Showing papers in "Journal of Productivity Analysis in 2004"
TL;DR: In this paper, a metafrontier production function model for firms in different groups having different technologies is presented, which enables the calculation of comparable technical efficiencies for firms operating under different technologies.
Abstract: This paper presents a metafrontier production function model for firms in different groups having different technologies. The metafrontier model enables the calculation of comparable technical efficiencies for firms operating under different technologies. The model also enables the technology gaps to be estimated for firms under different technologies relative to the potential technology available to the industry as a whole. The metafrontier model is applied in the analysis of panel data on garment firms in five different regions of Indonesia, assuming that the regional stochastic frontier production function models have technical inefficiency effects with the time-varying structure proposed by Battese and Coelli ( 1992).
1,133 citations
TL;DR: In this paper, the same period frontier is defined for both the adjacent and the base period Malmquist index and for all suggested definitions of same-period frontier, and it is shown that the standard decomposition into frontier shift and catching up effects gives inappropriate results when using DEA window analysis scores.
Abstract: The banking industry in Canada is essentially an oligopoly with five large participants controlling about 90% of the market. To evaluate the industry's performance over time, we need to deal with the problem of a small number of DMU's compared to the number of relevant inputs and outputs. To overcome this problem we use data envelopment analysis (DEA) window analysis, whereby efficiency scores for the 20 year period 1981–2000 are obtained. To measure productivity changes over time, Malmquist indices can be calculated from DEA scores. Using DEA window analysis scores, however, raise the question of how to define the “same period frontier” in a DEA window analysis. We show that for both the adjacent and the base period Malmquist index and for all suggested definitions of same period frontier, the standard decomposition into frontier shift and catching up effects gives inappropriate results when Malmquist indices are based on DEA window analysis scores.
336 citations
TL;DR: In this paper, the authors investigate the consistency of efficiency frontier methods on European banking samples and conclude that the lack of robustness between approaches, even if there are some similarities in particular between parametric approaches, indicates that there is some correlation between all frontier approaches and standard measures of performance.
Abstract: This paper investigates the consistency of efficiency frontier methods on European banking samples. We measure the cost efficiency of banks from five European countries (France, Germany, Italy, Spain, Switzerland) with three approaches: stochastic frontier approach, distribution-free approach, and data envelopment analysis. We compare means, correlation coefficients, two public policy issues, and the correlation with standard measures of performance. In general, we conclude in favor of the lack of robustness between approaches, even if there are some similarities in particular between parametric approaches. We do, however, observe some correlation between all frontier approaches and standard measures of performance.
293 citations
TL;DR: In this article, two new DEA models are presented for resource allocation in an intra-organizational scenario, where the DM has an interest in maximizing the efficiency of individual units at the same time that total input consumption or total output production is maximized.
Abstract: While conventional DEA models set targets separately for each DMU, in this paper we consider that there is a centralized decision maker (DM) who “owns” or supervises all the operating units. In such intraorganizational scenario the DM has an interest in maximizing the efficiency of individual units at the same time that total input consumption is minimized or total output production is maximized. Two new DEA models are presented for such resource allocation. One type of model seeks radial reductions of the total consumption of every input while the other type seeks separate reductions for each input according to a preference structure. In both cases, total output production is guaranteed not to decrease. The two key features of the proposed models are their simplicity and the fact that both of them project all DMUs onto the efficient frontier. The dual formulation shows that optimizing total input consumption and output production is equivalent to finding weights that maximize the relative efficiency of a virtual DMU with average inputs and outputs. A graphical interpretation as well as numerical results of the proposed models are presented.
285 citations
TL;DR: In this paper, the relationship between cost inefficiency and profitability in the U.S. life insurance industry was explored using the stochastic frontier (SF) method allowing the mean inefficiency to vary with organizational form and the outputs.
Abstract: This study explores the relationship between cost inefficiency and profitability in the U.S. life insurance industry. Earnings have particular importance to life insurance companies because earnings and capital determine the viability of the insurer. Since the life insurance industry is mature and highly competitive, cost efficiency may be the main driver of profitability. We derive cost efficiency using the stochastic frontier (SF) method allowing the mean inefficiency to vary with organizational form and the outputs. In addition, the estimation of the cost efficiency measure takes into account the underlying accounting concepts that generate the data and, consequently, the product mix (long-duration policies vs. short-duration policies) to avoid distorted estimates. Our results suggest that cost inefficiency in the life insurance industry is substantial relative to earnings, and that inefficiency is negatively associated with profitability measures such as the return on equity. The analysis of inefficiency and organizational form suggest that stock (shareholder-owned) companies are as efficient and profitable as mutual (policyholder-owned) companies.
205 citations
TL;DR: This paper examined the economic performance of U.S. farms to explore the potential of smaller farms to compete with larger entities, and ultimately to survive in a rapidly changing environment, using deterministic and stochastic frontier methods and survey data.
Abstract: The structural transformation of agriculture in recent decades has raised serious concerns about the future of the family farm. This study examines the economic performance of U.S. farms, to explore the potential of smaller farms to compete with larger entities, and ultimately to survive in this rapidly changing environment. We use deterministic and stochastic frontier methods and survey data to measure and evaluate factors underlying scale economies (SEC) and efficiency (SEF) of corn-belt farms for 1996–2001. Our results suggest that family farms are both scale and technically inefficient. Potential for the exploitation of significant scale and scope economies, and some greater technical efficiency, seem to be driving trends toward increased farm size and dwindling competitiveness of the small family farm.
172 citations
TL;DR: In this article, the authors introduce the concept of worst practice DEA, which aims at identifying worst performers by placing them on the frontier, where the worst performers are where the largest improvement potential can be found.
Abstract: The purpose of this paper is to introduce the concept of worst practice DEA, which aims at identifying worst performers by placing them on the frontier. This is particularly relevant for our application to credit risk evaluation, but this also has general relevance since the worst performers are where the largest improvement potential can be found. The paper also proposes to use a layering technique instead of the traditional cut-off point approach, since this enables incorporation of risk attitudes and risk-based pricing. Finally, it is shown how the use of a combination of normal and worst practice DEA models enable detection of self-identifiers. The results of the empirical application on credit risk evaluation validate the method. The best combination of layered normal and worst practice DEA models yields an impressive 100% bankruptcy and 78% non-bankruptcy prediction accuracy in the calibration data set, and equally convincing 100% and 67% out-of-sample classification accuracies.
143 citations
TL;DR: In this paper, the relationship between worker characteristics and productivity was examined using a matched worker-plant data set from Finnish manufacturing, where the panel data were used for estimating productivity and wage profiles according to average age, seniority, and education.
Abstract: The relationships of worker characteristics and productivity are examined using a matched worker-plant data set from Finnish manufacturing The panel data are used for estimating productivity and wage profiles according to average age, seniority, and education We measure productivity using the multilateral total factor productivity index We find that the wage returns to plant-specific seniority exceed productivity returns when seniority is high This result supports the hypothesis that human capital is not firm specific, and seniority related wages are used for incentive reasons, but may also be a symptom of sorting or insider influences on wage formation Plant average age improves productivity more than it increases wage when average age is low, but for higher ages the productivity and wage returns to age are fairly similar The returns to education in terms of wage and productivity are fairly close to each other for higher levels of education, but mid-level education is underpaid
114 citations
TL;DR: In this article, the effect of pesticides on the value of the marginal product of productive inputs is investigated in order to analyze technical interdependence between pesticides and productive inputs, which suggest substantial under-utilization of pesticides, which is consistent with earlier findings of parametric specifications.
Abstract: Many previous empirical studies on the productivity of pesticides suggest that pesticides are under-utilized in agriculture despite the general held believe that these inputs are substantially over-utilized. This paper uses data envelopment analysis (DEA) to calculate non-parametric measures of the value of the marginal product of pesticides. Furthermore, the effect of pesticides on the value of the marginal product of productive inputs is investigated in order to analyze technical interdependence between pesticides and productive inputs. Results suggest, in general, substantial under-utilization of pesticides, which is consistent with earlier findings of parametric specifications.
83 citations
TL;DR: In this paper, a flexible stochastic frontier model with random coefficients is proposed to distinguish technical inefficiency from technological differences across firms, which is made possible via the simulation-based approach, namely, Markov chain Monte Carlo method.
Abstract: This paper considers the measurement of firm's specific (in)efficiency while allows for the possible heterogeneous technologies adopted by different firms. A flexible stochastic frontier model with random coefficients is proposed to distinguish technical inefficiency from technological differences across firms. Posterior inference of the model is made possible via the simulation-based approach, namely, Markov chain Monte Carlo method. The model is applied to a real data set which has also been considered in Christensen and Greene (1976), Greene (1990), Tsionas (2002), among others. Empirical results show that the regression coefficients can vary across firms, indicating the adoption of heterogeneous technologies by different firms. More importantly, we find that, without considering this possible heterogeneity, the inefficiency of firms can be over-estimated.
73 citations
TL;DR: This work proposes to incorporate reverse inputs and outputs into a DEA model by returning to the basic principles that lead to the DEA model formulation, and compares the method to reverse scoring, the most commonly used approach, and demonstrates the relative advantages of the proposed technique.
Abstract: Data envelopment analysis (DEA) assumes that inputs and outputs are measured on scales in which larger numerical values correspond to greater consumption of inputs and greater production of outputs. We present a class of DEA problems in which one or more of the inputs or outputs are naturally measured on scales in which higher numerical values represent lower input consumption or lower output production. We refer to such quantities as reverse inputs and reverse outputs. We propose to incorporate reverse inputs and outputs into a DEA model by returning to the basic principles that lead to the DEA model formulation. We compare our method to reverse scoring, the most commonly used approach, and demonstrate the relative advantages of our proposed technique. We use this concept to analyze all 30 Major League Baseball (MLB) organizations during the 1999 regular season to determine their on-field and front office relative efficiencies. Our on-field DEA model employs one output and two symmetrically defined inputs, one to measure offense and one to measure defense. The defensive measure is such that larger values correspond to worse defensive performance, rather than better, and hence is a reverse input. The front office model uses one input. Its outputs, one of which is a reverse output, are the inputs to the on-field model. We discuss the organizational implications of our results.
TL;DR: In this article, the authors investigate if neoclassical production theory gives any guidance as to the nature of scale properties in the DEA model, and empirically explore such properties empirically.
Abstract: Policy recommendations concerning optimal scale of production units may have serious implications for the restructuring of a sector. The piecewise linear frontier production function framework (DEA) is becoming the most popular one for assessing not only technical efficiency of operations, but also for scale efficiency and calculation of optimal scale sizes. The main purpose of the present study is to investigate if neoclassical production theory gives any guidance as to the nature of scale properties in the DEA model, and empirically explore such properties. Theoretical results indicate that the DEA model may have more irregular properties than usually assumed in neoclassical production theory, concerning shape of optimal scale curves and the M-locus. The empirical results indicate that optimal scale may be found over almost the entire size variations in outputs and inputs, thus making policy recommendations about efficient scale difficult. It seems necessary to establish the nature of optimal scale before any practical conclusions can be drawn. Proposals for indexes characterizing the nature of optimal scale are provided.
TL;DR: In this paper, the authors developed separate mix and scale measures of dissimilarity, and showed that these can be additively aggregated into a measure of absolute dissimilarities, which is particularly relevant in the context of frontier analysis since the firms that exert the most influence on the resulting efficiency scores.
Abstract: A firm may be different from other firms either in terms of the mix or scale of its input-output vector. This paper develops separate mix and scale measures of dissimilarity, and shows that these can be additively aggregated into a measure of absolute dissimilarity. The mix measure is particularly relevant in the context of frontier analysis since it will identify the firms that exert the most influence on the resulting efficiency scores.
TL;DR: The authors proposed an approach to measure hospital performance based on a generalization of Banker and Morey (1986) and Forsund (1996), which considers quasi-fixed inputs explicitly, calculates their implicit cost, and quantifies returns to scale.
Abstract: This research proposes an approach to measure hospital performance based on a generalization of Banker and Morey (1986) and Forsund (1996). This approach considers quasi-fixed inputs explicitly, calculates their implicit cost, and quantifies returns to scale. The performance measure is decomposed into allocative and technical inefficiencies. Based on a very complete data set of Quebec hospitals, we find that significant inefficiencies of up to 17% ($700 CAN million) could have been saved through improved performance. Postestimation analyses that include qualitative measures of care suggest that differences in performance are attributable to differences in management or unobservable quality of care rather than patient case mix.
TL;DR: In this paper, the authors focus on the importance of the assumptions regarding how inefficiency should be incorporated into the specification of the data generating process in an examination of a sector's production or efficiency.
Abstract: We focus on the importance of the assumptions regarding how inefficiency should be incorporated into the specification of the data generating process in an examination of a sector's production or efficiency. Drawing on the literature on non-nested hypothesis testing, we find that the model selection approach of Vuong (1989) is a potentially useful tool for identifying the best specification before carrying out such studies. We include an empirical application using panel data on Spanish dairy farms where we estimate cost frontiers under different specifications of how inefficiency enters the data generating process (in particular, efficiency is introduced as an input-oriented, output-oriented and hyperbolic parameter). Our results show that the different models yield very different pictures of the technology and the efficiency levels of the sector, illustrating the importance of choosing the most correct model before carrying out production and efficiency analyses. The Vuong test shows that the input-oriented model is the best among the models we use, whereas the output-oriented model is the worst. This is consistent with the fact that the input- and output-oriented models provide the most and least credible estimates of scale economies given the structure of the sector.
TL;DR: A concept of global returns to scale (GRS) is developed as an indicator of the direction in which the most productive scale size (MPSS) of an efficient DMU is achieved.
Abstract: In a production technology, the type of returns to scale (RTS) associated with an efficient decision making unit (DMU) is indicative of the direction of marginal rescaling that the DMU should undertake in order to improve its productivity. In this paper a concept of global returns to scale (GRS) is developed as an indicator of the direction in which the most productive scale size (MPSS) of an efficient DMU is achieved. The GRS classes are useful in assisting strategic decisions like those involving mergers of units or splitting into smaller firms. The two characterisations, RTS and GRS, are the same in a convex technology but generally different in a non-convex one. It is shown that, in a non-convex technology, the well-known method of testing RTS proposed by Fare et al. is in fact testing for GRS and not RTS. Further, while there are three types of RTS: constant, decreasing and increasing (CRS, DRS and IRS, respectively), the classification according to GRS includes the fourth type of sub-constant GRS, which describes a DMU able to achieve its MPSS by both reducing and increasing the scale of operations. The notion of GRS is applicable to a wide range of technologies, including the free disposal hull (FDH) and all polyhedral technologies used in data envelopment analysis (DEA).
TL;DR: In this article, the authors advocate the use of the implicit Tornqvist quantity index to measure real GDP and find that the Laspeyres quantity index still used by the statistical agencies of most countries tends to underestimate real growth.
Abstract: Recently much attention has been devoted to superlative indexes in the context of the national accounts. In this paper we advocate the use of the implicit Tornqvist quantity index to measure real GDP. This index, which has been proposed by Diewert and Morrison (1986), has never received serious consideration in the literature. Yet, compared to the better-known Fisher index, the implicit Tornqvist index of real GDP has a number of advantages. Thus, it can be shown to be exact for the Translog GDP function, it allows for a complete multiplicative decomposition of nominal and real GDP, and it is consistent with state-of-the-art measures of total factor productivity that typically rely on the Tornqvist aggregation. Estimates for a sample of 26 countries are reported. We find that the Laspeyres quantity index still used by the statistical agencies of most countries tends to underestimate real growth. Over the 1960–1996 period, the cumulated shortfall was as much as 13.4% of GDP in the case of Japan.
TL;DR: In this paper, Data Envelopment Analysis (DEA) is used to identify congestion when the data show it to be present, estimate its amounts, and separate it from other forms of inefficiency.
Abstract: This paper deals with identifying and managing congestion. For this purpose, DEA (Data Envelopment Analysis) is used to identify congestion when the data show it to be present, estimate its amounts, and separate it from other forms of inefficiency. DEA is also used to identify where improvements may be made in the management of congestion and to estimate input decreases and output increases that may be made after managerial inefficiencies in managing congestion are eliminated. The treatment here differs from the usual approaches that are restricted to identifying sources and amounts of technical inefficiency and congestion to be eliminated. The focus is directed rather to efficiency of performances in the presence of inefficiencies imposed by, say, labor contracts or government regulations and policies. Other developments include a use of rates of substitution formulated in terms of slack variables that help to avoid instabilities associated with the very small values that are often encountered in the use of dual variables to determine the rates of substitution. These rates of substitution are intended for use in guiding allocations (or reallocations) of inputs between different plants (or other entities) in ways that can further improve performance without reducing the congesting inputs that are to be employed. Hence modifications are needed to extend the usual restrictions to movements on the efficiency frontier so that frontiers associated with congestion and other inefficiencies can be dealt with.
TL;DR: This paper measured structural changes as statistically significant breaks in either stochastic or deterministic time trends, and applied these measures to agricultural productivity and research and found that productivity has a break in 1925 accompanying agriculture's early experience with the Great Depression.
Abstract: Previous work on structural change in agriculture has failed to distinguish long-run trends from structural breaks leading to new trends. We measure structural changes as statistically significant breaks in either stochastic or deterministic time trends, and apply these measures to agricultural productivity and research. Productivity has a break in 1925 accompanying agriculture’s early experience with the Great Depression. Research trends shifted in 1930 as the Depression and new technology began to strongly influence efficient farm size and capitalization. After modeling lags between research and productivity impacts in a vector autoregression (VAR), we compare our results to earlier work by developing a procedure to estimate the rate of return to research from the impulse response function of the VAR.
TL;DR: In this paper, the authors explore an intermediate route between the Fisher and the Malmquist productivity indexes so as to minimize data requirements and assumptions about economic behavior of production units and their production technology.
Abstract: This paper explores an intermediate route between the Fisher and the Malmquist productivity indexes so as to minimize data requirements and assumptions about economic behavior of production units and their production technology. Assuming quantity data of inputs and outputs and the behavioral hypothesis of allocative efficiency, we calculate the exact value of the Fisher ideal productivity index using implicit shadow prices revealed by the choice of input–output mix. The approach is operationalized by means of a nonparametric data envelopment analysis (DEA) model. Empirical application to Finnish grass silage farms suggests that the Malmquist and the Fisher productivity indices yield similar results when averaged over firms, but there can be major differences in the results of the two approaches at the level of individual firms.
TL;DR: In this paper, the Fourier flexible cost function is used to construct a more general function form than the typical translog form, which can globally approximate a true (but unknown) cost function.
Abstract: The current paper constructs a Fourier flexible cost function, which is commonly known to be a more general function form than the typical translog form, and can globally approximate a true (but unknown) cost function. Both allocative and technical inefficiencies are considered using the Fourier function in the context of the parametric approach. The former is modeled using shadow input prices and the latter is formulated either by adding an extra term of scale parameter (when the Farrell's (1957) input technical inefficiency is assumed), or by correcting all the terms involving output quantities by a scale parameter (when the Farrell's output technical inefficiency is assumed). It is found that sample banks could save up to 23% of total costs, within the range of 3 and 69% uncovered by the previous works, in which allocative inefficiency plays a more important role than technical inefficiency. Furthermore, the cost of misallocated labor input alone constitutes more than 80% of total allocative inefficiency. Financial deregulation starting from 1991 in Taiwan appears to have improved economic efficiency of the banking industry.
TL;DR: In this paper, the authors evaluate the impact of technological opportunity on the productivity of R&D activities in three global industries, namely, chemical, computer, and electrical/electronic.
Abstract: Economists have managed to find a positive impact of R&D efforts on productivity. However, the empirical results of their studies have not explained the observed sectoral differences in this important impact. With due reference to three global industries, namely, chemical, computer, and electrical/electronic, the objective of this study is to evaluate the impact of technological opportunity on the productivity of R&D activities. Technological opportunity refers to the ease of achievement of innovations and technical improvements, which could be jointly represented by the intensities of knowledge spillovers, inter-firm research overlap and scope of research. In this study, the degree of technological opportunity is quantified by patent statistics. The empirical findings confirm a positive relationship between technological opportunity and the productivity of R&D effort, and the estimated rate of return falls within the range as reported by past studies.
TL;DR: In this article, a new procedure for the measurement of efficiency and technical change is presented, using DEA with three-dimensional data (box data), pooling over sectors, regions and time.
Abstract: A new procedure for the measurement of efficiency and technical change is presented, using DEA with three-dimension data (box data), pooling over sectors, regions and time. Until now, when pooling the data in panel applications it has been assumed that technology remained unchanged, so productivity change was entirely attributed to technical efficiency change. However, patterns of technology change and the decomposition into efficiency and technical change elements can be accomplished by means of restrictions on the general structure of the technology indexes. Under the assumption of non-regressive technical change, upper and lower bounds for efficiency and technical change are obtained. The new methodology is illustrated in an analysis of productivity growth in 13 manufacturing sectors in the Spanish regions from 1980 to 1992.
TL;DR: In this paper, a fuzzy clustering strategy is used to identify influential subsets without knowing which production plans are outliers a priori, and dominance is assessed in terms of the degree of belonging of a production plan in an influential subset.
Abstract: The identification of influential subsets in efficiency studies is an ongoing research concern. Seaver et al. (1999) have demonstrated the value of using a fuzzy clustering strategy to identify influential subsets without knowing which production plans are outliers a priori. From a fuzzy clustering perspective, dominance is assessed in terms of the degree of belonging of a production plan in an influential subset. From a production point of view, dominance is assessed in terms of pair-wise comparisons. These concepts of dominance within influential subsets are illustrated using the preprint insertion data set (Girod, 1996).
TL;DR: This article examined the role of imperfect competition in determining total factor productivity growth (TFPG) by bringing together a New Empirical Industrial Organization (NEIO) model and the TFPG model of Good, Nadiri and Sickles (1999).
Abstract: This article examines the role of imperfect competition in determining total factor productivity growth (TFPG) by bringing together a New Empirical Industrial Organization (NEIO) model and the TFPG model of Good, Nadiri and Sickles (1999). Application of the integrated model to 1973–1992 data from 29 food processing industries revealed that, overall, changes in markups, economies of scale, and demand growth contributed positively to TFPG while the disembodied technical change was a negative contributor. Furthermore, the factors underlying the TFPG estimates are interactive and their net effects are starkly different from the conventional Solow (1957) residual TFPG measures, underscoring the need to account for imperfect competition, returns to scale, and demand growth in analyses of this type.
TL;DR: In this article, the authors explored why the shares of factor inputs have not been measured correctly and concluded that the earlier findings are biased due to the miscalculation of factor shares which have produced low estimated total factor productivity (TFP) growth in the East Asian countries.
Abstract: This study first explores why the shares of factor inputs have not been measured correctly and concludes that the earlier findings are biased due to the miscalculation of factor shares which have produced low estimated total factor productivity (TFP) growth in the East Asian countries. Second, three approaches are proposed to empirically illustrate the impact of capital and labor shares on the estimates of TFP growth. It is suggested that TFP growth in the East Asian economies will be understated if net indirect taxes and imperfect competition profit are ignored. Finally, by taking the net indirect taxes and imperfect competition profits into account, the result of this paper indicates that Taiwan’s economy has enjoyed an average annual TFP growth rate of 3.6% over the period 1980–1999.
TL;DR: In this paper, the authors examined the dramatic change in production technology of the U.S. ocean liner shipping industry over the period 1971 through 1982 using panel data on 15 subsidized US.-flag liner firms.
Abstract: this study examines the dramatic change in production technology of the U.S. ocean liner shipping industry over the period 1971 through 1982 using panel data on 15 subsidized U.S.-flag liner firms. To estimate the changes in the production function due to the new technology, the switching regime method of Goldfeld and Quandt is applied to a translog variable profit function. Three regimes based on the proportion of the new technology reflected in a firm's fleet are identified. The constant returns to scale fleet size more than doubles across the three regimes.
Journal Article•
TL;DR: In this paper, the authors explore an intermediate route between the Fisher and the Malmquist productivity indexes so as to minimize data requirements and assumptions about economic behavior of production units and their production technology.
Abstract: This paper explores an intermediate route between the Fisher and the Malmquist productivity indexes so as to minimize data requirements and assumptions about economic behavior of production units and their production technology. Assuming quantity data of inputs and outputs and the behavioral hypothesis of allocative efficiency, we calculate the exact value of the Fisher ideal productivity index using implicit shadow prices revealed by the choice of input?output mix. The approach is operationalized by means of a nonparametric data envelopment analysis (DEA) model. Empirical application to Finnish grass silage farms suggests that the Malmquist and the Fisher productivity indices yield similar results when averaged over firms, but there can be major differences in the results of the two approaches at the level of individual firms.
TL;DR: In this paper, a new index number formula was proposed for the constant-elasticity-of-substitution (CES) function, which can be computed by simply substituting available prices and quantities into a known exact functional form.
Abstract: Introduction of new products into the market place poses a difficult problem for the calculation of a cost-of-living (COL) index. The problem is that the reservation prices of new products in the periods before their introduction are unobservable. This paper introduces a new index number formula that overcomes the problem. It is exact for the constant-elasticity-of-substitution (CES) function. Unlike the one introduced to the literature by Feenstra (1994), for which the elasticity of substitution has to be estimated using a separate econometric model, the new index can be computed by simply substituting available prices and quantities into a known exact functional form. The new index number formula is illustrated with the data used in Feenstra (1994).