Complex solutions of nonconcave dynamic optimization models

Summary In this paper we consider a class of time discrete intertemporal optimization models in one dimension. We present a technique to construct intertemporal optimization models with nonconcave objective functions, such that the optimal policy function coincides with any pre-specifiedC ² function. Our result is a variant of the approach presented in a seminal paper by Boldrin and Montrucchio (1986). Whereas they solved the inverse problem for the reduced form models, we address the different question of how to construct both reduced and primitive form models. Using our technique one can guarantee required qualitative properties not only in reduced, but also in primitive form. The fact that our constructed model has a single valued and continuous optimal policy is very important as, in general, nonconcave problems yield set valued optimal policy correspondences which are typically hard to analyze. To illustrate our constructive approach we apply it to a simple nonconcave model.We are grateful for the helpful comments of L. Montrucchio, K. Nishimura, T. Mitra and an anonymous referee. Financial support of the Austrian Science Foundation under contract No. P7783-PHY and No. J01003-SOZ is gratefully acknowledged. This paper was written while M. Kopel was visiting the Department of Economics, Cornell University.     

Dynamic R&D competition with memory

We consider a differential game of R&D competition and explore the impact of rivalry on the firms' investment behavior over time. Using closed-loop strategies and hence allowing for strategic interactions among rival firms we show that R&D spending by the individual competitor is increased due to competition in the race for priority. This leads us to argue that competitive encounters enhance R&D activities at the same time as increasing efficiency in the race for a technological breakthrough.     

The accomplishment of the Maastricht criteria with respect to initial debt

The reduction of government debt to 60% of the GDP in order to satisfy the requirements of the Maastricht Treaty for participation in the European Monetary Union is one of the primary economic-policy goals for most of the European Union countries. The first aim of the present paper is to characterize the optimal path of the primary surplus that leads to the achievement of this Maastricht target. Using optimal-control theory we are able to determine an upper bound of the public-debt-to-GDP ratio above which no retrenchment policy becomes effective. The second issue taken up is that of the sensitivity analysis with respect to the initial level of the debt-to-GDP ratio, the growth rate of the economy, the interest rate, the inflation rate, and the inverse of the velocity of the monetary base circulation.     

Price-raising drug enforcement and property crime: a dynamic model

Price-raising drug enforcement suppresses drug use, but it is expensive and may increase property crime. This has led to contradictory recommendations concerning how drug enforcement should or should not be used. We reconcile these recommendations by incorporating the enforcement's effects on both drug use and on property crime within an optimal-control model that recognizes whether convicted drug-involved property offenders are merely incarcerated or whether they receive some form of drug treatment.     

On the optimality of limit cycles in dynamic economic systems

The purpose of this paper is to derive conditions for the optimality of a limit cycle in a dynamic economic system and to interpret them economically. A fairly general two-state continuous-time nonlinear optimal control problem is considered. It turns out that for this class of models three different economic mechanisms can be identified as the possible source of limit cycles. One relates to an intertemporal substitution effect expressed in terms of complementarity over time, the second one is a dominating cross effect between the state variables of the system (i.e., the capital stocks in our model), and the third one is positive growth at the equilibrium.We acknowledge the helpful comments by William A. Brock, Gerhard Sorger, Franz Wirl, and two anonymous referees. The research was partly supported by the Austrian Science Foundation under contract No. P6601.     

On the persistence of corruption

This paper tries to answer the question why the phenomenon of corruption seems to be inherently existent in any society. The dynamic model presented shows how rational agents may generate multiple equilibria of corruption within the same kind of socio-economic system. We assume that the individual disutility caused by the loss of reputation from a corrupt transaction depends on the acceptance of corrupt behavior by the representative individual. Depending on the values of some key parameters like the marginal utility of corrupt behavior and the initial acceptance of corruption a completely corrupt equilibrium where all people completely accept corruption or a completely honest equilibrium where corruption is not accepted at all may be the limit state of the optimal path. Also inner equilibria in-between exist; however, they are always unstable.     

Anticipation effects of technological progress on capital accumulation: a vintage capital approach

Due to embodied technological progress new generations of capital goods are more productive. Therefore, in order to study the effects of technological progress, a model must be analyzed in which different generations of capital goods can be distinguished. We determine in what way the firm adjusts current investments to predictions of technological progress. In the presence of market power we show that a negative anticipation effect occurs, i.e. current investments in recent generations of capital goods decline when faster technological progress will take place in the future, because then it becomes more attractive to wait for new generations of capital goods. In case that only investments in new machines are possible, actually a whole wave of anticipation phases arises.     

Politico-economic cycles of regulation and deregulation

This paper considers politico-economic cycles that do not depend on the exogenous electoral cycles. More precisely, the paper develops a positive model of intertemporal subsidy strategies for an authoritarian and dynastic government. It will be shown — applying the Hopf bifurcation theorem — that cyclical strategies, i.e. waves of regulation, populism alternating with deregulation, cuts in social programmes, etc., may be optimal.     

Über einN-elementiges Modell der Reiz-Stichproben-Theorie mit stetigem Zeitparameter und zwei Antwortklassen

Zusammenfassung Es wird ein Modell der Reiz-Stichproben-Theorie [vgl.Atkinson u.Estes] mit stetigem Zeitparameter untersucht. Dabei handelt es sich um ein sogenanntes Pattern-Modell mitN Reizelementen und zwei Antwortklassen. Die den Systemablauf beherrschenden Differentialgleichungen werden hergeleitet und gel?st. Es werden Resultate über das Grenzverhalten der verknüpften stochastischen Prozesse erzielt, insbesonders über den effektiven Antwortproze?. Ferner werden Methoden zur Punktsch?tzung der unbekannten ParameterN (Anzahl der Reizelemente) undc (Lernrate) behandelt.

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Summary A model of stimulus sampling theory [cp.Atkinson andEstes] with continuous time parameter is investigated. We are concerned with a so-called pattern model withN stimulus elements and two response classes. The differential equations governing the system are derived and solved. Some results on the limit behaviour of associated stochastic processes are obtained, concerning especially the actual response process. Furtheron methods are treated for point estimation of the unknown parametersN (number of stimulus elements) andc (learning rate).