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.