A lot of the post is summarizing the differences between the two papers, including two big ones: Sabia and Burkhauser assume that workers under the old minimum wage will not get a raise, and they assume that those earning above the new minimum wage will not see a raise.
Obviously both are problematic and they make a big difference. When you deal with that, some measurement error issues in survey data (always be careful about survey data at the tails of the distribution especially - very high or very low income), and the quasi-experimental approach of Dube (rather than the simulation approach of Sabia and Burkhauser), their estimates for the impact on poverty are higher (18.9 percent of beneficiaries are poor rather than 11.3). Obviously this doesn't change the underlying conclusion that this is not a policy just targeted at the poor. As I tried to summarize in the last post, it's not clear why anyone would think it was in the first place. Just do a few calculations with a hypothetical wage earner and you'll see that most (just over 80% in Dube's case and just under 90% in Sabia and Burkhauser's case) shouldn't be living in poor families. This was the key insight of the post, in my opinion (bolding is mine):
"So to take stock, if you consider the Sabia and Burkhauser simulation results as “facts” you also are claiming that no worker reporting a wage below the old minimum will get a raise, and no one above the new minimum will get a raise. These are not very good assumptions, and they certainly are not facts.
Of course, you don’t have to make these assumptions. You could allow for spillovers. You could allow for wages to rise below the minimum. You could allow for measurement error in reported wages and other sources of income. But then you are not in a world where tabulating survey data gives you simple facts that are beyond reproach. You need to make additional assumptions to make causal claims. And we have not even begun to talk about behavioral effects—be they on labor demand side, or on labor supply side such worker search effort, etc. (And by the way those do not all go in the same direction.) So you could add a lot more assumptions and continue with the simulation route, or you could use quasi-experimental approach used in almost all of applied micro-economics to empirically estimate the effect of minimum wages on poverty and other outcomes. Of course, you would want to subject your identifying assumptions to specification checks and falsification tests to ensure you have reliable control groups; and you would account for possibly confounding policies such as state EITCs. And when you do all of that, and some more, you would probably end up with a paper like this one.
So where does this leave us? As I said in my paper, policies like cash transfers, food stamps, and EITC are better targeted to help the poor, although even there minimum wage are better thought of as complements and not substitutes. More generally, however, motivations behind minimum wage policies go beyond reducing poverty. The popular support for minimum wages is in part fueled by a desire to raise earnings of low and moderate income families more broadly, and by fairness concerns that seek to limit the extent of wage inequality, or employers’ exercise of market power. And the evidence suggests is that attaining such goals through increasing minimum wages is also consistent with a modest reduction in poverty, and moderate increases in family incomes at the bottom."