The researchers compared available information on donors’ direct political contributions and “bundling” — money raised on behalf of Mr. Obama by supporters — with data on the national income of host countries, their relative level of safety, and the robustness of their tourist industries.

Not surprisingly, the authors found that politically connected ambassadors, including former aides as well as donors, were statistically more likely to be posted to countries in the Caribbean, North America and Central America. But those whose political connections to Mr. Obama were measured in dollars, rather than administration service, had an increased chance of representing the United States in Western Europe, and a markedly smaller chance of serving in, say, Central Asia or sub-Saharan Africa. The study found that political ambassadors who had made campaign donations of $550,000, or bundled contributions of $750,000, had a 90 percent chance of being posted to a country in Western Europe.

And what do these postings “cost?” Ambassadorial appointments do not, of course, come with price tags. But by combining information on what current ambassadors contributed along with data on the desirability of the ambassadors’ host countries, Dr. Fedderke and Dr. Jett arrived at “implied prices” for a selection of highly sought positions. The figures did not represent how much donors actually gave or raised to get the jobs, the researchers said, but rather their theoretical value in fund-raising terms. Those numbers in turn give a sense, Dr. Fedderke said, of how attractive each posting is in relation to the others.

“What we can observe is data on contributions and postings,” Dr. Fedderke said in an interview. “And on the basis of that, we can infer an implicit valuation on postings in monetary terms — even if they haven’t contributed that much.”

When isolating a country’s wealth over other factors, Luxembourg came in at the top of the chart, with a posting there valued at $3.1 million in direct contributions, while an appointment to Portugal was predicted to have a value of $602,686 in personal contributions. The model suggests that bundlers can get the same posts for less: Portugal was valued at about $341,160 in bundled contributions, Luxembourg at $1.8 million.