# Why Do African Households Give Hospitality to Relatives?

Benoît Rapoport

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Why Do African Households Give Hospitality
to Relatives?

Benoît RAPOPORT

2000.112

CENTRE NATIONAL
DE LA RECHERCHE
SCIENTIFIQUE
# Why Do African Households Give Hospitality to Relatives?

Benoît RAPOPORT (TEAM, Université de Paris 1)*

(November 2000)

<footnote>* The comments of Andrew Clark, François Gardes, Gilles Grenêche, Shoshana Grossbard-Shechtman, Louis Lévy-Garboua and David Margolis are acknowledged with thanks. Earlier versions of this paper were presented at the XVIIèmes Journées de Micro-économie Appliquée (June 2000, Québec), the June 2000 meeting of the European Society for Population Economics (Bonn, Germany) and at seminars at the Institut National de la Recherche Agronomique, at the Institut National des Etudes Démographiques and at TEAM. Any errors are mine alone. I also thank Martin Wora and the Direction Générale de la Statistique et des Etudes Economiques (Gabon) for access to the EBC 92-94 data.</footnote>
Résumé : Ce texte empirique se propose d'expliquer pourquoi les ménages africains offrent souvent une hospitalité de long terme aux membres de leur parenté. Nous utilisons une enquête budget et consommation réalisée en 1994 au Gabon pour examiner deux types d'hypothèses et nous proposons une procédure en deux étapes afin de discriminer entre elles. Nous nous demandons si le nombre de parents logés et la décision d'accueil sont principalement le fait du chef de ménage, auquel cas l'ensemble du revenu du ménage nucléaire déterminera le nombre d'hébergés, ou s'ils sont plutôt choisis par la famille étendue et, dans ce cas, seule la partie du revenu que les parents peuvent observer aura de l'importance. Nous régressons donc le revenu du ménage nucléaire sur des variables que les parents pourraient utiliser pour l'évaluer. Dans une seconde étape, nous estimons à la fois la probabilité d'avoir un invité et le nombre de ces invités en introduisant parmi les régresseurs le revenu prédit et le résidu de la première étape. Le revenu prédit est interprété comme le revenu que la parenté attribue au ménage, tandis que le résidu est la partie inobservable du revenu du ménage nucléaire. Nous montrons que seule la partie observable du revenu du ménage a un effet sur la probabilité d'avoir un invité et sur le nombre de ceux-ci. Des estimations sont conduites pour les hommes adultes, les femmes adultes et les jeunes parents hébergés, et montrent que les résultats diffèrent dans une certaine mesure selon le sexe et l'âge des invités.

JEL: C35, D10, D82.

Mots-clés: Transferts familiaux, Composition de la famaille, Redistribution.

Abstract: This empirical paper proposes to explain why African households often provide long-term hospitality to relatives. We use a budget and consumption survey carried out in Gabon in 1994, examine two types of hypotheses, and propose a two-step procedure to discriminate between them. We address the question whether the number of guests and the hospitality decision mainly come from the head of household, in which case the whole income of the nuclear household will determine the number of guests, or if they come rather from the extended family, in which case only the part of income that relatives are able to observe will matter. We thus regress nuclear household income on variables that relatives could use to evaluate it. In a second step, we estimate both the probability of having a guest and the number of guests, introducing predicted income and the residual of first step among the regressors. Predicted income is interpreted as the income that the relatives attribute to the nuclear household, while the residual is the unobservable part of the nuclear household income. We show that only the observable part of household income has an effect on the probability of having a guest and on the number of them. Regressions are conducted both for male and female adults and for young guests, and show that conclusions differ to some extent depending on the sex and the age of the guests.

JEL: C35, D10, D82.

Keywords: Family Transfers, Family Composition, Redistribution.
# I Introduction

About half of households in Libreville and Port-Gentil (Gabon) have at least one guest, that is a member of the kinship who does not belong to the nuclear family (head, his spouses, their children and their grand-children common or not). This is not particular to Gabon, and can be found in a number of African countries. If intergenerational co-residence has now been studied for more than a decade (see Hayashi, 1995; Rosenszweig and Wolpin, 1985 and 1994; Amin, 1998, for example), hospitality given to relatives has not received much attention in economic literature. "Hospitality" here indicates having one or several guests, and typically lasts for several months, if not years. It therefore differs from the tradition of hospitality, very common in Africa, which consists in giving room and board to relatives or friends for a few days, for example while they are traveling. Hospitality can be considered as a form of in-kind transfer (cash and in-kind transfers between households are very frequent in Gabon: 88.5% of households received private transfers and 80.3% of households made at least one transfer in the survey data we use), but a very specific one, as it directly modifies household structure. Thus, households are larger in African than in Western countries not only because fertility is high, but due also to differential household composition. The lack of interest in this subject can be attributed to the reluctance to consider the household other than as a unit, and to the poor quality of information on biological ties between household members. However following the seminal papers of Manser and Brown (1980), McElroy and Horney (1981), Chiappori (1988, 1992) first designed to take relationships between spouses into account, relations between household members have received a lot of attention, both from a theoretical and empirical point of view. In this perspective, it is hard to believe that African households can be considered as units.

This paper is in the tradition of work on household formation, but with addition of guests. To this end, the household is divided into members of the nuclear family and guests, and we empirically study the determinants of the probability of having a guest and of the number of guests. Two hypotheses will be considered. First, the head is supposed to choose entirely freely if he would like to have a guest, and how many guests he wishes to have. Second it is relatives (the extended family) who make the decision. In the first case, the whole income will determine the number of guests; in the second case, only what can be observed is important. We use a two-step procedure to discriminate between these two hypotheses. In the
first step, nuclear household income is estimated on the basis of variables that are supposed to be observable by the relatives. In the second step, we estimate the probability of having a guest and the number of guests; among the regressors, we introduce both predicted income and the residual of the first step. The predicted income is interpreted as the income that the relatives attribute to the nuclear household, while the residual is the unobservable part of the nuclear household income. We then test if the first-step residual is significantly correlated with the presence of guests.

The knowledge of the motivation for hospitality firstly may help us to understand how African societies work. In the second place, it could help us to understand various behaviors (fertility, structure of consumption, labor-supply and investments in human capital), and *in fine* to make recommendations in order to favor economic development.

The paper is organized as follows. Section II briefly describes the Gabonese data. Section III proposes an overview of households in Libreville and Port-Gentil. In section IV, we present the two hypotheses that are tested in the empirical work. Section V addresses several econometric questions. Section VI presents the empirical results and section VII concludes.

## II Data

The survey we use in this paper was carried out in Libreville and Port-Gentil, the two main Gabonese cities, between 1992 and 1994. In 1992, an exhaustive census took place in Libreville and Port-Gentil in order to build a sampling base. A retrospective living standard survey concerning African households, the first since 1962, was carried out in 1993. However, for a number of reasons, it is not very satisfactory. In 1994, a sub-sample of 636 households was surveyed, half in June-July 1994 and half in October-December 1994 (Hereafter EBC 94). These households were followed for one month. Each member (above 16 for the girls and 18 for the boys) was given a notebook in which they daily noted expenditures and incomes. The great interest of this survey lies in the fact that actual biological ties between the members of the household were carefully measured. For this reason, this survey is quite original, as in African societies it is often difficult to know how people are really linked in the household, because of the system of kinship classifications. For example, in a patrilineal society, sons and
brother's sons are generally referred to by the same term. However, socio-demographic data
are unfortunately not very extensive as the survey was mainly designed in order to study
incomes and expenditures.

We will use in this study a subsample of only 355 family units, because important
information is missing in about one third of surveyed households, particularly when the head
did not fill out his notebook. Moreover, in a few dozen households, information on at least one
variable crucial for our analysis (mainly age of the head and surface area of the house<fnref n="1" />) is
missing.

III An overview of households in Libreville and Port-Gentil

As often in Africa, households are fairly large in urban Gabon: 5.84 members on average.<fnref n="2" /> They are generally built around a single income-earner (or a unique couple): the contribution of the head to the household income is, on average, 83%; the spouse of the head often brings the rest. In particular, there are almost no households in which two unmarried working people co-reside; the exceptions generally concern non-Gabonese households. Income comes mainly from work in two-parent households and in non-Gabonese one-parent households headed by a man, and also from transfers (from family or boy friend) in other one-parent households.

In the survey, the exact ties of a household member with the head are described by five
variables. The "side" indicates whether she belongs either to the kinship of the head, or to the
kinship of his or her spouse, or if she is a common child or grandchild. The "number of wife"
indicates to which wife the member is related when the head is polygamist.<fnref n="3" /> The "level of
kinship" shows if the subject is directly related to the head or through another member of the

<footnote n="1">¹ In fact one interviewer forgot to ask or to evaluate the surface area.</footnote>

<footnote n="2">² Statistics are computed on the basis of the subsample we use. They may slightly differ from those given by the 1992 exhaustive census or by the census carried out nationally in 1993 (Recensement Général de la Population et de l'Habitat, 1995).</footnote>

<footnote n="3">³ There are only a few polygamist households (2.2% of the households whose head is Gabonese; in the sample only one head lives with more than two wives), even though polygamy is legal in Gabon (unlike in Côte d'Ivoire, for example; see H. G. Jacoby, 1995). However female single heads often receive gifts from their "boy-friend". As generally only the head and his or her spouse(s) earn money, this is probably a kind of "disguised" polygamy that the data unfortunately do not allow us to measure accurately.</footnote>
household. The fourth variable is the identifier of this intermediary member, and the last is the tie with either the intermediary, or the head, or his (or her) spouse(s). For example, a nephew of the head will be labeled "son of the sister of the head" or "son of the brother of the head" if neither his mother nor his father is present, or "son of member x", if x (sister or brother of the head) is present.

Household members we called "intermediary" are not numerous, so sub-structures are not very common in Libreville and Port-Gentil. They nevertheless represent 14.3% of the members of the household (15.9% in households headed by a Gabonese; in fact, there is no such sub-structure in households headed by a non-Gabonese), and mainly concern girls with (very) young children. There are almost no dependent men with relatives.

The head, his spouse(s) and their children and grandchildren common or not (having a child from another union than the current one is not unusual in Gabon) represent 77.1% of the members of the household (71.9% when grandchildren are excluded). We will call hereafter this part of the household "the nuclear household" and other members will be referred to as "guests" or "members of the extended family". Thus about one quarter of the members of the household do not belong to the nuclear household. Not surprisingly, guests are less numerous in households headed by a migrant and are proportionally more numerous in one-parent households. But even in Gabonese two-parent households, they represent 18% of the members. Overall, there is at least one guest in 50.7% of the households (58.5% if the head is Gabonese). The following Table describes household composition more precisely.
<table><caption>Table 1 Household composition in Libreville and Port-Gentil</caption><thead><tr><th rowspan="3"></th><th colspan="4">TWO-PARENT HOUSEHOLDS</th><th colspan="4">ONE-PARENT HOUSEHOLDS</th></tr><tr><th colspan="4">HEADED BY A</th><th colspan="4">HEADED BY A</th></tr><tr><th colspan="2">MAN</th><th colspan="2">WOMAN</th><th colspan="2">MAN</th><th colspan="2">WOMAN</th></tr><tr><th></th><th>GABONESE</th><th>NON GABONESE</th><th>GABONESE</th><th>NON GABONESE</th><th>GABONESE</th><th>NON GABONESE</th><th>GABONESE</th><th>NON GABONESE</th></tr></thead><tbody><tr><td>Heads</td><td>12.5%</td><td>27.3%</td><td>13.0%</td><td>19.4%</td><td>72.6%</td><td>18.9%</td><td>56.2%</td><td></td></tr><tr><td>Spouses</td><td>13.0%</td><td>27.3%</td><td>13.0%</td><td>0.0%</td><td>0.0%</td><td>0.00%</td><td>0.0%</td><td></td></tr><tr><td>Sons</td><td>27.1%</td><td>14.9%</td><td>21.7%</td><td>9.0%</td><td>0.0%</td><td>17.2%</td><td>12.5%</td><td></td></tr><tr><td>Daughters</td><td>25.6%</td><td>21.5%</td><td>19.6%</td><td>10.3%</td><td>0.0%</td><td>25.1%</td><td>25.0%</td><td></td></tr><tr><td>Other descendants</td><td>3.8%</td><td>0.0%</td><td>6.5%</td><td>4.5%</td><td>0.0%</td><td>11.2%</td><td>0.0%</td><td></td></tr><tr><td><i>Total nuclear family</i></td><td><b>82.0%</b></td><td><b>91.0%</b></td><td><b>73.8%</b></td><td><b>43.2%</b></td><td><b>72.6%</b></td><td><b>72.4%</b></td><td><b>93.7%</b></td><td></td></tr><tr><td>Mothers</td><td>0.7%</td><td>0.0%</td><td>2.2%</td><td>1.3%</td><td>0.0%</td><td>1.5%</td><td>0.0%</td><td></td></tr><tr><td>Fathers</td><td>0.1%</td><td>0.0%</td><td>0.00%</td><td>0.00%</td><td>0.0%</td><td>0.6%</td><td>0.0%</td><td></td></tr><tr><td>Other ascendants</td><td>0.5%</td><td>0.0%</td><td>6.5%</td><td>0.6%</td><td>0.0%</td><td>1.1%</td><td>0.0%</td><td></td></tr><tr><td>Younger brothers</td><td>3.6%</td><td>0.8%</td><td>6.5%</td><td>8.4%</td><td>7.8%</td><td>4.1%</td><td>0.0%</td><td></td></tr><tr><td>Older brothers</td><td>0.2%</td><td>0.8%</td><td>0.0%</td><td>0.6%</td><td>3.9%</td><td>0.0%</td><td>0.0%</td><td></td></tr><tr><td>Younger sisters</td><td>1.9%</td><td>0.0%</td><td>0.0%</td><td>9.7%</td><td>2.0%</td><td>3.9%</td><td>0.0%</td><td></td></tr><tr><td>Older sisters</td><td>0.2%</td><td>0.0%</td><td>0.0%</td><td>3.2%</td><td>2.0%</td><td>0.2%</td><td>0.0%</td><td></td></tr><tr><td>Nephews</td><td>4.2%</td><td>0.8%</td><td>2.2%</td><td>12.3%</td><td>0.0%</td><td>6.4%</td><td>6.3%</td><td></td></tr><tr><td>Nieces</td><td>4.6%</td><td>3.3%</td><td>4.4%</td><td>13.6%</td><td>3.9%</td><td>4.9%</td><td>0.0%</td><td></td></tr><tr><td>Other collaterals</td><td>2.0%</td><td>3.3%</td><td>4.4%</td><td>7.1%</td><td>7.8%</td><td>4.9%</td><td>0.0%</td><td></td></tr><tr><td><i>Total extended family</i></td><td><b>18.0%</b></td><td><b>9.0%</b></td><td><b>26.2%</b></td><td><b>56.8%</b></td><td><b>27.4%</b></td><td><b>27.6%</b></td><td><b>6.3%</b></td><td></td></tr><tr><td>Total</td><td>100.0%</td><td>100.0%</td><td>100.0%</td><td>100.0%</td><td>100.0%</td><td>100.0%</td><td>100.0%</td><td></td></tr></tbody></table>

Table 1 shows that guests are almost always younger than the head or his spouses. In fact, hospitality is seldom given, for example, to older brothers. There is only one exception: the number of older siblings is important in households headed by a single male. But this is also the only case in which there is more than one income-earner: households headed by a single non-Gabonese man living with his older brother, both of whom are often in the labor force (and have often the same job), the head being generally the one who migrated first. Hospitality given only to younger relatives is not specific to the Gabon. Older often have obligations towards younger members of the family in African societies.

Table 1 also shows that, although family structure is more complex in Gabon than in Western societies, the household extends only to what could be called the " first circle of the extended family". Hospitality is limited to the parents, siblings, nephews and nieces of the members of the main couple. It is hard to know whether it is a recent phenomenon resulting from the economic transformation or from urbanization. However, Balandier (1982 [1955]) showed that, at the beginning of the fifties, in the Fang group (a patrilineal ethnic group coming from the North of the country), the core of the family was a segment (the *nd'è bòt*)
grouping together a grandfather (a *mvam*), his children and his grandchildren. It is interesting
also that the data reveal no difference between patrilineal and matrilineal societies with respect
to the distribution of ties of the household members with the head.<fnref n="4" />

The next section asks why there are so many guests in Gabonese households.

IV Why do Gabonese households have guests?

The aim of this empirical paper is to discriminate between two explanations. In the first
the hospitality decision is chiefly taken by the head or at least by the nuclear household. This
can be called a supply-hypothesis. The head offers hospitality to members of his extended
kinship, and chooses how many guests he wishes to welcome. Beckerian altruism (G. S.
Becker, 1981) or exchange models (B. D. Bernheim, A. Shleifer and L. A. Summers, 1985 and
D. Cox, 1987) are examples of this kind of hypotheses. For example, if the head of household
is altruist towards his relatives (their utilities enter positively in his utility function), he will
decide himself how much he wishes to transfer to his extended family, and thus how many
guests he will have. The same is true if he needs the attention of his relatives or their help with
domestic tasks.

The second hypothesis is that the decision is taken by the relatives or the family group.
It can be called a demand-hypothesis. It is not only the head who decides how many relatives
he wishes to welcome, but also the extended family. Social pressure and social norm models
are demand-hypotheses.<fnref n="5" /> For example, Rapoport (2000a) explains hospitality using a theory of
social pressure and social norms.

The two hypotheses have very different implications regarding the role of income. If the
decision is made by the head, the number of guests will be determined by the whole income of
the nuclear household. Guests are considered as goods by the head. The demand function for
guests will depend on household income. On the contrary, if guests are taken as a result of
(social) pressure, only the income observed by the extended family will be important, as the

<footnote n="4">⁴ Kolmogorov-Smirnov test of the equality of distributions. Corrected P-value: 0.88.</footnote>

<footnote n="5">⁵ This is not the case if the norm is fully internalized, as the head then takes himself the decision (see J. Elster, 1989). In this case, the possible set is only restricted (R. A. Posner, 1997).</footnote>
head will probably try to escape from this redistribution.<fnref n="6" /> Of course, the part of income that is observable depends on the activity of the income-earner. For example the income of a state employee is easier to observe than that of a craftsman or a shopkeeper (except if one shares the same activity).

### Supply hypotheses

An individual $h$ who is altruistic towards his relatives decides how he will share income between his own nuclear family and his kinship. Provided that there is an interior solution, at total transfer $T$ given, he will prefer to give money to several relatives than to one single relative, because of the decreasing marginal utility of income (the sum of utilities of two people receiving $T/2$ is higher than the utility of one people receiving $T$) and because $h$'s utility is a concave function of utility of people about which he cares (he derives more utility from two relatives with utility level $V/2$ than from one relative with level $V$). The basic altruism hypothesis does not explain why households have guests instead of simply giving cash or in-kind goods. Bruce and Waldman (1991) show that in-kind transfers can be an efficient solution to the Samaritan dilemma, but several other explanations are plausible. Individual $h$ may want to be sure that the relative he chose will really receive the transfer (targeting problem). Moreover, this form of transfer allows him to benefit from economies of scale. Of course, it implies that there will be a minimum amount ($T_1$) of income he has to transfer to each beneficiary (supposed identical), otherwise none of them will join the household. At given $T_1$, as the transfer function $T(R) = n*T_1$ is an increasing function of income, the demand for guests ($n$), increases with nuclear household income $R$. In this case, total income, both observable and unobservable, plays a role. The same is true if having guests gives status to the head, that is if head's utility depends on $n$ per se (provided that it is a normal good).

If hospitality is exchanged for attention or help for domestic tasks, the amount of transfer $T$ will also be an increasing function of $R$, provided that attention or help are normal goods. And once again, it is total income that matters. It does not necessarily imply that the head will prefer to have several guests. However, it will be the case if, for example, transfers

<footnote n="6">⁶ Experience shows that people often dissimulate their incomes even inside nuclear family. Spouses often ignore how much earns the other.</footnote>
are exchanged for domestic help and if effort is a concave function of earnings: the head will prefer to have one "employee" (paid *T*) rather than two (paid *T/2*).<fnref n="7" />

### Demand hypotheses

Assume now that *h* is not altruistic towards his relatives and that he does not need their attention or help. Rather, there is a norm in the family group, which obliges him to redistribute his income within the extended family. For example, this norm may state that *ex post* incomes must be identical, whatever *ex ante* incomes were. Among the Fang, "the rich man had in a way to pay for his security. He had therefore to show himself « very generous » (*esos*) towards one's family". "The society accepted the existence of the « rich »... provided that this « wealth », *akum*, was profitable to everybody".<fnref n="8" /> As long as everyone's contribution to the production of wealth is identical<fnref n="9" />, considering the norm, nobody can, or wants to, claim more than his own contribution. However, as soon as the productivities of agents differ, the more productive household members will experience tension between the desire for increasing their monetary earnings and the punishment following from the breach of the norm. The norm-enforcer, the family group, encounters the same problem as the income observability problem in optimal taxation theory. Family members will try to escape from redistribution. Hence only what relatives can observe will be shared among extended family members. The norm hypothesis may also help to understand why "hospitality" is a favorite means of transfer: in this way, the group can more easily control the income of its members.<fnref n="10" />

In order to discriminate between these two kinds of motives, we propose here a simple two-step test. In the first step, we regress the income of the nuclear household or its logarithm on the variables the extended family can observe, such as demographic variables, activity of the head, his age, the quality of housing. We interpret the result as the income the family attributes

<footnote n="7">⁷ Complementarity and task-specialization are explanations too.</footnote>

<footnote n="8">⁸ Bot Ba Njock (1960) quoted, page 140, by Balandier (1982 [1955]).</footnote>

<footnote n="9">⁹ We suppose, here, to simplify, that the production of the group is the sum of the individual productions, although externalities exist, for example, in the agricultural activities.</footnote>

<footnote n="10">¹⁰ This is in line with Rosenzweig (1988) and Rosenzweig and Stark (1989)</footnote>
to the household.<fnref n="11" /> The residual is interpreted as the part of income that relatives cannot observe. In a second step, we estimate, using a Poisson or a negative binomial regression, the number of guests or, with a probit, the probability of having a guest. In these regressions we use as independent variables the estimated income and the predicted residual of the first step, and other control variables. In the case of pressure motives, only the estimated income will have a positive effect. However, in the case of the supply-hypothesis, both these estimated variables will have a positive effect, and the estimated effects should be identical.<fnref n="12" />

## V Econometric considerations

This econometric approach raises two important problems. The first one refers to identification. We have to make the crucial assumption that the variables that the family and the economist can observe are identical, or more exactly that the extended family has no more information at its disposal than we have. Experience shows that household members, and a *fortiori* members of the extended family, do generally not know the head's earnings. In order to estimate earnings, we use regressors typically included in Mincer equations: age, school level, sex, sector, etc. The problem is more serious for the two other main sources of income. For example, if a member of the extended family knows that the head owns and rents one or several houses it will probably be possible for her to estimate the head's rental income, especially if she has already seen the houses in question. The same argument applies when considering transfers received by household members. Members of the extended family probably know whether a single female head is helped by her boyfriend, although they probably do not know exactly what she receives. However, if, for example, they know the boy friend in question, they will probably be able to evaluate his income and thus the amount of the transfer. Unfortunately, we have no information about the characteristics of the rented houses in the first case, and about the transfer donor in the second case. Several solutions can be envisaged. We could use dummy variables indicating whether the head rents out a house or if he receives

<footnote n="11">¹¹ Altonji *et alii* (1992) deal with the problem of asymmetric information on income, and use easily observable variables as instruments to estimate the income of the partner of altruistic transfers.</footnote>

<footnote n="12">¹² More specifically, as the test on the residual component is usually interpreted as an evidence of misspecification (endogeneity of income), a significant coefficient will either indicate that unobservable income has an effect on hospitality or that the model is misspecified. However, as shown below, the residual is never significant, what means that one cannot reject the joint assumption that the model is well specified (form this point of view) and that unobservable income has no effect.</footnote>
a transfer. However, as argued above, by doing so we certainly underestimate what relatives know. We will nevertheless present estimations using such dummies. Another possibility is to use the rental income or the amount of transfers, but in this case, we probably overestimate the amount of information. Another way to proceed would be to distribute these incomes (rental income, received transfers) into quintiles or deciles and to use dummies for these intervals, which poses the problem of the choice of the thresholds. The last possibility, the one we choose, is to use errors-in-variables models and to assume that transfers or rental incomes are measured with error (see Greene, 1997, for example).

Second, we need variables to identify both steps. The first step will be identified by non-linearity in the head's age and by several other variables, among which figures the rent or rent-equivalent paid by the head. The second step is much more difficult to identify. We use the surface area of lodgings (which is nevertheless correlated with the rent or rent-equivalent), dummies indicating if the housing has water or electricity, and another dummy indicating if the household is headed by a couple.

The second problem is common to all two-step estimations, as shown in Murphy and Topel (1985). Consider a model (model II, principal model or second-step model), among the regressors of which there are unobserved variables. These variables can be either replaced by their estimated or predicted values from another model (model I, auxiliary model or first-step model), or estimated jointly with the principal model. The second method (for example full information maximum likelihood) is often hard to implement: finding a joint distribution for the random components of the unobservables in two models may be difficult, as it is the case in most of our present applications. The first method, although easier to use, is not without drawbacks. If this (two-step) procedure generally yields consistent estimates of the second-step coefficients, the estimated standard errors are incorrect. If one assumes that the random components from first- and second-steps are independent, the estimated standard errors will always be underestimated, although this is not necessarily the case if independence is not assumed. Murphy and Topel (1985) propose a general solution for this problem.¹³ We present this in Annex III, together with the formulae applied to our case.
The procedure is as follows. First, we regress nuclear household income (ordinary least squares<fnref n="14" /> or errors-in-variables regressions<fnref n="15" />) on variables that the extended family members are able to observe, and we compute predicted ("observable") income and the residual ("unobservable income"). Second, we estimate the probability of having a guest by a probit, or the number of guests by a Poisson or negative binomial regression, including as regressors predicted income and the first step residual. Third, we correct the estimated variance-covariance matrix using Murphy and Topel's (1985) method. Last, we see if the estimated first-step residual has a significant impact on the probability of having a guest or on the number of guests; and, if this is the case, we test whether residual and predicted income have identical effects.

# VI Results

## VI.1 First-step results

Table A2 in annex II displays the first-step results where we predict income using variables that are both observable by relatives and correlated with income. We will comment on these only briefly, as this regression does not have a great deal of economic content.<fnref n="16" /> This step only tries to. The logarithm of income is preferred to its level for two reasons: both to be in line with Mincer's (1974) specification, and because log income fits the number of guests equation better than a quadratic or linear function of income.¹⁷ Not surprisingly, the effect of age on income is quadratic; education has a linear and significant (only at the 5 or 10% level) impact; working people have higher income than those who do not work, except for workers with low levels of qualifications. Tenants have higher income, and *ceteris paribus*, there are no differences between men and women. It is interesting to note that the presence of other workers in the household (part- or full-time) has no estimated effect. Neither the fact that the household received a transfer during the survey nor the amount of this transfer has a significant impact, but the logarithm of rental income is a good predictor for nuclear household income.

<footnote n="13">¹³ For example, Richaudeau (1999) corrects the variance-covariance matrix in a similar case to ours. His second step is a negative binomial regression, although his first step is a probit.</footnote>

<footnote n="14">¹⁴ In this case, robust standard errors are computed.</footnote>

<footnote n="15">¹⁵ With a reliability of .85.</footnote>

<footnote n="16">¹⁶ Notice that this regression does not simply measure permanent income, as we use some variables correlated with income (rent and transfers received) that are probably not predictors of permanent income.</footnote>
Next, the fact that the household made a transfer during the survey and household income are positively correlated. Lastly, the logarithm of rent (or rent-equivalent for homeowners) is a very good predictor of income. Overall, this set of observables explains about 60% of the variance of nuclear household income.

## VI.2 The probability of having a guest and the number of guests

In the second step, we use a probit to estimate the probability of having a guest, and a Poisson or a negative binomial process<fnref n="18" /> to estimate the number of guests; we introduce in the regression predicted log-income and the residual computed in the first step. A set of control variables reflecting household heterogeneity is added.

Table 2 displays the results for all guests without age or sex distinction. The first two columns refer to the OLS first step, and correspond to the first column of table A2 in Annex II, and the last two columns to the errors-in-variables first-step.

<footnote n="17">¹⁷ It is moreover easier to deal with a unique predicted variable and a unique residual in our two-step procedure.</footnote>

<footnote n="18">¹⁸ In most cases, tests of goodness of fit and tests of the overdispersion parameter reject the assumption that the endogenous variable is Poisson-distributed. However, this is not the case if we estimate the model for male</footnote>
<table><caption>Table 2 Estimation of the probability of having a guest and of the number of guests</caption><thead><tr><th rowspan="2"></th><th colspan="2">FIRST-STEP: OLS</th><th colspan="2">FIRST-STEP: ERRORS-IN-VARIABLES</th></tr><tr><th>P(GUEST)</th><th>NUMBER OF GUESTS</th><th>P(GUEST)</th><th>NUMBER OF GUESTS</th></tr></thead><tbody><tr><td>Predicted income of the nuclear household</td><td>0.739***<br>(0.187)</td><td>0.808***<br>(0.194)</td><td>0.713***<br>(0.181)</td><td>0.778***<br>(0.190)</td></tr><tr><td>Residual of first step</td><td>-0.076<br>(-0.130)</td><td>-0.089<br>(-0.141)</td><td>-0.083<br>(-0.132)</td><td>-0.091<br>(-0.145)</td></tr><tr><td>Number of members of the nuclear household (except head)</td><td>0.046<br>(0.031)</td><td>0.037<br>(0.030)</td><td>0.047<br>(0.031)</td><td>0.037<br>(0.030)</td></tr><tr><td>Number of full-time workers in the nuclear household (except head)</td><td>-0.027<br>(-0.212)</td><td>-0.156<br>(-0.206)</td><td>-0.009<br>(-0.214)</td><td>-0.140<br>(-0.208)</td></tr><tr><td>Number of part-time workers in the nuclear household (except head)</td><td>0.106<br>(0.178)</td><td>0.275*<br>(0.152)</td><td>0.110<br>(0.201)</td><td>0.285*<br>(0.172)</td></tr><tr><td>Surface area of housing per member of nuclear household</td><td>0.020***<br>(0.006)</td><td>0.003<br>(0.005)</td><td>0.020***<br>(0.006)</td><td>0.003<br>(0.005)</td></tr><tr><td>1 if the head is a tenant</td><td>-0.766***<br>(-0.202)</td><td>-0.999***<br>(-0.218)</td><td>-0.762***<br>(-0.203)</td><td>-0.986***<br>(-0.218)</td></tr><tr><td>1 if the housing has electricity</td><td>0.589*<br>(0.334)</td><td>0.644<br>(0.437)</td><td>0.589*<br>(0.335)</td><td>0.644<br>(0.430)</td></tr><tr><td>1 if the housing has water</td><td>-0.427*<br>(-0.217)</td><td>-0.334<br>(-0.218)</td><td>-0.425*<br>(-0.217)</td><td>-0.337<br>(-0.218)</td></tr><tr><td>Age of the head</td><td>-0.031***<br>(-0.008)</td><td>-0.027***<br>(-0.009)</td><td>-0.031***<br>(-0.008)</td><td>-0.027***<br>(-0.009)</td></tr><tr><td>1 if the household is headed by a couple</td><td>-0.191<br>(-0.253)</td><td>-0.805***<br>(-0.251)</td><td>-0.173<br>(-0.253)</td><td>-0.796***<br>(-0.258)</td></tr><tr><td>Logarithm of amount of transfers received</td><td>0.037*<br>(0.021)</td><td>0.039*<br>(0.022)</td><td>0.028<br>(0.021)</td><td>0.030<br>(0.021)</td></tr><tr><td>1 if belongs to patrilineal ethnic group</td><td>0.111<br>(0.295)</td><td>0.651*<br>(0.339)</td><td>0.153<br>(0.292)</td><td>0.702**<br>(0.339)</td></tr><tr><td>1 if belongs to matrilineal ethnic group</td><td>0.166<br>(0.285)</td><td>0.733**<br>(0.327)</td><td>0.213<br>(0.284)</td><td>0.787**<br>(0.327)</td></tr><tr><td>Logarithm of amount of transfers made</td><td>-0.029<br>(-0.024)</td><td>-0.042<br>(-0.026)</td><td>-0.026<br>(-0.024)</td><td>-0.039<br>(-0.026)</td></tr><tr><td>1 if lives in Port-Gentil</td><td>0.296<br>(0.197)</td><td>0.206<br>(0.208)</td><td>0.275<br>(0.197)</td><td>0.191<br>(0.205)</td></tr><tr><td>1 if the head is a woman</td><td>0.071<br>(0.251)</td><td>-0.340<br>(-0.252)</td><td>0.084<br>(0.254)</td><td>-0.335<br>(-0.257)</td></tr><tr><td>Intercept</td><td>-8.659***<br>(-2.085)</td><td>-9.247***<br>(-2.115)</td><td>-8.346***<br>(-2.021)</td><td>-8.873***<br>(-2.072)</td></tr><tr><td>log-likelihood</td><td>-196.514</td><td>-506.760</td><td>-196.330</td><td>-506.840</td></tr><tr><td>Pseudo-R<sup>2</sup></td><td>0.201</td><td>0.092</td><td>0.202</td><td>0.092</td></tr><tr><td>Nb of observations</td><td>355</td><td>355</td><td>355</td><td>355</td></tr></tbody></table>

adult guests only (see below Table 3). Thus, in this case, a Poisson-model has been estimated. In the other

<footnote>*** significant at the 1%-level; ** at the 5%-level; * at the 10%-level. t-statistics in brackets.</footnote>
Discussion

The first two rows of Table 2 show that, as expected, predicted income has a large
positive and highly significant impact on both the number of guests and the probability of
having a guest, which both theories predict: richer households have more guests, whatever the
motives for hospitality may be. However, the residual has no significant effect either on the
number of guests or on the probability of having a guest (the coefficient is even negative).

The conclusion of this test is therefore unambiguous: only the observable part of the
income, that is only what the relatives are able to observe, determines the number of guests.
What we called demand-hypotheses are thus preferred to supply-hypotheses. It does not mean
that the latter are irrelevant, but that the head of household is not entirely free to choose how
many guests he wishes to have. The number of guests is partly chosen by the extended family
and the head use information asymmetry to partly escape from family redistribution. Thus,
social pressure and social norms do matter. Moreover, this result is fully consistent with the
fact that transfers are often in-kind: the relatives claim for a part of what is easily observable
 Python

Other results

Let us now briefly discuss the signs and coefficients of other regressors. Notice first
that there is almost no difference between columns 2 and 4 and between columns 1 and 3. This
is not surprising as, in the first step, the logarithm of rental incomes in errors-in-variables
regression does not have much more explanatory power than the dummy in OLS, and neither
the logarithm of transfers received nor the dummy are significant (the R² statistics are not very
different: see Annex II).

The size of the nuclear family has no effect of the number of guests, What is more
important, is the *per* member surface area of housing of nuclear household, which has a
positive and significant effect, but only on the probability; there is no effect on the number of
guests, which is quite surprising.<fnref n="19" /> Once the family has decided that the household is able to

<footnote>cases, we used a negative binomial regression.</footnote>

<footnote n="19">¹⁹ An alternative specification with surface area and a qualitative variable measuring the quality of housing shows that the surface area of housing has no impact. As expected, it is the *per* member surface area that matters.</footnote>
give hospitality, what depends on the *per* member area, this variable becomes irrelevant to explain the number of guests received.<fnref n="20" /> However, the surface area is highly correlated with the rent or rent-equivalent, which is used as predictor for income, so the effects may not be separable.

The probability of having a guest and the number of guests both decrease with the age of the head. As pointed out in section III, guests are mainly brothers, sisters, nephews and nieces (recall that children and grandchildren are counted as members of the nuclear family, regardless of their age, which of course may be discussed). But the older the head, the older his siblings, nephews and nieces, and the more likely that his relatives will have found a job or got married. Older household heads are thus probably less solicited. Households headed by a Gabonese person have, as expected, more guests than households headed by a non-Gabonese person (two dummies show the membership of first patrilineal and second matrilineal ethnic groups, and the reference is households headed by a non-Gabonese person). The effects are nonetheless significant only at the 5% level, and are not significant regarding the probability of having a guest. Moreover, there are no differences according to the system of descent, which is interesting, as in patrilineal societies most things are inherited from the father and in matrilineal societies from the brother of the mother. This result means that inheritance seems to differ from hospitality obligations.

Tenants are less likely to have guests, and have fewer of them, than homeowners. The available income of the latter is more important, provided that they are not paying back a loan.<fnref n="21" /> The variables referring to comfort have opposing effects. They are, however, only significant in the probit regressions, and then only at the 10% level. To have electricity increases the probability of having a guest, while having water decreases it. If the positive impact of having electricity is unsurprising, it is not clear why households that have water have less guests. One explanation is that households that do not have water need people to get it. But in this case, the effect should probably be higher for female guests; Table 3 below shows that this is not true.<fnref n="22" /> Households headed by a woman have less guests (but with a higher

<footnote n="20">²⁰ We tried to take advantage of this fact to estimate zero-inflated negative binomial models, using this variable among others to determine the binary outcome. However, these estimates do not statistically differ from those that we present here (negative binomial models).</footnote>

<footnote n="21">²¹ (in Libreville and Port-Gentil, people often gradually build their house. It is possible to buy first the site, to install the foundations, to build a temporary wooden house, and to replace it later by a permanent structure. It is thus not uncommon that people build a house without getting into debt).</footnote>

<footnote n="22">²² Only 8.8% of households do not have water in Libreville, while this figure is 41.0% in Port-Gentil. However, public pumps are numerous in Port-Gentil, and walking time to get water is not very important.</footnote>
probability) than others, but the effect is not significant. Households with several income earners (they are rather rare) have more guests only if the other earners are part-time workers. This is not surprising, although one may think that the more workers in the household, the more it should be solicited. However other full-time workers are generally the spouse(s) of the head. Moreover, the dummy for households directed by a couple has a very significant negative effect. Once again, this is not surprising as in those households there is already at least one woman, and generally several children. The fact that the effect is larger for female guests than for male guests, and non-existent for children indicates that hospitality is, in part, offered in return for help in domestic tasks (see Table 3 and 4 below). On the contrary, only 66.0% of part-time workers belong to the main couple (compared to 86.2% of the full-time workers), so that households that have part-time workers other than the head will probably be more sought after.

The amount of transfers made by the nuclear household has a negative, although insignificant, effect, which may indicate that transfers and hospitality are, to some extent, substitutes. As the coefficient is not statistically different from zero, they are probably poor substitutes. In the same way, the amount of transfers received has a positive impact, which is only weakly significant if the first step is estimated by OLS and insignificant if it is estimated by errors-in-variables regression. This positive sign is an indication that households are perhaps compensated because they give hospitality, but once again, the effect is weak.<fnref n="23" />

Returning to our main result, we now investigate whether the effects we described above differ by the age and the sex of the guests. As research has illustrated, women are the main providers of household work. Hence hospitality might be given to them in return for domestic help, while this is not necessary the case for men and children.

### VI.3 Separate estimation by guests' sex and age

In this section, we present only the estimates of the errors-in-variables first-step. As shown in Table 2, there is little difference between OLS the errors-in-variables model in terms of results.

<footnote n="23">²³ These conclusions should be interpreted with caution, as the number of guests and transfers received and made are, to some extent, probably simultaneously determined. Simultaneous equation estimation is beyond the scope of the present paper.</footnote>
<table><caption>Table 3: Probability of having a guest and number of guests (adult male and adult female guests)</caption><thead><tr><th rowspan="2"></th><th colspan="2">FEMALE GUESTS<br>(17-55 YEARS OLD)</th><th colspan="2">MALE GUESTS<br>(17-55 YEARS OLD)</th></tr><tr><th>P(GUEST)</th><th>NUMBER OF<br>GUESTS</th><th>P(GUEST)</th><th>NUMBER OF<br>GUESTS</th></tr></thead><tbody><tr><td>Predicted income of the nuclear<br>household</td><td>0.489**<br>(0.198)</td><td>0.998***<br>(0.301)</td><td>0.389**<br>(0.182)</td><td>0.499**<br>(0.215)</td></tr><tr><td>Residual of first step</td><td>0.010<br>(0.154)</td><td>0.025<br>(0.230)</td><td>0.012<br>(0.137)</td><td>0.087<br>(0.165)</td></tr><tr><td>Number of members of the nuclear<br>household (except head)</td><td>-0.009<br>(-0.036)</td><td>-0.028<br>(-0.057)</td><td>0.086***<br>(0.032)</td><td>0.105***<br>(0.029)</td></tr><tr><td>Number of full-time workers in the<br>nuclear household (except head)</td><td>-0.035<br>(-0.221)</td><td>-0.438<br>(-0.346)</td><td>-0.409*<br>(-0.216)</td><td>-0.395<br>(-0.254)</td></tr><tr><td>Number of part-time workers in the<br>nuclear household (except head)</td><td>0.223<br>(0.216)</td><td>0.403<br>(0.275)</td><td>0.166<br>(0.218)</td><td>-0.017<br>(-0.251)</td></tr><tr><td>Surface area of housing per member of<br>nuclear household</td><td>0.009*<br>(0.005)</td><td>-0.0002<br>(-0.007)</td><td>0.009*<br>(0.005)</td><td>0.008*<br>(0.004)</td></tr><tr><td>1 if the head is a tenant</td><td>-0.668***<br>(-0.224)</td><td>-0.962***<br>(-0.361)</td><td>-0.368*<br>(-0.198)</td><td>-0.643**<br>(-0.252)</td></tr><tr><td>1 if the housing has electricity</td><td>0.754<br>(0.506)</td><td>0.321<br>(0.856)</td><td>0.073<br>(0.348)</td><td>0.064<br>(-0.441)</td></tr><tr><td>1 if the housing has water</td><td>-0.276<br>(-0.243)</td><td>-0.493<br>(-0.361)</td><td>-0.258<br>(-0.220)</td><td>-0.093<br>(-0.284)</td></tr><tr><td>Age of the head</td><td>-0.023**<br>(-0.009)</td><td>-0.023*<br>(-0.013)</td><td>-0.027***<br>(-0.008)</td><td>-0.036***<br>(-0.011)</td></tr><tr><td>1 if the household is headed by a couple</td><td>-0.325<br>(-0.288)</td><td>-1.249***<br>(-0.426)</td><td>-0.563**<br>(-0.256)</td><td>-0.537*<br>(-0.306)</td></tr><tr><td>Logarithm of amount of transfers<br>received</td><td>0.029<br>(0.023)</td><td>0.058<br>(0.035)</td><td>-0.019<br>(-0.020)</td><td>-0.019<br>(-0.023)</td></tr><tr><td>1 if belongs to patrilineal ethnic group</td><td>0.382<br>(0.360)</td><td>1.021<br>(0.638)</td><td>0.271<br>(0.300)</td><td>0.124<br>(0.371)</td></tr><tr><td>1 if belongs to matrilineal ethnic group</td><td>0.696**<br>(0.353)</td><td>1.329**<br>(0.622)</td><td>0.329<br>(0.296)</td><td>0.104<br>(0.374)</td></tr><tr><td>Logarithm of amount of transfers made</td><td>-0.050*<br>(-0.026)</td><td>-0.079*<br>(-0.040)</td><td>-0.002<br>(-0.024)</td><td>-0.001<br>(-0.029)</td></tr><tr><td>1 if lives in Port-Gentil</td><td>-0.148<br>(-0.220)</td><td>-0.214<br>(-0.343)</td><td>0.093<br>(0.194)</td><td>-0.029<br>(-0.242)</td></tr><tr><td>1 if the head is a woman</td><td>-0.177<br>(-0.277)</td><td>-0.784**<br>(-0.396)</td><td>-0.532**<br>(-0.251)</td><td>-0.283<br>(-0.300)</td></tr><tr><td>Intercept</td><td>-6.591***<br>(-2.172)</td><td>-12.366***<br>(-3.238)</td><td>-4.285**<br>(-1.972)</td><td>-5.815**<br>(-2.292)</td></tr><tr><td>log-likelihood</td><td>-149.793</td><td>-216.478</td><td>-183.045</td><td>-255.446</td></tr><tr><td>Pseudo-R<sup>2</sup></td><td>0.163</td><td>0.111</td><td>0.121</td><td>0.090</td></tr><tr><td>Nb of observations</td><td>355</td><td>355</td><td>355</td><td>355</td></tr></tbody></table>
<table><caption>Table 4: Probability of having a young guest and number of young guests</caption><thead><tr><th rowspan="2"></th><th colspan="2">YOUNG GUESTS<br>(0-10 YEARS OLD)</th><th colspan="2">YOUNG GUESTS<br>(0-16 YEARS OLD)</th></tr><tr><th>P(GUEST)</th><th>NUMBER OF GUESTS</th><th>P(GUEST)</th><th>NUMBER OF GUESTS</th></tr></thead><tbody><tr><td>Predicted income of the nuclear household</td><td>0.266<br>(0.238)</td><td>0.417<br>(0.312)</td><td>0.368*<br>(0.205)</td><td>0.463*<br>(0.252)</td></tr><tr><td>Residual of first step</td><td>-0.504***<br>(-0.190)</td><td>-0.583**<br>(-0.235)</td><td>-0.410**<br>(-0.163)</td><td>-0.357*<br>(-0.194)</td></tr><tr><td>Number of 17-55 years-old female guests</td><td>1.173***<br>(0.179)</td><td>1.007***<br>(0.167)</td><td>0.893***<br>(0.157)</td><td>0.812***<br>(0.131)</td></tr><tr><td>Number of members of the nuclear household (except head)</td><td>-0.023<br>(-0.044)</td><td>-0.015<br>(-0.056)</td><td>0.022<br>(0.033)</td><td>0.019<br>(0.041)</td></tr><tr><td>Number of full-time workers in the nuclear household (except head)</td><td>0.387<br>(0.249)</td><td>0.481<br>(0.302)</td><td>0.337<br>(0.223)</td><td>0.363<br>(0.257)</td></tr><tr><td>Number of part-time workers in the nuclear household (except head)</td><td>0.185<br>(0.267)</td><td>0.221<br>(0.291)</td><td>0.153<br>(0.239)</td><td>0.330<br>(0.228)</td></tr><tr><td>Surface area of housing per member of nuclear household</td><td>-0.012<br>(-0.007)</td><td>-0.013<br>(-0.009)</td><td>0.001<br>(0.006)</td><td>-0.003<br>(-0.007)</td></tr><tr><td>1 if the head is a tenant</td><td>-0.209<br>(-0.263)</td><td>-0.558<br>(-0.345)</td><td>-0.451*<br>(-0.234)</td><td>-0.679**<br>(-0.282)</td></tr><tr><td>1 if the housing has electricity</td><td>1.677*<br>(0.973)</td><td>1.995**<br>(0.935)</td><td>1.030*<br>(0.527)</td><td>1.621**<br>(0.721)</td></tr><tr><td>1 if the housing has water</td><td>-0.132<br>(-0.279)</td><td>-0.072<br>(-0.356)</td><td>-0.139<br>(-0.251)</td><td>-0.203<br>(-0.295)</td></tr><tr><td>Age of the head</td><td>-0.017<br>(-0.011)</td><td>-0.013<br>(-0.013)</td><td>-0.023**<br>(-0.010)</td><td>-0.026**<br>(-0.011)</td></tr><tr><td>1 if the household is headed by a couple</td><td>0.147<br>(0.343)</td><td>0.004<br>(0.450)</td><td>0.174<br>(0.309)</td><td>-0.045<br>(-0.375)</td></tr><tr><td>Logarithm of amount of transfers received</td><td>-0.001<br>(-0.027)</td><td>0.002<br>(0.034)</td><td>0.019<br>(0.024)</td><td>0.007<br>(0.029)</td></tr><tr><td>1 if belongs to patrilineal ethnic group</td><td>1.130**<br>(0.480)</td><td>1.322<br>(0.810)</td><td>0.756**<br>(0.373)</td><td>1.235**<br>(0.558)</td></tr><tr><td>1 if belongs to matrilineal ethnic group</td><td>0.865*<br>(0.468)</td><td>1.573**<br>(0.797)</td><td>0.392<br>(0.367)</td><td>1.234**<br>(0.553)</td></tr><tr><td>Logarithm of amount of transfers made</td><td>0.021<br>(0.032)</td><td>-0.029<br>(-0.042)</td><td>-0.009<br>(-0.028)</td><td>-0.031<br>(-0.034)</td></tr><tr><td>1 if lives in Port-Gentil</td><td>0.333<br>(0.249)</td><td>0.441<br>(0.318)</td><td>0.504**<br>(0.223)</td><td>0.484*<br>(0.264)</td></tr><tr><td>1 if the head is a woman</td><td>0.024<br>(0.330)</td><td>0.162<br>(0.416)</td><td>-0.031<br>(-0.299)</td><td>0.196<br>(0.345)</td></tr><tr><td>Intercept</td><td>-6.446**<br>(-2.752)</td><td>-9.333***<br>(-3.507)</td><td>-6.368***<br>(-2.259)</td><td>-8.387***<br>(-2.805)</td></tr><tr><td>log-likelihood</td><td>-114.200</td><td>-214.217</td><td>-144.727</td><td>-290.721</td></tr><tr><td>Pseudo-R²</td><td>0.362</td><td>0.220</td><td>0.305</td><td>0.182</td></tr><tr><td>Nb of observations</td><td>355</td><td>355</td><td>355</td><td>355</td></tr></tbody></table>
Notice first that pseudo-R² are much higher for young guests than for adults. In fact, for children, the main determinant of hospitality is the number of adult female guests.<fnref n="24" /> What is measured here is the presence of sub-structures that are mainly, as asserted above, composed by mothers and young children. This is particularly true for very young guests as only a few other variables have significant effects: whether the housing has electricity, whether the household is headed by a Gabonese (for guests below 10, the effect is stronger for the probability of having a young guest for patrilineal ethnic group and on the number of guests for matrilineal ethnic group); the dummy indicating if the head is a tenant and the age of the head have a significant impact only when one considers guests aged under 16.

The number of female guests sharply decreases if the household is headed by a couple and if the head is a woman, indicating that female guests are partly welcome as substitutes for a spouse because they help in domestic tasks. Jealousy is another reason that could be invoked to explain why households headed by a couple have less female guests. Surprisingly, the larger the household size, the more male guests it welcomes.

Our key variables have very different impacts. First, predicted income has no effect on the number of young guests (nor on the associated probability) and can be distinguished from zero only at the 10% level for guests under 16. Moreover, the residual has a large significant negative impact, which is, however, smaller when one adds guests between 11 and 16 years-old. If we do not split income up into observable and unobservable, the logarithm of income has a negative, although far from significant, impact on the probability of having a young guest or on the number of young guests (results not shown).²⁵ As in Table 2, predicted income has a positive and significant effect at the 5 or 1% level for adults, both male and female, while the residual has no effect. The effect of predicted income seems somehow to increase with the age of the guests; on the contrary, the effect of unobservable income seems to decrease with the age of the guests. This fact is hard to explain if supply-hypotheses are correct. The demand for guests could, of course, differ by the age and the sex of the guests. However, once again, the effects of both observable and unobservable incomes should not differ, and both should be

<footnote n="24">²⁴ Note that the sex of the head has no significant effect.</footnote>
positive. On the other hand, one can argue that income is more easily observed by adults than
by young people. Thus, if no adult can observe the income, and if hospitality is given under
family pressure or because of a norm, richer households will be more able to dissimulate their
income, and thus will have fewer guests.

VII Conclusion

This paper has tried to explain a widespread phenomenon in Africa: the hospitality that is given by households to relatives. We used a Gabonese survey that offers very good and reliable information on ties between household members. We then proposed a two-step procedure to discriminate between two hypotheses.

The main conclusion that can be drawn from this empirical study is that hospitality in Gabon is better explained by demand-hypotheses (social norm, family pressure) than by supply-hypotheses (altruism, exchange models): only the observable part of nuclear household income has an effect on the number of guests and on the probability of having at least one guest. However, motivations seem to differ by the age and sex of the guests. Very young guests are mainly accompanying people who follow their mother. Moreover, some evidence seems to indicate that women are given hospitality partly because they help in domestic tasks, although this is probably not the only reason, as unobservable income has no impact on the number of female guests, just as for the men. Our conclusion is also consistent with a risk-sharing hypothesis (see, for example, Posner, 1980). If information is asymmetric, only observable income will go into the redistribution pool, and transfers (hospitality being a form of transfer) will only concern what the contracting parties are able to observe.

More extensive data could help to overcome several limitations of this work. First, our
test is based on the crucial assumption that both the economist and relatives have the same
information at their disposal. This is unlikely to be the case, for example, with respect to
houses that the head rents or the people that make transfers to the head. The solution we
proposed (errors-in-variables) is approximative. Moreover, it only concerns information that

<footnote n="25"><sup>25</sup> This may be a misspecification problem (see above).</footnote>
we know to be incomplete. It would be interesting, in order to investigate more precisely our
point to ask household members what they think household income is, or how high they
evaluate the income of their relatives. In addition, information that is missing in EBC 94
regarding rented houses and transfer makers would be very useful as mentioned above.
Second, information on the household from which a guest comes is crucial if one wishes to
explore more fully the motives for hospitality. Moreover, it is preferable to estimate
simultaneously hospitality and transfers made and received by the household. These different
motives for hospitality (supply-hypothesis and demand-hypothesis) have very different
implications in several domains, investment in human capital, fertility, labor-supply,
consumption etc. For example, in the same spirit of the present text, Rapoport (2000b) shows
that, at age and sex structure given, household consumption depends on whether household
members belong to the nuclear family of the head or not: in particular, the food at home share,
which can be easily observed by the members of the household, decreases and the food away
from home share, which is harder to observe, increases when, at a given household size, the
number of guests increases.
# Annex

## Annex I: Descriptive Statistics

<table><thead><tr><th></th><th>MEAN</th><th>SD ERROR</th><th>MIN</th><th>MAX</th></tr></thead><tbody><tr><td>Logarithm of nuclear household income</td><td>12.507</td><td>0.930</td><td>8.316</td><td>15.215</td></tr><tr><td>Number of full-time workers in the nuclear household (except head)</td><td>0.197</td><td>0.439</td><td>0</td><td>3</td></tr><tr><td>Highest education level of other full-time workers in the nuclear hhd</td><td>1.727</td><td>4.041</td><td>0</td><td>20</td></tr><tr><td>Number of part-time workers in the nuclear household (except head)</td><td>0.068</td><td>0.338</td><td>0</td><td>4</td></tr><tr><td>1 if the head is a woman</td><td>0.290</td><td>0.454</td><td>0</td><td>1</td></tr><tr><td>1 if the head is in the armed forces</td><td>0.042</td><td>0.201</td><td>0</td><td>1</td></tr><tr><td>1 if the head is a manager</td><td>0.141</td><td>0.348</td><td>0</td><td>1</td></tr><tr><td>1 if the head has an intermediary position</td><td>0.127</td><td>0.333</td><td>0</td><td>1</td></tr><tr><td>1 if the head is an employee</td><td>0.059</td><td>0.236</td><td>0</td><td>1</td></tr><tr><td>1 if the head works in the service sector</td><td>0.141</td><td>0.348</td><td>0</td><td>1</td></tr><tr><td>1 if the head is a fisher or a farmer</td><td>0.031</td><td>0.174</td><td>0</td><td>1</td></tr><tr><td>1 if the head if a worker with high qualifications or an artisan</td><td>0.104</td><td>0.306</td><td>0</td><td>1</td></tr><tr><td>1 if the head is a driver</td><td>0.045</td><td>0.208</td><td>0</td><td>1</td></tr><tr><td>1 if the head if a worker with low qualifications</td><td>0.073</td><td>0.261</td><td>0</td><td>1</td></tr><tr><td>1 if the head is a student</td><td>0.011</td><td>0.106</td><td>0</td><td>1</td></tr><tr><td>1 if the head is retired</td><td>0.068</td><td>0.251</td><td>0</td><td>1</td></tr><tr><td>1 if the head is a tenant</td><td>0.400</td><td>0.491</td><td>0</td><td>1</td></tr><tr><td>Age of the head</td><td>39.496</td><td>11.44</td><td>18</td><td>80</td></tr><tr><td>Square of the age of the head</td><td>1690.420</td><td>1033.973</td><td>324</td><td>6400</td></tr><tr><td>School level of the head</td><td>9.361</td><td>4.624</td><td>1</td><td>20</td></tr><tr><td>1 if belongs to patrilineal ethnic group</td><td>0.358</td><td>0.480</td><td>0</td><td>1</td></tr><tr><td>1 if belongs to matrilineal ethnic group</td><td>0.408</td><td>0.492</td><td>0</td><td>1</td></tr><tr><td>1 if lives in Port-Gentil</td><td>0.33</td><td>0.471</td><td>0</td><td>1</td></tr><tr><td>Logarithm of rent or rent equivalent</td><td>-0.644</td><td>0.793</td><td>-2.996</td><td>1.609</td></tr><tr><td>1 if the nuclear household has rental incomes</td><td>0.208</td><td>0.407</td><td>0</td><td>1</td></tr><tr><td>Logarithm of rental incomes</td><td>2.315</td><td>4.538</td><td>0</td><td>14.159</td></tr><tr><td>1 if the nuclear household receives transfers from the family</td><td>0.873</td><td>0.333</td><td>0</td><td>1</td></tr><tr><td>Logarithm of amount of transfers received</td><td>8.854</td><td>3.716</td><td>0</td><td>13.337</td></tr><tr><td>1 if the nuclear household makes transfers</td><td>0.761</td><td>0.427</td><td>0</td><td>1</td></tr><tr><td>1 if household has guests</td><td>0.507</td><td>0.501</td><td>0</td><td>1</td></tr><tr><td>number of guests</td><td>1.335</td><td>2.236</td><td>0</td><td>17</td></tr><tr><td>number of 17-55 year old female guests</td><td>0.296</td><td>0.744</td><td>0</td><td>7</td></tr><tr><td>number of 17-55 year old male guests</td><td>0.358</td><td>0.659</td><td>0</td><td>3</td></tr><tr><td>number of guests under 11</td><td>0.392</td><td>1.006</td><td>0</td><td>7</td></tr><tr><td>number of guests under 17</td><td>0.603</td><td>1.356</td><td>0</td><td>10</td></tr><tr><td>Nuclear household size (except head)</td><td>3.507</td><td>3.434</td><td>0</td><td>28</td></tr><tr><td>Surface area of housing per member of nuclear household</td><td>22.145</td><td>21.495</td><td>1.714</td><td>180</td></tr><tr><td>1 if the housing has electricity</td><td>0.927</td><td>0.261</td><td>0</td><td>1</td></tr><tr><td>1 if the housing has water</td><td>0.806</td><td>0.396</td><td>0</td><td>1</td></tr><tr><td>1 if the household is headed by a couple</td><td>0.538</td><td>0.499</td><td>0</td><td>1</td></tr><tr><td>Logarithm of amount of transfers received from family</td><td>6.978</td><td>4.419</td><td>0</td><td>13.098</td></tr><tr><td>Logarithm of amount of transfers made</td><td>7.196</td><td>4.321</td><td>0</td><td>13.829</td></tr></tbody></table>
Annex II: First Step – Income Equations

<table><caption>Table A: First step: Estimation of nuclear household income, using variables that are observable by relatives</caption><thead><tr><th></th><th>OLS</th><th>ERRORS-IN-VARIABLES<br>REGRESSION</th></tr></thead><tbody><tr><td>Number of full-time workers in the<br>nuclear household (except head)</td><td>0.224<br>(0.190)</td><td>0.242<br>(0.161)</td></tr><tr><td>Highest education level of other full-time<br>workers in the nuclear household</td><td>0.019<br>(0.018)</td><td>0.015<br>(0.018)</td></tr><tr><td>Number of part-time workers in the<br>nuclear household (except head)</td><td>0.226<br>(0.151)</td><td>0.224**<br>(0.103)</td></tr><tr><td>1 if the head is a woman</td><td>-0.115<br>(-0.087)</td><td>-0.142<br>(-0.090)</td></tr><tr><td>1 if the head is in the armed forces</td><td>0.678***<br>(0.172)</td><td>0.743***<br>(0.193)</td></tr><tr><td>1 if the head is a manager</td><td>0.896***<br>(0.143)</td><td>0.942***<br>(0.142)</td></tr><tr><td>1 if the head has an intermediary<br>position</td><td>0.734***<br>(0.143)</td><td>0.784***<br>(0.139)</td></tr><tr><td>1 if the head is an employee</td><td>0.848***<br>(0.174)</td><td>0.877***<br>(0.166)</td></tr><tr><td>1 if the head works in the service sector</td><td>0.540***<br>(0.138)</td><td>0.593***<br>(0.131)</td></tr><tr><td>1 if the head is a fisher or a farmer</td><td>0.652***<br>(0.183)</td><td>0.711***<br>(0.216)</td></tr><tr><td>1 if the head if a worker with high<br>qualifications or an artisan</td><td>0.281*<br>(0.156)</td><td>0.326**<br>(0.150)</td></tr><tr><td>1 if the head is a driver</td><td>0.752***<br>(0.206)</td><td>0.794***<br>(0.191)</td></tr><tr><td>1 if the head if a worker with low<br>qualifications</td><td>0.235<br>(0.172)</td><td>0.289*<br>(0.157)</td></tr><tr><td>1 if the head is a student</td><td>0.521**<br>(0.250)</td><td>0.543<br>(0.335)</td></tr><tr><td>1 if the head is retired</td><td>0.183<br>(0.228)</td><td>0.189<br>(0.176)</td></tr><tr><td>1 if the head is a tenant</td><td>0.353***<br>(0.084)</td><td>0.379***<br>(0.089)</td></tr><tr><td>Age of the head</td><td>0.081***<br>(0.026)</td><td>0.079***<br>(0.019)</td></tr><tr><td>Square of the age of the head</td><td>-0.0009***<br>(-0.0003)</td><td>0.0008***<br>(-0.0002)</td></tr><tr><td>School level of the head</td><td>0.021**<br>(0.010)</td><td>0.020*<br>(0.011)</td></tr></tbody></table>
<table><tr><td>1 if belongs to patrilineal ethnic group</td><td>0.243**<br>(0.120)</td><td>0.182<br>(0.124)</td></tr><tr><td>1 if belongs to matrilineal ethnic group</td><td>0.327***<br>(0.113)</td><td>0.269**<br>(0.123)</td></tr><tr><td>1 if lives in Port-Gentil</td><td>-0.050<br>(-0.075)</td><td>-0.017<br>(-0.080)</td></tr><tr><td>Logarithm of rent or equivalent-rent</td><td>0.301***<br>(0.070)</td><td>0.318***<br>(0.058)</td></tr><tr><td>1 if the nuclear household has rental<br>incomes (or logarithm of amount)</td><td>0.281***<br>(0.097)</td><td>0.035***<br>(0.011)</td></tr><tr><td>1 if the nuclear household receives<br>transfers from the family (or logarithm<br>of amount)</td><td>-0.163<br>(-0.114)</td><td>0.007<br>(0.013)</td></tr><tr><td>1 if the nuclear household makes<br>transfers to the family</td><td>0.388***<br>(0.085)</td><td>0.364***<br>(0.082)</td></tr><tr><td>Intercept</td><td>9.648***<br>(0.578)</td><td>9.493***<br>(0.461)</td></tr><tr><td>R<sup>2</sup></td><td>0.593</td><td>0.597</td></tr><tr><td>Nb of observations</td><td>355</td><td>355</td></tr></table>

## Annex III: Murphy and Topel Correction

Here we assume that the first-step is estimated by ordinary least squares (or by an errors-in-variables regression) and the second-step by maximum likelihood, although Murphy and Topel (1985) treat several others cases.

The first-step is a linear model, and OLS estimator for $\theta_1$ is consistent:

$$y_{1i} = x_{1i}\theta_1 + u_i$$

The log-likelihood for the second step is $L_2 = \sum_{i=1}^{n} \ln f_2(y_{i2} | x_1, x_2, \theta_1, \theta_2)$. In our case, $f_2$ will be the density of either a normal distribution, a Poisson distribution or a negative binomial distribution.

Murphy and Topel (1985, see also Greene, 1997) show that $\sqrt{n}(\hat{\theta}_2 - \theta_2)^A \sim N(0, \Sigma)$ with
$\Sigma = R_2^{-1} + R_2^{-1} R_3' R_1^{-1} R_3 R_2^{-1}$ if the random components are independent, and

$\Sigma = R_2^{-1} + R_2^{-1} [R_3' R_1^{-1} R_3 - R_4' R_1^{-1} R_3 - R_3' R_1^{-1} R_4] R_2^{-1}$ otherwise.

$$R_1(\theta_1) = \sigma_1^2 (X_1' X_1)^{-1}$$

$$R_2(\theta_2) = E \frac{\partial L_2}{\partial \theta_2} \left( \frac{\partial L_2}{\partial \theta_2} \right)' = -E \frac{\partial^2 L_2}{\partial \theta_2 \partial \theta_2'}$$

$$R_3(\theta_1, \theta_2) = E \frac{\partial L_2}{\partial \theta_1} \left( \frac{\partial L_2}{\partial \theta_2} \right)' = -E \frac{\partial^2 L_2}{\partial \theta_1 \partial \theta_2'}$$

$$R_4(\theta_1, \theta_2) = \frac{1}{n} \sum_{i=1}^{n} u_i x_{1i} \left( \frac{\partial L_{2i}}{\partial \theta_2} \right)'$$

Notice that in the first case standard errors are always underestimated if we do not make the correction, while this is not necessarily the case when the random components are not independent.

$R_1$ will be estimated by $\hat{R}_1(\theta_1) = \hat{\sigma}_1^2 (X_1' X_1)^{-1}$ where $\hat{\sigma}_1^2 = \frac{\sum_{i=1}^n u_i^2}{n}$ (we do not carry out a correction for degrees of freedom, as in Murphy and Topel, 1985).

$R_2$ will be estimated by the hessian matrix of second step (another possibility is to use the outer product of gradients or BHHH estimator, see for example Greene, 1997).

$R_3$ will be estimated by the outer product of gradient vectors with respect to $\theta_1$ and $\theta_2$ of second step (another possibility is to use the second derivatives matrix).

In our case, the auxiliary model allows us to compute what we called observable income $E(y_{1i})$ and the unobservable component of income $u_i$.
The main model estimates the probability of having a guest (probit) or the number of guests (Poisson or negative binomial regression model). We suppose that the observed income $E(y_{1i})$, and the unobservable component $u_i$ are among the regressors.

We need to compute the gradient vectors of the second step with respect to $\theta_1$ and $\theta_2$. Let $\gamma_1$ be the coefficient of $E(y_{1i})$, $\gamma_2$ the coefficient of $u_i$ and $\beta$ the vector of coefficients of the others regressors. We have thus $\theta_2 = (\beta', \gamma_1, \gamma_2)'$ and $x_2^* = (x_2, E(y_{1i}), u_i)$.

In all the cases, by definition,

$$ \frac{\partial L_2}{\partial \theta_2} = \sum_{i=1}^{n} v_i x_2^{*i}, \text{ where } v_i \text{ is the score, that is } \frac{\partial L_2}{\partial (x_2^{*} \theta_2)}, \text{ which is given below in each case.} $$

Moreover, whatever the second-step is (probit, Poisson model or negative binomial), $\theta_1$ appears in $L_2$ only through $x_2^{*} \theta_2$. Hence

$$ \frac{\partial L_2}{\partial \theta_1} = \sum_{i=1}^{n} \frac{\partial L_{2i}}{\partial (x_{2i}^{*} \theta_2)} \frac{\partial (x_{2i}^{*} \theta_2)}{\partial \theta_1} = \sum_{i=1}^{n} v_i (\gamma_1 - \gamma_2) x_{1i}^{*}, \text{ as} \\ x_{2i}^{*} \theta_2 = x_{2i} \beta + \gamma_1 E(y_{1i}) + \gamma_2 u_i = x_{2i} \beta + \gamma_1 (x_{1i} \hat{\theta}_1) + \gamma_2 (y_{1i} - x_{1i} \hat{\theta}_1) = x_{2i} \beta + \gamma_2 y_{1i} + (\gamma_1 - \gamma_2) (x_{1i} \hat{\theta}_1) $$

$$ \text{Thus } R_3(\theta) = E \frac{\partial L_2}{\partial \theta_1} \left( \frac{\partial L_2}{\partial \theta_2} \right)' = \frac{1}{n} \sum_{i=1}^{n} (\gamma_1 - \gamma_2) v_i^2 x_{1i}^{*} x_{2i}^{*}, \text{ and} $$

$$ R_4(\theta) = \frac{1}{n} \sum_{i=1}^{n} v_i u_i x_{1i}^{*} x_{2i}^{*} $$

As we use $\hat{\sigma}_1^2$ as estimator for $\sigma_1^2$ in the first-step, all the factors $1/n$ cancel in the final results.
1. If the second step is a probit.

$$
\begin{align*}
\text{Prob}(y_{2i} = j) &= \Phi(q_i x_{2i} * \theta_2) \quad j = 0,1 \\
q_i &= 2y_{2i} - 1
\end{align*}
$$

$\Phi$ is the cumulative of the normal distribution, and $\phi$ its density.

Thus $L_2 = \sum_{i=1}^{n} \ln f_2(y_{2i} | x_1, x_2, \theta_1, \theta_2) = \sum_{i=1}^{n} \ln \text{Prob}(y_{2i} = j)$, and

$$
v_i = \frac{\partial L_{2i}}{\partial (x_{2i} * \theta_2)} = q_i \frac{\Phi(q_i x_{2i} * \theta_2)}{\Phi(q_i x_{2i} * \theta_2)}.
$$

2. If the second step is a Poisson model.

$$
\text{Prob}(y_{2i} = j) = \frac{e^{-\lambda_4} \lambda_4^j}{j!} \quad j = 0,1,\dots
$$

$$
E(y_{2i}) = \lambda_4 = e^{x_{2i} * \theta_2} = e^{x_{2i} \beta + \gamma_1 E(y_{1i}) + \gamma_2 u_i}
$$

$L_2 = \sum_{i=1}^{n} \ln f_2(y_{2i} | x_1, x_2, \theta_1, \theta_2) = \sum_{i=1}^{n} (-\lambda_4 + y_{2i} \ln \lambda_4 - \ln y_{2i}!)$

$$
L_2 = \sum_{i=1}^{n} \left( -e^{x_{2i} * \theta_2} + y_{2i} \ln(x_{2i} * \theta_2) - \ln y_{2i}! \right)
$$

$$
v_i = \frac{\partial L_{2i}}{\partial (x_{2i} * \theta_2)} = y_{2i} - x_{2i} * \theta_2 = y_{2i} - \lambda_4.
$$

3. If the second step is a negative binomial model (see, for example, Greene 1997).

$$
\text{Prob}(y_{i2} = j) = \frac{\Gamma\left(\frac{1}{\sigma^2} + j\right)}{\Gamma(j+1)\Gamma\left(\frac{1}{\sigma^2}\right)} \left( \frac{\lambda_i}{\lambda_i + \frac{1}{\sigma^2}} \right)^j \left( 1 - \frac{\lambda_i}{\lambda_i + \frac{1}{\sigma^2}} \right)^{\frac{1}{\sigma^2}} \quad j = 0,1,\dots
$$

$$
\lambda_i = e^{x_{2i} * \theta_2} = e^{x_{2i} \beta + \gamma_1 E(y_{1i}) + \gamma_2 u_i}
$$

$$
\sigma^2 \text{ satisfies } V(y_{2i} | x_{2i} *) = E(y_{2i} | x_{2i} *) + \sigma^2 (E(y_{2i} | x_{2i} *))^2
$$
$\Gamma$ is the gamma distribution.

$$L_2 = \sum_{i=1}^{n} \ln f_2(y_{2i} | x_1, x_2, \theta_1, \theta_2) = \sum_{i=1}^{n} \ln \text{Prob}(y_{2i} = j), \text{ and}$$

$$v_i = \frac{\partial L_{2i}}{\partial (x_{2i} * \theta_2)} = \frac{y_{2i} - x_{2i} * \theta_2}{1 + \sigma^2 x_{2i} * \theta} = \frac{y_{2i} - \lambda_i}{1 + \sigma^2 \lambda_i}.$$

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