There is an article and report by the Center for Economic and Policy Research (CEPR) where there are projections of a deficit in US military spending as China's economy grow. The assumptions in this report and the time frame is nuts. They are talking about a big deficit in 2050-2080 assuming higher than US per capita PPP growth in the Chinese economy for 75 years. To illustrate the absurdity of this, if we project that Google keeps growing at a higher rate trailing off slowly from 95% per quarter starting from $1.1B in Q1 2005, we can see that Google will nearly double every quarter and own both the USA and China in 2010 in the high growth scenario and 2012 in the slow growth and 2015 in the low growth. Thus Google will own both the US and Chinese military by 2015 and we will have pax Google.
On a slightly more analytical level, China is currently buying a lot of Russia gear and I think they are trying to buy stuff from France. Analysis of recent advances in China's military capability and here Much of the advance is from purchases of older russian fighters and submarines. That portion of the Chinese military budget has to be GDP based because they are using hard currency to buy subs and fighters. Similarly oil for the military has to be GDP based. A pure PPP only makes any kind of sense if China had a fully indigineous military development capability. As China gets richer, PPP and GDP will come together.
I am a China optimist but even I do not think its growth will race ahead of the USA for 75 years. Plus just catching economy and budget wise, China has to overcome the fixed military assets of the USA. The USA has more advanced submarines and aircraft carriers that they bought from previous years. That capability still will exist in the future.
Think of it this way. I am twenty times poorer than my gun collecting survivalist friend. I live in Missouri and he lives in California. My house would be 2/3 of the value of his house if my house was in California. If over thirty years I catch up with his salary on a purchasing power basis (I could buy the same stuff in Missouri that he can buy in California). It will still take me a long time to spend 10% of my money and build my own guns and fertilizer bombs to equal his collection even as my 7% salary increases continue to exceed his 3.5%.