THE MORISHIMA ELASTICITY OF SUBSTITUTION FOR THE VARIABLE PROFIT FUNCTION AND THE DEMAND FOR IMPORTS IN THE UNITED STATES*

In this article, I derive expressions for the Morishima elasticities of substitution (MES) for the variable profit function and estimate these elasticities to shed some light on the substitutability between imports, capital services, and labor services. The results reveal that capital services and imports are Morishima substitutes, irrespective of whether the price of capital services or imports changes, and imports and labor services are also Morishima substitutes, irrespective of whether the price of imports or the wage rate changes. Thus, an increase in the price of U.S. imports (through tariffs or duties) will result in substitution (in the Morishima sense) into labor and capital services.     

Substitution elasticities between durable and nondurable goods in the United States: New evidence from the dynamic Laurent system

This paper uses the dynamic Laurent demand system to jointly estimate the service flows from durable and nondurable goods. The parameter estimates are used to obtain the Morishima elasticity of substitution between goods for the United States from 1960:1 to 1991:4. One of the significant results of this study is that the Morishima elasticities of substitution vary over time instead of being constant. This result implies that the use of the CES functional form gives a poor approximation of the demand system for the data used in this paper. Another important result is that consumers adjust to their long-run equilibrium holding of consumption goods slowly rather than quickly.     

Restructuring hospital industry to control public health care expenditure: The role of input substitutability

In this paper we investigate the economic rationality of the bed downsizing process, characterising the hospital industry worldwide in the last decades, as a measure to control public health care expenditure. Considering a sample of Italian hospitals, we provide fresh evidence on the factor substitutability in the production of hospital services. Differently from other studies, based on North-American data and limited to pre-determined cost function models, we estimate a general specification (the Generalised Composite), and test it against traditional nested models (e.g. the Translog). For all the specifications we derive Allen, Morishima and Shadow elasticities of substitution between input pairs, obtaining a fairly consistent picture across all models and elasticity concepts. In particular, our results highlight a very limited degree of substitutability between factors in the production of hospital services, especially between beds and medical staff. These findings suggest that a restructuring policy of the hospital industry, which is confined to reducing the number of beds without involving workforce management, could not be a viable strategy for controlling public health care expenditure.     

Measuring Price Responsiveness Under a Profit Maximization Framework

The distinguishing feature of the study is in using a globally flexible functional form that permits one to calculate different types of elasticities under both constant and variable output hypotheses. The Symmetric Generalized McFadden cost function alongwith the output supply condition form the basis of the econometric model. To measure inputsubstitutabilities, we used Alien-Uzawa, Morishima, and Shadow elasticities of substitution. Empirical results, based on 300 farm households from West Bengal, India, show that fertilizer is most price sensitive input. It is a gross substitute for manure and human labor but complement to bullock labor. Manure is a gross substitute for all the inputs whereas human labor is gross complement to bullock labor. Using the Morishima measure we find that the fertilizer and bullock labor are complements when the price of the latterchanges. Similar complementary relationship is found between bullock and human labor due to changes in the price of human labor. All other inputs are Morishima substitutes. The Shadow elasticity of substitution estimates indicate that all factors are substitutes. The estimate of returns to scale indicates the presence of diminishing returns to scale.

     

The role of labour demand elasticities in tax incidence analysis with heterogeneous labour

Whether labour bears full burden of household level income and consumption taxes ultimately depends on the degree of substitutability among different types of labour in production. We find more variation in incidence patterns across households with less than perfectly substitutable heterogeneous labour than with perfectly substitutable homogeneous labour in production. This finding is based on results obtained from homogeneous and heterogeneous labour general equilibrium tax models calibrated to decile level income and consumption distribution data of UK households for the year 1994. We use labour supply elasticities implied by the substitution elasticity in households' utility functions and derive labour demand elasticities from the substitution elasticity in the production function. First version received: March 1998/Final version received: April 1999     

Optimal linear income taxation with general equilibrium effects on wages

The paper argues that the endogeneity of wages may make a considerable difference to optimal linear tax rates. In this case there is not only the usual direct redistribution via the fiscal system but also the general equilibrium redistribution due to the change in wages. Depending on the elasticity of substitution of the production function and the labour supply elasticities these may be reinforcing or opposing. It is shown that the general equilibrium effect may plausibly outweigh the direct effect so that net redistribution to the lower paid involves a wage subsidy financed by a lump-sum tax.     

An investigation of issues relating to where energy should enter the production function

This paper examines the impact of imposing different separability assumptions in the specifications of the standard hierarchical KLEM production function in a computable general equilibrium (CGE) model. The appropriate means of introducing energy to production functions has been a source of debate for a number of years. However, while modellers often subject results to parametric sensitivy analysis regarding the values associated with elasticities of substitution between inputs, it is rarely the case that the structure of the production function is subjected to testing. However, the chosen structure reflects the modeller's view about elasticity between different inputs and will have implications for model results wherever there are changes in relative prices. We illustrate our argument by introducing a simple demand shock to a CGE model of the Scottish economy (targeted at the energy supply sector) under different assumptions regarding the structure of the KLEM production function and separability assumptions therein.     

Capital–energy substitution in China: regional differences and dynamic evolution

This article estimates the capital–energy Allen elasticities of substitution in China’s 28 provinces over the period 1995–2011. The central finding is that the capital–energy substitution elasticity in each province exhibits significant heterogeneity. The article empirically analyses the sources of the differences in the capital–energy substitution elasticity. The embodied technical change and market distortions are found to have significant effects on the degree of substitution elasticity. Further factor market reforms, liberalisation and cooperation would improve the elasticity of capital–energy substitution.     

Complementarity in contests

To facilitate the study of contests in general equilibrium, we examine winner-take-all contests in which the prize is complementary to the effort of the contestants, as inputs are in production functions or final goods in utility functions. We focus on the effects of technological factors and endowments on the effort and the welfare of the contestants. Most of our findings differ considerably from the standard model of contests in which prize and effort are independent. In particular, we find a critical role for the elasticity of substitution between prize and effort. For example, under low elasticities of substitution, a higher prize reduces the effort exerted by the contestants.     

Elasticities of substitution between energy and non-energy inputs in China power sector

Energy substitution is considered as a key process to determine the economic outcome of decisions related to energy and environment policies. The sign and magnitude of energy substitution have been widely debated, and the results are divergent. This paper applies the translog cost function specification to estimate factor share equations based on the energy and non-energy inputs, whose coefficients are used to observe the energy degree of substitutability with the other traditional inputs for power industry in China. The results suggest that energy is the least price sensitive among three production factors. The four types of input elasticities (cross-price, Morishima's, Allen and McFadden's shadow elasticity of substitution) show that there are substantial substitution possibilities between energy and capital, while energy and labor have weak substitution. The findings imply that for power industry in China, to reduce energy consumption, more capital should be invested. With respect to labor, though, it appears less energy-saving potential.     

Long-run estimates of interfuel and interfactor elasticities

Meta-analyses of interfuel and capital-energy elasticities of substitution show that elasticity estimates are dependent on the type of data − time series, panel, or cross-section − and the estimators used. Econometric theory suggests that the between estimator might generate the best estimates of long-run elasticities but no existing estimates of elasticities of substitution have used it. Alternatively, Chirinko et al. argued in favor of estimating long-run elasticities of substitution using a long-run difference estimator. We provide estimates of China’s interfuel and interfactor elasticities of substitution using the between and long-run difference estimators. To address potential omitted variables bias, we add province level inefficiency and national technological change terms to our regression model. The results show that demand for coal and electricity in China is very inelastic, while demand for diesel and gasoline is elastic. With the exception of gasoline and diesel, there are limited substitution possibilities among the fuels. Substitution possibilities are greater between energy and labor than between energy and capital. The results are quite different to some previous studies for China but coincide well with the patterns found in meta-analyses for long-run estimates of elasticities of substitution.     

Non‐Homothetic Multisector Growth Models

Multisector growth (MSG) models are dynamic versions of computable general equilibrium (CGE) models. Non‐homothetic preference (utility) functions are required for the evolution of factor allocations and industrial structures in accordance with consumption expenditure patterns implied by the non‐unitary income elasticities observed in all budget data since Engel in the 1850s. But comparative static general equilibrium solutions and particularly solving the dynamics of MSG models require explicit specifications of all demand and cost (price) functions. On the demand side, the constant differences of elasticity of substitution (CDES) non‐homothetic indirect utility functions and Roy's identity provide the explicit Marshallian demand functions and budget shares. Sectorial constant elasticity of substitution (CES) cost functions and Shephard's lemma provide the explicit relative commodity price functions and the sectorial cost shares and capital–labor ratios. Walrasian equilibria are given by one equation and the multisector dynamics by three differential equations. Benchmark solutions are given for three cost regimes of a 10‐sector MSG model. History patterns of industrial/allocational evolutions are recognized.     

A class of changing elasticity of substitution production functions

This paper presents a new class of production functions with a changing elasticity of substitution between two input factors. Over a freely chosen number of intervals for the input factor intensity freely chosen elasticities of substitution can be imposed. The resulting production function can thus account for changing elasticities of substitution during the development of the factor intensity. The production function is applied in a calibration exercise and a novel normalization procedure is proposed. The theory behind this production technology builds on the functional normalization of CES production functions.     

Specification of production functions for analyzing technical change and factor inputs in agricultural development

This paper focuses on some vital issues involed in specifying the number of variables to be included in agriculture's production function and on the functional form that the agricultural production function should assume in the context of a computable general equilibrium model. When land and intermediate inputs (seeds and fertilizers) as well as capital and labor are included, modeling the agricultural sector can best be done in a more disaggregated format than simple Cobb-Douglas or CES specifications. After examining the transcendental logarithmic production function, the paper proposes to adopt ‘nested’ CES specifications on the basis of empirically observed elasticities of substitution.     

The impacts of Renminbi appreciation on trade flows and reserve accumulation in a monetary trade model

Given the rapidly growing reserves in Asia (China, Japan, Korea, and Taiwan) and the pressures from trading partners to revalue, there is a need to examine commercial policy in more than a pure barter model. Here we evaluate the joint impacts of exchange rate appreciation on trade flows and country surpluses using a general equilibrium trade model with a simple monetary structure in which the trade surplus is endogenously determined in the exchange rate setting country and the exchange rate is exogenous. We illustrate its application to the Chinese case using calibration to 2005 data. Our results, while elasticity dependent, suggest that the impacts of Renminbi (RMB) revaluation on the surplus are proportionally larger than on trade flows, and that changes in trade flows can be substantial. Different treatments of China's processing trade have small impact on changes in China's trade flow under RMB appreciation, but significant impacts on the change in the surplus. Results are elasticity dependent; larger substitution elasticities in preferences yield larger effects on trade flows and the surplus.     

Semi-non-parametric estimates of substitution for Canadian monetary assets

We estimate the dynamic Fourier expenditure system to obtain consistent estimates of short-run and long-run Morishima elasticities of substitution for Canadian liquid assets. We argue that the variability of the estimated elasticities and evidence of less than perfect substitution between monetary assets interferes with the successful use of simple-sum aggregates and traditional log-linear money-demand functions.
Calibrations semi-non-paramétriques de la substitution pour des actifs monétaires canadiens . Les auteurs calibrent le système dynamique de dépenses à la Fourier pour obtenir des estimations cohérentes des élasticités de substitution à la Morishima à court et à long termes pour des actifs monétaires canadiens. Ils suggèrent que la variabilité des élasticités estimées et la constatation que la substitution n'est pas parfaite entre les actifs monétaires rendent difficile un usage heureux des agrégats de simple somme et des fonctions log-linéaires de demande de monnaie.     

The aggregate elasticity of factor substitution with middle products

The elasticity of substitution between factors in production relates the change in the ratio of factors used in a production process to a given change in the factor price ratio. An aggregate concept of such an elasticity relates a change in overall factor endowments to the resulting change in factor prices. For a closed economy the behavior of consumers is an important part of such an aggregate elasticity, since endowment changes can bring about changes in commodity prices and resulting adjustments to factor prices. For a small open economy, commodity prices in typical models are exogenous. In the model with middle products, all final consumer goods are non-traded, so that local consumer behavior can affect factor prices. The aggregate elasticity of substitution is shown to be an average of production elasticities and demand elasticity even for a small open economy.     

Dynamic factor demands and adjustment costs: An analysis of bell Canada's Technology

In this paper a dynamic model of production is estimated for Bell Canada. The dynamics arise from the costs of adjustment associated with capital expansion. Estimation results showed that there are significant adjustment costs. Thus, the hypothesis of long-run cost minimization is rejected. As Bell Canada increases its capital stock by $1, there are additional adjustment costs of $0.36. This result implies that Bell Canada minimizes the present value of production and adjustment costs which results in a short-run equilibrium position. Price, substitution and output elasticities are estimated. In the short-run the inputs are substitutes and the price effects are highly inelastic. Overshooting occurs with respect to labour and material demands in the short-run since the demand for capital responds very little to output expansion. Returns to scale are also estimated in this cost of adjustment model. Bell Canada exhibits increasing returns to scale initially and then decreasing returns such that on average there are constant returns to scale with a scale elasticity of 1.08.     

A general equilibrium appraisal of energy policy in Mexico

This paper develops a static neoclassical general equilibrium model of the Mexican economy that focuses on production, consumption, and exports of energy goods. The specification of the model allows the government to set prices and production levels of energy goods exogenously. Domestic prices differ from international prices, and net exports of these goods are determined residually. The level of energy exports is a major factor in the determination of the government and trade deficits. The analysis presented in this paper serves as a case study of how to design and use an applied general equilibrium model to do policy analysis. An interesting feature is that the model itself is used to determine one of the key parameters, the elasticity of substitution of non-energy imports for domestic goods.     

Looking back, looking ahead: Biased technological change, substitution and the wage gap

The implications of ICT on wage inequality are studied by applying a CES production function with skilled and unskilled labour. Skill-biased technological change increases wage inequality. The result is reinforced in a two-sector general equilibrium model if the income elasticity of the demand for high-tech goods and the elasticity of substitution between final goods are larger than one.