A model for forecasting the substitution of one technology for another

Most technological changes can be described as a substitution of one material, process or product for another. Each such substitution, if successful, normally tends to follow an S-shaped (or “logistic”) curve: that is, it starts slowly as initial problems and resistances have to be overcome; then it proceeds more rapidly as the competition between the new and the old technology grows keener and the new technology gains an advantage; and finally, as the market for the new technology approaches saturation, the pace of substitution slows down. Sometimes, when the process is completed, the old technology continues to retain some specialized portion of the total market (i.e., a sub-market) for which it is particularly well adapted. In forecasting the course and speed of the substitution process especially when it has already begun and partially taken place, the simplest approach is to project a function having the appropriate S-shaped curve, using historical data to determine the free parameters of the function. While useful, especially where data are not available for a more sophisticated study, the simple curve-fitting techniques fail to take into account several important factors that affect economic and management decisions on the part of producers and intermediate users (as well as “final” consumers) and thereby influence the course which the substitution process is likely to take. To overcome this limitation, a simulation model has been developed at IR&T which allows some of these factors to be evaluated and incorporated explicitly and quantitatively. The model is described and its application is illustrated in the case of the substitution of plastic for glass in bottles. It is most applicable where the competing technologies are rather precisely defined, where a good deal of current technical and economic data are available, and where an in-depth analysis is desired. Because this particular forecast was made before the sudden precipitous increase in petroleum prices, which upsets the price relationships assumed in the forecast, there is discussion of the vulnerability of forecasts to political and other contra-economic developments.     

Determinants for forecasting technological substitution

This paper investigates the factors determining the rate of technological substitution and evaluates the prospects for forecasting models based on market-share data only. Studies on underlying causes for the substitution of one technology or product by another reveal the frequent presence of a number of factors. These factors are first discussed in general terms so as to establish their causal relationships with the rate of substitution. On the basis of the identified cause-effect relationships, a composite model is formulated that incorporates the impact of individual factors in a combination of additive and multiplicative interactions. The relative importance and sensitivity of different factors in describing the behavior of the substitution process is then studied through a system-dynamics application of the model. Finally, using three specific cases, a comparison is given between the forecasts made by the comprehensive model, incorporating factors that are known to have significant impact on the rate of substitution, with that of a generalized model for forecasting technological substitution.     

A Bayesian approach to aggregation in demand systems: smoothing with perfect substitution priors

Demand analysis requires aggregation of commodities. Some are imposed at the data collection level, leaving some for the estimation level. When data are collected, the implicit assumption underlying the aggregation is perfect substitutability: one gallon of gasoline is viewed by consumers as equivalent to another gallon; hence, the two are added together. While such aggregation can be carried out further by the data analyst, it is difficult to incorporate perfect substitutability into the estimation of direct demand systems. Perfect substitution in that context implies discontinuous demand functions, which are not nested within standard empirical demand systems. Perfect substitution is much more easily handled in a system of inverse demands, though an empirical method to impose perfect substitutability in an inverse demand system has not previously appeared in the literature. In this article, we develop such a method, which allows perfect substitutability to be imposed as a prior restriction. We use Leamer’s information contract curve as a tool to flexibly impose the substitution restriction and to investigate consistency between the data and prior. We illustrate the method with an application to inverse demands for fish in Korea.     

The automobile road to technological change : Diffusion of the automobile as a process of technological substitution

Advancement of the motor vehicle and its production methods is analyzed as a process of technological change. In a broader context, motor vehicles evolved as an integral component of road transportation through a series of interlaced substitutions of old by new technologies. Building on a large number of studies that described technological substitution processes, first it is shown how new energy forms replaced their predecessors and how the old marine-transport technologies were substituted by new ones. These examples constitute some of the oldest, empirically documented technological changes and show that many events in the dynamics of energy substitution and marine transport are related to technological changes in road transportation. It is shown that these substitution processes can be described by simple rules and that the replacement of old by new technologies in the energy and transport systems lasted about 80 years. The technological changes within road transportation, however, were more rapid. Replacement of horses by automobiles and older by newer generations of motor vehicles and production methods lasted only a few decades in the United States. Thus, technological substitutions within the road-transportation system were considerably shorter than the expansion of railroads, surfaced roads, all road vehicles together, and the more recent expansion of air transportation.     

Innovation diffusion with generation substitution effects

Markets of high technology products and services, such as telecommunications, are described by fast technological changes and rapid generational substitutions. Since the conventional modeling approaches that are based on diffusion models do not usually incorporate this important aspect into their formulations, the accuracy of the provided forecasts is consequently affected. The work presented in this paper is concerned with the development of a methodology for describing innovation diffusion, in the context of generation substitution. For this purpose, a dynamic diffusion model is developed and evaluated, based on the assumption that the saturation level of the market does not remain constant throughout the diffusion process but is affected by the diffusion of its descendant generation, as soon as the latter is introduced into the market. In contradiction to the conventional diffusion models, which assume static saturation levels, the proposed approach incorporates the effects of generation substitution and develops a diffusion model with a dynamic ceiling. The importance of such an approach is especially significant for markets characterized by rapid technological and generational changes. Evaluation of the proposed methodology was performed over 2G and 3G historical data and for a number of European countries, providing quite accurate estimation and forecasting results, along with important information regarding the rate of generation substitution.     

Modeling input–output impacts with substitutions in the household sector: A numerical example

Although there have been many elaborations of the basic input–output approach, including multi-regional models, dynamic models, models with variable coefficients, supply-side models, etc., these approaches all have the same limitation. The fixed-coefficients production function assumptions ignore substitutions in response to price changes that can be expected to accompany most shocks— skipping over the heart and soul of market economics. This research note suggests a simple approach to estimating new technical coefficients matrices after a shock so that the consequences of short-term substitution effects can be studied. Given a reduction in income (as reflected in the value added row), households are likely to make substitutions, reducing their final demand by less than the application of base-year I–O coefficients would indicate. But if ex post changed income and consumption can be observed, the application of RAS procedures can generate an appropriately modified A matrix. The resulting set of interdependent substitutions that occurred can be identified. Due to some well known limits in applying the traditional RAS approach, we reformatted it and suggest a new economic model that can link coefficient adjustments to degrees of a priori substitutability and complementarity. Based on this resolution, we look forward to detailed studies of specific coefficients and how they evolve over the short term.     

Substituting one risk increase for another: A method for measuring risk aversion

This paper defines the rate of substitution of one stochastic change to a random variable for another. It then focuses on the case where one of these changes is an nth degree risk increase, and the other is an m  th degree risk increase, where n>m?1$n>m?1$. The paper shows that the rate of substitution for these two risk increases can be used to provide a broader definition and two additional characterizations of the nth degree Ross more risk averse partial order. The implications for local intensity measures of nth degree risk aversion are also examined. The analysis organizes the existing results as well as generates new ones.     

Self-selection and Pareto efficient taxation

This paper analyses the set of Pareto efficient tax structures. The formulation of the problem as one of self-selection not only shows more clearly the similarity between this problem and a number of other problems (such as the optimal pricing of a monopolist) which have recently been the subject of extensive research, but also allows the derivation of a number of new results. We establish (i) under fairly weak conditions, randomization of tax structures is desirable; (ii) if different individuals are not perfect substitutes for one another in production, then the general equilibrium effects—until now largely ignored in the literature—of changes in the tax structure may be dominant in determining the optimal tax structure; in particular if the relative wage of high ability and low ability individuals depends on the relative supplies of labor, the optimal tax structure entails a negative marginal tax rate on the high ability individuals, and a positive marginal tax rate on the low ability individuals (the marnitude of which depends on the elasticity of substitution); (iii) if individuals differ in their preferences, Pareto efficient taxation may entail negative marginal tax rates for high incomes; while (iv) if wage income is stochastic, the marginal tax rate at the upper end may be 100%.Our analysis thus makes clear that the main qualitative properties of the optimal tax structure to which earlier studies called attention are not robust to these attempts to make the theory more realistic.     

Substitution and output effects in the neoclassical theory of the firm under imperfect competition

Since 1938, it has been established that the effect produced by a variation in an input price on the use of another input can be decomposed into a substitution effect and an output effect (or scale effect). Nevertheless, this distinction is still denied today by many authors. Here, one tries to establish in which manner imperfect competition in the product market alters the respective importance of substitution and output effects. Some implications are then derived about alternative manners of defining substitutability and complementarity between inputs.     

Optimal taxation of externalities interacting through markets: A theoretical general equilibrium analysis

This study develops a theoretical general equilibrium model to examine optimal externality tax policy in the presence of externalities linked to one another through markets rather than technical production relationships. Analytical results reveal that the second-best externality tax rate may be greater or less than the first-best rate, depending largely on the elasticity of substitution between the two externality-generating products. These results are explored empirically for the case of greenhouse gas and nitrogen emissions associated with biofuels and petroleum.     

Optimal component substitution within system evolution planning considering multiple-vendor,functionally equivalent commercial products

The use of commercial-off-the-shelf components (COTS) in systems with long-term life cycles eventually affects system functionality. Such systems must undergo component substitutions to avoid component obsolescence and maintain the system operationally effective. While performing such substitutions, sustainment costs must be kept within projected budgets, and system and component evolution must seamlessly provide continued availability. However, planning system evolution while minimising costs becomes a competing resource allocation problem (even more so when multiple manufacturers offer functionally equivalent COTS that can satisfy the system requirements). This research presents a mathematical model for calculating system life cycle costs while considering different substitution alternatives, and proposes an optimisation approach and a network model to obtain an optimal substitution sequence based on a minimisation criteria of life cycle costs. It was observed that upgrading the system with available technologies often results in better affordability than keeping the same technologies for the entire system life cycle.     

Productivity versus elasticity: a normalized constant elasticity of substitution production function applied to historical Soviet data

This study tests the extensive growth hypothesis, which would attribute the Soviet economic slowdown to low elasticity of substitution and over-investment rather than deteriorating productivity growth. To circumvent the low availability of data, widely applicable new methods for estimating productivity and elasticity of substitution were developed based on the normalized constant elasticity of substitution (CES) production function. One is an extended version of the Solow residual calculation, and the other is a direct estimation of the time-varying parameter normalized CES production function. The application of the methods to the Soviet data showed a decreasing trend in productivity growth and a low elasticity of substitution of approximately 0.25. The results neither reject nor support the extensive growth hypothesis because of uncertainty in the interpretation of the low elasticity of substitution. The results suggest that it is reasonable to assert that both deteriorating productivity growth and low elasticity of substitution caused the Soviet economic slowdown. Further empirical studies on productivity and elasticity of substitution in the Soviet and other economies are necessary to fully understand relations between productivity growth, elasticity of substitution and economic development.     

Substitution between games in the UK national lottery

Virtually all lottery agencies offer a variety of games to suit the tastes of players in an attempt to maximize revenue to the government. Using the UK National Lottery, which offers a variety of on-line and scratchcard games, the extent to which there is substitution or complementarity between games is evaluated Employing weekly data from the three UKNL lottery games offered over the sample period, it is found that own-game characteristics have, by far, the largest influence on sales. Some evidence is found suggesting that the lotto and scratchcard games are partial substitutes for one another. Thunderball sales appear independent of the other two games. Some evidence is also found that the Wednesday and Saturday drawings of the lotto game are substitutes. The overall conclusion is that Camelot has successfully designed and marketed three games that each appeal to bettors in different ways. Thus, sales from one game do not seem to seriously cannibalize the sales of the other games, with the exceptions noted above. Further, the introduction of another, temporary game (Big Draw 2000) contributed to net sales. These results also suggest that the games do not appear to be complements to each other, indicating that the various arguments as to why the games may be so (transactions costs, brand awareness, and the portfolio effect) do not appear to be very strong.     

Electric vehicles: Market penetration and positive externalities

In this paper, we develop a methodology for approximating the market penetration potential for electric vehicles (EVs). The model is dynamic in nature and explicitly accounts for the competitive effects of conventional vehicles. Unlike many previous models, it does not require an estimation of the time required to achieve a 50% market share. Instead, the model allows one to endogenously determine the rate of market penetration, as well as the ceiling level. We note that some electric vehicle characteristics limit marketability to consumers unaffected by the disadvantages associated with operating EVs. These characteristics are accounted for in the model by the use of a substitution index. The addition of the substitution index allows one to explicitly account for variations in prices, climate, and geographic contour, all of which affect market potential. Electric vehicles are expected to result in positive social benefits by way of reduced pollution emissions and because of the concomitant decrease in the consumption of gasoline that market adoption would bring about. However, the social benefits will not be captured in the market and will not, therefore, encourage the use of these alternatives to conventional vehicles. This means that the rate of adoption of electric vehicles will be slower than is socially optimal, which is a potential argument for government subsidies for electric vehicles. In this paper, we explore a method for analyzing the benefits associated with the adoption of electric vehicles.     

Dynamics of social factors in technological substitutions

Diffusion models of technological innovations are often based on an epidemic structure which has a good fit to historical data but whose communication assumptions lack explanatory power. They assume a simplified decision process, uniform decision criteria across adopters categories, and a fully interconnected social structure. The objective of this paper is to show that the dynamics of social factors during technological substitutions have significant effects on substitution patterns. The success of a paradigmatic shift is not only a function of technological characteristics but also depends on change agents and many social dynamics. Such complexity requires analysis at several levels of granularity. We start with cognitive processes at the individual level using concepts from cognitive psychology and decision making under uncertainty and then move to interpersonal communications at the aggregate social level. We show that population heterogeneity generates different decision criteria and a social topology which greatly affect perceptions and the formation of expectations. The structure of interpersonal networks also explains how the relevance and credibility of information impact the critical mass dynamics of technology adoption. A more complete model accounting for social interactions provides a useful framework for understanding complex substitution patterns and reducing the risk of misreading the market.     

Combining Contingent Valuation and Choice Experiments. A Forestry Application in Spain

When many good variants are to be valued, like in several forest management programs which differ in the attribute levels, the Contingent Valuation Method may not be a practical option, given the cost and time involved to value each variant separately. There are at least three alternative procedures in such situations. One (i) is to apply an attribute based valuation method like a Choice Experiment (CE); another (ii) is to conduct a CVM and a CE exercise and estimate a joint model; a third one (iii) is to use the CVM estimates to value a base scenario, and then use the CE results to adjust the CVM estimates for any new different scenario. A numerical simulation and an empirical application to an afforestation program in Spain show that the latter is the procedure that yields closer values to the CVM estimations, followed by (ii).      

Market behavior and the types of production functions

The paper presents a unified approach to theory and estimation of production functions based on a simple observation that any production function has a unique representation of its isoquants in terms of the differential equation which may be observable in market. Expressing the marginal rate of substitution between two inputs as the differential equation in these two inputs, various classes of production functions are obtained by integrating this differential equation. Not only does this general approach yield a systematic framework for all known forms but it also generates new types of production functions. Empirical application is also indicated.     

Asymmetric effects of exchange rate changes on the demand for money in China

In order to account for currency substitution, the majority of recent studies relating to the specification of the demand for money include the exchange rate as another determinant of the demand for money. However, those who have estimated the demand for money in China have been unable to find any significant effects of exchange rate changes on the demand for money by the Chinese. We show that this is due to the assumption that exchange rate changes have symmetric effects. Once depreciations are separated from appreciations of the yuan, those exchange rate changes are shown to have significant effects on the demand for money in China, but in an asymmetric manner.     

Two‐level CES Production Technology in the Solow and Diamond Growth Models*

The two‐level CES aggregate production function—that nests a CES into another CES function—has recently been used extensively in theoretical and empirical applications of macroeconomics. We examine the theoretical properties of this production technology and establish existence and stability conditions of steady states under the Solow and Diamond growth models. It is shown that in the Solow model the sufficient condition for a steady state is fulfilled for a wide range of substitution parameter values. This is in sharp contrast with the two‐factor Solow model, where only an elasticity of substitution equal to one is sufficient to guarantee the existence of a steady state. In the Diamond model, multiple equilibria can occur when the aggregate elasticity of substitution is lower than the capital share. Moreover, it is shown that for high initial levels of capital and factor substitutability, the effect of a further increase in a substitution parameter on the steady state depends on capital–skill complementarity.