Market Penetration of New Energy Technologies, Study notes of Technology

Download Market Penetration of New Energy Technologies and more Study notes Technology in PDF only on Docsity! ....----------------, NREL/TP-462-4860 • UC Category: 233 • DE92016409 Market Penetrati Technologies of New Energy Daniel J. Packey h..~ ..,-.. ~I~-I .... ...... --, National Renewable Energy Laboratory (formerly the Solar Energy Research Institute) 1617 Cole Boulevard Golden, Colorado 80401-3393 A Division of Midwest Research Institute Operated for the U. S. Department of Energy under Contract No. DE-AC02-83CHI0093 Prepared under Task No. AS815440 February 1993 NOTICE This report was prepared as an account of work sponsored by an agency of the United States government. Neither the United States government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, com­ pleteness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily con­ stitute or imply its endorsement, recommendation, or favoring by the United States government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States government or any agency thereof. Printed in the United States of America Available from: National Technical Information Service U.S. Department of Commerce 5285 Port Royal Road Springfield, VA 22161 Price: Microfiche A01 Printed Copy A04 Codes are used for pricing all publications. The code is determined by the number of pages in the publication. Information pertaining to the pricing codes can be found in the current issue of the following publications which are generally available in most libraries: Energy Research Abstracts (ERA); Govern­ ment Reports Announcements and Index (GRA and I); Scientific and Technical Abstract Reports (STAR); and publication NTIS-PR-360 available from NTIS at the above address. TP-4860 A wide selection of techniques is essential for analysts challenged with forecasting the market penetration of new technologies. These technologies are in various stages of development and have varying amounts of data available about them. For example, some RETs are so new or are evolving so rapidly that much data about them are lacking. In these cases, techniques demanding less data and resources should be used. Other RETs have a longer track record so more quality data are available. To obtain the most statistically significant prediction, the most sophisticated method that fits the data available should be used. Some prediction methods are more effective than others at different developmental stages of new technologies (Figure S-2). Generally, as the new technology matures, the amount of data about that technology increases, allowing use of more sophisticated data-demanding methods that require more resources for analysis. Market Penetration of New Energy Technologies contains an extensive, up-to-date bibliography in which analysts can locate material that details various forecasting techniques. The bibliography also includes some citations on special topics related to market forecasting such as small-sample properties of econometric techniques. Effective Methods: Effective Methods: Effective Methods: • Subjective estimation • Cost models • lime-series models lime-series models • Historical analogy • Market survey • Cost models • Market survey • Diffusion models • Diffusion models • Historical analogy • Econometrics Figure S-2. Some prediction methods are more effective that others at different developmental stages of new technologies. v TP-4860 Table of Contents Introduction and Statement of Purpose . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 1 Section 1: Subjective Estimation Methods .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 4 Panel Consensus Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 4 Delphi Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 5 Section 2: Market Surveys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 7 Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 7 Section 3: Historical Analogy Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 8 Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 8 Section 4: Cost Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 9 Weighted Average Cost of Capital .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 10 Marginal Cost of Capital . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 10 Net Present Value. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 11 Total Life-Cycle Cost . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 12 Levelized Cost of Energy ............................................. 13 Levelization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 13 Revenue Requirements ............................................... 14 Internal Rate of Return. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 15 Simple Payback Period .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 16 Discounted Payback Period . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 16 Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 17 Section 5: Diffusion Models ................................................ 18 Bass Model ....................................................... 18 Fourt and Woodlock Model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 19 Mansfield Model ................................................... 21 Blackman Model ................................................... 21 Fisher and Pry Model ........... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 21 Kalish Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 23 Kalish and Lilien Model .............................................. 23 Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 23 Section 6: Time-Series Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 27 Simple Deterministic Extrapolation Models . . ... . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 27 Stochastic Time-Series Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 29 Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 31 vi TP-4860 Table of Contents {concluded} Section 7: Econometric Models .............................................. 32 Ordinary Least Squares. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 33 Dummy Variable ................................................... 35 Generalized Least Squares . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 36 Nonlinear Regressions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 36 Two-Stage Least Squares ............................................. 39 Seemingly Unrelated Regression ........................................ 40 Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 41 Section 8: Summary and Conclusions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 43 References .............................................................. 44 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 48 vii TP-4860 Given the nature of RETs, we adopted a pragmatic approach for this report on market penetration models. The data available for the analysis ofRETs are not homogeneous. In some circumstances, there exists a rich data base and, in other areas, the data are limited or even lacking. Moreover, RETs have a tendency to be regionally specific. Consequently, cases develop in which even data on the same RET may not be generalized for a different region (e.g., regional climatic differences). This situation necessitated a broad review of the available market penetration models. Circumstances dictated (primarily data limitations) that the more elaborate models were not feasible. Consequently, the more esoteric models, such as spectral analysis, are not included. Moreover, composite system dynamics approaches (e.g., Fossil2, C.O.A.L. and Vescuso's model) were not reviewed. Specifically, Fossil2 was not reviewed because (1) Fossil2 is much more than a market penetration model, and (2) as a composite system dynamics model, Fossil2 utilizes a variety of approaches. For example, cost models and a logistic curve are incorporated in Fossil2. As such, there is not a unique approach to describe but rather, a combination of approaches. Composite models themselves are not uniform; different composite models choose different items on the market penetration methodology menu. Therefore, even though we do not address composite models per se, we do address the individual models that make up the composite models. The logic behind this approach is that once you understand the methods that make up the model, you are in a better position to evaluate the model itself. We strove to be consistent. Not only do we address composite models from their individual market penetration segments but we address other models in the same fashion. For example, cost models are often combined with other model forms, such as diffusion models, to model market penetration. A common approach used to estimate the market penetration of solar technologies (and other RETs) is to use a logistic curve incorporating cost data (Warren 1980). Models and methods are used for a variety of purposes. Tactically speaking, it was necessary to choose a section to present each method. For example, the logistic curve is addressed in the diffusion model section of this report. Therefore, in order to avoid repetition, only the specified model components are discussed in each section. The other model structures are discussed in their appropriate sections, and mention is made when other models or methods can be incorporated. To provide meaningful support for technologies that are newly emerging, it was necessary to present the simpler, less data-demanding techniques. However, we made efforts to illustrate some of the more advanced techniques when practicable. Thus, advanced techniques, which in some instances could be useful, are presented. For example, we introduce a heretofore unused approach for market penetration analysis, Zellner's seemingly unrelated regression. This new method is an econometric approach that allows for the simultaneous examination of interactive influences across a number of RETs. We considered the following market penetration methods: • Subjective estimation methods • Market surveys • Historical analogy models • Cost models • Diffusion models 2 TP-4860 • Time-series models • Econometric models. 3 TP-4860 Section 1: Subjective Estimation Methods When dealing with forecasting methodologies, one has to be careful not to fall into the trap of characterizing one technique as subjective (e.g., judgmental forecasting) and another technique as non­ subjective (e.g., econometric). Even the most technically objective forecasting models require many subjective assumptions (Tyebjee 1987). The choice of a particular data transformation or of a particular functional form, seemingly only a technical detail, can and does change a model's forecast (Wachs 1982). Thus, the choice of a proper modeling technique cannot be one of a subjective (normative) versus objective (positive) model in a Friedmanian sense (Friedman 1953). But rather, the choice of an appropriate modeling technique resides along a subjective input continuum, with judgmental forecasting methods at one extreme and randomly selected samples, employing statistically valid and theoretically correct econometric analysis, at the other. No matter how sophisticated the analysis, there will always remain a certain amount of residual uncertainty. This residual uncertainty necessitates a degree of subjective judgment to be used by the analyst in the forecast modeling process (Raju and Teotia 1985). Because of the newness of the innovation process itself, residual uncertainties and poor market data are the normal condition when analyzing the market penetration of new or emerging technologies. Thus, adjustments and decisions on the sufficiency of modeling techniques must be made accordingly. Subjective estimation methods or judgmental forecasting methods can be simple: a sole entrepreneur's decision to market a product based on intuition or gut-feelings. Or these methods can be complex: a formal decision-making process utilizing a panel consensus or Delphi method (Geurts and Reinmuth 1980). The market penetration method may be a simple brainstorming session or complexly morphological. It mayor may not require detailed quantitative or qualitative data as input. The critical identifying distinction, separating it from all other methods, is that for subjective estimation methods the evaluation and transformation of the information from raw data to a market penetration forecast is carried out primarily within the human brain (EPRI 1991). Although an Electric Power Research Institute (EPRI) study found that utilities tended to use the more sophisticated methods, a majority of manufacturing companies relied on expert judgment and time-series models to forecast new product sales (EPRI 1991). Thus, we have focused a significant portion of our attention on those areas. Subjective estimation methods are typically used when there is little or no historical data or when existing data is suspect (EPRI 1991). Two subjective estimation techniques will be discussed: the panel consensus method and the Delphi method. Panel Consensus Method In the panel consensus method, key centralized decision makers, or a group of top management personnel, experts, and other individuals who are knowledgeable about the new technology, are brought together to determine subjective estimates of a product's market penetration. This technique assumes that the organization possesses (or has access to) experts who have special knowledge of the new technology and use this knowledge to effectively forecast the product's market development. It assumes that each expert recognizes the other experts' importance and accepts their input in a consensus-building activity. Each recognizes the special competence of the others and thus the group benefits through the assimilation of the experts' collective knowledge (Geurts and Reinmuth 1980). Experts may internally make the decision (e.g., a company employing in-house experts) or just provide information to key centralized decision makers (e.g., an executive board or regulatory body). 4 TP-4860 Section 2: Market Surveys The purpose of market surveys is to obtain information from decision makers on their decision-making criteria, technological preferences, and planned behavior. In addition, market surveys can be used to elicit responses from decision makers on their willingness to consider new technologies and on those factors the decision makers view as decisive. In certain circumstances, market surveys can aid in decision modeling. One example is the application of decision modeling to the acceptance of new electricity­ generating technologies (Stover 1978). Market surveys for new products or technologies are sometimes referred to as intention surveys. Intention surveys are commonly used for automobiles and can be used for new technologies as well (Raju and Teotia 1985). Market or intention surveys for new technologies can be accurate if the following conditions are met (EPRI 1991): • Event falls within a forecast horizon of two years or less • Forecasted event is important to the people surveyed • Respondents have definite behavioral plans • Respondents can be relied upon to report correctly • Respondents have the authority and ability to actuate planned behavior • New information is unlikely to radically change the respondents' plans. Evaluation There are several potential problem areas for market or intentions surveys. First, intentions and actual behavior are not identical. Expected future behaviors are subject to change and can change as a result of market forces not anticipated by the surveyor included in the survey's design. Second, the individuals answering the survey may not be in a sufficient authority position to actuate the planned behavior. Third, the individual may not be sufficiently knowledgeable of the new technology to assess the marketability of the new technology or its potential impact on the market. Fourth, the predictive power of the survey's planned behavioral responses is valid for a limited period of time (Raju and Teotia 1985). Fifth, businesses tend to be secretive about their planned intentions (EPRI 1991). Finally, even if businesses do respond, it may be difficult to obtain a full and truthful revelation of their prefer~nces (Varian 1984). 7 TP-4860 Section 3: Historical Analogy Models Historical analogy is a prediction method that compares an existing product's market pattern to a new product or technology. The market penetration path is assumed to be the same for both technologies. Historical analogy models generally assume that the technologies are of a sufficiently analogous nature as to exist in approximately identical market structures. If this is the case, then the new technology's market penetration share will approximate the existing technology's market penetration share's pattern over the technology's life cycle. The historical analogy model can be particularly useful for introducing new technology in different regions. In this case, the life-cycle adoption rates for a new technology in one region may provide a suitable approximation for the market penetration rates of the new technology in another region (EPRI 1982).2 However, the historical analogy model does not explicitly consider other non-time exogenous variables (Raju and Teotia 1985). Evaluation There are two main areas of concern. First, the analysis hinges on the appropriateness of the analogous technology. For tightly aligned technologies, historical analogy may be sufficient. However, the existence of a closely aligned technology may be a mixed blessing. A closely aligned technology may represent additional potential competition; competition that did not exist when the closely aligned product or technology was introduced. For loosely related technologies, the accuracy of historical analogy methods may rapidly deteriorate. Such may be the case for truly novel or pioneering technologies (EPRI 1991). Second, the historical analogy model does not take into consideration non-time exogenous variables. Consequently, the explanatory value of this type of model is limited. Moreover, in situations where there is sufficient historical data, alternative, more sophisticated modeling techniques,3 such as time-series or econometric methods, may provide more meaningful estimates. 2'fhis point is discussed in the comments on the "neighborhood effects," in the diffusion model section of this report. 3Some of these estimating techniques will be discussed in subsequent portions of this report. 8 TP-4860 Section 4: Cost Models Cost models estimate market penetration as a function of the cost-related aspects of the product or technology. Cost estimates and the discount rate are typically used as the critical factors. A range of technologies are selected, and the cost estimates are calculated. These cost estimates are then normalized. The comparative normalized cost of the technology is then used to calculate the product or technology's annual and long-run market share (EPRI 1982). Thus, cost models, on their own merit, are used to determine the adoption of new technologies. However, cost models are often combined with other model forms, such as diffusion models, to model market penetration. A common approach used to estimate the market penetration of solar technologies (and other RETs) is to use a sigmoid-shaped logistic curve incorporating cost data4 (Warren 1980). The logistic curve is addressed in the diffusion model section of this report. Therefore, in order to avoid repetition, only the cost model components will be discussed in this section. The other model structures will be discussed in their appropriate sections, and mention will be made when cost models can be incorporated. There are generally four phases incorporated in cost models. First, the set of competing technologies are identified. Second, the initial and after-tax costs are estimated over the life of the technology. Third, a cost model is selected, and the costs are organized so that they can be calculated in a comparable fashion. Finally, the degree of market penetration of each technology is estimated from the normalized cost (Raju and Teotia 1985; and Weijo and Brown 1988). Because there are many cost models (Raju and Teotia 1985) it was necessary to select a manageable subset of the available models. We selected the following 10 commonly used methods to discuss in this report: • Weighted average cost of capital • Marginal weighted average cost of capital • Net present value • Totallife-cycle cost • Levelized cost of energy • Levelization 4For example, the market share equation could be specified as MS j = =_C_?_ ~ C:y L-ri-l 1 where MSj is the market share and Cj represents the cost of technology i. 9 $15000 10000 .-..... , TP-4860 Nominal Cash Flow ..•. ----_ ...... - ... ' ...... ,'" ..... -.-.-.-.-.-.-.-.-.-.-.-.-.~.~.~.~.-............... Present ...... _._._._ •. Value Cash Row 5000 O~~----r---~----r----r----~---r----~--~----~- 1 3 5 7 9 Time Figure 4-1. Comparison of nominal and present values of the same cash flow Total Life-Cycle Cost Total life-cycle costs (fLCC) are the total costs incurred through the ownership of an asset over the asset's life span (Brown and Yanuck 1980). The TLCC type of analysis takes into consideration all significant dollar costs (in time equivalent form) that are incurred as a result of the project. Positive discounted values of revenues are treated as negative costs and are subtracted from total costs on an equivalent time basis (Le., discounted). TLCC can then be represented as TLCC = I - S + M + R + E (4-6) where TLCC is the present value of the total life-cycle cost, I is the present value of the investment costs (including finance charges), S is the present value of the expected salvage value, M is the present value of the non-fuel operation and maintenance and repair costs, R is the present value of the replacement costs, and E is the present value of the energy costs (Ruegg 1987). Totallife-cycle cost is composed of the present value of many different types of costs. Care should be taken that equivalent present value techniques are used on all of the components of TLCC. The estimated dollar value for operations and maintenance expenses are often not of the same form as the estimated dollar values for the other costs. For example, if operations and maintenance expenses are calculated by multiplying the level of output by some fixed proportion, then the result of this method of calculating the 12 TP-4860 operations and maintenance expenses is not a present value for operations and maintenance expenses. This would introduce bias into the estimate of TLCC. Levelized Cost of Energy The levelized cost of energy is used to compare alternative energy generating or producing technologies. Generally, comparisons between the cost of energy generated by a renewable energy resource and a standard generation unit consuming fossil fuel could use the levelized cost of energy in its analysis. More specifically, the levelized cost of energy approach is used by the U. S. Department of Energy for use in many of its five year research and development plans and NREL's Renewable Energy Technology Evolution Rationales. The levelized cost of energy (LCOE) is the dollar amount that must be recovered for each unit of energy produced over the lifetime of the system, which, if discounted according to when it is produced, will equal the discounted life-cycle cost of the system. LCOE is represented as LCOE = ----:'~TL_C_C __ L:l [Qt + (1 +d)1 (4-7) where LCOE is the levelized cost of energy, TLCC is the totallife-cycle cost, ~ is the firm's energy output at time t, d is the discount rate, and N is the number of time periods (Short 1983). It is interesting to note that if the system output remains constant over time, the equation for LCOE reduces to LCOE = (TLCC/Q) (UCRF) (4-8) where TLCC is the totallife-cycle cost, Q is the firm's output, and UCRF is the uniform capital recovery factor.' Levelization Levelization is a technique that is commonly used in the utility industry to compare equivalent annual payment streams among alternatives facing the decision maker. The levelization process is essentially the same as previously described for the levelized cost of energy. That is, cash flows are discounted to their present value, then are levelized by multiplying the present value by the UCRF. A uniform payment stream, escalating at a constant rate (.AP), can be levelized through the following single equation that combines the present value and the capital recovery factor calculation: (4-9) where LC is the levelized cost, ~ is the cash flow to be levelized, k equals [(1 +.AP) + (1 + d)], d is the discount rate, n is the number of time periods, and UCRF is the uniform capital recovery factor. In the previous expression, it is assumed that the price escalation is measured in the same type of dollars (Le., either constant or current) as is used for the discount rate, d. Note that if there is no escalation in price (Le., .AP = 0), then LC = ~. 'The uniform capital recovery factor (UCRF) = d(1 +d)" + [(1 + d)" - 1]. 13 TP-4860 The effect of the levelization of a cash flow is illustrated in Figure 4-2. $15000 10000 5000 Cash Flow ---------------- Levelized Cash Flow O~_r--_,----.---_r----r_--_r--~----~--~----~- 1 3 5 7 9 TIme Figure 4-2. Comparison of a cash flow with a levelized cash flow Revenue Requirements Another method commonly used by the utility industry to examine investment alternatives is the revenue requirements method. The revenue requirements method calculates the amount of revenues necessary to meet all costs and achieve a certain preset after-tax rate of return. The revenue requirement method examines the various elements of the cost of service. These elements include carrying charges and expenses. Carrying charges include book depreciation, property and income taxes, return on equity, return on debt, and insurance. Expenses include fuel, operating and maintenance expenses (EPRI 1987). This costing method is well known and described in the EPRI technical assessment guide (TAG). Businesses apply the revenue requirement method to project costs over the investment's useful life. The general decision rule for utilities is to choose the alternative for which the present value of the multiperiod 14 TP-4860 Evaluation An advantage to cost models is that the cost factors can be specified in a straightforward manner (Raju and Teotia 1985). The cost models take advantage of all the price/cost information available in the market. As such, to the extent that the price/cost reflects the level of information in the marketplace, the cost models can incorporate the market's information on the product or technology. There are three areas of concern in cost models. First, cost models usually adopt a cost function and then act as if this cost function is the sole determinant of market behavior. As such, cost models do not fully consider other aspects of the decision-making process. Two examples are non-priced environmental costs and information not fully assimilated in the marketplace. Second, the costing methods usually employed are by and large deterministic. For example, Mitre has used a logistic function with the ratio of a conventional system to a solar energy system's life-cycle cost as one of its explanatory variables in measuring market penetration (Rebibo et al. 1977 and EPRI 1982). Formal uncertainty analysis is difficult to accomplish in deterministic models. However, the market shares of the levelized cost of energy and required revenues cost models can be represented in terms of a distribution that incorporates a certain degree of uncertainty in the cost estimate (Raju and Teotia 1985). Third, cost models require data on the product or technology's associated costs. In some instances, cost models would require estimates of future costs of new products or technologies that have been in existence for only a short time. The degree of potential variability between the actual costs of a new technology and the future cost estimates could be great. 17 TP-4860 Section 5: Diffusion Models Diffusion models represent a major segment of the market penetration modeling literature and activity. As such, diffusion models will be examined in detail. Diffusion models9 estimate the degree of entry of a new product into the marketplace. The discussion on diffusion models addresses the following models: • Bass (1969) • Fourt and Woodlock (1960) • Mansfield (1961) • Blackman (1974) • Fisher and Pry (1971) • Kalish (1985) • Kalish and Lilien (1986). In general, diffusion models are composed of two segments, innovators and imitators. Innovators are individuals who are the first to spontaneously adopt new technologies. Here, spontaneous means that the innovators are not influenced by previous adopters but rather by some other external change agent, such as advertising (EPRI 1991). The imitator segment is influenced by' the number of people who have already purchased the product or technology. This segment will increase relative to the number of innovators over time (Teotia and Raju 1986). The imitators are said to be influenced internally. Thus, innovators are influenced by mass-media communications (external) and imitators are influenced by word­ of-mouth communications (internal) with those who already have purchased the product (Lekvall and Wahlbin 1973). In essence, the model implicitly assumes an information transfer between the innovators and the imitators (Teotia and Raju 1986). Bass Model The Bass model (1969) is a generalized form that can be used to illustrate other commonly used diffusion models. Moreover, by relaxing some of the usual restrictions made on diffusion models, recent devel­ opments in diffusion modeling can be demonstrated. The basic diffusion model can be expressed as n(t) = dN(t) = p[M - N(t)] + ~ N(t)[M - N(t)] dt M (5-1) ~e discussion of diffusion models focuses directly on diffusion models and only addresses econometric techniques tangentially. In diffusion models, econometrics is used as a tool to obtain parameter estimates. A variety of methods (e.g., ordinary least squares, maximum information likelihood, and nonlinear least squares) have been used to estimate the same or similar parameters. Therefore, econometrics is a peripheral issue for diffusion models. Econometric techniques are discussed later and will include issues relevant to diffusion models. 18 TP-4860 where net) is the rate of adopters at time t, N(t) is the cumulative number of adopters, M is the ultimate number of adopters, p represents the adoptive influence that is independent of prior adoptions, and q represents the adoptive influence that depends on imitation or learning (Mahajan, Muller, and Bass 1990). The term p[M - N(t)] in the previous equation represents the number of purchasers who are not influenced by other individual's purchase decisions. The term q/M N(t)[M - N(t)] represents the number of purchasers who are swayed by the number of previous buyers. The terms p and q are referred to as the coefficient of innovation and the coefficient of imitation, respectively (Bass 1969). Typically, P and q are assumed to be constants. The adopter distribution assumes an initial pM level of purchasers who buy the product at the beginning of the process. There exists a point T, which indicates the maximum adoption level. T" is also the inflection point of a sigmoid (S-shaped) cumulative adoption function. The cumulative adoption function is symmetric around T* such that the interval range 0 to T" is a mirror image of the range T* to 2T (Mahajan, Muller, and Bass 1990). The discussion of sigmoid functions, points of inflections, and symmetry can be somewhat mystifying and obtuse. Therefore, Figure 5-1 is included (a graphical representation of the Bass model) to help clarify the discussion. lo Figure 5-1 consists of three graphs. Figure 5-1(a) is a graphic representation of the typical shape of the Bass model. The graph is divided into two areas: (1) the amount of adoption attributed to individuals influenced by external sources (innovators), and (2) the amount of adoption attributed to individuals influenced by internal factors (imitators). Figure 5-1(b) is composed of two graphs. The first graph illustrates the inflection point and the symmetry range [0 - T*, T* - 2T]. The second graph illustrates a sigmoid cumulative adoption function. The S-shaped nature of the cumulative adoption function is a commonly made assumption. Most diffusion models use some form of the sigmoid shape. The reason for the use of an S-shaped curve is usually given in terms of market evolution. In the beginning, initial market penetration is slow. This is due to (among other factors) the lack of information, bottlenecks, and buyer uncertainties. As these factors are effectively addressed, and innovators interact with imitators, the growth rate in the intermediate stage accelerates. Finally, the product approaches market saturation, and the growth rate declines (feotia and Raju 1986). Although most diffusion models use an S-shaped function, it is not universally true. Alternative specifications are used. The main criticism of smooth symmetric functions is that there exists no unquestionable, logically intuitive reason why the functions should be symmetric. It is given (Le., assumed in the model) that there are two distinct adopter groups. These two groups are assumed to consist of different individuals who are affected by different factors and behave differently. The basic argument is that symmetry is a mathematical convenience and does not portray a reflection of reality. Fourt and Woodlock Model One way to affect the shape of the market adoption path is by adjusting the coefficients of innovation and imitation. The coefficients of innovation (P) and imitation (q) have a direct effect on the diffusion model's estimation of market penetration. If we assume that the coefficient of imitation equals zero (q = 0), then the diffusion process excludes imitators and is based purely on the innovation effect; this lOfigure 5-1 was originally created by Mahajan, Muller, and Bass (1990) and is reproduced with the consent of the American Marketing Association. 19 TP-4860 f = exp[2o(t _ ~)] (1 - f) (5-4) where f is the market share, 0 is one-half the annual fractional growth in the early years, and to is the time when market share equals 50% (feotia and Raju 1986). Fisher and Pry applied their approach to a number of industries. For example, they studied synthetic versus natural fibers, plastic versus leather, synthetics versus natural rubber, and plastic versus metal in cars. An interesting conclusion of Fisher and Pry's work was that this model indicates that once a tech­ nology has 5 % of the market, it is highly probable that the process will continue until the new technology completely replaces the former technology. This result followed from Fisher and Pry's assumed pattern of market penetration12 and is sufficiently startling to merit additional attention. In order to understand how Fisher and Pry arrived at their conclusion, it is necessary to examine how the cumulative number of adoptions (N[tD is functionally related (via F[t]) to the market potential (M). Using the generalized Bass (1969) model, this can be expressed as N(t) = MF(t) . (5-5) If we assume that M is a constant13 (as is assumed in most diffusion models using the generalized Bass form) then we can differentiate F(t) with respect to time and arrive at M dF(t) = [p + qF(t)][M - MF(t)]' dt (5-6) where p, q, F(t), and M are the same as previously defined. Dividing through by M we obtain (EPRI 1991) dF(t) = [p + qF(t)][1 - F(t)] dt (5-7) The previous equation indicates that the rate of change in relative cumulative adoption is a function of p, q, and F(t) and is independent of the market size (EPRI 1991). Thus, the Bass model assumes that the market potential is set at the time of introduction and remains fixed (Mahajan and Peterson 1978). The independence of the cumulative adoption to market size is a criticism that has been repeatedly leveled against the standard diffusion models. Theoretically, there is no reason for a fixed adopter population. A more reasonable assumption would be to assume a changing adopter population (Mahajan, Peterson, Jain, and Malhotra 1979). For example, a product's effective geographical boundary can change over time. A product from one region can expand into another "untapped" adjacent region and capitalize on positive word-of-mouth communication across regions. This effect is referred to as the "neighborhood effect" (Mahajan, Muller, and Bass 1990). 12Fisher and Pry referred to market penetration as market substitution. l~is assumption will be relaxed later in this section. 22 TP-4860 Kalish Model Another objection to the fixed potential adopters assumption is that the adopter population could be affected by price and internal communications (Kalish 1985). Kalish's diffusion model illustrates the relaxation of the restrictive fixed potential adopter population assumption and expresses the potential adopter population met) as b + 1 met) = IIloexp[ -aP(t) ] b + N(t) (5-8) IIlo where a and b are constants, Illo is the initial potential adoption population, pet) is the price at time t, and [(b + 1)/(b + N(t)/Illo)] is the internal effect on the adoption population. Kalish and Lilien Model In addition to questioning the assumption on fixed potential adoption populations M, modelers questioned the assumption of a constant coefficient of innovation (P), and the positive assumption on the imitation influence (q). Kalish and Lilien (1986) developed a model that treated adoption populations as a function of price, related the innovation coefficient (P) to the level of advertising, and allowed for a quality­ varying internal feedback (i.e., positive or negative). The Kalish and Lilien model that incorporated advertising and the possibility of both positive and negative internal feedback is Set) = [N(t)hP(t) - X(t)] {R[A(t)] + J3Q(t)} (5-9) where X(t) is the cumulative adopters at time t, Set) is the new adopter at time t (Le., X[t] - X([t-1]), N(t) is the market potential when price equals zero, pet) is price as a function of time, h is the fraction of market potential that finds price (P[t]) acceptable, A(t) is the external information level in the marketplace (e.g., advertising ,and communication effects), Q(t) is the perceived product quality at time t, R[A(t)] is the market response at t to A(t), and J3 indicates the market response to Q(t). Kalish and Lilien applied this approach to a proposed photovoltaic program sponsored by the U.S. Department of Energy. Evaluation As a general statement, the inclusion of price or a cost-oriented variable affecting the adoption of a new technology is important and merits discussion. First, this allows the cost models presented previously to be directly incorporated into the diffusion model. Second, in models that use a logistic function to estimate market penetration, it is important to have the behavioral response based on market indicators of competitiveness (e.g., the new technology's normalized revenue requirement) and not on just time. Market competitiveness variables arrive at market penetration estimates based on straightforward, competitive market criteria; whereas a time variable represents a collection ofundefmed factors that move relentlessly forward, reflecting an unswerving, positive trend. In his review of solar energy, market penetration models, Warren (1980) states: The assumptions underlying these two distinct representations of a logistic curve are subtle but important. If the horizontal axis measures economic competitiveness, then the behavioral lag represented by the logistic curve is based upon changing economic competitiveness. When the solar technology is only marginally better than the conventional technology, a few innovators will adopt the solar technology. However, as the solar technology becomes more 23 TP-4860 clearly economically superior, a "bandwagon" effect occurs which gradually dissipates as the majority of the market is captured . .. . so that its potential market is defined as that portion of the total market in which it can be competitive. On the other hand if time is used as the measure on the horizontal axis, then the behavioral lag is due to combinations of several factors, including the economic advantage of the solar energy technology, the initial uncertainty, and the extent of the commitment required to adopt the solar energy technology .... thus the potential market is the total market. This distinction is important because almost all empirical evidence in support of the logistic curve relates market penetration to time rather than to economic competitiveness, thus undermining the degree of confidence one can place in solar energy market penetration analysis. Modelers still continue to use Bass' basic model structure, focusing their efforts on making refmements in the model's specification, components, and assumptions. The critical components of diffusion models, in a general sense, are the specification of the potential adopters (M), the coefficient of innovation (P), the coefficient of imitation (q), and the function that defines the product's diffusion over time (F[tD. M, p, and q have already been discussed; let us now focus on F(t). Common functional forms for F(t) are the cumulative normal, logistic, lognormal, and Gompertz functions14 (feotia and Raju 1986). One of the main areas of interest is how F(t) will perform over time (Le., dF/dt). Historically speaking, there are three major criticisms of diffusion models. Diffusion models have been faulted for fixed coefficients of imitation, the maximum rate of penetration occurring at 0.50 of the market and an arbitrary symmetric functional form of dF(t)/dt (Easingwood, Mahajan, and Muller 1983). For ease of comparison, a list of some of the functional forms of various models are presented in Table 5-1. Previously in this section, a model was presented that allowed both the coefficient of innovation and the coefficient of imitation to vary. Table 5-1 clearly indicates that concerns about artificial restriction for symmetry and midpoint inflections are not universally present for diffusion model dF(t)ldt equations. Consequently, although the three concerns were validly held in the past, the current literature has revealed that these problems have been addressed. Even though the problems of restrictive assumptions on adopter populations and the coefficients of innovation and imitation have been addressed in the literature, other problems remain. The discussion of the remaining issues focuses on three problem areas. First, the diffusion of an innovation is independent of all other innovations. Moreover, diffusion models do not consider the simultaneous diffusion of multiple innovations (Mahajan and Peterson 1978). This is a critical shortcoming if the adoption of one innovation depends on the diffusion of another innovation. An example is compact disc software and hardware (Mahajan, Muller and Bass 1990). It is obvious that the rate of diffusion of compact discs is related to the already purchased compact disc players.1s However, standard diffusion models would ignore this linkage. l~e Gompertz function is considered less restrictive than the logistic and lognormal functions (Lakhani 1979). 15 Another example would be the classic razor and razor blade marketing strategy. 24 TP-4860 Section 6: Time-Series Models Time-series models are the logical extension of the following supposition: given that a technology's history spans a workable length of time, an analyst might reasonably entertain the possibility of inferring from its history the path that the technology is most likely to follow in the future (Nelson 1973). It may not be possible to adequately explain the behavior of a time function (yJ by relating Yt to economic variables. This is often the situation when economic data are not available or when the economic data are of sufficiently poor quality that analytically derived results would be suspect. Thus, it may not be desirable to model Yt within a structural econometric model (Pindyck and Rubinfeld 1981). In such a case, time-series analysis may provide a useful alternative. Moreover, time-series analysis can be a useful comparison tool for other analytical methods, such as simultaneous equation systems (Chow 1983). Within a stable system, a number of time-series models could effectively describe the past behavior of time function Yt and be useful in predicting the future behaviors of the same variable. For the purposes of this report, the following five time-series approaches are discussed: • Simple extrapolation models • Autoregressive models • Moving average models • Mixed autoregressive and moving average models • Autoregressive integrated moving average models. Not discussed are the more advanced time-series models such as spectral analysis or time-varying coefficients and their application to time-series modeling.16 The primary reason for the exclusion of the spectral analysis and other advanced models is that these models are data intensive. That is to say, they require extensive data sets. Unfortunately, extensive time-series data sets are not common in the market penetration analysis of new energy technologies. Consequently, these models are not included in this report. The simple extrapolation and autoregressive models can be executed on spreadsheet software (e.g., Lotus 123 and Excel), but the more technically sophisticated models will require more advanced software such as SAS or TSP. Simple Deterministic Extrapolation Models The discussion on simple extrapolation models focuses on two approaches: (1) linear trends and (2) exponential growth models. These are two commonly used models in market penetration analysis. The discussion on linear trends also shows how the linear trend model can be simply extended to address simple nonlinear (Le., quadratic and polynomial) trends.17 These models are usually deterministic. Deterministic models provide point estimates when used for forecasting purposes. Therefore, deterministic models provide no information on the error structure around these forecasted estimates. 16For those interested in spectral analysis or time-varying coefficients, please see Chow (1983). 17Extrapolation methods can also be useful in estimating the values of missing observations in data sets. 27 TP-4860 Linear Trend Models The simplest extrapolation model is the linear trend model. If there is reason to believe that the time function y/8 increases by a constant amount for each time period, and it is believed that this trend will continue into the future, then the analyst can predict future values of Yt by fitting a trend line to the relationship (6-1) where Yt is the value of y at time t, t is a time variable indicator, 30 is a constant, and a1 is the constant absolute relationship over time. The variable t is referred to as a time variable indicator because t is usually set to equal 0 in the base period and allowed to increase by lover each successive period (t = 0, 1, 2, 3, ... , T). In order to predict the value of y one period in the future cr + 1), the analyst simply calculates (6-2) In certain instances, the functional relationship Yt is nonlinear. In these situations, the analyst may fmd a quadratic specification provides a more accurate description of Yt behavior over time. The linear extrapolation method can be extended to a nonlinear quadratic method by simply specifying the relationship as (6-3) where Yt is the value of y at time t, t is a time variable indicator, ao is a constant, a1 is the constant relationship over time, and az is the effect on y from the square of the time indicator. This type of extrapolation can be extended to include higher order polynomials (Yt = 30 + a1t + azt2 + ~f + etc.) with little difficulty. Exponential Growth Curves In market penetration analysis, it may be more reasonable to assume that Yt increases at a constant per­ centage rate rather than at an absolute amount per period.19 If this is the case, then the linear trend model would severely underestimate the future values of y after some time. To avoid this problem, the exponential growth curve method is used.20 The exponential growth curve method is specified as (6-4) where Yt is the value of y at time t, t is a time variable indicator, A and r are constants chosen to maximize the correlation of the relation with Yt over time. If one chooses the exponential growth curve method to forecast, then a forecast of one time period into the future would be given by 18)'t could be defined to be new technology sales or total sales in the market. l~ote: this is not true for higher order polynomials. 2OAnother approach employs a linear model in a double logarithmic specification, Le., a logarithmic autoregressive trend model log Yt = 80 + a1 log Yt-l (Pindyck and Rubinfeld 1981). Autoregressive models are discussed later in this section. 28 TP-4860 Y = Aer(T+I) T+I (6-5) where YT+l is the value of y at time T+ 1, T+ 1 is the time indicator one period in the future, and r and A are defmed the same as for equation (6-4) (pindyck and Rubinfeld 1981). Stochastic Time-Series Models Autoregressive Model Thus far, we have assumed that Yt is only affected by time. The methods presented previously in this section imply that Yt behaves mechanically over time-time being the only exogenous consideration. This implies that once the process has begun, it will continue to operate-Yt continually and systematically responding to the passage of time. Individuals have argued that a more reasonable approach is to examine the economic variables based on the historical performance of the economic variable itself (Nelson 1973). The argument is basically that the factors that affected the economic variable in the past have been captured in the economic variable's market performance. It is then assumed that those factors, which affected the economic variable in the past, will continue to do so in the future. Thus, the argument goes, the future performance of an economic variable can be predicted from its past. This is particularly true for short-term forecasts (Judge et al. 1982). The argument is that structural changes are unlikely to occur in the brief time period under examination. One method that uses the variable's past values is the autoregressive model (AR). The specification for the autoregressive model is . Y =ay +a v + ... +av +e t 1 t-l 2J t-2 P"' t-p t (6-6) where Yt-i is the value of y, i time periods in the past, a;'s are the parameter estimates of the influence on Yt from itself i periods past, Et is the residuals or unexplained variations between what would be predicted by the equation and the actual Yt values. The model presented above is said to be of order p because there are Yt-p past values of Yt used to explain the market performance of Yt21 . The number of past periods selected is determined by what is necessary in order to obtain random residuals, Et. It is desired that the random residuals are serially independent and uncorrelated, having a mean value of zero and constant finite variance for all t (Chow 1983). If the residuals possess these properties, then time-series analysts refer to the residuals as white noise? (Judge et al. 1982). Notice that the autoregressive model23 is no longer deterministic. The inclusion of the residual or error term has changed the modeling process from deterministic to stochastic. 2IThe accepted way to indicate an autoregressive model of order pis AR(P). The p coefficient estimates can be determined through the use of the Yule-Walker equations in a straightforward manner (Pindyck and Rubinfeld 1981). Moreover, autoregressive and moving average techniques are widely recognized, and direct parameter estimation is available via a variety of computer software packages (Judge 1982). 22Jf the residuals are normally distributed, then they are said to be Gaussian white noise. 23 All subsequent models in this section are not deterministic. 29 TP-4860 Section 7: Econometric Models Econometric analysis uses historical data to estimate a functional relationship between a dependent or endogenous variable (e.g., installation of a new technology) and independent or exogenous variable(s) that have an influence (e.g., cost). There are two general approaches to the econometric estimation of market penetration, indirect and direct. The indirect approach consists of three steps. First, a technology is selected and an econometric model is specified to estimate the technology's sales. Second, another econometric model is specified to estimate the total sales of market facing the technology. Finally, the sales of the specific technology is divided by total market sales; the level and degree of market penetration of the technology are calculated. The direct approach estimates the technology's market share using the technology's market share as the dependent variable.26 Although the end results should be the same, the focus and implications of the two approaches are quite different. In the indirect approach, the analyst is attempting to estimate not only the growth of the new technology but the growth of the total industry as well. This approach allows technological and market restrictions or constraints to be placed on total sales or the sales of the new technology. In some instances, it may be important to limit sales within reasonable bounds. The direct approach addresses only the market share of the new technology. The behavior of the total industrial market is left to be developed elsewhere. The indirect approach is directly concerned with the size of the total market; the direct approach requires the size of the total market to be determined exogenously. There are numerous ways of econometrically addressing these two approaches. Basically, one can break down the various econometric approaches into two sets of two mutually exclusive categories. Set one consists of linear and nonlinear models. The second set is composed of single and simultaneous equation systems. Space does not permit an exhaustive review of all of the econometric techniques that may be applicable to market penetration analysis. Therefore, it was necessary to restrict the number of econometric techniques discussed. Selection of the reviewed econometric methods was based on approaches that were commonly used or methods that, with little effort, could be included in the menu of econometric approaches used to estimate market penetration. The following econometric techniques will be discussed in this section: • Ordinary least squares • Dummy variable technique • Generalized least squares • Nonlinear regression • Two-stage least squares • Seemingly unrelated regressions. 26Please see the Blackman model in Section 5. 32 TP-4860 Econometrics is a combination of economic theory and statistics. The analyst uses the economic theory to hypothecate a functional relationship between a dependent variable and a set of independent variables.27 Statistical methods are then used to estimate the quantitative parameters in the function (EPRI 1982). Ordinary least-squares can be found in most spreadsheet software. However, the more sophisticated econometric techniques will require advanced statistical software packages such as SAS. The use of econometric methods is a well-defined practice and allows for the employment of a large store of diagnostic tools. Generally, econometric analysis is used to develop an equation that can be used in some predictive capacity. These estimated values are compared to actual values, and residuals are calculated. The existence of a disturbance term implies that econometrics is a stochastic process. Thus, uncertainty can be treated explicitly, and confidence intervals can be calculated around predicted values. The main drawback of econometric analysis is that the data requirements can be significant. Market penetration forecasting using econometric analysis generally includes four steps: (1) identification, (2) specification, (3) estimation, and (4) prediction. The first step requires the identification of the exogenous factors affecting the variable under examination. The second step requires the analyst to specify the relationship between the dependent and independent variable (e.g., a linear or nonlinear relationship). The third step requires the estimation of the parameter coefficients of the independent variables, which enumerates the relationship between the endogenous and exogenous variables. Finally, the parameter coefficients are used with forecasted independent variables to predict the future behavior of the dependent variable (EPRI 1982). One of the primary concerns in econometric analysis is the acquisition of the most efficient, unbiased, and consistent coefficients for use in estimation and prediction. Of fundamental importance in the estimation of the most unbiased and consistent estimators is the characteristics of the residual or disturbance terms. In general, the desired characteristics of the error terms are that they have a zero mean (E[e] = 0),28 a constant variance (<T~,29 and are uncorrelated to each other> (Kennedy 1983). A good deal can be learned about the various econometric methods by examining the error structure. When appropriate, the discussion of a particular econometric method will also include a discussion of a particular problem in the disturbance terms-a problem that the econometric technique was designed to account for or correct. Ordinary Least Squares The simplest econometric technique is univariate ordinary least squares. In this method, the dependent variable (yJ is linearly related to an independent variable (xJ. For example, one can hypothecate that an individual's consumption is a function of his or her income. The univariate ordinary least squares functional form is expressed as T1 A set could consist of only one independent variable. 28Jf E[e] ¢ 0 then a systematic bias is said to exist. 29for example, there exists a homoskedastic residual structure. 3Opor example, autocorrelation does not exist. 33 TP-4860 (7-1) where Yt is the dependent variable, :lCt is the independent variable, O! is a constant, and III is the constant linear relationship between the dependent variable and the independent variable. The unexplained residuals are the differences between what the specified relationship estimates the value of the dependent variable to be and what the dependent variable's actual value is. The parameter coefficients O! and Il are obtained by selecting values that minimize the sum of the square of the residuals, hence, the name "least squares." The accuracy of the prediction will be based on how small the deviation between the actual and the estimated dependent variable can be. The typical reasons why error terms are said to exist are: (1) leaving out important variables from the equation, (2) the unpredictable behavior of people, (3) varying behavior among individuals, and (4) errors of measurement (Kelejian and Oates 1981). The understanding of the ordinary least squares or linear regression technique is sometimes aided by a graphical illustration. Figure 7-1 illustrates a univariate linear regression. y • • •• ..... . . . rr· • • • • •••••• • • • • •• • • • Figure 7-1. Ordinary least squares regression 34 • x TP-4860 y • • x Figure 7-2. Nonlinear regression An alternative nonlinear estimation approach is one used in the logit probability model. (The logit function is shown in Figure 7-3.) The logit model is based on the cumulative probability function Pi = F(Z) = F(a + (jX) = __ 1~ 1 + e -cz.) 1 = ------,--1 + e -(ex + f3X.) (7-7) where Pi is the probability that a corporation will make a certain choice given knowledge of Xi (Pindyck and Rubinfeld 1981). Let expression 7-7 represent a certain probability of choosing an alternative given an existing cost structure _ ri p. -- 1 n. 1 (7-8) where Pi is the approximate probability of choice P(i) for each identical group, rj equals the number of times the first alternative is chosen by corporations with costs of i, and II; is the number of corporations with costs of i. 37 TP-4860 The logit probability model can be expressed in semi-logarithmic form as r. (...:) p. n. r. log , = log--' - = log , 1 - Pi (1 _ (ri) (ni - ri) = Q( + (3X. + 8. , , (7-9) ni where Pi is the approximate probability of choice P(i), ri equals the number of times the first alternative is chosen by corporations with costs of i, Il; is the number of corporations with costs of i, Q( is a constant, {3 is the parameter estimate on the effects of corporate costs, X; is the corporate costs of firm i, and €i is the error term (pindyck and Rubinfeld 1981). Market Share 1 o Market Variable Figure 7-3. Logit function 38 TP-4860 Two-Stage Least Squares Thus far, only single equation systems have been discussed. In single equation systems, each equation is estimated individually. Single equation systems use only the information provided by that particular relationship or equation (Maddala 1977). Situations can occur in which the dependent variables are determined by the simultaneous interaction of several relationships. If this is the case, then a one-equation model is insufficient to estimate the actual relationships between the dependent and independent variables, and simultaneous equation estimation is indicated (Kennedy 1983). This commonly occurs when estimating market phenomena. Often it is insufficient to only estimate the demand for a product or technology. Market interactions between supply and demand are often missed if the analysis is only focused on demand or supply. A preferable approach would be to model both supply and demand in a simultaneous system, thereby using all of the market information available in the estimation procedure. Over the years, econometricians have developed a number of techniques to address problems with simultaneous equation systems. The approach discussed here is two-stage least squares (2SLS). There were four reasons 2SLS was chosen to be presented here. First, 2SLS is easily understood and intuitively appealing. Second, if an equation system can be estimated, 2SLS will provide consistent estimates of the estimated parameter coefficients. Third, 2SLS makes relatively modest demands on computer time (Kelejian and Oates 1981). Finally, 2SLS is a recognized approach that is commonly included in statistical packages found in computer software. The 2SLS procedure uses the information available from the specification of the equation system to obtain estimates for each structural parameter. In the first stage, the 2SLS procedure involves the creation of an instrument, while, in the second stage, 2SLS uses that instrument to calculate the structural parameters. Let there be a market system such that the structural model for the demand and supply of a new technology can be specified36 as (7-10) (7-11) where <1 is the amount of a new technology in the market at time t, ex and {3i'S are estimated parameter coefficients, Pt is the price for Q at time t, ~ is the amount of corporate profit at time t, Wt is another independent variable (e.g., demand for the finished corporate product), and f.Lt is the error term. Before the 2SLS procedure can be initiated, it is necessary to specify the previous two equations in reduced form. Through mathematical manipulation, the reduced form develops a separate equation for 36rfhe approach illustrated here was adopted from Pindyck and Rubinfeld (1981). 39 TP-4860 variables; therefore, econometric analysis possesses the ability to address market issues beyond the scope of other forms of analysis. Econometric models are stochastic. Therefore, uncertainty analysis and confidence interval construction is possible. The main and, in some instances, crippling drawback to econometric analysis is that some forms of econometric analysis have significant and demanding data requirements. 42 TP-4860 Section 8: Summary and Conclusions This report examined a broad spectrum of market penetration analysis techniques. Discussed were various aspects of subjective estimation methods, market surveys, historical analogy models, cost models, diffusion methods, time-series techniques, and econometric procedures. In examining these techniques, it became evident that no one market penetration method is a panacea. The choice of market penetration method is, in part, controlled by the available data. The data available for RET market penetration analysis is not uniform. Consequently, analysts must be flexible in their choice of models and be aware of the market penetration methodologies available. The market penetration technique selected should be the one that utilizes the available knowledge to the fullest. In some instances, this may necessitate combining a number of methods. For example, it may be necessary (because of lack of specific data) to use subjective estimates in cost methods incorporated in diffusion models. In general, stochastic models are preferred over deterministic models because they are more accurate, possess the ability to address uncertainty and confidence intervals, and allow for statistically valid diagnostic review and the objective determination of model design. However, when there exists a dearth of information, there exists a useful role for deterministic analysis, historical analogy methods, market surveys, and subjective judgments. This report was designed to review market penetration models to help develop understanding of the market penetration studies for RETs. Seven broad categories, with more than 30 different models, methods, or techniques were covered. This was done to provide the reader with the necessary broad base to make informed decisions or judgments. In a continuation of this effort, this report includes an extensive bibliography. This bibliography was carefully chosen to provide the reader with an up-to-date, well-rounded selection of material on market penetration. Moreover, articles and books on specific topic areas outside the purview of market penetration analysis, but tangentially related to it, are also included (e.g., small-sample properties of econometric techniques [Summers 1965]). 43 TP-4860 References Au, Tung and Thomas P. Au. 1983. Engineering Economicsfor Capital Investment Analysis. Boston: Allyn and Bacon. Bass, Frank M. 1969. "A New Product Growth Model for Consumer Durables." Management Science. 15:215-227. Blackman, A. Wade, Jr. 1974. "The Market Dynamics of Technological Substitutions." Technological Forecasting and Social Change. 6:41-63. Box, G. E. P. and G. M. Jenkins. 1976. Times Series Analysis: Forecasting and Control. Rev. ed., San San Francisco: Holden-Day. Brown, Robert J. and Rudolph R. Yanuck. 1980. Life-Cycle Costing: A Practical Guide for Energy Managers. Atlanta: Fairmont Press Inc. Charles River Associates Inc. 1986. CapitalBudgetingfor Utilities: The Revenue Requirements Method. EPRI Research Project EA-4879, Palo Alto: Electric Power Research Institute. 1920-3-1. Chow, G. C. 1965. "Review of the Growth of Television Ownership in the United Kingdom Since the War: A Lognormal Model by A. P. Bain." Econometrica. 33:657-659. Chow, Gregory C. 1983. Econometrics. New York: McGraw-Hill. Easingwood, Christopher, Vijay Mahajan, and Eitan Muller. 1981. "A Nonsymmetric Responding Logistic Model for Forecasting Technological Substitution." Technological Forecasting and Social Change. 20: 199-213. Easingwood, Christopher J., Vijay Mahajan, and Eitan Muller. 1983. "A Nonuniform Influence Innovation Diffusion Model of New Product Acceptance." Management Science. 2(3):273-295. Electric Power Research Institute (EPRI). October 1982. Methodsfor Analyzing the Market Penetration of End-Use Technologies: A Guide for Utility Planners. EA-2702. Palo Alto, CA: Electric Power Research Institute. Electric Power Research Institute (EPRI). 1987. 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