Capital-labor Substitution Research Articles

Dynamic Inefficiency in an Overlapping Generations Economy with Production

Reichlin (JET, 1986) has shown in an OLG model with productive capital that whenever the steady state is locally indeterminate and undergoes a Hopf bifurcation, it is Pareto-optimal. While these results were established under the assumption of Leontief technology, the author has partially extended them to show that the Hopf bifurcation is robust with respect to the introduction of capitallabor substitution. In this note, we prove that the Pareto-optimality of the steady state does not extend to technologies with capital-labor substitution. When the steady state is a sink or undergoes a Hopf bifurcation, it is characterized by over-accumulation with respect to the Golden Rule - the interest rate is negative - hence not Pareto-optimal. Most importantly, it follows that stabilization policies targeting the steady state leave room for welfare losses associated with productive inefficiency, apart from the very special case of Leontief technology.

Indeterminacy with small externalities: The role of non‐separable preferences

In this paper we consider a Ramsey one‐sector model with non‐separable homothetic preferences, endogenous labor and productive external effects arising from average levels of capital and labor. We show that indeterminacy cannot arise when there are only capital externalities but that it does occur when there are only labor external effects. We prove that sunspot fluctuations are fully consistent with small market imperfections and realistic calibrations for the elasticity of capital–labor substitution (including the Cobb‐Douglas specification) provided the elasticity of intertemporal substitution in consumption and the elasticity of labor supply are large enough.

Indeterminacy in discrete-time infinite-horizon models with non-linear utility and endogenous labor

We consider a discrete-time two-sector model with sector specific externalities in which the technologies are given by CES functions with asymmetric elasticities of capital–labor substitution, and the preferences of the representative agent are given by a CES additively separable utility function defined over consumption and leisure. We first show that when the labor supply is infinitely elastic, the steady state is always saddle-point stable, no matter what the elasticity of intertemporal substitution in consumption and the size of externalities are. We then prove that when the elasticity of intertemporal substitution in consumption is sufficiently large, local indeterminacy requires a low enough elasticity of the labor supply.

Overlapping Generations Model with Endogenous Labor Supply: General Formulation

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.

Sunspot Fluctuations in Two-sector Economies with Heterogeneous Agents

We study a two-sector model with heterogeneous agents and borrowing constraint on labor income. We show that the relative capital intensity difference across sectors is crucial for the conditions required to get indeterminacy and endogenous fluctuations. The main result shows that when the consumption good is sufficiently capital intensive, local indeterminacy arises while the elasticities of capital–labor substitution in both sectors are slightly greater than unity and the elasticity of the offer curve is low enough. Locally indeterminate equilibria are thus compatible with a low elasticity of intertemporal substitution in consumption and a low elasticity of the labor supply. As recently shown in empirical analysis, these conditions appear to be in accordance with macroeconomic evidences.

Indeterminacy in dynamic models: When Diamond meets Ramsey

We consider an aggregate two-periods overlapping generations model with endogenous labor, consumption in both periods of life, homothetic preferences and productive external effects coming from the average capital and labor. We show that under realistic calibrations of the parameters, in particular a large enough share of first period consumption over the wage income, local indeterminacy of equilibria cannot occur with capital externalities alone. It can nevertheless occur when there are only, even very small, vanishing labor externalities provided that the elasticity of capital–labor substitution and the wage elasticity of the labor supply are large enough. We also show that if labor externalities are slightly stronger, but still small enough to be plausible, and the elasticity of labor supply is larger, local indeterminacy occurs in a Cobb–Douglas economy. Finally, we show that a locally indeterminate steady state is generically characterized by an under-accumulation of capital. It follows therefore that while agents live over a finite number of periods, the conditions for the existence of locally indeterminate equilibria are very similar to those obtained within infinite horizon models and that from this point of view, Diamond meets Ramsey.

DUAL LABOR MARKET AND ENDOGENOUS FLUCTUATIONS

We study the influence of wage differential on the emergence of endogenous fluctuations. In this way, we introduce a dual labor market, based on the Shapiro–Stiglitz efficiency wage theory in an overlapping generations model. We show that wage inequality is a source of endogenous fluctuations. Indeed, a sufficiently strong wage differential leads to the occurrence of cycles of period 2 and local indeterminacy. Moreover, in contrast to several existing contributions, these results depend neither on increasing returns to scale nor on the degree of capital–labor substitution.

Dynamic effects of government expenditure in a finance constrained economy

This paper introduces constant government expenditure in Woodford's finance constrained model (J. Econ. Theory, 1986) with capital–labor substitution as presented in Grandmont, Pintus and de Vilder (J. Econ. Theory, 1998) and investigates how government expenditure influences local dynamics near multiple steady states, depending upon the elasticity of substitution between capital and labor in production.

Unemployment, wage bargaining, and the capital-labor substitution

Unemployment, wage bargaining, and the capital-labor substitution

That Elusive Elasticity: A Long-Panel Approach to Estimating the Capital-Labor Substitution Elasticity

The elasticity of substitution between capital and labor features prominently in several areas of economic research. However, a consensus estimate remains elusive. We develop an estimation strategy that filters panel data in an original way and avoids several pitfalls - difficult-to-specify dynamics, transitory time-series variation, and positively sloped supply schedules - inherent in investment equations that can bias the estimated elasticity. Results are based on an extensive panel containing 1,860 manufacturing and non-manufacturing firms. Our model generates a precisely estimated elasticity of approximately 0.40. The method developed here may prove useful in estimating other structural parameters from panel datasets.

An estimation of US industry-level capital–labor substitution elasticities: support for Cobb–Douglas

A key parameter that determines the distributional impacts of a policy shift in general equilibrium models is the elasticity of substitution between capital and labor. Despite the importance of this parameter in applied modeling, its identification continues to pose a challenge. Given the structure of most growth models, we posit that the true relationship between capital and labor is likely to be close to Cobb–Douglas. Using a rich new data set from the Bureau of Economic Analysis (BEA), we estimate substitution elasticities for 28 industries that cover the entire economy, and provide an indication of the long- and short-run ranges of those estimates. We fail to reject the Cobb–Douglas specification in 20 of the 28 industries. These findings lend support to the Cobb–Douglas specification as a transparent starting point in simulation analysis.

Endogenous business cycles: Capital–labor substitution and liquidity constraint

It is well known from the literature that the introduction of liquidity constraints in infinite-horizon economies may be responsible for the occurrence of local indeterminacy and sunspot fluctuations. Yet, the question of the robustness of such phenomena when the constraints are progressively relaxed, and the possibility of intertemporal arbitrage on the part of the agents increases, remains open. In this paper we study such an issue by departing from the Cazzavillan et al. (J. Economic Theory 80 (1998) 60–107) framework with heterogeneous agents, financial constraint on wage income, and positive externalities in aggregate capital and labor. We observe that local indeterminacy and sunspot fluctuations persist for a wide range of amplitudes of the liquidity constraint, although they finally disappear when the ‘degree’ of liquidity of the economy is made arbitrarily large.

Indeterminacy and Endogenous Fluctuations with Arbitrarily Small Externalities

In this paper we study the occurrence of local indeterminacy, endogenous fluctuations, and bifurcations in a simple non-monetary 2-period overlapping generations economy (in which people do not consume when young) with capital-labor substitution, elastic labor supply, and productive externalities. We show that, in contrast with the local dynamics generated by many one-sector models of capital accumulation studied in the current literature, local indeterminacy and, therefore, stationary stochastic equilibria driven by self-fulfilling beliefs (sunspots), as well as multiple stationary equilibria, are pervasive phenomena when the elasticity of input substitution is large and when the size of externalities is arbitrarily small. We also demonstrate that, when externalities are arbitrarily small, the Cobb–Douglas production function, often used for its analytical tractability in many models, is structurally unstable: it is always associated with uniqueness of the steady-state, but any small perturbation of the elasticity of input substitution leads to the existence of two stationary equilibria, which may be close to each other, with the consequence that the dynamics may be qualitatively very different from those originated in the unit elasticity case. Journal of Economic Literature Classification Numbers: E32, C62.

Putty-Clay and Investment: A Business Cycle Analysis

This paper develops a dynamic stochastic general equilibrium model with putty-clay technology that incorporates embodied technology, investment irreversibility, and variable capacity utilization. Low short-run capital-labor substitutability native to the putty-clay framework induces the putty-clay effect of a tight link between changes in capacity and movements in employment and output. As a result, persistent shocks to technology or factor prices generate business cycle dynamics absent in standard neoclassical models, including a prolonged lump-shaped response of hours, persistence in output growth, and positive comovement in the forecastable components of output and hours. Capacity constraints result in nonlinear aggregate production function that implies asymmetric responses to large shocks with recessions steeper and deeper than expansions. Minimum distance estimation of a two-sector model that nests putty-clay and neoclassical production technologies supports a significant role for putty-clay capital in explaining business-cycle and medium-run dynamics.

Energy, capital and technological change in Colombia: a comparative analysis with the United States

John Moroney, in his article Energy, Capital and Technological Change in the United States (1991), specifies and estimates aggregated production functions designed to identify the roles of capitallabor substitution, energylabor substitution and technological change as sources of labor productivity growth. My work is based on the paper of John Moroney mentioned above, and has the objective of making an analysis similar to that made by Moroney but in the Colombian context. The goal of this work is to identify the impact on labor productivity of energy, capital and technological change, using appropriated CobbDouglas models. The paper also presents a comparative analysis of two cases.

The Macroeconomics of Specificity

Specific quasi-rents build up in a wide variety of economic relationships, and are exposed to opportunism unless fully protected by contract. The recognition that such contracts are often incomplete has yielded major insights into the organization of microeconomic exchange. Rent appropriation, we argue, also has important macroeconomic implications. Resources are underutilized, factor markets are segmented, production suffers from technological with creation, recessions are excessively sharp, and expansions run into bottlenecks. While, depending on the nature of the shock, expansions may require reinforcement or stabilization, recessions should always be softened. In the long run, institutions, such as those governing capital-labor relations, may evolve to alleviate the problem by balancing appropriation. Technology choice will also be affected, with the appropriated factor partially appropriation as manifested in the role capital-labor substitution played in the rise of European unemployment.

Jobless growth: appropriability, factor substitution, and unemployment

A central determinant of the political economy of capital-labor relations is the appropriability of specific quasi-rents. This paper is concerned with the general-equilibrium interaction of appropriability and characteristics of technology - namely, the embodiment of technology in capital and capital-labor substitutability in the technological menu. Technological embodiment means that the supply of capital is effectively much less elastic in the short than in the long run, and is therefore more exposed to appropriability; technology choice implies that an attempt at appropriating capital will induce a substitution away from labor in the long run, and constitutes a mechanism to thwart appropriation. Shifts in European labor relations in the last three decades offer a good laboratory in which to explore the empirical relevance of those mechanisms. The evolution of the labor share, the profit rate, the capital-output ratio, and unemployment - which we examine more particularly in the case of France - appears highly supportive.

Multiple Steady States and Endogenous Fluctuations with Increasing Returns to Scale in Production

The purpose of this paper is to study the influence of the elasticity of capital–labor substitution and of the labor supply elasticity on the existence of multiple Pareto-ranked stationary equilibria, local indeterminacy, bifurcations, and expectations-driven fluctuations in economies with external and internal increasing returns to scale in production. This is done through general geometrical methods that do not depend upon particular specifications for preferences and technology. For the sake of concreteness, the analysis focuses on the model with heterogeneous agents and financial constraints presented in Woodford (J. Econ. Theory40(1986), 128–137) and extended by Grandmont, Pintus, and de Vilder (“Capital–Labor Substitution and Competitive Nonlinear Endogenous Business Cycles,” CREST Working Paper 9728, 1997) to account for capital–labor substitution. Increasing returns to scale are incorporated in two different market structures: — an economy with aggregate production externalities and perfectly competitive markets, — an economy with increasing returns internal to the firm and imperfect competition in the product(s) market(s) only.Journal of Economic LiteratureClassification Numbers: C61, E32.

Capital–Labor Substitution and Competitive Nonlinear Endogenous Business Cycles

We develop simple geometrical methods to study local indeterminacy, bifurcations, and stochastic (sunspot) equilibria near a steady state, in nonlinear two dimensional economic models. We present in particular a simple, constructive, geometrical characterization of the support of stochastic sunspot equilibria, not only arbitrarily near a steady state, but also along local bifurcations. These methods are applied to a simple aggregative model to study in particular the influence of capital–labor substitution and of the aggregate labor supply wage elasticity on the occurrence of competitive endogenous deterministic or stochastic fluctuations.Journal of Economic LiteratureClassification Numbers: E32, C62.

Putty-Clay and Investment: A Business Cycle Analysis

This paper develops a dynamic stochastic general equilibrium model with putty-clay technology that incorporates embodied technology, investment irreversibility, and variable capacity utilization. Low short-run capital-labor substitutability native to the putty-clay framework induces the putty-clay effect of a tight link between changes in capacity and movements in employment and output. As a result, persistent shocks to technology or factor prices generate business cycle dynamics absent in standard neoclassical models, including a prolonged hump-shaped response of hours, persistence in output growth, and positive comovement in the forecastable components of output and hours. Capacity constraints result in a nonlinear aggregate production function that implies asymmetric responses to large shocks with recessions steeper and deeper than expansions. Minimum distance estimation of a two-sector model that nests putty-clay and neoclassical production technologies supports a significant role for putty-clay capital in explaining business cycle and medium-run dynamics.