### 4.1 Empirical approach

How remittances affect development depends mainly on their use. The aim of this study is to examine whether remittances‐receiving households have higher expenditures on education and health, and how this relationship is affected by female bargaining power. Several previous studies have contributed to a pessimistic perception by observing that the inflows are mainly used for food and current expenses (for a review, see Chami et al. (
2003
)). Yet, remittances ‐ like any other source of income ‐ are fungible and increase total income. Even if they are not directly invested in human capital, they can lower liquidity constraints, and hence other sources of income may be invested. Thus, the whole expenditure pattern of the households has to be examined. Recent studies include a remittances variable as a regressor in a system of household demand equations (e.g. Zarate‐Hoyos (
2004
), Taylor and Mora (
2006
) and Adams and Cuecuecha (
2010
)). An advantage of this approach is its consistency with consumer demand models which assume that income from diverse sources is pooled. One disadvantage is the potential endogeneity of remittances, which has to be addressed. Migration (and consequently remittance receipt) selects on both, observable and unobservable characteristics. To address the endogeneity of remittances, an instrumental variable (IV) approach is applied.

After analyzing the impact of remittances on household’s budget allocation, a gender‐dimension is taken into account. The first challenge is to find a variable that measures intra‐household bargaining power. Exogenous variables typically used to measure female bargaining power, like wealth upon marriage, are not stated in the ECV‐5. Following Guzmán et al. (
2008
), the best proxy available is the sex of the household head. However, the gender of the household head is correlated with explanatory variables which implies that gender (as remittances) is endogenous. As no reasonable instrument for gender exists, we apply a matching procedure to make male and female headed households comparable, and run separate regressions.

In the third part of the analysis, the impact of the gender of the migrant and the receiver is evaluated. To this end, we focus on a subsample of 616 remittance‐receiving households with migrants. Here, the mentioned principal‐agent problem can arise as the household in the home country is in fact spending the transfer. In spite of possibly gender‐specific preferences of the migrants, these may not be reflected in the use of remittances.

### 4.2 Econometric model

In the empirical analysis, a proper functional form for the econometric model has to be chosen. A popular form is the Working‐Leser curve which relates budget shares linearly to the logarithm of total household expenditures and additional variables (Working (
1943
); Leser (
1963
)).^{5} In this study, the model is specified as follows:

{w}_{\mathit{ij}}={\alpha}_{i}+{\beta}_{i}\mathit{log}\frac{{x}_{j}}{{n}_{j}}+{\psi}_{i}\mathit{log}\left({n}_{j}\right)+{\eta}_{i}{\pi}_{j}+{\theta}_{i}{R}_{j}+{\epsilon}_{\mathit{ij}},

(1)

or in a shorter notation

{w}_{\mathit{ij}}={\mu}_{i}{X}_{j}+{\epsilon}_{\mathit{ij}},

(2)

where *w*
_{
ij
} is the budget share of expenditure category *i*
by household *j*, *x*
_{
j
} is total household expenditures, *n*
_{
j
} is household size (thus \frac{{x}_{j}}{{n}_{j}} is per‐capita expenditures). The term *π*
_{
j
}
is a vector of household characteristics that may affect expenditure behavior, *R*
_{
j
}
captures whether the household receives remittances, and *ε*
_{
ij
} is an error term. In the short notation *X*
_{
j
}
represents all right hand side variables of the model including the intercept. The dependent variables reflect the categories of household expenditures, namely “food”, “housing”, “education”, and “health”. Not every household has expenditures on each category which implies censored dependent variables. Expenditure on a category is observed only if the household’s desired expenditure exceeds some threshold which depends on the lumpiness of the goods as well as the opportunity cost. Estimation techniques that fail to consider the censoring of the dependent variables give rise to biased parameter estimates. Thus, the following participation equation is added to equation (2):

{w}_{\mathit{ij}}^{\ast}={\gamma}_{i}{Z}_{j}+{u}_{\mathit{ij}}.

(3)

The dependent variable {w}_{\mathit{ij}}^{\ast} is unobservable, but has an observable realization of one if *w*
_{
ij
}
takes on a positive value and zero otherwise. The term *Z*
_{
j
}
is a vector that contains all explanatory variables included in equation (2), and some additional variables which allow for identification, and *u*
_{
ij
} is an error term.^{6} In addition, the budget shares are not independent of each other. A positive shock in the budget share “food”, for example, results in higher expenses on “food” which leads to smaller expenses in at least one other budget share. The error terms across equations are correlated. The model is an equation system with dependent variables censored by latent variables.

Estimating a censored system of equations is no easy task. Until 1999, the popular Heien and Wessells (
1990
) two‐step estimation procedure was considered the standard approach. Yet, Shonkwiler and Yen (
1999
) (henceforth SY) point out an inconsistency and show that this estimator performs poorly in Monte Carlo simulations. They hence suggest an alternative, consistent two‐step estimator which has found wide applicability in empirical work as it has a solid theoretical foundation and is easy to implement. In the first step, the probability of participation in each expenditure category is estimated using a probit regression. The results are then used in the second step, to weight the expenditure equations in the system, and to construct a selection term. Despite its popularity, this method has been criticized, since it relies on the assumption that the residuals follow a normal distribution, and are homoscedastic in the participation equation. Any violation of the assumptions will result in biased and inconsistent estimation results. Sam and Zheng (
2010
) (henceforth SZ) hence propose a two‐step estimator similar in spirit to SY that uses Klein and Spady (
1993
) (hereafter denoted by KS) semiparametric single‐index model instead of a probit regression in the first step. The semiparametric KS estimator makes no distributional assumptions, but it assumes a linear index function to avoid the curse of dimensionality. Being asymptotically efficient in the sense that it attains the semiparametric efficiency bound, it is the most efficient two‐step estimator compared to other semiparametric estimators. Moreover, KS perform Monte Carlo simulations which indicate that their estimator is considerably more accurate than a probit estimation when the errors are not normally distributed. In contrast, the efficiency losses are modest when the error distribution is standard normal.

Both methods start with an estimation of the participation equations:

P({w}_{\mathit{ij}}^{\ast}=1|{Z}_{j})={F}_{i}({\gamma}_{i}{Z}_{j}).

(4)

Whereas the probit model assumes *F*
_{
i
}(·)
being the normal cumulative distribution function (cdf), the semiparametric method estimates the coefficients {\widehat{\gamma}}_{i} and the unknown continuous distribution function {\widehat{F}}_{i}(\xb7).^{7} The estimate of *γ*
_{
i
}
is obtained by maximizing the quasi‐loglikelihood function:

l\left({\gamma}_{i}\right)=\sum _{n=1}^{N}\left({w}_{\mathit{ij}}^{\ast}\mathit{log}\left({\widehat{F}}_{i}\right({\gamma}_{i}{Z}_{j}\left)\right)+(1-{w}_{\mathit{ij}}^{\ast})\mathit{log}(1-{\widehat{F}}_{i}({\gamma}_{i}{Z}_{j}\left)\right)\right).

(5)

In the second step, the following system of equations is estimated:

{w}_{\mathit{ij}}=\widehat{F}\left({\widehat{\gamma}}_{i}{Z}_{j}\right)\left(\right.{\mu}_{i}{X}_{j}+{\lambda}_{i}\left({\widehat{\gamma}}_{i}{Z}_{j}\right)\left)\right.+{\u03f5}_{\mathit{ij}},

(6)

where all variables are defined as before, and *λ*
_{
i
}(·)
is a selection control function. If the error term is normally distributed (SY), *λ*
_{
i
}(·) is simply the Heckman (
1979
) control term {\theta}_{i}\frac{\varphi \left({\widehat{\gamma}}_{i}{Z}_{j}\right)}{\Phi \left({\widehat{\gamma}}_{i}{Z}_{j}\right)}, where *Φ*(·) denotes the cdf, *ϕ*(·)
is the normal probability density function (pdf), and *θ*
_{
i
} are coefficients to be estimated.

Applying the SZ method, *λ*
_{
i
}(·)
is unknown because the distribution of the error terms is not specified. To estimate the control term, Newey (
1999
) approximates *λ*
_{
i
}(·)
with a power series expansion of the transformed index {\tau}_{\mathit{ij}}=f\left({\widehat{\gamma}}_{i}{Z}_{j}\right). That is

{\lambda}_{i}(\xb7)=\sum _{k=1}^{K}{\theta}_{\mathit{ik}}{\tau}_{\mathit{ij}}^{k-1}=(1,{\theta}_{i2}{\tau}_{\mathit{ij}},{\theta}_{i3}{\tau}_{\mathit{ij}}^{2},\dots ,{\theta}_{\mathit{iK}}{\tau}_{\mathit{ij}}^{K-1}),

(7)

where the first term cannot be identified separately from the constant term. Here, the order *K* is chosen such as to minimize the mean squared error for each equation.

We use a power series of inverse Mill’s ratio of the normalized estimated index.^{8} The semiparamteric estimator imposes a scale and location normalization for identification. To reverse it, we use the constant and slope coefficients, *Π*
_{0} and *Π*
_{1}, respectively, that we obtain from a probit estimation of {w}_{\mathit{ij}}^{\ast} on the index \left({\widehat{\gamma}}_{i}{Z}_{j}\right). The inverse Mill’s ratio of the normalized estimated index is then:

{\tau}_{\mathit{ij}}=\varphi ({\widehat{\Pi}}_{0}+{\widehat{\Pi}}_{1}({\widehat{\gamma}}_{i}{Z}_{j})/\Phi ({\widehat{\Pi}}_{0}+{\widehat{\Pi}}_{1}\left({\widehat{\gamma}}_{i}{Z}_{j}\right)).

(8)

The first order term is hence the Heckman correction, and will be sufficient if the error term is normally distributed.

The SZ method assumes a more general form of equation (4). Therefore, it has the advantages of generating consistent and efficient estimates without relying on distribution assumptions, and accommodating a certain form of heteroscedasticity. Since semiparametric methods are extremely computationally demanding, the SY method is preferred if its assumptions are not violated. To exploit the information contained in the cross equation error correlations, the system of equations is estimated jointly for the full household sample using iterative nonlinear SUR (with both methods).^{9}

### 4.3 Endogeneity of remittances

In a thought experiment whereby a number of households are randomly drawn from the population, and subsequently “treated” with remittance receipt, the impact of remittances on household expenditure patterns could be examined. As such an experiment is not possible, the problem of endogeneity arises, i.e. the variable remittance receipt is correlated with the residual. Migration of one household member is a precondition for the receipt of remittances. The occurrence of one member migrating depends heavily on household characteristics. Variables that may “explain” migration may also be correlated with household expenditure patterns. These variables may include observable characteristics, such as household income and the educational level, as well as unobservable characteristics like the degree of risk aversion or ambition. In the absence of random assignment, an estimation strategy that allows for identification of the treatment effect has to be employed, such as a matching procedure, difference‐in‐difference estimation or an instrumental variable (IV) approach. McKenzie et al. (
2010
) use a natural experiment to compare different methods in estimating the income gains from migration. Their findings suggest that migration selects on both, observable and unobservable characteristics, and that an IV approach with good instruments works best among the non‐experimental methods.

Although an IV approach is preferable, it relies heavily on the exogeneity assumption. Variables which explain remittance receipt but are uncorrelated with the expenditure patterns have to be employed. In this study, identification of the causal effect (the local average treatment effect LATE) relies on instruments that exploit information on former remittance receipt within the community. From the ECV‐4, the previous round of the survey, we construct the variable “Remittances in the community in 1999” which is the proportion of remittance receiving households in the community in the year 1999. This variable is interacted with the proportion of household members with secondary and tertiary education, respectively, to allow for the variability of the instrument at the household level (Amuedo‐Dorantes and Pozo (
2006
); Hanson and Woodruff (
2003
)). Justification lies in the fact that historical migration developed networks which can promote future migration. On the other hand, historical migration rates are exogenous as they occurred in the past, and are hence not affecting current consumption.

### 4.4 Endogeneity of gender

Next, we turn to the gender‐dimension of our analysis. Table 2 has already shown that household characteristics differ substantially for female and male headed households. The gender of the household head is likely to be correlated with the residual, i.e. gender is endogenous. The impact of remittances will be different even in the absence of gender‐specific preferences. To make female and male headed households comparable, this study uses a matching procedure.^{10} The idea behind matching is to find for each “treated” observation (i.e. female headed household) its “non treated” or “control” counterpart (i.e. male headed household) with equal characteristics. If the number of variables is large or variables take on many values (like total per‐capita expenditures here), exact matching becomes impossible. Common practice is then to use some form of inexact matching that balances the covariates as well as possible. The idea of coarsened exact matching (CEM) developed by Blackwell et al. (
2009
) is to coarsen each variable into groups, for example, we split total household expenditures by quartile. Subsequently, a set of strata is created which contain all observations with the same values of the coarsened data. One possible stratum hence may contain all individuals from the first expenditure quartile, which live in an urban area, have no children, etc. Observations in strata that contain at least one treated and one control unit are retained, and units in the remaining strata are removed from the sample. If a stratum does not contain the same number of treated and control units, observations are randomly dropped to obtain the same number.