Keywords 1. Introduction 2. W h y should we care? 2.1. Technical aspects of linear models 2.2. In... more Keywords 1. Introduction 2. W h y should we care? 2.1. Technical aspects of linear models 2.2. Indeterminacy and propagation mechanisms in real models of business cycles 2.3. Indeterminacy and propagation mechanisms in monetary models of business cycles 3. Indeterminacy in real models 3.1. A framework for comparing different models 3.2. The one-sector model with increasing returns 3.3. The two-sector model with increasing returns 3.4. The two-sector model with constant marginal returns 3.5. Fixed costs and the role of profits 3.6. Models with variable markups 4. Indeterminacy in monetary models 4.1. Monetary models with one state variable and fixed labor supply 4.2. Money in the utility function and the production function 4.3. Monetary models with one state variable and a variable labor supply 4.4. Monetary models with several state variables 5. Indeterminacy and policy feedback 5.1. Fiscal policy feedback 5.2. Monetary policy feedback 5.3. Interest rate rules and indeterminacy 5.4. Monetary models and sticky prices due to frictions in the trading process 6. Indeterminacy and models o f endogenous growth 7. Some related work
have all indirectly contributed to the ideas in this paper and we thank them without implicating ... more have all indirectly contributed to the ideas in this paper and we thank them without implicating them in any mistakes that might remain. We also thank two anonymous referees of this journal for their very thorough reading of the …rst draft of this paper and for providing suggestions for that have signi…cantly improved the …nal version.
The conjecture by Ryder and Heal that optimal closed orbits exist in a growth model with intertem... more The conjecture by Ryder and Heal that optimal closed orbits exist in a growth model with intertemporal dependent preferences is rigorously proved.
Studies in Nonlinear Dynamics & Econometrics, 1996
The possibility of cycles and chaos arising from nonlinear dynamics in economics emerged in the l... more The possibility of cycles and chaos arising from nonlinear dynamics in economics emerged in the literature in the 1980s, and it came as a surprise. 1 The possibility of deterministic cycles in economic models had been noted before, for example in the well-known multiplier-accelerator models, but not in equilibrium models with complete markets, no frictions, and full intertemporal arbitrage. 2 The reason for the surprise was understandable: deterministic fluctuations in equilibrium models involve predictable changes in relative prices which should be ruled out by intertemporal arbitrage. In models of overlapping generations, however, finite lives can restrict complete arbitrage over time. As a result, some people thought, and still think, that cycles that are shorter than the agents' postulated lifespans would not be possible in equilibrium models, and therefore are irrelevant for business-cycle analysis. This view is clearly wrong, and of course ignores the extensive literature on cycles and chaos in optimal growth models with infinitely lived agents. In such models deterministic cycles in relative prices occur easily, but the amplitudes of the cycles remain within bounds of the discount rate. 3 It is not difficult to show in the context of multisector growth models, say with Cobb-Douglas production functions, that for any positive discount rate there is a large class of technologies for which cycles occur. (See Benhabib and Rustichini [1990].) Getting chaos, however, is harder. Recent works by Sorger (1992), by Mitra (1995), and by Nishimura and Yano (1995) give lower bounds for the discount rate, below which chaos is ruled out for one-sector models of optimal growth. Yet even in that context, going to a multisector framework may considerably lower the bounds on the discount rate thus far established. A second reason for the attention that chaotic dynamics received in the economics literature regards prediction. The common wisdom has been that economic fluctuations are driven by exogenous shocks. Chaotic dynamics not only supplied an alternative explanation for at least some part of economic fluctuations, but also provided an excuse for economists' difficulties with forecasting. Sometimes, however, an important feature of chaotic dynamics that makes forecasting difficult, namely, sensitive dependence on initial conditions, is used in a cavalier way to explain short-run dynamics, forgetting that the effect of sensitive dependence becomes significant only after some periods, but not in the very short run. When it became obvious that very-standard equilibrium models could easily generate cycles and chaos, the attention in the literature naturally turned to the empirical plausibility of such dynamics. The most interesting approach, inspired by developments in natural sciences and mathematics, was also atheoretical, and reminiscent of VAR methods of time series. 4 The idea was to try to infer whether a particular economic time series was generated by a deterministic, low (at most four-or five-) dimensional system that was chaotic, or whether it came from a simple (linear) stochastic system. It is not difficult to see that such inferences are hard to make when the time-series data is short, as is the case with most economic series, with the exception of financial data. It is not surprising, then, that many applications of this approach are in the area of finance, but even there, where we have very high-frequency data, it is hard to pick up fluctuations that may occur at lower
ABSTRACT In the present paper, we construct a continuous time model of economic growth with posit... more ABSTRACT In the present paper, we construct a continuous time model of economic growth with positive externalities and with variable capacity utilization, and study the global equilibrium paths in this model. If there is a homoclinic orbit or a periodic solution in this model, equilibrium is globally indeterminate. We show that positive externalities can yield multiple steady states, a one-parameter family of homoclinic orbits, and a two-parameter family of periodic solutions. It is also shown that there exists a sunspot equilibrium in this model.
In this paper we explore whether the changing composition of output in response to technology sho... more In this paper we explore whether the changing composition of output in response to technology shocks can play a significant role in the propagation of shocks over time. For this purpose we study two multisector RBC models, with two and three sectors. We find that, while the two sectors model requires a high intertemporal elasticity of substitution of consumption to match the various dynamic properties of U.S. macroeconomic data, the three sector model has a strong propagation mechanism under conventional parameterizations, as long as the factor intensities in the three sectors are different enough.
Lecture Notes in Economics and Mathematical Systems, 1984
Various authors have investigated the dynamic theory of factor demands by considering the “costs ... more Various authors have investigated the dynamic theory of factor demands by considering the “costs of adjustment” faced by the firm. See Eisner and Strotz [5], Treadway [15], Lucas [8], Lucas and Prescott [9], Mortensen [12], Brock and Scheinkman [3] and Scheinkman [14]. In such models the firm maximizes the present value of its profit stream under the constraint that changing the levels of factor inputs involves costs of adjustment. One can then obtain optimal time paths for investments, that is for the accumulation or decumulation of the stocks of factor inputs. Under certain assumptions on the structure of the model, the optimal time paths of the stock of factors asymptotically approach some long-run equilibrium value. In particular Brock and Scheinkman [3] and Scheinkman [14] have studied conditions under which factor levels globally converge to some steady state equilibrium.
Publisher Summary Traditional approaches to growth theory have modeled the process of growth as a... more Publisher Summary Traditional approaches to growth theory have modeled the process of growth as arising from decisions to invest in physical capital and from technological progress. This chapter discusses the implications of introducing technological progress and human capital into the Barro–Becker model of endogenous fertility. Harrod-neutral technical progress, apart from human capital, is incorporated into the analysis. One of the implications of technical progress is that steady states are no longer in levels; they represent growth paths of per capita variables like output and consumption on capital. The dynamic behavior of physical capital will be monotonic or oscillatory, depending on the elasticity of a certain altruism function that may also be viewed as the elasticity of an inverse demand curve for children. This elasticity, which is always equal to unity in the Barro–Becker model, also plays a major role in determining the existence of multiple steady states.
Page 1. Review of Economic Studies (1981) XLVIII, 459-471 0034-6527/80/00390459 $02.00 ? 1981 The... more Page 1. Review of Economic Studies (1981) XLVIII, 459-471 0034-6527/80/00390459 $02.00 ? 1981 The Society for Economic Analysis Limited Rational Choice and Erratic Behaviour JESS BENHABIB University of Southern California and ...
Keywords 1. Introduction 2. W h y should we care? 2.1. Technical aspects of linear models 2.2. In... more Keywords 1. Introduction 2. W h y should we care? 2.1. Technical aspects of linear models 2.2. Indeterminacy and propagation mechanisms in real models of business cycles 2.3. Indeterminacy and propagation mechanisms in monetary models of business cycles 3. Indeterminacy in real models 3.1. A framework for comparing different models 3.2. The one-sector model with increasing returns 3.3. The two-sector model with increasing returns 3.4. The two-sector model with constant marginal returns 3.5. Fixed costs and the role of profits 3.6. Models with variable markups 4. Indeterminacy in monetary models 4.1. Monetary models with one state variable and fixed labor supply 4.2. Money in the utility function and the production function 4.3. Monetary models with one state variable and a variable labor supply 4.4. Monetary models with several state variables 5. Indeterminacy and policy feedback 5.1. Fiscal policy feedback 5.2. Monetary policy feedback 5.3. Interest rate rules and indeterminacy 5.4. Monetary models and sticky prices due to frictions in the trading process 6. Indeterminacy and models o f endogenous growth 7. Some related work
have all indirectly contributed to the ideas in this paper and we thank them without implicating ... more have all indirectly contributed to the ideas in this paper and we thank them without implicating them in any mistakes that might remain. We also thank two anonymous referees of this journal for their very thorough reading of the …rst draft of this paper and for providing suggestions for that have signi…cantly improved the …nal version.
The conjecture by Ryder and Heal that optimal closed orbits exist in a growth model with intertem... more The conjecture by Ryder and Heal that optimal closed orbits exist in a growth model with intertemporal dependent preferences is rigorously proved.
Studies in Nonlinear Dynamics & Econometrics, 1996
The possibility of cycles and chaos arising from nonlinear dynamics in economics emerged in the l... more The possibility of cycles and chaos arising from nonlinear dynamics in economics emerged in the literature in the 1980s, and it came as a surprise. 1 The possibility of deterministic cycles in economic models had been noted before, for example in the well-known multiplier-accelerator models, but not in equilibrium models with complete markets, no frictions, and full intertemporal arbitrage. 2 The reason for the surprise was understandable: deterministic fluctuations in equilibrium models involve predictable changes in relative prices which should be ruled out by intertemporal arbitrage. In models of overlapping generations, however, finite lives can restrict complete arbitrage over time. As a result, some people thought, and still think, that cycles that are shorter than the agents' postulated lifespans would not be possible in equilibrium models, and therefore are irrelevant for business-cycle analysis. This view is clearly wrong, and of course ignores the extensive literature on cycles and chaos in optimal growth models with infinitely lived agents. In such models deterministic cycles in relative prices occur easily, but the amplitudes of the cycles remain within bounds of the discount rate. 3 It is not difficult to show in the context of multisector growth models, say with Cobb-Douglas production functions, that for any positive discount rate there is a large class of technologies for which cycles occur. (See Benhabib and Rustichini [1990].) Getting chaos, however, is harder. Recent works by Sorger (1992), by Mitra (1995), and by Nishimura and Yano (1995) give lower bounds for the discount rate, below which chaos is ruled out for one-sector models of optimal growth. Yet even in that context, going to a multisector framework may considerably lower the bounds on the discount rate thus far established. A second reason for the attention that chaotic dynamics received in the economics literature regards prediction. The common wisdom has been that economic fluctuations are driven by exogenous shocks. Chaotic dynamics not only supplied an alternative explanation for at least some part of economic fluctuations, but also provided an excuse for economists' difficulties with forecasting. Sometimes, however, an important feature of chaotic dynamics that makes forecasting difficult, namely, sensitive dependence on initial conditions, is used in a cavalier way to explain short-run dynamics, forgetting that the effect of sensitive dependence becomes significant only after some periods, but not in the very short run. When it became obvious that very-standard equilibrium models could easily generate cycles and chaos, the attention in the literature naturally turned to the empirical plausibility of such dynamics. The most interesting approach, inspired by developments in natural sciences and mathematics, was also atheoretical, and reminiscent of VAR methods of time series. 4 The idea was to try to infer whether a particular economic time series was generated by a deterministic, low (at most four-or five-) dimensional system that was chaotic, or whether it came from a simple (linear) stochastic system. It is not difficult to see that such inferences are hard to make when the time-series data is short, as is the case with most economic series, with the exception of financial data. It is not surprising, then, that many applications of this approach are in the area of finance, but even there, where we have very high-frequency data, it is hard to pick up fluctuations that may occur at lower
ABSTRACT In the present paper, we construct a continuous time model of economic growth with posit... more ABSTRACT In the present paper, we construct a continuous time model of economic growth with positive externalities and with variable capacity utilization, and study the global equilibrium paths in this model. If there is a homoclinic orbit or a periodic solution in this model, equilibrium is globally indeterminate. We show that positive externalities can yield multiple steady states, a one-parameter family of homoclinic orbits, and a two-parameter family of periodic solutions. It is also shown that there exists a sunspot equilibrium in this model.
In this paper we explore whether the changing composition of output in response to technology sho... more In this paper we explore whether the changing composition of output in response to technology shocks can play a significant role in the propagation of shocks over time. For this purpose we study two multisector RBC models, with two and three sectors. We find that, while the two sectors model requires a high intertemporal elasticity of substitution of consumption to match the various dynamic properties of U.S. macroeconomic data, the three sector model has a strong propagation mechanism under conventional parameterizations, as long as the factor intensities in the three sectors are different enough.
Lecture Notes in Economics and Mathematical Systems, 1984
Various authors have investigated the dynamic theory of factor demands by considering the “costs ... more Various authors have investigated the dynamic theory of factor demands by considering the “costs of adjustment” faced by the firm. See Eisner and Strotz [5], Treadway [15], Lucas [8], Lucas and Prescott [9], Mortensen [12], Brock and Scheinkman [3] and Scheinkman [14]. In such models the firm maximizes the present value of its profit stream under the constraint that changing the levels of factor inputs involves costs of adjustment. One can then obtain optimal time paths for investments, that is for the accumulation or decumulation of the stocks of factor inputs. Under certain assumptions on the structure of the model, the optimal time paths of the stock of factors asymptotically approach some long-run equilibrium value. In particular Brock and Scheinkman [3] and Scheinkman [14] have studied conditions under which factor levels globally converge to some steady state equilibrium.
Publisher Summary Traditional approaches to growth theory have modeled the process of growth as a... more Publisher Summary Traditional approaches to growth theory have modeled the process of growth as arising from decisions to invest in physical capital and from technological progress. This chapter discusses the implications of introducing technological progress and human capital into the Barro–Becker model of endogenous fertility. Harrod-neutral technical progress, apart from human capital, is incorporated into the analysis. One of the implications of technical progress is that steady states are no longer in levels; they represent growth paths of per capita variables like output and consumption on capital. The dynamic behavior of physical capital will be monotonic or oscillatory, depending on the elasticity of a certain altruism function that may also be viewed as the elasticity of an inverse demand curve for children. This elasticity, which is always equal to unity in the Barro–Becker model, also plays a major role in determining the existence of multiple steady states.
Page 1. Review of Economic Studies (1981) XLVIII, 459-471 0034-6527/80/00390459 $02.00 ? 1981 The... more Page 1. Review of Economic Studies (1981) XLVIII, 459-471 0034-6527/80/00390459 $02.00 ? 1981 The Society for Economic Analysis Limited Rational Choice and Erratic Behaviour JESS BENHABIB University of Southern California and ...
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