Macroeconomic Implications of Inequality and Income Risk

Finance and Economics Discussion Series

Federal Reserve Board, Washington, D.C.

ISSN 1936-2854 (Print)

ISSN 2767-3898 (Online)

Macroeconomic Implications of Inequality and Income Risk

Aditya Aladangady, Etienne Gagnon, Benjamin K. Johannsen, and William B.

Peterman

2021-073

Please cite this paper as:

Aladangady, Aditya, Etienne Gagnon, Benjamin K. Johannsen, and William B. Peterman (2021). Macroeconomic Implications of Inequality and Income Risk," Finance and Economics Discussion Series 2021-073. Washington: Board of Governors of the Federal Reserve System, https://doi.org/10.17016/FEDS.2021.073.

NOTE: Sta working papers in the Finance and Economics Discussion Series (FEDS) are preliminary materials circulated to stimulate discussion and critical comment. The analysis and conclusions set forth are those of the authors and do not indicate concurrence by other members of the research sta or the Board of Governors. References in publications to the Finance and Economics Discussion Series (other than acknowledgement) should be cleared with the author(s) to protect the tentative character of these papers.

Macroeconomic Implications of Inequality and Income Risk

Aditya Aladangady	Etienne Gagnon	Benjamin K. Johannsen
	William B. Peterman
	November 16, 2021

Abstract

We explore the long-run relationship between income risk, inequality, and the macroeconomy in an overlapping-generations model in which households face uncertain streams of labor income and returns on their savings. To manage those risks, households can apportion their savings to a bond, whose return is safe and identical across households, and a productive asset, whose return is uncertain and can differ persistently across households. We find that greater polarization in households' labor income and returns on their savings generally accentuates households' demand for risk-free assets and the compensation they require for bearing risk, leading to higher measured income and wealth inequality, a lower risk-free real interest rate, and higher risk premiums. These findings suggest that the factors behind the observed rise in inequality over the past few decades might have contributed to the observed fall in the risk-free real interest rate and widening gap between the risk-free real interest rate and the rate of return on capital. We also find that the magnitude of the decline in the risk-free real interest rate and offsetting rise in risk premiums depend importantly on the source of income polarization, with the effects being especially large when greater inequality is caused by increased dispersion in returns on risky assets. Thus, the macroeconomic implications not only depend on the amount of inequality, but also the source of this inequality.

JEL Codes: D31, D33, E21, E25, J11.

Keywords: income and wealth inequality, heterogeneous returns, risk-free real interest rate, risk premium.

• 20th Street and Constitution Avenue NW, Washington DC, 20551. The views expressed in this paper are those of the authors only and do not reflect the views of the Federal Reserve System or its staff. We thank Rebecca Wasyk for her terrific optimization and parallelization of our computer code; without her expertise, our project would have been computationally much more challenging. We also thank Sarah Baker, Kathy Bi, Kenneth Eva, and Rahul Kasar for their superb research assistance. We are grateful for comments and suggestions from seminar participants at the Federal Reserve Board, Paris School of Economics, Federal Reserve Bank of San Francisco, May 2019 Midwest Macro conference, 2019 congress of the Société Canadienne de Science Économique, and 2021 annual meetings of the Society for Economic Dynamics. Comments can be directed to [e-mail], [e-mail],

[e-mail], and [e-mail].

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• Introduction

Income and wealth have become increasingly concentrated in the hands of the richest households in the past few decades. Analysis based on the Federal Reserve's Survey of Consumer Finances (SCF) suggests that the top 10 percent of U.S. households now receives almost half of aggregate income and owns nearly 80 percent of aggregate net worth, both up notably from earlier decades.1 In this paper, we explore how a rise in income polarization that exacerbates wealth inequality affects the macroeconomy, and whether the associated effects depend on the drivers of income polarization. In particular, we quantify how polarization in households' labor earnings and in the return on their savings affects real economic activity, saving decisions, and interest rates in a general-equilibrium,overlapping-generations model.

Our results suggest that increased polarization in labor income and the returns on savings are plausible contributors to the observed rise in inequality measures, the estimated decline in the trend of the risk-free real interest rate, and the apparent widening of the gap between the risk-free real interest rate and the real rate of return on capital over the past few decades (documented below). Intuitively, greater income heterogeneity accentuates households' desire to save against potential changes in income. The increased desire to save leads to a fall in the risk-free real interest rate. It also causes households, when deciding the composition of their savings portfolio, to require greater compensation to bear risk (that is, higher risk premiums), thus leaving the risky return on capital little changed.2 The magnitude of the decline in the risk-free real interest rate and the offsetting rise in risk premiums depend on the source of income polarization, with the effects being especially large when greater inequality is caused by increased dispersion in returns on risky assets rather than by greater dispersion in labor income. Additionally, we illustrate how the implications for output and the capital stock also hinge on the nature of household income risk. Overall, the results underscore that the macroeconomic effects of inequality not only depend on the extent of income and wealth heterogeneity but also on households' ability to manage income risk through their portfolio decisions.

Most quantitative explorations of the links between inequality and the macroeconomy have focused on heterogeneous labor earnings as the source of inequality. This focus has been facilitated by the relative availability of data on labor compensation, which show that labor income dispersion across workers is not only pervasive, even when measured within demographic and skill groups, but it has increased over time. However, there is growing recognition that heterogeneity in labor income alone is insufficient to account for the observed extent of inequality and its evolution.3 In addition, the increased availability of panel data on household asset returns point to significant and persistent heterogeneity in households' saving behavior and the returns generated by their assets.4

• These statistics are from Wolff (2021). Estimates of the extent and evolution of income and wealth inequality can be sensitive to data sources and definitions; see Bricker et al. (2016). Unless indicated otherwise, the household-level
  and aggregate concepts of "wealth" used throughout our paper are on a net rather than gross basis.
  2Our analysis focuses on idiosyncratic risks. Aggregate risks may operate through similar channels at the household
  level.
  3See, for example, Gabaix et al. (2016) and De Nardi and Fella (2017).
  4For evidence on heterogeneous saving rates and risk tolerance, see Dynan, Skinner, and Zeldes (2004), Saez and

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Furthermore, understanding the implications of income polarization requires the consideration of how household manage risk through their saving portfolio decisions, an aspect that is often missing from models that abstract from heterogeneous returns.

Given these observations, we reexamine the relationship between inequality, income risk, and the macroeconomy in a life-cycle model that allows for polarization in both labor income and asset returns across households.5 Our heterogeneous agents, overlapping-generation model builds on the Bewley-Huggett-Aiyagari (BHA) framework. As is typical with this framework, we assume that households are subject to persistent idiosyncratic labor income shocks each period until they reach retirement. Thereafter, they rely on their savings and social security transfers to sustain consumption. We extend the BHA framework by positing that households can allocate their savings to two kinds of assets. A safe asset-modeled as a one-periodbond-offers the same deterministic return to all households. A risky asset-modeled as physical capital-offers a stochastic return that, in contrast to most previous studies, varies both across households and over time.6 Households face a cost of adjusting their holdings of the risky asset, making that asset less liquid than the risk-free asset and inducing most households to hold both types of assets in equilibrium. The production side of our model is neoclassical. Therefore, the effect on economic activity and the relationship between measured inequality and output ultimately depend on how income risk affects incentives to save and how much of that saving is apportioned to the risky capital asset. We examine the model's general equilibrium in which all aggregate prices and quantities are determined endogenously, including in asset markets.

To explore the longer-run macroeconomic implications of various potential drivers of inequality, we compare the stationary equilibrium under our baseline calibration with the stationary equilibria under four alternative parameterizations that lead to equal-size increases in wealth inequality, as measured by the Gini coefficient of the distribution of wealth. In our first and second alternative parameterizations, we boost inequality in labor income across households by raising the volatility and persistence, respectively, of innovations to labor income. In our third and fourth alternative parameterizations, we similarly increase inequality in asset income across households by raising the volatility and persistence, respectively, of innovations to households' returns on the risky asset. Each of these four alternative parameterizations creates extra dispersion in total household income and, ultimately, greater concentration of wealth among the richest households.

A key finding is that increased income polarization, as captured by our four alternative param-

Zucman (2016), Bach, Calvet, and Sodini (2018), Crawley and Kuchler (2020), and Sias, Starks, and Turtle (2020). For panel-data evidence of differences in asset returns across households, see Fagereng et al. (2020), Bach, Calvet, and Sodini (2020), and Gomez (2018).

• Other possible contributors to inequality not explored in our study include inheritances (for example, Wolff and Gittleman (2014)), heterogeneous preferences (for example, Krusell and Jr. (1998), Toda (2019), and Carroll et al. (2017)), heterogeneous household labor supplies (for example, Flavin and Yamashita (2002; 2011) and Yum (2018)), and changes in tax rates and transfers (for example, Kaymak and Poschke (2016) and Cao and Luo (2017)). Because our approach to modeling labor income and asset returns is somewhat reduced form, the effects of other contributing
  factors may be conflated to some extent with the channels that we model.
  6One exception is Guvenen, Kambourov, et al. (2019), who introduce idiosyncratic returns to saving through a three-state entrepreneurial shock.

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eterizations, is a plausible contributor to increased income and wealth inequality and the fall in safe interest rates observed in recent decades in the United States and other advanced economies. In particular, greater riskiness in labor income or asset income in our parameterizations amplifies precautionary motives, which, in turn, boosts the demand for the safe asset and lowers the risk- free real interest rate. It also leads to an increase in the risk premium that households require as a compensation for bearing risk. On net, the rise in the risk premium offsets, in large part, the decline in the risk-free real interest rate, leaving the expected real rate of return on capital little changed across alternative parameterizations. This finding is consistent with the relative stability of the realized rate of return on capital in recent decades, as documented by Gomme, Ravikumar, and Rupert (2011). Accordingly, increased inequality is a plausible contributor to the observed divergence between the risky and the risk-free real interest rates.7

Though the direction of these effects is the same across alternative parameterizations, their magnitudes differ considerably depending on the origins of a rise in inequality. We find the largest swings in the risk-free real interest rate and risk premium when greater inequality originates from changes in the risky asset return process. Intuitively, households' ability to mitigate income risk through savings in capital units is curtailed when the return on physical capital has greater per- period volatility or persistence. Accordingly, when inequality originates from greater polarization in risky asset returns, households seek to channel a larger share of their savings toward the safe asset. Households' desire to rebalance their portfolios further lowers the risk-free real interest rate and raises the risk premium in equilibrium. We also find that changes in inequality that are caused by increases in the persistence of the labor income and risky return processes have smaller macroeconomic effects than changes caused by increases in the per-period volatility of innovations to these processes. Although both kinds of changes lead to greater income and wealth polarization in the long run, changes caused by increases in persistence make household income more predictable over short horizons; therefore, the precautionary motives that drive macroeconomic effects are not as pronounced as when greater income polarization originates from more volatile innovations.

In contrast to the effects on the risk-free real interest rate and risk premium, which go in the same directions across the four parameterizations, the signs of the effects on the capital stock and real output vary. When the labor income process is more volatile, households accumulate more savings in both assets and the higher level of physical capital leads to higher output.8 When the return on capital is more volatile, the model instead predicts declines in the aggregate stock of capital and real output because households seek to rebalance their portfolios away from the productive capital asset. These results caution that the relationship between inequality and overall economic performance is complex and ultimately depends not only on the extent of wealth inequality, but also on how changes in income processes affect the incentives to invest in assets linked to the productive capacity of the economy.

In addition to the alternative parameterizations described in the previous paragraph, we consider

• For alternative explanations, see Caballero, Farhi, and Gourinchas (2017) and Marx, Mojon, and Velde (2019).
  8The direction of these effects echoes those found in the Aiyagari (1994) model, in which physical capital is the

only asset available to hedge labor income risk.

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