")) %>%
  mutate(State= ifelse(nj=="0","PA","NJ")) %>%
  na.omit() %>%
  group_by(State,Time) %>%
  summarise(nm= mean(fte)) 

nm4$nm_round <- round(nm4$nm, 2)

nm4 %>%
  ggplot(aes(Time, nm,group=State)) +
  geom_line(aes(color=State)) +
  labs(y="Full-time equivalent employment", x="") +
  scale_color_manual(values=c("#66B2FF", "#660066")) +
  ggtitle("Average Employment per Store") +
  theme_linedraw() +  
  geom_text_repel(aes(label = nm_round), color = "black", size = 4)