[O]ne source (to get the needed data) is the American Veterinary Medical Association (AVMA), which puts out a survey roughly every five years on the pet population in the U.S. going back to 1983. (And possibly earlier, but I couldn't recover earlier surveys.) Using figures from those surveys on the population of cats, dogs, birds, and horses -- which grew from 125 million to 172 million between 1983 and 2007 -- and Biggs' veterinary services spending, I calculated per-capita expenditures for pet care between 1984 and 2006. I did the same for humans and rebased everything to $1 in 1984:
As you can see, pet care grows at a much slower than humans. My original caveats about per-capita spending are still applicable and given the models limitations (ie he lumped many different types of animals together) I still think this is has limited relevancy. Ideally, it would weigh the various animals given how much they contribute to the overall spending, but even that wouldn't solve everything.

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