Solow to Becker-Lucas

We provide a unified growth model to study the transition from the Solow economy which only uses labor and physical capital in production to the Becker-Lucas economy which uses an additional new accumulative factor, human capital, in production. The model starts with the Solow economy, with the Becker-Lucas technology of production available but not profitable at the beginning. Due to the diminishing returns to physical capital, the Becker-Lucas production becomes feasible and starts automatically after physical capital stock reaches a trigger point. We examine the full dynamics of main macroeconomic variables during this transformation process, including a remarkably long period when these two economies coexist. Our theory shows even if assuming a slightly lower TFP growth rate in the Becker-Lucas production than Solow, the transition could still happen due to the efficiency improvement from human capital accumulation. Model calibration shows the labor share will firstly drop during this economic transformation, therefore providing a potential new theoretical explanation for the phenomenon of labor share decline which has recently attracted broad attention. The accumulation of human capital together with the enlarging Becker-Lucas economy does have contributed to this dynamics. Moreover, our model also predicts a rebound of the labor share towards the end of the transformation from the Solow economy to the Becker-Lucas economy and provides a new explanation for skill premium change.