Xavier Jaravel now has a paper on this important topic:
Using detailed product-level data in the retail sector in the United States from 2004 to 2013, this paper shows that product innovations disproportionately benefited high-income households due to increasing inequality and the endogenous response of supply to market size. Annualized quality-adjusted inflation was 0.65 percentage points lower for high-income households, relative to low-income households. Using national and local changes in market size driven by demographic trends plausibly exogenous to supply factors, the paper provides causal evidence that a shock to the relative demand for goods (1) affects the direction of product innovations, and (2) leads to a decrease in the relative price of the good for which demand became relatively larger (i.e. the long-term supply curve is downward sloping). A calibration shows that this channel can explain most of the observed difference in quality-adjusted inflation rates across the income distribution.
Also see my old paper with Alex, “Who Benefits from Progress?”