On geometric ergodicity of the commodity pricing model

We provide a simple proof of geometric ergodicity for Samuelson's (1971) commodity pricing model. The proof yields a rate of convergence to the stationary distribution stated in terms of model primitives. We also provide a rate of convergence for prices to the stationary price process, and for the joint distribution of the state process to the stationary state process.     

Indeterminacy Arising in Multi-sector Economies

We characterize a large class of constant-returns-to-scale economies with standard Cobb–Douglas production technologies, which, when perturbed to incorporate external effects, exhibit indeterminacy or multiple equilibria. The perturbations are constrained to maintain overall constant returns to scale. We characterize the magnitude of the external effects that yield multiple equilibria in terms of the parameters of the unperturbed economy. We show that it is very easy to construct large and plausible classes of economies that exhibit indeterminacy with constant returns to scale, and with external effects that are arbitrarily small.
JEL Classification Numbers: E00, E3, O40.     

Investigating Collaborative R&D Using Patent Data: The Case Study of Robot Technology in Japan

The growing trend of collaborative R&D initiated by firms has been well documented. However, the evidences regarding basic questions such as the benefits of collaboration and the motives of firms are still mixed. The main novelty of this paper is to investigate these questions by using comprehensive patent data with a focus on information concerning inventors. We consider the case of robot technology in Japan since early 1990s and get the following results. First, collaboration with external research partners lead to a higher quality of the invention. Second, the determinants and motives, which encourage firms to engage in collaborative research, differ depending on the partner they are collaborating with. Copyright © 2011 John Wiley & Sons, Ltd.     

Equilibrium dynamics in discrete-time endogenous growth models with social constant returns

The existing literature establishes possibilities of local determinacy and dynamic indeterminacy in continuous-time two-sector models of endogenous growth with social constant returns. The necessary and sufficient condition for local determinacy is that the factor intensity rankings of the two sectors are consistent in the private/physical and social/value sense. The necessary and sufficient condition for dynamic indeterminacy is that the final (consumable) good sector is human (pure) capital intensive in the private sense but physical (consumable) capital intensive in the social sense. This paper re-examines the dynamic properties in a discrete-time endogenous growth framework and finds that conventional propositions obtained in continuous time need not be valid. It is shown that the established necessary and sufficient conditions on factor intensity rankings for local determinacy and dynamic indeterminacy are neither sufficient nor necessary, as the magnitudes of time preference and capital depreciation rates both play essential roles. We have benefitted from discussion with Robert Becker, Eric Bond, Michael Kaganovich, Karl Shell and participants of the Midwest Macroeconomic Conference in Chicago and the Midwest Economic Theory and International Trade Meetings at Indiana University. The fourth author acknowledges financial support from the Institute of Economics and Business Administration of Kobe University and the Institute of Economic Research of Kyoto University to enable this international collaboration.     

The old-age security hypothesis revisited

"Children's altruism toward parents is allowed in a two-overlapping-generations model with endogenous fertility. Parents raise children because, when retired, they expect gifts from their children who are essentially a capital good. Individuals' behavior between generations is examined by analyzing a Nash equilibrium, which is then compared with a social planner's optimal allocation. The pay-as-you-go public pension program is viewed as the optimal gifts from the optimal allocation when the latter is implemented. The effect on fertility of the introduction of a capital market is also analyzed. The validity of the old-age security hypothesis is shown to depend on the parameters of utility and cost functions."     

Indeterminacy and cycles in two-sector discrete-time model

Summary. We consider a discrete-time two-sector Cobb-Douglas economy with positive sector specific external effects. We show that indeterminacy of steady states and cycles can easily arise with constant or decreasing social returns to scale, and very small market imperfections. This is in sharp contrast with most of the contributions in the literature in which increasing social returns are required to generate indeterminacy. Received: July 31, 2000; revised version: June 5, 2001