The Journal of Socio-Economics 37 (2008) 2278–2290

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The Journal of Socio-Economics

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X-inefficiency in the use of income to attain economic satisfaction

Mariano Rojas ∗

Department of Economics, Facultad Latinoamericana de Ciencias Sociales - Mexico, and Universidad Popular Autonoma del Estado de Puebla,21 Sur 1103, Col. Santiago, Puebla 72160, Mexico

a r t i c l e i n f o

Article history:Received 22 September 2007Received in revised form 12 March 2008Accepted 3 April 2008

JEL classification:D1 (D11, D12, D13)D61I31

Keywords:Subjective well-beingEconomic satisfactionX-inefficiencyConsumptionIncomeMexico

a b s t r a c t

This investigation uses a subjective well-being approach to provide a novel empirical answerto an old normative debate in economic literature: whether consumers use efficiently theirincome. Based on a large database from Mexico, the paper shows that there exists substantialX-inefficiency in the use of income; even when a relaxed criterion to define the thick frontieris followed. X-inefficiency in the use of income can emerge from personal errors and fromsocial-organization deficiencies. Sustainable development concerns make it critical to focuson reducing X-inefficiency as an alternative way to increase economic well-being.

© 2008 Elsevier Inc. All rights reserved.

1. Introduction

This paper states that the pursuing of greater economic well-being can be attained not only by having more resourcesbut also by using them efficiently. There are two non-exclusive roads for increasing economic well-being: a first road isassociated to the long-standing tradition of emphasizing raises in income; this tradition can be traced back to the birth ofpolitical economy (Pasinetti, 2005) and it has led to economics overstressing income growth. The second road is associatedto using income more efficiently; Frank (2005, p. 70) suggests that “people might have been able to spend their money inother ways that would have made them happier, yet for various reasons did not”. This second road states that people maynot use their income efficiently to attain economic well-being; in other words, it states that there is X-inefficiency in the useof income. The study of X-inefficiency in the use of income has been widely neglected by economics, probably because of itsemphasis on the assumptions of rationality and non-observable economic well-being.

Increasing economic well-being through income growth is becoming a difficult task because of limited economicresources and a fragile ecosystem. Hence, it is imperative to explore alternative ways of attaining more economic well-being with the same income. The reduction of X-inefficiency in the use of income could be an alternative if inefficiencyis shown to be large. This paper deals with the existence and magnitude of X-inefficiency. It shows that inefficiency issubstantial.

∗ Tel.: +52 222 8888936.E-mail address: mariano.rojas.h@gmail.com.

1053-5357/$ – see front matter © 2008 Elsevier Inc. All rights reserved.doi:10.1016/j.socec.2008.04.001

M. Rojas / The Journal of Socio-Economics 37 (2008) 2278–2290 2279

The paper follows a subjective well-being approach to study economic well-being. An economic satisfaction (ES) variableis constructed based on some satisfaction questions. Hence, it is possible to study the role of income in generating economicwell-being, as well as the existence of X-inefficiency in the use of income.

Thus, the paper addresses the existence and magnitude of X-inefficiency in the relationship between income and economicsatisfaction. The empirical analyses are based on a large cross-section database from Mexico. An economic satisfactionvariable net of a person’s affective state is constructed. A thick-frontier methodology is used to calculate an efficient frontier.Different indicators for X-inefficiency are calculated. It is found that X-inefficiency is relatively large, that many years ofincome growth would be required to attain what could be achieved by reducing X-inefficiency, and that X-inefficiency is aphenomenon presented at all income levels. Thus, there seems to be an enormous waste of current economic resources.

Because of its magnitude and presence in all income groups X-inefficiency is a phenomenon that requires further attention.Further research should focus on policies to reduce X-inefficiency as an alternative way to increasing income. In other words,economics should be concerned not only about increasing the endowment of resources for economic well-being, but alsoabout its efficient use.

The paper is structured as follows: Section 2 discusses the X-inefficiency concept and its application to the relationshipbetween income and economic well-being. This section elaborates on the reasons for expecting X-inefficiency in the use ofincome to be large. Section 3 explains the database as well as the construction of the relevant variables; special considerationis placed in the construction of the economic satisfaction variable and on getting rid of noise introduced by a person’s affectivestate at the moment of the interview. Section 4 uses a thick-frontier approach (TFA) to estimate X-inefficiency in the use ofincome. This section develops several indicators of X-inefficiency, and it studies whether X-inefficiency varies along incomegroups. Section 5 presents the main conclusions from the investigation.

2. Literature review

2.1. On the X-inefficiency concept

Leibenstein (1966) noted that firms and organizations work neither as hard nor as effectively as they could. He introducedthe X-inefficiency concept to refer to an inappropriate use of the organization’s resources to attain its objectives. The conceptwas introduced as part of the literature on the theory of the firm. The idea of firms acting inefficiently generated a debate inthe literature (Stigler, 1976; Leibenstein, 1978).

X-inefficiency refers to the difference between a firm’s efficient output – which depicts the maximum attainable outputfor a given level of input – and its current output (Kwan and Eisenbeis, 1996; Berger and Mester, 1997):

Xinef = q∗(Mi) − q(Mi)q∗(Mi)

(1)

where Xinef is the X-inefficiency, q* the efficient output, q the observed output, M the inputs vector and i denotes agent i.In the theory of the firm, X-inefficiency emerges because of administrative problems within the firms. It is understood

as a mistake that originates from both personal errors and organizational deficiencies. In principle, competition could driveX-inefficiency out of the market (Alchian, 1950); however, Leibenstein (1975, 1976) states reasons for this not being the case.

Economic theory has stressed the study of X-inefficiency in the production side (Berger and Humphrey, 1991; Berger andMester, 1997; Berger et al., 1993; Caves and Barton, 1990; Fried et al., 1993; Gardner and Grace, 1993; Green and Mayes,1991).

There are reasons to believe that X-inefficiency may be substantial in the income-allocation side, as well as to believethat competition forces do not perform well in reducing X-inefficiency in the consumption side. However, economic researchhas completely neglected X-inefficiency in the consumption/income-allocation side—a recent paper by Earl (2007) discusessome factors that could imply X-inefficiency in the consumption side. It is very likely that research has been deterred by theabsence of a measurable output variable for consumer’s allocation of income. The increasing acceptance by economists ofthe subjective well-being approach allows working with a measurable output for income-allocation: economic satisfaction.

2.2. Subjective well-being: an observable output for income use

There has been little research – but a lot of conjecture – about the existence of X-inefficiency in the income-allocation andconsumption literature. The absence of a measurable output variable for consumer’s allocation of income has led researchersto use variables such as food and nutritional intake; however, these variables are intermediate rather than final goals.1

The emergence of the ‘economics of happiness’ literature (Easterlin, 1974, 1995, 2001; Clark and Oswald, 1994; Di Tellaet al., 2001; Ferrer-i-Carbonell and Frijters, 2004; Frey and Stutzer, 2000, 2002; Layard, 2005; Oswald, 1997; van Praagand Ferrer-i-Carbonell, 2004; Stutzer, 2004) provides not only the tools, but also the epistemological support and academic

1 Research using variables such as food and nutritional intake face the same critique advanced by Stigler (1976) to the study of X-inefficiency in theproduction side: that it fails to recognize differences in objectives among producers. It is rather curious that while Stigler (1976) argues in favor of allowingfor differences in producers’ objectives, Stigler and Becker (1977) argue in favor of assuming that consumers do have the same utility function.

2280 M. Rojas / The Journal of Socio-Economics 37 (2008) 2278–2290

endorsement to have an observable output variable for consumers’ use of income2: economic satisfaction.3 Hence, economicsatisfaction is used to study the existence and magnitude of X-inefficiency in the use of income to attain economic well-being.

2.3. X-inefficiency in the use of income

2.3.1. The role of income in economicsEven though utility lost much of its well-being substance in the ordinal-utility approach, microeconomic theory still

stresses the fundamental role of income as a mean to attain higher economic well-being. Economists also stress the impor-tance of income through the vast literature on economic growth – economic growth is justified because of its presumedpositive well-being impact, and through the poverty literature – poverty is associated to low income. Hence, economic the-ory recognizes that income is an important resource – maybe the most important one – for economic well-being. Thus, itis possible to think of a production function where income is the input variable and economic satisfaction is the outputvariable.4

ESi = f (Yi) + (�i − �i) f ′Y > 0 (2)

where ES: economic satisfaction; Y: income; v: stochastic error term that is assumed independent and identically dis-tributed with mean 0 and constant variance; �: non-negative random independently distributed error used to capture theX-inefficiency; f: refers to an efficient or frontier relationship5; i: refers to person i.

All observations would be in the frontier if persons were using their income efficiently (�i = 0 for all i); observed dispersionat any income level would originate from factors such as affective states influencing a person’s answer to an economicsatisfaction question (Schwarz and Strack, 1991, 1999) and other conditions of the interview. On the other hand, X-inefficiency(�i > 0 for some i) would imply that many observations are beneath the efficient frontier and that a substantial part of theobserved dispersion in economic satisfaction at any income level would be explained by deviations from this frontier.

In a world where income is used efficiently, it is only through higher income that economic satisfaction can be raised;thus, economic policy should emphasize economic growth as the road for increasing economic well-being. However, in thepresence of X-inefficiency in the use of income, economic policy could also focus on the reduction of X-inefficiency as analternative way to increase economic well-being. Thus, economic research should focus not only on increasing resources butalso on increasing their efficient use to generate economic satisfaction; and economists should be concerned about usingeconomic resources efficiently as much as they are about increasing their quantity.

2.3.2. Economic theory and X-inefficiency in income useIn a resemblance of the production situation, X-inefficiency in the use of income could emerge from personal errors as

well as from organizational deficiencies. X-inefficiency refers to the existence of a correctable mistake. It could originatefrom persons’ errors in allocating their income; in this case, persons should be willing to accept that an error exists andshould be capable – probably with some assistance or information – of modifying their behavior. X-inefficiency could alsooriginate from a social-organization deficiency; so that even if each person is acting correctly within society’s norms, thesenorms lead them to an inefficient use of their income in attaining economic satisfaction.

The existence of (systematic) personal errors is rejected by neoclassical economic theory based on the rationality assump-tion. It has been recognized that it is futile to discuss the validity of the neoclassical maximization hypothesis, since it canalways be re-formulated to make any action seem rational (Boland, 1981). However, there is a growing literature questioningthis assumption and stating that systematic personal errors in consumption may be normal.

Simon (1982) states that human capabilities to solve relatively complex decision problems are limited. Thaler (1992)further elaborates on humans’ limitations to behave as rational agents. He states (Thaler, 2000) that consumption theoryis incomplete to model real consumers—who are slow learners and heterogeneous in their cognitive capabilities. He alsoargues for greater consideration of the role of psychological states in the behavior of consumers by incorporating compulsivebehavior (Weinberg and Gottwald, 1982; Rook, 1987), persuaded behavior (Packard, 1957; Galbraith, 1958), and self-controlproblems (Ameriks et al., 2004). Deci and Ryan (1985), Hanley and Wilhelm (1992), Kasser and Ryan (1993, 1996), and Kasser(2002) have further studied the role of psychological needs in consumption. They show that persons may follow the wrongstrategy of attempting to satisfy their underlying psychological needs through higher consumption. This wrong strategyleads people to make substantial expenditures while attaining little satisfaction; social and commercial persuasion fostersthese wrong consumption decisions.

2 ‘The use of income’ refers to a concept broader than consumption, since it also incorporates savings considerations.3 The economics-of-happiness literature usually works with happiness and life-satisfaction variables. However, it has been found that income is weakly

related to happiness and life satisfaction; there seem to be more things in life than the standard of living, and for most people there seem to be moreimportant things, which are unrelated to income (Rojas, 2006a). Hence, for the purposes of this study it is better to focus on economic satisfaction, whichrefers to satisfaction in one domain of life and which is strongly related to income.

4 This function resembles the indirect utility function.5 It is possible for the efficient frontier to differ across a person’s socio-demographic situation; e.g. age, education, gender, and marital status.

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Recent work from the behavioral-economics school has further questioned the rationality assumption. Thaler (1980)argues that a rational theory of consumption is prescriptive rather than descriptive. Pioneer work in behavioral economicsshows that choice is sensitive to the framing of decisions (Tversky and Kahneman, 1974, 1981, 1986), that decision makers dofollow heuristics (Kahneman and Tversky, 1982, 1984), and that decision makers are prone to prediction biases (Kahnemanand Tversky, 1973, 1979). Loewenstein and Schkade (1999) have shown that there may be systematic mistakes in people’sprediction of their experienced utility from consumption decisions, and that people have mayor problems foreseeing adapta-tion and habituation processes. Hsee and Hastie (2006) and Hsee and Leclerc (1998) have further elaborated on consumptionrules and erroneous consumption decisions. Kahneman (1994) discusses the challenges raised by behavioral studies to therationality assumption in economics. Camerer and Loewenstein (2003) and Rabin (1998, 2002) further question the ratio-nality assumption. Recent studies about the neurology of decision-making also support their arguments (Camerer et al.,2005).

Scitovsky (1976) mentioned that some persons may lack skills to make correct consumption decisions. In addition, hestates that some consumers may fall into an adverse-selection trap by spending too much in comfort and too little instimulation, which leads them to lower than possible satisfaction.

In a recent contribution, Earl (2007) elaborates on reasons for X-inefficiency in consumption being possible. Some reasonsfor consumers being likely to err are: the increasing complexity of products and the existence of synergies when they arejointly consumed. The increasing variety of products consumers must choose from. The acceleration in innovation andobsolescence rates of products, which makes it almost impossible to keep track of all advances and complicates appropriatepurchasing–timing decisions. The reduction in consumer’ social networks that used to provide useful information on productsand consumption practices. Complexity in the design of contracts for consumption of services (e.g. difficulties in foreseencontingencies and in specifying expected results). Consumers’ lack of training in making correct decisions, in special whenchanging personal and surrounding situations make their previous consumption rules obsolete.

Income-allocation decisions are taken within a specific household context. Hence, they are influenced by intra-householdarrangements and norms (Rojas, 2006b). The role of intra-household arrangements has been widely neglected by individu-alistic consumer theory.

The argument of personal errors taking place in the consumption side is strengthened by the difficulty for market forcesto play a corrective function. Inefficient consumers are not driven out of the ‘consumers market’ by consumer-competitionforces; consumers may remain in the market as long as they have purchasing power, independently of whether theirpurchasing power is efficiently used.

It must be recognized that persons making income-allocation decisions are much more than the individualistic consumersportrayed by economic theory. Persons not only live in a society but they are shaped and defined as such within their society.X-inefficiency in the use of income could emerge not only from personal errors but also from social organizational deficiencies.

Smith and Marx recognized the relevance of relative income, so that a person or household income had to be placed withina social context. Veblen (1927) argued for the conspicuous role of consumption; Duesenberry (1949) focused on the roleof relative income in explaining savings; and Leibenstein (1950) discussed the existence of interdependent preferences.6

Easterlin (1974) showed that happiness depends on relative income. Hirsch (1976) introduced the notions of positionalsocieties and positional goods. Carlsson et al. (2005) and Alpizar et al. (2005) have studied the positional role of goods. Thereis no research on people’s capacity to accurately foresee how their relative position will be affected by the purchasing ofsome commodities; however, findings from the behavioral-economics school make it possible to hypothesize that status-conscious people may err by unforeseen social interactions and, in consequence, by believing that the positional attributesof a commodity will last long (Frank, 2005; Cooper et al., 2001).

Status is a crucial variable in most societies, and in some of them consumption has attain a central role as status indicator.Fromm (1976) warned about the importance some societies placed on having rather than on being. Some people are morevulnerable to consumption-based status races (Hopkins and Kornienko, 2004) because of their values and their upbringing(Kasser, 2002; Kasser et al., 2002; Phelps, 2005). Furthermore, these consumption-based status races may generate a socialgame where rational agents end up overspending and overworking (Schor, 1992, 1998, 2002; Dupor and Liu, 2003).

Postmodernist philosophers and sociologists provide a deeper questioning of the role consumption plays in societies.Foucault (1969) talks about ‘the disappearance of the subject’; he means that the person, as an agent dissociated from her7

consumption bundle and with a pre-consumption identity, has disappeared in modern societies. Postmodernists state thatin modern times a person’s identity is defined within a consumption society, and it cannot be detached from consumptiontrends and excesses. Thus, multifaceted autonomous persons have been diminished to no more than plain consumers, whoplay an instrumental role within the consumption-society machinery. Persons are no longer driving societies, but they havebecome gadgets with a mere consumption role in these societies.

In a modern society consumption does not take place to satisfy an objective need, but it is determined by the production ofsocial distinction (Bourdieu, 1986), status value, and significance codes (Baudrillard, 1998, 2000). Non-autonomous personsare easily seduced by consumption tendencies, by ostentation desires, and by induced feelings of insatiability that foster their

6 See also Postlewaite (1998) for a discussion of the social basis of interdependent preferences.7 This paper uses a gender-biased style for simplicity of exposition; there is no intention of offending persons of any gender.

2282 M. Rojas / The Journal of Socio-Economics 37 (2008) 2278–2290

Table 1Descriptive statistics for subjective economic well-being variables

Mean Standard deviation

Income satisfaction 4.27 1.21Purchasing power satisfaction 4.23 1.18Housing condition satisfaction 4.66 1.16Financial satisfaction 4.45 1.20

Economic satisfaction 4.41 1.01

consumption desires.8 Because their identity cannot be dissociated from their consumption, these consumers have becomecompletely malleable (Lipovetsky, 1983, 1987) and may end up having lower economic satisfaction than autonomous persons,even when they are spending more.9

3. Database and variables

3.1. The survey

A survey was conducted in five states of central and south Mexico as well as in the Federal District (Mexico City) duringOctober and November of 2001.10 A stratified-random sample was balanced by household income, gender, and urban–ruralareas. The sample of 1540 questionnaires had a response rate of 96% with respects to household income. The sample size isacceptable for inference in central Mexico.

3.2. The variables

Economic satisfaction (ES) variable: four questions related to satisfaction in the economic domain of life were asked:how satisfied are you with your income? (income); how satisfied are you with what you can purchase? (purchasing power);how satisfied are you with your housing conditions? (housing condition); and how satisfied are you with your household’sfinancial situation? (financial situation). Each satisfaction question had a seven-option verbal answering scale, ranging fromextremely unsatisfied to extremely satisfied: extremely unsatisfied, very unsatisfied, unsatisfied, neither unsatisfied norsatisfied, satisfied, very satisfied, extremely satisfied. Satisfaction questions were handled as cardinal variables, with valuesbetween 1 and 7; where 1 was assigned to the lowest satisfaction level and 7 to the highest.

Economic satisfaction is constructed as a simple average of these four satisfaction variables.11 Table 1 shows some descrip-tive statistics for the satisfaction variables, as well as for the constructed economic satisfaction variable. On average, people arein between satisfied and neither satisfied nor unsatisfied with their economic situation. Satisfactions with housing conditionand with financial situation are – on average – greater than with income and purchasing power.12 It is also observed thatthere is a relatively high degree of dispersion in these satisfaction variables.

Equivalent income variable (Yswb-eq): The survey gathered information about household income, household income depen-dents, and their age structure. It has been shown that economic satisfaction does show significant scale economies in familysize (Rojas, 2007) Thus, this investigation uses a subjective well-being equivalent income constructed by Rojas (2007) andwhich has been shown to better explain economic satisfaction. The Yswb-eq of a household with household income YH andsize S – with composition of adults, teenagers and children equal to Sadu, Stee, and Sch, respectively – is calculated as

Yswb-eq(Sadu, Stee, Sch) = YH

(S0.9076adu + S0.8240

tee + S1.0404ch )

0.5119(3)

Thus, the Yswb-eq implies substantial scale economies within the family; as well as differences by age structure. A similarmethodology has been used by van Praag and van der Sar (1988) and van Praag and Ferrer-i-Carbonell (2004).

Affect balance scale (ABS): Schwarz and Strack (1991, 1999) have shown that subjective answers are sensitive to the affectivestate of the interviewee. Although the impact of a person’s affective state is expected to be stronger for happiness and life-satisfaction assessments than for economic satisfaction assessments, it is important to recognize that economic satisfactionvariables could be influenced by a person’s affective state. This investigation considers the effect of a person’s affective state

8 Galbraith (1958) advanced the creation-of-needs argument; four decades later, Kotler (1999) provides support to his argument.9 Recent research in the economics-of-happiness has studied the formation of aspirations and the role of evaluation norms in economic satisfaction. See

van Praag and Ferrer-i-Carbonell (2004) and Stutzer (2004).10 The author expresses his gratitude to CONACYT, Mexico for a grant that financially supported this research.11 Hence, the values for the constructed economic satisfaction variable can be interpreted in the 1–7 categorical range. It was found that results do not

change substantially if the economic satisfaction variable is constructed through factorial analysis techniques rather than as a simple average.12 The four satisfaction variables are highly correlated. In fact, a factorial analysis indicates that the first principal component captures 72.5% of the variance

observed in the four satisfaction variables. Thus, it is expected for the main results not to be very sensitive to the inclusion or exclusion of one underlyingvariable, or to the way these four variables are reduced to a single dimension.

M. Rojas / The Journal of Socio-Economics 37 (2008) 2278–2290 2283

Table 2Explaining economic satisfaction

Coefficient Prob. > t

Constant 0.737 0.00Ln Y 0.335 0.00Mood 0.575 0.00Emotion 0.844 0.00Gender −0.042 0.36Age −0.004 0.03Education 0.078 0.00Married −0.085 0.13Stable partner −0.234 0.04Separated −0.077 0.58Divorced −0.109 0.53Widowed 0.155 0.27

R2 0.280

on her subjective economic evaluation as noise; however, this assumption could be a matter of debate.13 An ABS questionnaire(Bradburn, 1969) was applied to gather information about the affective state of the interviewee. This questionnaire has beenwidely used; it consists of 10 items related to positive and negative affects. Answers are coded so as to have a value of 1in case of positive affect and a value of 0 in case of negative affect. A principal-components technique was applied to the10 items, and two main variables were constructed: a Mood variable (tired, lonely, bored, depressed, and irritated), whichis expected to reflect a more stable affective state, and an Emotional variable (interested, proud, pleased, feeling wonderful,things going as wanted), which is expected to reflect a more transitional affective state. These variables are rescaled to a 0–1scale, their value increases with positive affect.

Demographic and Social Variables: The survey also gathered information about the interviewee’s education, age, gender,and marital status.

3.3. Calculating a structural economic satisfaction (SES)

It was stated earlier that a person’s affective state influences her economic satisfaction assessment. A person’s affectivestate could introduce unwanted noise in the study of X-inefficiency in the relationship between income and economicsatisfaction; for example, X-inefficient observations could show up as efficient ones if a person is in a positive affectivestate when interviewed. Hence, this investigation assumes that there is an underlying economic satisfaction which is netof the interviewee’s affective state; this underlying variable better reflects a person’s economic satisfaction. The followingprocedure is used to calculate the structural economic satisfaction (SES) variable.

3.3.1. The impact of a person’s affective stateThe following regression is run to estimate the impact of a person’s affective state on her reported economic satisfaction:

ESi = ˛0 + ˛Y ln Yi + ˛MMi + ˛EEi + ˇZi + �i (4)

where ES: economic satisfaction; Y: household equivalent income; M: mood state; E: emotional state; Z refers to a vectorof control variables: gender, age, education, and marital state (single is category of reference) ˇ is a vector of parameters; irefers to person i; �: error term.

Table 2 shows the estimated coefficients for regression (4), an OLS estimation technique is used. It is observed that moodand emotional state do have a large and statistically significant impact on a person’s economic satisfaction. Moving from oneextreme to the other in a person’s affective state would raise her economic satisfaction in about 1.4 points.14

3.3.2. Calculating an underlying SESA SES variable is calculated by neutralizing the impact of a person’s affective state. Every person is assumed to have the

sample mean mood and emotional states (0.66 and 0.61, respectively) rather than their corresponding affective states.15 Thus,SES refers to the economic satisfaction of a person who is in an average affective state, and it is calculated as

SESi = ESi − ˆ M(Mi − M) − ˆ E(Ei − E) (5)

where SESi: person i’s SES; M: sample mean for mood state; E: sample mean for emotional state.

13 A person’s affective state could reflect transitional emotional factors, as well as her personality. Up to a certain degree, her affective state could be relatedto her economic condition; however, her affective state could also depend on many other factors. For a discussion of the relationship between emotion andcognition see the book by Frijda et al. (2000).

14 The magnitude of this value can be illustrated by comparison to the impact of income: it would be needed for income to increase about 70 times toachieve a similar increase in economic satisfaction.

15 Two persons in the sample got a SES value above 7; hence, their SES value was set to be equal to 7.

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Table 3Structural economic satisfaction (SES) along income groups

Income group Number of observations Mean SES Standard deviation for SES

Bottom1 73 3.82 0.922 71 3.86 0.953 74 3.91 0.824 73 4.07 0.845 74 4.12 0.916 71 4.04 0.747 65 3.88 0.908 81 4.06 1.029 72 4.31 0.8110 71 4.58 0.8011 77 4.42 0.9212 74 4.24 0.8513 68 4.58 0.9314 72 4.64 0.8115 73 4.60 0.9416 73 4.74 0.7917 74 4.80 0.7918 71 4.81 0.8519 76 5.12 0.80

Top20 72 5.15 0.75

3.3.3. SES along income groupsObservations in the sample are ordered based on their income, and 20 income groups are formed. Each group contains

about 5% of the observations in the sample. Table 3 presents the number of observations in each income group, as well as theirSES mean and standard deviation values. As expected, mean SES tends to increase with income. The study of X-inefficiencyemphasizes the existence of relatively large standard deviation values. It is observed that with a deviation of one positivestandard deviation with respect to her group’s mean value, a person in the bottom income group could have the same SESthan a person with a mean value in income group 16, and a larger SES than a person in the top income group with onestandard deviation below her mean value. This high dispersion in SES in all income groups indicates that it is possible tohave highly satisfied and highly unsatisfied persons in all income groups.

4. X-inefficiency in the use of income

Inefficiency is measured based on how far a person’s economic satisfaction deviates from a “best observed practice” forher corresponding income (an efficient frontier). The efficient frontier is unknown and must be estimated from informationfrom the data set. There are three approaches to estimate the frontier: data envelopment analysis (DEA), stochastic frontierapproach (SFA), and TFA (Bauer, 1990; Bauer et al., 1991, 1993) This investigation follows a TFA to estimate the highest possiblelevel of economic satisfaction for a person with a given income; thus, rather than having an efficient curve the paper assumesan area of efficiency.

4.1. Observations in the thick frontier

Observations in each income group are divided into two groups: those observations in each income group with higheconomic satisfaction are assumed to belong to the frontier, and their X-inefficiency is assumed to be equal to zero.16

Observations in each income group with relatively low economic satisfaction are assumed to reflect X-inefficiency in the useof income to attain economic satisfaction; these observations are placed beneath the efficient frontier (Bauer et al., 1991).

There is no clear criterion to identify the number of observations considered as efficient in each income group. Some tech-niques have been advanced to identify the efficient observations, such as a recursive methodology proposed by Wagenvoortand Schure (2006); however, these techniques do not get rid of arbitrariness in the decision. The decision about the numberof observations placed in the frontier depends on practical reasons such as the number of observations available, as well ason the desire to follow either a strict or a lenient criterion. This investigation follows a lenient criterion, with about one-thirdof all observations placed in the frontier. If X-inefficiency is found to be large even under a lenient criterion then the paper’smain argument (that X-inefficiency is significant) is strengthened. Observations in each income group are ordered basedon their economic satisfaction and the top third of the observations in each income group are considered as efficient and

16 It is said that this methodology estimates relative-to-best-observed-practice X-inefficiency, because the true efficient frontier could be above theselected observations and not be observed at all.

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Table 4Structural economic satisfaction and income levels mean values along income groups for observations in and out of the efficient frontier

Income group Number of observations Structural economic satisfaction Incomea

In frontier Out of frontier Mean in frontier Mean out of frontier In/out Mean in frontier Mean out of frontier In/out

Bottom1 25 48 4.92 3.25 1.51 446 416 1.072 25 46 4.94 3.27 1.51 814 799 1.023 25 49 4.83 3.45 1.40 1,078 1,082 1.004 25 48 4.99 3.59 1.39 1,343 1,304 1.035 25 49 5.07 3.63 1.40 1,580 1,561 1.016 25 46 4.85 3.60 1.35 1,786 1,777 1.017 25 40 4.78 3.32 1.44 2,016 2,006 1.018 25 56 5.18 3.57 1.45 2,190 2,203 0.999 25 47 5.15 3.86 1.33 2,451 2,438 1.0110 25 46 5.35 4.16 1.29 2,705 2,690 1.0111 25 52 5.33 3.98 1.34 2,962 2,970 1.0012 25 49 5.18 3.77 1.37 3,266 3,327 0.9813 25 43 5.47 4.07 1.34 3,744 3,678 1.0214 25 47 5.46 4.20 1.30 4,278 4,202 1.0215 25 48 5.57 4.09 1.36 4,898 4,928 0.9916 25 48 5.52 4.33 1.27 5,785 5,741 1.0117 25 49 5.61 4.39 1.28 7,017 6,930 1.0118 25 46 5.66 4.35 1.30 8,876 8,629 1.0319 25 51 5.95 4.72 1.26 11,832 11,897 0.99

Top20 25 47 5.94 4.73 1.26 19,558 22,676 0.86

Whole sample 500 955 5.29 3.92 1.35 4,431 4,573 0.97

a Monthly subjective-well-being equivalent household income in Mexican pesos. Exchange rate approximately US$1 dollar for 9.3 Mexican pesos.

Table 5Socio-demographic indicators in and out of the frontier

Mean in frontier Mean out of frontier In/out

Gender (male = 1) 0.52 0.55 0.95Age 33.7 36.4 0.93Education 4.17 3.94 1.06

are placed in the efficient frontier. The rest of observations in each income group are considered as inefficient.17 Dispersionacross observations in the frontier is assumed to emerge from stochastic factors; while observations out of the frontier areassumed to reflect X-inefficiency in the use of income to attain economic satisfaction. Hence, 500 out of 1472 total observa-tions are classified as efficient ones; they do represent 34% of all observations. Because of the lenient criterion, the frontiercan be considered as being very thick.

Table 4 reports some descriptive statistics about the number of observations, the mean SES, and the mean income forobservations in and out of the efficient frontier in each income group. A good classification should imply substantial differ-ences in SES but not in income between observations in and out of the frontier; the classification used in this investigationsatisfies that condition.

On average, there are substantial differences in economic satisfaction between observations in and out of the frontier.Observations in the frontier report an economic satisfaction that is, on average, 35% higher than that reported by observationsout of the frontier. This figure is about 50% for observations in the bottom income groups and about 26% for observations inthe top income groups.

It is also observed in Table 4 that, on average, there is no difference in income levels between observations in and out of thefrontier. Furthermore, there are not significant differences in mean income between observations in and out of the frontieracross income groups; the highest income group becomes the exception, where mean income is lower for observations in thefrontier. In general, this is a favorable characteristic, because it implies that any difference in economic satisfaction betweenobservations in and out of the frontier cannot be attributed to differences in income levels. In consequence, it is sound tostate that differences in economic satisfaction cannot be attributed to differences in income but to differences in the wayincome is used to attain economic satisfaction.

Table 5 further explores differences in socio-demographic characteristics for observations in and out of the frontier. It isobserved that differences in gender, age and education between persons in and out of frontier are not large. People in thefrontier are slightly more educated and younger, and there are relatively more females in the frontier that out of the frontier.

17 It is clear that the magnitude of the estimated X-inefficiency is very sensitive to the strictness of the criterion. A very strict criterion does imply higherestimated X-inefficiency than a lenient one.

2286 M. Rojas / The Journal of Socio-Economics 37 (2008) 2278–2290

4.2. Estimating the frontier

The 500 observations in the frontier are used to estimate the efficient frontier; which represents the best-observedpractice in the use of income to attain economic satisfaction. The following regression is used

SESi = ˛ef0 + ˛ef

Y ln Yi + ˇefZi + �i i�efficient observations (6)

All variables have been previously defined.Table 6 shows the results from the econometric exercise, an OLS estimation technique is used. It is observed that income

is a relevant variable in explaining economic satisfaction in the frontier, as well as age. Education is slightly relevant, whilegender does not make a difference. Marital status plays a role.

The estimated parameters in Eq. (6) are used to calculate the corresponding efficient economic satisfaction for thoseobservations out of the frontier.

4.3. X-inefficiency indicators

The following formula uses the estimated coefficients from the efficient frontier to calculate the corresponding efficientSES for those observations placed out of the frontier:

SESefj = ˆ ef

0 + ˆ efY ln Yj + ˆ efZj j�inefficient observations (7)

The difference, in satisfaction points, between the corresponding efficient SES and the current one for an inefficientobservation j is given by

XDiffinef−j = SESef

j − SESj (8)

X-inefficiency, as a percentage of the efficient SES, for an inefficient observation j is given by

Xinef−j(SESef) =(SESef

j − SESj)

SESefj

× 100 (9)

X-inefficiency, as a percentage of the current inefficient SES, for an inefficient observation j is given by

Xinef−j(SES) =(SESef

j − SESj)

SESj× 100 (10)

A monetary valuation of X-inefficiency in terms of a person’s income is calculated as

MV(Xinef−j) =[(

e(XDiff

inef−j/ ˆ ef

Y ))

− 1]

× 100 (11)

Formula (11) indicates the required percentage change in a person’s current income to generate an increase in economicsatisfaction of equal magnitude to the one that could be attained by eliminating X-inefficiency in the use of income. Theformula assumes that additional income generates economic satisfaction at the rate estimated in Eq. (6). It could be arguedthat the impact of income on economic satisfaction is over-estimated in the present investigation due to the cross-sectionnature of the database (see McBride, 2001). A lower true value for the ˛Y coefficient further increases the monetary valuationof X-inefficiency and provides additional support for this investigation’s main argument: that X-inefficiency is substantial.

Table 6Explaining structural economic satisfaction for observations in the frontier

Coefficient Prob. > t

Constant 2.759 0.00log Y 0.322 0.00Gender 0.000 0.99Age −0.004 0.06Education 0.026 0.12Married −0.063 0.21Stable partner −0.052 0.64Separated 0.098 0.51Divorced 0.269 0.24Widowed 0.277 0.06

R2 0.354

M. Rojas / The Journal of Socio-Economics 37 (2008) 2278–2290 2287

Table 7Descriptive statistics for X-inefficiency indicators for observations out of the efficient frontier

XDiffinef

Xinef(SESef) Xinef(SES) MV(Xinef)

Mean 1.35 25.86 39.08 56,752Standard deviation 0.62 12.03 26.76 277,600Median 1.27 24.19 31.91 5,048Minimum 0.11 1.87 1.91 39Maximum 3.48 66.32 196.91 4,896,917

4.4. Magnitude of X-inefficiency

Table 7 shows the computation of X-inefficiency indicators for those observations placed out of the efficient frontier. Ineconomic satisfaction points, X-inefficiency ranges from 0.11 to 3.48 points. These observations are, on average, 1.35 economicsatisfaction points beneath what could be attainable for their income, based on the best observed practice. On average, X-inefficiency represents about 26% of the efficient economic satisfaction levels. In terms of current economic satisfaction,X-inefficiency represents, on average, 39%; which means that by eliminating X-inefficiency, people could increase theireconomic satisfaction in about 39%, on average, with respect to their current satisfaction levels, with no need to increasetheir income.

How much additional income is needed to generate an increase in economic satisfaction of equal magnitude to what couldbe attained by elimination X-inefficiency? Under the assumption of additional income generating economic satisfaction atthe rate estimated in Eq. (6), an increase in income of 56752% is required, on average. The median monetary valuation ofX-inefficiency for the inefficient observations is 5048%.

4.5. Monetary valuation of X-inefficiency: years of income growth

How many years of sustained income growth a person needs to achieve the economic satisfaction that could be attainedby eliminating her X-inefficiency? Formula (12) calculates the required number of years that a person j would need to attainthe same economic satisfaction that could be attained by eliminating her X-inefficiency, under the assumption that herincome grows at an annual rate of g.

N(g)j = ln((MV(Xinef−j)/100) + 1)ln(1 + g)

(12)

Table 8 elaborates on the number of years that would be required to achieve an economic satisfaction similar to whatcould be attained by eliminating X-inefficiency, for different growth rates and under the assumption that additional incomegenerates economic satisfaction at the rate estimated in Eq. (6). This monetary valuation of X-inefficiency is a personal-levelexercise, and Table 8 presents descriptive statistics.

At an annual rate of income growth of 3%, about 142 years would be required, on average, to get an increase in eco-nomic satisfaction similar to what could be achieved by eliminating X-inefficiency. In other words, it could be stated thatX-inefficiency in the use of income represents, on average, 142 years of income growth at a rate of 3%. This figure ranges from11 years for the less inefficient observations to 365 years for the most inefficient ones. The median inefficient observationin the sample would require 133 years of sustained income growth at 3% to increase her economic satisfaction in a similaramount than to what could be achieved by eliminating her X-inefficiency.

The higher her income grows the fewer years a person needs to attain the same goal. Hence, only 44 years would berequired, on average, at an annual rate of growth of 10%.

At the national level, it is clear that the required number of years that would be needed to attain the same economicsatisfaction that could be attained by eliminating X-inefficiency would depend on both the patterns of economic growth andof X-inefficiency across income groups.

Table 8Required years of income growth to compensate for X-inefficiency at different annual rates of income growth in years

Annual rate of growth

3% 4% 5% 6% 10%

Mean 142 107 86 72 44Standard deviation 65 49 39 33 20Median 133 101 81 68 41Minimum 11 8 7 6 3Maximum 365 275 221 185 113

2288 M. Rojas / The Journal of Socio-Economics 37 (2008) 2278–2290

Table 9X-inefficiency by income group mean values for different X-inefficiency indicators for inefficient observations

Income group XDiffinef

Xinef(SESef) Xinef(SES) MV(Xinef) N(0.05)

Bottom1 1.33 29.1 43.9 17,511 84.82 1.51 31.6 50.6 44,525 96.23 1.51 30.5 47.6 43,993 96.04 1.41 28.2 42.5 28,512 89.85 1.42 28.2 44.2 89,622 90.76 1.50 29.4 44.5 30,032 95.27 1.80 35.1 58.1 99,948 114.68 1.61 31.1 52.4 152,799 102.39 1.35 25.9 38.2 36,248 85.810 1.08 20.7 30.2 89,835 68.911 1.23 23.4 34.1 23,524 78.212 1.54 29.1 44.1 36,260 98.113 1.33 24.7 37.6 96,725 84.514 1.20 22.3 31.5 23,821 76.715 1.36 24.9 37.6 47,198 86.516 1.18 21.4 30.6 40,160 75.117 1.19 21.3 30.0 39,450 75.618 1.30 23.0 33.3 123,312 82.519 1.04 18.1 24.7 37,843 66.4

Top20 1.23 20.6 27.8 32,812 78.3

4.6. X-inefficiency by income group

X-inefficiency in the use of income could be a phenomenon concentrated on some income groups. For example, it couldbe argued that it mostly takes place at high-income levels, where people can easily err in their income use with no seriousconsequence. It could also be argued that middle class groups do have consumption patterns that promote an inefficientuse of income. It would not be expected for X-inefficiency to be large at low-income levels, because people are forced touse their income efficiently to satisfy their basic needs; however, because of this reason, an incorrect use of income atlow-income levels could generate large X-inefficiency. Furthermore, low- and high-income groups could get trapped bysocial-organization deficiencies that foster an inefficient use of income.

Table 9 shows the X-inefficient indicators by income group. It is observed that X-inefficiency in the use of income isa phenomenon that shows up in all income groups. People in the bottom income group could increase their economicsatisfaction in about 44% if their X-inefficiency were eliminated, with no need to increase their income. They would needabout 85 years of income growth – at an annual rate of 5% – to reach an economic satisfaction similar to what they couldattain by eliminating their X-inefficiency.

People in the low-income groups do have high X-inefficiency indicators. X-inefficiency is not an exclusive phenomenonof rich groups; it shows up in all income groups.

People in the top income group could increase their economic satisfaction in about 28% with no need to increase theirincome if their X-inefficiency were eliminated. They would need 78 years of income growth – at an annual rate of 5% – toreach an economic satisfaction similar to what they could attain by eliminating their X-inefficiency.

5. Conclusions

Economic growth constitutes the unique road towards greater economic satisfaction in a world where income is usedefficiently. However, an alternative road appears in the case of substantial X-inefficiency in the use of income: economicsatisfaction can also be raised through a better use of income. Economic research, as well as public policy, could also focuson the reduction of X-inefficiency to pursue greater economic well-being. The pursuing of greater economic well-being isbased not only on having more resources but also on using them efficiently.

This paper has shown that there is X-inefficiency in the use of income to attain economic satisfaction. X-inefficiency isfound to be substantial, even when using a lenient criterion to define the efficient frontier. Furthermore, X-inefficiency isa widespread phenomenon; it shows up at all income levels. There could be enormous gains in economic satisfaction byreducing X-inefficiency.

The existence of X-inefficiency in the relationship between income and economic satisfaction implies that it is possible toattain more economic satisfaction with the same income. It would also be possible to get more economic satisfaction froman increase in income if it is combined with a reduction in X-inefficiency; it would be possible to talk about pro-efficientincome growth.

X-inefficiency could emerge from personal errors in the use of income, as well as from social-organization deficiencies.While economists have placed an enormous effort in understanding economic growth, little is known about personal and

M. Rojas / The Journal of Socio-Economics 37 (2008) 2278–2290 2289

societal factors that foster an inefficient use of income. Greater concern for the sustainability of the planet has raised theperceived costs of increasing economic well-being through economic growth; hence, it may have become optimal to focuson the reduction of X-inefficiency in the use of income as an alternative road towards greater economic well-being.

Economics needs to place more attention to X-inefficiency in the use of income, to its causes, and to the relationshipbetween X-inefficiency and some economic policies and social trends. The study of X-inefficiency clearly falls within eco-nomics’ scope of concern in using resources efficiently. Research in this area has been deterred by the assumption of economicagents being rational, by some reluctance to work with reported economic well-being measures, and by overstressing out-of-context individuals at the expense of persons—who are defined as such within a social organization. It may be that acomplete understanding of the sources of X-inefficiency requires considering factors that the current compartmentalizationof knowledge has placed beyond the arbitrarily defined boundaries of economics.

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