One-sector Model Research Articles

Carbon Price and Optimal Extraction of a Polluting Fossil Fuel with Restricted Carbon Capture

Among technological options to mitigate greenhouse gas (GHG) emissions, Carbon Capture and Storage technology (CCS) seems particularly promising. This technology allows to keep on extracting polluting fossil fuels without drastically increasing CO2 atmospheric concentration. We examine here a two-sector model with two primary energy resources, a polluting exhaustible resource and an expensive carbon-free renewable resource, in which an environmental regulation is imposed through a cap on the atmospheric carbon stock. We assume that only the emissions from one sector can be captured. Previous literature, based on one-sector models in which all emissions are capturable, finds that CCS technology should not be used before the threshold has been reached. We find that, when technical constraints make it impossible to capture emissions from both sectors, this result does not always hold. CCS technology should be used before the ceiling is reached if non capturable emissions are large enough. In that case, we find that energy prices paths must differ between sectors reflecting the difference of social cost of the resource according to its use. Numerical exercise shows that the initial carbon tax should equal 52$/t CO2 and that using CCS before the ceiling is optimal.

Intraindustry trade and the skill premium: Theory and evidence

We explore theoretically and empirically the relationship between intraindustry trade and the skill premium. Our model features a Chamberlinian-type mechanism of income distribution based on quasi-homothetic consumer preferences, non-homothetic production, and factor-biased scale economies at the firm level. The analysis focuses on a two-country, one-sector model of intraindustry trade with two factor inputs consisting of high-skilled and low-skilled labor. We find that a move from autarky to free trade (a) raises the output of the representative firm and its level of total factor productivity, and (b) reduces (raises) the relative wage of high-skilled workers under the hypothesis of output-skill substitutability (output-skill complementarity). Plant-level evidence from Mexico supports the empirical relevance of the proposed income-distribution mechanism.

How Costly is CPI Inflation Targeting: A Two Sector Model with No Labor Mobility

This paper studies the welfare costs of price rigidities in a closed economy without labor mobility. First, in a one-sector model, I find a significant welfare cost of price rigidities under a standard Taylor rule, especially when labor is immobile. In the one-sector model, strict CPI inflation targeting is able to eliminate the welfare cost of price rigidities, with or without labor mobility. Then, I develop a vertically integrated two-sector model with nominal and real rigidities where there is a natural distinction between the rates of inflation in the final and intermediate goods sectors. In the two-sector model, the real rigidities are introduced by assuming that labor is immobile across sectors and firms. In the model, labor immobility plays an allocative role and causes large fluctuations in hours of work. This, in turn, magnifies the welfare costs of nominal rigidities. I find that the welfare costs range from 1.62 percent to 2.33 percent of consumption per period for different degree of price rigidities under an estimated Taylor rule over the Volcker and Greenspan years. Taking the household welfare under optimal (Ramsey) monetary policy as a benchmark, I show that an optimal modified Taylor rule with two measures of inflation is able to bring welfare closer to the benchmark value and reduces the welfare costs substantially, even if labor mobility is restricted.

A Markovian infectious model for dependent default risk

Modelling dependent defaults has long been a central issue for credit risk measurement and management. To address this important issue, we introduce a Markovian infectious model to describe the dependent relationship of default processes of credit securities. The central tenant of the proposed model is the concept of common shocks which is one of the major approaches to describe insurance risk. Using real data default data, we compare the proposed model to some existing default risk models, such as one-sector and two-sector models discussed in Ching et al. (2008, 2010). A log likelihood ratio test is adopted for the purpose of model comparison. Our empirical results reveal that the proposed model outperforms both the one-sector and two-sector models. We also illustrate the application of the proposed model for quantitative risk measurement. In particular, numerical results for both the crisis value-at-risk and the crisis expected shortfall are provided.

Book Reviews

Kent P. Kimbrough of Duke University reviews “Capital Accumulation and Economic Growth in a Small Open Economy” by Stephen J. Turnovsky,. The EconLit Abstract of the reviewed work begins “Investigates the process of economic growth in a small open economy and considers whether it is sensitive to the economy’s productive structure. Discusses a basic growth model with fixed labor supply; a basic growth model with endogenous labor supply; transitional dynamics and endogenous growth in one-sector models; two-sector growth models; nonscale growth models; a basic model of foreign aid; and foreign aid, capital accumulation, and economic growth--some extensions. Turnovsky is Castor Chair of Economics at the University of Washington. Index.”

An empirical study of structural factors and regional growth in China

Based on data of 31 Chinese provinces over the period 1980–2004, the study in this paper presents new evidence on the effects of structural shocks and structural transformation on growth and convergence among the Chinese regions. The division of overall regional growth in labour productivity into three components – growth due to structural shocks, growth due to structural transformation and a ‘residual’ indicating growth due to region-specific changes – provides us with a better framework than the traditional one-sector Solow growth model for attributing growth and convergence to various different sources. Among other findings, the study has shown that during 1990–1999, structural shocks worked to widen the gap between rich regions and poor regions in China, while structural transformation worked to narrow the gap.

Chaos and capacity utilization under increasing returns to scale

Abstract It has been shown that adding variable capacity utilization of capital to a one-sector model with a mild production externality can produce local indeterminacy. In this paper, I provide a global analysis of this model and provide sufficient conditions for the existence of Euler equation branching. I show that this branching allows for regime switching equilibria implying ω-chaos and positive topological entropy – two notions of chaotic behavior.

Interpreting Investment-Specific Technology Shocks

Investment-specific technology (IST) shocks are often interpreted as multi-factor productivity (MFP) shocks in a separate investment-producing sector. However, this interpretation is strictly valid only when some stringent conditions are satisfied. Some of these conditions are at odds with the data. Using a two-sector model whose calibration is based on the U.S. Input-Output Tables, we consider the implications of relaxing several of these conditions. In particular, we show how the effects of IST shocks in a one-sector model differ from those of MFP shocks to an investment-producing sector of a two-sector model. Importantly, with a menu of shocks drawn from recent empirical studies, MFP shocks induce a positive short-run correlation between consumption and investment consistent with U.S. data, while IST shocks do not.

Fiscal Policy Reforms and Dynamic Laffer Effects

We examine the impact of fiscal policy reforms on the long-run government budget balance in a one-sector model of endogenous growth with factor income taxes, a tax on consumption, non-productive public goods expenditures, and a labour-leisure trade-off. In addition, we allow for different structures of government expenditures and public debt. We analytically show that, when performing a dynamic Laffer effect analysis, there exists a set of conditions that hold for a number of endogenous growth models. We find that for the euro area an improvement in the long-run government budget balance is always obtained for a lower tax rate on capital income but is only obtained for a substantial lower tax rate on labour income. Moreover, we show that when lower taxes on factor income are financed by higher taxes on consumption, there exists a wide array of combinations for which there is an improvement in both the long-run government budget balance and lifetime welfare. These combinations, however, differ in their implications for labour supply and immediate welfare effects.

Endogenous skill cycles

This paper explores the ability of a class of one-sector models to generate endogenous skills cycles. Skills cycles are here defined as endogenous fluctuations of the composition of equilibrium allocation of labor services. We consider a one sector economy in which there exist one type of capital stock and a finite number of different labor services, which are assumed to be heterogeneous along the skill/productivity dimension. We apply the Hopf bifurcation theorem and provide necessary conditions on the model’s parameters for having a closed orbit as the economy’s stable set. We also develop a numerical example (based on the United States economy) showing how this closed orbit can appear under reasonable parameter values.

James Tobin and Growth Theory: Financial Factors and Long-Run Growth

Although Tobin 1955 was one of the founding papers of the neoclassical one-sector growth model with smooth substitution between capital and labor, James Tobin's contributions to long-run growth theory throughout his career stood apart from other neoclassical growth models because of his emphasis on portfolio substitution between money and capital as a possible source of the non-neutrality of money even in the long run. This paper examines Tobin's contributions to growth theory over more than four decades and the relationship of his work to the evolution of modern growth economics.

Indeterminacy and the elasticity of substitution in one-sector models

This paper introduces a new production externality via factor substitution and explores its effects on generating indeterminacy in one-sector growth models. With the elasticity of substitution depends on the average level of capital intensity, indeterminacy is possible as long as the steady-state level of capital is below the normalized level of the CES production function. Given that the elasticity of factor substitution is decreasing in capital and the marginal product of capital is decreasing in terms of the elasticity, indeterminacy can occur because efficient factor substitution from capital deepening offsets the diminishing returns of capital.

Expectation Driven Business Cycles with Limited Enforcement

We explore the implications of shocks to expected future productivity. In a setting with limited enforcement of financial contracts, firms have to post to obtain external finance. In a real one-sector model with this type of collateral constraint, positive news about future productivity implies an increase in stock prices, as well as the other properties of an expectation-driven business cycle. Furthermore, these properties are obtained with standard consumption preferences and capital adjustment costs.

Jealousy and underconsumption in a one-sector model with wealth preference

The present paper examines the effects of consumption externalities on economic performance in a one-sector model with wealth preference. The presence of the wealth preference generates a wealth effect in consumption growth, which plays a crucial role for consumption externalities to have impacts on the economy. Our main findings are: (i) regardless of the assumption of inelastic labor supply, the distortionary effect of consumption externalities stays in the long run; (ii) the income tax as well as the consumption tax can modify the efficiency; and (iii) the numerical simulations supplement theoretical findings.

Convergence speed and preference externalities in a one-sector model with elastic labor supply

In a one-sector model with elastic labor supply where consumption and leisure externalities are incorporated, we examine the impact of preference externalities on convergence speed.

INDETERMINACY IN A ONE-SECTOR MODEL REVISITED: DEMAND VERSUS SUPPLY-SIDE INDETERMINACY

This paper explains how indeterminacy in a one-sector model may arise due to externalities in the disutility of labor supply, which is termed as demand-side indeterminacy. This contrasts supply-side indeterminacy that is driven by externalities in the production function as exemplified by Benhabib and Farmer (Journal of Economic Theory, 1994). For the one-sector models considered, I find that indeterminacy arises more easily from the demand than from the supply side. In addition, demand and supply-side indeterminacy generate different cyclical patterns of wages, a feature that is useful for identifying episodes of self-fulfilling prophecies within the two types of indeterminacy.

A ONE-SECTOR GROWTH MODEL WITH CONSUMPTION STANDARD: INDETERMINATE OR DETERMINATE?

In a representative agent, one-sector growth model in which the discounting is decreasing in the consumption standard measured as the current average consumption flow, Drugeon (1998) establishes local indeterminacy. This paper extends Drugeon’s setup in the discount rate. In our setup, the consumption standard is a habit stock that a weighted average of the whole history of average consumption flows in the past. Local indeterminacy emerges only when the speed of habit formation tends to infinity; otherwise, local indeterminacy cannot appear, no matter how large the habit affects the discount rate.

What Do We Know and Not Know about Potential Output?

Potential output is an important concept in economics. Policymakers often use a one-sector neoclassical model to think about long-run growth, and often assume that potential output is a smooth series in the short run--approximated by a medium- or long-run estimate. But in both the short and long run, the one-sector model falls short empirically, reflecting the importance of rapid technical change in producing investment goods; and few, if any, modern macroeconomic models would imply that, at business cycle frequencies, potential output is a smooth series. Discussing these points allows us to discuss a range of other issues that are less well understood, and where further research could be valuable.

A Discrete Heterogeneous-Group Economic Growth Model with Endogenous Leisure Time

This paper proposes a one-sector multigroup growth model with endogenous labor supply in discrete time. Proposing an alternative approach to behavior of households, we examine the dynamics of wealth and income distribution in a competitive economy with capital accumulation as the main engine of economic growth. We show how human capital levels, preferences, and labor force of heterogeneous households determine the national economic growth, wealth, and income distribution and time allocation of the groups. By simulation we demonstrate, for instance, that in the three-group economy when the rich group's human capital is improved, all the groups will economically benefit, and the leisure times of all the groups are reduced but when any other group's human capital is improved, the group will economically benefit, the other two groups economically lose, and the leisure times of all the groups are increased.

Optimal Consumption in a Growth Model with the CES Production Function

This article studies the optimization problem of maximizing the expected discounted present value of lifetime utility of consumption in the framework of one-sector neoclassical growth model with the Constant Elasticity of Substitution (CES) production function. We establish the existence of a classical solution of the Hamilton–Jacobi–Bellman (HJB) equation associated with this problem by the technique of viscosity solutions under the strict concavity of the utility function, and hence derive an optimal consumption from the optimality conditions in the HJB equation.