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.     

Learning of cycles and sunspot equilibria by Genetic Algorithms

We analyze the learning behaviour of a Simple Genetic Algorithm in an overlapping generations model with one consumption good and fiat money. It is shown by simulations, that in cases where periodic equilibria exist the equilibrium of period two is learned by a Genetic Algorithm and not the monetary steady state. We further show that proper coding leads to convergence of the GA towards the sunspot equilibrium. If individuals who believe in the impact of sunspots are brought together with individuals who ignore the sunspots, the sunspot believes will in most cases drive the other individuals out of the population.     

When do thick venture capital markets foster innovation? An evolutionary analysis

In this paper, we examine the trade off between different effects of the availability of venture capital on the speed of technological progress in an industry. We consider an evolutionary industry simulation model based on Nelson and Winter (1982), in which R&D efforts of an incumbent firm generate technological know-how embodied in key R&D employees, who might use this know-how to found a spinoff of the incumbent. Venture capital is needed to finance a spinoff, so that the expected profits from founding a spinoff depend on how easily venture capital can be acquired. Accordingly, thick venture capital markets might have two opposing effects. First, incentives of firms to invest in R&D might be reduced and, second, if spinoff formation results in technological spillovers between the parent firm and the spinoffs, the generation of spinoff firms might positively influence the future efficiency of the incumbent’s innovation efforts. We study the manner in which this tradeoff influences the effect of venture capital on innovation expenditures, speed of technological change and evolution of industry concentration in several scenarios with different industry characteristics.     

On economic applications of the genetic algorithm: a model of the cobweb type

This paper explores the idea of using artificial adaptive agents in economic theory. In particular, we use Genetic Algorithms (GAs) to model the learning behavior of a population of adaptive and boundedly rational agents interacting in an economic system. We analyze the behavior of a GA in two versions of a model of the cobweb-type, one in which firms make only quantity choices, and the other one in which firms first decide to exit or to stay in the market, and subsequently decide how much to produce. We present simulations with different coding schemes and interpret the rather surprising differences between the results for different setups by employing the mathematical theory for GAs with state-dependent fitness functions. In particular, we explain the relationship between coding and convergence properties of GAs.     

R&D competition versus R&D cooperation in oligopolistic markets with evolving structure

This paper considers investment behavior of duopolistic firms subject to technological progress. It is assumed that initially both firms offer a homogeneous product, but after a stochastic waiting time they are able to implement a product innovation. Production capacities of both firms are product specific. It is shown that firms anticipate a future product innovation by under-investing (if the new product is a substitute to the established product) and higher profits, and over-investing (in case of complements) and lower profits, compared to the corresponding standard capital accumulation game. This anticipation effect is stronger in the case of R&D cooperation. Furthermore, since due to R&D cooperation firms introduce the new product at the same time, this leads to intensified competition and lower firm profits right after the new product has been introduced. In addition, we show that under R&D competition the firm that innovates first, overshoots in new-product capacity buildup in order to exploit its temporary monopoly position. Taking into account all these effects, the result is that, if the new product is neither a close substitute nor a strong complement of the established product, positive synergy effects in R&D cooperation are necessary to make it more profitable for firms than R&D competition.     

Innovation source,advancement stage and company stock returns

The purpose of this paper was to measure the short- and long-term impact of innovation announcements on the stock returns of service companies. In order to study the predictors of the abnormal stock returns, the study takes the adoption and diffusion theory as its conceptual background. The research was based on an event study and buy-and-hold methods. It encompassed 398 announcements released for 121 companies in EU member states between February 2011 and December 2016. The study deepens the dialogue on the role of the source of innovation and its advancement stage. It indicates a positive market reaction to high innovation advancement stage announcements in comparison to low advancement stage ones. Furthermore, it suggests a positive market reaction to in-house development in comparison to collaborative development and copying. Finally, the research signals that the innovation advancement stage complements its source by clarifying its relationship with abnormal market value changes.     

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.     

Long horizon versus short horizon planning in dynamic optimization problems with incomplete information

Summary. This paper compares the implications of short and long horizon planning in dynamic optimization problems with the structure of a standard one-sector growth model if agents have incomplete knowledge about the production function. Agents know the output and rate of return at the current capital stock and use an estimation of the production function based on this knowledge to determine current consumption. For standard utility functions without wealth-effects both long and short planning horizons yield convergence to the steady state - however at a faster rate than optimal -, or fluctuations around the steady state, and in both cases, long horizon planning yields a policy which locally at the steady state is closer to the optimal one than short horizon planning. On the other hand, for preferences with wealth effects where the intertemporal optimal path exhibits fluctuations, long horizon planning destabilizes the path and short horizon planning can generate paths which are qualitatively closer to the optimal one and yield higher discounted utility.Received: 5 April 2001, Revised: 15 September 2003, JEL Classification Numbers: C61, D83, D90.Herbert Dawid: The author would like to thank Richard Day for numerous stimulating discussions which led to this article and an anonymous referee for helpful comments