A theory of the saving rate of the rich

Ma, Qingyin; Toda, Alexis Akira

doi:10.1016/j.jet.2021.105193

Cited by 14 publications

(12 citation statements)

References 38 publications

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“…(2020). The asymptotic linearity of

\overset{c}{true}

follows from Ma and Toda (2021, Theorem 3). Noting that

\begin{matrix} E false[\overset{β}{true} {\overset{false~}{R}}^{1 ‐ γ} false] = E false[β G^{1 ‐ γ} {false(R false/ G false)}^{1 ‐ γ} false] = E false[β R^{1 ‐ γ} false], \end{matrix}

the limit () follows from their Example 2.…”

Section: Model Of Capital and Labor Pareto Exponentsmentioning

confidence: 95%

“…Our empirical analysis in Section 3 suggests that (i) the capital income Pareto exponent is smaller than the labor one (i.e., capital income is more unequally distributed than labor income), and (ii) the correlation between capital and labor income Pareto exponents is weak. To explain these empirical findings, we present a simple dynamic model of consumption and savings, which builds on one of the authors’ previous works (Ma et al ., 2020; Ma and Toda, 2021). Our model is more specialized but the characterizations are sharper.…”

Section: Model Of Capital and Labor Pareto Exponentsmentioning

confidence: 99%

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Capital and Labor Income Pareto Exponents Across Time and Space

Vries

Toda

2021

Review of Income and Wealth

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We estimate capital and labor income Pareto exponents across 475 countryyear observations that span 52 countries over half a century .We document two stylized facts: (i) capital income is more unequally distributed than labor income in the tail; namely, the capital exponent (1-3, median 1.46) is smaller than labor (2-5, median 3.35), and (ii) capital and labor exponents are nearly uncorrelated. To explain these findings, we build an incomplete market model with job ladders and capital income risk that gives rise to a capital income Pareto exponent smaller than but nearly unrelated to the labor exponent. Our results suggest the importance of distinguishing income and wealth inequality.

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“…(2020). The asymptotic linearity of

\overset{c}{true}

follows from Ma and Toda (2021, Theorem 3). Noting that

\begin{matrix} E false[\overset{β}{true} {\overset{false~}{R}}^{1 ‐ γ} false] = E false[β G^{1 ‐ γ} {false(R false/ G false)}^{1 ‐ γ} false] = E false[β R^{1 ‐ γ} false], \end{matrix}

the limit () follows from their Example 2.…”

Section: Model Of Capital and Labor Pareto Exponentsmentioning

confidence: 95%

Section: Model Of Capital and Labor Pareto Exponentsmentioning

confidence: 99%

Capital and Labor Income Pareto Exponents Across Time and Space

Vries

Toda

2021

Review of Income and Wealth

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“…The asymptotic analysis step of our approach exploits the asymptotic linearity of policy functions in models with homothetic utility as well as the analytical characterization of the Pareto exponent as the solution to an eigenproblem. Although the asymptotic linearity of policy functions with homothetic preferences is intuitive, a rigorous proof with an exact analytical characterization of asymptotic slopes was obtained only recently by Ma and Toda (2021, 2022) after the working paper version of this paper (Gouin‐Bonenfant and Toda (2018)) was circulated. To analytically characterize the Pareto exponent of the wealth distribution in a general Markovian environment, we apply the recent results from Beare and Toda (2022), who characterize the Pareto exponent as a solution to an eigenproblem.…”

Section: Introductionmentioning

confidence: 99%

“…Appendix A of the Online Supplementary Material (Gouin‐Bonenfant and Toda (2023)) formally defines the asymptotic problem and heuristically discusses the asymptotic linearity of policy functions in an abstract dynamic programming setting. For a rigorous proof of asymptotic linearity as well as an analytical characterization of asymptotic slopes, see Ma and Toda (2021, 2022).…”

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confidence: 99%

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Pareto extrapolation: An analytical framework for studying tail inequality

Gouin-Bonenfant

Toda

2023

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We develop an analytical framework designed to solve and analyze heterogeneous‐agent models that endogenously generate fat‐tailed wealth distributions. We exploit the asymptotic linearity of policy functions and the analytical characterization of the Pareto exponent to augment the conventional solution algorithm with a theory of the tail. Our framework allows for a precise understanding of the very top of the wealth distribution (e.g., analytical expressions for top wealth shares, type distribution in the tail, and transition probabilities in and out of the tail) in addition to delivering improved accuracy and speed.

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Unbounded Markov dynamic programming with weighted supremum norm Perov contractions

Toda

2024

Econ Theory Bull

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A theory of the saving rate of the rich

Cited by 14 publications

References 38 publications

Capital and Labor Income Pareto Exponents Across Time and Space

Capital and Labor Income Pareto Exponents Across Time and Space

Pareto extrapolation: An analytical framework for studying tail inequality

Unbounded Markov dynamic programming with weighted supremum norm Perov contractions

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