http://econsmalaysia.blogspot.my/2013/05/gdp-deflator-inflation-consumer.html. Here read this. Its almost a non-related type of measurement
From the article:
The differences in calculation are quite substantial and meaningful – they’re not looking at the same thing. In fact, calculating the GDP deflator is fairly convoluted as these things go – first tabulate all goods and services in current prices, then measure the same goods and services in prices prevailing in the base year, then calculate the ratio of current price production to constant price production. This ratio (multiplied by 100) is the GDP Deflator index, from which growth rates (inflation) can be calculated.
The CPI on the other hand, is based on changes in prices only, as the volume of goods consumed by a “representative” (average) household is taken to be fixed. The index is just a weighted average of the changes in prices across the same basket of goods.
As an example, below are the GDP deflator and CPI for Malaysia, which show weak correlation
The key thing to understand is that while both can be affected by broad macro policy (like loose money), they do not neccessarily always drive each other, as the GDP deflator could be driven by a surge in export commodity pricing that is largely captured by foreign firms with little corresponding increase in pay to local workers and consequently little increase in CPI.
The relationship would have to be examined in terms of a single economy because the weight of outside factors confounds the relationship between the CPI and GDP