We study dynamics of interactions among economic growth, population, and environmental quality when stochastic shocks in these systems display long‐memory property. We make two important contributions. First, we show that the long‐memory persistence in economic growth is determined jointly by the convergence speed of shocks in both environmental quality and population. Second, by simulating a modified Solow‐Swan economy we demonstrate that the convergence‐speed of shocks in these systems significantly affects the long‐run growth trajectory of output. Our empirical examination evince that adjustment of output to long‐run equilibrium is very slow, thanks to the slowly dissipating population and pollution shocks.