It finds that CPI indices overstate inflation at the purchaser level, as households switch to cheaper vendors of the same (or similar) goods in down-turns. This makes sense, as the demand for paid labour declines, the opportunity cost of shopping time declines – so we invest more in searching for the best price.
If one re-weights price indices to reflect this shopping around, one finds that actual prices paid decline to a greater extent in downturns. The above chart shows that the difference between the average price paid and the effective price increases as the unemployment rate rises.
A related finding is that sales are pro-cyclical (more of them when the economy is good) — possibly because as shoppers get more price sensitive, the returns to sales by expensive stores (who have most of the sales) are lower as they attract fewer customers.
Due to the decline in sales when there are large demand shocks the phillips curve will appear to flatten — with observed with inflation falling by less than you would expect given the increase in the unemployment rate.