Arin Dube new working paper entitled "Minimum wages and the distribution of family incomes."
Here is his short summary:
The paper tries to make sense of the existing literature, while providing new (and I would argue better) answers to old questions such as the effect on the poverty rate, and also conduct a more full-fledged distributional analysis of minimum wages and family incomes using newer tools.
Here is the abstract:
I use data from the March Current Population Survey between 1990 and 2012 to evaluate the effect of minimum wages on the distribution of family incomes for non-elderly individuals. I find robust evidence that higher minimum wages moderately reduce the share of individuals with incomes below 50, 75 and 100 percent of the federal poverty line. The elasticity of the poverty rate with respect to the minimum wage ranges between -0.12 and -0.37 across specifications with alternative forms of time-varying controls and lagged effects; most of these estimates are statistically significant at conventional levels. For my preferred (most saturated) specification, the poverty rate elasticity is -0.24, and rises in magnitude to -0.36 when accounting for lags. I also use recentered influence function regressions to estimate unconditional quantile partial effects of minimum wages on family incomes. The estimated minimum wage elasticities are sizable for the bottom quantiles of the equivalized family income distribution. The clearest effects are found at the 10th and 15th quantiles, where estimates from most specifications are statistically significant; minimum wage elasticities for these two family income quantiles range between 0.10 and 0.43 depending on control sets and lags. I also show that the canonical two-way fixed effects model---used most often in the literature---insufficiently accounts for the spatial heterogeneity in minimum wage policies, and fails a number of key falsification tests. Accounting for time-varying regional effects, and state-specific recession effects both suggest a greater impact of the policy on family incomes and poverty, while the addition of state-specific trends does not appear to substantially alter the estimates. I also provide a quantitative summary of the literature, bringing together nearly all existing elasticities of the poverty rate with respect to minimum wages from 12 different papers. The range of the estimates in this paper is broadly consistent with most existing evidence, including for some key subgroups, but previous studies often suffer from limitations including insufficiently long sample periods and inadequate controls for state-level heterogeneity, which tend to produce imprecise and erratic results.
Update: Here is the key graph from the paper (click for larger version):