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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.
The interplay between growth and public debt is addressed considering a Barro‐type (1990) endogenous growth model where public spendings are financed through taxes on income and public debt. The government has a target level of public debt relative to GDP, and the long‐run debt‐to‐GDP ratio is used as a policy parameter. We show that when debt is a large enough proportion of GDP, two distinct balanced‐growth paths (BGPs) may coexist, one being indeterminate. We exhibit two types of important trade‐offs associated with self‐fulfilling expectations. First, we show that the lowest BGP is always decreasing with respect to the debt‐to‐GDP ratio while the highest one is increasing. Second, we show that the highest BGP, which provides the highest welfare, is always locally indeterminate while the lowest is always locally determinate. Therefore, local and global indeterminacy may arise and self‐fulfilling expectations appear as a crucial ingredient to understand the impact of debt on growth, welfare, and macroeconomic fluctuations. Finally, a simple calibration exercise allows to provide an understanding of the recent experiences of many OECD countries.
We study the existence of endogenous competitive equilibrium cycles under small discounting in a two-sector discrete-time optimal growth model. We provide precise concavity conditions on the indirect utility function leading to the existence of period-two cycles with a critical value for the discount factor that can be arbitrarily close to one. Contrary to the continuous-time case where the existence of periodic-cycles is obtained if the degree of concavity is close to zero, we show that in a discrete-time setting the driving condition does not require a close to zero degree of concavity but a symmetry of the indirect utility function’s concavity properties with respect to its two arguments.
We investigate the extent to which standard one sector RBC models with positive externalities and variable capacity utilization can account for the large hump-shaped response of output when the model is submitted to a pure sunspot shock. We refine the Benhabib and Wen (2004) model considering a general type of additive separable preferences and a general production function. We provide a detailed theoretical analysis of local stabilities and local bifurcations as a function of various structural parameters. We show that, when labor is infinitely elastic, local indeterminacy occurs through Flip and Hopf bifurcations for a large set of values for the elasticity of intertemporal substitution in consumption, the degree of increasing returns to scale and the elasticity of capital–labor substitution. Finally, we provide a detailed quantitative assessment of the model and conclude with mixed results. We show that although the model is able theoretically to generate a hump-shaped dynamics of output following an i.i.d. sunspot shock under realistic parameter values, the hump is too persistent for the model to be considered fully satisfactory from an empirical point of view.
This chapter presents a brief overview of the career and main contributions of Professor Jean-Michel Grandmont. It also provides a summarized description of the 16 papers written in his honor by his friends and colleagues.
This book presents the state-of-the-art in non-linear dynamics and sunspots. These two topics have been the core of an international conference on instability and public policies in a globalized world, organized at Aix-Marseille School of Economics and GREQAM in honor of Jean-Michel Grandmont. He has made significant contributions on general equilibrium theory, monetary theory, learning, aggregation, non-linear dynamics and sunspots. This book assembles contributions by Jean-Michel Grandmont's colleagues, students and friends that have been influenced by his works and that are at the frontier of research in this domain today.
We analyze a version of the Benhabib and Farmer (1996) two-sector model with sector-specific externalities in which we consider a class of utility functions inspired from the one considered in Jaimovich and Rebelo (2009) which is flexible enough to encompass varying degrees of income effect. First, we show that local indeterminacy and sunspot fluctuations occur in 2-sector models under plausible configurations regarding all structural parameters—in particular regarding the intensity of income effects. Second, we prove that there even exist some configurations for which local indeterminacy arises under any degree of income effect. More precisely, for any given size of income effect, we show that there is a non-empty range of values for the Frisch elasticity of labor and the elasticity of intertemporal substitution in consumption such that indeterminacy occurs. This contrasts with the results obtained in one-sector models in both Nishimura et al. (2009), in which it is shown that indeterminacy cannot occur under either GHH and KPR preferences, and in Jaimovich (2008) in which local indeterminacy only arises for intermediary income effects.
This note introduces to the literature streams explored in the special section on international financial markets and banking systems crises. All topics tackled are related to the Great Recession. A brief overview of the research questions and related literatures is provided.
We investigate the role of nonseparable preferences in the occurrence of macroeconomic instability under a balanced-budget rule where government spending is financed by a tax on labor income. Considering a one-sector neoclassical growth model with a large class of nonseparable utility functions, we find that expectations-driven fluctuations occur easily when consumption and labor are Edgeworth substitutes or weak Edgeworth complements. Under these assumptions, an intermediate range of tax rates and a sufficiently low elasticity of intertemporal substitution in consumption lead to instability.
We analyze local indeterminacy and sunspot-driven fluctuations in the standard two-sector model with additively separable preferences. We provide a detailed theoretical analysis enabling us to derive relevant bifurcation loci and to characterize the steady-state local stability properties as a function of various structural parameters influencing the degree of increasing returns to scale, the amount of intertemporal substitution in consumption, and the elasticity of the aggregate labor supply curve. On the theoretical side, we prove the existence of both a flip and a Hopf bifurcation locus in the corresponding parameter space. We also show that local indeterminacy can be obtained under any labor supply elasticity or under an arbitrarily low elasticity of intertemporal substitution in consumption. On the empirical side, we find that indeterminacy and sunspot fluctuations are robust features of two-sector models, prevailing for most empirically plausible calibrations for these parameters. (This abstract was borrowed from another version of this item.)
In this paper we investigate if government balanced-budget rules together with endogenous taxation may lead to aggregate instability in an endogenous growth framework. After highlighting the differences with the exogenous growth framework, we prove that under counter-cyclical consumption taxes, while there exists a unique balanced growth path, sunspot equilibria based on self-fulfilling expectations occur through a form of global indeterminacy. In addition, we argue that this result is empirically plausible for a large set of OECD countries and that it may also emerge with endogenous income taxes.
We examine the impact of balanced-budget labor income taxes on the existence of expectation-driven business cycles in a two-sector version of the Schmitt-Grohé and Uribe (SGU) [(1997) Journal of Political Economy 105, 976–1000] model with constant government expenditures and counter-cyclical taxes. Our results show that the destabilizing impact of labor income taxes strongly depends on the capital intensity difference across sectors. Local indeterminacy is indeed more likely when the consumption good sector is capital intensive, as the minimal tax rate decreases, and less likely when the investment good sector is capital intensive, as the minimal tax rate increases. The implication of this result can be quantitatively significant. Indeed, when compared to SGU, local indeterminacy can be either completely ruled out for all OECD countries when the investment good is sufficiently capital intensive or drastically improved, delivering indeterminacy for a larger set of OECD countries, if the consumption good is sufficiently capital intensive. Focusing however on recent estimates of the sectoral capital shares corresponding to the empirically plausible case of a capital intensive consumption good, we find that there is a significant increase of the range of economically relevant labor tax rates (from a minimum tax rate of 30% to 24.7%) for which local indeterminacy arises with respect to the aggregate formulation of SGU.