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

Abstract

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.

1. 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. Although not a new concept, the mention of committed quantities in demand analysis is basically nonexistent in these reviews. Rowland et al. [2] (p. 406) define committed quantities “… as the quantities of goods that are consumed in the short run with little regard for price; demand is almost perfectly price inelastic”. A consumer first purchases committed quantities and then allocates their leftover income (often denoted as supernumerary income) to the non-committed quantities for the goods [3,4,5]. Complicated searching for literature on committed quantities is the fact that a wide range of terms are used to refer to this concept. Among the terms used are: committed [3,4,6,7,8,9,10,11,12,13,14], subsistence [5,15,16,17,18,19,20,21,22], non-discretionary [23], necessary [4], required [15], baseline [22,24], pre-allocated [11], pre-determined [24], and pre-committed consumption [2,25,26,27,28].

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 non-committed 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.

2. Concept of Committed Quantities

2.1. 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 them—which 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.

2.2. 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, price-based policies must have larger increases in price to decrease consumption than when no consumption is committed.

3. Economic Modeling of Committed Quantities

3.1. 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,

$$\max U\left(x\right) \mathrm{subject} \mathrm{to} p^{\prime }x=\mu$$

(1)

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 $\mu$ denotes a consumer’s nominal income (hereafter income). The solution to this constrained maximization problem gives the Marshallian (or ordinary) demand functions, $x\left(p,\mu \right).$ 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., $x\left(tp,t\mu \right)=x\left(p,\mu \right)$ 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., $V\left(p,\mu \right)=U\left(x\left(p,\mu \right)\right)$. Properties of the indirect utility function are: (i) nonincreasing in $p$ and nondecreasing in $\mu$; (ii) homogeneity of degree zero in $p, \mathrm{and} \mu$; (iii) quasiconvexity in $p$; and (iv) continuity at all $p$ and $\mu$ [50]. These properties of the indirect utility, along with the positivity, are often denoted as the regularity conditions [49].

3.2. 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,

$$x_i={\beta }_i{c}_1\frac{p_1}{p_i}+\dots +{\beta }_i{c}_n\frac{p_n}{p_i}-c_i+\frac{{\beta }_i\mu }{p_i}.$$

(2)

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, ${\beta }_i$, on the goods [3]. With these assumptions, Equation (2) becomes

$$x_i=c_i+\frac{{\beta }_i\left(\mu -{\sum }_j{p}_j{c}_j\right)}{p_i}$$

(3)

where $\mu -\sum _j{p}_j{c}_j$ 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

$$p_i{x}_i=p_i{c}_i+{\beta }_i\left(\mu -{\sum }_{i=1}^n{c}_i{p}_i\right) \mathrm{or}$$

(4)

$$p_i{x}_i=p_i{c}_i+{\beta }_i\mu .$$

(5)

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 ${\beta }_i$ 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

$$w_i=\frac{c_i{p}_i}{\mu }+\frac{\overline{\mu }}{\mu }\left\{{\alpha }_i+{\sum }_{j=1}^n{\gamma }_{ij}\ln p_j+{\beta }_i\ln \frac{\overline{\mu }}{P}\right\}$$

(6)

where $c_i$ denotes the committed quantity of good i, $\overline{\mu }=\mu -{\sum }_{i=1}^n{c}_i{p}_i$ denotes the supernumerary income, and ${\sum }_{i=1}^n{c}_i{p}_i$ denotes expenditure on committed consumption. To avoid nonlinearity, Bollino [6] uses Stone’s price index of $\ln P=$ ${\sum }_{i=1}^{\mathrm{n}}{w}_i\ln p_{i }$ to generate a linear approximation. To satisfy the integrability conditions of additivity, homogeneity, and symmetry, the following restrictions are imposed on the GAIDS model,

$${\sum }_{i=1}^n{\alpha }_i=1,{\sum }_{i=1}^n{\beta }_i=0, {\sum }_{j=1}^n{\gamma }_{ij}=0, \mathrm{and} {\gamma }_{ij}={\gamma }_{ji}.$$

(7)

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

$$w_i=\frac{c_i{p}_i}{\mu }+\frac{\overline{\mu }}{\mu }\left\{{\alpha }_i+{\sum }_{j=1}^n{\gamma }_{ij}\ln p_j+{\beta }_i\ln \frac{\overline{\mu }}{P}+\frac{{\lambda }_i}{\beta \left(p\right)}{\left[\ln \frac{\overline{\mu }}{P}\right]}^2\right\}$$

(8)

where ${\lambda }_i$ denotes the effect of quadratic Engel curves on the expenditure share and $\beta \left(p\right)={\prod }_{i=1}^n{p}_i^{{\beta }_i}$ is a Cobb–Douglas price aggregator function [33]. In addition to Equation (7), ${\sum }_{i=1}^n{\lambda }_i=0$ is imposed to satisfy integrability and regularity conditions.

If committed quantities are not considered, and the Engel curve is linear ($c_i=0$ and ${\lambda }_i=0$), Equation (8) reduces to the AIDS model [55],

$$w_i={\alpha }_i+{\sum }_{j=1}^n{\gamma }_{ij}\ln p_j+{\beta }_i\ln \frac{\mu }{P}$$

(9)

where ${\alpha }_i$ 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

$$w_i=\frac{c_i{p}_i}{\mu }+\frac{\overline{\mu }}{\mu }\left\{m_i\left(U\right)+{\sum }_{j=1}^n{\gamma }_{ij}\ln p_j\right\}$$

(10)

where $m_i\left(U\right)$ denotes a general function of utility ($U$) [34]. Following Lewbel and Pendakur [56], Hovhannisyan and Shanoyan [34] suggest replacing $m_i\left(U\right)$ by ${\sum }_{r=\mathrm{o}}^R{\beta }_{ir}{y}^r$ where r denotes the order of a polynomial function. Defined as implicit utility and interpreted as a measure of the log real supernumerary expenditures, $y=\ln \overline{\mu }-w^{\prime }\ln p$ 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],

$${\sum }_{i=1}^n{\beta }_{i0}=1,{\sum }_{i=1}^n{\beta }_{ir}=0 \forall r=1,\dots R, {\sum }_{j=1}^n{\gamma }_{ij}=0, \mathrm{and} {\gamma }_{ij}={\gamma }_{ji}.$$

(11)

if committed quantities are not considered, Equation (10) becomes the EASI system of [56],

$$w_i=m_i\left(U\right)+{\sum }_{j=1}^n{\gamma }_{ij}\ln p_j.$$

(12)

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].

3.3. 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.

3.4. 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].

4. Studies Explicitly Considering Committed Quantities

A sample of studies that explicitly consider committed quantities are given in

Table 1. Sampling of Studies Summary Considering Pre-commitments in Estimated Energy Demands.

Study	Year	Country	Commodity	Energy Focus	Data	Obs.	Stated Model
[4]	1954	UK	Meat/fish/dairy/fats, fruit/vegetables, drink/tobacco, household expenses, durable goods, other	No	1920–1938 yearly	19	LES
[58]	1969	USA	Food, clothing, shelter, misc.	No	Annual 1948–1965	18	LES
[59]	1978	India	Fuel, light	No	National Survey	Not stated	LES
[60]	1987	UK	Natural gas, electricity	Yes	1972–1983 (12 years), Family Expenditure Survey	51,059	Derived from a two-stage budgeting model
[16]	1994	Taiwan, China	Seven commodity groups	No	Annual 1951–1990	Not given	LES
[23]	1997	USA	Electricity, natural gas, fuel oil, liquefied petroleum gas	Yes	1980, 1982, 1984, 1987, and 1990 consumption surveys	7823	LES
[61]	2000	Italy	Housing and fuel	Yes	1973–1992 household survey—Italian General Statistical Office	1729	LES, GAIDS, GQAIDS—various demographic specifications
[5]	2001	USA	Water	No	1981–1985, 186 community level	9340	Stone–Geary, GCD
[29]	2004	Spain	Water	No	1991–1999, private water company	108	Stone–Geary
[62]	2004	USA	Beef, pork, poultry	No	First quarter 1982–third quarter 1999	71	GAIDS
[26]	2007	USA	Beef, pork, poultry, fish	No	1976–2001 quarterly	104	AIDS, GAIDS
[63]	2009	Spain	Beef, pork, fish, lamb, chicken	No	Monthly January 1997 to September 2006, Government	Not given	AIDS, GAIDS
[33]	2011	China	beef/mutton, pork, poultry, seafood, vegetables, fruits, rice, other grains, milk/dairy products, eggs, fats/oil	No	Cross-sectional surveys of Chinese households between 1995 and 2003	1991 for 1995 and 4380 for 2003	GQAIDS
[7]	2012	Thailand	Electricity, fuel, food, water, and other nonfood	Yes	2006 Socio-Economic Survey	44,918	LES, input/output
[8]	2014	Italy	Electricity	Yes	January 2010–September 2011 Italian Power Exchange	>4400/hourly	GAIDS
[17]	2015	United Arab Emirates	Food, clothing, housing, furniture, transportation, medical care, recreation, miscellaneous	No	Monthly April 2007 to March 2008	12/month	LES
[64]	2015	Italy	Electricity	Yes	January 2010–December 2011 Italian Power Exchange	>4200/hourly	AIDS, GAIDS
[10]	2016	Italy	Electricity	Yes	January 2010–December 2011 Italian Power Exchange	>4200/hourly	GAIDS
[9]	2016	106 countries	Energy oil equivalents—Toe	Yes	Annual 2000–2013	Not given	GAIDS
[2]	2017	USA	Natural gas, oil, coal	Yes	1980–2014 Annual	35	GAIDS, AIDS
[11]	2017	64 countries	Energy consumption	Yes	1978–2012 Annual	2007	GAIDS, AIDS
[18]	2017	Taiwan, China	Electricity	Yes	1999–2014, National Survey	3297–3299 varies by income	Stone–Geary
[24]	2017	USA	Six food categories, canned fruit, fresh fruit, frozen fruit, canned vegetables, fresh vegetables, frozen vegetables	No	Monthly 2004 through 2014 Nielsen Homescan	132	AIDS, GAIDS
[34]	2019	Russia	Seven food categories	No	Quarterly surveys from 2007 to 2014	Not given	GEASI
[19]	2021	Sweden	Electricity	Yes	2005–2008 metered survey	13,482	Based on the Stone–Geary utility
[65]	2021	USA	Water	No	2010 and 2015	52	GEASI
[14]	2022	Italy	Wholesale electricity	Yes	January 2020–December 2020 hourly	>250,000 per month	GAIDS
[28]	2022	Thailand	Natural gas, petroleum, coal/lignite	Yes	Quarterly 1993–2019	108	GQAIDS, GAIDS, QAIDS, AIDS
[22]	2022	China	Coal, oil gas, coke, electric power, petrol, gas	Yes	Database of CGE model based on the 2012 input–output tables of China published by the National Bureau of Statistics	139 sectors, three primary factors (labor, capital, land), six economic entities, and eight types of circulation services	CGE modeling not stated how they use of committed quantities
[21]	2022	South Africa	Electricity, Liquid fuels (Petroleum)	Yes	2000–2018 Annual	18	LES

Focus: Energy is one of the main focuses—yes or no. Abbreviation: Obs.—number of observations, AIDS—Almost Ideal Demand System, GAIDS—Generalized Almost Ideal Demand System, LES—Linear Expenditure System, GQAID—Generalized Quadratic Almost Ideal, QAIDS—Quadratic Almost Ideal Demand System, GCD—Generalized Cobb–Douglas, GEASI—Generalized Exact Affine Stone Index. Toe—Ton of oil equivalent.

and

Table 2. Sampling of Studies Objectives and Findings.

Study	Year	Objective(s)	Com 1	Comments
[4]	1954	Derive a system of demand equations that possess economic theoretical desirable properties	No	Establishes a demand system from a simple expenditure system that satisfies theoretical conditions. Suggests a theory of limiting quantities is necessary.
[58]	1969	Examine different functional forms and estimation methods	Yes	Many habit models did not provide theoretically consistent estimates. Future work should examine more general forms of demand.
[59]	1978	Influence of prices and income on household consumption. Analyze destabilizing effects of changes in demand in grain markets	No	Estimates of positive, committed quantities result in price-inelastic demand. Increases in food grain prices may impact energy and light less than other commodities.
[60]	1987	Model household demand using microdata	No	Elasticities vary across households.
[16]	1994	Estimate aggregate consumer-demand behavior for Taiwan consumers	No	Subsistence parameters are positive for all commodity groups except the group of transport and communication. Negative subsistence parameters imply price-elastic demand.
[23]	1997	Discuss energy demand and expenditure patterns by race	No	Welfare depends on committed consumption. Policy impacts by race are not clear-cut. Welfare changes implied by marginal shares may be offset by non-discretionary patterns.
[61]	2000	Examine approaches to incorporate demographics into demand estimation	No	Compensated price elasticity indicates housing and fuel are luxury goods for households with fewer than two kids. Housing and fuel become more inelastic as the number of kids increases.
[5]	2001	Compare parsimony functional form to flexible forms that require more parameters	Yes	Stone–Geary results are comparable to flexible forms. Consumer committed water use level is >50% after accounting for system losses. Stress-committed consumption is short-run and needs to include long-run determinants.
[29]	2004	Not stated, examine how committed quantities may change over time for various policy implications.	Yes	Policies are not effective until the threshold level is reached, which is between 40% and 73% of consumption, depending on if the fixed component is allowed to change over time. Allowing fixed consumption to change reduces the committed quantity. Change possibility illustrates habits and durable ownership, and the rate of depreciation of habits is 0.46.
[62]	2004	Investigate consumers’ response to information on contaminants in meats.	Yes	Committed quantities are 86%, 57%, and 53% for beef, pork, and poultry. Response to food safety concerns is small relative to price responses.
[26]	2007	Investigate how consumers respond differently to income, price, and committed consumption.	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.
[63]	2009	Determine the effects of food safety information effects on meat demand	Yes	Elasticities from GAIDS are more consistent with the characteristics of the fish and meat markets in Spain than those from the AIDS model.
[33]	2011	Examine food demand structure and its dynamics in urban China	Yes	The structure of food demand in 1995 and 2003 differs. Urban Chinese households appear to generally consume no commodity in committed quantities except eggs in 1995, while there was committed consumption of fine grains in 2003.
[7]	2012	Evaluate the effect of pollution tax policy on consumption, economic growth, and reducing emissions in both long and short term	Yes	Uses demand elasticity results in the input–output model. All minimum consumption levels are significant. Committed levels are electricity and fuel—10, food—45, nonfood—44, and water—1 as a percent of expenditures.
[8]	2014	Construct a theoretical model of demand behavior to estimate hourly demand elasticities at the consumer level	No	Consumer elasticities are larger when substitutes are available and during peak hours, weekdays, and the winter.
[17]	2015	Use compensated elasticities to examine household welfare of price increases	Yes	Total committed levels vary by household income ranging from 22 to 31% of expenditures. Discretionary income allocated to transportation ranges between 26 and 38% and housing between 26 and 38%.
[64]	2015	Test whether agents behave rationally in the electricity market	No	GAIDS is statistically better than AIDS. Committed quantities differ for some hours of the day.
[10]	2016	Develop a design to determine zonal prices using individual electricity bids	No	Optimal pricing can increase welfare.
[9]	2016	Design optimal carbon pricing making use of household demand behavior	No	Optimal pricing can reduce carbon emissions and improve worldwide welfare.
[2]	2017	Determine how accounting for committed levels may influence demand responses to price changes	Yes	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.
[34]	2019	Estimate committed demand for key food commodities and estimate elasticities that account for commitments	Yes	Committed quantities account for 59, 72, 98, and 67% of cereal, eggs, fats/oils, and sugar 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.

. 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.

4.1. 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.

4.2. 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.

4.3. 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.

4.4. 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.

4.5. 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.

5. 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.