In some models job search is just about the posted wage, but I suspect that is the easiest kind of search to do. In reality, search covers multiple dimensions, for instance wage but also working conditions, such as the comfort of your job post, how much of a jerk the boss is, and so on.
If the minimum wage is hiked, the higher nominal wage will indeed induce more search, because the pecuniary gain from a good match is higher.
That said, a higher minimum wage will to some extent induce employers to lower the non-pecuniary quality of the job. At the very least, there will be more uncertainty about the non-pecuniary aspects of the job. Imagine a new job seeker: “I’ve read Gordon Tullock — now I’m wondering if they are going to turn down the air conditioner in the back room where I will be working.”
That uncertainty in fact raises the costs of job search and makes the results of that search less certain. In this regard, you can think of a higher minimum wage as a tax on job search.
If you think job search is mainly about the posted wage, you won’t be very worried about this affect. Alternatively, if you think job search is mainly about finding a good match along the non-pecuniary dimensions, you might be very worried about it indeed. And it will make it harder for minimum wage hikes to boost employment by inducing more labor search.
For this post, I am indebted to a conversation with the excellent Matthew Lilley.