Purpose Using data from 1820 onwards in a group of seven countries, namely, Australia, Chile, Denmark, France, the UK, Italy and the USA, the authors investigate if there is a long-run equilibrium relationship between the two variables (GDP and population). Design/methodology/approach Using fractional integration and cointegration methods, this paper deals with the analysis of the relationship between GDP and population using historical data. Findings The authors' results show first that the two series are highly persistent, presenting orders of integration close to or above 1 in practically all cases. Testing cointegration between the two variables, the results are quite variable depending on the methodology and the bandwidth numbers used, but if cointegration takes places, it only occurs in the cases of France, Italy and the UK. Research limitations/implications The fact that the orders of integration of all series is close to 1 indicate high levels of persistence with shocks having permanent effects and requiring strong measures to recover the original trends. Practical implications Any shock affecting the series will have a permanent nature, persisting forever. Originality/value Updated time series techniques based on concepts such as fractional integration and cointegration are used.