Elasticities of Substitution and Complementarity: A Synthesis

We derive the relationships between the net and gross elasticities of substitution and complementarity (i.e., the elasticities that refer either to the conditional or unconditional, direct or inverse demand system) in the general case of non-homothetic, variable-returns-to-scale technologies. We also show that the so-called Hicks Elasticity of Complementarity (Hicks, Oxford economic Papers 22, 289–296 (1970)) is dual to a full-fledged elasticity of gross input substitution that we call the Hotelling/Lau Elasticity of Substitution (Lau, Production Economics: A Dual Approach to Theory and Applications. Amsterdam: North-Holand (1978)). The former is, in fact, the proper elasticity of substitution in the case of the inverse, unconditional input demand. Our results should clarify some issues about the input substitutability classification.     

Hedonic estimation of housing demand elasticity with a markup over marginal costs

We show that recent developments in hedonic pricing theory allow modeling of the equilibrium pricing function as the marginal cost of an additional housing unit plus a markup that varies inversely with the elasticity of demand. Useful information about demand elasticity at a given point on the envelope function can be recovered from the hedonic regression and limited information on marginal costs. In particular, the elasticity of the envelope with respect to any characteristic such as interior area provides information on the elasticity of demand. Relative price elasticities (i.e., elasticities that vary from a base value in a known way with interior area, unit type or neighborhood characteristics) can be computed from the elasticity of the hedonic envelope. Like Yinger (2010), our method is based on a single hedonic equation.We test our method using sales of new high rise condominiums in two districts within Shenzhen, China: Futian and Longgang. The results strongly confirm the main hypothesis of this paper: price elasticity with respect to size is increasing for more complex types of units. Together with estimates of marginal costs of production, these results imply that relative demand elasticity is declining for larger, more complex units.     

Financial reforms and money demand: Evidence from 20 developing countries

The effects of financial reforms on money demand (M1) are analysed with estimates for two sets of sub-samples and two break dates for twenty developing Asian and African countries. In all cases, the magnitude of income elasticity does not change significantly when compared with sub-samples and whole sample periods. Using CUSUM and CUSUMSQ tests, we find that the demand for money functions in our selected countries are temporally stable and therefore the respective monetary authorities may target money supply as the conduct of monetary policy.     

Capital–labor substitution and equilibrium indeterminacy

This paper examines the quantitative relationship between the elasticity of capital–labor substitution in production and the conditions needed for equilibrium indeterminacy (and belief-driven fluctuations) in a one-sector growth model. With variable capital utilization, the substitution elasticity has little quantitative impact on the minimum degree of increasing returns needed for indeterminacy. However, when capital utilization is constant, a below-unity substitution elasticity sharply raises the minimum degree of increasing returns because it imposes a higher effective adjustment cost on labor hours. Overall, our results show that empirically-plausible departures from the Cobb–Douglas production specification can make indeterminacy more difficult to achieve.     

WHAT DETERMINES THE ELASTICITY OF SUBSTITUTION BETWEEN CAPITAL AND LABOR? A LITERATURE REVIEW

This paper provides the first comprehensive review of the empirical and theoretical literature on the determinants of the elasticity of substitution between capital and labor. Our focus is on the two-input constant elasticity of substitution (CES) production function. We start by presenting four concise observations that summarize the empirical literature on the estimation of . Motivated by these observations, the main part of this survey then focuses on potential determinants of capital–labor substitution. We first review several approaches to the microfoundation of production functions where the elasticity of substitution (EOS) is treated as a purely technological parameter. Second, we outline the construction of an aggregate elasticity of substitution (AES) in a multi-sectoral framework and investigate its dependence on underlying intra- and inter-sectoral substitution. Third, we discuss the influence of the institutional framework on the extent of factor substitution. Overall, this survey highlights that the effective elasticity of substitution (EES), which is typically estimated in empirical studies, is generally not an immutable deep parameter but depends on a multitude of technological, non-technological, and institutional determinants. Based on these insights, the final section identifies a number of potential empirical and theoretical avenues for future research.     

The industrial demand for energy

This paper uses a constant elasticity of substitution production function to examine the extent of factor substitutability in the production of industrial goods. Subsequently, the degree of interfuel substitution is estimated and it is demonstrated that all energy sources are substitutable. Finally, the stability of the demand for various energy sources is empirically tested for and it is concluded that over the period of investigation the demand has in fact remained unaltered.     

Capital,labor, and derived demand for information: Evidence from China

In this paper, information capital is considered as a separate input of production along with noninformation capital and labor. The substitution possibility among information capital, noninformation capital and labor has been estimated by nonlinear iterative algorithm using Chinese data for 1995–2017. The empirical results from the study imply that estimates of Chinese input substitution degree and productivity are underestimated without including information capital as an input separate from noninformation capital. When information capital and labor are combined, the contribution ratio of labor force may increase. Information capital interacts with noninformation capital and labor to promote economic development and production efficiency.     

On the Ramsey equilibrium with heterogeneous consumers and endogenous labor supply

In this paper, we address the stability issue, stressing the role of labor supply, in a Ramsey model with heterogeneous households subject to borrowing constraints. Making labor supply endogenous leads us to prove the existence of two kinds of steady state: the one where everybody supplies labor, the other where only the most patient agent refrains from working. Going beyond models with inelastic labor supply, we show how preferences of impatient agents affect the saddle-path stability of each type of steady state and the occurrence of endogenous cycles. When their elasticity of intertemporal substitution in consumption exceeds one, instability and cycles are less likely, requiring lower degrees of capital-labor substitution. Conversely, elasticity values below one promote the emergence of fluctuations. We end the paper by showing the existence of the intertemporal equilibrium under market incompleteness, using a local approach based on the first-order conditions.     

Factor substitution and taxation in a finance constrained economy

In this paper, we examine the effects of constant-rate factor taxation on macroeconomic stability in the Woodford (1986) model. Our focus is on how the degree of factor substitution, as measured by the elasticity of factor substitution (EOS) in production, affects different balanced-budget tax rules. Analytically, we show that indeterminacy can occur under capital income taxation only when the EOS is very low, whereas indeterminacy under labor income taxation is not subject to the EOS restriction. This finding is robust when we tax all of the factor incomes with equal rates. Thus, in terms of macroeconomic stability, taxing capital income is preferred to taxing labor income.     

Tax rate uncertainty,labor supply and saving in a nonexpected utility maximizing model

The effects of uncertainty in rate of return tax rate, wage income tax rate and a comprehensive tax rate which affects both return to saving and wage income are analyzed in a nonexpected utility maximizing framework of Selden (1978). We consider a two period model where the agent works and saves. The effect of rate of return tax rate uncertainty on labor supply and saving critically depends on the magnitude of the elasticity of intertemporal substitution. A wage income tax rate uncertainty on the other hand unambiguously raises work effort while its effect on saving again depends on the magnitude of the intertemporal substitution elasticity. For empirically plausible magnitudes of the intertemporal substitution elasticity, saving responds positively to wage income tax rate risk. The effect of a comprehensive tax rate uncertainty on labor supply and saving, however, depends solely on the magnitude of the elasticity of intertemporal substitution.     

Tax enforcement policies,tax evasion and time allocation

Several studies examine the effect of tax rates on households’ labor supply decisions in attempts to account for observed differences in work hours across countries. Interestingly, these studies fail to consider a fundamental action associated with taxation: tax evasion. This paper introduces, into a general equilibrium model of household labor supply, the possibility that households can evade labor income taxes. We show that the relationship between tax-enforcement policies, the elasticity of substitution between consumption and leisure and the elasticity of substitution between formal and informal work is key to explain formal labor supply in major OECD countries. In a model without informal work, there is a positive relationship between the elasticity of substitution and the tax rate on formal income and people tend to work more. This is the case for the United States, Greece, Finland and the United Kingdom. This relationship becomes negative once informal activities are introduced and the model can explain formal labor supply better in countries where agents work relative less, i.e., in Austria, Denmark, France, Germany, Spain, Norway and Sweden. We also obtain estimates of hours worked in the informal sector for these countries.     

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.     

Factor taxation and labor supply in a dynamic one-sector growth model

This paper studies a class of AK-type growth models with factor income taxes, public capital stock and labor–leisure trade offs. While a higher capital tax rate reduces economic growth in the short run, the long-term growth effect is ambiguous and remains ambiguous even if the level of tax rate is larger than the degree of government externality. A higher labor income tax rate has ambiguous growth effects both in the short and long runs. However, if the intertemporal elasticity of substitution for labor supply is sufficiently small, a higher labor tax rate always lowers economic growth in the long run, despite the existence of productive government taxation.     

Corporate income taxation of multinationals and unemployment

Within a two-country model with involuntary unemployment, this paper investigates corporate income taxation under separate accounting versus formula apportionment. In contrast to separate accounting, under formula apportionment the corporate tax policy causes a fiscal externality that results from unemployment. This externality is the highest when the apportionment formula contains the payroll factor only. It is minimized for the pure sales (property) formula, if the substitution elasticity is low (high). The unemployment externality tends to compensate other externalities such that tax rates become inefficiently low. The deviation from the efficient tax policy is minimized when the apportionment formula contains the sales factor only.     

The effect of labor supply changes on output: empirical evidence from US industries

In this paper we examine the relationship between labor supply and industry-level output in the context of the specific factors model. Jones (Trade, balance of payment and growth: essays in honor of Charles P. Kindleberger, Amsterdam, pp 3–21, 1971) shows that a rise in the amount of labor in the economy will increase the output in all industries. We empirically show which industry output is predicted to expand more when the size of labor force grows. Unlike the commonly used Rybczynski Theorem (Economica 22:336–341, 1955) of the Heckscher-Ohlin model, the specific factors model shows that a comparison both of labor intensities and labor demand elasticities plays an important role in determining which output expands relatively more when the size of labor force grows. For this purpose, we illustrate the importance of the parameters of the model in determining how changes in the labor supply affect the output change, with special reference to elasticities of substitution in production. We estimate the elasticity of substitution by using CES production function and show how these estimates describe the general equilibrium of production with one mobile factor (labor) and 25 industries of the US economy using data for 1979–2001. We show that the increase in the supply of labor raise output in all industries, but the magnitudes of the increases in some industries are more than others depending on the value of the elasticity of substitution along with factor intensities between industries. The largest output effect occurs for educational, health care and social service, where a 1 % supply of labor increase would raise output 10.5 %. However, the growth in the labor supply has a small impact on output growth in the range of 0.1–0.6 % in agriculture, petroleum, coal product and finance and insurance industries.     

Arbitrage, equilibrium, and gains from trade: A counterexample

We present a counterexample to a theorem due to Chichilnisky (Bulletin of the American Mathematical Society, 1993, 29, 189–207; American Economic Review, 1994, 84, 427–434). Chichilnisky's theorem states that her condition of limited arbitrage is necessary and sufficient for the existence of an equilibrium in an economy with unbounded short sales. Our counterexample shows that the condition defined by Chichilnisky is not sufficient for existence of equilibrium. We also discuss difficulties in Chichilnisky (Economic Theory, 1995, 5, 79–107).     

超越对数函数要素替代弹性公式修正与估计方法比较

对超越对数函数要素替代弹性估计方法进行专门研究,修正了超越对数生产函数要素替代弹性公式错误,梳理超越对数成本函数各类替代弹性定义,综合考虑数据易得性、估计可靠性、定义合意性以判定各类估计方法的相对优劣。研究发现,受困于共线性难题,基于超越对数生产函数计算替代弹性效果不佳;基于超越对数成本函数计算替代弹性更具优势,影子替代弹性凭借出色的理论性质与强稳健性成为首选。     

Technical efficiency and region The U.S. manufacturing sector 1972–1977

In this paper we estimate the extent of technological bias in an interregional context for U.S. manufacturing during the period 1972–1977 using a factor augmenting production function approach. We present estimates of the elasticity of factor substitution for each of the 48 states in the sample using a variable elasticity of substitution production function. Next, we use these estimates to generate estimates of the rates of change in the efficiencies of capital and labor inputs and compare these estimates across states and census regions. We also examine and compare estimates of total factor productivity across states and regions. We ,find that the average annual rates of growth of capital efficiency during the period are 5.5 percent in the Northeast, 5.3 percent in the Northcentral, 5.6 percent in the West and 3.1 percent in the South. The rates of change of the efficiencies of labor are found to be negative across all regions except the South. The rates of change of total factor productivity are found to be 1.7 percent in the Northeast, 2.3 percent in the Northcentral, 2.4 percent in the West and 1.7 percent in the South. We also find that between 33 percent and 56 percent of the growth of output across regions is due to technical progress.     

Generic properties of the core and equilibria of pure exchange economies

We show that for an open dense set of markets with a continuum of traders the number of equilibrium allocations [which by the celebrated theorem of ^{Aumann (Econometrica. 1964, 32. 39–50)} coincide with the core allocations for such markets are finite. This presents a limiting case result that complements similar asymptotic theorems for cores of large economies proved by ^{Bewley (Econometrica 1973, 41, 425–454)}, and ^{Dierker (Journal of Mathematical Economics 1975, 2. 155–169)}. If we require that the measure on the space of agents be one with a finite number of atoms of equal weight, our reasoning recovers the classical results obtained by ^{Debreu (Econometrica. 1970. 38, 387–392)} for economies with a finite number of agents.     

Business cycle fluctuations and learning-by-doing externalities in a one-sector model

We consider a one-sector Ramsey-type growth model with inelastic labor and learning-by-doing externalities based on cumulative gross investment (cumulative production of capital goods), which is assumed, in accordance with Arrow (1962), to be a better index of experience than the average capital stock. We prove that a slight memory effect characterizing the learning-by-doing process is enough to generate business cycle fluctuations through a Hopf bifurcation leading to stable periodic orbits. This is obtained for reasonable parameter values, notably for both the amount of externalities and the elasticity of intertemporal substitution. Hence, contrary to all the results available in the literature on aggregate models, we show that endogenous fluctuations are compatible with a low (in actual fact, zero) wage elasticity of the labor supply.