Non‐Linearity and Cross‐Country Dependence of Income Inequality

• Published date: 01 March 2020
• Author: Leena Kalliovirta,Tuomas Malinen
• Date: 01 March 2020
• DOI: http://doi.org/10.1111/roiw.12377

© 2019 Internation al Association for Re search in Inco me and Wealth

227

NON-LINEARITY AND CROSS-COUNT RY

DEPENDENCE OF INCOME INEQUALITY

By Leena KaLLiovirta

Natural Reso urces Institute Finl and

AND

tuomas maLinen*

University of Helsinki

We use top income data and the newly developed regime-switching Gaussian mixture vector autoregres-

sive model to explain the dynamics of income inequality in developed economies within the past 100

years. Our results indicate that the process of income inequality consists of two equilibria identifiable

by high inequality and high income fluctuations, and low inequality and low income fluctuations. Our

results also imply that income inequality in the United States is the driver of income inequality in other

developed economies. High wages and capital gains are found to be the likely channels for the U.S.

influence.

JEL Codes: C32, C33, D30

Keywords: top 1 percent income share, GMAR, multiple equilibria, developed economies

1. introduction

The history of the distribution of product, or income, inequality is embodied

by large fluctuations in the share of income massing at the top.1 According to

Piketty 2014 (p. 274), in the history of inequality “there have been many twists and

turns and certainly no irrepressible, regular tendency toward a natural equilib-

rium.” In a similar vein, Roine and Waldenström (2011) found global and

1Estimates on the level of global income inequality vary (see, among others, Sala-i-Martin, 2002;

Anand and Segal, 2008; Milanovic, 2015), but the share of the total income going to the top income

earners has not been this high in many developed economies since the 1920s (Alvaredo etal., 2013).

Note: We thank Donald Andrews, Timothy Armstrong, Stephane Bonhomme, Andrea Brandolini,

Petri Böckerman, Mario Holzner, Vanesa Jordá, Markus Jäntti, Vesa Kanniainen, Tero Kuusi, Markku

Lanne, Mika Meitz, Peter Phillips, Prasada Rao (the editor), an anonymous referee, Pentti Saikkonen,

James Stodder, Rami Tabri, the participants at the IAAE 2015 annual meeting in Thessaloniki, the

ECINEQ 2015 meeting in Luxembourg, the UNU-Wider conference of trends, topics, measurement

and policies of income inequality in Helsinki, the 2013 annual meeting of the Eastern Economic

Association in New York, and the seminar audiences at universities of Helsinki and Yale for useful

comments and suggestions. All remaining errors are our own. Tuomas gratefully acknowledges finan-

cial support from the OP-Pohjola Group’s Research Foundation (grant no. 201400069 and 201100007)

and from the Finnish Cultural Foundation (grant no. 00160604). Leena thanks the Academy of Finland

(grant no. 268454) and the Cowles Econometrics Program for financial support.

*Correspondence to: Tuomas Malinen, Department of Political and Economic Studies, University

of Helsinki, P.O. Box 17 (Arkadiankatu 7), FIN–00014 University of Helsinki, Finland (tuomas.ma-

linen@helsinki.fi).

Review of Inc ome and Wealth

Series 66 , Number 1, March 2020

DOI : 10.1111 /roi w.123 77

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Review of Income and Wealth, Series 66, Number 1, March 2020

228

© 2019 Internation al Association for Re search in Inco me and Wealth

country-specific break points from the top 1 percent income share series, which

indicate that the process of income inequality could consist of different phases or

equilibria. This study finds further evidence to support this by indicating that

income inequality follows a regime-switching process where higher inequality leads

to higher variance in income shares and vice versa. Our results also indicate that

changes in income inequality in the United States (U.S.) have driven inequality in

other developed economies during the past 100 years.

The structure of income inequality has varied quite heavily throughout the

past century. In the period prior to World War II, high incomes consisted mostly of

returns to capital, which was the main reason for high inequality during that era

(Piketty and Saez, 2013; Piketty, 2014). However, the biggest driver of the resur-

gence of income inequality in developed economies after the 1970s has been the

increasing share of high wages (Piketty, 2014). The variance of earnings has also

been on the rise in developed economies during the same period (see, e.g., Daly

Valletta 2008; Gottschalk and Moffitt, 2009; Beach et al., 2010). Although increas-

ing variance of earnings has occurred during a period marked by increasing income

inequality, research on their relationship has been almost non-existent.2 Moreover,

to our knowledge, there are no studies looking at the possible dependence of

income inequality of one individual country on that of others. In this study, we set

out to fill these gaps.

As argued by Piketty (2014), income inequality seems not to have been fol-

lowing any kind of mean reversing process (see above). This has been confirmed in

many econometric studies, which have been unable to reject the unit root hypothesis

in the autoregressive models for different measures of income inequality (see, among

others, Mocan, 1999; Parker, 2000; Jäntti and Jenkins, 2010; Malinen, 2012; Herzer

and Vollmer, 2013). However, this is a problematic result, as the series of commonly

used measures of income inequality, such as the Gini index and the top income

share, are bounded between 0 and 1, while the unit root series has a time-increasing

variance. The breaks in the top 1 percent income share series identified by Roine

and Waldenström (2011) could be one reason for the non-rejection of unit root

hypotheses. If breaks are actually shifts between different phases of income inequal-

ity identified by, for example, different levels of variance, there would be no ten-

dency toward a single equilibrium, but shifts between multiple equilibria. A linear

autoregressive model would be misspecified due to the observed jumps, whereas the

so-called trend-break models would ignore the strong autocorrelation in the series.

We employ a newly developed Gaussian mixture autoregressive (GMAR)

model studied in Kalliovirta et al. (2015) and its multivariate generalization, the

Gaussian mixture vector autoregressive (GMVAR) model by Kalliovirta et al.

(2016), to estimate the dynamic properties of income inequality. We use the GMAR

and GMVAR models to identify the different regimes created by the breaks and

autoregressive dynamics in the top income series, because they are able to model

multiple equilibria. We analyze the top 1 percent income share data ranging from

the end of the 19th century to the beginning of the 21st century for six countries:

Australia, Canada, France, Finland, Japan, and the U.S.

2In the only study we could find, Beach etal. (2010) show that a rise in the total earnings variance

in Canada after 1982 is mostly attributable to an increase in overall inequality.