Authors’ response: Politicization with misrepresentation: on de-trending in time series analysis

Professor Catalano referred to our good faith and peer-reviewed empirical article1 as equivalent to ‘dog food, the grocer would have to pull … from the shelf’.2 He attributed political motives to us as the basis for our findings. Call us crazy, but we stand by the view that such criticisms are ad hominen, and far from ad rem. Despite that, and Professor Catalano’s current claim to the contrary, in our initial rejoinder3 we explicitly acknowledged that his commentary also included a number of serious substantive arguments. Indeed, the vast majority of our response involved a detailed discussion of the substantive points he made, most of which he does not acknowledge in his current letter. Instead, Professor Catalano continues to politicize our motives and misrepresents our response in an additional way. Professor Catalano says that we claimed that when we used an ARIMA model to ‘filter’ out a trend from the time series data on infant mortality, we continued to find a statistically significant and quantitatively important association between the residuals from this filtering process and the president’s party. We actually claimed the opposite.3 If one removes the trend from the infant mortality series using standard procedures in the literature such as cubic splines or simple or fractional polynomials, visual inspection of the residuals shows a pattern that strikingly mirrors the pattern of changes in the party of the president (see Figure 2 in our article1). If one removes the trend using an ARIMA model, there is no evident pattern in the residuals. Our disagreement with Professor Catalano is whether, for our research purpose, we should be de-trending using a variety of cubic splines or polynomials, or using an ARIMA model. The figure in our response to Professor Catalano’s commentary was meant to illustrate the difference between our preferred de-trending method and a best-fitting ARIMA model.3 [For fit statistics of nine different ways of de-trending the series see Table 1 and its discussion in the appendix to our paper (available as Supplementary data at IJE online)]. As the figure in our response3 illustrates, fitting an ARIMA process to the infant mortality series would filter out the variation that exists in low and medium frequencies of the data. This is critical. To exemplify the nature of the variation contained in the infant mortality series, we reported the results of our Fourier decomposition series analysis in the appendix to our article1 (available as Supplementary data at IJE online). It formally shows the infant mortality series includes both low frequency variation (the downward trend) and medium frequency variation. This medium-run variation has a period of approximately 16 years, and it mirrors the president’s party, rising during the years in which the president was a Republican and falling during years in which the president was a Democrat. This need not have been true. Professor Catalano misunderstands our cubic spline procedure to de-trend the data and the rationale behind what constitutes a trend and what does not. In theory, a depiction of a long-run trend should be insensitive to short-term, year-specific variation, which is precisely what the residualized series attempts to represent. We did not imply that ‘autocorrelation in a time series divides into good and bad’, as Catalano argues; our concern is that, in this case, the ARIMA model ‘filters’ out the medium-run frequency. In his initial commentary,2 Professor Catalano also suggested that carrying out a comparative vs single-country approach would constitute a best test of our hypothesis. And so we did. As we noted in our response,3 after de-trending the series using a cubic spline (instead of using Box–Jenkins methods), we once again found that the estimated coefficient of the presidential party affiliation was precisely estimated and very similar to the coefficient we reported in our paper. Thus, whatever method one uses to filter the data, and whether one uses a comparative or a single-country approach to test our hypothesis, over the past half-century in the USA, at medium frequencies, there appears to be an association between the president’s party affiliation and national and race-specific infant mortality. This finding showed to be substantial and remarkably robust to a variety of model specifications.1 Whether this robust association is causal, spurious or reflects something else systematically associated with the president’s party affiliation, we do not know, but given the magnitude of its possible implications, and the importance of understanding persistent excess US infant mortality rates, we believe it is worth further investigation.