Indeterminacy in Two-Sector Models of Endogenous Growth with Leisure

This paper demonstrates that preference structure may play a pivotal role in generating indeterminacy in the stylized model of endogenous growth. By examining two-sector models of endogenous growth with human capital formation, we show that if the utility function of the representative family is not additively separable between consumption and pure leisure time, indeterminacy may hold even if production technologies satisfy social constant returns. We also examine models with quality leisure in which leisure activities require human capital as well as time. In contrast to the pure-leisure time model, we find that the quality-leisure time model generally needs increasing returns to scale technologies to generate indeterminacy. It is also shown that nonseparability of utility function is crucial for generating indeterminacy in the quality leisure model as well.endogenous growth, two-sector models, endogenous labor supply, indeterminacy

Preference Structure and Indeterminacy in Two-Sector Models of Endogenous Growth

This paper demonstrates that preference structure may play a pivotal role in generating indeterminacy in stylized models of endogenous growth. By examining two-sector models of endogenous growth with human capital formation, we show that if the utility function of the representative family is not additively separable between consumption and pure leisure time, indeterminacy may hold even if production technologies satisfy social constant returns. We also examine models with quality leisure in which leisure activities require human capital as well as time. It is shown that non-separable utility may be relevant for generating indeterminacy in this setting as well.

Local and global indeterminacy in two-sector models of endogenous growth

In this paper we consider a two-sector endogenous growth model where the productions of the final good and human capital require economy-wide external effects. Assuming constant returns to scale at the private and social levels, we show that local and global indeterminacy of equilibrium paths are compatible with any values for the elasticity of intertemporal substitution in consumption and any sign for the capital intensity difference across the two sectors.Two-sector model, endogenous growth, economy-wide externalities, local and global indeterminacy

Fiscal policy and indeterminacy in models of endogenous growth

This paper investigates the dynamic behavior of two-sector models of endogenous growth with sector-specific external effects, and government expenditure financed by distortionary taxation. When this type of external effect is combined with a sufficient degree of capital taxation in a Lucas–Uzawa endogenous growth model, continua of equilibria will emerge in the region of the balanced growth paths. By contrast, indeterminacy is not possible when either sector-specific external effects or factor taxation are added to the model in isolation. In the second part of the paper, we demonstrate that if labor supply is endogenous, indeterminacy can be consistent with much lower degrees of increasing returns to scale. Furthermore, certain types of fiscal policy will be associated with multiple balanced growth paths and the existence of a poverty trap. Finally, in the last part of the paper, we demonstrate that if physical capital is employed in both sectors of the economy, indeterminacy will emerge for varying combinations of factor taxation and external effects, even when returns to scale are constant at the social level

Equilibrium Dynamics in Discrete-Time Endogenous Growth Models with Social Constant Returns

The existing literature establishes possibilities of local determinacy and dynamic indeterminacy in continuous-time two-sector models of endogenous growth with social constant returns. The necessary and sufficient condition for local determinacy is that the factor intensity rankings of the two sectors are consistent in the private/physical and social/value sense. The necessary and sufficient condition for dynamic indeterminacy is that the final (consumable) good sector is human (pure) capital intensive in the private sense but physical (consumable) capital intensive in the social sense. This paper re-examines the dynamic properties in a discrete-time endogenous growth framework and finds that conventional propositions obtained in continuous time need not be valid. It is shown that the established necessary and sufficient conditions on factor intensity rankings for local determinacy and dynamic indeterminacy are neither sufficient nor necessary, as the magnitudes of time preference and capital depreciation rates both play essential roles.Sectoral Externalities, Endogenous Growth, Dynamic Determinacy/Indeterminacy.

Sector-Specific Externalities and Endogenous Growth under Social Constant Returns

By examining two-sector models of endogenous growth with physical and human capital, this paper demonstrates that indeterminacy of equilibrium may emerge even in the absence of social increasing returns. The first model we examine assumes that both final good and new human capital production sectors employ physical as well as human capital under social constant returns but private decreasing returns due to the presence of sector-specific externalities. It is shown that a small divergence between private and social factor intensity conditions generates indeterminacy of equilibrium rather easily even under constant returns. I addition, we show that introducing endogenous labor supply may enhance the possibility of indeterminacy. Some extensions and intuitive interpretation of the indeterminacy conditions are also presented

Indeterminacy in Two-Sector Models of Endogenous Growth with Leisure

This paper demonstrates that preference structure may play a pivotal role in generating indeterminacy in the stylized model of endogenous growth. By examining two-sector models of endogenous growth with human capital formation, we show that if the utility function of the representative family is not additively separable between consumption and pure leisure time, indeterminacy may hold even if production technologies satisfy social constant returns. We also examine models with quality leisure in which leisure activities require human capital as well as time. In contrast to the pure-leisure time model, we find that the quality-leisure time model generally needs increasing returns to scale technologies to generate indeterminacy. It is also shown that nonseparability of utility function is crucial for generating indeterminacy in the quality leisure model as well

Local and global indeterminacy in two-sector models of endogenous growth

In this paper we consider a two-sector endogenous growth model where the productions of the final good and human capital require economy-wide external effects. Assuming constant returns to scale at the private and social levels, we show that local and global indeterminacy of equilibrium paths are compatible with any values for the elasticity of intertemporal substitution in consumption and any sign for the capital intensity difference across the two sectors

Fiscal policy, increasing returns, and endogenous fluctuations

We examine the quantitative implications of government fiscal policy in a discrete-time one-sector growth model with a productive externality that generates social increasing returns to scale. Starting from a laissez-faire economy that exhibits an indeterminate steady state (a sink), we show that the introduction of a constant capital tax or subsidy can lead to various forms of endogenous fluctuations, including stable 2-, 4-, 8-, and 10- cycles, quasi-periodic orbits, and chaos. In contrast, a constant labor tax or subsidy has no effect on the qualitative nature of the model's dynamics. We also show that the use of local steady-state analysis to detect the presence of multiple equilibria in this class of models can be misleading. For a plausible range of capital tax rates, the log-linearized dynamical system exhibits saddle-point stability (suggesting a unique equilibrium) while the true nonlinear model exhibits global indeterminancy. Finally, we explore the use of a state-contingent capital subsidy/tax scheme for stabilization purposes. We show that a local control policy designed using the log-linearized model can rule out sunspot equilibria near the steady state but may not prevent fluctuations arising from global indeterminacy. We proceed to use the nonlinear model to design a policy that can stabilize the economy against all forms of endogenous fluctuations and select a globally unique equilibrium.Fiscal policy ; Business cycles ; Chaotic behavior in systems

Congestible Public Goods and Indeterminacy in a Two-sector Endogenous Growth Model

This paper develops a new mechanism for local indeterminacy in a constant-return, two-sector, human capital enhanced growth model, with productive public spending financed by the income taxation in the goods sector. The use of productive public goods services is subject to an external congestion effect in association with the quantity of aggregate physical as well as human capital used in the economy. We establish local indeterminate equilibrium paths driven by the congestion effect. The possibility of local indeterminacy emerges because under constant returns, the congestion effect reduces the marginal contribution of public goods services and increases the marginal contribution of physical as well as human capital, thereby making the social marginal products to deviate from those of the firm’s perspective.two-sector model, indeterminacy, congestion