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Estimating an economic-efficient frontier for dishwasher consumer choice

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Abstract

Dishwashers are a ubiquitous appliance in households in the USA. They combine capital, energy, and water to provide a relevant household service, namely dishwashing. The economic efficiency of dishwashers has been previously assessed using data envelopment analysis (DEA). The approach addresses the technical efficiency of dishwashers based on possible trade-offs between capital and energy. It further draws from the technical efficiency scores an efficient frontier for dishwashing based on these two input factors. We argue that water could also be a relevant input factor to that frontier, especially from the perspective of consumer choice. We develop a DEA model that includes water as an additional input and test if adding water to the analysis contributes to the efficiency frontier. We find that water does have some effect on the frontier, as the DEA model that includes water as an input factor leads to a richer set of efficient possibilities for dishwashing, where energy and water are traded off. We rely on our method and findings to propose two approaches to inform dishwasher consumer choice. One is extending an energy label to include dishwasher water consumption, as a means to inform consumers on their possible trade-offs between energy and water consumption at different levels of appliance price and quality. The other one is disclosing the DEA efficiency scores we estimate as an indicator of the overall economic efficiency of each dishwasher model.

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Notes

  1. Estimated from the US Census Bureau report on extended measures of well-being (Siebens 2013).

  2. AHAM (2015) estimates shipments of dishwashers to reach 7.4 million units in 2015, and to increase to 7.8 million units in 2016.

  3. Calculated from the US Geological Survey (USGS) estimates of typical average person consumption of residential water by end-use per day (https://water.usgs.gov/edu/qa-home-percapita.html).

  4. They will further provide the dishwashing service at different levels of quality.

  5. The notion of a dishwasher economic-efficient frontier refers here to a Pareto optimum frontier, where neither of the input factors—price and energy and water consumption—can be reduced without increasing at least one of the other two factors.

  6. In economics, a production function refers to a mathematical function that relates the physical output of a production process to the physical inputs (or production factors) required to produce that output.

  7. DEA is a non-parametric method introduced by Charnes et al. (1978) to construct deterministic economic efficiency frontiers. They elaborated on Farrell (1957) to propose an approach that estimates relative efficiency scores for a set of peer production units. For more on DEA concepts and applications, see Cooper et al. (2011). For an extensive bibliography on DEA, see Gattoufi et al. (2004). For surveys and statistics on DEA publications, see Emrouznejad et al. (2008) and Emrouznejad and Yang (2017). For applications of DEA to energy and environmental studies, see Zhou et al. (2008).

  8. A DEA technical efficiency score is a distance-based performance metric that expresses how efficiently inputs to and/or outputs from an economic production process are combined. Blum (2015) follows a DEA input-minimizing approach to express performance as to what extent the capital and energy associated with producing a certain amount of an energy service can be—as evidenced from data available on existing technologies that produce the energy service—contracted to their least possible combinations.

  9. In the case of Blum (2015), the efficient frontier delineates an isoquant curve that shows, based on data available on the capital and energy required by technologies that produce the energy service, that neither of the two input factors can be reduced without increasing the other factor.

  10. In production economics, returns to scale refers to what extent quantitative changes in inputs/outputs of a production process result in proportionate changes in its outputs/inputs. When the proportion holds for any level of production, the process is said to exhibit constant returns to scale. When changes in inputs/outputs result in more- or less-than-proportional changes in outputs/inputs, the process exhibits respectively increasing (or sometimes non-decreasing) and decreasing (or sometimes non-increasing) returns to scale. A process that responds to changes with different proportionalities at different levels of production is said to exhibit variable returns to scale. The scale efficiency of a production process expresses to what extent the economic inefficiency of that process can be associated with the process being operated out of its optimal scale. For more on returns to scale and scale efficiency in DEA, see Banker and Thrall (1992) or Kumar and Gulati (2008).

  11. More specifically, they find that the dishwashing energy service is delivered under non-decreasing returns to scale. As they rely on Blum’s (2015) input-minimizing DEA approach, with given, fixed outputs, their finding means that—for a certain range of dishwashing service—changes in the amount of service delivered require either equal or less-than-proportional changes in capital and energy.

  12. This is consistent with Dubin (1985), who represents appliance choice as a production function that relates an amount of a certain household end-use service to the capital and other inputs required for the service. In addition, Fernandez-Castro and Smith (2002) demonstrate how DEA is consistent with the characteristic view of consumer-choice in the economics literature.

  13. Dishwashers in the market can be high energy-efficient but low water-efficient, low energy-efficient but high water-efficient, and both energy- and water-efficient or inefficient. We elaborate on this in “The dishwasher consumer choice-efficient frontier” section where we describe the dishwasher models available in the market.

  14. When compared to the economic technical efficiency estimated only from capital and energy.

  15. We elaborate on this in section “Estimating an economic input efficiency frontier for dishwashers.”

  16. Their DEA framework fits well to this analysis, as it (a) concentrates on the basic input factors (capital and energy) associated with the energy service and (b) accounts for potential scale inefficiency. Richter (2010, 2011) has also assessed the economic technical efficiency of dishwashers, yet from the perspective of consumer habits when using the appliance.

  17. This process is also known as variable selection, and typically refers to cases where the number of inputs and/or outputs in a DEA model is too large compared to the number of peer units being evaluated. Although this is not the case here, we rely on methods for variable selection in DEA available in the literature to support our analysis. For more on variable selection in DEA see, for example, Tsai and Molinero (2002) and Butler and Ling (2005).

  18. Doyle and Green (1991) used it to compare computer printers; Doyle and Green (1994) to benchmark microcomputers; Khouja (1995) and Baker and Talluri (1997) to identify industrial robots that provide the best combinations of vendor specifications; Odeck and Hjalmarsson (1996) to evaluate the efficiency of trucks used in road construction and maintenance; Fernandez-Castro and Smith (2002) to compare diesel cars; and Staat et al. (2002) to benchmark compact cars in order to find the ones that maximize customer value.

  19. Chini et al. (2016) quantify technical potential energy and water savings in the US residential sector. Kahrl and Roland-Holst (2008) use input-output economics to explore the interrelationships between energy price and water consumption in China. House and House (2012) examine how consumers exposed to dynamic pricing of electricity and water shift water consuming for household services during peak energy use periods. Davis (2008) use data from a field trial to investigate how households that purchased more energy-efficient clothes washers eventually use more energy and water due to behavioral responses to the higher efficiency (rebound effect). Ruddell and Dixon (2014) investigate whether households in some arid areas in Arizona, USA, trade-off water and energy use, and find that water and energy consumption mirror each other and more efficient households tend to consume more of both water and energy (rebound effect). Results from Davis (2008) and Ruddell and Dixon (2014) are consistent with the notion that—at operation time—energy and water are complements.

  20. The US Department of Energy’s Technical Support Document (US DOE 2016a), which provides technical analysis and results in support to the final rule on energy efficiency standards for residential dishwashers, presents positive dishwasher incremental manufacturing costs for decreasing energy and water use. Higher price could also be a signal of higher product quality (Wolinsky 1983; Milgrom and Roberts 1986). This implies that some manufacturers consider energy and/or water efficiency as a value-added feature, and pack other high value-added, more costly design options into the more energy- and/or water-efficient models. In addition, higher prices could also be due to manufacturer markups, supported by brand loyalty and/or information asymmetry. In section “The dishwasher consumer choice-efficient frontier,” we provide more details on price variation for same energy and/or water use observed in our sample.

  21. We use dishwasher capacity as our proxy for the dishwashing service the appliance provides. Any additional qualitative aspect of the washing service (e.g., cleanliness) or the washing process (e.g., reduced cycle time, reduced noise) might add to the dishwasher price and eventually, deviate from the optimal combinations of input factors required to meet the appliance’s very basic purpose of washing a certain amount of dishes.

  22. One dishwasher is dominant with respect to another dishwasher if it requires less of at least one of the input factors and no more of the other input factors to provide the same amount of service when compared to the dominated unit.

  23. Adding inputs and/or outputs to a DEA model allows for the observations in the dataset to be projected in a larger number of orthogonal directions (Nataraja and Johnson 2011). This leads to overly optimistic efficiency scores and many of the observations in the dataset to falsely qualify as efficient (Podinovski and Thanassoulis 2007). The effect is sometimes referred to as the curse of dimensionality in DEA (Simar and Wilson 2008).

  24. This corresponds to our null hypothesis that water does not matter to dishwashing efficiency.

  25. For more on the KS test see, for example, Massey (1951).

  26. The method follows a backward elimination approach, where (a) a DEA model that includes the variable is evaluated and (b) a DEA model that does not include the variable is evaluated taking as inputs/outputs (depending on the DEA input/output orientation used) the virtual-efficient DMUs from the previous model. It is proven that the marginal effect calculated from the procedure above can be estimated from the ratio ρ of the efficiency scores from the DEA models that include and does not include the variable being tested (Pastor et al. 2002). The relevance of the variable is then assessed based on the statistical significance of having more than 1 − ρ percent increase in efficiency scores for more than p percent of the DMUs, compared to a certain level of desired effect expressed by ρ0 and p0.

  27. In order to exhibit some potential for improving efficiency, a candidate DEA input is expected to be highly positively correlated with the technical efficiency scores from the DEA program from where it is omitted. The rationale here is that the candidate input is more likely to contribute to the frontier if the units that are currently far from the frontier have lower values of that input. In our case, that means having dishwashers with low water consumption to score low technical efficiency scores in DEA program [0]. If, otherwise, the dishwashers with lower water requirements are already in or close to the frontier derived from our DEA program [0], adding water to the DEA model will not add much to the dishwasher consumer choice-efficient frontier.

  28. This is also referred to in the literature as second-stage DEA efficiency analysis. See, for example, McDonald (2009), Ramalho et al. (2010), and Simar and Wilson (2011) for more on use of regression analysis to post-process DEA scores.

  29. Fractional regression was introduced by Papke and Wooldridge (1996) to model data whose dependent variable are in proportional form. It has been used with DEA, for example, by Ramalho et al. (2010) and Castro and Guccio (2014).

  30. The amount of correlation is related to the additional information that each variable contributes to the DEA efficiency scores. An alternative, fourth statistical test to be considered for variable selection is the principal component analysis (PCA)-DEA. The method was independently developed by Ueda and Hoshiai (1997) and Adler and Golany (2001), and used by Adler and Yazhemsky (2010) and Bayraktar et al. (2012). However, empirical studies have shown that PCA-DEA works well with small sample size, is robust to correlations between variables above 0.80, and is vulnerable to technology choice. We show in section “The dishwasher consumer choice-efficient frontier” that none of these assumptions hold in our data. In addition, the main power of PCA-DEA has to do with solving the “curse of dimensionality” problem, which we do not have in our model and data.

  31. This has been suggested by an anonymous reviewer.

  32. www.consumerreports.org.

  33. Energy Guide is administered by the US Federal Trade Commission (www.consumer.ftc.gov/articles/0072-shopping-home-appliances-use-energyguide-label). Energy Star is a program jointly run by the US Environmental Protection Agency and the US Department of Energy (www.energystar.gov).

  34. There is, however, mixed empirical evidence on whether they are effective at affecting customer decision-making (Park et al. 2007).

  35. The DEA literature provides several alternative schemes for classifying DMUs using approaches that combine the estimated efficiency scores, peer weights, multi-tiered frontiers, and other related parameter estimates. For example, Charnes et al. (1986, 1991) combine efficiency scores, type of frontier, and weights from the dual form of the DEA for classification. Other authors have proposed classification schemes that combine parameter estimates from DEA models with machine-learning approaches (Thanassoulis 1996; Hong et al. 1999). Another approach suggests combining efficiency estimates with a classification process based on multi-tiered frontiers obtained from iteratively estimating DEA efficiency scores after excluding efficient units from previous runs of the DEA model (Hong et al. 1999; Bi et al. 2014). Still, another approach suggests a clustering process using the piecewise production functions based on the fully efficient production possibilities derived from the DEA model, along with the estimated efficiency scores (Po et al. 2009; Amin et al. 2011). We tried several of these approaches individually and in combination, with results that are neither very intuitive nor admit to some easily interpretable groups without further analysis. The latter represents, on its own, a detailed and complete research subject to be addressed as part of future work on how to use DEA estimates to cluster and classify energy and water consuming durable goods.

  36. Refers to manufacturer-suggested retail price (MSRP). Data collected from manufacturer catalogs.

  37. Calculated from the water consumption per cycle available in US DOE (2015) and an average dishwasher use estimated as 215 cycles per year (US DOE 2012: §430.23 Test procedures for the measurement of energy and water consumption).

  38. Therefore, each dishwasher model is a notional choice of a presentative consumer. This way, our efficiency analysis can be imagined as representative of a consumer evaluating a heterogeneous suite of dishwashers available in the market.

  39. A linear regression over the data points in Fig. 1 results in a highly statistically significant value for the slope, with an R2 of 0.98 and normalized residuals ranging from −9.0 to 25.2%. Whereas the first two metrics suggest a strong relationship between energy and water, the dispersion of residuals indicates a relevant variability in the combinations of energy and water efficiency across dishwasher models in the market.

  40. This is possible because the VRS DEA programs we use account for the difference in capacity across units from both categories.

  41. This is consistent with Sexton et al. (1986) who state that DEA efficiency estimates cannot decrease when additional inputs are added to the model.

  42. The table also includes for each frontier the number of inefficient peers, as well as the efficiency score and efficient peers from the DEA program [0] for the units moved to the frontier as water is added to the DEA program.

  43. In addition to the fully efficient DMUs reported in Table 2, there are 16 weakly efficient dishwashers in the DEA program [0] and 18 in the program [1]. Interesting to note, in both DEA programs the only input where weakly efficiency is observed is in price. Slacks in that input are likely due to additional quality and/or markups associated, for example, with brand, and range from 5.3 to 76.6% of the efficient price.

  44. As expected, units with lower water consumption are more likely to have their efficiency improved when water is accounted for in the DEA model.

  45. See in Table 2 the dishwashers with water consumption equal to 430 gal per year.

  46. Indeed, as represented in Table 2, eight of those units are promoted to the frontier in the DEA program [1].

  47. According to the test procedure in the US dishwashers are tested with clean dishes and no assessment of washing performance is undertaken (unlike in the International Standard IEC 60436: Electric Dishwashers for Household Use—Methods for Measuring the Performance, http://standards.globalspec.com/std/9967823/iec-60436). If a consumer buys a new dishwasher and the appliance does not perform as well as expected, the householder will either start to pre-treat dishes before loading or use a heavier program. The energy and water consumed for washing the dishes will then differ from the (reference) consumptions used for this analysis (anonymous reviewer).

  48. In addition, Pan et al. (2004) suggest that some retailers strategically advertise a low price but do not actually honor the posted prices, i.e., they “bait and switch.”

  49. Accounting for emissions externality costs in inputs to our DEA model was suggested by an anonymous reviewer.

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Acknowledgements

This work was supported by the Office of Energy Efficiency and Renewable Energy (Solar Technologies Office) of the US Department of Energy under Lawrence Berkeley National Laboratory Contract No. DE-AC02-05CH1131. We acknowledge Prof. Luiz F. L. Legey, COPPE/PPE, Universidade Federal do Rio de Janeiro, Brazil, and six anonymous reviewers for their valuable comments on a draft version of this paper.

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  1. Energy Efficiency Standards Group, Energy Analysis and Environmental Impacts Division, Energy Technologies Area, Lawrence Berkeley National Laboratory, 1 Cyclotron Rd Bld 90, Berkeley, CA, 94720, USA

    Helcio Blum & Edson Okwelum

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  1. Helcio Blum
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  2. Edson Okwelum
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Correspondence to Helcio Blum.

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This article has not been reviewed by its institutional funders. The assumptions, views and opinions expressed in the article are solely those of the authors, and do not reflect or represent any official view, opinion, position or policy of Lawrence Berkeley National Laboratory or any agency of the U.S. government.

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Blum, H., Okwelum, E. Estimating an economic-efficient frontier for dishwasher consumer choice. Energy Efficiency 11, 1325–1340 (2018). https://doi.org/10.1007/s12053-018-9627-7

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