To analyze the effect of a minimum wage increase, a famous study examined a "natural" experiment that occurred for two adjacent states. This New Jersey-Pennsylvania study on the effect of minimum wage on employment was mentioned in Stock and Watson. It conducted a comparison in means "before" and "after" analysis to assess average employment changes per restaurant between the treatment group (New Jersey) and the control group (Pennsylvania). The following presents average employment levels per restaurant for the two groups.
PA NJ
FTE Employment before 23.33 20.44
FTE Employment after 21.17 21.03
In addition, the authors of the minimum wage study 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. The following information is provided:
Low wage High wage
FTE Employment before 19.56 22.25
FTE Employment after 20.88 20.21
where FTE is short for "full time equivalent" and the numbers give average employment per restaurant.
Calculate the change in the treatment group, the change in the control group, and finally the differences-in-differences estimate. Is the estimate positive or negative?