US-specific correlation between immigrant proportion and cultural sophistication

In his article Why Should We Restrict Immigration?, Bryan Caplan writes:

America’s top two cultural centers, California and New York, have the largest foreign-born populations in the country— 26 percent and 20 percent, respectively (U.S. Census Bureau 2003). While states with few immigrants—like Alabama (2 percent foreign-born), Arkansas (3 percent), Montana (2 percent), North
Dakota (2 percent), South Dakota (2 percent), and West Virginia (1 percent)—enjoy great natural beauty, even their tourism bureaus would not paint them as cultural meccas.

Caplan makes the same point in a blog post titled Who Wants to Move to Minnesota?:

In the comments, Steve Sailer cites:

Moynihan’s Law of Proximity to the Canadian Border: on just about any socially positive measure, there is a positive correlation between a state’s ranking and it’s distance from the Canadian border: e.g., Minnesota is usually in the top ten states on anything.

Not in population, where it’s only #21.  And with no offense to my readers frm Minnesota, I have to ask Steve: If Minnesota’s so great, why don’t you move there?  Even if Steve’s got special circumstances, why aren’t millions of other Americans flooding into this promised land?  I grant that weather’s a factor, but here are two of comparable importance:

1. Minnesota’s high rankings are largely arithmetic, not causal.  Whites have above-average performance, and Minnesota’s over 85% white (non-Hispanic), so Minnesota has above-average performance.  But this doesn’t mean that whites who move to Minnesota enjoy a much higher quality of life than they would in their current state.

2. Minnesota is, well, boring.  And a big part of the reason is lack of immigration to bring varied food, entertainment, and yes – diversity.

"The Efficient, Egalitarian, Libertarian, Utilitarian Way to Double World GDP" — Bryan Caplan