Their results had two major components: a meta-analysis (Card and Krueger 1995) and statistical analysis of data gathered in a natural experiment (Card and Krueger 1994). In their meta-analysis, they quantitatively examine over 30 time series studies of the minimum wage. They find that as more data becomes available, the statistical significance of the employment effect of minimum wages declines. That is, additional data results in finding that it is less and less likely that increased minimum wages decrease employment.
The most famous natural experiment Card and Krueger analyzed arose when New Jersey raised its minimum wage at a time when Pennsylvania kept its minimum wage unchanged. Card and Krueger "surveyed 410 fast-food restaurants in New Jersey and eastern Pennsylvania before and after the rise". They found no evidence that rises in minimum wages reduce employment.
Card is well-regarded by economists, as evidenced by his receipt of the John Bates Clark medal (Freeman 1997). Card and Krueger's book, Myth and Measurement, which repeats these results received a lengthly review in the Journal of Economic Literature. Kennan (1995) concludes: "Myth and Measurement is a serious, well-written book, well worth reading..." Kennan also calls for more resources to be devoted to data collection.
Naturally, this work generated controversy. Neumark and Wascher (2000) is probably the most well-known rexamination of the New Jersey case (Card and Krueger 2000 is a response). As far as I know, their meta-analysis has received no extended criticism. Given this work, I don't see how one can conclude that politically-feasible increases in the minimum wage will have large employment-decreasing effects.
Recently, Card (2005) has done some empirical work on immigration. You may sometimes encounter the claim that these recent results are inconsistent with his earlier work on minimum wages. This claim of inconsistency makes sense if you interpret Card's results to be about the elasticity of demand and supply in labor markets. These empirical results, however, are consistent if you think labor markets are not described by a model of supply and demand.
- Card, David (2005). "Is the New Immigration Really So Bad?", working paper(?)
- Card, David and Alan B. Krueger (1994). "Minimum Wages and Employment: A Case Study of the Fast-Food Industry in New Jersey and Pennsylvania", American Economic Review, V. 84, N. 4 (Sep.): 772-793.
- Card, David and Alan B. Krueger (1995). "Time-Series Minimum-Wage Studies: A Meta-Analysis", American Economic Review, V. 85, N. 2 (May): 238-243.
- Card, David and Alan B. Krueger (2000). "Minimum Wages and Employment: A Case Study of the Fast-Food Industry and Pennsylvania: Reply", American Economic Review, V. 90, N. 5 (Dec.): 1397-1420.
- Freeman, Richard B. (1997). "In Honor of David Card: Winner of the John Bates Clark Medal", Journal of Economic Perspectives, V. 11, N. 2 (Spr.): 161-178.
- Kennan, John (1995). "The Elusive Effects of Minimum Wages, Journal of Economic Literature, V. 33, N. 4 (Dec.): 1950-1965.
- Neumark, David and William Wascher (2000). "Minimum Wages and Employment: A Case Study of the Fast-Food Industry in New Jersey and Pennsylvania: Comment", American Economic Review, V. 90, N. 5 (Dec.): 1362-1396.