Over the past three decades, analysis of dynamics has come to the forefront of macroeconomic theory. A key impetus for progress on this front has been the connections developed between equilibrium growth theory, on one hand, and the field of nonlinear dynamics, on the other. Kazuo Nishimura's work has been at the center of these advances, and the lines of research he initiated remain an exciting area of study for young researchers with strong technical skills.

It is a great honor and a great pleasure for me to pay tribute to the accomplishments of Kazuo Nishimura on the occasion of this special issue. He is a great scientist, whose contributions I deeply admire and respect, and he is a good friend.

Ramsey equilibrium models with heterogeneous agents and borrowing constraints are shown to yield efficient equilibrium sequences of aggregate capital and consumption. The proof of this result is based on verifying that equilibrium sequences of prices satisfy the Malinvaud criterion for efficiency.

This paper proves the existence of competitive equilibrium in a single-sector dynamic economy with heterogeneous agents, elastic labor supply, and complete asset markets. The method of proof relies on some recent results concerning the existence of Lagrange multipliers in infinite-dimensional spaces and their representation as a summable sequence and a direct application of the inward-boundary fixed point theorem.

This paper shows that complex dynamics arises naturally in deterministic discrete choice problems. In particular, it shows that if the objective function of a maximization problem can be written as a function of a sequence of discrete variables, and if the (maximized) value function is strictly increasing in an exogenous variable, then for almost all values of the exogenous variable, any optimal path exhibits aperiodic dynamics. This result is applied to a maximization problem with indivisible durable goods, as well as to a Ramsey model with an indivisible consumption good. In each model, it is shown that optimal dynamics is almost always complex. These results are illustrated with various numerical examples.

This paper studies the nature of long-run behavior in a two-sector model of optimal growth. Under some restrictions on the parameters of the model, we provide an explicit solution of the optimal policy function generated by the optimal growth model. Fixing the discount factor, we indicate how long-run optimal dynamics changes as a key technological parameter (labor output ratio) changes. For a particular configuration of parameter values, we also provide an explicit solution of the unique absolutely continuous invariant ergodic distribution generated by the optimal policy function.

We consider an overlapping-generations economy with two consumption goods. There are two sectors that produce a pure consumption good and a mixed good that can be either consumed or used as capital. We prove that the existence of Pareto-optimal expectations-driven fluctuations is compatible with standard sectoral technologies if the share of the pure consumption good is low enough. Following Reichlin's [Journal of Economic Theory 40 (1986), 89–102] influential conclusion, this result suggests that some fiscal policy rules can prevent business-cycle fluctuations in the economy by driving it to the optimal steady state as soon as they are announced.

The capital intensity takes an important role in two-sector and multisector growth models. Surprisingly very few empirical studies have been conducted so far except by Kuga (1967). This fact implies that few people have ever tried to perform any empirical research to study whether the two-sector and multisector optimal growth models could explain the economic development properly based on the empirical data. Although we witnessed fairly active theoretical research on two-sector and multisector growth models in the 1990s and recent years, R. M. Solow has thrown doubt on the capital intensities [in Philippe Aghion and Steven Durlauf (eds.), Handbook of Economic Growth, Vol. 1A (2005, pp. 3–10)]. Our purpose is to measure the capital intensities of the consumption good and the investment good sectors mainly in the postwar Japanese economy, and also in other OECD countries. By so doing, we will demonstrate that the capital intensity does matter and our empirical evidence will strongly support the common assumption that the consumption goods sector is more capital-intensive than the capital goods sector.

This paper provides conditions for bounding tail probabilities in stochastic economic models in terms of their transition laws and shock distributions. Particular attention is given to conditions under which the tails of stationary equilibria have exponential decay. By way of illustration, the technique is applied to a threshold autoregression model of exchange rates.

Many economic analyses are based on the property that the value of a commodity vector responds continuously to a change in economic environment. As is well known, however, many infinite-dimensional models, such as an infinite–time horizon stochastic growth model, lack this property. In the present paper, we investigate a stochastic growth model in which dual vectors lie in an L∞ space. This result ensures that the value of a stock vector is jointly continuous with respect to the stock vector and its support price vector. The result is based on the differentiation method in Banach spaces that Yano [Journal of Mathematical Economics 18 (1989), 169–185] develops for stochastic growth models.

In this paper we use a simple model with a single Cobb–Douglas firm and a consumer with a CRRA utility function to show the difference between the equity premia in the production-based Brock model and the consumption-based Lucas model. With this simple example we show that the equity premium in the production-based model exceeds that of the consumption-based model with probability 1.

This paper uses the old Keynesian representative agent model developed by Roger E. A. Farmer [Expectations, Employment and Prices. New York: Oxford University Press (2010)] to answer two questions: (1) Do increased government purchases crowd out private consumption? (2) Do increased government purchases reduce unemployment? Farmer compared permanent tax-financed expenditure paths and showed that the answer to (1) was yes and the answer to (2) was no. We generalize his result to temporary bond-financed paths of government purchases that are similar to the actual path that occurred during WWII. We find that a temporary increase in government purchases does crowd out private consumption expenditure as in Farmer. However, in contrast to Farmer's experiment, we find that a temporary increase in government purchases can also reduce unemployment.