The hopf bifurcation and the existence and stability of closed orbits in multisector models of optimal economic growth

It is shown that under very general circumstances, the standard optimal growth model with two or more capital goods can give rise to optimal trajectories that are limit cycles. An example with a nonjoint production Cobb-Douglass technology giving rise to closed cycles around a unique steady state is constructed. The stability of orbits is also studied.     

The Chinese Stock Market Does not React to the Japanese Market: Using Intraday Data to Analyse Return and Volatility Spillover Effects

In this paper, we use high‐frequency data to explore the effects of return and volatility spillover during periods in which trading hours in China and Japan overlap. Specifically, we utilize 5‐min returns to estimate fractionally integrated asymmetric power autoregressive conditional heteroskedasticity and fractionally integrated exponential generalized autoregressive conditional heteroskedasticity models, then use the models' standardized residuals to employ a cross‐correlation function approach that tests for the degree to which the Chinese and Japanese markets affect each other. Results indicate a unidirectional influence of the Chinese stock market on Japanese markets in terms of return. This result is likely attributable to restrictions on foreign investment in the Chinese market and the lack of diversified international portfolios among individual Chinese investors.     

Transboundary Pollution in a Dynamic Game Model

We consider a dynamic game model in which N countries produce a single product that is not traded. Production results in emissions that accumulate a stock of pollution in each country. Households in each country derive utility from consuming the product but face costs depending on the level of the country-specific stock of pollution as well as the pollution stocks of the other countries. We distinguish three different cost scenarios. For all three, we show the existence of a Markov perfect equilibrium (MPE) and derive the collusive outcome. The MPEs are associated with the case where countries fail to coordinate their policies, while the collusive solutions correspond to the coordinated policy.
JEL Classification No.: C73.     

Commodity Spread Option with Cointegration

We derive the valuation formula of a European call option on the spread of two cointegrated commodity futures prices, based on the Gibson–Schwartz with cointegration (GSC) model. We also analyze the American commodity spread option including the early exercise premium representation and an analytical approximation valuation formulae with cointegration. In the numerical analysis, we compare the spread option values calculated by the GSC model and the Gibson–Schwartz (GS) model that ignores cointegration. Consistent with the intuition that the cointegration prevents the prices from diverging, the GSC model prices the commodity spread option lower than the GS model which have longer maturity of more than 6 years. In other words, the GS model may overprice the commodity spread options for those with longer maturity without taking account of cointegration. Thus, incorporating cointegration is important for valuation and hedging of long-term commodity spread options such as large scale oil refining plant developments.     

Optimal Pricing Strategy in the Case of Price Dispersion: New Evidence from the Tokyo Housing Market

We adopt a multistage search model, in which the home seller's reservation price is determined by her or his opportunity cost, search cost, discount rate and additional market parameters. The model indicates that a greater dispersion in offer prices leads to higher reservation and optimal asking prices. A unique dataset from the Tokyo condominium resale market enables us to test those modeled hypotheses. Empirical results indicate that a one percentage point increase in the standard deviation of submarket transaction prices results in a two‐tenths of a percent increase in the initial asking price and in the final transaction price. Increases in the dispersion of market prices enhance the probabilities of a successful transaction and/or an accelerated sale.     

Bifurcation and sunspots in the continuous time equilibrium model with capacity utilization

In the present paper, we construct a continuous time model of economic growth with positive externalities and with variable capacity utilization, and study the global equilibrium paths in this model. If there is a homoclinic orbit or a periodic solution in this model, equilibrium is globally indeterminate. We show that positive externalities can yield multiple steady states, a one-parameter family of homoclinic orbits, and a two-parameter family of periodic solutions. It is also shown that there exists a sunspot equilibrium in this model.     

Working and Training: A Nonlinear Dynamic Analysis of Human Capital Development

We tend to think of workers completing their education and then entering the workforce, where they will gradually develop their skills. In fact, however, a worker's career may be characterized not only by this gradual buildup of job-related skills but also by recurrent education, i.e. the phenomenon whereby a worker alternates between earning-intensive periods and training-intensive periods along his career path. In this study, we build a dynamic optimization model of earning/training decisions of a worker in which these patterns of his career path can be explained in an integrated manner.     

A theory of heterogeneous city growth

We consider an economy with three cities producing different outputs. Two cities produce intermediate goods, a type 1 city producing an intermediate “agricultural” good with capital and labor only, and a type 2 city producing an intermediate “industrial” good with capital, labor, and human capital. A type 3 city produces the final good which is obtained from the two intermediate goods and labor. The asymmetric introduction of human capital allows us to prove that the three cities experience, at equilibrium, heterogeneous endogenous growth rates which are proportional to the growth rate of human capital. We show that the “industrial” type 2 city is characterized by the larger growth rate while the “agricultural” type 1 city experiences the lower growth rate, and thus the type 3 city is characterized by a growth rate which is a convex combination of the two former growth rates. This implies that the relative size in terms of output of the “agricultural” city decreases over time. This property allows us to recover the empirical fact that most non‐agricultural production occurs in growing metropolitan areas. But, simultaneously, as we prove that total labor employed in each city is proportional to the total population, the relative population size distribution of cities is constant over time, as shown in empirical studies.