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.     

State tax changes and quasi-experimental price elasticities of U.S. cigarette demand: An update

This paper uses 336 state tax changes across the U.S. spanning 42 years (1956–1997) to provide an updated look at the quasi-experimental price elasticities of cigarette demand. It also studies the sensitivity of these elasticity estimates to changes in the cigarette market over time as well as their sensitivity to border-effect purchases. Besides replicating earlier findings, the results show a downward trend in these elasticities over time and sensitivity to border effect purchases. Policy implications are discussed. We dedicate this article to the memory of Julian Simon.     

Variable elasticity of substitution in urban housing production

The notion that the elasticity of substitution in urban housing production should vary with changing intensities of land use seems to be realistic and theoretically viable. Hence the variable elasticity of substitution production function has been proposed by some authors. However, it suffers from a serious shortcoming that the elasticity of substitution should not exceed unity. To allow for flexibility in the range of the elasticity of substitution, we explore a general functional form for the housing production function, the weak disposability of inputs production function in particular. Our empirical findings, based on the Santa Clara County single-family housing data, provide evidence that this general function is a more accurate specification of urban housing production than the variable elasticity of substitution function.     

Durbin’s random substitution and conditional Monte Carlo

Durbin (Biometrika 48:41–55, 1961) proposed a method called random substitution, by which a composite problem of goodness-of-fit can be reduced to a simple one. In this paper we provide a method of finding the p-value of any test statistic, for a composite goodness-of-fit problem, based on the simulation of a large number of conditional samples, using an analog of Durbin’s proposal in a reverse-type application. We analyze a Bayesian chi-square test proposed in Johnson (Ann Stat 32:2361–2384, 2004) which relies on a single randomization and relate it with Durbin’s original method. We also review a related proposal for conditional Monte-Carlo simulation in Lindqvist and Taraldsen (Biometrika 92:451–464, 2005) and compare it with our procedure. We show our method in a non-group example introduced in Lindqvist and Taraldsen (Biometrika 90:489–490, 2003).     

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。     

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 GMLE based Buckley–James estimator with modified case–cohort data

We consider the estimation problem under the linear regression model with the modified case–cohort design. The extensions of the Buckley–James estimator (BJE) under the case–cohort designs have been studied under an additional assumption that the censoring variable and the covariate are independent. If this assumption is violated, as is the case in a typical real data set in the literature, our simulation results suggest that those extensions are not consistent and we propose a new extension. Our estimator is based on the generalized maximum likelihood estimator (GMLE) of the underlying distributions. We propose a self-consistent algorithm, which is quite different from the one for multivariate interval-censored data. We also show that under certain regularity conditions, the GMLE and the BJE are consistent and asymptotically normally distributed. Some simulation results are presented. The BJE is also applied to the real data set in the literature.     

Politico-economic transition

Political and economic transitions of non-market economies often go hand in hand. We propose an economic theory of this transition process, which highlights how the success of such a transition depends upon the policies chosen in the new democratic environment. In this paper, economic success is characterized by the continual adoption of new technology (and economic growth), which requires costly human capital investment. The political choice is whether to allow the adoption of new technology. As a non-market economy begins its transition, agents with human capital specific to a particular technology find it in their interest to vote against continued innovation. As such, the transition to a market economy can be choked off. Our theory has the following features: (i) an economic transition is associated with a substantial drop in output; (ii) it is in the interest of large groups in the population to resist laissez–faire, as factor payments equal marginal products in the post–reform economy; (iii) although the joint move to democracy and a market economy does make people better off, it is insufficient for the transition to be successful, as the number of agents with a vested interest against continued innovation grows; and (iv) a temporary\/ restriction on voting rights which ensures a laissez-faire regime is sufficient to produce long-run\/ prosperity. This restriction may not be only one capable of overcoming the anti–innovation interests. Other mechanisms such as supermajority rules on policy changes may also guarantee laissez–faire.     

The Deegan–Packel index for simple games with a priori unions

In this paper we define and axiomatically characterize an extension of the Deegan–Packel index for simple games with a priori unions. A real-world example illustrates this extension.     

Advantageous redistribution with three smooth CES utility functions

We present a parametric example of three-country advantageous redistribution with two Cobb–Douglas utility functions and one CES utility function for which the elasticity of substitution is 1/2. This paper indicates that the possibility of advantageous redistribution strongly depends on the three countries’ taste patterns, endowment distributions, and the elasticity of substitution. In particular, we will show with specific examples that greater difference between the donor and recipient’s taste patterns and a lower elasticity of substitution can increase the chance of advantageous redistribution.     

Long-run growth and welfare effects of public policies with distortionary taxation

In a one-sector growth model with infrastructure investment, we study the impact of fiscal policies on growth. The government collects taxes on labor income and profits. The government uses these revenues to purchase infrastructure investment, provide utility enhancing government services, and to provide transfer payments to the households. We show that the balanced growth rate is an increasing function of the percent of government revenues that goes to infrastructure. We find that the growth maximizing mix of taxes depends on the elasticity of substitution between inputs. In particular, with distortionary taxes, the growth maximizing tax rate on capital is higher the lower the elasticity of substitution between private physical capital and public capital. In addition, the growth maximizing size of the government is higher when the elasticity of substitution between public and private inputs is low. We also investigate welfare effects of other public expenditures as well. Depending on the elasticity of substitution in production, the welfare implications of different public policies can be substantial.     

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.     

Production Technology Estimates and Balanced Growth

Capital‐labour substitution and total factor productivity (TFP) estimates are essential features of many economic models. Such models typically embody a balanced growth path. This often leads researchers to estimate models imposing stringent prior choices on technical change. We demonstrate that estimation of the substitution elasticity and TFP growth can be substantially biased if technical progress is thereby mis‐specified. We obtain analytical and simulation results in the context of a model consistent with balanced and near‐balanced growth (i.e. departures from balanced growth but broadly stable factor shares). Given this evidence, a constant elasticity of substitution production function system is then estimated for the US economy. Results show that the estimated substitution elasticity tends to be significantly lower using a factor‐augmenting specification (well below one). We are also able to reject conventional neutrality forms in favour of general factor augmentation with a non‐negligible capital‐augmenting component. Our work thus provides insights into production and supply‐side estimation in balanced‐growth frameworks.     

Analyzing an extension of the isotonic regression problem

In this paper an extension of the classical problem of isotonic regression is first considered. This problem extends the criterion of minimizing convex functions by considering a more general situation. To solve this problem, the max–min formulae are extended by means of the concept of change-level vector, leading to new formulae and algorithms. Moreover, we will find explicit expressions for every isotonic regression when the solution is not unique by considering both max–min and change-level formulae. An immediate implication from the considered extension is that bounds for isotonic regressions can be stated. Furthermore, the problem of finding solutions within a horizontal band in the plane can now be solved. Finally, some practical applications are discussed.     

CES technology and business cycle fluctuations

We contribute to an emerging literature that brings the constant elasticity of substitution (CES) specification of the production function into the analysis of business cycle fluctuations. Using US data, we estimate by Bayesian-Maximum-Likelihood methods a standard medium-sized DSGE model with a CES rather than Cobb–Douglas (CD) technology. We estimate a elasticity of substitution between capital and labour well below unity at 0.15–0.18. In a marginal likelihood race CES decisively beats the CD production and this is matched by its ability to fit the data better in terms of second moments. We show that this result is mainly driven by the implied fluctuations of factor shares under the CES specification. The CES model performance is further improved when the estimation is carried out under an imperfect information assumption. Hence the main message for DSGE models is that we should dismiss once and for all the use of CD for business cycle analysis.     

中国工业行业资本-劳动替代弹性估计及影响因素研究

基于超越对数生产函数的随机前沿模型估计2001—2015年中国工业行业的资本-劳动替代弹性,并对其影响因素进行分析,结果表明：劳动密集型行业的资本-劳动替代弹性普遍高于技术密集型行业,而后者又普遍高于资本密集型行业;行业开放程度、研发密度、产权属性、资本-劳动比、资产负债率、《劳动合同法》实施以及金融危机等因素都会影响资本-劳动替代弹性。     

Age-dependent investing: Optimal funding and investment strategies in defined contribution pension plans when members are rational life cycle financial planners

A defined contribution pension plan allows consumption to be redistributed from the plan member's working life to retirement in a manner that is consistent with the member's personal preferences. The plan's optimal funding and investment strategies therefore depend on the desired profile of consumption over the lifetime of the member. We investigate these strategies under the assumption that the member is a rational life cycle financial planner and has an Epstein–Zin utility function, which allows a separation between risk aversion and the elasticity of intertemporal substitution. We also take into account the member's human capital during the accumulation phase of the plan and we allow the annuitisation decision to be endogenously determined during the decumulation phase.We show that the optimal funding strategy involves a contribution rate that is not constant over the life of the plan but is age-dependent and reflects the trade-off between the desire for current versus future consumption, the desire for stable consumption over time, the member's attitude to risk, and changes in the level of human capital over the life cycle. We also show that the optimal investment strategy during the accumulation phase of the plan is ‘stochastic lifestyling’, with an initial high weight in equity-type investments and a gradual switch into bond-type investments as the retirement date approaches in a way that depends on the realised outcomes for the stochastic processes driving the state variables. The optimal investment strategy during the decumulation phase of the plan is to exchange the bonds held at retirement for life annuities and then to gradually sell the remaining equities and buy more annuities, i.e., a strategy known as ‘phased annuitisation’.     

How to optimize the allocation of research resources? An empirical study based on output and substitution elasticities of universities in Chinese provincial level

Although significant progress has been made in China's basic research in recent years, there remains a wide gap between research in China and that from developed countries. How to optimize the allocative efficiency of research resources is of great importance for increasing research output. In this paper, using the fixed effect stochastic frontier model based on the translog production function, we estimate output and substitution elasticities of research and development (R&D) inputs at universities in China's provincial level during 2009–2016. We find that the R&D technical efficiency of China's universities, after a rapid growth, has tended to become relatively stable. Improvements of internationalization degree and exogenous R&D capabilities are conducive to promoting R&D technical efficiency, whereas expenditures from government grants inhibit the promotion of R&D technical efficiency; the effects of R&D capital deepening and internet penetration are not evident. The output elasticity of R&D capital is much higher than that of R&D personnel, suggesting that R&D capital is the main driving force of research output. The substitution elasticity between R&D capital and personnel has experienced a change from substitution to complementary since 2014. To realize sustained growth of research output, we should increase R&D input with positive output elasticity or reduce R&D input with negative output elasticity, making the necessary trade-offs according to the substitution relationship between the two R&D inputs.     

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.     

THE ELASTICITY OF CAPITAL–LAND SUBSTITUTION IN THE HOUSING CONSTRUCTION SECTOR OF A RAPIDLY URBANIZED CITY: EVIDENCE FROM TURKEY

This paper estimates the elasticity of capital-land substitution for the housing market in Ankara, the capital city of Turkey. Using constant elasticity of substitution (CES) and variable elasticity of substitution (VES) production functions and cross-section data, the paper provides new information to compare the housing supply elasticity of Ankara with that of the USA and the UK cases. Our regression results reveal that housing supply in Ankara is highly inelastic due to the uniform construction regime of local authorities. Moreover, we find that there is a considerable spatial differentiation of urban land density measures within the capital city. Because of the incomplete urbanization process, the elasticity of capital-land substitution is significantly higher in the outer parts of the city.