Your Textbook Mentions Use of a Quasi-Experiment to Study the Effects

Your textbook mentions use of a quasi-experiment to study the effects of minimum wages on employment using data from fast food restaurants. In 1992, there was an increase in the (state)minimum wage in one U.S. state (New Jersey)but not in neighboring location (Eastern Pennsylvania). To calculate the $\hat { \beta } _ { 1 } ^ { \text {diffs-in-diffs } }$ you need the change in the treatment group and the change in the control group. To do this, the study provides you with the following information $$\begin{array} { | l | c | c | } \hline & P A & N J \\\hline \begin{array} { l } \text { FTE Employment } \\\text { before }\end{array} & 23.33 & 20.44 \\\hline \text { FTE Employment after } & 21.17 & 21.03 \\\hline\end{array}$$ Where FTE is "full time equivalent" and the numbers are average employment per restaurant.
(a)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?
(b)If you look at $\hat { \beta } _ { 1 } ^ { \text {diffs-in-diffs } }$ , is this number primarily due to a change in the treatment group or the control group? Is this what you expected?
(c)The standard error for $\hat { \beta } _ { 1 } ^ { \text {diffs-in-diffs } }$ is 1.36. Test whether or not the coefficient is statistically significant, given that there are 410 observations. If you believed that the benefit from small minimum wage increases outweighed the cost in terms of employment loss, would finding that this coefficient was not statistically significant discourage you?