Question

On April 1 1992, NJ increased its minimum wage to $5.05, at the time the highest minimum wage in the country. David Card and Alan Krueger saw an opportunity to understand how the minimum wage affects employment. They surveyed fast food restaurants in February 1992 (before increase) and November 1992 (after increase) in both NJ and in PA (which did not change its minimum wage in this time period). The survey asked how many employees they had. They then ran the following regression:

Employees = α + β1NJ + β2November + β3(NJ × November) + ϵ

Where NJ = 1 if the restaurant is in NJ and = 0 if in PA; November = 1 if the response is from November (after increase) and = 0 if response is from February (before increase); Employees are the number of full-time employees. They estimated that: βˆ 3 = 2.76 with a standard error of 1.36

a) What is the t-statistic for the estimate of βˆ 3? Given that our sample size is large, how is the t-statistic distributed? How do you know this?

b) Is βˆ 3 significant at the 5% level? How do you know? Why did you make the comparison you did to answer this?

c) How do you interpret β3?

d) Why were (some) economists surprised by this result?

Answer 1

a) t statistic = 3​ ÷ standard error

= 2.76 ÷ 1.36 = 2.029

If the sample size is large, then the t statistic is normally distributed. This is because, the larger the sample size the more close will the sample be to the normally distributed population.

b) At 5% significance level, the test statistic value is 1.96. If the estimated t statistic exceeds this critical value, we reject the null hypothesis that 3 = 0. So, the comparison with critical value us made.

Here since estimated t value - 2.029 > 1.96, the  3 is statistically significant at 5% significance level.

c) 3 is an interaction variable which shows by how much the mean number of employees in a restaurant in NJ change post the increase in minimum wages differs from the mean number of employees in a restaurant in PA before the increase in minimum wage.

d) Generally, a higher minimum wage increases the cost to the producers and therefore they employ less labour, leading to decrease in employment. The significant 3 result was surprising for some economists because it implied that the number of employees actually increased post the increase in minimum wage and that to in NJ where the increase in minimum wage actually occured.