The Matthew effect is typically summarized by “the rich get richer and the poor get poorer”. In this paper, we rely on German social security data that allow us to follow workers over the entire working life to provide evidence for such a Matthew effect for income, where low-risk individuals have higher average income growth and ac-cumulate more wealth. Among workers, there is a group, the “unlucky” few, who not only face low income growth on average but also highly volatile incomes. Most income fluctuations, unemployment risk, and bad health outcomes are concentrated in this group. Looking at their wealth, one sees that these workers accumulate little even in comparison to their lower incomes. On top, they earn meager returns on what they manage to save, because they invest in poor return (i.e. liquid and safe) assets. On the other hand, the vast majority of workers face a much calmer income process with little turbulence over the life cycle, they have steady income growth, and can thus use high-return assets as savings devices.
? We thank Tatjana Mika and Michael Stegmann for their help regarding questions on the data.
We thank conference participants at the mini conference on heterogeneous agents at Zurich and Kurt Mitman, Xavier Ragot for helpful comments and remarks. Financial support by ADEMU - 649396 grant is gratefully acknowledged. Kuhn thanks the DFG for financial support (DFG No. 433368816). Ploj gratefully acknowledges financial support from the DAAD, the Bonn Graduate School of Economics, and the DFG research training group 2281 “The Macroeconomics of Inequality.” The usual disclaimer applies.
We document these facts by combining largely unexplored data from the Ger-man retirement records on employment histories of males in West GerGer-many with information on households’ balance sheets. As in other data sources (Guvenen, Kara-han, Ozkan, and Song, 2015), we document that income fluctuations have fat tails.
Yet, we also document that this is driven to a significant extent by substantial and persistent heterogeneity in income risk across workers. While most workers face lit-tle income fluctuations, a smaller fraction has very volatile incomes. Most unemploy-ment is highly concentrated within cohorts of workers and low-pay, no-pay cycles are prevalent among workers who become unemployed. We find that within one cohort 20 percent of workers account for around 80 percent of all transitions into unemployment. In the same vein, we also find a high concentration of changes in health status (healthy to sick) within cohorts, although health risks appear to be less concentrated than the incidences of unemployment.
Matching the income risks to household balance sheet data, we document that those who face the highest risks in the labor market earn the lowest returns in the as-set market and also accumulate substantially less wealth even relative to their lower incomes. We rationalize this outcome as a result of persistent risk types. While house-holds live most of the time in tranquil times with small income fluctuations, they can occasionally transit into a state of labor market turbulence. On average this happens rarely, once in 20 years, and mostly after a large negative income shock. This turbu-lent labor market situation persists for a significant period of time as we estimate the average duration of the turbulence to be around five years. The household optimally reacts to the negative income shock that preceded the labor market turbulence by drawing from its savings to smooth the negative income shock. In the aftermath of the shock, the household structures its portfolio in a way that it provides more in-surance against negative income draws and this happens at the expense of worse old-age insurance. Because the portfolio becomes safer and more liquid, it earns lower returns.
We show in a calibrated model that such dynamics explain well the systematic differences in household portfolios and their returns both in the cross-section as well as over the life cycle. In the model, households face income shocks and stochastic transitions between risk types. They self-insure against these shocks by investing either into a low-return liquid asset that they can access at no cost every period or into an illiquid asset with higher but also risky returns. We model the illiquidity as a saving commitment, where the household can change the per-period flow into or out of its illiquid account by paying an adjustment cost. Such a saving contract, therefore, resembles a typical mortgage contract or traditional life insurance that pays out at retirement.
In both model and data, differences across risk groups in terms of wealth, portfo-lios, and returns increase as households age. For example, at age 40 high-risk house-holds have a 50% lower wealth to income ratio, their portfolios contain a 20% higher share of liquid assets and they earn 20% lower returns on their assets compared
to low-risk households. The presence of idiosyncratic second-order income risk in-creases aggregate capital accumulation and reduces welfare for low-risk households.
The average household who enters the labor market as the low-risk type would con-sequently be willing to forgo 4% of its lifetime consumption to avoid living in the economy with second-order risk.
Related literature.This paper relates primarily to two strands of literature. First, it adds to the literature that investigates the heterogeneity in labor market risk. Go-ing back at least to Hall (1982), economists have documented that workers have very different working lives. Recent empirical work has corroborated this finding and concluded that a representative earnings process will struggle to account for the regularities of earnings dynamics in the data (Guvenen, Karahan, Ozkan, and Song, 2015; Arellano, Blundell, and Bonhomme, 2017; Jung and Kuhn, 2018; Kara-han, Ozkan, and Song, 2019; Kuhn and Ploj, 2020; Morchio, 2020). Findings of the literature show that labor income risk varies, among others, across age (Karahan and Ozkan, 2013; Blundell, Graber, and Mogstad, 2015; Jung and Kuhn, 2018; Kuhn and Ploj, 2020), educational and skill groups (Mukoyama and Şahin, 2006; Blun-dell, Graber, and Mogstad, 2015) and with the business cycle (Storesletten, Telmer, and Yaron, 2004; Bayer, Luetticke, Pham-Dao, and Tjaden, 2019). The increased availability of large detailed administrative data has also allowed for more granu-lar and less parametric analysis of the heterogeneity in labor market risk with an increased focus on the higher moments of the earnings growth rate distribution (Gu-venen, Karahan, Ozkan, and Song, 2015; Manuel, Blundell, and Stéphane, 2017).
Our paper follows the spirit of these papers and presents additional evidence that workers systematically vary in terms oflifetimeearnings risk, and that these differ-ences can be to a large degree attributed to differdiffer-ences in lifetime unemployment and health risk. In this view, our work therefore also complements that of Schmillen and Möller (2012) and Morchio (2020) who report a high concentration of lifetime unemployment using German and U.S. data.
Second, we also contribute to the literature that studies the implications of het-erogeneity in labor market risk for household savings behavior and portfolio hetero-geneity. Findings of this literature predominantly show that income risk reduces the demand for risky assets, although the estimated effects are often small and insignifi-cant (Guiso, Jappelli, and Terlizzese, 1996; Heaton and Lucas, 2000, 2001; Angerer and Lam, 2009; Palia, Qi, and Wu, 2014). Recently, Fagereng, Guiso, and Pistaferri (2018) find much larger effects than previously documented after improving on the identification of wage risk variability. Corroborating these findings, Chang, Hong, Karabarbounis, Wang, and Zhang (2020) also show that the empirically estimated response of the risky share to wage risk can be explained with a standard portfolio
choice model that is augmented with idiosyncratic, time-varying income volatility.1 We complement these findings on the empirical side and provide additional evidence for the effect of risk heterogeneity on wealth accumulation, portfolio returns, and asset participation. Furthermore, we also introduce a portfolio choice model with a frictional saving commitment, which we show can well explain the observed life-cycle patterns of heterogeneity in portfolio liquidity and wealth accumulation across households with different labor market risk.
The remainder of the paper is structured as follows. In Section 2.2 we introduce the data from the German social security records and present evidence on hetero-geneity in unemployment risk, health risk, wage risk, and earnings risk. Section 2.3 explores the consequences of labor market risk heterogeneity for household savings decisions and portfolio composition using the HFCS data. In Section 2.4, we study the consequences of labor market risk through the lens of incomplete markets mod-els. Finally, Section 2.5 concludes.