The macroeconomics of immigration

No, this isn’t a question about the real world economics of immigration, this is merely a question about the basic model, viewed as model along.

Let’s say more migrants arrive in a country.  One view, held by Bryan Caplan, is that (ceteris paribus) the monetary base is fixed, so now the monetary base per capita has decline.  Thus immigration is deflationary.  There are more people and not more money, alternatively you could say that the demand to hold money has gone up.  (I am, by the way, blogging this with Bryan’s permission.)

Another view, mine, is that the new immigrants shift out both the aggregate demand and aggregate supply curves, and the net effect can be either inflationary or deflationary.  Even given a fixed monetary base, M2 likely will go up, as for instance banks will find they have more desirable loans to make, for instance to the new arrivals.  Optimal reserve requirements and money multiplier variables are likely to change, so the fixed monetary base need not choke off a demand increase.

Who is right and under which conditions?