Optimal Long-run Money Growth Rate in a Cash-in-Advance Economy with Labor-Market Frictions

Been-Lon Chen, Shian-Yu Liao, Dongpeng Liu, Xiangbo Liu

IEAS Working Paper No. 22-A003, August 2022

We revisit the Friedman rule in a labor search model and extend Heer (2003), Coo-ley and Quadrini (2004), and Wang and Xie (2013) to one that allows for endogenous growth.We show that, even without a liquidity effectoraCIAconstraintonfirms’ wage payment, ourmodel offers a different channel for moderate money growth to increase welfare. Intuitively, ina one-sector endogenous growth economy, the technology is of constant returns with respectto capital. When the labor market is frictional, a moderate increase in money growth inducesan expansion in vacancy and employment. Labor and capital are complements in production.With an increase in employment, when the technology is neoclassical, the decreasing returnin capital leads to a lower marginal product of labor.  However, in an endogenous growthframework wherein the technology exhibits socially constant returns in capital, the marginalproduct of labor is constant. Due to a constant marginal product of labor, modest inflationraises employment, enlarges economic growth, and increases welfare. Moreover, the optimallong-run inflation rate departs from the Friedman rule, even when the Hosios rule holds. Fi-nally, wefind that our model with sustainable growthfits the data better than that withoutsustainable growth.