Inequality and household size: A microsimulation for Uruguay

Demographic factors are among the most important determinants of the evolution of income distribution and of its derived indicators such as poverty and inequality indexes. The relationship between inequality and demographic factors is a complex one, as many aspects – including household size and age composition – are involved. These elements are closely linked to fertility, whose differential patterns may be relevant. If fertility rates increase for the poor but decrease for the rich, this may affect income growth downwards in the short and medium run and have a considerable impact on inequality and poverty. This impact is exerted through a direct channel, as increasing the number of children in the household decreases per capita available income, or indirectly, as it may affect adults' decisions about labour market participation or hours of work. With a long run perspective, children from poorer households, which are more numerous, will accumulate less human capital and both income growth and its distribution will be affected (see for example De La Croix & Doepke, 2003). Given this, accounting for fertility differentials between the rich and the poor households is essential because it may have relevant consequences in the medium and long run. Moreover, if differential patterns of fertility have consequences on poverty and inequality, public policies affecting fertility may provide non expected gains in terms of poverty and inequality.

Concerns about the evolution of inequality in Latin America in recent decades have been in the core of academic discussion, as after the growing trend of the 90s, income inequality began to decrease in the 2000s, and the region made a strong progress towards reducing income disparities. The levels of fertility, on the other hand, have dropped significantly since the mid 50s. From 1990 on the trend decelerated but went on: total fertility rate went from 3 children per woman in 1990–1995 to the replacement level (2.1) by 2010–2015 (Figure 1.A in the Annex). These general trends in inequality and fertility are shared by many countries in the region, including Uruguay.

Income inequality and poverty increased between 1996 and 2004 in Uruguay, whereas household size, or more specifically the number of children per household, decreased on average, but its changes were not uniform along the income distribution. After 2004, poverty started to fall and from 2007 on, both income inequality and poverty decreased significantly, whereas the number of children per household continued its decreasing path. This article addresses the relationship between these three dimensions: poverty, inequality and the number of children per household, based on a microeconometric decomposition technique. A similar study for Argentina concluded that fertility decisions contributed considerably to changes in poverty and inequality in that country in the period 1980–1990 (Marchionni & Gasparini, 2007). Similar results are found by Badaracco (2014) for a set of Latin American countries, with the exception of Uruguay which shows a different pattern.¹

In what follows, we focus on the relationship between changes in poverty and inequality and the dynamics of the number of children per household in Uruguay between 1996 and 2013, using a microeconomic perspective. The article is organized as follows: first we present some basic information about poverty, inequality and household size in Uruguay (Section 2). Then we outline the methodology of the microeconometric decompositions presented in the article (Section 3). Afterwards, we discuss the main results of our microsimulations (Section 4) and then present some final comments (Section 5).

Uruguay is a small Latin American country, which stands out in the region for its relatively low levels of income inequality and poverty. It was classified as a middle income country until 2013, when it became high income for the first time. Average per capita household income increased in the beginning of the period and until 1999. After that, a period of recession began, and finished in the severe economic crises of 2002 and 2003. This recessive episode was due to a series of domestic and external shocks and implied an acute crisis of the financial system. In 2002 GDP (Gross Domestic Product) fell 11 % and the exchange rate slumped 90%. Household income, on the other hand, suffered a severe drop starting in 2000 (Figure 1). Between 2000 and the end of 2003, it decreased 28%. Although GDP began to recover in 2003, household income again decreased significantly that year (16%), and it only began to recover in 2004. Starting in 2006 household income climbed significantly, expanding almost 10% per year until 2009. From then on, with a brief interruption in 2012, household income grew at a more moderate rate of 4% annually. By the end of the period, household income reached and surpassed the pre-crises level.

In regard to income inequality, after remaining stable until the mid-nineties (Vigorito, 1999), all the inequality indexes showed an increasing trend during the recession and in the aftermath of the outbreak of the economic crisis in 2002. The Gini index for per capita household income, for example, was 0.42 in 1996 and rose to 0.44 in 2007 (Figure 1). From that year on, it has shown a sustained decrease, reaching its lowest figure in the last thirty years in 2013 at 0.38.

The increase in income inequality at the household level until 2006 comes from the labour market, as it is mainly explained by the increase in wage inequality. This is related to the fact that returns to skills increased significantly during the nineties. Different factors may have influenced the evolution of returns: openness, skill biased technological change, changes in wage bargaining, different evolution of real public transfers, among others (Bucheli & Furtado, 2005; PNUD, 2005). Other studies have underlined the importance of the suppression of centralized wage setting mechanisms, the drop in minimum wages and the lack of a social protection system oriented to the most deprived households as factors explaining the increase in inequality up to 2006 (Amarante et al., 2014). The relative importance of each factor as an explanation of the increase in inequality remains a matter of discussion. The decline in inequality after 2007 has also been related to different factors in the literature: the reduction in labour income inequality, the tax reform and the effect of noncontributory cash transfers (Amarante et al., 2014; Llambί et al., 2016), the significant increase in minimum wages (ECLAC, 2014) and the formalization in the labour market (Amarante et al., 2016). As in other countries in the region, the decline in the wage skill premium may have been related to the increase in the relative demand of unskilled workers, associated to commodity boom or related services (De la Torre & Pienknagura, 2012; Gasparini et al., 2012).

Figure 1

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Poverty remained stable between 1996 and 1999 but amid a period of recession increased significantly during 1999–2002 (Figure 2).² Furthermore, it continued on the upward trend in 2003 and 2004, standing at 30% on the latter year (more than doubling the figure of 1999). This increase is associated to the economic crises, which implied significant increases in the unemployment rate and reductions in real wages. In 2005, after three years of GDP recovery, poverty started to recede. This trend went on during the following years and towards the end of the studied period. In 2013, poverty stood at 12%, below pre-crisis levels and almost a third of the values registered just a decade ago. Some of the factors that explain the decrease in inequality also explain the decrease of poverty. In effect, non contributory cash transfers, increases in minimum wages and the increased demand of unskilled workers have translated into higher incomes at the bottom of the distribution, leading to lower poverty.

Figure 2

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Poverty profiles about Uruguay always emphasize the differences of poverty incidence among age groups (Amarante et al., 2005; PNUD, 2005; World Bank, 2004). Child poverty was 22.3% in 2013, whereas poverty incidence among the whole population was 12.0%.² This difference between child and adult poverty incidence is found for most Latin American countries, although the pattern is more acute in the case of Uruguay (see Rossel, 2013).

Consistently with these differences in poverty by age, there are significant differences in the number of children per household depending on the type of household and especially on the educational level of household head (Table 1)⁴. Besides differences in levels, the dynamics of the number of children per household were differential along the distribution. The number of children decreased during the last fifteen years in all households, no matter the educational level. Overall, it decreased almost 21%, changing from 1.66 to 1.32 (estimations based on households whose head is younger than 50). Nevertheless, the rates were differential according to the household head’s education, being higher the higher the level of education of the household head. Whereas the number of children decreased 6.2% for those households where the head had primary education or less, it decreased 33.6% when we consider households headed by persons with tertiary education (Table 1).

The analysis by income deciles shows a similar pattern: changes were differential by income deciles (Table 2). The mean average change in the number of children for households belonging to deciles 1 to 5 was −15% for the period 1996–2013, whereas the figure for deciles 6 to 10 was −33%.

Microsimulation techniques have emerged as useful instruments for economic analysis and policy recommendations. The well-known micro-econometric decompositions proposed by Oaxaca (1973) and Blinder (1973) for the study of the labour markets are early examples of the application of this technique. A generalized approach was developed by Bourguignon, Ferrerira, and Lustig (2004), and applied in Bourguignon, Forunier, and Gurgand (2001), among others. In this article, we use this method to assess the importance of the number of children per household on mean income, income distribution and poverty. Our analysis is based on household micro data for a specific Latin American country, Uruguay. Examples of micro-simulations for fertility decisions can be found in Ferreira and Leite (2002) and Marchionni and Gasparini (2007).

We take the adaptation of micro-simulation techniques proposed by Marchionni and Gasparini (2007) to analyse the role of fertility in Argentina. Following their proposal, (D_t) is per capita household income distribution corresponding to the (N) individuals in an economy in time (t:⁵)

where (y_it) is the ratio between (Y_h), total income of the household, and (N_h,) the family size

Family size is the sum of adults (A_ht) and children (Ch_ht) in the household:

Per capita household income of individual (i) is affected by fertility decisions in two ways: the increase in the number of children increases the denominator of the equation and, keeping other things constant, reduces per capita income for all household members. The number of children also affects the labour participation decision of some household members, modifying hours of work or the probability of participating in the labour market, and so affecting the numerator of the equation.

Total household income (Y_ht) is the sum of labour (L) and non labour incomes (NL) of all household members:

Non labour incomes are exogenously determined, whereas individual i’s labour income is the product of the hourly wage rate (w) and the number of hours of work (L).⁶

Labour market decisions can be modelled as originally proposed in Heckman (1974).⁷ Labour market reduced form equations are derived from a structural system obtained from a utility maximization problem of labour-consumption decisions. Wages (w*) are interpreted as marginal valuations of labour. They are a function of hours of work and other personal characteristics, and represent the minimum wage for which the individual would accept to work a certain number of hours. In equilibrium, if the individual decides to work, the number of hours devoted to labour should equate their marginal value (w*) with the wage received (w). If the marginal value is greater than the wage offered, given the individual’s characteristics, the person chooses not to work.

Then it is possible to model market determinants of wages offered (w) as a function of personal characteristics (standard Mincer equation). In equilibrium, the number of hours of work adjusts to make w=w*. Under general conditions, it is possible to derive a reduced form for the equilibrium relations in which wages and hours of work are expressed as functions of the exogenous variables. In this way, the model has two equations, one for wages (w*) and the other for hours of work (L*). These variables are functions of factors that affect wages (X₁) and hours (X₂), and that may or may not have elements in common. For our specific purposes, the number of children, (Ch), enters the labour supply equation. (ε₁) and (ε₂) represent unobservable factors that affect the determination of hours and wages respectively.

For estimation purposes, we observe positive values of (w*) and (L*) only for those individuals that actually work. So the reduced form model for wages and hours of work for individual (i) can be specified as:

With:

It can be assumed that:

The specification of labour market equations corresponds to the Tobit Type III model in Amemiya (1985). The parameters can be estimated through Heckman’s maximum likelihood method, using a censored version of (7) as selection equation, and estimating (6) using a Tobit model.

Fertility decisions, or more precisely the number of children in the household, are determined by some household observable characteristics (Z_ht), some unobservable characteristics (ε_3ht), and the vector of parameters (η_t) that describe fertility decision:

In order to simulate the number of children in year (t) if the fertility parameter were that of (t’), we followed the strategy proposed in Marchionni and Gasparini (2007). Since the objective is to simulate changes in the number of children as a consequence only in the parameters of fertility, it is necessary to keep unobservable factors fixed. To do this, they characterize each household by the quantile it occupies in the distribution of children in year (t). The simulated number of children for each household will be the one that places it in the same quantile of the distribution of children with the relevant parameters of (t’), conditional on the observable characteristics in (t).

The combination of the above equations implies that household income depends on the following variables and parameters:

where X and Z may have variables in common.

The change of some of the parameters in this equation allows simulating incomes. In our case, we would like to simulate the number of children that household (h) in year (t) would have if fertility parameters were that of year (t’), that is $C{h}_{ht}({\eta }_t^{\text{'}})$.

Once the counterfactual number of children $C{h}_{ht}({\eta }_t^{\text{'}})$ is estimated, per capita household income in equation (2) has to be recalculated, as the denominator changes. The change in income distribution resulting of this change in the number of children is called fertility-size effect. It reflects the contribution of the change in fertility parameters η to the change in income distribution through the direct channel, the change in the number of household members.

The second step consists on estimating the hours of work using the counterfactual number of children. With a different number of children, hours of work of individuals will change and this will imply different individual and household income. This implies computing the income that an individual of household (h) would have had at time (t) if the labour market participation decisions had changed in response to the number of children simulated using the fertility parameters of time (t), keeping all other things constant, even the number of people in the household. This simulated individual income allows to compute a simulated household income, and to compute the distributional impact of a change in the hours worked by individual (i) caused by a change in the number of children between years (t) and (t’). The family size in the denominator is kept constant. This effect is called the hours-size effect.

Marchionni and Gasparini (2007) propose a third simulation consisting of considering the counterfactual distribution in time (t) if parameter λ took the value estimated in year (t’). This parameter reflects the impact of a change in the number of children on individual’s hours of work. The distributional impact of changes in these parameters of the hours of work equation is named hours-parameter effect.

In order to perform the second and third micro-simulations, results on the simulated hours of work for all individuals, and their predicted wages, are needed. This implies having residuals for the hours of work and the wage equations for all individuals. These residual terms are not available for individuals who are not working at year (t). To obtain an estimation of residuals from both the hours of work and the wage equation, they were randomly sampled from the distribution of residuals (hours and wage) for working people at time (t). If the resulting prediction for year (t) is not consistent with the participation behaviour of the individual in year (t), these residuals were discarded. The process goes on until convergence was achieved.

Due to data availability, our main variable is the number of children per household instead of a direct indicator of fertility. The number of children is often used as a proxy for fertility in the economic literature (Klasen & Woltermann, 2005; Marchionni & Gasparini, 2007; among others). For biparental and lone households, the number of children acts as a very good proxy for fertility, although for extended households the relationship is not so close (see Amarante & Perazzo, 2011). Before going on, we should clarify some caveats of our methodology. It is basically a micro econometric decomposition, and so it is subject to the limitations often underlined in the literature, probably the most important being that only first order or partial equilibrium effects are considered. In our specific case, we capture first order impacts of demographic changes on income and its distribution. But these impacts on income could induce subsequent changes in fertility, which are not considered in our results. Moreover, demographic changes may have been induced by income modifications, and that is not captured by our model.

Our microsimulations are based on data from the Uruguayan household surveys (Encuesta Continua de Hogares) for 1996, 2007 and 2013. The survey is carried out by the Instituto Nacional de Estadistίca (INE) and covers the whole year, collecting detailed information about socioeconomic characteristics of households, income by sources and labour force attainment. The years considered in this study include a change in the coverage of the survey: up to 2005 the survey was restricted to urban centres of 5,000 inhabitants and more (85 per cent of the population), from 2006 on it has national coverage. Also, since 2006, the size of the survey was considerably expanded.⁸

In this section we present our main findings. First, we describe the main results related to the estimation of the fertility equation (4.1). In second place we describe results related to the estimation of labour market equations (4.2) and finally we present the results from micro-simulations (4.3).

Changes in fertility behaviour along the income distribution have been overlooked in inequality and poverty studies. By quantifying the direct and indirect effects of these demographic changes for Uruguay, we show that they have played a role in the evolution of inequality and poverty over the past twenty years. When compared to previous research, our results indicate that demographic changes and their effects have been different in Uruguay than in other countries. In effect, Marchionni and Gasparini (2007) found that changes in fertility contributed to a reduction in income inequality and poverty Argentina between 1980 and 1998, whereas Badaracco (2014) also found that changes in fertility patterns prompted greater income equality and helped reducing poverty in Argentina, Brazil, Chile and El Salvador, while hindering inequality and poverty reduction in Uruguay, especially in the 90s.

Our results confirm that in Uruguay changes in the average number of children per household have not been similar along the income distribution. The in depth analysis we provide indicates that higher decreases took place among the less vulnerable population, leading to negative poverty and distributive implications.

These results mainly derive from a direct fertility size effect, resulting from the evolution of the parameters that govern fertility decisions. The change in these parameters has led to higher poverty and inequality in both periods considered in this article. Indirect effects, through the labour market (hours of work), operated in general terms in the opposite direction, but do not seem to have played a central role as their magnitude is smaller.

If no changes in fertility had taken place, poverty, and inequality would have been lower by the end of the period. Part of the changes in inequality and poverty can be accounted for changes in the reproductive behaviour, although this is not the central driving force.

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Author details

1. Veronica Amarante

   Organismos Internacionales / Comisión Económica para América Latina y el Caribe, Uruguay

   For correspondence

   veronica.amarante@cepal.org