Most of us - and that would include many elite players with a vested psychological interest in a negative answer - are inclined to say yes. In fact, it's not just "yes" but "yes, obviously; everyone knows this".
It turns out that "everyone" may be wrong. IM Ken Regan, GM Bartlomiej Macieja and Guy Haworth have co-authored an academic paper (Regan and Haworth are computer scientists, Macieja studied physics) arguing that ratings have remained stable since their inception. Their paper offers an objective method to examine the issue, and the data tested by that method support their surprising conclusion.
To grossly oversimplify, their test procedure is to use a computer engine to examine players' games, comparing their moves (post-opening) to those found by an engine. This generates what they call an Intrinsic Performance Rating (IPR), and a large sample size reveals that ratings and IPRs correlate over time; ergo, no inflation.
Don't buy it? That's what the paper is for: check out all the gritty details for yourself!