Indeterminancy and Sunspots with Constant Returns

We show that indeterminacy can easily arise in multi-sector models that have constant variable returns to scale and very small market imperfections. This is in sharp contrast to models that require increasing returns to generate indeterminacy, and which have been criticized on the basis of recent empirical estimates indicating that returns to scale are roughly constant, and that market imperfections are small. We also show that we can calibrate our constant returns model with sunspots, using standard parametrizations to produce a close match to the moments of aggregate consumption, investment, output and employment in U.S. data.Indeterminacy, multiple equilibria, sunspots

Intertemporal Complementarity and Optimality: A Study of a Two-Dimensional Dynamical System

We study the underlying structure of the two-dimensional dynamical system generated by a class of dynamic optimization models, which allow for intertemporal complementarily between adjacent periods, but which preserve the time additively separable framework of Ramsey models. Specifically, we identify conditions under which the results of the traditional Ramsey type theory are preserved even when the intertemporal independence assumption is relaxed. Local analysis of this theme has been presented by Samuelson (1971). We establish global convergence results and relate them to the local analysis, by using the mathematical theory of two-dimensional dynamical systeintertemporal complementarity, supermodularity, monotonicity, turnpike property

Trade and Indeterminacy in a Dynamic General Equilibrium Model

This paper introduces sector-specific externalities in the Heckscher-Ohlin two-country dynamic general equilibrium model to show that indeterminacy of the equilibrium path in the would market can occur. Under certain conditions in terms of factor intensities, there are multiple equilibrium paths from the same initial distribution of capital in the world market, and the distribution of capital in the limit differs among equilibrium paths.Externalities, Economic models, Market

Stochastic Optimal Growth when the Discount Rate Vanishes

It has been shown that long-run optimality of the limit of discounted optima when the discount rate vanishes is implied by a condition on the value function of the optimal program. We suggest a new method to verify this condition in the context of one-sector optimal growth. The idea should be more widely applicable.

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.Sectoral Externalities, Endogenous Growth, Dynamic Determinacy/Indeterminacy.

Multiple equilibria in two-sector monetary economies: an interplay between preferences and the timing for money

In this paper, we study the occurrence of local indeterminacy in two-sector monetary economies. In order to capture the credit market imperfections and the liquidity services of money, we consider a general MIUF model with two alternative timings in monetary payments: the Cash-In-Advance timing, in which the cash available to buy goods is money in the consumers' hands after they leave the bond market but before they enter the goods market, and the Cash-After-the-Market timing, in which agents hold money for transactions after leaving the goods market. We consider three standard specifications of preferences: the additively separable formulation, the Greenwood-Hercovitz-Huffman (GHH) [18] formulation and the King-Plosser-Rebelo (KPR) [21] formulation. First, we show that for all the three types of preferences, local indeterminacy easily arises under the CIA timing with a low enough interest rate elasticity of money demand. Second, we show that with the CAM timing, determinacy always holds under separable preferences, but local indeterminacy can arise in the case of GHH and KPR preferences. We thus prove that compared to aggregate models, two-sector models provide new rooms for local indeterminacy when non-separable standard preferences are considered.Money-in-the-utility-function, Indeterminacy, Sunspot equilibria

Macroeconomic volatility and welfare loss under free-trade in two-country models

This paper investigates the interlinkage in the business cycles based on sunspot fluctuations of large-country economies in a free-trade equilibrium. We consider a two-country, two-good, two-factor general equilibrium model with Cobb-Douglastechnologies, sector-specific externalities and linear preferences. We also assume constant social returns in the investment good sector but decreasing social returns in the consumption good sector. We first identify the determinants of each country's accumulation pattern in autarky equilibrium, and second we show that some country's sunspot fluctuations may spread throughout the world once trade opens even if the other country has determinacy under autarky. We thus prove that under free-trade, globalization and market integration may have destabilizing effects on a country's competitive equilibrium. Finally, we characterize a configuration in which opening to international trade improves the stationary welfare at the world level but deteriorates the stationary welfare of the country which imports investment goods and exports consumption goods. We thus show that in opposition to the standard belief, international trade may not be beneficial to all trading partners in the long run. Moreover, we prove that for some country, international trade may have contrasted consequences as it may at the same time improve the stationary welfare and have a destabilizing effect.Two-country general equilibrium model, free-trade, local indeterminacy, sunspot fluctuations, capital intensities, decreasing social retur

Indeterminacy and business-cycle fluctuations in a two-sector monetary economy with externalities

We consider a two-sector economy with money-in-the-utility-function and sector-specific externalities. We provide conditions on technologies leading to the existence of local indeterminacy for any value of the interest rate elasticity of money demand, provided the elasticity of intertemporal substitution in consumption is large enough. Moreover, we show that the occurrence of multiple equilibria is intimately linked with the existence of a flip bifurcation and period-two cycles.Money-in-the-utility-function ; two-sector economy ; sector-specific externalities ; indeterminacy ; period-two cycles ; sunspot equilibria

A two-country dynamic model of international trade and endogenous growth: multiple balanced growth paths and stability

We formulate a two-country endogenous growth model which explain joint determination of long-run trade patterns and world growth rates. After providing the existence and local stability of the continuum of balanced growth paths, we show that main standard trade propositions hold under some modifications and that, subject to certain conditions concerning social and private rankings of factory intensities between production sectors, the higher is the growth rate, the smaller is the volume of international trade among balanced growth paths in the continuum.

Global Externalities, Endogenous Growth and Sunspot fluctuations

We consider a two-sector economy with Cobb-Douglas technologies,labor-augmenting global external effects and increasing social returns. We prove the existence of a normalized balanced growth path and we give conditions for the occurrence of sunspot fluctuations that are compatible with both types of capital intensity configuration at the private level provided the elasticity of intertemporal substitution in consumption admits intermediary values. We finally show that the existence of period-two cycles requires the consumption good to be physical capital intensive at the private level.Global externalities; increasing returns; endogenous growth; intertemporal substitution in consumption; indeterminacy; sunspot fluctuations; period-two cycles