Constant Elasticity Model Research Articles

The Legendre transform-dual-asymptotic solution for optimal investment strategy with random incomes

. This article studies an optimal control problem for the financial investment strategy with random incomes. The investment portfolio is simplified to be composed of a risk-free asset and a risky asset. The price of a risky asset is followed by a constant variance elasticity (CEV) model. We consider any correlation coefficient ρ ∈ [ − 1 , 1 ] between the income risk and the risk of risky asset. By applying the Legendre transformation, dual theory, and asymptotic expansion approach, we obtain an asymptotic strategy for the exponential utility function. Numerical examples are presented to illustrate the effects of parameters on the optimal strategy.

Modeling shipping accidents economic loss and the compensation in Nigeria

The arbitrary reservation of between 25 and 45 % of premium revenue as funds for the compensation of insured unexpired marine risks by underwriters in Nigeria, in line with local insurance regulations, has created a problem of financial insolvency, making it impossible for underwriters to provide timely and adequate compensation for insured shipping risks. The aim of the study is to overcome this challenge by formulating models based on the coefficient of elasticity of the relationships between shipping accident economic loss, the value of seaborne trade, and compensation funds maintained for insured shipping risks. 21 years of time series data from 1999 and 2019 were obtained from secondary sources. Log-log constant elasticity model was used to analyze the data. The results indicate that, for each 1 % increase in shipping accident economic loss, compensation funds maintained for shipping accident economic risks increase by 0.364 %. The policy implications are discussed and models developed for the reservation of funds for sustainable compensation of insured shipping risks are developed.

The Log of Gravity at 15

We review the contribution of “The Log of Gravity” (Santos Silva and Tenreyro, Rev Econ Stat 88:641–658, 2006), summarize the main results in the ensuing literature, and provide a brief review of the state-of-the-art in the estimation of gravity equations and other constant-elasticity models.

Gasoline demand elasticities in the world’s energy gluttons: a time-varying coefficient approach

In this paper, we estimate the price and income elasticities for gasoline demand in selected energy gluttons-China, India, USA, Russia, and Japan. Specifically, we employ a time-varying parameter approach which adequately deals with potential parameter instabilities and nonlinearities and effectively captures price and income elasticity variations over time, with each time period having its own set of coefficients. Our empirical findings reveal the following: gasoline consumption is price-inelastic and income-inelastic, there are movements in both the price and income elasticities, and the movements generally correspond with business cycle patterns of each of the countries; overall, sensitivity to price and income changes increase during periods of economic crises. Constant elasticity models overestimate price and income elasticities, and income is predominantly more elastic than price. Our conclusion is that policy mechanisms that are price-based such as gasoline taxes are likely to be unsuccessful in achieving consumption-cum-pollution reduction objectives in the energy gluttons. Such policies may, however, be effective if they ensure that gasoline prices rise at a greater rate than income. Such policies may also be useful for revenue-raising purposes.

A Synthesis: 1. Aggregation, Income Distribution and Consumer Demand (Muellbauer,J.) 2. Specifications and Aggregation Theory: Ch 3, 3. Estimation of Linear Expenditure System (Pollak,R.A. And Wales,T.J.) 4. Aggregate Consumer Behavior Without Exact Aggregation (Nicol,C.J.)

The four papers on aggregation theory and estimation of demand function together provide a complete picture starting from the underlying theory of aggregation and specification to empirical estimation of demand functions. The first paper is about the aggregation across consumers. The second paper explores the properties associated with the Constant Slutsky Elasticity (CSE) model which is closely related to the absolute price version of the Rotterdam Model. The third paper estimates a complete system of demand equations making full use of the restrictions implied by economic theory. This is done using the model formulated by Stone namely, Klein-Rubin. The fourth paper estimates a model of consumer behavior by pooling Canadian cross sectional and time series data. An attempt is made in this synthesis to collate the four papers and understand the entire theory behind demand functions and see how demand functions are estimated empirically after incorporating elements such as leisure, household size to make the theory fit the reality. The first half of the section will draw from the first two papers to understand the theory of aggregation. The following section will draw from the next two papers on empirical estimates to understand the application of theory.

Demand for pneumococcal vaccination under subsidy program for the elderly in Japan

BackgroundVaccination programs often organize subsidies and public relations in order to obtain high uptake rates and coverage. However, effects of subsidies and public relations have not been studied well in the literature. In this study, the demand function of pneumococcal vaccination among the elderly in Japan is estimated, incorporating effects of public relations and subsidy.MethodsUsing a data from a questionnaire survey sent to municipalities, the varying and constant elasticity models were applied to estimate the demand function. The response variable is the uptake rate. Explanatory variables are: subsidy supported shot price, operating years of the program, target population size for vaccination, shot location intensity, income and various public relations tools. The best model is selected by c-AIC, and varying and constant price elasticities are calculated from estimation results.ResultsThe vaccine uptake rate and the shot price have a negative relation. From the results of varying price elasticity, the demand for vaccination is elastic at municipalities with a shot price higher than 3,708 JPY (35.7 USD). Effects of public relations on the uptake rate are not found.ConclusionsIt can be suggested that municipalities with a shot price higher than 3,708 JPY (35.7 USD) could subsidize more and reduce price to increase the demand for vaccination. Effects of public relations are not confirmed in this study, probably due to measurement errors of variables used for public relations, and studies at micro level exploring individual’s response to public relations would be required.

The Infeasibility of Free Trade in Classical Theory: Ricardo's Comparative Advantage Parable has no Solution

In this paper, formal models of Ricardo's comparative advantage parable, which include general forms of consumer price response behavior, are constructed from a detailed textual exegesis of Ricardo's story. Using these models, the comparative advantage parable is shown to be mathematically over-determined and therefore generally unsolvable. To reinforce this conclusion, a numerical solution is derived for a constant elasticity version of the model. A necessary condition for the existence of a solution to the constant elasticity model is that two price elasticities of demand must be functions of the other two price elasticities of demand. General formulas are derived expressing this dependency. When realistic elasticities for wine are set, the model can only be solved if Portuguese demand for English cloth is unrealistically elastic. This demonstrates that sustainable and mutually beneficial trade between England and Portugal can only be realized through managed trade.

MEMS based acoustic thermomechanical characterization of aluminum 6061-T651 beams

Temperature-based testing is an important tool in determining the mechanical characteristics of structures. Metallic structures, such as aluminum beams, respond to temperature variations. Similarly, Young’s modulus of elasticity of the material has a temperature dependence that contributes significantly to the overall mechanical qualities of the material. In this work, a method based on flexural frequency response is described in which the variation in the experimental 5th natural frequency under thermal loading is employed to extract the coefficient of thermal dependence of Young’s modulus. This coefficient is then employed in the theoretical model to validate the experimental 2nd, 3rd, 4th and 5th natural frequencies of the aluminum beam. A micro-electro-mechanical-systems based microphone is used to monitor the frequency response of the beam. Constant geometry and constant elasticity models are presented and compared. The proposed method is applied to an aluminum 6061-T651 beam. Experimental results are in good agreement with the theory.

A Test and Re-Estimation of Taylor’s Empirical Capacity–Reserve Relationship

In 1977, Taylor proposed a constant elasticity model relating capacity choice in mines to reserves. A test of this model using a very large (n = 1,195) dataset confirms its validity but obtains significantly different estimated values for the model coefficients. Capacity is somewhat inelastic with respect to reserves, with an elasticity of 0.65 estimated for open-pit plus block-cave underground mines and 0.56 for all other underground mines. These new estimates should be useful for capacity determinations as scoping studies and as a starting point for feasibility studies. The results are robust over a wide range of deposit types, deposit sizes, and time, consistent with physical constraints on mine capacity that are largely independent of technology.

THE CRIME-CONTROL EFFECT OF INCARCERATION: DOES SCALE MATTER?*

Research Summary: Several prominent empirical studies estimate models of a constant proportional effect of prison on crime, finding that effect is substantial and negative. A separate literature argues against the crime-reducing effect of prison but mainly on theoretical grounds. This second literature suggests that the elasticity of the prison/crime relationship is not constant. We provide a model that nests these two literatures. Using data from the United States over 30 years, we find strong evidence that the negative relationship between prison and crime becomes less strongly negative as the scale of imprisonment increases. This revisionist model indicates that (1) at low levels of incarceration, a constant elasticity model underestimates the negative relationship between incarceration and crime, and (2) at higher levels of incarceration, the constant elasticity model overstates the negative effect. Policy Implications: These results go beyond the claim of declining marginal returns, instead finding accelerating declining marginal returns. As the prison population continues to increase, albeit at a slower rate, after three decades of phenomenal growth, these findings provide an important caution that for many jurisdictions, the point of accelerating declining marginal returns may have set in. Any policy discussion of the appropriate scale of punishment should be concerned with the empirical impact of this expensive and intrusive government intervention.

Infrastructure investment and Canadian manufacturing productivity

This paper examines the relationship between Canadian public infrastructure and private output using a Constant Elasticity and Substitution-Translog (CES-TL) cost model to describe the interaction of the public and private sectors. The CES-TL was first specified by Pollak et al. (1984). We find public capital a substitute for private capital within the Canadian manufacturing sector. Additionally, the services of public capital enhance the productivity of private capital. Canadian manufacturing costs are characterized by economies of scale, indicating that less than optimal plant sizes dominated Canadian manufacturing sector during the study period. Advances in disembodied technical progress are also indicated.

The potential for greenhouse gases mitigation in household sector of Iran: cases of price reform/efficiency improvement and scenario for 2000–2010

Iran's demographic profile is sharply youth oriented and this upcoming generation's needs for employment and housing, coupled with low-energy efficiency vectors and consumption patterns, has created a constant rise in energy demand and greenhouse gas (GHGs) emissions in the residential sector. Improved energy efficiency as a national policy lynchpin for demand reduction and GHGs mitigation, has become commonplace. OPEC countries however, Iran included, suffer an obvious lack of consumer incentive because of low fuel prices. This study evaluates the twin impacts of price reform and efficiency programs on energy carriers’ consumption and GHGs mitigation in the Iranian housing sector. For this purpose, the demand functions for energy carriers, has been developed by econometrics process models.The results reveal that price elasticity for electricity demand in the Constant Elasticity Model for the short-run while the long-run is −0.142 and −0.901, respectively. In the Variable Elasticity Model the 250% increase in electricity rates in the short-run resulted in a price elasticity change from −0.02 to −0.475, hence the 250% increase in electricity pricing for the long-run resulted in the price elasticity change from −0.15 to −2.0.Finally, aided by a Scenario-Based Approach the impact of fuel pricing and efficiency improvement in trends of energy demand and GHGs emission were assessed in a Scenarios Base, developed on two different cases of Business-as-Usual (BAU) and Management. The results indicate that in the BAU case between 2000 and 2011, the energy demand and CO2 emission increases with an annual growth rate of 7.5% and 6.8%, respectively.Comparatively, if the energy carriers’ price is increased to border price and energy efficiency programs are implemented, they will stimulate carriers’ demand and CO2 emissions growth rate decreases to 4.94% and 3.1%, respectively.

Quantile-regression estimates of cigarette demand elasticities for the United States

Using a simple model and state-level cross-section U.S. data from 1993 to 1999, quantile-regression estimates of price elasticity and income elasticity for cigarette demand are obtained. It is noted that price elasticity shows a sizable variation across the high and low quantity-quartiles. There is a similar variability in the income elasticity, but most of these estimates lack statistical significance. Besides providing an indication of the variation in the price (and income) elasticity for different consumption levels, the exercise suggests some interpretative caution in regard to estimates from constant-elasticity models.

Water pollution abatement by Chinese industry: cost estimates and policy implications

Data on pollution abatement costs in Chinese industry suggest that the benefits of stricter discharge standards should be weighed carefully against the costs. China's current regulatory system provides an economic incentive to abate by charging a levy on pollution that exceeds the standard. But changing to a full emissions charge system would greatly reduce total abatement costs. Using factory-level data provided by China`s National Environmental Protection Agency (NEPA) and the Tianjin Environmental Protection Bureau, Dasgupta, Huq, Wheeler, and Zhang estimate the costs of water pollution abatement for Chinese industry. Using their econometric results, they analyze the cost-effectiveness of current pollution control policy in China and conclude that: - For each pollutant, marginal abatement costs exhibit great differences by sector, scale, and degree of abatement. Ratios of 20:1 in each dimension are not uncommon. - The benefits of stricter discharge standards should be weighed carefully against the costs. For a sample of 260 factories, a shift across the existing range of standards entails a present value difference in abatement costs of $330 million. - Emissions charges as low as $1 a ton would be sufficient to induce 80 percent abatement of suspended solids for cost-minimizing factories. Charges of $3 a ton, $15 a ton, and $30 a ton would be sufficient to induce 90 percent abatement of suspended solids, chemical oxygen demand, and biological oxygen demand, respectively. - The current regulatory system provides an economic incentive to abate by charging a levy on pollution that exceeds the standard. But the results of this analysis suggest that changing to a full emissions charge system would greatly reduce overall abatement costs. For the sample of 260 factories, the current overall abatement rate could be attained under a charge system with present-value savings of $344 million. At a cost equivalent to that of the current system, uniform pollution charges would produce much better environmental quality. Approach: To measure the costs of abatement, they use joint abatement cost functions that relate total costs to treatment volume and the simultaneous effect of reductions in suspended solids, chemical oxygen demand, biological oxygen demand, and other pollutants. Tests of alternative functional forms suggests that a simple (constant elasticity) model fits the data as well as a complex (translog) models does, permitting sophisticated policy experiments with relatively simple calculations. This paper - a product of the Environment, Infrastructure, and Agriculture Division, Policy Research Department - is part of a larger effort in the department to understand the economics of industrial pollution control in developing countries. The study was funded by the Bank's Research Support Budget under research project The Economics of Industrial Pollution Control in Developing Countries (RPO 680-20).

Water pollution abatement by Chinese industry: cost estimates and policy implications

Factory-level data are used to estimate water pollution abatement costs for Chinese industry. Joint abatement cost functions are utilized which relate total costs to treatment volume and the simultaneous effect of reductions in suspended solids, chemical oxygen demand, biological oxygen demand and other pollutants. Tests of alternative functional forms suggest that a very simple (constant elasticity) model fits the data as well as a complex (translog) model, permitting sophisticated policy experiments with relatively simple calculations. From the results, the cost-effectiveness of current pollution control policy in China is analysed. Basic conclusions are (1) The benefits of stricter discharge standards should be weighed carefully against the costs. For the sample of 260 factories, a shift across the existing range of standards entails a present-value difference of US$330 million in abatement costs. (2) Emissions charges as low as US$1.00/ton would be sufficient to induce 80% abatement of suspended solids for cost-minimizing factories. Charges of US$3, US$15 and US$30 per ton would be sufficient to induce 90% abatement of TSS, COD and BOD. (3) The current regulatory system provides an economic incentive to abate by charging a levy on pollution in excess of the standard. However, the results suggest that changing to a full emissions charge system would greatly reduce overall abatement costs. For the 260 factories in the sample, the current overall abatement rate could be attained under a charge system at a reduced annual cost whose present value is US$344 million.

Imperfect competition, functional forms, and the size and distribution of research benefits

AbstractThe effects of functional forms for supply and demand on the size and distribution of the returns to research are examined under a range of forms of competition. Under perfect competition, the choice of functional form is relatively unimportant for the estimation of research benefits. Under imperfect competition, the combination of the choice of functional forms for supply and demand and the nature of the research‐induced supply shift can have profound implications for the results. Functional form plays a much more important role than in the competitive model. The most important contrast is between the constant elasticity model and the linear model (along with various cases of a generalized linear model). These findings are illustrated using a combination of analytical results and numerical simulations.

Imperfect competition, functional forms, and the size and distribution of research benefits

Abstract The effects of functional forms for supply and demand on the size and distribution of the returns to research are examined under a range of forms of competition. Under perfect competition, the choice of functional form is relatively unimportant for the estimation of research benefits. Under imperfect competition, the combination of the choice of functional forms for supply and demand and the nature of the research-induced supply shift can have profound implications for the results. Functional form plays a much more important role than in the competitive model. The most important contrast is between the constant elasticity model and the linear model (along with various cases of a generalized linear model). These findings are illustrated using a combination of analytical results and numerical simulations.

Life Expectancy of International Cartels: An Empirical Analysis

This paper examines the empirical relation between market structure and life expectancy for cartels that were active in international commodity markets throughout this century. I consider two alternative empirical formulations and estimate their parameters recognizing that durability cannot take negative values. Both formulations predict that increases in either market shares or intercartel concentration prolong life expectancy but disagree in the relative importance of these two factors. The application of tests to discriminate among the two formulations does not support constant-elasticity models.

INCOME ELASTICITIES OF DEMANDS FOR FOODS IN GREAT BRITAIN

This paper describes analysis of data from the National Food Survey to determine the influences of household income and composition on household demand for foods in 1974, 1979, 1980 and 1982. The paper focuses on fats, cheese and carcase meats. The analysis uses household level data, regarding zero expenditures as arising because of infrequent purchasing and the expenditure‐income relationship used in the Almost Ideal Demand Model. This is in contrast with the analysis reported by the National Food Survey Committee which uses a constant elasticity model and averaged income and expenditure data.

STABILITY OF THE STATE SALES TAX INCOME ELASTICITY

Revenue stability for a tax source is defined here as the situation where the income elasticity of revenues is countercyclical; that is, the elasticity rises in a recession and declines in an expansion. A sales tax revenue function is conceptualized in a manner such that the income elasticity is endogenous and a function of the position in the business cycle, the interest rate, and the inflation rate. Short-run income elasticities are then measured based on the economic conditions existing over the past eight years. A varying elasticity model is employed to estimate the revenue function for ten categories of sales. The short-run efosticities shift dramatically over the years, with those for durable goods falling in recessions and rising in expansions, and those for nondurable goods rising in recessions and falling in expansions. The aggregate sales tax elasticity moves in a procyclical fashion, evidencing that the sales tax is unstable. A varying elasticity model is demonstrated to provide improved forecasts over the historical period compared with a constant elasticity model.