Inflation vs GDP growth as factors driving down the US debt-to-GDP ration post-WW2

Question

I'm trying to figure out how much inflation (vs GDP growth) shrank the debt-to-GDP ratio (in the decade or so) post-WW2 in the US. I found one paper that says:

In 1946, the debt ratio was 108.6 percent. Inflation reduced this ratio about 40 percent within a decade. [...]

In 1946, just after the end of World War II, gross Federal debt reached 121.7 percent of GDP and the share held by the public was 108.6 percent. Over the next 30 years, debt as a percentage of GDP decreased almost every year, due primarily to an expanding economy as well as inflation.

But how much was due the expanding economy and how much due to inflation? (Is that 40% from the abstract just due to inflation?)

Answer 1

Look at the implicit price deflator for GDP. Using the annual series, 1946=11.05, 1956=15.32, so 38.6% increase. (Source: FRED database)

I don’t have time to look at the paper, but that’s possibly what was meant. Not an entirely convincing methodology, but you would have to do something with the deflator as well as nominal GDP to allocate changes.

Answer 2

As double-check, using data from Bernardini et al., for the US, they report 3.4% average inflation and 3.7% (average) real GDP growth over a 28-year period ('46-'74), so that's about 47.8% "contribution" of inflation in this sense.

(Bernardini et al. report CPI inflation rather than the GDP deflator.)