Twins are proposed by Rosenzweig and Wolpin (1980; 2000) as a ‘shock’ to the quantity
of children that is uncorrelated with parent preferences or unobserved determinants of other
family and child outcomes. Adjustment of investment in the schooling of other children in the
family due to the occurrence of twins can then test the quantity-quality substitution hypothesis.
They found support for the trade-off of quantity-quality on non-twin siblings in rural Indian
households observed in 1970. A larger sample of twins collected in China provides the basis for
estimating the impact of a twin on the quality of earlier- or later-born siblings, providing bounds
to the magnitude of the cross effects, adjusted for substitution effects between siblings
(Rosenzweig and Zhang, 2006). However, when twins are an instrument for fertility, the
estimated quantity-quality trade-off tends to be smaller in absolute value than when estimated by
direct association, that is, ordinary least squares (OLS). This could be due to the twin instrument
being weak either because it occurs for only a small fraction of births (for example, one per cent)
or because the underlying causal relationship is in fact weak and appears important only in biased
single-equation associations (that is, OLS). The heterogeneity in parent preferences or other
unobserved determinants of behavior could inversely affect child quantity and quality (Schultz,
2005).
Other studies have exploited twins as an instrument for fertility to assess how exogenous
fertility affects the mother’s market labour supply. These studies in high- and low-income
countries generally confirm that the twin instrumental variable estimate of the effect of a birth on
the mother’s market labour supply tends to be absolutely smaller (negative) than the OLS
estimate. The Durbin-Wu-Hausman specification test rejects the exogeneity of fertility in the
determination of the mother’s allocation of time to market work (Schultz, 2005), implying that the
consistent instrumental variable estimate is preferred over the OLS estimate.
This twin-based cross effect of fertility on mothers’ labour supply may help to explain
how policies which reduce fertility can facilitate modern economic growth, by adding to the per
capita supply of labour and increasing the human capital of future generations. Finally, if parents
when they have fewer children increase life-cycle savings for their support in old age, policies
that facilitate a decline in fertility could raise savings and further augment growth rates. But
estimates of these three potential cross effects of fertility-reducing population policies remain
currently speculative.
The other instrument commonly used to identify the consequences of fertility on the