Ad hominen or ad rem? Good autocorrelation or bad?

Rodriguez et al.1 have invoked two defences against my commentary2 on their recent report of an association between Republican presidencies and infant mortality.3 First, they label my criticism as ‘ad hominen’. This powerful juju implies that I could find no fault in their argument and could discredit it only by discrediting them. I think most readers of IJE will find my criticisms entirely ad rem. I, moreover, had no need to resort to ad hominem criticism since the paper in question presented much to criticize. Second, the authors claim that ARIMA modelling identifies and controls for higher-order autocorrelation that arises from public policy and does not, therefore, provide a fair test of their hypothesis. To put it simply, the authors imply that autocorrelation in a time series divides into good and bad—bad includes that which makes the estimation of confidence intervals difficult whereas good includes that which induces association between the dependent and independent variables. They further claim that when they applied a (2,1,2) ARIMA model to the infant mortality data they still found an association. I believe I have a creditable record as a time-series analyst. As such, I can find no identification strategy by which a (2,1,2) ARIMA model would fit the US infant mortality series. As Bayes described long ago, whether association arising from shared autocorrelation makes us more confident about a causal argument depends on our ‘priors’. Those who believe, as a matter of political faith, that Republican presidents do bad things to the governed will find shared autocorrelation compelling evidence of causation. Those who want Republicans to govern will dismiss the association by citing, explicitly or intuitively, the Granger/Wiener causality theorem. The rest of us will go on wondering how to understand ‘political epidemiology’. How does it differ from political economy, policy analysis or programme evaluation? Can we agree a line at which it becomes rhetoric? And when we offer time-series associations as evidence, does whether we control for autocorrelation influence where we draw that line?