- Natural experiments, especially one comparing and contrasting New Jersey and Pennsylvania.
- A meta-analysis of previous published research on minimum wages.
For natural experiments, I look to a paper by Dube and others. Here's their abstract:
"We use policy discontinuities at state borders to identify the effects of minimum wages on earnings and employment in restaurants and other low-wage sectors. Our approach generalizes the case study method by considering all local differences in minimum wage policies between 1990 and 2006. We compare all contiguous county pairs in the U.S. that straddle a state border and find no adverse employment effects. We show that traditional approaches that do not account for local economic conditions tend to produce spurious negative effects due to spatial heterogeneities in employment trends that are unrelated to minimum wage policies. Our findings are robust to allowing for long term effects of minimum wage changes." -- Andrajit Dube, T. William Lester, and Michael Reich. "Minimum Wage Effects Across State Borders: Estimates Using Contiguous Counties". Review of Economics and Statistics, V. 92, N. 4 (Nov. 2010): 945-964.
For meta-analysis, I look to some studies by Doucouliagos and others. Here's the abstract of an accessible working paper:
"Card and Krueger’s (1995a) meta-analysis of the employment effects of minimum wages challenged existing theory. Unfortunately, their meta-analysis confused publication selection with the absence of a genuine empirical effect. We apply recently developed meta-analysis methods to 64 US minimum wage studies and corroborate that Card and Krueger’s findings were nevertheless correct. The minimum wage effects literature is contaminated by publication selection bias, which we estimate to be slightly larger than the average reported minimum-wage effect. Once this publication selection is corrected, little or no evidence of a negative association between minimum wages and employment remains. --Hristos Doucouliagos and T. D. Stanley (2008). "Publication Selection Bias in Minimum-Wage Research? A Meta-Regression Analysis". Deakin University, Australia.
I don't expect orthodox economists to absorb any time soon my unoriginal point that economic theory gives no foundation for the belief that minimum wages must lead to disemployment, even when one abstracts from less than perfect competition, principal agent problems, information asymmetries, etc. After all, mainstream economists are trained in mumpsimus.