Overview of Committed Quantities in Commodity Demand Analysis with a Focus on Energy

: An overview of the literature considering committed quantities in demand estimation for various commodities with an emphasis on energy commodities is presented. This overview provides a deﬁnition and the history of committed quantities, along with different theoretical modeling methodologies. Committed quantities are quantities that are consumed in the short run with little regard for price. Previous studies suggest that committed quantities for various commodities range from 15 to 98% of consumption. The inclusion of committed quantities appears to improve estimates generally, but it is not clear-cut. Problems arise when estimated committed quantities are negative or larger than the consumption amount. This review concludes with a recommendation that further research is necessary to resolve such issues, provide an improved understanding of the committed quantities in estimation, and ﬁll in knowledge gaps concerning committed quantities ranging from theoretical to practical issues.


Introduction
Over 30 review articles dating back to the mid-1970s exist concerning energy management, forecasting, and demand. Verwiebe et al. [1], for example, provide a listing of over 28 reviews of demand analysis studies and review 419 articles published since 2015.
Considering committed quantities in demand studies corresponds closer to observed consumer behavior. This better reflection of consumer behavior may lead to statistical estimations satisfying economic demand theory. Therefore, including committed quantities may ultimately lead to better policy implications and recommendations relative to studies not considering such quantities. For example, elasticities estimated considering and not considering commitments lead to different estimates with different policy implications and recommendations. Without considering committed quantities, one would erroneously apply the estimated elasticity to all quantities and not to the correct amount of only noncommitted quantities. The error depends on the committed quantity. Compared to the total number of economic demand studies, the consideration of committed quantities is deficient. It is hoped this overview will stimulate research on committed quantities from basic theoretical to applied studies and not only in economic demand but also other socio-economic areas. This overview of committed quantities includes a discussion of various commodities (including energy, water, and food); however, the focus is on energy. First, why committed quantities arise is provided along with their importance. Most of this literature is older, but the reasons for committed quantities have not changed. Next, an economic definition of consumer demand (henceforth, demand) is presented along with several demand models of committed quantities. Various applications to energy and other commodities are presented to illustrate the range of commodities that committed quantities may apply; the discussion focuses on results pertaining to committed quantities. Incorporating committed quantities into models may provide better analyses of policy implications. Committed quantities are a short-run phenomenon in which the quantity demanded responds little to price. Failure to recognize this lack of response, one may erroneously conclude that a policy will cause a large change in consumption when in fact consumption may change little; price-based policies only impact the non-committed quantity and not the committed quantity [19,27,29]. Our goal here is not to provide a complete extensive review of demand analysis literature but to provide an overview of committed quantities in economic demand analysis.

Factors Giving Rise to Committed Quantities
The concept of committed quantities arises early in the literature. Possibly the first mention of the committed quantities concept is by Samuelson [3] (p. 88), who interprets the constant term in demand systems by assuming consumers " . . . always buy a necessary set of goods . . . ". The literature on energy and water stresses the importance of the capital stock of durable goods in determining committed quantities, thereby affecting how people can respond to price changes. Data difficulties, however, exist in obtaining capital stock measures [30][31][32]. Durable goods such as industrial equipment [31] and a wide range of appliances, including refrigerators, HVAC, and washing machines [5,22], give rise to committed quantities. Further, housing decisions (location and size) impact committed quantities [2]. The need for food also gives rise to committed quantities [4,[33][34][35]. Policies need to consider that in the short run, demand responses are limited; in the longer run, capital stock is variable [36] and eating habits change. Bohi [31] adds to this discussion by noting that for industrial users, technology is not continuous and input use and output may be lumpy. This also holds true for households. Committed quantities may change as economic agents adjust their durable goods by time of the year [18,29].
Appliances and industrial equipment are not the only goods that give rise to committed quantities. Transit literature has long recognized the impact of vehicle efficiency, size, weight, ownership, and/or stock, along with traffic levels, on the demand for fuel [37][38][39][40]. Urban forms also influence energy consumption [41]. Urban characteristics, including community layout, planting and area, house size, construction, and housing density, affect residential energy demand [42,43]. Such characteristics are slow to change and can lead to committed energy use.
Behavioral and structural changes may alter the responsiveness of energy demand to price changes [44]. Such changes, however, are not costless, and people do not invest in efficient equipment if they believe a price increase is temporary, implying inertia in consumption is related to slow changes in stocks [45]. Much of the research on change in behavior associated with modes of travel depends on attitude theories from social psychology [46]. Two trends in transportation research are: behavior depends on constraints and choices and the importance of habits [46]. Effective policy interventions need to consider and work with people's habits.
While economic incentives influence purchases of energy, they only explain a portion of observed behavior [47]. Sorrell [47] (p. 78) states, "Most decisions relevant to energy consumption are taken in the context of limited or asymmetric information about energy (service) costs by actors who are greatly constrained in their ability to respond to those costs even in circumstances where they are aware of and paying close attention to themwhich is rarely the case". Verwiebe et al. [1] (p. 25) find few studies incorporate energy prices stating that price is "Rarely considered as a predictor because demand has low price elasticity, price swings only in liberalized markets, difficult to obtain future values to use in predictions". Such results may arise by failure to consider committed quantities properly.

Importance of Considering Committed Quantities
To clarify committed quantities, consider heating oil, as the price of heating oil fluctuates, consumers do not go out and buy or sell their homes or heating units. They are committed to some quantity of heating oil during the winter, the committed level; however, not all heating oil is committed. Consumers can adjust their thermostats in response to price fluctuations. Because most electrical appliances are durable in nature, electricity use is another example of a considerable amount of consumption being committed. For example, refrigerators require a certain amount of electricity to maintain proper temperatures for maintaining food quality. Humans commit to a certain level of food consumption, despite food price increases, to fulfill their physiological requirements for energy and nutrients. Moreover, some people may commit to food consumption to improve their health or to manage their medical conditions. Meanwhile, some people may consume committed quantities because of addictions, such as sugar, drugs, drinks, and tobacco. Policymakers should be aware of the existence of such commitments when establishing price-based policies that target consumption reduction. Water consumption is another example of committed quantities with minimum consumption necessary for bathing, washing clothes, and landscape. How a commodity is defined impacts the level of commitment. Demand for a specific brand of gasoline, for example, will have a much smaller committed level than the demand for gasoline. No study was found that addressed if committed quantities for different commodities should be treated differently. It appears from the reviewed studies, both from a theoretical standpoint and practical application, treatment of different commodities should not differ.
Estimation of elasticities may be biased if committed quantities exist but are not considered [34]. Further, the use of elasticities may be incorrect, as illustrated in the following example. Consider a commodity that has an elasticity of −0.5, which indicates a one percent increase in price decreases quantity demanded by 0.5 percent. Currently, the consumption of the commodity is 100 units, of which 80 units are committed. A policy intervention is being considered, which would increase price by one percent. The correct short-run consumption is 80 + (20 − (20 × 0.5)) = 90 units. If one incorrectly assumes all consumption responses to the policy, the estimated consumption would be 100 − (100 × 0.5) = 50 units. As such, with the presence of committed consumption, pricebased policies must have larger increases in price to decrease consumption than when no consumption is committed.

What Is Demand?
Demand refers to a schedule of prices of a good and quantity demanded, where the quantity demanded is the amount of the good that buyers are willing and able to purchase at a given price [48]. In the neoclassical demand theory, demand is derived assuming a consumer solves the constrained utility maximization problem, where bold letters denote matrices, U denotes the utility function of a consumer, x denotes an n × 1 vector of n goods, p denotes an n × 1 vector of prices, and µ denotes a consumer's nominal income (hereafter income). The solution to this constrained maximization problem gives the Marshallian (or ordinary) demand functions, x(p, µ). Marshallian demand functions have the properties of positivity, additivity, homogeneity, and symmetric and negative semidefinite substitution matrix [49]. Positivity requires quantity demanded to be positive. Additivity requires the sum of expenditures on each good to equal the income. Homogeneity of degree zero in all prices and income requires the quantities demanded to remain unchanged when all prices and income change in the same portion, i.e., x(tp, tµ) = x(p, µ) where t is any positive constant. Symmetric and negative semidefinite substitution matrix assures cross-price effects among two goods are the same regardless of any good price change. In empirical demand analysis, these properties, known as integrability conditions, should be tested [49].
Substituting the Marshallian demand into the utility function, one obtains the indirect utility function, i.e., V(p, µ) = U(x(p, µ)). Properties of the indirect utility function are: (i) nonincreasing in p and nondecreasing in µ; (ii) homogeneity of degree zero in p, and µ; (iii) quasiconvexity in p; and (iv) continuity at all p and µ [50]. These properties of the indirect utility, along with the positivity, are often denoted as the regularity conditions [49].

Including Committed Quantities in Demand Functions
The most common approaches to include committed quantities are the linear expenditure (LES), generalized almost ideal demand (GAIDS), and the generalized exact affine Stone index (GEASI) demand systems. These approaches are briefly presented. Samuelson [3] gives an economic interpretation of intercept terms in linear functions between quantity demanded for good i, x i , prices, p i , and income, µ, as noted earlier, the interpretation is that consumers always buy a set of necessary goods, c i , and spend supernumerary income, the amount of income remaining after spending on the committed quantity, in constant proportions, β i , on the goods [3]. With these assumptions, Equation (2) becomes where µ − ∑ j p j c j denotes supernumerary income.
The linear expenditure system is attributed to Geary [51], which derived the system based on the utility function underlying Klein and Rubin's [52] model. The estimation of the linear expenditure system was pioneered by Stone [4]. This system became known as the Stone-Geary utility function [53], with some papers calling it the Stone-Geary demand system. Stone [4] (p. 512) refers to Samuelson's [3] necessary quantities as " . . . quantities to which consumers are in some sense committed . . . ". He proposes a linear expenditure system that satisfies the integrability restrictions. Stone's [4] expenditure system is Equation (4) represents a system considering committed quantities, and Equation (5) represents a system that does not have committed quantities. To fulfill the integrability restrictions, all β i must be nonnegative and add to unity [15]. Since Stone's [4] work, several demand systems have been introduced with little interpretation of intercept terms provided, including the Rotterdam model [54] and the almost ideal demand system (AIDS) [55]. Bollino [6] incorporates committed quantities into the AIDS model developing the generalized version of AIDS known as the GAIDS model. The expenditure share on good i in the GAIDS model is where c i denotes the committed quantity of good i, µ = µ − ∑ n i=1 c i p i denotes the supernumerary income, and ∑ n i=1 c i p i denotes expenditure on committed consumption. To avoid nonlinearity, Bollino [6] uses Stone's price index of ln P = ∑ n i=1 w i ln p i to generate a linear approximation. To satisfy the integrability conditions of additivity, homogeneity, and symmetry, the following restrictions are imposed on the GAIDS model, Expanding Bollino's [6] model, Hovhannisyan and Gould [33] introduce the generalized quadratic almost ideal demand system (GQAIDS), which includes committed quantities, but instead of a linear Engel curve, the Engel curve is assumed to be quadratic. The expenditure share of good i in the GQAIDS model is where λ i denotes the effect of quadratic Engel curves on the expenditure share and i is a Cobb-Douglas price aggregator function [33]. In addition to Equation (7), ∑ n i=1 λ i = 0 is imposed to satisfy integrability and regularity conditions. If committed quantities are not considered, and the Engel curve is linear (c i = 0 and λ i = 0), Equation (8) reduces to the AIDS model [55], where α i is the intercept term. Hovhannisyan and Shanoyan [34] generalize the exact affine Stone index (EASI) demand system proposed by Lewbel and Pendakur [56] to incorporate committed quantities. Expenditure share on good i of the generalized EASI (GEASI) demand model is where m i (U) denotes a general function of utility (U) [34]. Following Lewbel and Pendakur [56], Hovhannisyan and Shanoyan [34] suggest replacing m i (U) by ∑ R r=o β ir y r where r denotes the order of a polynomial function. Defined as implicit utility and interpreted as a measure of the log real supernumerary expenditures, y = ln µ − w ' ln p is a vector of affine transform of the log of Stone's price index deflated supernumerary expenditures. w is a vector of implicit Marshallian budget shares, which are Hicksian budget shares after substituting y for U. In the GEASI demand system, the integrability restrictions are [34], if committed quantities are not considered, Equation (10) becomes the EASI system of [56], note that the AIDS budget share is linear in prices and income, whereas the EASI budget share is linear in prices and polynomial in income [56].

Factor Demand in Production
Although this overview concentrates on consumer demand, there is a demand for factors of production which, like all demand, is a relationship between the price of the factor and quantity. It is generally assumed a firm's objective is either profit maximizing or cost minimizing, but factor demand relationships can be obtained from other objectives [57]. Like consumer demand, factor demand arises from maximizing behavior. Consider a simple one-factor case in a competitive market in which factor demand is a function of input prices and a product's price (exogenously determined). Factor demand is given by the marginal value function after it intersects the average value product from above, which forces demand to start at a quantity greater than zero [57]. This quantity can be viewed as a committed quantity, that is, if production is going to occur, a minimum level of input is necessary. When a firm is not in a competitive market, deriving its factor demand is more complicated; however, the production process and not the market structure is an important determinant of the minimum amount of input necessary for production to occur.

Limitation of Committed Quantities
The above methods do not require committed quantities to be positive or less than the total quantities demanded. Incorporating committed consumption creates ambiguous arguments under these two conditions. Authors differ in their interpretation of negative committed quantities. Negative committed consumption may be explained by consumers' standard of living; as consumers become poorer, they may no longer feel committed to certain quantities [4]. If a good's committed quantity is negative (positive), its demand is own-price elastic (inelastic) [58]. A positive committed quantity implies a necessary good because it is positive at zero income level, whereas a negative committed quantity implies a luxury good because it will become positive when the income level exceeds a certain amount [13]. It is only suggestive of interpreting estimated values as committed quantities; when they are negative, such an interpretation is not applicable [59]. Negative committed quantities can be interpreted as a marginal response of the committed expenditure to the price [26,33]. The negativity of committed quantities may be due to unknown troubles of model misspecification or measurement errors in the data [26]. To avoid this issue, nonnegative conditions can be imposed on committed parameters when estimating [17]. Another drawback is that when the total consumption of a good is less than its committed quantity, the interpretation of the system may not explain the consumers' actual behavior [4].

Studies Explicitly Considering Committed Quantities
A sample of studies that explicitly consider committed quantities are given in Tables 1 and 2. Committed quantities for different commodities and systems have been examined in various countries. Studies have considered a single commodity such as electricity or water. Multicommodity systems vary in commodities included based on the study's objective(s). With respect to energy, some systems only consider energy commodities coal, natural gas, and petroleum, whereas other studies consider energy as one commodity in a broader system of commodities. The number of observations varies greatly from only a handful of observations to thousands of observations. Demand models with committed quantities have been estimated for hourly to yearly data.   Yes U.S. consumers' committed levels are 74%, 73%, and 0% of total estimated consumption for beef, pork, and poultry, whereas, for Japan, the levels are 67%, 0%, 0%, and 60% (fish). GAIDS is preferred to AIDS for both U.S. and Japan. Committed level percent of average consumption are oil-87%, natural gas-60%, and coal-69%. Larger price changes are necessary to achieve a given policy change when committed levels are considered.
[11] 2017 Examine the impact of the adoption of renewable energy sources (RES) on consumer welfare No Adoption of RES can temper higher energy costs associated with fossil fuels. Countries with mild weather will benefit more from RES adoption.
[18] 2017 Examine the efficiency and equity of increasing-block pricing in Taiwan's residential electricity sector Yes Committed averages of committed levels are larger in the summer than in non-summer periods and are almost the same for each income quantile. Over the 16 years, the average basic subsistence level per capita changes little.
[24] 2017 Examine the effect ignoring committed quantities and theoretical regularity conditions will have on food demand Committed quantities vary greatly by commodity, including some negative values. The discretionary portion of consumption is more elastic than the baseline consumption. [19] 2021 Investigate the potential for shifting electricity use between peak and off-peak hours Yes Subsistence (committed) levels are larger during peak than off-peak and larger in the winter than summer. The committed peak level is about 50% of the average usage during peak hours. The policy implication is there are limits to household response to prices, at least in the short run.
[65] 2021 Evaluate water demand recognizing water interrelationships and precommitments Yes Residential water precommitment is 79% of total demand, and bottled water precommitment level is 23%. Ignoring precommitment demands can lead to erroneous policy recommendations [14] 2022 Investigate the impact of COVID-19 on price responsiveness of electricity demand No Economic activities were adopted to avoid the effects of the lockdown on the economy. During the period of heavy lockdown, price elasticity was reduced, but after easing the lockdown, elasticity increased. Estimated hourly price elasticities of demand are inelastic, with none greater than 0.3 in absolute value.
[28] 2022 Determine if linear or nonlinear Engel curve better explains better the relationship between income and energy consumption and if systems with committed levels better model energy consumption

Yes
Models with committed levels and nonlinear Engel curves appear to be more appropriate. Committed levels as a percentage of average consumption: coal and Lignite-38, natural gas 15, and petroleum products-64% [22] 2022 Examine environmental regulation measures using a CGE No Example of commitments important in model development but never discussed or used. [21] 2022 Evaluate the relationship between electricity prices and household welfare No Report a positive statistically significant own price elasticity of electricity-questionable result. Positive and significant income elasticity from electricity. Liquid fuel elasticities are non-significant. 1 Com-indicates if the study discusses commitment level and/or impact after estimation, yes-no.

Statistical Evidence
A logical question to ask is whether there is statistical evidence considering committed quantities improves the estimates of demand systems. To address this question, studies have compared forms with and without committed quantities. Inferences from these comparisons are committed quantities statistically improve estimates, but models with and without committed quantities are similar statistically [28]. It, however, should be noted that comparisons are based on published results interested in committed quantities, so there may be a bias toward indicating models with committed quantities are better.
Studies have compared models in energy-related studies. In testing five different functional forms, Atalla et al. [11] conclude the best model includes committed quantities, capital stocks, and climate variables, along with cross-price, own price, and income effects. Atalla et al. [11] (p. 118) state, "In the economic estimation, the main advantage of committed quantities is to relieve the constraint to Engel curves to pass through the origins." Atalla et al. [12], in comparing GAIDS to not only the AIDS model but also the Cobb-Douglas and the linear expenditure system, conclude the GAIDS specification is superior. Additional function forms, including the GQAIDS model, are tested in Bollino et al. [61] and Duangnate and Mjelde [28]. Based on likelihood ratio tests of the 16 estimated systems, Bollino et al. [61] conclude GQAIDS without demographic characteristics is better than either the GAIDS or a linear expenditure system. Duangnate and Mjelde [28] find the GQAIDS model is preferred based on the encompassing tests.
Gaudin et al. [5] and Martínez-Espiñeira et al. [29] assume consumer behavior follows the Stone-Geary utility and construct a demand function for water as a function of price, income, and exogenous variables. Gaudin et al. [5] find the Stone-Geary results have seasonality patterns similar to the results obtained for the generalized Cobb-Douglas demand model if the exogenous variables used in the Cobb-Douglas model are linearly incorporated in the Stone-Geary demand estimation. They conclude the Stone-Geary results are comparable to those of more complex flexible forms. Comparing the performance of models considering fixed and dynamic committed quantities, Martínez-Espiñeira et al. [29] find the overall fit improves when committed quantities are a function of past consumption and precipitation. Tonsor and Marsh's [26] findings suggest the more general GAIDS model is preferred to the AIDS model in modeling food demand in the U.S. and Japan. For a food demand system, Senia and Dharmasena [24] find the GAIDS model fits the data better than the AIDS model, considering model fit parameters, and Wald tests on the committed parameters.

Theoretical Evidence
Testing the theoretical restrictions of integrability and regularity helps determine the validity of estimated demand functions. Satisfying the integrability conditions guarantees the existence of a utility function used to derive the demand functions, and the corresponding indirect utility should satisfy the regularity conditions to justify optimizing behavior and duality theory [49]. Imposing integrability conditions in empirical estimations circumvents issues regarding the number of parameters to be estimated and observations. Barnett and Serletis [49] (p. 210) state, " . . . the usefulness of the currently popular parametric approach to empirical demand analysis depends on whether the theoretical regularity conditions of neoclassical microeconomic theory (positivity, monotonicity, and curvature) are satisfied". Explicitly checking regularity conditions, Rowland et al. [2] find GAIDS satisfies regularity conditions for all observations, but the AIDS model only satisfies the positivity condition leading them to conclude GAIDS specification performs better. In Senia [66], positivity is satisfied for both the AIDS and GAIDS systems. Monotonicity is violated at six observations in the AIDS system, and for no observations in the GAIDS system, leading him to include committed quantities provides a better system. Bollino [61] finds systems incorporating demographic specifications generally satisfy concavity and Slutsky negativity conditions in all their systems, including QAIDS, but details are not presented. As noted by Rowland et al. [2], regularity conditions arise due to maximizing behavior of consumers and aggregating to the national level may lead to the conditions being violated. No study discussed why considering committed quantities leads to theoretical restrictions being satisfied. The most likely reason is committed quantities better represent consumer behavior.

Committed Levels
Although including committed quantities may improve models' statistical properties, does that improvement lead to better economic interpretation or policy analyses? As noted earlier, if the committed level is small, a policy-induced price change will impact most of the consumption, and the committed quantity will play a small, inconsequential role. Therefore, a logical question is what levels of committed quantities have been reported. Only a small number of studies, however, report levels of committed quantities. In these studies, committed levels represent a sizable amount of short-run consumption. Reported committed levels as a percentage of average consumption in the U.S. are 87% for oil, 60% for natural gas, and 69% for coal [2]. Smaller committed percentage levels are reported by Duangnate and Mjelde [28] for Thailand: 38% for coal and lignite, 15% for natural gas, and 64% for petroleum products. Hung et al. [18], over 16 years of data, find committed levels for electricity changed little from year to year. For water, reported committed quantities are at least 40% and up to 79% of water consumption [5,29,65]. Committed quantities for meat in the U.S. and Japan differ but remain a large component for some commodities [26]. Committed quantities for beef, pork, and poultry in the U.S. are 74%, 73%, and 0% [26], and 86%, 57%, and 53% [62]. Committed quantities for beef, pork, poultry, and fish in Japan are 67%, 0%, 0%, and 60% [26]. Committed quantities for vegetables, rice, other grains, and fats/oil in China are 27%, 38.5%, 19.9%, and 20.7% [33], whereas, in Russia, committed quantities for cereals, eggs, fats/oil, and sugar are 58.9%, 72.1%, 97.6%, and 66.7% [34]. There is no further discussion why commitment consumption for fats/oil in Russia is nearly 100%.
Studies have allowed committed quantities to vary across economic agents [19,24,33,61] and time [19,26]. Allowing committed quantities to vary does not affect the unit of measurement [25]. Allowing committed quantities to vary across households, the quantities are assumed to depend on demographic variables. Committed quantities varying over time are estimated as a function of monthly/quarterly quantitative variables, time trends, and other variables such as temperature. Such estimations can capture external factors that influence committed quantities.
As expected, reported committed quantities vary by commodity definition, but regardless of commodity, levels up to 98% have been reported. At such levels, committed quantities affect how consumption reacts to price changes.

Elasticities
Many studies' objectives are to either report or use income (expenditure) and price elasticities calculated from the estimated demand equations. Often only price elasticities are reported without explicit recognition of the type of elasticity. If not stated, reported elasticities are usually Marshallian elasticities [5,18,19,21,29,60], most likely because Marshallian demand is assumed to be observable as a function of price and income. When the type of elasticity is stated, elasticity is usually either Marshallian elasticities [7,8,10,12,63], compensated [17,61], or both [16,24,26,34]. Allen and Morishima elasticities are also reported in Rowland et al. and Duangnate and Mjelde [2,28]. It should be noted that regardless of the system, studies have reported elasticities that are of the wrong sign and/or statistically insignificant. Using aggregated data and data over a short period (e.g., yearly data), such findings on elasticities may be an expected outcome. Further, if committed quantities change over time, estimates may be insignificant.
Own-price elasticities associated with models with committed quantities should be larger in absolute value (more elastic) than those associated with models without committed quantities. The reason is committed quantities do not respond or respond very little to price changes. Non-committed quantities are the only quantities that respond. Estimated elasticities from demand systems without committed quantities are a combination of committed and non-committed quantities. How such a combination impacts estimated values is an empirical issue. Senia [66] provides a graphical analysis of an effect of a subsidy on a commodity with and without committed quantities. Without committed quantities, the graph is the standard supply and demand graph, but with committed quantities, the horizontal axis is no longer quantity but quantity minus committed quantity.
Of the 33 elasticities presented in Rowland et al. [2], elasticities are larger in absolute value in 26 of the elasticities in the GAIDS compared to the AIDS model, with all own-price elasticities (coal, natural gas, and petroleum) being more elastic in the GAIDS system. Similarly, 78% of the elasticities calculated are more elastic in the GAIDS system compared to the AIDS system in Senia [66]; however, only two of the 12 own-price elasticities are more elastic in the GAIDS system. In contrast, 68% of the elasticities presented in Duangnate and Mjelde [28] are larger in absolute values for the non-committed systems. However, for own-price elasticities, only 54% are more elastic in the non-committed systems. In Radwan et al. [63], only three (beef, lamb, and fish) of the five own-price elasticities are more elastic in the GAIDS model compared to the AIDS model, with expenditure elasticities being more elastic in only two of the five elasticities in the GAIDS model.

Interpretation of Committed Quantities and Elasticities
Up to this point, the discussion has generally been working under the definition of committed quantities as defined in Rowland et al. [2]; in this definition, the committed quantity varies little in the short run with respect to the price. However, because there are no restrictions on the signs of the estimated values, studies have either suggested or found estimated negative committed quantities. Such negative quantities are nonsensical in the above definition. In addressing this problem for the linear expenditure system, Pollak and Wales [58] interpret positive, committed quantities as committed levels and state if positive, the commodities' own-price elasticity of demand is inelastic, but they do not present estimated elasticities. The only interpretation for negative quantities is the commodity is own-price elastic; such an interpretation implies that estimated committed parameters cannot be interpreted as committed quantities. Estimated committed quantities and own-price elasticities estimated from the linear system presented in Radhakrishna [59] are in line with those reported in Pollak and Wales [58] for interpretation. Rowland et al. [2], as a counterexample, find positive, committed quantities, but their own price is elastic for some commodities in a GAIDS model. The use of the linear expenditure models versus GAIDS models may be part of this issue. Different interpretations highlight the need for further development and investigation of committed quantities in demand.

Discussion
This overview highlights the importance of committed consumption and its application in various commodities. Evidence from existing studies reveals that considering committed quantities may improve not only the statistical and theoretical performance of empirical analyses but also policy implications. A nagging question, however, arises, "Why do so few studies explicitly consider commitments in either estimating demand equations or in discussing estimated equations?" In the authors' search, fewer than 20 articles were found solely focusing on energy demand with committed quantities. Although additional research is necessary on committed quantities, it appears that including committed quantities statistically improves estimates and allows the model to satisfy economic theory. Further, including committed quantities is intuitively pleasing. One can conclude that including committed quantities provides "better" insights into the effectiveness of a policy in influencing consumption.
Most empirical models have shortcomings, and those incorporating committed quantities are no exception. Economic interpretations of negative committed quantities is controversial, and the meaning of estimated committed quantities that are larger than the estimated quantities demanded remains unsettled. Further studies are needed to address these limitations. As far back as 1954, it was noted, " . . . limitation of the general form can in principle be overcome if a theory of the limiting quantities can be developed" [4] (p. 526). This statement remains true today; an improved understanding of the committed quantities in estimation is necessary. Empirical evidence on the magnitude of elasticities between systems with and without committed quantities is sparse and inconclusive. Research should address this issue, as elasticities are often used in policy analysis.
Large knowledge gaps exist concerning committed quantities ranging from theoretical to practical issues. Our knowledge base would be advanced if future research began at the theoretical level by developing new models which incorporate committed quantities that are consistent with committed quantities being in the utility function. New policies' and technologies' effects on committed quantities are relatively unknown. How committed quantities change due to policies and new technologies should be investigated. Policy and technology affecting energy use range from simple changes, such as LED lighting requirements, to costly changes, such as installing residential solar panels or subsidizing electric vehicles. There are possible interactions among energy sources, committed quantities, and these policies. For example, electric vehicles may decrease committed levels for petroleum but increase committed levels for natural gas. LED lighting should decrease committed levels for electricity generation. As another example, policies emphasizing renewable energy sources for electricity generation will most likely have only a small effect on the committed use of electricity but will impact committed quantities of inputs into generation. These are longer-term issues related to the changes in committed quantities. Little to no research on these issues has been conducted, creating not only a large knowledge gap but also opportunities for future research. Such research will ultimately lead to better policy analyses and recommendations. Further, because most studies on committed quantities are at yearly or quarterly time frames, the analysis of shorter time frames may provide additional insights into committed quantities. Although the discussion has focused on energy, most, if not all, it is relevant to other commodities.