That article is not talking about the multiplier effect. It is talking about consumers consumption smoothing...buying automobiles after the minimum wage goes up because there has been a permanent increase in their income. From the article: "Our estimates are silent about the aggregate effects of a minimum wage hike."

I've read a lot of the econ literature in this area, and have never seen a defense of the minimum wage on the basis of multiplier effects. Too few people are working at the minimum wage. And, the minimum wage is too blunt of a instrument to try to counteract business cycles.