Higher minimum wage means the poorest people have more money, then they turn around and spend that money at Walmart.

The poorest people do not directly benefit from minimum wage, because they don't have jobs. Many participants in the informal economy are also very poor.

One option I didn't think of in the ancestor is that people pushed into the informal sector may still be showing up as employed in the sources being referenced: people making a lower-than-minimum-wage living as e.g. junk collectors are sometimes counted as such depending on methodology. We could pick out this effect by asking for personal earnings as well as employment status: if higher minimum wages are coming out of corporate margins somewhere, we'd expect average earnings (at least in the lower segment of the workforce) to go up, but we wouldn't expect that if it's pushing people into the informal sector. A survey would probably have to be carefully designed to have the resolution to pick this up, though.