The invariant distribution of wealth and employment status in a small open economy with precautionary savings

Bayer, Christian; Rendall, Alan D.; Wälde, Klaus

doi:10.1016/j.jmateco.2019.08.003

Cited by 14 publications

(9 citation statements)

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“…A Poisson process (Q(t)) t 0 with intensity > 0 on 14 It would also imply a constant domestic wage rate. In the presence of unemployment as in Bayer et al (2019), the domestic capital stock would adjust accordingly. 15 Readers interested in understanding means can go to section 4.2 immediately.…”

Section: Preliminariesmentioning

confidence: 99%

“…The derivation works in analogy to deriving the wealth distribution in the next section. 30 We know from more abstract (probability based) work by Bayer et al (2019) that processes like our age and the related wealth process are characterized by the existence of a unique long-term distribution which is stable. The latter means that for all (meaningful) initial distributions, an initial distribution converges over time to this unique and stable long-term distribution.…”

Section: The Age Distributionmentioning

confidence: 99%

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The Dynamics of Pareto Distributed Wealth in a Small Open Economy

2021

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We study a small open economy displaying Pareto-distributed wealth resulting from random death. The government runs a distribution scheme on inheritance. We present the mathematical background that allows to study the dynamics of means. We end up with ordinary differential equations for the mean of age and of individual and government wealth. We also study distributional dynamics analytically. Starting from any distribution of age and wealth, the aggregate distribution converges, both on a transition path towards a steady state and on a transition path towards balanced growth, to an exponential distribution of age and a Paretodistribution of wealth. The findings are illustrated for different distribution schemes.

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Section: Preliminariesmentioning

confidence: 99%

Section: The Age Distributionmentioning

confidence: 99%

The Dynamics of Pareto Distributed Wealth in a Small Open Economy

2021

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“…We can express the transition across health states of an individual by a stochastic differential equation similar to the transition across states of employment (see e.g. appendix B .1 to Bayer et al, 2019 or Khieu and Wälde, 2020). We can also directly write down ordinary differential equations for an individual to be in a certain state s at t .…”

Section: The Modelmentioning

confidence: 99%

Projecting the Spread of COVID19 for Germany

Donsimoni

Glawion²,

Plachter

et al. 2020

Preprint

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We model the evolution of the number of individuals that are reported to be sick with COVID-19 in Germany. Our theoretical framework builds on a continuous time Markov chain with four states: healthy without infection, sick, healthy after recovery or after infection but without symptoms and dead. Our quantitative solution matches the number of sick individuals up to the most recent observation and ends with a share of sick individuals following from infection rates and sickness probabilities. We employ this framework to study inter alia the expected peak of the number of sick individuals in a scenario without public regulation of social contacts. We also study the e¤ects of public regulations. For all scenarios we report the expected end of the CoV-2 epidemic.We have four general …ndings: First, current epidemiological thinking implies that the long-run e¤ects of the epidemic only depend on the aggregate long-run infection rate and on the individual risk to turn sick after an infection. Any measures by individuals and the public therefore only in ‡uence the dynamics of spread of CoV-2. Second, predictions about the duration and level of the epidemic must strongly distinguish between the o¢ cially reported numbers (Robert Koch Institut, RKI) and actual numbers of sick individuals. Third, given the current (scarce) medical knowledge about long-run infection rate and individual risks to turn sick, any prediction on the length (duration in months) and strength (e.g. maximum numbers of sick individuals on a given day) is subject to a lot of uncertainty. Our predictions therefore o¤er robustness analyses that provide ranges on how long the epidemic will last and how strong it will be. Fourth, public interventions that are already in place and that are being discussed can lead to more and less severe outcomes of the epidemic. If an intervention takes place too early, the epidemic can actually be stronger than with an intervention that starts later. Interventions should therefore be contingent on current infection rates in regions or countries. of the modelling initiative of the Deutsche Gesellschaft für Epidemiologie for comments and discussions. We are deeply indebted to Damir Stijepic for the initial numerical solutions and the initial calibration. Our biggest debt of gratitude is owed to Matthias Birkner who has been advising and teaching us on stochastic models for many years. : medRxiv preprint over, will lie between 500 thousand and 5 million individuals. While this seems to be an absurd large range for a precise projection, this re ‡ects the uncertainty about the long-run infection rate in Germany. If we assume that Germany will follow the good scenario of Hubei (and we are even a bit more conservative given discussions about data quality), we will end up with 500 thousand sick individuals over the entire epidemic. If by contrast we believe (as many argue) that once the epidemic is over 70% of the population will have been infected (and thereby immune), we will end up at 5 million cases.De…ning the end of the epi...

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“…This allows to study wealth of domestic dynasties and government wealth independently of each other.17 This idea was employed previously inBayer et al (2019).18 This extends the AK approach of e.g Toda (2014)…”

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confidence: 99%

“…. Our earlier version(Birkner et al 2021) also followed the AK approach.19 In the presence of unemployment as inBayer et al (2019), the domestic capital stock would adjust accordingly.20 Readers interested in understanding means can go to Sect. 4.2 immediately.…”

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confidence: 99%

The dynamics of Pareto distributed wealth in a small open economy

2022

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We study a small open economy with labor, capital accumulation, random death, taxation and a government budget balanced in the long run. We offer methods that provide ordinary differential equations for means and analytical expressions for densities. The latter is achieved by solving stochastic differential equations analytically and deriving the density from this solution. Starting from any distribution, the aggregate distribution converges, both on a transition path towards a steady state and on a transition path towards balanced growth, to a Pareto-distribution. We provide an intuitive economic interpretation for a stationary long-run density with an infinite mean in an economy on a balanced growth path. We also show how government tax policy can lead to non-monotonic links between the equilibrium growth rate of the economy and risk aversion of households.

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The invariant distribution of wealth and employment status in a small open economy with precautionary savings

Cited by 14 publications

References 46 publications

The Dynamics of Pareto Distributed Wealth in a Small Open Economy

The Dynamics of Pareto Distributed Wealth in a Small Open Economy

Projecting the Spread of COVID19 for Germany

The dynamics of Pareto distributed wealth in a small open economy

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