Conditions for prosperity and depression of a stochastic R&D model under regime switching

The stochastic research and development (R&D) model plays an important role in economic growth theories. To explain the growth performance of the economy under regime switching, we first establish sufficient criteria that ensure economic prosperity, nonprosperity and depression in the R&D model disturbed by white and color noise. Then, we determine the threshold between prosperity and depression. Furthermore, we estimate an upper bound of the growth rates of technological progress and capital accumulation in the prosperity case. The results indicate that color noise sensitively impacts the growth performance of the economy in the R&D model. Finally, numerical simulations are conducted to verify our theoretical work.