To Analyze the Effect of a Minimum Wage Increase, a Famous

Essay

To analyze the effect of a minimum wage increase, a famous study used a quasi-experiment for two adjacent states: New Jersey and (Eastern)Pennsylvania. A $\hat { \beta } _ { 1 } ^ { \text {diffs-in-diffs } }$ was calculated by comparing average employment changes per restaurant between to treatment group (New Jersey)and the control group (Pennsylvania). In addition, the authors provide data on the employment changes between "low wage" restaurants and "high wage" restaurants in New Jersey only. A restaurant was classified as "low wage," if the starting wage in the first wave of surveys was at the then prevailing minimum wage of $4.25. A "high wage" restaurant was a place with a starting wage close to or above the $5.25 minimum wage after the increase.
(a)Explain why employment changes of the "high wage" and "low wage" restaurants might constitute a quasi-experiment. Which is the treatment group and which the control group?
(b)The following information is provided $$\begin{array} { | l | c | c | } \hline & \text { Low wage } & \text { High wage } \\\hline \text { FTE Employment before } & 19.56 & 22.25 \\\hline \text { FTE Employment after } & 20.88 & 20.21 \\\hline\end{array}$$ Where FTE is "full time equivalent" and the numbers are average employment per restaurant.
Calculate the change in the treatment group, the change in the control group, and finally $\hat { \beta } _ { 1 } ^ { \text {diffs-in-diffs } }$ Since minimum wages represent a price floor, did you expect $\hat { \beta } _ { 1 } ^ { \text {diffs-in-diffs } }$ to be positive or negative?
(c)The standard error for $\hat { \beta } _ { 1 } ^ { \text {diffs-in-diffs } }$ is 1.48. Test whether or not this is statistically significant, given that there are 174 observations.