Does the Law of Diminishing Returns Apply to Infant Motality Decline?

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Hopkins Population Center
Objective: This paper examines time series data on infant mortality from 21 countries to demonstrate an appropriate test of the hypothesis that percentage reductions in infant mortality are larger when infant mortality is lower. Prior research expounding this hypothesis has dubbed it "the Matthew effect". Method: Time series for infant mortality can be modeled as X t = m + q1 X t-1 +e t where e t is identically and independently distributed. If q1=1 it is easily demonstrated that the time series has an asymptotic distribution with infinite variance. The correct test to apply in this situation is the Dickey-Fuller test which we use to test the statistical significance of q1 in a regression analysis of Dlog IMR t = m + q1 log IMR t-1 +e t. Evidence that q1 is significant and negative would support the claim that there is a Matthew Effect in infant mortality. This paper uses time series data on IMR from 21 nations for 1870-1988. Several additional lagged values of Dlog IMR were appended using an Akaike Indicator Criterion to select the preferred specification. Transformations of IMR other than simple logarithms were explored. Results: With the preferred specification, the Dickey-Fuller test rejected the presence of any Matthew Effect in all but three countries. The rejection of a Matthew Effect was robust to alternative specifications of the lag structure of IMR and to various transformations of IMR other than logarithmic. Conclusion: Based on 20th century data there is scarce evidence that percentage reductions in infant mortality are generally smaller in higher mortality countries. Large percentage reductions in infant mortality are possible for countries at any stage in economic development and are likely to be reflective of durable advances in human knowledge, social institutions, and physical capital.