Disinflation due to weak demand or rapid supply growth?

We compare the United States, the euro zone and China. If we compare core inflation rates (excluding rents imputed to homeowners), we see fairly high inflation in the euro zone, low inflation in the United States and zero inflation in China. Does this hierarchy of inflation rates between the three countries/regions stem from differences in the growth of demand for goods and services or from differences in the growth of the supply of goods and services? Total demand for goods is growing much faster in the United States and China than in the euro zone. Productivity gains are also growing much faster in the United States and China than in the euro zone. The hierarchy of inflation rates therefore stems from the increase in the supply of goods and services, not from the increase in the demand for goods and services. If demand for goods and services were at the root of inflation rate gaps, inflation would be lower in the euro zone than in China or the United States.