Income, health, and spurious cointegration

Abstract: Data for many nations show a long-run increase, over many decades, of income, indexed by GDP per capita, and population health, indexed by mortality or life expectancy at birth (LEB). However, the short-run and long-run relationships between these variables have been interpreted in different ways, and many controversies remain open. It has been claimed that population health and income are cointegrated, and that this demonstrates a positive long-run effect of income on population health. We show, however, that an empirically tested cointegration between LEB and GDP per capita is not a sound method to infer a causal link. For a given country it is easy to find computer-generated data or time series of real observations, related or unrelated to the country, that according to standard methods, are also cointegrated with the country's LEB. More generally, given a trending time series, it is easy to find other series, observational or artificial, that appear cointegrated with it. Thus, standard cointegration methodology, often used in empirical investigations, cannot distinguish whether cointegration relationships are spurious or causal.