Control Interno

5.3.1

Set-up

In the model, we consider a decision-maker who has to choose between two actions: one that perpetuates her initial status and one that has the potential of improving her initial status.

11_{See Stark and Taylor (1991) for a general introduction to relative deprivation, Deaton (2001) for}

an application to health, Stark (2006) for an application to growth. For empirical papers on relative deprivation, see for example Duclos and Grégoire (2002).

The initial status of the decision-maker is denoted by 0 (with the set of all possible

initial social status denoted by ). The decision-maker aspires to achieve a new social status and we denote the target status byb = + 0, 0, 2 [0; K] where K is

some large but …nite number. We interpret as a measure of how high decision-maker aspires. Low aspirations correspond to values of close to zero while high aspirations correspond to values of close toK. In what follows, we will refer to as the aspiration level of the decision-maker.

The decision-maker has to choose an action a _{2 f}a; a_g where a denotes the action that perpetuates her initial status while a denotes an action that has the potential of changing her initial status in a manner described below.

Let the …nal or achieved status be denoted by 1. The production function for 1 is

speci…ed as follows:

a = a₎ 1 = 0 with probability 1; (5.1)

a = a₎ 1 = 0 with probability 1 p

1 =bwith probability p

where p is the probability that the decision-maker attaches to di¤erent outcomes. In general,p will be a combination of objective data (the decision-makers own experience, the signals she observes based on the experience of others (role models)) and prior subjective beliefs (the degree of con…dence or optimism of the decision-maker). In what follows, both interpretations of pwill be used.

The payo¤s to the decision maker is given by b( 1) c(a; 0) where b( 1) denotes

the bene…t the decision-maker obtains at the achieved social state and c(a; 0) is the

cost of action which depends on the initial status of the individual. We rewrite these payo¤s as b( + 0) c(a; 0) and make the following assumption:

Assumption 1

status-quo yields no bene…t and the bene…t function is increasing in aspirations; (ii) c(a; 0) = 0 for all 0: perpetuating the status-quo is costless.;

(iii) c(a; 0) = c( 0)>0and continuous and decreasing in 0:any attempt to change

the status-quo is costly but the cost of doing so is lower the higher is the initial status. In this way, the initial status is a measure of the level of disadvantage of the decision-maker.

5.3.2

Optimal Actions with Exogenously Generated Aspira-

tions

In this subsection, we take the decision-maker’s aspirations, subjective beliefs and initial status as given. The individual will choosea =a if and only if

pb( + 0) c( 0) 0 (5.2)

Suppose the initial was picked at random from [0; K] (where K is some large but …nite number) according to some continuous pdf g(p) (with associated cdfG(p)). Next, given the p, ; 0, the individual chooses a2 fa; ag.

The following result characterizes the optimal choice of the decision-maker:

Proposition 15 (Optimal action as a function of p and 0) Suppose payo¤s

satisfy assumption 1. Then, there exists a threshold level of aspirations ^ (p; 0)>0such

that that the decision-maker attempts to change her initial social status i¤ ^ (p; 0);

moreover the threshold ^ (p; 0) is decreasing in both p and 0. The probability that the

decision-maker will choose a is1 G( ^ (p; 0)) which is increasing in both p; 0 as well.

Proposition 15 shows that initial advantage and self-con…dence are substitutes for aspirations. That is, the more disadvantaged the decision-maker is (respectively the lower self-con…dence), the higher aspirations she needs in order to …nd it convenient to undertake an action that has the potential to change her status-quo.

Note that by assumption 1, both 0 (the initial status of the decision-maker) and

p (the probabilities that the decision-maker attaches to di¤erent outcomes) are key characteristics of the decision-maker. The main implication of Proposition 1 is that initial status disadvantage and low level of self-con…dence is positively associated with low aspirations and as a consequence, low achievement. Speci…cally, (i) holding initial status …xed, a person with a low p (low level of con…dence) requires a higher level of aspirations than a person with a highp(high degree of con…dence) in order to undertake an action that changes her status quo, (ii) holding beliefs …xed, a person with a low 0

(initial disadvantage) require a higher level of aspirations than a person with a high 0

(initial advantage) in order to undertake an action that changes his status quo.

Let p0 denote the prior of the decision-maker which, we assume, the decision-maker

takes as given. Supposep0 is picked at random from[0;1]according to some continuous

pdf f(p) (with associated cdf F(p)). Next, given the p0, ; 0, the individual chooses

a _{2 f}a; a_g. The following proposition characterizes the optimal choice of the decision- maker:

Proposition 16 (Optimal action as a function of and 0) Suppose payo¤s

satisfy assumption 1. If p0 is picked from [0;1] according to some continuous pdf f(p)

(with associated cdf F(p)), the probability that the decision-maker will choose a is 1

F(^p( ; 0))which is increasing in both and 0.

Note that there is no guarantee that p^( ; 0) 1. If p^( ; 0) > 1, the decision-

maker will never choosea.

The main implication of Proposition 16 is that initial status disadvantage and low as- piration levels is positively associated with low self-con…dence and as a consequence, low achievement. Moreover, initial advantage and aspirations are substitutes for con…dence. Consider a simpli…cation of the model by assuming that there are only two levels of aspirations _f0; 0 _>0g.

Suppose the decision-maker chooses a from _f0; 0 _{>0g taking into account the}

fact that by changing she a¤ects her own choice. The following result characterizes the conditions under which aspirations failure emerges endogenously in such a situation:

Proposition 17 (aspirations failure) If p0 <p^( 0; 0), the decision-maker will op-

timally choose = 0.

Proposition 17 is telling us that even if the person is rational enough to anticipate the e¤ect of ther aspirations on her choices, for a su¢ ciently low level of initial background or self-con…dence, it is optimal for the person to choose to have no aspirations to change her status-quo.