Alain Venditti

Faculty ,  CNRS

Macro, labor and international economics
Venditti
Status
Research professor
Research domain(s)
Macroeconomics
Thesis
1994, Aix-Marseille Université
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Contact
alain.venditti[at]univ-amu.fr
+33(0)4 13 55 25 81
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AMU - AMSE
5-9 Boulevard Maurice Bourdet, CS 50498
​13205 Marseille Cedex 1

Abstract This paper introduces a novel mechanism driving endogenous business cycle fluctuations within a frictionless three-sector intertemporal equilibrium model. We emphasize the critical role of consumer preferences as a primary driver of cyclical dynamics by considering a consumption bundle composed of a pure consumption good and a mixed consumption-investment good that simultaneously serves as both a final consumption good and a capital-accumulating investment good. Endogenous fluctuations naturally arise from sectoral capital intensity differences, an intertemporal consumption trade-off between the two goods, or the interaction of both mechanisms. We offer a detailed characterization of the economy's dynamics, identifying the Hopf bifurcation conditions that trigger persistent cyclical behavior. Additionally, we explore the periodicity of the resulting limit cycles, providing insights into how shifts in preferences and sectoral complementarities can generate self-sustained macroeconomic fluctuations.
Keywords Three-sector intertemporal equilibrium growth models, Business cycles fluctuations, Hopf bifurcation, Endogenous cycle, Periodicity
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Abstract How will structural change unfold beyond the rise of services? Motivated by the observed dynamics within the service sector we propose a model of structural change in which productivity is endogenous and output is produced with two intermediate substitutable capital goods. In the productive sector the accumulation of specialized skills leads to an unbounded increase in TFP, as sector becoming asymptotically dominant. We are then able to recover the increasing shares of workers, the increasing real and nominal shares of the output observed in productive service and IT sectors in the US. Interestingly, the economy follows a growth path converging to a particular level of wealth that depends on the initial price of capital and knowledge. As a consequence, countries with the same fundamentals but lower initial wealth will be characterized by lower asymptotic wealth.
Keywords Two-sector model, Technological knowledge, Constant elasticity ofsubstitution, Non-balanced endogenous growth, Structural change, Kaldor and Kuznets facts
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Abstract When can exogenous changes in beliefs generate endogenous fluctuations in rationalexpectation models? We analyze this question in the canonical one-sector and two-sector models of the business cycle with increasing returns to scale. A key feature of ouranalysis is that we express the uniqueness/multiplicity condition of equilibirum pathsin terms of restrictions on five critical and economically interpretable parameters: theFrisch elasticities of the labor supply curve with respect to the real wage and to themarginal utility of wealth, the intertemporal elasticity of substitution in consumption,the elasticity of substitution between capital and labor, and the degree of increasingreturns to scale. We obtain two clear-cut conclusions: belief-driven fluctuations cannotexist in the one-sector version of the model for empirically consistent values for thesefive parameters. By contrast, belief-driven fluctuations are a robust property of thetwo-sector version of the model—with differentiated consumption and investmentgoods—, as they now emerge for a wide range of parameter values consistent withavailable empirical estimates. The key ingredients explaining these different outcomesare factor reallocation between sectors and the implied variations in the relative priceof investment, affecting the expected return on capital accumulation.
Keywords Income effect, Expectations, Endogenous fluctuations, Belief-driven business cycles
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Abstract We present an overview of selected contributions of the Journal of Mathematical Economics’ authors to growth theory in the last half century. We start with the classical optimal growth theory within a benchmark multisector model and outline the successive developments in the analysis of this model, including the turnpike theory. Different refinements of the benchmark are considered along the way. We then survey the abundant literature on endogenous fluctuations in two-sector models. We conclude with two strong trends in the recent growth literature: green growth and infinite-dimensional growth models.
Keywords Growth theory, Multisector models, Turnpike theory, Green growth, Infinite dimensional growth models, Optimization
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Abstract To what extent protectionism affects growth and (de)stabilizes the economies? Although the impact of protectionism on growth has been widely explored without reaching a consensus, few has been said on its impact on macroeconomic stability. The present paper attempts to gauge more precisely its implications using a Barro-type (Barro, 1990) endogenous growth model with public debt and credit constraint where tariffs are a proxy of protectionism. Our main result is to show that when the debt level is high, and the share of foreign goods in total consumption is large enough, increasing tariffs may have a destabilizing effect generating some expectation coordination failures between multiple equilibria. We also exhibit some trade-off between tariffs and growth as tariffs are beneficial only to the low growth equilibrium which may only appear when the international interest rate is low enough. Finally, focusing on the local stability property, we show that the high BGP is always characterized by local indeterminacy, while the low BGP is always a saddle point. We then prove that tariffs may be responsible for the existence of large self-fulfilling fluctuations.
Keywords Public debt, Tariffs, Small open economy, Credit constraint, Global and local indeterminacy
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Abstract This paper provides a long-run cycle perspective to explain the behavior of the annual flow of inheritance. Based on the low- and medium frequency properties of long time bequests series in Sweden, France, UK, and Germany, we explore the extent to which a two-sector Barro-type OLG model is consistent with such empirical regularities. As long as agents are sufficiently impatient and preferences are non-separable, we show that endogenous fluctuations are likely to occur through two mechanisms, which can generate independently or together either period-2 cycles or Hopf bifurcations. The first mechanism relies on the elasticity of intertemporal substitution or equivalently the sign of the cross-derivative of the utility function whereas the second rests on sectoral technologies through the sign of the capital intensity difference across two sectors. Furthermore, building on the quasi-palindromic nature of the degree-4 characteristic equation, we derive some meaningful sufficient conditions associated to the occurrence of complex roots and a Hopf bifurcation in a two-sector OLG model.
Keywords Two-sector overlapping generations model, Altruism, Bequest, Endogenous fluctuations, Quasi-palindromic polynomial, Periodic and quasi-periodic cycles
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Abstract This paper is an introduction to the special issue of Mathematical Social Sciences on Advances in growth and macroeconomic dynamics in memory of Carine Nourry.
Keywords Inequalities and income distribution, Migration and networks, Existence of equilibria, Macroeconomic stability and fluctuations
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Abstract The relationship between public debt, growth and volatility is investigated in a Barro-type (1990) endogenous growth model, with three main features: we consider a small open economy, international borrowing is constrained and households have taste for domestic public debt. Therefore, capital, public debt and the international asset are not perfect substitutes and the economy is characterized by an investment multiplier. Whatever the level of the debt-output ratio, the existing BGP features expectation-driven fluctuations. If the debt-output ratio is low enough, there is also a second BGP with a lower growth rate. Hence, a lower debt does not stabilize the economy with credit market imperfections. However, a high enough taste for domestic public debt may rule out the BGP with lower growth. This means that if the share of public debt held by domestic households is high enough, global indeterminacy does not occur.
Keywords Indeterminacy, Credit constraint, Public debt, Small open economy
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Abstract This paper is a tribute for Carine Nourry for this special issue of Mathematical Social Sciences.
Keywords Deep and endearing person, Director of the school AMSE, Internationally recognized
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Abstract 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.
Keywords Aggregate instability, Local indeterminacy, Expectations-driven fluctuations, Laboreincome taxes, Balanced-budget rule, Infinite-horizon two-sector model, Capital intensity difference
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Abstract 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.
Keywords Urban dynamics, Human capital, Heterogeneous growth rates, Endogenous growth, City inequalities
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Abstract 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.
Keywords Two-sector optimal growth model, Strong and weak concavity, Small discounting, Period-two cycles
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Abstract 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.
Keywords Sunspot equilibria, Self‐fulfilling expectation, Global indeterminacy, Time‐varying consumption tax, Endogenous growth
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Abstract 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.
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Abstract 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.
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Abstract 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.
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Abstract 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.
Keywords International transmission, Financial instability, Financial frictions, Credit crunch, Banking and sovereign debt crisis
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Abstract 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.
Keywords Indeterminacy, Expectations-driven business cycles, Labor income taxes, Balanced-budget rule, Non-separable preferences, Economie quantitative
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Abstract 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.
Keywords Sector-specific externalities, Sunspots, O41, Infinite-horizon two-sector model, Indeterminacy, Income and substitution effects, Social and Behav Sciences, Economics, Game Theory, Economic Theory/Quantitative Economics/Mathematical Methods, Economic Growth, E32, C62
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Abstract 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.
Keywords Economie quantitative
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Abstract We investigate the effects of collateral and monetary policy on economic growth within a Ramsey equilibrium model where agents have different discount factors. Introducing liquidity constraints in segmented markets where (poor) impatient agents without collateral have limited access to credit, we study their implications in terms of welfare and business cycles (based on deterministic cycles through bifurcations and self-fulfilling prophecies). We find that an accommodative monetary policy may be growth-enhancing and welfare-improving (through the inequality reduction) while making unpleasant fluctuations more likely. Conversely, a regulation reinforcing the role of collateral and tempering the financial market imperfections may stimulate the economic growth while pursuing the goal of stabilization. © 2016 Elsevier Inc.
Keywords Sunspots, Stabilization policies, Heterogeneous agents, Endogenous fluctuations, Collateral, Balanced growth
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Abstract Imposing some constraints on public debt is often justified regarding sustainability and stability issues. This is especially the case when the ratio of public debt over GDP is restricted to be constant. Using a Ramsey model, we show that such a constraint can however be a fundamental source of indeterminacy, and therefore, of expectations-driven fluctuations. Indeed, through the intertemporal budget constraint of the government, income taxation negatively depends on future debt, i.e. on the expected level of production. This mechanism ensures that expectations on the future tax rate may be self-fulfilling. We show that this is promoted by a larger ratio of debt over GDP.
Keywords Public debt, Indeterminacy, Income taxation, Endogenous cycles, Endogenous cycles
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Abstract This is an introduction to the special section on financial frictions and debt constraints.
Keywords Public debt constraints, Incomplete markets, Credit and borrowing constraints, Constrained efficie
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Abstract We analyze sunspot-driven fluctuations in the standard two-sector \RBC\ model with moderate increasing returns to scale and generalized no-income-effect preferences à la Greenwood, Hercovitz and Huffman [13]. 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. We show that local indeterminacy occurs through flip and Hopf bifurcations for a large set of values for the elasticity of intertemporal substitution in consumption, provided that the labor supply is sufficiently inelastic. Finally, we provide a detailed quantitative analysis of the model. Computing, on a quarterly basis, a new set of empirical moments related to two broadly defined consumption and investment sectors, we are able to identify, among the set of admissible calibrations consistent with sunspot equilibria, the ones that provide the best fit of the data. The model properly calibrated solves several empirical puzzles traditionally associated with two-sector \RBC\ models.
Keywords Two-sector model, Sunspots, Sector-specific externalities, Real business cycles, Indeterminacy
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Abstract We introduce public debt in a Ramsey model with heterogenous agents and a public spending externality affecting utility which is financed by income tax and public debt. We show that public debt considered as a fixed portion of GDP can have a stabilizing or destabilizing effect depending on some fundamental elasticities. When the public spending externality is weak and the elasticity of capital labor substitution is low enough, public debt can only be destabilizing, generating damped or persistent macroeconomic fluctuations. Whereas when the public spending externality and the elasticity of capital labor substitution are strong enough, public debt can be stabilizing, driving to monotone convergence an economy experiencing damped or persistent fluctuations without debt.
Keywords Economie quantitative
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Abstract In the present paper, we consider a two-country, two-good, two-factor general equilibrium model with CIES nonlinear preferences, asymmetric technologies across countries and decreasing returns to scale. It is shown that aggregate instability and endogenous fluctuations may occur due to international trade. In particular, we prove that the integration into a common market on which countries trade the produced good and the capital input may lead to period-two cycles even when the closed-economy equilibrium is saddle-point stable in both countries. Copyright Springer-Verlag Berlin Heidelberg 2014
Keywords Endogenous fluctuations, Aggregate instability, Aggregate instability, C62, E32, Economics general, Economic theory, End, F43, F11, Perfect foresight dynamic general equilibrium model, O41, Nonlinear preferences, International trade, Social and Behav Sciences, Economics, Game Theory
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Abstract We re-examine the destabilizing role of balanced-budget fiscal policy rules based on consumption taxation. Using a one-sector model with infinitely-lived households, we consider a specification of preferences derived from Jaimovich (2008) [14] and Jaimovich and Rebelo (2009) [15] which is flexible enough to encompass varying degrees of income effect. When the income effect is not too large, we show that there exists a Laffer curve, which explains the multiplicity of steady states, and that non-linear consumption taxation may destabilize the economy, promoting expectation-driven fluctuations, if the elasticity of intertemporal substitution in consumption is sufficiently larger than one and the tax rate is counter-cyclical with respect to consumption. Numerical illustrations also show that consumption taxation may be a source of instability for most OECD countries for a wide range of structural parametersʼ configurations. We finally prove the robustness of our conclusions if we consider a discrete-time setup.
Keywords Indeterminacy, Income effect, I, Endogenous business cycles, Consumption taxes, Balanced-budget rule
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Abstract The aim of this paper is to discuss the role of the returns to scale at the private and social levels on the local determinacy properties of the steady state in a continuous-time two-sector economy with sector-specific externalities. First we show that when labor is inelastic, for any configuration of the returns to scale, local indeterminacy is obtained if there is a capital intensity reversal between the private and the social levels. Second, we prove that when labor is infinitely elastic, saddle-point stability is obtained as soon as the investment good sector has constant social returns while local indeterminacy arises if the investment good sector has increasing social returns, provided the consumption good is labor intensive at the social level and the elasticity of intertemporal substitution in consumption admits intermediary values. Finally, we show that local indeterminacy requires a low elasticity of labor when the investment good has constant social returns, but requires either low enough or large enough elasticity of labor when the investment good has increasing social returns.
Keywords Economie quantitative
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Abstract We consider a one-sector Ramsey-type growth model with inelastic labor and learning-by-doing externalities based on cumulative gross investment (cumulative production of capital goods), which is assumed, in accordance with Arrow (1962), to be a better index of experience than the average capital stock. We prove that a slight memory effect characterizing the learning-by-doing process is enough to generate business cycle fluctuations through a Hopf bifurcation leading to stable periodic orbits. This is obtained for reasonable parameter values, notably for both the amount of externalities and the elasticity of intertemporal substitution. Hence, contrary to all the results available in the literature on aggregate models, we show that endogenous fluctuations are compatible with a low (in actual fact, zero) wage elasticity of the labor supply.
Keywords Local determinacy, Hopf bifurcation, Business cycle fluctuations, Inelastic labor, Learning-by-doing externalities, One-sector infinite-horizon model
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Abstract We consider a one-sector Ramsey-type growth model with inelastic labor and learning-by-doing externalities based on cumulative gross investment (cumulative production of capital goods), which is assumed, in accordance with Arrow [4], to be a better index of experience than the average capital stock. We prove that a slight memory effect characterizing the learning-by-doing process is enough to generate business cycle fluctuations through a Hopf bifurcation leading to stable periodic orbits. This is obtained for reasonable parameter values, notably for both the amount of externalities and the elasticity of intertemporal substitution. Hence, contrary to all the results available in the literature on aggregate models, we show that endogenous fluctuations are compatible with a low (in actual fact, zero) wage elasticity of the labor supply.
Keywords Hopf bifurcation, Business cycle fluctuations, Inelastic labor, Learning-by-doing externalities, One-sector infinite-horizon model, Local determinacy, Modèles unisectoriels, Externalité d&#039, apprentissage par la pratique, Offre de travail inélastique, Fluctuations endogènes, Bifurcations de Hopf, Détermination locale
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Abstract We consider a two-sector overlapping generations model with homothetic preferences. Under standard conditions on technologies, upon large enough values for the share of first period consumption over the wage income, we prove that the dynamic efficiency and local uniqueness of the competitive equilibrium hold. On the contrary, for lower values of the share of first period consumption over the wage income which imply dynamic inefficiency of the steady state, local indeterminacy arises when the elasticity of intertemporal substitution in consumption is large enough.
Keywords Two-sector OLG model, Efficiency, Local uniqueness
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Abstract The aim of this paper is to discuss the roles of the elasticity of intertemporal substitution in consumption and the elasticity of the labor supply on the local determinacy properties of the steady state in a two-sector economy with CES technologies and sector-specific externalities. Our main results provide necessary and sufficient conditions for local indeterminacy. First we show that the consumption good sector needs to be capital intensive at the private level and labor intensive at the social level. Second, we prove that under this capital intensity configuration, the existence of sunspot fluctuations is obtained if and only if the elasticity of intertemporal substitution in consumption is large enough but the elasticity of the labor supply is low enough. In particular, we will show on the one hand that when the labor supply is infinitely elastic, the steady state is always saddle-point stable, and on the other hand that when the elasticity of intertemporal substitution in consumption is infinite, labor does not have any influence on the local stability properties of the equilibrium path.
Keywords Indeterminacy, Sector-specific externalities, Constant returns, Capital-labor substitution, Intertemporal substitution in consumption, Elastic labor, Indeterminacy
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Abstract This paper develops a one-sector overlapping generations model with endogenous labor supply and nonseparable preferences. It demonstrates that local indeterminacy arises easily under gross substitutability as soon as there exist multiple steady states. We show also that, depending on whether leisure and second-period consumption are gross substitutes, local indeterminacy holds for very different parameter configurations. If gross substitutability is satisfied, the existence of multiple equilibrium paths requires the share of capital in the total income to be strong enough with respect to the elasticity of capital-labor substitution. On the other hand, if gross substitutability is violated, local indeterminacy necessitates the share of capital in the total income to be weak enough with respect to the elasticity of capital-labor substitution.
Keywords Endogenous labor supply, Indeterminacy, Endogenous cycles, Overlapping generations, Endogenous labor supply
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Abstract We present an overview of selected contributions of the Journal of Mathematical Economics' authors in the last half century. We start with the classical optimal growth theory within a benchmark multisector model and outline the successive developments in the analysis of this model, including the turnpike theory. Different refinements of the benchmark are considered along the way. We after survey the abundant literature on endogenous fluctuations in two-sector models. We conclude with two strong trends in the recent growth literature: green growth and infinite-dimensional growth models.
Keywords Infinite-dimensional growth models, Optimization, Green growth, Turnpike theory, Multisector models, Growth theory
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Abstract The Balassa-Samuelson effect is still an important phenomenon in the theory of economic development, as Balassa states, "As economic development is accompanied by greater inter-country differences in the productivity of tradable goods, differences in wages and service prices increase, and correspondingly so do differences in purchasing power parity and exchange rates." To the best of our knowledge, the Balassa-Samuelson effect has not been formally examined in the framework of optimal growth theory. By embedding the Balassa-Samuelson's original model in an optimal growth model setting, we investigate the validity of the Balassa-Samuelson effect in such a case and show that the Balassa-Samuelson effect follows from one of the properties of the optimal steady state.
Keywords Two sector optimal growth, Optimal steady state, Saddle-point stability, Phase diagram, Hamiltonian, Capital intensity
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Abstract When can exogenous changes in beliefs generate endogenous fluctuations in rational expectation models? We analyze this question in the canonical one-sector and two-sector models of the business cycle with increasing returns to scale. A key feature of our analysis is that we express the uniqueness/multiplicity condition of equilibirum paths in terms of restrictions on five critical and economically interpretable parameters: the Frisch elasticities of the labor supply curve with respect to the real wage and to the marginal utility of wealth, the intertemporal elasticity of substitution in consumption, the elasticity of substitution between capital and labor, and the degree of increasing returns to scale. We obtain two clear-cut conclusions: belief-driven fluctuations cannot exist in the one-sector version of the model for empirically consistent values for these five parameters. By contrast, belief-driven fluctuations are a robust property of the twosector version of the model-with differentiated consumption and investment goods-, as they now emerge for a wide range of parameter values consistent with available empirical estimates. The key ingredients explaining these different outcomes are factor reallocation between sectors and the implied variations in the relative price of investment, affecting the expected return on capital accumulation.
Keywords Belief-driven business cycles, Endogenous fluctuations, Expectations, Income effect
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Abstract The Balassa-Samuelson effect ("BS effect") has attracted attention as a theory to explain the stagnation of the Japanese economy over the past 30 years. In particular, it has been used to explain the long-term depreciation of the real effective exchange rate since 1995. Furthermore, macroeconomic data show that the BS effect explains well Japan's long-term economic stagnation. However, the BS effect was originally derived theoretically for small open economies, not for large economies like Japan. In other words, the BS effect cannot be theoretically applied to large economies. This is a serious problem in applying the BS effect empirically. In this paper, we embed Balassa-Samuelson's original argument into the optimal growth theory framework. That is, we set up an optimal growth problem for large countries. It is then shown that there exists a stable optimal steady state and that the BS effect is more directly valid in that optimal steady state. In other words, as a long-run property, the BS effect is applicable to large as well as small countries, although, contrary to the small open economy case, it does not depend on the capital shares of the two sectors.
Keywords Balassa-Samuelson effect, Capital intensity, Optimal steady state, Two-sector optimal growth models
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Abstract To what extent protectionism affects growth and (de)stabilizes the economies? Since 2018, some countries have resorted to protectionist measures as the United States. Although the impacts of protectionism on growth have been widely explored without reaching a consensus, few has been said on its impacts on macroeconomic stability. The present paper attempts to gauge more precisely its implications using a Barro-type (1990) endogenous growth model with public debt and credit constraint where tariffs are a proxy of protectionism. Our main result is to show that when the debt level is high, and the share of foreign goods in total consumption is large enough, increasing tariffs may have a dramatic destabilizing effect generating some expectation coordination failure between multiple equilibria and the possible existence of large self-fulfilling fluctuations. We also exhibit some trade-off between tariffs and growth as tariffs are beneficial only to the low growth equilibrium which may only appear in the globally indeterminate case. We also propose some numerical illustrations confirming the destabilizing impact of tariffs in the case of the US economy. We finally propose an Event Study analysis to confront our results. While our effects appear short lasting, two quarters, we show that the implementation of protectionism destabilizes the US economy in the short run.
Keywords Global and local indeterminacy, Credit constraint, Small open economy, Tariffs, Public debt
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Abstract Macroeconomic models in which exogenous, self-fulfilling changes in expectations play a significant role in output fluctuations are often discarded on two claims: they require implausible calibrations of structural parameters and they are enable to account for several empirical features associated with demand shocks. We show that these claims are only valid to the extent that they are applied to one-sector models. In contrast, we prove that two-sector models allow the existence of self-fulfilling prophecies for a large set of empirically realistic values for all the structural parameters, and that a two-sector model submitted to sunspot shocks can account not only for all the standard stylized facts associated with demand shocks, but also for other dimensions of the business cycle that standard RBC-type models cannot explain.
Keywords Indeterminacy, One and two-sector models, Endogenous labor supply, Income effect, Productive externalities, Permanent and transitory shocks
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Abstract Following the recent contribution of Beaudry et al. [8], we exploit a three-sector optimal growth model without frictions to provide new insights regarding the emergence of endogenous medium-term fluctuations. Notably, our 3-sector model shows that matching the empirical evidence critically depends on agents' preferences, particularly the consumption of a bundle of (at least) two final goods. Endogenous fluctuations are therefore likely to occur through both relative inter-sector differences in capital intensity and intertemporal consumption allocations based on substitution effects between the two final consumed goods. We thoroughly characterize the economy's dynamics and establish the existence of clear conditions related to (Hopf) bifurcation values, as well as closely examining the theoretical periodicity of the corresponding limit cycles. Using a calibration of the US economy, our model is able to reproduce the observed peak range of spectral density at around 8 to 10 years of the cyclical component of gross domestic product, gross private investment, personal consumption expenditures, and of the corresponding price deflator series. Furthermore, such limit cycles are generated under very plausible technological parameters and estimates of the elasticities of intertemporal substitution.
Keywords Three-sector optimal growth models, Mid-term fluctuations, Hopf bifurcation, Endogenous cycle, Periodicity
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Abstract How will structural change unfold beyond the rise of services? Motivated by the observed dynamics within the service sector we propose a model of structural change in which productivity is endogenous and output is produced with two intermediate substitutable capital goods. In the progressive sector the accumulation of knowledge leads to an unbounded increase in TFP, as sector becoming asymptotically dominant. We are then able to recover the increasing shares of workers, the increasing real and nominal shares of the output observed in progressive service and IT sectors in the US. Interestingly, the economy follows a growth path converging to a particular level of wealth that depends on the initial price of capital and knowledge. As a consequence, countries with the same fundamentals but lower initial wealth will be characterized by lower asymptotic wealth.
Keywords Kaldor and Kuznets facts, Structural change, Non-balanced endogenous growth, Constant elasticity of substitution, Technological knowledge, Two-sector model
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Abstract This paper provides a long-run cycle perspective to explain the behavior of the annual flow of inheritance as identified by Piketty [51] for France and Atkinson [3] for the UK. Using a two-sector Barro-type [9] OLG model with non-separable preferences and bequests, we show that endogenous fluctuations are likely to occur through period-2 cycles or Hopf bifurcations. Two key mechanisms, which can generate independently or together quasi-periodic cycles, can be identified as long as agents are sufficiently impatient. The first mechanism relies on the elasticity of intertemporal substitution or equivalently the sign of the cross-derivative of the utility function whereas the second rests on sectoral technologies through the sign of the capital intensity difference across two sectors. Furthermore, building on the quasi-palindromic nature of the degree-4 characteristic equation, we derive some meaningful sufficient conditions associated to the occurrence of complex roots in a two-sector OLG model. Finally, we show that our theoretical results are consistent with some empirical evidence for medium- and long-run swings in the inheritance flows as a fraction of national income in France over the period 1896-2008.
Keywords Altruism, Bequest, Periodic and quasi-periodic cycles, Quasi-palindromic polynomial, Endogenous fluctuations, Optimal Growth, Two-sector overlapping generations model
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Abstract The relationship between public debt, growth and volatility is investigated in a Barro-type (1990) endogenous growth model, with three main features: we consider a small open economy, international borrowing is constrained and households have taste for domestic public debt. Therefore, capital, public debt and the international asset are not perfect substitutes and the economy is characterized by an investment multiplier. Whatever the level of the debt-output ratio, the existing BGP features expectation-driven fluctuations. If the debt-output ratio is low enough, there is also a second BGP with a lower growth rate. Hence, lower debt does not stabilize the economy with credit market imperfections. However, a high enough taste for domestic public debt may rule out the BGP with lower growth. This means that if the share of public debt hold by domestic households is high enough, global indeterminacy does not occur.
Keywords Small open economy, Public debt, Credit constraint, Indeterminacy
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Abstract We consider an economy with three cities producing different outputs. Two cities produce intermediate goods, a type 1 producing an intermediate "agricultural" good with capital and labor only, and a type 2 producing an intermediate "industrial" good with capital, labor and human capital, and the last 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 the 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 formers. This implies that the relative size in terms of output of the "agricultural" city decreases over time. This property allows to recover the empirical fact that most nonagricultural 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.
Keywords Urban dynamics, Human capital, Endogenous growth, Heterogeneous growth rates, City inequalities
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Abstract 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.
Keywords Two-sector optimal growth model, Strong and weak concavity, Small discounting, Period-two cycles
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Abstract 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.
Keywords Small discounting, Two-sector optimal growth model, Strong and weak concavity, Period-two cycles
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Abstract We propose a model of non-balanced endogenous growth in which the final good, which can be either consumed or used as capital, is produced using two intermediate inputs, one being “knowledge-intensive”. Agents working in the knowledge-intensive sector need to accumulate technological knowledge and thus have to decide how to split their individual unit of time between accumulation of technological knowledge (research) and work. Agents working in the second sector do not need to accumulate knowledge and thus devote all their individual unit of time to work. Individual knowledge therefore becomes a labor-augmenting factor, and knowledge accumulation leads to an unbounded increase in TFP in the knowledge-intensive sector, and thus to endogenous capital deepening. The asymmetry in the growth rates of TFP leads to non-balanced growth. Labor (number of workers) reallocations across sectors occur, leading to a greater increase in output for the knowledge-intensive sector. We show that non-balanced growth is consistent with Kaldor facts, as the asymptotic equilibrium is above all characterized by a constant interest rate and capital share in national income. However, the economy follows a growth path converging to a particular level of wealth that depends on the initial price of capital and knowledge. As a consequence, countries with the same fundamentals but lower initial wealth will be characterized by lower asymptotic wealth. We therefore extend the Lucas [19] finding and prove the existence of non-convergence across countries in a framework with structural change.
Keywords Two-sector model, Technological knowledge, Non-balanced endogenous growth, Structural change, Kaldor and Kuznets facts
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Abstract 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.
Keywords Endogenous growth, Time-varying consumption tax, Global indeterminacy, Self-fulfilling expectations, Sunspot equilibria
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Abstract 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) [18] 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.
Keywords Aggregate instability, Local indeterminacy, Expectations-driven fluctuations, Labor income taxes, Balanced-budget rule, Infinite-horizon two-sector model, Capital intensity difference
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Abstract The interplay between growth and public debt is addressed considering a Barro-type [1] endogenous growth model where public spending is financed through taxes on income and public debt. Debt is assumed to be a fixed proportion of GDP which is used as a policy parameter by the government. We first show that when debt is a large enough proportion of GDP, two distinct BGPs may co-exist, one being indeterminate. Therefore, local and global indeterminacy may arise and self-fulfilling expectations appear as a crucial ingredient to understand the impact of debt on growth and on macroeconomic fluctuations. We then exhibit two types of important trade-off associated with self-fulfilling expectations. First, we show that the lowest BGP is always decreasing with respect to the ratio of debt/GDP while the highest one is increasing. As a result, depending on the BGP selected by agents’ expectations, the relationship between debt and growth is not always negative. Second, we show that the highest BGP, which provides the highest welfare, is always locally indeterminate while the lowest is always locally determinate. Therefore, depending on the expectations of agents, when debt is increasing, large fluctuations associated to self-fulfilling believes may occur and be associated at the same time with welfare losses if there is a coordination on the low steady-state. Finally, a simple calibration exercise allows to provide an understanding of the recent experiences of many OECD countries.
Keywords Endogenous growth, Public spending, Public debt, Sunspot fluctuations
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Abstract We analyze a version of the Benhabib and Farmer [3] 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 [14] 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. [19], in which it is shown that indeterminacy cannot occur under either GHH and KPR preferences, and in Jaimovich [13] in which local indeterminacy only arises for intermediary income effects.
Keywords Indeterminacy, Sunspots, Income and substitution effects, Sector-specific externalities, Infinite-horizon two-sector model
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Abstract We analyze sunspot-driven fluctuations in the standard two-sector RBC model with moderate increasing returns to scale and generalized no-income-effect preferences à la Greenwood, Hercovitz and Huffman [13]. 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. We show that local indeterminacy occurs through flip and Hopf bifurcations for a large set of values for the elasticity of intertemporal substitution in consumption, provided that the labor supply is sufficiently inelastic. Finally, we provide a detailed quantitative analysis of the model. Computing, on a quarterly basis, a new set of empirical moments related to two broadly defined consumption and investment sectors, we are able to identify, among the set of admissible calibrations consistent with sunspot equilibria, the ones that provide the best fit of the data. The model properly calibrated solves several empirical puzzles traditionally associated with two-sector RBC models.
Keywords Indeterminacy, Sunspots, Two-sector model, Sector-specific externalities, Real business cycles cycles
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Abstract 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.
Keywords Indeterminacy, Sector-specific externalities, Real business cycles, Sunspots, Two-sector model
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Abstract We investigate the role of non-separable preferences on 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 non-separable utility functions, we find that expectations-driven fluctuations easily occur when consumption and labor are Edgeworth substitutes or weak Edgeworth complements. Under these properties, an intermediate range of tax rates and a sufficiently low elasticity of intertemporal substitution in consumption lead to instability.
Keywords Indeterminacy, Expectations-driven business cycles, Labor income taxes, Balanced-budget rule, Non-separable preferences
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Abstract Imposing some constraints on public debt is often justified regarding sustainability and stability issues. This is especially the case when the ratio of public debt over GDP is restricted to be constant. Using a Ramsey model, we show that such a constraint can however be a fundamental source of indeterminacy, and therefore, of expectation-driven fluctuations. Indeed, through the intertemporal budget constraint of the government, income taxation negatively depends on future debt, i.e. on the expected level of production. This mechanism ensures that expectations on the future tax rate may be self-fulfilling. We show that this is promoted by a larger ratio of debt over GDP.
Keywords Indeterminacy, Endogenous cycles, Public debt, Income taxation
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Abstract We introduce public debt in a Ramsey model with heterogenous agents and a public spending externality affecting utility which is financed by income tax and public debt. We show that public debt considered as a fixed portion of GDP can have a stabilizing or destabilizing effect depending on some fundamental elasticities. When the public spending externality is weak and the elasticity of capital labor substitution is low enough, public debt can only be destabilizing, generating damped or persistent macroeconomic fluctuations. Whereas when the public spending externality and the elasticity of capital labor substitution are strong enough, public debt can be stabilizing, driving to monotone convergence an economy experiencing damped or persistent fluctuations without debt.
Keywords Endogenous cycles, Heterogeneous agents, Public spending, Public debt, Borrowing constraint
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Abstract We investigate the effects of collaterals and monetary policy on growth rate dynamics in a Ramsey economy where agents have heterogeneous discount factors. We focus on the existence of business-cycle fluctuations based on self-fulfilling prophecies and on the occurrence of deterministic cycles through bifurcations. We introduce liquidity constraints in segmented markets where impatient (poor) agents without collaterals have limited access to credit. We find that an expansionary monetary policy may promote economic growth while making endogenous fluctuations more likely. Conversely, a regulation reinforcing the role of collaterals and reducing the financial market imperfections may enhance the economic growth and stabilize the economy.
Keywords Collaterals, Heterogeneous agents, Balanced growth, Endogenous fluctuations, Stabilization policies
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Abstract We investigate the role of preferences in the existence of expectation-driven instability under a balanced budget rule where government spendings are financed by a tax on labor income. Considering a one-sector neoclassical growth model with a large class of preferences, we find that expectation-driven fluctuations are more likely when consumption and labor are Edgeworth substitutes. Under this property, an intermediate range of tax rates and a sufficiently low elasticity of intertemporal substitution in consumption lead to instability. Numerical simulations of the model support the conclusion that labor income taxation is a plausible source of instability in most OECD countries.
Keywords Indeterminacy, Expectation-driven business cycles, Labor income taxes, Balanced-budget rule, Infinite-horizon model
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Abstract In the present paper, we consider a two-country, two-good, two-factor general equilibrium model with CIES non-linear preferences, asymmetric technologies across countries and decreasing returns to scale. It is shown that aggregate instability and endogenous fluctuations may occur due to international trade. In particular, we prove that the integration into a common market on which countries trade the produced good and the capital input may lead to period-two cycles even when the closed-economy equilibrium is saddle-point stable in both countries.
Keywords Perfect foresight dynamic general equilibrium model, International trade, Aggregate instability, Endogenous fluctuations, Non-linear preferences
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Abstract We analyze sunspot-driven fluctuations in the standard 2-sector RBC model with moderate increasing returns to scale. 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. With GHH preferences, we show that local indeterminacy occurs through flip and Hopf bifurcations for a large set of values of the elasticity of intertemporal substitution in consumption if the labor supply is sufficiently inelastic. With additively-separable preferences, we prove that local indeterminacy occurs through flip and Hopf bifurcations for any value of the elasticity of the labor supply, and can even be compatible with an arbitrarily low elasticity of intertemporal substitution in consumption. Finally, we provide a detailed quantitative analysis of the model. Computing, on a quarterly basis, a new set of empirical moments related to two broadly defined consumption and investment sectors, we are able to identify, among the set of admissible calibrations consistent with sunspot equilibria, the ones that provide the best fit of the data. The model properly calibrated solves several empirical puzzles traditionally associated with 2-sector RBC models.
Keywords Indeterminacy, Sunspots, Two-sector model, Sector-specific externalities, Real business cycles
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Abstract We introduce public spending, financed through income taxation, in the Ramsey model with heterogeneous agents. Public spending as a source of welfare generates more complex dynamics. In contrast to previous contributions focusing on similar models but with wasteful public spending, limit cycles through Hopf bifurcation and expectation-driven fluctuations appear if the degree of capital-labor substitution is large enough to be compatible with capital income monotonicity. Moreover, unlike frameworks with a representative agent, our results do not require externalities in production and are compatible with a weakly elastic labor supply with respect to wage.
Keywords Heterogeneous agents, Indeterminacy, Endogenous cycles, Public spending, Endogenous labor supply, Borrowing constraint
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Abstract Existing literature continues to be unable to offer a convincing explanation for the volatility of the stochastic discount factor in real world data. Our work provides such an explanation. We do not rely on frictions, market incompleteness or transactions costs of any kind. Instead, we modify a simple stochastic representative agent model by allowing for birth and death and by allowing for heterogeneity in agents' discount factors. We show that these two minor and realistic changes to the timeless Arrow-Debreu paradigm are sufficient to invalidate the implication that competitive financial markets efficiently allocate risk. Our work demonstrates that financial markets, by their very nature, cannot be Pareto efficient, except by chance. Although individuals in our model are rational; markets are not.
Keywords Inefficient markets, Heterogeneous agents, Overlapping generations, Sunspots, Extrinsic uncertainty, Excess volatility
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Abstract We consider a two-sector two-good two-periods overlapping generations model with inelastic labor, consumption in both period of life and homothetic CES preferences. There are two consumption goods, one pure (non-durable) consumption and one consumable (durable) capital good which can be either consumed or invested. Assuming gross substitutability and a capital intensive pure consumption good, we prove the existence of efficient endogenous fluctuations through a Hopf bifurcation if the share of the consumption of young in the composite good is low enough. We also show that some fiscal policy rules can improve welfare and prevent the existence of business-cycle fluctuations in the economy by driving it to the optimal steady state as soon as it is announced.
Keywords Two-sector OLG model, Multiple consumption goods, Dynamic efficiency, Endogenous fluctuations
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Abstract We examine the impact of balanced-budget consumption taxes on the existence of expectations-driven business cycles in two-sector economies with infinitely-lived households. We prove that, whatever the relative capital intensity difference across sectors, aggregate instability can occur if the consumption tax rate is not too low. Moreover, we show through a numerical exercise based on empirically plausible tax rates that endogenous business-cycle fluctuations may be a source of instability for all OECD countries, including the US.
Keywords Aggregate instability, Indeterminacy, Expectations-driven fluctuations, Consumption taxes, Balanced-budget rule, Infinite-horizon two-sector model
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Abstract Studies of optimal growth in a multisector framework are generally addressed in reduced form models. These are defined by an indirect utility function which summarizes the consumers' preferences and the technologies. Weak concavity assumptions of the indirect utility function allow one to prove differentiability of optimal solutions and stability of steady state. This paper shows that if the consumption good production function is concave-gamma, and the instantaneous utility function is concave-rho, then the indirect utility function is weakly concave, and its curvature coefficients are bounded from above by a function of gamma and rho.
Keywords Indirect utility function, Social production function, Multisector optimal growth model, Weak concavity
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Abstract We consider an OLG economy with two consumption goods. There are two sectors that produce a pure consumption good and a mixed good which 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 (1986, Journal of Economic Theory, 40, 89-102) influential conclusion, this result suggests that some fiscal policy rules can prevent the existence of business-cycle fluctuations in the economy by driving it to the optimal steady state as soon as it is announced.
Keywords Two-sector OLG model, Multiple consumption goods, Dynamic efficiency, Endogenous fluctuations, Local indeterminacy
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