The Household Demand Model

Describe the microeconomic Household Demand Model of Fertility. What does the model predict about price-income effects, the quantity quality trade-off and the income benefits of childbearing. In this context what are the variables one might target to reduce population growth in less developed countries?

We may be interested in understanding fertility decisions, because it is generally believed that population growth is detrimental to economic development (c.f. the Solow growth model and lessons from the British Industrial Revolution) and so we would advise policymakers to try and reduce population growth. The death rate has been falling across the globe since the 1960s (by 50% according to Schultz) as a result in medical advancements and the cheapening of drugs (as well as globalisation which meant this knowledge could diffuse across the world more easily), yet many LDCs have not followed the same transition path with respect to birth rates as developed countries did. By understanding why a couple decide to have a child (at the margin) we may be able to reduce these incentives, so as to limit population growth.

Fertility was an area largely ignored by economists up until the 1960s and 1970s. Prior to this fertility was incorporated into the Malthusian framework which assumed that fertility would be maximised and was only constrained through positive or preventive checks. Positive checks are when high population levels would lead to a drastic fall in income levels that means subsistence was no longer possible, thus leading to droughts, famines or diseases which caused high death rates to keep the population in check. Preventive checks occur when low incomes reduce the age of first marriage and so reduces the fertility level. North-West Europe was characterised by the European Marriage Pattern (Laslett) whereby birth outside of marriage was frowned upon and couples were encouraged to set up their own household upon marriage. These two defining features meant that when incomes were low (caused by previous levels of high population growth; a combination of increased fertility and decreased mortality) couples deferred marriage because they couldn’t afford to establish a household and thus also deferred childbearing, thereby lowering future population growth and causing the wage level to increase. This crude Malthusian framework doesn’t provide a lot of insight into fertility decisions themselves, didn’t match the empirical decline of falling fertility with rising incomes (the Malthusian model, and the EMP would predict rising fertility because households can be established earlier), and does not follow the tradition of neoclassical economics with rational maximising agents.

In the 1960s and 1970s, Becker, Willis and Easterlin developed the household demand model of fertility. This model posits a couple as being rational agents who wish to maximise their utility function, which incorporates pleasure from children, subject to their income constraint, which is expanded to include time. As we shall see this model is much more able to explain our empirical findings that as incomes rise, fertility falls.

Our utility function, following Willis, is given as U = U(N,Q,S) where N is the number of children, Q is the quality of each child and S is an aggregate basket of other commodities which the couple derive utility from. For simplicity it is assumed that the quality of each child is constant, so that we assume no favouritism occurs, something which psychologists have cast doubt on, for example it is normally the case that the first born is given greater attention and as a result has higher quality. The production function is given as C = NQ where C is child services and is the product of the number and quality of a child. We can obviously see that we can increase child services by increasing either the number of children, the quantity of children or both; and this gives rise to the quantity-quality trade-off (see below).

The budget constraint is given as I = NQπc + NPn + QPq + Sπs where pi represents the shadow cost. As a result, by maximising utility subject to our constraint, we get derived demand for children as a function of (I, πc, πs, Pn, Pq).

In this model we have taken a one-period static approach, and assumed that both the male and female in the relationship are making the fertility decision, and so have equal weighting within the utility function and income constraint; and that couples have perfect information. In reality the assumption that a household is composed of a male and female may not accurately describe developed country societies today (although it may do a better job at explaining societies in developing countries, which are a lot more traditional than their Western counterparts); the rise of single parents – often the mother – means that one party bears much more cost than the other, and can still derive utility from seeing the child if this is permitted; this also implicitly assumes a conventional couple form, and ignores the situation of adoption. Moreover, it is unlikely that both men and women in the relationship will have equal power (and weighting), it is more likely that the man is more dominant, perhaps because of his physical strength, his role as the main wage earner (a result of path-dependent societal norms), and due to cultural beliefs, hence it may be more appropriate to use some form of Nash bargaining theory to evaluate the utility of each side of the couple, which would further complicate matters. If we were to do this then we might assume that fertility would be higher than in the equal weighting situation, because men have more dominance and face less costs from having more children (both in terms of bearing and rearing) then they are likely to want to demand more children than the woman would perhaps desire. The assumption of perfect information also seems unlikely in reality, as a couple may have had no experience in dealing with children before, and so don’t know the full costs of constantly being responsible for a child, nor do they know exactly the level of utility they will gain from having a child, because this has previously never been observed. Furthermore the probability of conceiving, and then having a successful pregnancy, along with the child surviving, are all unlikely to be unknown, and thus add a degree of uncertainty to our analysis.  Fundamentally we have to assume that it is possible for a woman to maximise fertility. Again this critique is perhaps more apt for describing developed countries, as it is likely that females have some experience of looking after children (i.e. younger relatives or other relations) in developing countries (Cain).

The quantity quality trade-off is that a couple can decide between having lots of children, having fewer children but giving them high quality, or having a mixture of the both. Rosenzweig and Wolpin find evidence that twins are associated with a decline in the education levels of other children in the family, this means that a higher (unexpected) quantity leads to reduced quality.  It may be more likely that when child-survival rates are low (i.e. high child mortality rate) that it is more cost-effective to have many children – to increase the probability that some survive – but invest low quality in them, as they may not survive and this quality investment will thus be wasted.

The wealth elasticity is expected to be positive (Becker), i.e. an increase in wealth causes higher fertility, because an increase in wealth does not affect the optimising behaviour of individuals, but instead gives couples more income to afford a greater number of children. This means that children are normal goods. The quality elasticity is likely to be substantially larger than the quantity elasticity, which gives rise to the quantity-quality trade-off: with higher incomes, families are expected to increase quality much more than quantity. This is based on empirical findings that high income families have only slightly larger, or sometimes smaller, family sizes than lower income families, but they spend more on each child (Becker). This means that the substitution effect of a wage increase is negative (fertility falls), but the income effect is positive (fertility increases). Duesenberry and Blake show that the substitution effect is greater than the income effect, reasonably assuming that parents would choose child quality independently of their own living standards, and hence rising incomes leads to lower fertility (which matches the empirical data).

A rising wage increases the opportunity cost of time spent rearing children (we believe this only affects the woman who is typically the housewife) and the shadow price of having children rises relative to other satisfactions, because child-rearing is so time intensive.

The income benefits of childbearing arise from its capacity as an investment good and its direct labour productive income on top of the indirect productive capacity of a child. Firstly children can act as an investment good because parents expend resources into them at a young age (they invest), and this investment then means that the child grows and can get a job earning an income, it might then be expected that when the parent gets old that the child then looks after the parent (and pays the investment back). Consequently, this would imply that fertility is higher when interest rates are higher, because children are seen as a more attractive investment opportunity. However, in reality it might be questionable whether this plays much of a role in fertility decisions considering that credit market access is much greater nowadays (and this is expanding in the developing world too), lowering interest rates and reducing the investment opportunities arising from having children. Furthermore, the development of the welfare system in many countries means that a couple no longer has to rely on their children to look after them in their old age, and so this cultural trait is becoming unnecessary. Moreover, the welfare system means that a given couple do not have to have children themselves, as the children of other couples will be contributing to the welfare system which looks after this couple in old age. Secondly, children can be productive both in the labour market – generating an income which the parents can use to supplement their own income with – and indirectly by doing household chores, collecting fuel and water, or looking after other members of the family (and so freeing the time of the woman, who can instead engage in income-labour). Cain finds that in a typical Bangladeshi village, that a male becomes a net producer by the age of 12 (and is no longer a burden on the family), compensate for their own cumulative consumption by the age of 15 and additionally the cumulative consumption of a sister by the age of 22. This shows that children may be quite an important source of income, and may therefore be an important decision in why couples have children: to increase their income. Hence, this factor can explain why there is a boy preference – because they have greater earning potential; but this poses the question of why these societies continue with the cultural norm of preventing females from earning an income, when it might do well to increase the incomes of families (although in the short run, may depress wages due to the influx in labour supply). One could extend this hypothesis (that children are demanded for their ability to earn an income) to developed countries, where children themselves aren’t allowed to work until adulthood, by considering the effect of the welfare system where some are compensated (e.g. single mothers) for having children; this therefore acts as an incentive to increase fertility.

Of the factors examined so far we can come up with some policy implications to attempt to reduce fertility. Our first policy is to increase the wage of women, which can be achieved by giving them better access to the labour market (so that they can rise to the highest-paid jobs) and increase their education, along with reducing social restrictions on women working. We focus on the woman’s wage because it is the woman who typically has to look after the child, and so an increasing wage means an increasing opportunity cost of having children. If we changed the males wage then this may not have any effect on the opportunity cost of having children (there would be no substitution effect), but there may be an income effect resulting in more children demanded. Moreover, education can have further benefits – on top of raising women’s wages – in that it gives woman access to knowledge on contraception and family planning, increasing their efficiency (and so reducing the number of unwanted pregnancies) and may give women more bargaining power in the relationship dynamic.

Secondly we can reduce the benefits of having children, which we recall are as investment goods and a source of income. To reduce their influence as an investment good the government could improve access to credit markets – perhaps through a state bank, or subsidies, better technology and infrastructure – so that families can save their money through more institutional routes than through children. We might also attempt to reduce the interest rate, perhaps through monetary policy in a closed economy! Improving the welfare system so that a couple don’t have to rely on their children to look after them (both in terms of providing an income – pensions – and in terms of physical care – social care) in their old age. To reduce the role of children as a source of income we could introduce laws which prohibits children of a certain age from working. Furthermore, mandatory education laws requiring children to go to school means they will also have less use in the house (doing chores) and so may discourage having more children for this purpose. However, on its own, education may reduce the cost of having children (along with the benefit) because some of the cost of child-rearing activities is reduced, providing that education is free (which it almost must, given that it is mandatory). Additionally, improving infrastructure, through better transport and electrification, would reduce the usefulness of children who have to collect water and fuel for the household; again reducing their benefit, and hence derived demand.

Finally, the government might try to internalise some of the costs a parent faces, so that when making its decision it considers all costs and benefits, and not just the costs they privately face. To accomplish this might be difficult whilst maintaining equality-smoothing policies but it might also be induced through cultural changes which encourage families to consider the full cost of their fertility decision.

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