^{1}

Empirical evidence shows that Mexican workers frequently chose a lower-yielding retirement savings manager over a higher-yielding one, damaging their prospects for retirement income. This research paper shows that such puzzling behavior can occur as a product of the unobservable private history between workers and the companies clustered around a common brand-name, in an example of what is known as the

La evidencia empírica revela que los trabajadores formales en México frecuentemente cambian a una nueva Administradora de Fondos para el Retiro que otorga un menor rendimiento neto que la anterior, afectando su perspectiva de ingresos al momento del retiro. En este artículo de investigación se muestra que tal comportamiento puede ocurrir a causa de la historia no observable de la interacción entre los trabajadores y las compañías agrupadas alrededor de una marca publicitaria común, en un ejemplo de lo que se conoce como

As in some other countries where defined-contribution retirement pensions are in place, in México’s pension system workers are required by law to choose a specialized private financial company, called ^{2}

To offer a plausible explanation to such puzzle, a theoretical model is developed in the current paper. It is based on the fact that most ^{3}

In the case of the theoretical setting proposed in this model, the service offered by

An important item should be notice at this point. Even if the motivation for this research project comes from the

The analysis presented in this paper is divided as follows. In the next section, the relevant literature regarding retirement fund choice is reviewed. In the third section, the model of

In addition to the evidence on retirement fund’s switches presented above, the fact that workers show certain unresponsiveness to pricing or return considerations has been previously reported in the literature. For instance (^{4}

In the existing literature, there are two main research lines that may explain Afore’s choice rationality mismatch as a product of a behavioral bias in the decision-making process. In the first one, researchers assume that people do not follow at least one of the three basic features identified by Bernartzi and Thaler in the standard theories of saving, and that creates a bias in the retirement fund selection process.^{5}

Regarding the first line of research, in (

Also within the first line of research is the

Finally, into the same line of research, there is some literature that shows that the worker is unaware of his retirement adequacy. For instance,

Notwithstanding the literature described above has been dominant in the last decade, recently, a second line of research is emerging, one that does not rely on the behavioral biases emerging when the three standard assumptions described by

One example of the second research line is under construction. It concentrates on incentives that may explain workers disregard for retirement income adequacy. For instance,

Another example of the second line of research is the

Finally, the model presented in the current paper is also within the second line of research, as it assumes that workers maximize their expected utility, can correctly appraise the offers from

The

The setting presented here can generate that a rational, utility maximizing worker may show behavior in accordance with the observed rationality mismatch in

In this section, the decision model for retirement fund choice is built as a long term informed financial decision, using the existence of a function that can store the private history dealings between two partners developed by

To simplify the environment without the loss of generality, assume that there are three agents in the economy. Two retirement funds,

In the modelled economy there is also a minimum monthly pension, similar to the one in place in some OECD countries.^{6}

This has a simplifying effect, establishing a lower bound in the monthly income for pensioners. So, in this model, we can assume that there can be only two results that ^{7}

a minimum pension balance, denoted as

a higher amount that ensures a larger monthly pension than the minimum.

For notation purposes let’s denote the payoff coming from _{
A
} , and similarly, as _{
B
} , the payoff coming from

where

Therefore, under the current framework, there will be two

At this point, a concept developed by

Therefore, in the current model we have a worker that will choose an

To incorporate this into the current model, let _{
i
} be the discrete variable that measures the number of bad experiences in previous meetings between the worker and the brand in the time before the _{
i
} follows a Poisson process, and it produces a match specific probability function _{
A
} is drawn from _{
A
} in the case the worker is estimating the probability of _{
B
} is drawn form _{
B
} otherwise. Also, assume that

Let _{
i
} for _{
A
} and _{
B
} intersect, such that

This implies that for low values of a given _{i} , that is, relatively low number of bad
experiences the worker will have a lower expectancy for AFORE-A to dishonor its
commitment than AFORE-B to do it. The opposite is also true, for higher values of a
given _{i
} . Therefore payoff for the worker for each possible path chosen will take the
following form

where

And the problem that the worker has to solve is given by

For this setting there have been identified two possible equilibria in pure strategies. We
called them

For the worker to choose the

Which occurs whenever

This can be derived from Equations (3), (4) and (5), using simple algebraic manipulations and

which implies uniqueness of equilibrium in pure strategies.

Therefore, depending on the value of a given _{i
} regarding

For instance, for the high equilibrium to exist and be unique, it is sufficient to prove that

As if Equation (7) holds, from Equation (1) we have

and with that low equilibrium will not be feasible, so high equilibrium will exist and be unique. Then, from algebraic manipulation of equation (7) the necessary condition for existence can be derived, which is

which occurs whenever a given _{
i
} provides the necessary condition for the high equilibrium,

However, as was previously mentioned, the empirical evidence shows that this is not always the
case, in some rather frequent instances workers chose the lower-yielding

From Equations (1) and (6) - (8) it can be shown, after a simple algebraic manipulation that, when a relatively high occurrence of bad experiences between the worker and the financial institution is present, both equilibria are possible as there is an overlap in the feasibility and equilibrium conditions for both of them.

That is, when

This result also has a nice intuitive explanation: for high enough bad experiences, the
deciding factor will be the relative return offered by the

So, for an informed worker with the necessary skills to determine

These results have an important impact on public policy recommendations. Under the current
model assumptions, it may always be a portion of

The model presented so far is simple and produces intuitive, strong predictions in the sense that may explain the rationality mismatch existing in the retired fund management market in México in an original manner. However, as any simple model that tries to break ground has limitations and potential to grow. In this section such features are discussed and some further research proposals are presented.

The first point to be discussed is simplicity. In this model there are some instances of
simplification that may be relaxed to allow for more complex interactions. One
example is the assumption of the long term commitment contract between the

The second point to be discussed is that in most literature on the subject, there is an
underlying assumption that is probable not good to rely on, which is that the past
net return is used as a predictor of long term retirement fund performance. For
instance, the Mexican retirement fund regulator, ^{8}

The third point to be discussed, is the lack of space in the model presented in this
manuscript for strategic behavior on the ^{9}

A fourth and last point to discuss, that is already being addressed, is the development of
empirical research pursuing to show the existence of the halo effect in the

The model presented in the current research paper, departs from the assumptions that workers
are rational, financially literate and have all the information needed at hand to
build the expected return of any given

The model produces intuitively sound predictions. On one hand, the model forecasts that, when
there is a low occurrence of bad brand experiences, people will choose the higher
yielding

So, this is the main contribution of the current manuscript, this model provides a way in
which a rational worker can choose a lower-yielding

CONSAR, the retirement savings regulator in México, classifies worker’s transfers between Afores in three categories. A negative transfer is a switch to an Afore that offers a lower net return than the incumbent. A neutral transfer is a switch to Afore that offers a net return located between the same as and less than 5% higher than the incumbent. A positive transfer is the complement (

In fact, from eleven companies offering retirement account management services in the Mexican market, there is only one standalone Afore (

Recall that the Chilean pension reform was the first of its kind in the early 80’s, followed by México and other Latin American and Easter European countries in the 90’s, therefore, both retirement account systems share similar features and problems.

See (

Notice that this paper borrows some features from the basic environment developed in

For empirical evidence that support the value investment philosophy applied to stock markets see

To see the oficial press release on the matter please refer to