Inequality, cost of living, and productivity
Recent research has indicated that the prices of goods consumed by low-income households have been rising faster than those consumed by high-income households. This observation is concerning as it might imply a further deterioration in the dispersion of nominal income.
In this paper, Ezra Oberfield presents a simple example of a model with non-homothetic preferences and productivity improvements directed toward goods with a larger market size. The author assumes a balanced growth path (BGP) along which: a) under the assumption of a stable income distribution, there are perpetual differences in measured inflation across individuals; b) under the assumption of higher after-tax wage inequality, measured growth is slower and there is a larger gap in measured inflation between the top and bottom of the income distribution; but c) under both income distributions, productivity growth improves welfare at the same rate for all households:
Across BGPs, despite the gap in measured output and productivity growth, there is no gap in the rate of welfare improvements. Further, even though the BGP with more inequality exhibits a larger gap in inflation between the rich and poor, the productivity improvements that cause this actually ameliorate inequality rather than exacerbate it.
Inequality and Measured Growth
Author: Ezra Oberfield
From: Princeton University
Inequality, cost of living, and business cycles
Jacob Orchard examines the cyclical behavior of low-income versus high-income household price indices in this paper. He creates 119 product sectors in the Consumer Expenditure Survey (CEX) that represent the same type of spending from 1991 to 2019. Then he sorts households into five different income quintiles and constructs a measure of the relative importance of a product in a low-income household’s consumption basket. Using price data for a subset of products from 1967-2020, he can observe the cyclical behavior of necessity and luxury goods prices over seven different recessionary periods. He shows that 24 months after a 25 basis point contractionary monetary policy shock, aggregate expenditure falls by approximately 2 percent but the aggregate share of spending devoted to necessity products increases by 5 percent, and relative necessity prices increase by around 2.5 percent.
Finally, Orchard uses a quantitative New Keynesian model that incorporates non-homothetic preferences and can be calibrated to the US economy. He finds:
[T]he difference in cost-of-living between low and high-income households varies systematically over the business cycle: increasing during recessions and subsiding during expansions. This cost-of-living channel is yet another reason why recessions are particularly costly for low-income households.


Cyclical Demand Shifts and Cost of Living Inequality
Author: Jacob Orchard
From: University of California, San Diego