Saving at the top and the long-run relationship between wealth and income inequality

ABSTRACT

This paper analyzes the joint long-run evolution of wealth and income inequality. We find that top wealth and income shares were cointegrated over the past century in France and the US. We rationalize this finding in two macroeconomic heterogeneous agent models featuring growth and incomplete markets, respectively. In both frameworks, the co-movement of top wealth and income shares is determined by the relative saving rate at the top, i.e. the ratio of the saving rate of rich individuals to the aggregate saving rate. Our empirical results suggest that relative saving rates at the top have been fairly stable over time, thus explaining the observed tight co-movement between top wealth and income shares over the past century.

KEYWORDS:

• Income inequality
• wealth inequality
• top shares
• saving rates
• cointegration
• error correction
• heterogeneous agents

JEL CLASSIFICATION:

• D31
• E21
• E25
• N32
• N34

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

¹ A detailed exposition of the model and associated derivations can be found in the Appendix.

² In the model that we consider here, the return on capital is deterministic and homogeneous across groups. Introducing stochastic and potentially heterogeneous returns would allow to differentiate between net saving (excluding capital gains) and gross saving (including capital gains) following Fagereng et al. (2019). However, the basic notion conveyed in Equation (6)(6) $s{h}_W^i={\tilde{s}}^{i}s{h}_Y^i$(6) would carry over subject to an appropriate redefinition of the RSR.

³ Castañeda, Díaz-Giménez, and Ríos-Rull (1998) model a multiple-type economy with 5 different types of agents – we keep the model as parsimonious as possible.

⁴ See the Appendix for a more detailed exposition of the model and the numerical solution method.

⁵ Wage and the interest rate are constant in equilibrium and thus do not have a time subscript (Aiyagari 1994).

⁶ Aiyagari (1994) shows simulation results with $\sigma =0.2$ and $0.4$.

⁷ Castañeda, Díaz-Giménez, and Ríos-Rull (1998) choose $\mu =1.5$, Aiyagari (1994) also shows results for $\mu =3$.

⁸ CCR and FMOLS rely on semi-parametric corrections to eliminate the correlation between the income share and ${\epsilon }_t$. The DOLS approach involves adding additional leads and lags of $s{h}_{Y_t}$ to soak up the long-run correlation between innovations to income shares and ${\epsilon }_t$.

⁹ In contrast, the data coverage for other countries is too sparse or short along the time series dimension for a sensible econometric analysis of the long-run relationship. For example, income shares for Germany and the UK are only available from 1980 onwards.

¹⁰ For France, income shares are interpolated for 1913/1914 (based on earlier data) and wealth shares in 1928/1934/1961/1963. For the US, income shares are interpolated for 1963 and 1965.

¹¹ The wealth data in WID for France is from Garbinti, Goupille-Lebret, and Piketty (2020), US data stems from Saez and Zucman (2016). Income shares for France are based on Garbinti, Goupille-Lebret, and Piketty (2018), for the US on Piketty, Saez, and Zucman (2018). For further details on the exact definitions, concepts and calculation methods underlying the wealth and income shares see these papers and Alvaredo et al. (2016).

¹² The most well-known tests by Engle and Granger (1987) and Phillips and Ouliaris (1990) test the null hypothesis of no cointegration against the alternative of cointegration by performing unit root tests on OLS residuals. The procedure proposed by Gregory and Hansen (1996) explicitly tests the null hypothesis of no cointegration against the alternative of cointegration with a possible regime shift. In contrast, the methodology by Hansen (1992) tests for OLS parameter instability and features a null hypothesis of cointegration. Finally, the bounds test by Pesaran, Shin, and Smith (2001) is based on an ARDL(p,q) model and works for both I(0) and I(1) variables, thereby constituting a more general test for a long-run relationship in levels.

¹³ These averages are calculated using the personal saving rate, U.S. Bureau of Economic Analysis, Personal Saving Rate [PSAVERT], retrieved from FRED, Federal Reserve Bank of St. Louis; https://fred.stlouisfed.org/series/PSAVERT, July 5, 2018. For France, they rely on the series Taux d’épargne des ménages, retrieved from INSEE, https://www.insee.fr/fr/statistiques/2830268, July 5, 2018. The drop in the French saving rate is most remarkable from the 1980s onwards; the average saving rate was 14.3% over the period 1980–2014. A similar result can also be seen from the data from Piketty (2011) and Piketty, Saez, and Zucman (2018), as shown.

¹⁴ Following their findings, the average saving rate for stock owners dropped from 13.2% in 1984–1989 to 8.6% in 1989–1994, while those for non-stock owners barely moved from 7.7% to 7.6% (see Table 2 in Juster et al. 2005). This corresponds to a decline of the RSR from 1.71 to 1.13.