If you just want to look at accidental
death, I would note that most of the decrease in fatal gun accidents
in the US occured before there was an increase in handgun ownership

Table 2.1 of Kleck’s “Point Blank” shows that handgun sales jumped
dramatically around 1965 — from around 0.5M per year to 1-2M per year
afterwards. This is presumably the reason for the increase in the
percentage of households owning handguns from 16% in the early sixties
to 25% in the late eighties. (Table 2.2 of Kleck)

Table 7.1 of Kleck shows that the fatal gun accident rate declined
from 2.4 per 100k population in 1933 to 1.21 in 1965 and then to 0.57
in 1987. That is a decrease of 1.19 before handgun ownership
increased, and a decrease 0.64 afterwards. The rate of decrease was
slower after 1965 than before.

Chris BeHanna wrote:

From 1967 to 1987, the U.S. accidental gun death rate
declined by more than two thirds while the handgun stock simultaneously
increased by 273%. (Kates et al, “Guns and Public Health: Epidemic of
Violence or Pandemic of Propaganda?” Tenn. L. Rev., Spring, 1995 –
I’d give you a page number but the article is at home).

Page 567: “Over the twenty year period 1967-1986, the number of
handguns increased 173%, while the fatal gun accident rate decreased
by almost two-thirds.” Dear me, you seem to have embellished Kates’
factoid by changing “almost two-thirds” to “more than two-thirds” and
173% to 273%. That wasn’t a very nice thing to do, Chris.

Mr Kates has also done some embellishing of his own, though with a bit
more subtlety than Chris has. Firstly he has chosen to use 1967-1986 as
his twenty year period. 1967 just so happened to be a year with an
unusually large number of fatal accidents. Kleck’s tables actually go
to 1987, and if he had used 1968-1987 he would only have been able to
claim a decrease of one half instead of two thirds. Secondly, notice
that he has compared the change in the gun accident rate (number of
gun accidents divided by the size of the population) with the change
in the absolute number of handguns (not divided by the size of the
population). Once again this skews the comparison in the direction
Kates prefers. A less misleading version would be: “Over the twenty
year period 1968-1987, the number of handguns per person increased by
90%, while the fatal gun accident rate decreased by one half.”

Even this one has problems: most of the new handguns went to households
that already had handguns — the percentage of households with handguns
did not increase that much. A better version might be: “”Over the twenty
year period 1968-1987, the fraction of households with handguns
increased by 5 percentage points, while the fatal gun accident rate
decreased by one half.”

This still shows that an increase in handgun ownership was associated
with a decrease in gun accidents, but obviously this wasn’t dramatic
for Kates.