Do Shocks to Income Distribution Permanently Change Consumption Distribution? Time Series of Cross-Sectional Distributions with Common Stochastic Trends ∗ Yoosoon Chang † , Changsik Kim ‡ , Hwagyun Kim § and Joon Y. Park ¶ Abstract Yes, but how? To answer the questions, we develop a new framework and methodology for the time series analysis of cross-sectional distributions with stochastic trends. Often individual time series of cross-sectional distributions have nonstationary persistent components that may be characterized effectively as functional unit roots. This paper shows how to model and analyze the pres- ence of common trends in multiple time series of such cross-sectional distri- butions. Then, we use income and expenditure data from the Consumer Ex- penditure Survey to investigate dynamic interactions between the household income and consumption distributions. Interesting relations prevail between the household income and consumption distributions, and we provide economic explanations using a simple two-sector growth model with heterogeneous agents. Previous version: June 16, 2014 This version: October 11, 2016 JEL Classification: C33, C12, C13 Keywords and phrases : Time series of cross-sectional distributions, distributional unit roots and cointegration, income and consumption dynamics, income response functions to con- sumption. * This version is prepared for the presentation at the 2014 Panel Conference in Japan by Yoosoon Chang. The authors are grateful to Minkyeong Baik for her excellent research assistance. † Department of Economics, Indiana University ‡ Department of Economics, Sungkyunkwan University § Department of Finance, Mays Business School, Texas A&M University ¶ Department of Economics, Indiana University and Sungkyunkwan University