Estimation of causal effects of fertility on economic wellbeing: evidence from rural Vietnam

Estimating the effects of demographic events on households living standards introduces a range of statistical issues. In this paper we analyze this topic considering our observational study as a quasi-experiment in which the treatment is expressed by childbearing events between two time points and the outcome is the change in equivalized household consumption expenditure. Our main question concerns how one can best estimate causal effects of demographic events on households economic wellbeing. We first provide a brief discussion of different methods for causal inference stressing their differences with respect to the underlying assumptions and data requirement. In particular, we contrast methods relying on the Uncounfoundedness Assumption (UNA), such as regressions and propensity score matching, with methods allowing for selection on unobservables, such as the Instrumental Variable (IV) estimators. We stress the fact that these methods are not equivalent in what they estimate. With Regressions and Propensity Score Matching (PSM) we can identify and estimate the Average Treatment Effect (ATE) and the Average Treatment effect on the Treated (ATT), while IV methods give the Local Average Treatment Effect (LATE). Since LATE is the average causal effect of the treatment on the sub-group of compliers, it is generally different from ATE and ATT. Moreover, different instruments identify the effect on different groups of compliers giving different estimates of LATE. A problem for policy making is that the compliers are in general an unobserved sub-group. However, IV methods estimate relevant policy parameter if the instrument itself is a potential policy variable. We demonstrate these issues with an application on data derived from the Vietnam Living Standard Measurement Study.