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The instrumental variable (IV) estimator in a cross-sectional or panel regression model is often taken to provide valid causal inference from contemporaneous correlations. In this exercise we point out that the IV estimator, like the OLS estimator, cannot be used effectively for causal inference without the aid of non-sample information. We present three possible cases (lack of identification, accounting identities, and temporal aggregation) where IV estimates could lead to misleading causal inference. In this light, we re-examine the relationship between Chinese provincial birth rates and economic growth. This exercise highlights the potential pitfalls of using too much temporal averaging to compile the data for cross sectional and panel regressions and the importance of estimating both (x on y and y on x) regressions to avoid misleading causal inferences. The GMM-SYS results from dynamic panel regressions based on five-year averages show a strong negative relationship running both ways, from births to growth and growth to births. This outcome, however, changes to a more meaningful one-way relationship from births to growth if the panel analysis is carried out with the annual data. Although falling birth rates in China have enhanced the country?s growth performance, it is difficult to attribute this effect solely to the one-child policy implemented after 1978.