Are Engel curve estimates of CPI bias biased?

"A recent literature has advanced the use of Engel curves to estimate overall CPI bias. In this paper, I show that the methodology is sensitive to the modeling of household demography. Existing estimates of CPI bias do not account for the changing effect of household size on budget shares, and this can lead to omitted variable bias. Since the effect of household size on demand changes over time the drift in Engel curves attributed to CPI bias is partially explained by this effect. My estimates of the annual rate of CPI bias from 1888 to 1935 are changed by at least 25%, and usually more than 50%, once the changing effect of household size is accounted for"--National Bureau of Economic Research web site.