Two-sector Endogenous Growth Model Research Articles

Importing Human Capital: Immigration in the Endogenous Growth Model

During the last decade immigration has accounted for a third of the growth in the population of the United States. Although immigration policy is always controversial, much of the public's recent anxiety has focused on the relatively low levels of skill and education, that today's immigrants bring to the country. Many researchers express alarm at the decline in immigrant skills, suggesting that the continued incorporation of these immigrants will ultimately hamper the performance of the U.S. economy and harm the economic well being of native-born Americans. To study the effects of immigration on economic growth and the welfare of the native-born we construct a two-sector endogenous growth model with overlapping dynasties. We use the model to calculate the effects of changes in the rate of immigration, or changes in the relative skill-levels of new immigrants to the United States, on steady state growth rates and the welfare of native households. We also examine the possibility that high rates of immigration between countries in the developing world can create multiple balanced growth paths and poverty traps.

On Taxation in a Two-Sector Endogenous Growth Model with Endogenous Labor Supply

This paper examines the effects of taxation on long-run growth in a two-sector endogenous growth model with (i) physical capital as an input in the education sector and (ii) leisure as an additional argument in the utility function. The analysis of the effects of taxation - including income taxation, capital income taxation and labor income taxation - distinguishes between the case with a unique (interior) balanced growth path and the case with multiple balanced growth paths. Due to the flexibility of labor supply, taxation of income may induce agents to spend more or less time on leisure activities. In the case of income taxation, where capital and labor income are taxed equally, the resulting effect on the growth rate is negative. The contribution of endogenous leisure is confined to reducing or increasing the size of the effect on the growth rate. If only capital income is taxed, the direction of the effect may reverse. In that case, the positive effect of the increase in total non-leisure time dominates the direct negative effect, implying that capital taxation increases the long-run growth rate.

Effects of flat-rate taxes: to what extent does the leisure specification matter?

This paper explores the implications that the specification of the leisure activity has on the effects of alternative forms of taxation in a two-sector endogenous growth model of the US economy. Growth and welfare effects of tax reforms are shown to depend markedly on the leisure specification. We also compute the optimal tax structure of factor incomes and consumption taxation. The optimal tax rate on capital income is rather robust to the leisure specification. However, the balance between consumption and labor income taxation and the effects of shifting to the optimal tax structure vary considerably across leisure specifications.

Democracy, rent seeking, public spending and growth

Does democratization imply faster growth, less corruption and less inefficiency? Past studies yield ambiguous results on the effects of democracy on economic performance and growth. We develop a simple two-sector endogenous growth model that shows both very young and mature democracies grow faster than countries in mid stages of democratization, producing a ‘U’ effect. This effect results from the pattern of rent seeking as it diverts from the provision of public goods. Rent-seekers act as monopolistic competitors. Initially, more democracy increases their number, raising aggregate rents. However, rents per rent-seeker fall with the number of rent seekers. Due to this crowding effect and the increased competition among rent seekers, aggregate rents fall in mature democracies. Thus, rents show an ‘inverted-U’ effect in relation to democracy. We find fairly robust supportive evidence for the latter.

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.

Multiple transitional growth paths in endogenously growing open economies

This paper extends research in indeterminacy literature to a small open economy, two-sector endogenous growth model. It shows that a continuum of equilibria exist in two situations, (i) the production functions exhibit social constant returns to scale with very small or even negligible externalities; and (ii) the production functions are standard constant returns to scale without externalities but the government implements asymmetric tax policies across sectors.

Dynamics of Output Growth, Consumption and Physical Capital in Two-Sector Models of Endogenous Growth

Abstract We report the results of an experimental investigation of a key axiom of economic theories of dynamic decision making – namely, that agents plan. Inferences from previous investigations have been confounded with issues concerning the preference functionals of the agents. Here, we present an innovative experimental design which is driven purely by dominance: if preferences satisfy dominance, we can infer whether subjects are planning or not. We implement three sets of experiments: the first two (the Individual Treatments) in which the same player takes decisions both in the present and the future; and the third (the Pairs Treatment) in which different players take decisions at different times. The two Individual treatments differed in that, in one, the subjects played sequentially, while, in the other, the subjects had to pre-commit to their future move. In all contexts, according to economic theory, the players in the present should anticipate the decision of the player in the future. We find that over half the participants in all three experimental treatments do not appear to be planning ahead; moreover, their ability to plan ahead does not improve with experience, except possibly when we force subjects to pre-commit to their future decision. These findings identify an important lacuna in economic theories, both for individual behaviour and for behaviour in games. Address for correspondence: John D Hey, Department of Economics and Related Studies, University of York, Heslington, York YO10 5DD, UK. Tel: 0044 1904 433 786 Fax: 0044 1904 433 759. E-mail: jdh1@york.ac.uk Bone: University of York, UK, jdb1@york.ac.uk Hey: LUISS, Italy and University of York, UK, jdh1@york.ac.uk Suckling: University of York, UK, jrs1@york.ac.uk

The Closed-Form Solution for a Family of Four-Dimension Non-Linear MHDS

In this paper I propose a method for solving in closed form a general class of four-dimension non-linear modified Hamiltonian dynamic systems. This method may be used to study several intertemporal optimization problems with a predetermined structure, involving unbounded technological constraints as well as multiple controls and state variables. The method is developed here by solving the first order conditions corresponding to the socially optimal solution to the Lucas (1988) two-sector model of endogenous growth.

Equilibrium Dynamics in a Two-Sector Model with Taxes

In this paper we are concerned with the equilibrium dynamics of a two-sector model of endogenous growth with distortionary taxes. We show that for certain parameters values and tax schemes every equilibrium orbit—except the steady state solution—is non-interior; i.e., there are times in which one of the sectors is inactive. This analysis confirms that in multisector models the set of easily checkable, universal conditions that can guarantee the interiority of equilibrium solutions is rather limited. Journal of Economic Literature Classification Numbers: D90, E22.

Multiplicity, Overtaking and Convergence in the Lucas Two-Sector Growth Model

This paper provides the complete closed-form solution to the Lucas two-sector model of endogenous growth. We study the issues of existence, uniqueness, multiplicity, positivity, transitional dynamics and long-run growth, related to the competitive equilibrium paths. We identify the parameter range where the different results hold and deduce the entire trajectories for the original variables. We revise the results on convergence and overtaking which arise from this model, and prove that the parameterization currently used as the background for an explanation of economic miracles and disasters, is not satisfactory because of its counterintuitive implications.

Business cycles in a two-sector model of endogenous growth

This paper analyzes the impact of cyclical volatility on long-term economic growth: does growth increase or decrease with increased cyclical volatility? We construct a stochastic two-sector model of endogenous growth to analyze this question in detail. We will show that economic growth is higher in the presence of business cycles, since people devote more time to learning activities in an uncertain economic environment. Human capital is a hedge against future income uncertainty. Hence, the rate of economic growth will be higher in a stochastic environment. Based on a calibration of the model, we find that economic growth increases by 0.46%-point as a result of observed business cycle variability. When account is taken of the interaction between the model's general equilibrium and the cycle, welfare gains (measured in units of a permanent percentage increase in consumption) from eliminating business cycle volatility are approximately 1.87%.

Environmental policy in an endogenous growth model with human capital and endogenous labor supply

This paper analyses environmental fiscal policy within a two-sector endogenous growth model with elastic labor supply. Pollution is modeled as a side product of production. The framework allows us to analyze the consequences of an environmental tax on the economic dynamics. Both transitional dynamics and balanced growth path are computed and the response to an environmental tax change is explored. Short- and long-run welfare costs are also computed. We show that an environmental tax change induces a sharp contrast between short- and long-run effects. The magnitude of this contrast depends on the agents’ aptitude to substitute studying time for leisure.

Stages of growth in economic development

The paper analyses a two-sector model of endogenous growth with two common features of economic development: stages of sustained growth and underdevelopment traps. The model also demonstrates the transitional issues of a temporary underdevelopment trap, seemingly sustainable growth, and a slowdown in productivity growth. The temporary underdevelopment trap occurs when an economy exhibits a regime of extensive growth (i.e. slowly declining growth in physical capital with no growth in human capital), but thereafter starts a transition to sustained growth. Seemingly sustainable growth happens when an economy exhibits a regime of intensive growth (i.e. both capitals grow initially) but the growth of human capital subsequently ceases and the economy eventually finds itself in a zero growth trap. The model also exhibits the possibility of a slowdown in productivity growth as a temporary phenomenon during the transition from the low growth stage to the high growth stage of an economy facing a new “industrial” revolution.

Tax Reform and Public Spending Trade-offs in an Endogenous Growth Model with Environmental Externality

This paper analyzes the trade-offs between fiscal policy reform and public expenses structures within a two-sector endogenous growth model with an environmental externality. Transitional dynamics, balanced growth path and welfare cost of alternative policy are computed. We show that taxes structure change leads to a lower welfare cost.

Equilibrium Dynamics in a Two-Sector Model with Taxes

In this paper we are concerned with the equilibrium dynamics of a two-sector model of endogenous growth with distortionary taxes. We show that for certain parameters values and tax schemes every equilibrium orbit--except the steady state solution--is non-interior; i.e., there are times in which one of the sectors is inactive. This analysis confirms that in multisector models the set of easily checkable, universal conditions that can guarantee the interiority of equilibrium solutions is rather limited.

Indeterminacy and Government Spending in a Two-Sector Model of Endogenous Growth

This paper analyzes the dynamic behavior of a two-sector model of endogenous growth with unproductive government spending. In this model, we prove that the subspace of the parameter space where the equilibrium exhibits indeterminacy is larger, the larger the fraction of government revenues devoted to government expenditures is, the more patient consumers are, and the more consumers are willing to substitute consumption intertemporally. Our analysis shows that, with the introduction of unproductive government spending, indeterminacy becomes a plausible property of the dynamic equilibrium in a two-sector growth model with factor taxes as the only market imperfection. We also show that, when the fraction of government revenues devoted to government expenditures is large, plausible fiscal policies may cause the equilibrium to exhibit indeterminacy. Journal of Economic Literature Classification Numbers: E62, O41, H31.

Environmental Fiscal Policy in an Endogenous Growth Model with Human Capital

This paper analyses environmental fiscal policy within a two-sector endogenous growth model with elastic labour supply. Pollution is modelled as a side product of production. The framework allows us to analyse the consequences of an environmental tax on the economic dynamics. Both transitional dynamics and balanced growth path are computed and the response to an environmental tax change is explored. Short-run and long-run welfare costs are computed too. We show that an environmental tax change induces a sharp contrast between short-run and long-run effects. The magnitude of this contrast depends on the agents' aptitude to substitute studying time for leisure.

The Return to Capital and Convergence in a Two Sector Model of Endogenous Growth

This paper obtains a simple algebraic derivation of the transitional dynamics of a two-sector endogenous growth model. This paper finds that the return to capital and the growth rate of output fall over time on the transition path if the initial ratio of physical capital to human capital is lower than the steady state level. It also shows that two sector endogenous growth models are consistent with the evidence on conditional convergence found by Barro (1991) and Mankiw, Romer, and Weil (1991). Neoclassical growth models and endogenous growth models are impossible to distinguish in terms of the falling rate of return on capital or in terms of conditional convergence. [O41]

Transitional dynamics in a two-sector non-scale growth model

Abstract This paper shows how, under plausible conditions, the transitional dynamics in a two-sector R&D-based non-scale growth model are represented by a two-dimensional stable saddlepath, thus enriching the transitional adjustment paths relative to that of the standard two-sector endogenous growth model. The transition speed itself is variable both through time and across sectors. Capital and knowledge grow at very different rates, consistent with the empirical evidence. Numerical simulations are used to characterize the transition paths in response to a range of specific shocks. In some cases, capital or knowledge may overshoot their respective long-run responses, during the transitional dynamics.

Welfare-maximizing tax structure in a model with human capital

This paper studies the welfare-maximizing tax structure in a two-sector model of endogenous growth with human capital. Here, tax structure refers to the mix of taxes which satisfy an exogenously given government budget constraint.