Galor and Ryder [Journal of Economic Theory 49 (1989), 360–375] establish conditions for the existence of equilibrium in a Diamond-type overlapping-generations (OLG) model. Although theoretically appealing, these conditions are implicit and not convenient to apply. This paper provides explicit and easily applied conditions for the existence and uniqueness of steady-state equilibrium, with which one only needs to check the first derivatives of the production and utility functions and their interactions, with no need to solve the optimization problem. Our theorems on the existence and uniqueness of steady-state equilibrium can be applied to a larger class of OLG models that do not require second-order differentiability of the production and utility functions. We present examples to show how to check the existence and uniqueness of equilibrium.

Theoretically, two-country real business cycle models with time-separable preferences and complete markets predict that cross-country investment correlations will be negative. The opposite is true in the data. This phenomenon has been described by Backus et al. [in Cooley (ed.), Frontiers of Business Cycle Research, pp. 331–356 (Princeton, NJ: Princeton University Press, 1995)] as a quantity anomaly. This paper proposes to address this discrepancy by allowing the nonseparability of preferences over time. Here, we incorporate internal habit formation into consumption. Our model predicts the empirically plausible value of cross-country investment correlation without sacrificing other business cycle statistics. The results are robust to the degree of spillovers and persistence in the specification of the productivity shocks.

In this paper we explore how income inequality affects growth in a dynastic family model with bequests (physical capital) and investment in human capital for children. For tractability, we abstract from factor markets and focus on household production, which is prevalent in developing countries. We explore a joint distribution of bequests and human capital and track the evolution of income distribution across generations. We show that initial inequality has a positive indirect effect on average output growth by lowering the ratio of physical to human capital, besides its standard negative direct effect. If education is mainly privately (publicly) provided, then income inequality retards (promotes) growth outside the balanced growth path. On the balanced growth path, inequality always hinders growth.

An adaptive step-size algorithm [Kushner and Yin, Stochastic Approximation and Recursive Algorithms and Applications, 2nd ed., New York: Springer-Verlag (2003)] is used to model time-varying learning, and its performance is illustrated in the environment of Marcet and Nicolini [American Economic Review 93 (2003), 1476–1498]. The resulting model gives qualitatively similar results to those of Marcet and Nicolini, and performs quantitatively somewhat better, based on the criterion of mean squared error. The model generates increasing gain during hyperinflations and decreasing gain after hyperinflations end, which matches findings in the data. An agent using this model behaves cautiously when faced with sudden changes in policy, and is able to recognize a regime change after acquiring sufficient information.

This paper is dedicated to the memory of the great statistician Melvin J. Hinich, with whom we were in contact about this research prior to his untimely death from a tragic fall. We develop a neoclassical growth model with habit formation to exhibit an equilibrium nonlinear relationship between aggregate consumption growth and income growth. We first provide empirical evidence consistent with this relationship both for the United States and France, and we reject the hypothesis of a random walk for consumption. We then estimate this nonlinear relationship. We find for both countries robust evidence of persistence, nonlinearity, and cyclicity in the relationship between consumption and income.

Zhang [Tariff and Equilibrium Indeterminacy, available at http://mpra.ub.uni-muenchen.de/13099/ (2009)] shows that endogenous tariffs (or energy taxes) and endogenous labor income taxes are equivalent in generating local indeterminacy. Using methods developed by Stockman [Journal of Economic Theory 145 (2010), 1060–1085], we extend Zhang's analysis to prove that endogenous tariffs and endogenous labor income taxes are also equivalent in generating global indeterminacy (chaotic equilibria) under a balanced-budget rule. More precisely, we show that the existence of Euler equation branching in an arbitrarily small neighborhood of a steady state can imply topological chaos in the sense of Devaney. In addition, Euler equation branching occurs regardless of the local uniqueness of the equilibrium around the steady state.

This paper examines the effect of the elasticity of technological substitution on the existence of equilibrium indeterminacy in two-sector economies. Following recent empirical evidence, the elasticity of substitution between capital and labor is below unity and we find that this requires a higher degree of productive externalities in order to still be able to produce indeterminate equilibria. However, empirically realistic rates of substitution do not rule out indeterminacy.

This paper estimates time-varying forward-looking monetary policy reaction functions for the central banks of France, Germany, Italy, and the United Kingdom. We utilize the framework developed by Kim [Economics Letters 91 (2006) 21–26] and Kim and Nelson [Journal of Monetary Economics (2006) 1949–1966] to deal with the issue of endogeneity in a time varying–parameter model. Our results find substantial time variation in the conduct of monetary policy in these four countries, which cannot be adequately captured by the conventional fixed-coefficient approach. Our findings suggest that there was a significant decline in the Bank of France's and the Bank of Italy's response to the German interest rate in 1992, and it coincided with the breakdown of the exchange rate management system in Europe. Our results suggest that the Bank of England was slower than the Bundesbank to increase its response to expected inflation, as its response to inflation became more than one-for-one only in the early 1980s.

This note analytically examines the interrelations between macroeconomic (in)stability and investment adjustment costs in a one-sector endogenously growing small–open economy representative-agent model. We show that under costly capital accumulation, the economy exhibits indeterminacy and sunspots if and only if the equilibrium wage–hours locus slopes upward and is steeper than the household's labor supply curve. By contrast, the economy without adjustment costs for capital investment always displays saddlepath stability and equilibrium uniqueness, regardless of the degree of increasing returns inaggregate production.