Question

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 β₁ᵈᶦᶠᶠˢ⁻ᶦⁿ⁻ᵈᶦᶠᶠˢ 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.

the standard error for β₁ᵈᶦᶠᶠˢ⁻ᶦⁿ⁻ᵈᶦᶠᶠˢ is 1.48. test whether or not this is statistically significant, given that there are 174 observations.____

Answer 1

To determine if the effect of a minimum wage increase is statistically significant, a t-test using the difference-in-differences estimator (β1diff-in-diff) combined with the standard error and number of observations is performed. Studies, including Card and Krueger (1994), typically show that minimum wage increases do not have large effects on employment.

Step-by-step explanation:

To test whether the minimum wage increase between New Jersey (treatment group) and Pennsylvania (control group) had a statistically significant effect on employment, we can use the difference-in-differences estimator (β1diff-in-diff). With a standard error of 1.48 and 174 observations, the significance of this estimator can be tested using a t-test. A t-test compares the estimator to the standard error, typically against a critical value derived from the t-distribution with 173 degrees of freedom (n-1) to determine if β1 is significantly different from zero.

As the specific value of the estimate (β1) is not provided, we cannot calculate the exact t-statistic nor the p-value here. However, typically, if the absolute value of the t-statistic is greater than approximately 2 (which can vary depending on the level of confidence), then the result can be considered statistically significant. The t-value is calculated as β1 / SE(β1), where SE is the standard error. If |t| > 2, where t is the t-statistic, the effect of the minimum wage on employment is statistically significant.

According to studies, including those by Card and Krueger (1994), minimum wage increases do not have large employment effects, often showing no significant effects on employment or even small increases. This could provide context to the statistical results, suggesting that even if a significant change is detected, the practical significance in terms of employment numbers might be minimal.