Are the minimum wage and EITC complements? And if so, when?

In response to Greg Mankiw’s recent NYT piece, I’ve been hearing the argument again that the minimum wage and wage subsidies are complements.  According to this view, if you have only wage subsidies, employers will lower what they offer to the workers and capture too much of the value of the subsidy.  A higher minimum wage is supposed to prevent this from happening and thus ensure that workers capture more of the gains.

Even if you accept every premise of this argument, I am not sure how it is supposed to apply today, at least within a Keynesian framework.  For the Keynesians, the employment problem today is almost purely one of demand, not labor supply.  To spur more hiring, we therefore should wish the employers to capture more of the surplus.  A belief in hysteresis makes it all the more compelling simply to get potential workers into a job as soon as possible.

So a higher minimum wage and wage subsidies might be complements at some time period, but they should not be effective complements today.  Furthermore, if demand problems are going to be with us for a long time (not my view), a higher minimum wage and wage subsidies might not be complements anytime soon.

I recall @ModeledBehavior having made some related points on Twitter.