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Altruistic or calculators? The case of intra-household

What motivates an individual to send money to his family, while he bears the costs associated with their migration? Is it pure altruism or is he waiting in return family and social recognition? The transfer behavior can be explained by a strategy they clear the migrant or bargaining power within the family, what is the role of social norms in this decision? How can we model the behavior of a migrant representative considering altruism, self interest, social pressures and implicit contracts interact in making its decision?
A microeconomic analysis of transfer is very important, particularly for developing countries (DCs): Why?
First, migration is a phenomenon that affects massively developing countries, whether internal migration (from rural to mostly urban) or migration across borders to more developed countries. Furthermore, financial transfers
reveal an issue more important than the country of origin is underdeveloped because it is characterized by low initial earnings, economic inequality and a strong income volatility (Rapoport and Docquier , 2006): thus private transfers by acting on these three characteristics have significant effects on developing countries and therefore deserve a special interest
Finally, market failures and credit insurance systems encourage more people to replace the banking and financial institutions, through domestic contracts are often implicit. This again is an element justifying the importance of remittances in developing countries, mostly affected by these failures.

Without addressing all the theoretical models that have been developed, we can present some reasons given in the literature to explain the behavior of microeconomic transfer.

I. A formulation without common measure: Altruism or Selfishness pure?
Since Becker (1974) we model the economic behavior through an altruistic utility function that depends not only on the consumption of the migrant but also the consumption of his family. We distinguish unilateral altruism only when the migrant seeks to satisfy the utility of other family members and bilateral or reciprocal altruism when his family is also seeking to maximize the utility of the migrant. The probability of transfer depends Revenue migrant, its degree of altruism and the level of income of other household members. Fairly simple, repeating ratings used by Rapoport and Docquier (2006), we consider an individual migrant noted (m), a household receiving the funds paid (h), which maximizes a utility function U, with an initial income R, and C consumption an amount transferred T. The formulation of the simple utility that follows is inspired by Stark (1985) which presented a model of pure altruism unilateral / or reciprocal

be altuisme the degree of the migrant and recipient household (reciprocity in altruism)
Vi (Ci) a positive and concave function of consumption. Assume that Vi (Ci) = Vi (R-T), which allows us to rewrite the utility function of the migrant:

By maximizing the latter function, we obtain the amount of transfers T * maximizes the value attached by the migrant and his household of origin. We get:

So the optimal transfer depends positively on income and the degree of altruism of the migrant and the recipient's income negatively. In this context of pure altruism, we can add if the initial income increases by one, the optimal transfer increases as a unit:

This very restrictive assumption forces us to quickly release the theory of pure altruism. Indeed, as pointed Funkhouser (1995), empirical studies contradict this perfect proportionality between the change in income and migrant transfers paid.

There is a theory that is totally opposed to model transfer behavior as an exchange , Thus aiming to serve the interest of the migrant. Thus, by paying money to the migrant relatives trying to acquire services in return (members left behind have to deal with his elders and children, or manage its heritage ... etc.). This configuration transfers is advanced by Cox (1987) Cox, Eiser and Jimenez (1998) and Rapoport and Docquier (2006).

Suppose transfers are paid to buy a level of service provided X, the utility functions become based on levels of consumption and services in the country of origin
Vi (Ci, X) with i = m , h.
As pointed out by R & D (2006), it is assumed that members left behind will accept the exchange as long as the transfer offsets the cost of service, often estimated opportunity cost:

Thus bypassing the utility function for initial income and level of service provided by the recipient household transfer, we show that transfers increase with the level of service provided but react ambiguously to an increase in income household remained in place. Is the contribution of these theoretical developments initiated by Cox (1987) : Under certain conditions, higher income beneficiaries may cause an increase in transfers from the migrant.

To illustrate Cox (1987) took the case of intergenerational transfers and showed a positive relationship between transfers paid by the parents and the child's income: more income increases, its marginal utility consumption decreases and therefore it requires more remittances to offset the high cost of service to his parents. This relationship ultimately depends on the bargaining power of both parties. In this logic, a higher income the individual beneficiary or an increase in public transfers tend to increase the bargaining power of the person in question, which may require a higher amount of transfers from the migrant for a given level of service. Here we reconcile theory with a stylized fact already met: the rise of public transfers does not automatically drop private transfers (crowding out), because if we consider partially altruistic agents, the bargaining power of the beneficiary increases .

II. Strategic behavior revenue optimization
This notion of strategic behavior within the game theory is advanced by Stark (1985) and Stark and Wang (2002). Transfer to a simple objective: it can allow the migrant to increase its current income received by host region. When newly arrived migrants have higher levels of training and heterogeneous skills, the employer considers the individual productivity of an employee through the average productivity of its group. Thus, the migrant has an incentive to provide funds to unqualified relatives so they are not tempted to migrate and thus in turn reduce productivity group average. This theory is based on highly restrictive assumptions, assuming that individual productivity is not measurable in the short term and that the employer has an overview on the average productivity of the group (Rapoport and Docquier 1998 speaks of knowledge "pre Anthropology -required "). Stark concludes that only the skilled should find an advantage to migrate. Stark and Wang (2002) and within the first hypothesis assumes that the employer can quickly see the individual productivity of the migrant. In this context, the skilled migrant seeking to maximize its income by assuming that there will be more non-qualified the labor market, the more his own remuneration will be increased. Thus, transfers are used to finance the cost of migration of unskilled relatives arriving on the same labor market and highlight the highest qualification of the first wave of migrants.

More formally, we set m and h m with potential migrants who are more qualified. Pi is the proportion of productivity of h in terms of productivity m. If both remain in the region of origin, the remuneration is clear: win Rh m and h wins:

If the individual migrates m alone, the migrant receives remuneration equal to his marginal product, or Rom, but if it is joined by h, then its earnings decline in the average productivity of both migrant

If remittances strategic intervene so that the individual unqualified am an income at least equivalent to what would have obtained if migrated:

and that the migrant does not see his income reduced by income:

then transfers encourage unqualified to remain in their region of origin and the migrant can maximize its income. According
Stark, this approach allows strategic transfers to question some studies that overestimate the share of altruism in explaining transfers. Indeed, predictions of such models are very close to those obtained in a migrant's altruistic, but the underlying reasons are not the same.

And so rather than seeing the migrant as a pure altruist or a strategist, one who takes his decision, we consider an interaction of social and family influence in his decision making?


Family and Social Interactions in the decision of the individual



I. Insurance and moral hazard.
Developing countries are particularly affected by the volatility of their income, intrinsically linked to their dependence vis-à-vis agriculture and weak systems of risk pooling. Indeed, in the absence of credit market and insurance , poor countries become more vulnerable to price shocks and hence income and can be found in the migration and financial transfers, a means of pooling risks. Thus, as pointed out several studies, it is possible to observe the arrangements of families (implicit contracts) to send some members to urban areas or abroad in order to pool the risk agricultural and eligible for re-allocation of resources potential (Stark and Levhari, 1982 Rozenzweig, 1988, Lambert 1994).
We study a household with two successive periods, consisting of two individuals h and m receiving income ₀ initial R, which in the second period may vary randomly R1min up with probability p and with probability p R1max-1. Rural income is volatile and uncertain. The two agents have the same utility function, because the uncertainty of farm incomes affect everyone the same way.

One of the two individuals decide to migrate in the second period to obtain a stable income. The cost of migration can not be supported by one person shall not be less than the initial joint household income (Ro \u0026lt;2RO). The burden of the cost of migration is supported by two distribution of costs should be decided in the first period, taking into account the volatility of income in the second half. Rapoport and Docquier formalizes the implicit family contract as follows:

where delta is the share of the cost of migration (c) supported by the migrant himself, Tp and T1-p are transfers according that the prosperity of the period, lambda is the "Family weight" of the individual who does not migrate (bargaining power) and Vh its level of utility in the first period. Thus, the implicit contract provides that the value attached to the two individuals be maximized under the constraint of financing the cost of migration and economic context in decision making.
The two utility functions to maximize can be written:

The theory of insurance provides very close predictions of the theory of altruistic migrant. Nevertheless, time horizons are different, because in this theoretical framework, the transfer decision is sequential in time and temporal effects are not the same.

II. Investment and credit market failures
Lucas and Stark (1985) studied the behavior of the individual in the context of Botswana, by developing a model they call "tempered altruism" or "enlightened selfishness" demonstrating the dualism of human behavior. Very simply, it is assumed that transfers are a contractual arrangement agreed by the migrant and his family of origin, contract inter-temporal and reciprocal. Migrants from urban areas are often more educated and better trained than the family members remained in the field. But the initial cost of education and the cost of migration is often borne by the family, and in fact partly justifies future transfers of the migrant: it is a loan repayment at interest (Cox & Jimenez 1992, Cox, Eser & Jimenez 1998, Ilahi & Jafarey 1999). The migrant compensates for the absence of credit market and the family invests in the education of one member to obtain a future pension. That's intertemporal arbitrage where every part of the contract maximizes its own utility but in which social norms and inter-generational coming interfere choice.

III. Bargaining power and volume of shipments
Aisa, and Larramona Andaluz (2011) have developed a negotiation model which aims to the volumes transferred by a bargaining game between the migrant and his family. The most direct consequence of this type of model is the demonstration of a relationship between nonmonotonic revenues of the two 'parties' and the amount of remittances. Already Cox et al. (1998) had introduced the important concept of bargaining power between the generations. Such modeling requires defining the determinant of the bargaining power of members of a family: it is primarily a latent threat "Threat Point" as a threat of divorce or break the implicit contract between two parties . The authors choose a cooperative environment and a Nash solution to characterize their bargaining model. So the transfer volumes determined by utility maximization are Pareto efficient.
The optimization model is written as the migrant (m) should consider the usefulness of his family (h), with a share of altruism in its decision, within budget constraints of h and m :

Q with the level of family service rendered by non-migrants, which costs them pQ and the degree of altruism. Finally, after resolution of the program determining the optimal levels of service * Q Record and Cm * and Ch * consumption optimal, the optimal solution for the amount transferred T * written:

or the volume of transfers associated with the situation Pareto efficient. At this level, no bargaining power is even built. Indeed, the first step according to the authors, is to define the critical point or the status quo of the negotiation process. In the literature it is often assumed that divorce or the breakdown of the domestic contract is the threat (non-cooperative solution) that determines the bargaining power and the distribution of welfare between the migrant and his family. In their model, the authors assume that this point is characterized by the complete absence of altruism (beta = 0), no transfer is made and each maximizes his own utility. the solution is not cooperative. Thus, during the negotiation process, the solution of Nash General Equilibrium is achieved by maximizing the following:

with theta ∈ [0,1] the bargaining power of migrants and (1-theta) than his family, exogenous parameters in the model (De Haas, 2007). Thus, once the first order conditions specified, the utility levels optimized, the authors obtain the transfer amount T * that maximizes this utility as part of a negotiation process.

This result reinforces the idea that the migrant has more bargaining power, the lower volumes shipped is important. Conversely, the relationship between the degree of altruism, migrant's income and transfers are more ambiguous, the sign of the derivatives just depends on the bargaining power, but also levels of utility in non-cooperative situation. The authors finally show that the relationship between income and migrant remittances is a non monotonic function.

IV. Mixed models
authors have sought to model the transfer behavior in a less categorical, mixing incentives seen so far. For example, we may assume that the implicit contracts family will meet both a motive for investment (and therefore interest loan) and a pattern of insurance and risk diversification. The very notions of altruism and selfishness are intertwined automatically under the influence of social norms and attention directed to features of society of origin. Domestic contracts
whether implied or otherwise, are often subject to strategic decisions that affect individual motivations of the original transfers. Thus, Chami, Fullenkamp & Jahjah, 2005 and Naiditch & Vranceanu, 2009 show that to move mechanically causes an asymmetry of information that pushes migrant family or playing a dominant position to influence the transfer decision. Naiditch & Vranceanu, 2009 have developed an original model called Signal, which is to assume that asymmetric information situation, the migrant uses amounts transferred to signal social success to his family, which has no information to judge. Thus, transfers are no longer a monotonic function of the migrant's income, since in a precarious situation, wanting to ensure a high social status in his home region would contract its disposable income to send transfer rates.




Library
- Aisa, and Larramona Andaluz (2011) How does bargaining power affects remittances? Economic Modelling, January-March 2011


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