Why would deflation converge to the rate of global economic growth? I'd think that the opposite tends to be true, eg. the inflation is often correlated with growth.
In 2013, we produce 21 million apples, so we could say that each bitcoin is worth 1 apple. In 2014, we produce 42 million apples, which is 100% annual GDP growth. Each bitcoin is worth 2 apples, which is a 100% appreciation in the value of the currency, aka. deflation.
Grow the (effective) money supply with lending and deposit accounts, and apples / dollar falls. When things are growing, people know there is money to be made, and so expect they are more likely to be paid back, and so lend more freely.