Time evolution of income distributions with subgroup decompositions

Abstract

In this paper, we propose a two-step decomposition procedure for studying the functional time series of income distribution (ID) of a population under a subgroup classification. Using the law of total probability, we first decompose the overall ID as a linear combination of the subgroup IDs weighted by the subgroup shares. In the second step, we use a functional principle component analysis to decompose the subgroup ID as a class of orthonormal functions with time-varying coefficients. We then apply this two-step decomposition to develop a class of models for exploring the ID evolution, the ID change, and the dynamics of various distributional features at different levels ranging from broad to specific. For empirical illustration, we apply the proposed methods to explore Taiwan’s family ID evolution from 1981 to 2014.

Keywords:

• Distribution evolution
• functional principal component analysis
• income distribution
• subgroup decomposition

JEL CLASSIFICATION:

• C22
• C52
• D31

Correction Statement

This article has been republished with minor changes. These changes do not impact the academic content of the article.

Notes

1 The SFIE is conducted annually with randomly sampled families (more information about the survey is available at http://eng.stat.gov.tw/np.asp?ctNode=1542), and the data is accessible by application at the website of the Survey Research Data Archive (SRDA) of the Center for Survey Research of Academia Sinica https://srda.sinica.edu.tw/index_en.php. The macroeconomic data are downloaded from the National Statistics website of the DGBAS http://statdb.dgbas.gov.tw/pxweb/Dialog/statfile9L.asp.

Additional information

Funding

Yi-Ting Chen is grateful to the Ministry of Science and Technology of Taiwan for research supports (NSC102-2410-H-001-006). The research of Ruey S. Tsay is supported in part by the Booth School of Business, University of Chicago.