Many of you have been asking this question. Robert Waldmann reports:
…what about Card and Krueger. Empirical estimates of the effect of the minimum wage on employment suggest that the effect is very small. One famous study by Card and Krueger showed a positive effect of an increase in the minimum wage. The logic used by Card and Krueger to understand how this could happen suggests that things are different now.
Their logic is basically that firms can choose to pay a low wage and have a high quit rate and take a long time to fill vacancies or pay a high wage and have fewer quits and fill vacancies more quickly. If they are forced to pay the higher wage, their desired level of employment will be lower, but that level is the sum of employment plus vacant jobs. A binding minimum wage can reduce the number of vacant jobs by more than it reduces the sum of employment plus vacant jobs. Thus more employment.
I think this is not relevant to the current situation. There are very few vacant jobs. Quit rates are low. According to their logic, the effect of the minimum wage on employment depends on the unemployment rate. The evidence of a small effect is almost all from periods of unemployment far below 10%. I don't think it is relevant to the current situation.
Waldmann makes other excellent points in his post, which is on the minimum wage more generally. I would add that there are many good critiques of the original study and the most plausible belief is still the traditional result, namely that minimum wage laws have a (slight) negative effect on employment.