In this paper, we analyze the relationship between nominal and real GDP growth for G7 countries for the period 1971 – 2018. A visual inspection of the data indicates the presence of a threshold, above which the structure of the relationship between nominal and real GDP growth rates changes from a positive one to a flat one. Moreover, the volatility of real growth is observed to be higher at high rates of nominal GDP growth. We first test for the presence of a two regime non-linearity by using the Sup F test of Andrews (1993). Due to the presence of heteroskedasticity we also apply the Sup MZ test of Ahmed et al. (2017). Both tests operate under an unknown change point and the latter also allows for heteroskedasticity. The results of the tests point to the presence of a "demand deficiency" regime for low nominal demand growth rates and to a "harmful inflation" regime for higher nominal GDP growth rates, these results have strong implications for guiding recent policy discussions on nominal GDP targeting.