Poverty and Aspirations Failure

We develop a theoretical framework to study the psychology of poverty and 'aspirations failure'. In our framework, the rich and the poor share the same preferences - and also a behavioral bias in setting aspirations. Greater downside risks imposed by poverty exacerbates the effects of this behavioral bias: the poor are more susceptible to both an aspirations failure and pessimism about the likelihood of achieving success. Poverty limits the set of people whose life experiences the poor consider relevant for forming their own beliefs and aspirations. Mitigating behavioral poverty traps require policies which go beyond reducing material deprivation.


Introduction
are the cause of poverty -or its consequence. Do the poor remain deprived because they lack hope, motivation and aspirations -or, in the words of Bertrand et al. (2004), is it that 'the poor may exhibit the same basic weaknesses and biases as do people from other walks of life, except that in poverty, ....the same behaviors ...lead to worse outcomes'?
In this paper, we examine this latter view of internal constraints and poverty traps rigorously.
To understand the psychology of poverty and low aspirations, we examine an important behavioral bias (or 'internal constraint') that individuals su¤er from, in setting life goals or aspirations: they underestimate how their aspirations evolve over their lifetime, as a consequence of their e¤ort. Both the rich and the poor su¤er from this bias, but poverty imposes an additional constraint on the poor: they face much greater downside risk in their lives. 6 Such risk greatly exacerbates the adverse e¤ects of the behavioral bias in setting aspirations. By a¤ecting the e¤ort choices of the poor, it makes them more susceptible to an aspirations failure, i.e. a failure to aspire to, and achieve, their own best possible outcome.
To understand the behavioral bias in aspirations, perhaps we can consider the familiar example of academics. When students apply for a graduate program, their only aspiration is to get into a good program. Little do they anticipate that once they get there, they will then want to write a great job market paper and get a good job. And once they have the job, that they will want to work towards good publications, and after the publications, lots of citations, and so on. In the ladder of their life's aspirations, they are typically able to visualize only one rung above at a time -but not the entire pathway of how far they can travel.
This bias does not operate very di¤erently among the poor, at their own level. However, greater downside risk lowers their expected bene…t of investing e¤ort towards any goal: when you're worried about whether you will get a good crop to have enough to eat, and your child is performing at a mediocre level in school, it makes you think twice about whether its worth hiring a remedial teacher to help him along. But lower e¤ort increases the odds of low performance -and feeds into lower aspiration and achievement in the long run. As Banerjee and Du ‡o (2011, p. 92), talking about the reasons for poor education outcomes in developing countries, put it "...The teacher ignores the children who have fallen behind and the parent stops taking interest in their education. But this behavior creates a poverty trap even where none exists in the …rst place. If they give up, they will never …nd out that perhaps the child could have made it. And in contrast, families that assume that their children can make it, or families that don't want to accept that a child of theirs will remain uneducated, which tend to be, for historical reasons, more elite families, end up con…rmed in their 'high'hopes." Our formulation of aspirations is based on three premises well-grounded in the behavioral economics literature, as well as in evidence from across the social sciences (which we present in Section 3). First, a person's aspirations level is a reference point 7 : other things equal, a (higher) aspirations level (adversely) a¤ects the satisfaction a person receives from a particular outcome. 8 On the ‡ip side, higher aspirations also spur greater e¤ort (see Section 3 for systematic evidence on this).
Choosing a life goal or aspiration is a forward looking exercise. Here, individuals do not choose their e¤ort and aspirations independent of each other. In other words, aspirations are endogenous reference points. This is our second key premise. 9 This endogeneity is because of a two-way feedback: achieving higher aspirations requires greater e¤ort -but higher e¤ort spurs greater aspirations too, through the outcomes achieved. In the words of Aldous Huxley: " every ceiling, when reached, becomes a ‡oor..." If individuals were fully rational, they would recognize how their aspirations shift with every achievement, and would choose their e¤ort level accordingly. In practice, however, people typically fail to fully recognize this latter feedback; they are only able to see one step above, at a time. This is our third key premise. This behavioral shortcoming can be likened to a form of projection bias (Loewenstein et al., 2003) -inasmuch as people's current state limits their ability to correctly project their aspirations reference point in a di¤erent state.
While both the poor and the rich are equally a-icted by such a bias, the burden of greater downside risk that the poor face makes them more susceptible to an aspirations failure. The intuition underlying this result is as follows. Think of two individuals who have the same initial aspiration level, one rich and the other poor. At this given aspiration level, the poor person would optimally choose a lower e¤ort level than the rich one, due to a lower expected marginal bene…t from e¤ort driven by risk. However, the feedback from e¤ort to aspirations implies that the lower e¤ort of the poor person will cause his aspiration level to diverge from that of the rich person. Thus, in equilibrium, the poor person has two reasons to put in low e¤ort: not only are his expected net bene…ts lower, his aspiration level, i.e. the reference point which determines his marginal bene…t of e¤ort, is endogenously lower as well.
The poor end up with lower aspirations and achievements than their best possible outcome, in 7 This idea dates back to Simon (1955) and more recently, Selten (1998). 8 See, for instance, Medvec et al. (1995) who study the expectations and emotions of Olympic athletes and …nd that bronze medal winners tend to have a higher level of satisfaction than silver medal winners. 9 Conceptually, our idea of endogenous aspirations is in line with Köszegi's (2010) concept of personal equilibrium, in which agents derive utility from physical outcomes as well as from rational beliefs about physical outcomes ("anticipation"), and these two payo¤ components can interact. See also Köszegi and Rabin (2006) on reference-dependent preferences, as well as Shalev (2000) and Dalton and Ghosal (2010). equilibrium -but also with more pessimistic beliefs about achieving success. 10 An implication of pessimistic equilibrium beliefs of a poor person is that, when he sees a successful individual, he over-attributes that success to high endowment (talent) -rather than realize how it could be the outcome of a process of gradual evolution of aspirations with e¤ort, over time. Hence he infers that he is incapable of achieving such outcomes given his endowment, and aspires lower than the best he is capable of. Indeed, many poor parents regard their children as lacking the intelligence needed to complete school and hence choose not to invest in it (see Section 2 for evidence on this). In this sense, poverty curtails a poor person's capacity to aspire, in the spirit of Appadurai (2004).
Next, we address the issue of belief formation: people's aspirations choices may be governed not only by objective risk factors, but also by those in their environment. How do people choose this set of individuals whose life outcomes they regard are relevant in forming their own beliefs and aspirations? To put it di¤erently, who do they choose to include in their 'cognitive window'? 11 The trade-o¤ in choosing the size of this window is between similarity of others'initial condition to one's own and the likelihood of obtaining new information based on their life choices. 12 Greater risk causes the poor to place a higher premium on similarity and thus shrinks their cognitive window.
Such self-imposed 'ghettoization'is consistent with …ndings in the sociology literature that the poor often develop a strong inbred sense of identity -so that certain e¢ cient behaviors may be shunned because they are perceived to be appropriate only for 'the other'. 13 Two types of poverty traps emerge from our analysis: standard poverty traps that are driven by external (resource) constraints, but also behavioral poverty traps characterized by low e¤ort, low aspirations and pessimistic beliefs. While external constraints imposed by poverty are a trigger for internal constraints, the latter become an independent source of disadvantage in behavioral poverty traps. Therefore, policy approaches that in ‡uence beliefs and aspirations among the poor are essential to break this latter kind of trap.
This paper contributes to the emerging literature that examines the behavioral aspects of poverty.
Closely related papers on aspirations include Bogliacino and Ortoleva (2011), Genicot and Ray (2011) and Stark (2006), all of which have a more macro focus than ours. They study the e¤ect of aspirations on income distribution and growth. Moreover, aspirations and cognitive windows in these models are exogenous to the individual. Banerjee and Mullainathan (2010) provide a model to 1 0 This is consistent with the concept of Learned Helplessness (Seligman, 1982, Abramson et al., 1978. It also …ts with wide-ranging evidence that, as compared to the rich, the poor have a more 'external' Locus of Control (the belief that external factors control life outcomes more than one's own e¤ort). See Section 2 for more evidence on this. 1 1 See Rao and Walton (2004) for a compelling set of case studies and analyses on this issue. 1 2 We provide a formal measure of similarity in Section 5. 1 3 See for instance, work by MacLeod (1995), Rainwater (1970) and others on the prevalent culture of disadvantaged neighborhoods.
understand how poverty may persist due to a di¤erent behavioral constraints -a lack of self-control in the consumption of certain goods. However, unlike in our framework, they explicitly assume that the poor are more susceptible to this weakness than the rich -and this allows them to explain some seemingly irrational actions of the poor.
The remainder of the paper is organized as follows. Section 2 describes some important patterns associated with the psychology of poverty persistence and discusses alternative explanations. Section 3 presents the formal model of aspirations and e¤ort choice. Section 4 examines the channel through which poverty increases the likelihood of an aspirations failure. Section 5 studies the policy implications of our analysis. Section 6 provides a discussion of our results and concludes. Proofs of all propositions are collected in the appendix.

The Psychology of Poverty
Persistent poverty is an issue that has been of central focus in economics for several decades. In this section, we discuss evidence that suggests, despite the plausibility of the existing explantations in the economic literature, there are important aspects of this phenomenon that aren't adequately accounted for. We review the existing research on poverty persistence from a range of disciplines in the social sciences, and make our case for the theory presented here.

Beliefs, Aspirations and Poverty
Social psychologists have extensively documented the psychological traits associated with poverty.
The lack of hope and aspirations are a typical characteristic in the personality of the poor population. Moreira (2003), for example, studied the poor in the North-eastern Brazil and pointed out that "as the poor lose their values, they no longer believe in themselves. They go through a process of Nihilism [denial of hope]". Moreira provides evidence that the greatest part of the poor population has these nihilistic characteristics, submitting themselves to the destiny that is 'given by God'. 14  . These poor youth also demonstrate less faith in their own academic abilities, in their overall intelligence and have the lowest academic aspirations across all income quintiles.
The extent to which individuals believe they can control events that a¤ect them has been widely studied in social psychology under the name of "locus of control" (Rotter, 1954). Individuals with "external" locus of control believe that powerful others, fate or chance are the most important determinants of outcomes. Those with "internal" locus of control, however, believe that outcomes result primarily from their own e¤orts. There is vast evidence showing an income gradient in measures of external locus of control: poor and minorities have higher external locus of control than other more advantaged sections of society (Furnham, 1986;Poortinga et al., 2008). Anthropologist Arjun Appadurai (2004) goes a step further, and argues that not only poor people may have pessimistic beliefs and low aspirations, but they may lack the capacity to aspire to "contest and alter the conditions of their own poverty." The capacity to aspire is seen as a cultural capacity related to the way in which people visualize the future and engage in forward looking behavior.
Poverty and Low Aspirations: Lack of Opportunity or Information?
Arguably, such pessimistic beliefs and low aspirations among the poor could be driven purely by a lack of opportunity, or a lack of information about pathways out of poverty. Consider the opportunity channel: a poor person may not want to aspire to be a lawyer because he wouldn't have the funds to pay his studies. Objectively, being a lawyer is not an achievable status for this person and it is entirely rational not to aspire to it. In this case, enlarging the opportunity set would su¢ ce for the person to aspire higher and eventually become a lawyer. However, this opportunity channel alone is inconsistent with very recent empirical evidence from …eld experiments. For example, in Kenya, Miguel and Kremer (2004) provide evidence that only 57% of the sample picked-up the free deworming pills, which were shown to greatly improve children's health and school performance. in Kenya despite being o¤ered convenient opportunities to buy fertilizer at reasonable prices.
A second possible explanation for low aspirations among the poor is that they su¤er from an informational disadvantage: they simply don't know about the bene…ts of certain opportunities.
However, the available evidence is not fully convincing on this count either. For instance, farmers in Busia, Kenya (mentioned above) had ample opportunity both to learn how to use the fertilizer, and to realize that the rates of return from its use were as high as 70%. Take up was low despite this. In a somewhat di¤erent context, Jensen (2010) reports the results of a …eld experiment in the Dominican Republic, where students were informed about the actual return di¤erential between primary and secondary/tertiary education, which they had previously underestimated. There was a substantial increase in perceived returns to education -but almost no discernible e¤ect on the actual rates of completion of secondary schooling. Such lack of responsiveness among the poor suggests that constraints imposed by the lack of opportunity or access to information alone do not fully explain the stubborn persistence of poverty -or the psychological traits associated with it.
Pessimism and Low Aspirations: Cause or Consequence of Poverty?
In this paper, we argue that pessimism and low aspirations among the poor are the consequence of an interaction between their greater exposure to risk and a commonly prevalent aspiration bias.
Risk is a hard reality of poverty. As To summarize, poverty sti ‡es aspirations of the poor because high risk adversely a¤ects their e¤ort choices -and hence their beliefs about their ability to alter the conditions of their existence.
The less e¤ort they invest in getting out of poverty, the more they end up believing that there is little they can do about it. This is the gist of the behavioral bias call "learned helplessness" (Abramson et al., 1978). Hence, providing information or opportunity alone may not be enough to draw out people caught in persistent poverty. We now provide a formal exposition of the ideas expressed above.
3 Aspirations and Achievement: Model Outline

Preferences: Aspirations as Reference Points
We consider an individual characterized by a given initial endowment 0 . He must choose a costly e¤ort e 2 E that will determine the probability distribution over his …nal outcome 2 : We assume that is a closed bounded interval and E is a closed, bounded set (possibly …nite), <, E < and that all payo¤ relevant functions are continuous. He has an aspiration (or goal) g 2 with regard to his …nal outcome. Given his aspiration g, the payo¤ he receives from an e¤ort e equals his expected bene…t from this e¤ort, net of his cost of e¤ort -as described by the utility function below: In the expression above, p( ; e; 0 ) is the likelihood of a person achieving a particular outcome for an e¤ort level e, and it is increasing in e: b( ; g) is the bene…t he obtains from achieving outcome , which could be a¤ected by his goal g. c (e) is the cost of e¤ort e which is increasing in e as well.
We now elaborate on the individual arguments of the utility function above, in line with the key premises of our framework, justifying our modeling choices along the way with well-documented evidence.
Our …rst key premise is that individual aspiration serves as a reference point for the bene…t he derives from achieving a …nal outcome. In our framework, this is captured by the feature that the marginal bene…t b ( ; g) of a better outcome is greater for a person with a higher aspiration level g. Formally, this complementarity between and g can be stated as follows: is increasing in and satis…es increasing di¤erences in and g i.e. for 0 and g 0 g, In words, the incremental gain from enhanced social status is greater the higher the aspiration level.
When b ( ; g) is twice continuously di¤erentiable, @ @ b( ; g) > 0 and @ 2 @ @g b( ; g) > 0. The Kahneman and Tversky (1979) utility function with loss aversion is a good example of a utility function that satis…es Assumption 1. 16 A direct implication of this assumption is that a person with a higher aspiration level has an incentive to try harder to achieve a better outcome. Aspirations are, in this sense, motivators of greater e¤ort. This premise is consistent with wide-ranging evidence from psychology and economics. and c(e).

How Poverty imposes External Constraints
As we argue in Section 2, one important di¤erence in the external constraints faced by the poor and the rich is that the poor experience considerably greater downside risk in their lives. Such risks adversely a¤ect the probability that their e¤ort leads to success in achieving a particular outcome.
In order to capture this, we make the following assumption:  g; if < g ( g); 0 < < 1 if g, In this example, the DM's frustration from falling short of her aspiration is greater than her pleasure from exceeding her aspirations -but we can also have utility functions with symmetric e¤ects of gains and losses relative to the reference point, that satisfy Assumption 1. Note that, in the above example, b( ; g) is always decreasing in g for some values of so that the assumption is consistent with the idea that a high level of aspiration can induce frustration.
An alternative formulation b( ; g) = ( ) K( g) 2 (where ( ) is increasing in , and the constant K is chosen to ensure that b( ; g) is increasing in ) also satis…es assumption 1 but has the feature that b( ; g) is increasing in g whenever g < .
(iii) c(e) is increasing and continuous in e.
Assumption 2 (i) states that the rich have a higher likelihood of achieving a higher …nal outcome with a given e¤ort level e. Furthermore, this gap in the success probabilities of the rich and poor increases at higher e¤ort levels. 17 Assumption 2(ii) ensures that a person with a high initial 0 has the incentive to put in higher than the minimum possible e¤ort, to maintain his initial status.
Assumption 2(iii) simply states that the cost of e¤ort is increasing in e¤ort e.
Greater downside risk implies that, for any given aspiration level, the expected outcome that a poor person can achieve for the e¤ort he puts in, is lower. 18 But what determines individual aspirations? No doubt, there could be multiple in ‡uences: environmental factors such as a person's family background, the norms of the community in which he lives and the opportunities available, economic or otherwise do matter -as well as traits internal to the individual. To the extent that it is the …rst set of in ‡uences that matter, a person's aspirations may be described as 'exogenous'or independent of his e¤ort choice. We consider this simple (perhaps simplistic) case …rst.

E¤ort Choice under Exogenous Aspirations
In principle, it could be argued that if aspirations are life goals, there is no reason why a poor person cannot have the same aspirations as richer individuals. In this case, the exogenous aspiration level g 0 can be treated as common across all individuals, rich or poor. The following proposition clari…es the link between e¤ort and initial status for …xed exogenous aspirations: Proposition 1: For an exogenously …xed level of aspirations g 0 , under Assumption 2, e¤ ort is an increasing function of 0 .
Proof: See appendix.
The above proposition implies that for a given aspiration level, the gap between aspiration and achievement will be greater for the poor. This is because greater risk reduces their (expected) net marginal bene…t of e¤ort, which lowers their incentive to expend as much e¤ort or resources towards that goal. We could refer to such a gap between aspiration and outcome as achievement failure. A poor person is more prone to such achievement failure -but it is perfectly rational for him to choose a lower e¤ort level that results in such an outcome.

Aspirations as Endogenous Reference Points
Perhaps it is more natural to think of a case where individuals choose their aspiration level, rather than have it set for them. After all, how far people aspire depends on their own beliefs about what they can achieve with e¤ort. Setting one's aspirations is a forward looking process. Given that aspirations a¤ect the satisfaction from the outcome realized, people would not aspire to an outcome that is perceived as unattainable. Thus, in choosing the e¤ort they want to put in, they implicitly choose what they want to aspire to, i.e. aspirations are endogenous to e¤ort choice, they are endogenous reference points. This is our second key premise. As ethnographer MacLeod's (1995, p.15) points out "aspirations re ‡ect an individual's view of his or her own chances for getting ahead and are an internalization of objective probabilities". With this interpretation in mind, we de…ne an aspirations level g as the expected outcome, given individual e¤ort: Of course, with uncertainty (captured by the probability of achieving a particular outcome p( ; e; 0 )), the individual will to aspire to the expected …nal outcome of his e¤orts. Our formulation has the desirable feature that, in the absence of uncertainty (i.e., when …nal status is a deterministic function of e¤ort), the aspiration level of the individual is simply the …nal outcome he will achieve given his e¤ort.
Of course, the endogeneity of aspirations also implies that they also evolve with our e¤ort choices.
When we achieve a particular goal we had set for ourselves, our goals tend to shift too. In the words of Aldous Huxley: " Every ceiling, when reached, becomes a ‡oor...." 19

Aspiration Choice of a Rational Decision Maker
So far, we have laid out two key premises: (i) that aspirations are reference points that a¤ect our utility from achieving a particular outcome -but (ii) they are endogenous reference points, in that they also evolve with our e¤ort choices. Using these two premises, let us carry out the following thought experiment. Consider a fully 'rational'person, one who internalizes the fact that in choosing an e¤ort level today, he is also a¤ecting his lifetime aspiration, and hence the bene…t he will get from the achieved outcome as well. How will such a far-sighted person optimally choose his e¤ort and life aspiration level?
We formalize the answer in the concept of a standard solution, as de…ned below: As De…nition 1 shows, a rational person recognizes that e¤ort and aspirations feed into each other over the course of his lifetime. Given this positive feedback, he would jointly choose both e¤ort and aspiration levels, so as to achieve his best possible outcome and utility. 20 We certainly do not claim that most individuals are far-sighted enough to recognize this feedback, and make decisions in this manner. Rather, this provides us with a normative benchmark against which we evaluate how most people set their aspirations.
A point to note here is that a fully 'rational' poor person would aspire lower than an equally ambitious richer counterpart: at any given e¤ort level, his expected outcome is lower, due to higher downside risk he faces -and setting an aspiration (reference point ) that is as high as his richer counterpart would only diminish the utility he would derive from any achievement. Of course, given his weaker initial condition 0 , this more modest aspiration and e¤ort choice of a poorer person cannot be regarded as an aspiration failure.

Aspiration Choice of a Behavioral Decision Maker
Admittedly, most people setting their life's aspirations are not rational in the sense described above.
Speci…cally, in carrying out this forward-looking exercise, they do not fully internalize how their life aspirations are shaped by their e¤ort choices. 21 In the ladder of our life's aspirations, we are typically able to see only rung above at a time. We refer to decision-makers with such lack of foresight as 'behavioral' decision-makers (and that includes most of us!). Our third central premise, then is that while choosing e¤ort e, a behavioral decision-maker takes his life aspiration g as …xed (rather than endogenously evolving with e¤ort and outcomes), hence imposing a negative externality on 2 0 Note that s(e; 0 ) is continuous in e and as E is compact, hence the set of solutions S is non-empty -and there could be multiple solutions. However, by de…nition, any two distinct standard solutions must yield the same payo¤. 2 1 Our framework is also consistent with a scenario where the decision-maker partially internalizes the feedback from actions to aspirations with probability . In such scenario, the decision-maker in a behavioral decision chooses e¤ort to maximizeũ(e; g) = u(e; g) + (1 )v(e). This is analogous to the formulation adopted in Lowenstein et al.
While his aspiration g is exogenous to his e¤ort e , we will require that his aspirations and e¤orts are mutually consistent, i.e., he has rational expectations in choice of aspirations and e¤orts. Let Proof. See appendix.
Proposition 2 shows that when an individual ignores how his aspirations are in ‡uenced by his e¤orts, there are multiple levels of e¤ort and aspirations that are solutions to his optimization problem. Across these behavioral solutions, higher e¤ort levels are paired with higher aspirations levels. Thus, the lack of foresight in a behavioral decision-maker creates room for the possibility that he may choose a lower e¤ort-aspiration pair, than the best possible one he could expect to achieve.
We refer to such a person as being internally constrained, and such an outcome as an aspiration failure. Formally: That is, the marginal bene…t of additional e¤ort, taking into account that aspirations depend on e¤ort via (:), should be zero. A behavioral solution, however, must satisfy the following …rst order condition at an interior solution: 0 = @ e u(e ; g ; 0 ), g = Z 2 p( ; e ; 0 ) d : That is, the marginal bene…t of additional e¤ort, at the aspiration level consistent with chosen e¤ort via (:), is equal to zero. These two conditions do not typically overlap. This fact is summarized in Lemma 2 below.

Lemma 2.
When e¤ ort is a continuous variable, the decision maker is, typically, internally constrained.

Thus, when an individual fails to anticipate the positive feedback of his e¤ort choices on his life
aspirations, he will end up choosing a suboptimal e¤ort-aspiration pair than the best outcome he can achieve. Consistent with his e¤ort choices, we note that his equilibrium beliefs p( ; e ; 0 ) about the likelihood of success based on his own e¤orts, will be suboptimal as well.

Poverty and Aspirations Failure
In this sub-section, we examine how the greater downside risk imposed by poverty may exacerbate the likelihood of such aspirations failure. We begin by identifying the e¤ect of an individual's initial status 0 on the solutions to the behavioral decision-making problem. and (e ( 0 ); g ( 0 )) ; are increasing in 0 .
Proof: See appendix. . . We assume that the lowest e¤ort e 1 will perpetuate the individual's status quo for surei.e. p ( 0 ; e 1 ) = 1 and p 0 ; e 1 = 0 for all 0 6 = 0 so that g 1 ( 0 ) = (e 1 ; 0 ) = 0 . We assume that behavioral solutions can be payo¤ ranked so that the maximal solution (the highest possible e¤ort-aspiration pair (e S ( 0 ) ; g S ( 0 ))) dominates all other solutions in B ( 0 ) and is the unique standard solution. 24 To see how an equilibrium e¤ort and aspiration level is selected, consider the initial aspiration level g 0 of an individual, which is drawn from a distribution with pdf f (:) (and cdf F (:)) common to the rich and the poor. g 0 is irrelevant for a fully 'rational'(standard) decision-maker, because he internalizes the feedback from e¤orts to aspirations. Therefore, he will always only pick a standard solution (e S ; g S ) as his e¤ort/aspiration choice, no matter what his g 0 is. A behavioral decisionmaker's e¤ort choice will be a¤ected by g 0 , because he takes his aspiration level as given,rather than endogenous to his e¤ort. The selection mechanism involves two stages: (i) an initial aspiration level g 0 generated and given g 0 , the individual chooses an e¤ort level e; (ii) given e, the actual aspiration level (i.e. expected outcome) is realized via the function (e) = R 2 p( ; e; 0 ) d . Given the above selection mechanism, Proposition 3 addresses how poverty and initial disadvantage exacerbate the likelihood of aspirations failure in his case. There are just two e¤ort levels, high and low e¤ort. At this given aspiration level, the poor person would optimally choose a lower e¤ort level than the rich, due to higher risks involved. However, the feedback from e¤ort to aspirations implies that the lower e¤ort of the poor person will cause his aspiration level to diverge from that of the rich person. Thus, in equilibrium, the poor person has two reasons to put in low e¤ort: not only the risks he faces is higher, his aspiration level, i.e. the reference point which determines his marginal bene…t of e¤ort, is endogenously lower as well. In this sense, poverty curtails a poor person's capacity to aspire, in the spirit of Appadurai (2004). Then, the complementarity between goals and outcomes implies that poverty raises this threshold level of initial aspirations e g ( 0 ) a poor person must have to choose higher e¤ort. If he is no di¤erent from a rich person in this respect (as we have assumed), he converges to a payo¤ dominated solution more often.
Another point to note here is that, in equilibrium, a poor person is likely to perceive a higher downside risk. It is important to distinguish between objective risk faced by a poor person and his subjective equilibrium beliefs here. While greater risk a¤ects his objective probability of success p ( ; e; 0 ) at a given e¤ort level, his e¤ort choices under an aspiration bias skew his equilibrium beliefs about success through e¤ort further downward. This is consistent with a more external locus of control among the poor, as widely documented by the evidence.
An implication of such beliefs in equilibrium, is that the poor tend to over-estimate the role of a high initial endowment 0 in achieving a certain level of success. On observing a successful person, they fail to appreciate how that success could be the result of a gradual evolution of his aspirations and e¤ort over time. Hence they decide that such success is unattainable for themselves, given their own endowment. As the evidence in Section 2 shows, many poor persons decide that their children are not capable of completing school, because they lack the intelligence to do so.

Poverty Traps and Beliefs
So far, we have seen how higher exposure to risks faced by the poor interact with their behavioral weaknesses (internal constraints) to make them more susceptible to an aspirations failure. In this section, we relate our analysis so far to poverty persistence and pathways out of it. A positive feature of our model is that it allows us to study, within a unique framework, the e¤ectiveness of multiple kinds of policy interventions -those that aim to relax external constraints, but also those that work on relaxing internal constraints. We begin by clarifying the reasons why both types of interventions are necessary. To do so, we adapt our analysis so far to a simpli…ed framework with two e¤ort levels fe; eg and corresponding expected outcomes g ( 0 ) = R 2 p( ; e; 0 ) d and g ( 0 ) = R 2 p( ; e; 0 ) d .

Standard versus Behavioral Poverty Traps
Based on our discussion following Proposition 3, two types of poverty traps can arise in our framework. The …rst is a standard poverty trap driven by material deprivation. As pointed out in Section 3, when individual's su¤er from an aspirations bias, their initial aspiration level g 0 a¤ects their equilibrium e¤ort and aspirations choice. The lower their initial endowment 0 , the higher is the threshold level of initial aspirationg ( 0 ) they need to push them towards a high e¤ort choice.
However, there could exist wealth levels (and hence, success probabilities) so low that the expected outcome of high e¤ort falls below this threshold i.e. g ( 0 ) <g ( 0 ) (see Figure 1). In this case, e; g ( 0 ) is both the unique behavioral and standard solution. Consistent with the conventional view in economics, interventions that solely focus on altering the external constraints (i.e., 0 ) of individuals caught in this type of poverty trap will be welfare enhancing. However, even when initial material deprivation is less extreme a behavioral poverty trap may still arise. As Figure   2 illustrates, the threshold level of initial aspirations required to justify high e¤ort level is lower i.e. Here, e; g ( 0 ) and (e; g ( 0 )) are both behavioral solutions because e¤ort choice is not constrained by initial material disadvantage 0 but initial aspirations g 0 . If g 0 g ( 0 ), the individual is caught in a behavioral poverty trap with low equilibrium e¤ort/aspirations and pessimistic beliefs; the individual escapes a behavioral poverty trap if g 0 g ( 0 ). 25 If a person is located in such a behavioral poverty trap, policies that improve his initial condition 0 may succeed in lifting his out of material deprivation, but he could still be caught in an "aspirations trap". For example, lowering the downside risk will mitigate aspirations failure, but for those caught in a behavioral poverty trap, this may not be enough -given their more pessimistic equilibrium beliefs and aspirations.
Thus, the gist of our analysis so far is that, while internal constraints such as pessimistic beliefs originally arise due to external constraints imposed by poverty, in equilibrium they could become an independent source of disadvantage for the poor. The kinds of poverty traps described above have two implications. The …rst is that, under acute poverty, the e¤ectiveness of policies targeted to relax external constraints will be maximized if they also reduce internal constraints (for example, by reshaping beliefs). The second is that there exist conditions where relaxing internal constraints alone (without altering external ones) can alter behavior and reduce the persistence of poverty. In what follows, we focus on policies that complement the relaxation of external constraints, through direct or indirect e¤ects on individual aspirations.

Similarity and Belief Formation (p)
In this sub-section, we concern ourselves with the question of changing pessimistic beliefs p( ; e; 0 ) among the poor to break poverty traps. So far, we have focused on how objective risks may depress their aspirations. However, it could be argued that aspirations are shaped by subjective beliefs, which are also in ‡uenced by the life experiences of those around us. Any discussion on how to change beliefs among the poor must account for these in ‡uences as well. This brings us to an own? The answer to these questions is important to understand how the beliefs of the poor about e¤ort and success can be favorably in ‡uenced through this approach. We introduce the concept of role models and similarity into our framework to address these issues.

Role Models and Similarity
Consider an internally constrained individual i located in an aspirations trap. Suppose the individual observes an 'external signal' j 0 ; e; j 1 = K + j 0 -i.e. information on an individual j with initial status, j 0 who chose high e¤ort e and achieved a …nal outcome j 0 + K. We say that an external signal belongs to the 'cognitive window 'of a person i if he chooses high e¤ort e after observing the signal. To see when such an outcome is likely, we introduce the notion of similarity, and endow the individual with a similarity function s : ! [0; 1] where s j 0 ; i 0 = 0 denotes no similarity and s j 0 ; i 0 = 1 denotes full similarity (Gilboa and Schmeidler, 2001). This function quanti…es how similar an individual perceives his own initial status to be, to that of the potential role model. 26 A continuous similarity function consistent with Gilboa and Schmeidler (2001) is: where s j 0 ; i 0 = 1 when j 0 = i 0 and s j 0 ; i 0 is decreasing in the distance between j 0 and i 0 . 27 After observing a signal j 0 ; e; j 1 = K + j 0 individual i updates his prior p i on the payo¤s from choosing high e¤ort e, yielding a posterior expected payo¤ of [s j 0 ; i . This is equivalent to where p i 1 are individual i 0 s posterior beliefs about the likelihood of changing his (initial) status. Note that his posterior beliefs p i 1 are increasing in his perceived similarity, s j 0 ; i 0 . In choosing the optimal size of his 'cognitive window', the sample of individuals from which a person can potentially draw role models, he faces a trade-o¤. Ideally, what he wants to observe is someone who is identical (similarity one) to himself in initial status, but with a higher level of aspirations and achievement. However, a person very similar to himself is likely to have the same aspirations, and make the same decisions too. In order to increase the likelihood of observing an individual with higher aspirations and achievement, he has to compromise on similarity, by including some of those with a higher initial status than himself in his cognitive window. The following proposition identi…es the factors that a¤ect the width of an individual's cognitive window. 2 6 Gilboa and Schmeidler (2001) provide an axiomatic treatment of choice determined by similarity weighted payo¤ estimation. The problem is familiar from econometrics where one might want to infer the conditional distribution p (y 2 Ajx 0 ) where the sample frequency of x 0 is zero i.e. p(x 0 ) = 0. Assume that all variables are unidimensional. In such scenarios, it is standard in econometrics to use a uniform kernel estimate (Hardle, 1990;Manski, 1995) which is an estimate of the sample frequency with which y 2 A amongst those observations x i such that jx i x 0 j < d (where d is the sample speci…c bandwidth chosen to con…ne attention to those observations in which x i is close to x 0 ). In a sample with n observations, the expression for the uniform kernel estimate is : Then, the uniform kernel estimate corresponds to a "bandwidth" similarity function where . Thus, the size of his cognitive window is decreasing in c (e) and increasing in b K + 0 ; g ( 0 ) as well as his prior beliefs p i .
Proof. See appendix.
Proposition 4 captures the idea that there is a threshold degree of (perceived) similarity needed for a individual to include a person in his cognitive window. It shows that the greater risk a person faces, the narrower is his cognitive window. Thus, poor people who face higher risk may set tighter restrictions on similarity, in choosing the set of people whose experience in ‡uences their beliefs.
This is consistent with evidence from the sociology literature on poverty, which shows that the poor often tend to develop a strong inbred sense of identity that consciously makes them shun actions associated with those regarded as dissimilar to themselves (MacLeod, 1995). Thus, greater risk, by narrowing the set of people who are included in the cognitive window of the poor, they may weaken their perceptions about the link between e¤ort and success, leading to a further reduction in their p(:):

Breaking Behavioral Poverty Traps: Policy Implications
Taken together, our description of behavioral poverty traps and the result of Proposition 4 imply that anti-poverty initiatives aiming to tackle persistent poverty need to be mindful of two important issues: (i) the need to reshape beliefs among the poor, in addition to providing resources and (ii) the importance that the poor accord to similarity, in forming their beliefs. To quote Bandura again, "failure to address the psychosocial determinants of human behavior is often the weakest link in social policy initiatives. Simply providing ready access to resources does not mean that people will take advantage of them." (The Psychologist, 2009, p. 505) 28 Bandura cites the case of a national literacy programme in Mexico, wherein people who were skilled at reading were urged to organize small self-study groups to teach others how to read. It was a good idea -but there were few takers. Upon conducting a survey, Bandura's team identi…ed three beliefs among poor illiterate persons that impeded participation: that reading is learnable only when one is young, that they lacked the ability to master such a complex skill, that an educated person wouldn't be interested in devoting time to them. In collaboration with the Population Media Centre (PMC), Bandura developed a soap-opera that worked to allay these speci…c mis-beliefs. 29 2 8 This quote and the material below is based on a lecture by Alberto Bandura to the British Psychological Society of which an edited version was published in The Psychologist (2009).
This resulted in a dramatic increase in the take up rates for the program. 30 The above project in Mexico is part of Bandura's larger multi-country collaboration with the PMC to create soap operas that reshape beliefs among the poor, to help them navigate their way out of poverty. 31 These soap-operas emphasize the similarity between their target audience and the life-experiences of the opera characters. 32 Bandura argues that it is such similarity that has allowed the target audience to identify with the drama characters over the course of the opera series, resulting in a signi…cant change in aspirations and e¤ort. 33

Discussion and Conclusion
We have developed a simple framework to study the psychology of poverty and aspirations failure.
In ‡uential psychologists such as Bandura (1991) and social psychologists such as Beck (1970) and Seligman (1975) have argued that the belief that one's behavior can e¤ect change is central to the path out of helplessness. Our model shows how well-documented phenomena such as learned helplessness, pessimistic beliefs and an external locus of control among the poor may be a consequence of poverty, rather than a cause. This arises through an interaction between two factors: (i) all individuals, rich or poor, fail to appreciate how their e¤ort choices shape their aspirations over timebut the poor pay a bigger price for this failure because (ii) poverty exposes them to greater downside risk, which further lowers their incentive to put in e¤ort. Their lower e¤ort choices give rise to lower aspirations and more pessimistic equilibrium beliefs.
Here, we have chosen to capture the external constraints imposed by poverty in terms of greater downside risk. Arguably though, higher exposure to risk is not the only factor that can lower the net bene…t of e¤ort for the poor, as compared to the rich. This will also happen if the poor face higher cost of e¤ort. For instance, simply saying that one lives in a poor neighborhood may diminish a poor 3 0 The day after one epilogue by an admired movie star, 25,000 people showed up to enrol in the self-study programme. Viewers were more informed than non-viewers about the literacy program. Enrolment rose from 90,000 in the year before the televised series, to one million during the year of the series and an additional 400,000 in the year after. 3 1 Soap operas have been created to tackle beliefs and social issues among the poor, in several developing countries: Sudan(forced marriage, genital mutilation), Kenya(property rights for women), India (gender inequality in childrearing, education for girls), Tanzania (family planning, AIDS). 3  A poor person could also receive a lower marginal bene…t of e¤ort, simply because the aspiration reference points in his social environment are lower. In our analysis here, we have consciously chosen to focus on the role of factors internal to an individual, to explain the psychology of poverty and aspiration failure. However, the process of aspiration formation and its evolution over time is inherently a dynamic one. For instance, Hirshman's "tunnel e¤ect" refers to the phenomenon whereby others success may in ‡uence an individual's aspirations and beliefs about their own success over time. Incorporating these two key elements into the study of poverty and aspirations o¤er the promise of interesting avenues for future research.

Proof of Proposition 2:
By continuity of u(e; g; ; 0 ) in e and by the compactness of e, e(g; 0 ) is non-empty. For e 0 e and g 0 g, note that is increasing in so that p( ; e 0 ; 0 ) …rst order stochastically dominates p( ; e; 0 ).
By continuity e(g; 0 ) is non-empty and as payo¤s satisfy increasing di¤erences in (e; g), it follows that there exists a maximal and minimal element in e(g; 0 ) which is increasing in g.
Finally, p( ; e 0 ; 0 ) …rst order stochastically dominates p( ; e; 0 ) for e 0 e, (e; 0 ) is increasing in e. Therefore, by Tarski's …x point theorem, B is non-empty and there exists a maximal and minimal element in B.

Proof of Lemma 2:
A set of decision problems is diverse if and only if for each (e; g) 2 e it contains the decision problem with utility function and feedback e¤ect de…ned, in a neighborhood of (e; g), by u + g for parameters in a neighborhood of 0.
A property holds generically if and only if it holds for a set of decision problems of full Lebesgue measure within the set of diverse smooth decision problems.
By computation, the …rst order condition 34 characterizing an interior standard solution is Perturbations of the utility function do not a¤ect the …rst order conditions characterizing the outcome of a behavioral decision (and hence hence (e ; g ) but they do a¤ect the preceding equation and via the …rst order condition characterizing the outcome of a standard decision problem a¤ect (ê;ĝ). Therefore, (e ; g ) 6 = (ê;ĝ) generically.
Therefore, (g n 1 ( 0 ) ;g n ( 0 )) is the basin of attraction of the behavioral decision outcome (e n ; g n ). Then if g 0 2 (g n 1 ( 0 ) ;g n ( 0 )), the individual will choose e n and there will end up with an aspiration level g n i.e. the behavioral decision (e n ; g n ). Therefore, the probability with which the internal constraint binds is equal to the probability that g 0 is not in the basin of e¤ort of the behavioral (and standard) decision (e S ; g S ) which, in turn, is the probability that g 0 <g S 1 ( 0 ) which is F (g S 1 ( 0 )). Asg S 1 ( 0 ) is decreasing in 0 , the probability that internal constraint binds, F (g S 1 ( 0 )), is decreasing in 0 . Therefore, the lower is the initial status of the individual the greater is the probability that the internal constraint binds and in a behavioral decision.
Note that by assumption 2,g 1 ( 0 ) > 0 so (e 1 ; g 1 ( 0 ) = 0 ) is also a behavioral solution. Moreover, by a similar argument to the one made above,g 1 ( 0 ) is decreasing in 0 , the probability that internal constraint binds, F (g 0 ( 0 )), is decreasing in 0 . Therefore, the lower is the initial status of the individual the lower is the probability that (e 1 ; g 1 ( 0 ) = 0 ) is selected.

Proof of Proposition 4
Note that As p i 1 is increasing in s j 0 ; i 0 , p i 1 > p i whenever s j 0 ; i 0 > 0 and as s j 0 ; i 0 ! 0, p i 1 ! p i : Therefore, the updating of priors after observing the peer is an example of similarity based learning.
Moreover, observe that if s j 0 ; i 0 = 1, p i 1 = 1+p i 2 . Therefore, even when the two individuals have an identical initial status, s 0 0 ; 0 = 1, individual j will be included in the aspirations neighborhood of individual i if and only if 1+p i 2 p i i 0 . Thus, whenever 1+p i 2 p i i 0 , a person located at 0 will never alter his behavior by observing a successful peer, even if the peer is identical in initial status.
How similar does the successful individual need to be in order to inspire a change in individual i?
The fraction on the right hand side of inequality (12) is increasing inp i i 0 and decreasing in p i . Aŝ , it follows that the size of the aspirations neighborhood of the person located at i 0 is smaller when (i) the cost of choosing e is higher; (ii) the bene…t of achieving a higher …nal status is lower and (iii) the prior beliefs of the individual are more pessimistic (lower p i ).