Has there been much research on rating inflation? Magnus Carlsen's draw in yesterday's round of the 2012 London Chess Classic assured that his rating in the next published FIDE rating list will surpass Kasparov's previous record of 2851. I've seen/heard passionate chess fans debate the relative merits of Carlsen's rating achievement versus Kasparov's versus, say, Fischer's. To be clear, that's not what I'm after here.

One crucial element of such discussions is the notion of whether Elo ratings in general have undergone inflation over time: are there so many more 2700+ grandmasters today than there were 20 years ago because of a general rise in playing strength, or just because of some overall inflationary trend in the numbers? I'm also not trying to solicit bare opinions about whether or not that's so. What I am interested in knowing:


  What serious research attempts have been made to answer the empirical question as to whether FIDE Elo ratings have naturally inflated over time because of something other than a rise in overall strength in the player pool?


The Wikipedia entry on the Elo rating system has a little bit to say about the matter, and also points to an article by Jeff Sonas of Chessmetrics. In addition to any pointers to work by others, I, for one, would also welcome an answer that gives a clear, concise summary of Sonas' main points.
I am surprised that the paper "Intrinsic Chess Ratings" by Ken Regan and Guy Haworth hasn't been posted yet. It is exactly what's asked for, serious research into rating inflation. PDF

Basically they got games from three periods (1976-1979, 1991-1994, 2006-2009), in several rating ranges (e.g. both players within 10 points of 2200, within 10 points of 2300, etc), and excluded types of games that might be anomalous, like team matches. Read the paper, it looks quite thorough.

Then they compared the games systematically with Rybka 3.

Some sentences from the conclusion: 


  We conclude that there is a smooth relationship between the actual
  players’ Elo ratings and the intrinsic quality of the move choices as
  measured by the chess program and the agent fitting. Moreover, the
  final sfit values obtained are nearly the same for the corresponding
  entries of all three time periods.


In my view, it's quite solid evidence against the existence of rating inflation.