Inequality, Redistribution and Mobility by Rodríguez Juan Gabriel;Bishop John A.;

Author:Rodríguez, Juan Gabriel;Bishop, John A.;
Language: eng
Format: epub
Publisher: Emerald Publishing Limited
Published: 2020-10-22T00:00:00+00:00

1. INTRODUCTION

In a survey of income mobility, Jäntti and Jenkins (2015) make a basic distinction between intergenerational mobility that refers to income change between generations of parents and children, and intra-generational mobility which deals with the change of income of individuals between one year and another during their lifetime. In the latter case, a distributional change can have up to three components: (average) income growth, structural mobility (change in relative inequality), and exchange mobility (re-ranking of individuals1). Ruiz-Castillo (2000) and Silber and Weber (2005) attempted indeed to isolate these three components.

The focus of many of the measures of intra-generational income mobility that have appeared in the literature has in fact been on mobility between two periods, with notable exceptions including the works of Shorrocks (1978), Maasoumi and Zandvakili (1986), and Tsui (2009). Tsui (2009) offers a coherent framework to analyze multi-period income mobility. His approach is closely related to his previous work on multidimensional income inequality (Tsui, 1995, 1999). Tsui (2009) chose a relatively “weak” definition of complete immobility since he assumed that there is immobility if there is no exchange mobility. A stronger definition of complete immobility is that adopted, for example, by Shorrocks (1978) and Maasoumi and Zandvakili (1986), because they took as immobility benchmark a situation where “the relative income of each individual does not change over time” (Shorrocks, 1978, p. 381). In other words, complete immobility requires the absence of structural as well as of exchange mobility.2

Building on this notion of immobility, we propose a new framework for the measurement of income mobility over several time periods, whereby multi-period mobility can be interpreted as the degree of association between the individuals and the time periods.

To operationalize this idea, let yit be the income of individual i at time t. Our chosen benchmark amounts in fact to the existence of independence between the rows and the columns of the matrix of the incomes yit., that is, between the individuals and the time periods. In other words, there will be complete income immobility if for all individuals i and time periods t the observed share is identical to the expected share that would be observed under independence between the rows and the columns of the matrix of incomes yit. As will be shown in Section 2, our definition of complete immobility turns out to be identical to that adopted by Shorrocks (1978) and Maasoumi and Zandvakili (1986), but the way we formulate this definition of immobility allows us to derive new measures of multi-period mobility.

At this stage, we should note that the gaps between the observed shares sit and the expected shares wit may be positive or negative. We will assess mobility as inequality across these gaps and will adopt an absolute inequality measurement framework and use absolute Lorenz curves (Moyes, 1987) for partial orders. The analytical framework we adopt reminds us somehow of the proposals made by Joe (1985) and Greselin and Zenga (2004) in the context of contingency tables, but neither of them is intended or suited for measuring mobility.

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