Life expectancy, educational attainment, and fertility choice

This paper explores the role of mortality as a determinant of educational attainment and fertility, both during the demographic transition and after its completion. Two main points distinguish our analysis from the previous ones. Together with the investments of parents in the human capital of children, traditional in the fertility literature, we introduce investments of adult individuals (parents) in their own education, which ultimately determines productivity in both the goods and household sectors. Second, we let adult longevity affect the way parents value each individual child. Increases in adult longevity or reductions in child mortality eventually raise the investments in adult education. Together with the higher utility derived from each child, this tilts the quality-quantity trade off towards less and better educated children, and increases the growth rate of the economy. This setup can explain both the demographic transition and the recent behavior of fertility in “post-transition” countries. Evidence from historical experiences of demographic transition, and from the recent behavior of fertility, education, and growth generally supports the predictions of the model.

Optimal two-sided tests for instrumental variables regression with heteroskedastic and autocorrelated errors

This paper considers two-sided tests for the parameter of an endogenous variable in an instrumental variable (IV) model with heteroskedastic and autocorrelated errors. We develop the nite-sample theory of weighted-average power (WAP) tests with normal errors and a known long-run variance. We introduce two weights which are invariant to orthogonal transformations of the instruments; e.g., changing the order in which the instruments appear. While tests using the MM1 weight can be severely biased, optimal tests based on the MM2 weight are naturally two-sided when errors are homoskedastic. We propose two boundary conditions that yield two-sided tests whether errors are homoskedastic or not. The locally unbiased (LU) condition is related to the power around the null hypothesis and is a weaker requirement than unbiasedness. The strongly unbiased (SU) condition is more restrictive than LU, but the associated WAP tests are easier to implement. Several tests are SU in nite samples or asymptotically, including tests robust to weak IV (such as the Anderson-Rubin, score, conditional quasi-likelihood ratio, and I. Andrews' (2015) PI-CLC tests) and two-sided tests which are optimal when the sample size is large and instruments are strong. We refer to the WAP-SU tests based on our weights as MM1-SU and MM2-SU tests. Dropping the restrictive assumptions of normality and known variance, the theory is shown to remain valid at the cost of asymptotic approximations. The MM2-SU test is optimal under the strong IV asymptotics, and outperforms other existing tests under the weak IV asymptotics.