Constant Elasticity Of Substitution Research Articles

Estimating elasticities of substitution with nested CES production functions: Where do we stand?

Abstract Prompt by an increasing interest by climate change modelers, a rich literature estimating elasticities of substitution in a nested CES production framework has recently developed. This article reviews such literature. We critically describe the nesting structures, estimation approaches, data sources and aggregation, econometric techniques, and types of substitution elasticities used by previous literature, to offer a comprehensive description of the various options available to a researcher attempting this estimation. We also provide suggestions for potential improvements to the estimation process. In particular, we warn researchers to use CES production functions with caution in empirical applications given their restrictive build-in assumptions.

Altruism and Selfishness in Believable Game Agents: Deep Reinforcement Learning in Modified Dictator Games

This article focuses on using deep reinforcement learning, specifically proximity policy optimization, to train agents in a social dilemma game, modified dictator game, in order to investigate the effect of selfishness and altruism on the believability of the game agents. We present the design and implementation of the training environment, including the reward functions which are based on the findings of established empirical research, with three agent profiles mapped to the three standard constant elasticity of substitution (CES) utility functions, i.e., selfish, perfect substitutes, and Leontief, which measure different levels of selfishness/altruism. The trained models are validated and then used in a sample game, which is used to evaluate the believability of the three agent profiles using the agent believability metrics. The results indicate that players find altruistic behaviour more believable and consider selfishness less so. Analysis of the results indicates that human-like behavior resulting from the application of artificial intelligence evolves from perceived human behavior rather than the observed. The analysis also indicates that selfishness/altruism may be considered as an extra dimension to be included in the believability metrics.

Intratemporal nonseparability between housing and nondurable consumption: Evidence from reinvestment in housing stock

Using the data on maintenance expenditures and self-assessed house value, I separate the measure of individual housing stock and house prices, and use these data for testing whether nondurable consumption and housing are characterized by intratemporal nonseparability in households’ preferences. I find evidence in favor of intratemporal dependence between total nondurable consumption and housing. My findings indicate the elasticity of intratemporal substitution between nondurable consumption and housing is higher than the elasticity of intertemporal substitution for composite consumption bundles. Moreover, assuming CES utility, my results are indicative about complementarity between nondurable consumption and housing in the intratemporal preferences.

Intertemporal utility with heterogeneous goods and constant elasticity of substitution

We characterize intertemporal utility functions over heterogeneous goods that feature (i) a constant elasticity of substitution between goods at each point in time and (ii) a constant intertemporal elasticity of substitution for at least one of the goods. We find that a standard, stationary intertemporal utility function is consistent with these two properties if and only if it either is of the intertemporal constant elasticity of substitution (ICES) form, that is, if all elasticities of substitution are identical, or if the instantaneous utility function is Cobb–Douglas. We also characterize the families of stationary intertemporal utility functions that feature either (i) or (ii), but not the respective other property.

Application of a modified CES production function model based on improved PSO algorithm

In the analysis of the economic growth factors, people often use the CES (constant elasticity of substitution) production function model to calculate the contribution rate of influencing factors to economic growth. However, the traditional CES production function model does not consider the period characteristic of technological progress on economic growth, so this paper puts forward a modified CES production function model. On the parameter estimation of the model, this paper presents an improved PSO (particle swarm optimization) algorithm with high precision and fast convergence. Using the modified CES production function model, this paper provides a scientific method to calculate the contribution rates of all factors influencing the economic growth. Finally, this paper performs the empirical analysis of the contribution rates of all factors influencing China’s economic growth.

Estimating input-mix efficiency in a parametric framework: application to state-level agricultural data for the United States

ABSTRACT This paper contributes to the productivity literature by demonstrating novel econometric methods to estimate input-mix efficiency (IME) in a parametric framework. Input-mix efficiency is defined as the potential improvement in productivity with change in input mix. Any change in input-mix (e.g., land to labou r ratio) will result in change in productivity. The advantage of this approach is that it does not require data on input prices to estimate the mix efficiency levels. A nonlinear input-aggregator function (e.g., Constant Elasticity of Substitution) is used to derive an expression for input-mix efficiency. Bayesian stochastic frontier is estimated for obtaining mix efficiency using US state-level agricultural data for the period 1960–2004. Significant variation in input-mix efficiency is noted across the states and regions, attributable to diverse topographic and geographic conditions. Furthermore, comparisons of allocative and mix efficiencies provide insightful policy implications. The production incentives such as taxes and subsidies could help farmers in adjusting their input mix in response to changes in input prices, which can affect the US agricultural productivity significantly. The proposed methodology can be extended by i) using flexible functional forms; ii) introducing various time- and region-varying input aggregators; and iii) defining more sophisticated weights for input aggregators.

Tenaga Kerja Produksi Dan Non Produksi Padaindustri Makanan Di Indonesia (Production and Non Production Workers on Food Industry In Indonesia)

This study aims to determine the role of production and non-production workers in the large and medium-scale food industry in Indonesia and to determine the response of the food industry to the demand for production and non-production labor on changes in several input factors in the production process. The fixed effect model in panel data analysis is performed on secondary data in the form of raw data of the Manufacturing Industry Annual Survey in 2013-2015. Demand for production and non-production labor is obtained through the derivation of the production function of Constant Elasticity of Substitution (CES). The results showed that non-production labor had a positive and significant effect on output in all industrial categories, while production labor had only a positive and significant effect on the overall industry category, non-export oriented and located in regions outside of Java. Production and non-production workers are complementary. Demand for production and non-production labor is affected by changes in wages, respectively. The food industry is labor intensive and applies a high wage system (efficiency wage theory).

Markups in a two-country monopolistic competition model of trade with heterogeneous consumers

The paper develops a two-country monopolistic competition model of trade featuring country-specific consumer tastes. The accounting for heterogeneity in tastes is achieved by assuming different elasticities of substitution in the CES utility function for different country consumers. The proposed framework extends the canonical Krugman’s approach by revealing new effects regarding markups response to consumer heterogeneity and trade liberalization. Specifically, the model predicts that, depending on the preference structure, trade liberalization may lead either to decrease or increase in the level of markups, charged by monopolistically competitive firms across destination countries.

The Variable Elasticity of Substitution Function and Endogenous Growth: An Empirical Evidence from Vietnam

Purpose: To specify a Variable Elasticity of Substitution function (VES), in which the estimated Elasticity of Substitution (ES) can give some implications for the tendency of economic growth in the Vietnames manufacturing sector. Design/Methodology/Approach: The contribution and the relevant methodology is based on the Bayesian approach having some advantages over the frequentist method: (i) the simulation and prediction results are more reliable in Bayesian analysis due to combining prior knowledge about parameters with obverved data to compose a posterior model, whereas the frequentist approach is based only on available data; (ii) in probability sense, Bayesian credible intervals have a straightforward interpretation compared to frequentist confidence intervals. The Bayesian nonlinear regresion performed is suitable for fitting production functions and depicting economic growth. Findings: The specified VES function has the ES greater than one and this finding contradicts many previous empirical studies in the growth theory. This result points to the possibility of unbounded endogenous growth in the Vietnamese manufacturing sector. Practical implications: Based on the empirical results, in order to realize the possibility of endogenous growth for the studied Vietnamese manufacturing sector, policies of enforcing investment are needed. To raise the level of science and technique, as well as human capital of the Vietnamese enterprises, at the same time, there is great necessity to encourage R&D activities in both the private and public sectors. Originality/Value: Although this study organically builds upon recent studies about the link between the VES, the elasticity of factor subsitution and economic growth, its results proved that the VES is more appropriate than the Cobb-Douglas and the Constant Elasticity of Substitution (CES) to explain economic growth in the view of capital-labor relationship.

How to Explain When the ES Is Lower Than One? A Bayesian Nonlinear Mixed-Effects Approach

Most studies in Vietnam use the Cobb-Douglas production function and its modifications for economic analysis. Extremely rigid presumptions are a main weak point of this functional form, particularly if the elasticity of factor substitution (ES) is equal to one, which hides the role of the ES for economic growth. The CES (constant elasticity of substitution) production function with more flexible presumptions, concretely its ES, is not unitary, and has been used more and more widely in economic investigations. So, this study is conducted to estimate the average ES through the specification of an aggregate CES function for the Vietnamese nonfinancial enterprises. By performing Bayesian nonlinear mixed-effects regression via Random-walk Metropolis Hastings (MH) algorithm, based on the data set of the listed nonfinancial enterprises of Vietnam, the author found that the CES function estimated for the researched enterprises has an ES lower than one, i.e., capital and labor are complimentary. This finding shows that Vietnamese nonfinancial enterprises can confront a downward trend of output growth.

A New Class of Production Function

In this article, we propose a new class of production functions in the new classical theory of economics and study its qualities based on Euler’s relation of quasi-homogeneous functions. In a market economy environment, it is crucial to establish a firm’s profitability and draw conclusions about the operation and to make a variety of assumptions using a function that is more consistent with reality in the future. We showed that the quasi-homogeneous function is a general form of the well known production functions such as Cobb-Douglas and Constant Elasticity of Substitution (CES). We have made some qualitative and quantitative analysis and compare our results with the classical models using statistical data of Japan.

A Note on the Importance of Normalizations in Dynamic Latent Factor Models of Skill Formation

In this paper we highlight an important property of the translog production function for the identification of treatment effects in a model of latent skill formation. We show that when using a translog specification of the skill technology, properly anchored treatment effect estimates are invariant to any location and scale normalizations of the underlying measures. By contrast, when researchers assume a CES production function and impose standard location and scale normalizations, the resulting treatment effect estimates are biased. Interestingly, the CES technology with standard normalizations yields biased treatment effect estimates even when age-invariant measures of the skills are available. We theoretically prove the normalization invariance of the translog production function and then produce several simulations illustrating the effects of location and scale normalizations for different technologies and types of skills measures.

The Elasticity of Intertemporal Substitution: A Tool to Constrain Profligate Government Spending

We construct a theoretical model to explain profligate electoral fiscal behaviour and to provide a tool, namely the estimated elasticity of intertemporal substitution, for the fiscal authorities to detect and timely constrain such behaviour to promote fiscal prudence. The key is to obtain data on the incumbent party preferred sequence of public consumption levels over time. The model frames this case using a CES utility function and provides one possible mechanism to explain why there are so many examples in the empirical literature that find insignificant electoral biases in fiscal variables.

Investigations to the price evolutions of goods exchange with CES utility functions

The price evolutions of goods exchange in multi-agent market are investigated by employing the kinetic theory. Assume that a closed market consists of two groups (A and B) of agents, who have the same preferences for goods. The constant elasticity of substitution (CES) utility function which contains Cobb–Douglas utility function and Leontief utility function, is used to describe the agent’s preferences. A system of linear Boltzmann type equation is given to describe the probability distributions of goods for agents of the two groups, in which the agents are allowed to adopt certain trading strategies to maximize their utility and improve their wealth conditions. We assume that agents in group A put all their goods into the market for maximum utility, while agents in group B aim to acquire maximal utility from goods exchange by suitably selecting the percentage of goods which are exchanged. The effects of different trading strategies on commodity price and wealth distribution are discussed. The results show that the trading strategies of agents in group B have effectively improved their wealth status under certain assumptions. Also, a general system of nonlinear Boltzmann equation for the probability distributions of goods is given to describe the pricing issues of goods exchange for agents. The numerical experiments of nonlinear Boltzmann equations demonstrate how the trading strategies and preferences of agents modify the price of goods.

The consumer's index

AbstractConsumer's surplus measures the area under the demand curve between two prices, but is path dependent. There exists a path such that consumer's surplus tracks utility and an explicit formula is known for CES utilities. This paper shows that the CES‐based formula holds for any homothetic utility, and I call it the consumer's index. The index modifies consumer's surplus in two ways: the change in income is measured by its growth factor and the area under the demand curve is normalized by income.

Disaster probability, optimal government expenditure for disaster prevention and mitigation, and expected economic growth

As global climate warms, the occurrence frequency and loss of natural disaster are both increasing, posing a great threat to the sustainable development of human society. One of the most important approaches of disaster management is to prevent disaster and reduce disaster loss through fiscal expenditure of government; however, the optimal proportion of expenditure for disaster prevention and mitigation has always been a difficult issue that people concern about. First, this paper, after considering the impact of disaster on human capital, established a resident-manufacturer-government decision making model which contains the probability of disaster, and then solved the optimal proportion of government expenditure for disaster prevention and reduction as well as the expected economic growth rates under different conditions. Second, through numerical simulation method, this paper studied the impacts of such factors as coefficient of risk aversion and elasticity coefficient of substitution on the optimal proportion of disaster prevention and reduction expenditure. Third, through constant elasticity of substitution (CES) production function and ridge regression method, this paper verified the applicability of the proposed model with the data of the expenditures for disaster prevention and mitigation of Hunan Province in 2014. Finally, this paper summarized the research results and put forward corresponding suggestions on policy. The theoretical model proposed in this paper enriches the related researches of disaster economics, and the conclusions of empirical analysis can provide government departments with useful reference for the practice of disaster prevention and mitigation.

The alpha-mixture of survival functions

AbstractThis paper presents a flexible family which we call the $\alpha$ -mixture of survival functions. This family includes the survival mixture, failure rate mixture, models that are stochastically closer to each of these conventional mixtures, and many other models. The $\alpha$ -mixture is endowed by the stochastic order and uniquely possesses a mathematical property known in economics as the constant elasticity of substitution, which provides an interpretation for $\alpha$ . We study failure rate properties of this family and establish closures under monotone failure rates of the mixture’s components. Examples include potential applications for comparing systems.

Differential discounting in the economic evaluation of healthcare programs

BackgroundThe question of appropriate discount rates in health economic evaluations has been a point of continuous scientific debate. Today, it is widely accepted that, under certain conditions regarding the social objective of the healthcare decision maker and the fixity of the budget for healthcare, a lower discount rate for health gains than for costs is justified if the consumption value of health is increasing over time. To date, however, there is neither empirical evidence nor a strong theoretical a priori supporting this assumption. Given this lack of evidence, we offer an additional approach to check the appropriateness of differential discounting.MethodsOur approach is based on a two-goods extension of Ramsey’s optimal growth model which allows accounting for changing relative values of goods explicitly. Assuming a constant elasticity of substitution (CES) utility function, the growth rate of the consumption value of health depends on three variables: the growth rate of consumption, the growth rate of health, and the income elasticity of the willingness to pay for health. Based on a review of the empirical literature on the monetary value of health, we apply the approach to obtain an empirical value of the growth rate of the consumption value of health in Germany.ResultsThe empirical literature suggests that the income elasticity of the willingness to pay for health is probably not larger but rather smaller than 1 and probably not smaller but rather larger than 0.2. Combining this finding with reasonable values of the annual growth rates in consumption (1.5–1.6%) and health (0.1%) suggests, for Germany, an annual growth rate of the consumption value of health between 0.3 and 1.5%.ConclusionIn the light of a two-goods extension of Ramsey’s optimal growth model, the available empirical evidence makes the case for a growing consumption value of health. Therefore, the current German practice of applying the same discount rate to costs and health gains introduces a systematic bias against healthcare technologies with upfront costs and long-term health effects. Differential discounting with a lower rate for health effects appears to be a more appropriate discounting model.

Energy import costs in a flexible input-output price model

A fundamental assumption of the input-output (IO) model is a fixed relationship between interindustry flows. In the price version of the model, the assumption of fixed-coefficients prevents the optimal mix of inputs being adjusted when relative prices change. The aim of this paper is to evaluate the role of energy import prices in the IO price model without the usual non-substitution technology inherent to the input-output structure. The analysis includes alternative substitution possibilities for the elements that comprise the sectoral costs, which are empirically implemented from an IO dataset. The various substitution scenarios are defined by three different cost structures: the Leontief, Cobb-Douglas and Constant Elasticity of Substitution (CES) functions. The empirical application to the Catalan economy illustrates the relevance of the flexibility option used for explaining the quantitative influence of energy import prices on domestic prices. Adapting the traditional input-output model to include factor substitution makes it possible to overcome the rigidity in transmitting price impacts, and illustrates a range of possible effects.

A Note on Concavity Conditions of Cobb–Douglas and CES Production Function with at Least Two Inputs

In microeconomics, the strict concavity is a very important property of a production function. In 2010, Avvakumov et al. gave a necessary and sufficient condition for the strict concavity of the Cobb–Douglas and constant elasticity of substitution (CES) production function with at least two inputs. To derive these conditions, the negative definiteness of the Hessian for both production functions was examined using certain recurrences for the principal corner minors. The purpose of this note is to complement the proof of Avvakumov, Kiselev, Orlov & Taras’ev ( 2010 , Computational Mathematics and Modeling, 21(3), 336–378) by showing that the use of recurrences and mathematical induction is not necessary, and that a necessary and sufficient condition for the strict concavity can be obtained by considering a particular square matrix, whose determinant can be calculated directly using the rule for the determinant of a lower or upper triangular matrix. JEL Classifications: C60, C65, D21, D24