This study develops a Schumpeterian growth model with endogenous entry of heterogeneous …rms to analyze the e¤ects of monetary policy on economic growth via a cash-in-advance constraint on R&D investment. Our results can be summarized as follows. In the special case of a zero entry cost, an increase in the nominal interest rate decreases R&D, the arrival rate of innovations and economic growth as in previous studies. However, in the general case of a positive entry cost, an increase in the nominal interest rate a¤ects the distribution of innovations that are implemented and would have an inverted-U e¤ect on economic growth if the entry cost is su¢ ciently large. We also calibrate the model to aggregate data of the US economy and …nd that the growth-maximizing in ‡ation rate is about 3%, which is consistent with recent empirical estimates.JEL classi…cation: O30, O40, E41