Intertemporal allocation with incomplete markets

Kuhle, Wolfgang

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URN: urn:nbn:de:bsz:180-madoc-30282
Document Type: Doctoral dissertation
Year of publication: 2010
Place of publication: Mannheim
University: Universität Mannheim
Evaluator: Ludwig, Alexander
Date of oral examination: 3 August 2010
Publication language: English
Institution: Außerfakultäre Einrichtungen > Mannheim Research Institute for the Economics of Aging (MEA) (- 6/2011) (Börsch-Supan) (Börsch-Supan)
Subject: 330 Economics
Classification: JEL: E21 E13 E22 E62 H55 E44 E25 E23 H63 ,
Subject headings (SWD): Goldene Regel , Kapitaltheorie , Öffentliche Schulden , Generationenvertrag , Risikoverteilung , Optimaler Wachstumspfad , Bevölkerungswachstum
Individual keywords (German): Überlappende Generationen , Goldene Regel , Kapitaltheorie , Staatsverschuldung , Intergenerationaler Risikoaustausch , Optimales Bevölkerungswachstum
Keywords (English): Golden Rule , Capital Theory , Public Debt , Pension Systems , Intergenerational Risk Sharing , Optimal Population , Overlapping Generations
Abstract: This thesis consists of five neoclassical parables which characterize efficient and inefficient allocations in the two-generations-overlapping model. Chapter 2 of this thesis gives exact general conditions for the existence of an interior optimum growth rate for population in the neoclassical two-generations-overlapping model. In an economy where high (low) growth rates of population lead to a growth path which is efficient (inefficient) there always exists an interior optimum growth rate for population. In all other cases there exists no interior optimum. The Serendipity Theorem, however, does in general not hold in an economy with government debt. Moreover, the growth rate for population which leads an economy with debt to a golden rule allocation can never be optimal. Chapter 3 is concerned with the role of the two-part golden rule as the watershed between equilibria which are dynamically efficient and those, which are inefficient. In an economy where agents differ regarding their labour endowment, the golden rule allocation ceases to serve as such a demarcation line. Except for the special case where all agents possess a linear Engel-curve with identical slope, some agents' maximum steady state utility will always be associated with a capital intensity exceeding (falling short of) the golden rule level. This result stems from the fact that the competitive markets entail an intra-generational redistribution of resources once the capital intensity is altered. If heterogeneity is introduced on the preference side, we find that the golden rule is never optimal for all agents. Consequently, earlier results in the literature on the two-part golden rule with heterogeneous agents are not warranted. Chapter 4 studies the structural differences between implicit and explicit government debt in a two-generations-overlapping model with stochastic factor-prices. If a government can issue safe bonds and new claims to wage-indexed social security to service a given initial obligation, there exists a set of Pareto-efficient ways to do so. This set is characterized by the conflicting interests of the current young and the yet unborn generations regarding the allocation of factor-price risks. However, it is shown that there will always exist a simple intertemporal compensation mechanism which allows to reconcile these conflicting interests. This compensation mechanism narrows the set of Pareto-efficient debt structures until only one remains. This result hinges on the double-incomplete markets structure of stochastic OLG models where households can neither trade consumption loans nor factor-price risks privately. The last chapter studies how the upcoming demographic transition will affect the returns to risky capital and safe government debt. In a neoclassical two-generations-overlapping model we show that the entrance of smaller cohorts into the labor market will lower both interest rates. The risky rate, however, will react more sensitive than the risk free rate. Consequently, the risk premium deteriorates during the transition.
Translation of the title: Intertemporale Allokation auf unvollständigen Märkten (German)
Translation of the abstract: In dieser aus fünf Aufsätzen bestehenden Dissertation werden im Rahmen des neoklassischen Modells überlappender Generationen effiziente und ineffiziente Allokationen charakterisiert. Die ersten beiden Kapitel befassen sich mit der Rolle der Goldenen Regel als Effizienzkriterium. In Kapitel 2 wird die normative Bedeutung der Goldenen Regel im Rahmen des Problems der optimalen Bevölkerungswachstumsrate untersucht. Dabei werden exakte notwendige und hinreichende Bedingungen für die Existenz einer inneren optimalen Bevölkerungswachstumsrate gegeben. In einem zweiten Schritt wird in Kapitel 3 im Rahmen einer Ökonomie mit heterogenen Haushalten gezeigt, dass die Goldene Regel nur dann effiziente und ineffiziente Steady States voneinander trennt, wenn alle Haushalte eine lineare Engelkurve mit identischer Steigung besitzen. In Kapitel 4 wird die Interaktion von intergenerationalem Risikoaustausch, Kapitalverdrängung und staatlicher Verschuldung untersucht. Aus den strukturellen Unterschieden von impliziten (umlagefinanzierte Rente) und expliziten (Staatsanleihen) Staatsschulden wird eine optimale Verschuldungsstruktur abgeleitet. Diese kann, ausgehend von jeder anderen Verschuldungsstruktur, auf paretoverbessernde Art und Weise erreicht werden. (German)
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