Friday, January 2, 2015

The fine difference between GDP deflator and CPI

GDP Deflator and CPI or Consumer Price Index are both price level indices, with two crucial differences in the way they are calculated:

1) GDP deflator keeps quantities fixed at the "current year", whereas CPI keeps quantities fixed at the "base year".

So, going from 2013 (assuming that is the base year) to 2014 (current year), the value of the deflator in 2014 will be calculated using weights for different goods that correspond to their weights as observed in the 2014 economy. 

Deflator as of 2014 = Σ [P2014 (i) * X2014 (i)] / Σ [P2013 (i) * X2014 (i)] 

Or in other words, Deflator= (Nominal GDP in 2014 / Real GDP in 2014)

On the other hand CPI keeps quantities fixed at the "base year", so in this case:

CPI as  of 2014 = Σ [P2014 (i) * X2013 (i)] / Σ [P2013 (i) * X2013 (i)] 

(Fairly obvious, but let's note that P's represent prices, X's represent quantities)

2) In both cases above, I used a summation with variable i. It is important to note that in the case of deflator, the "i" loops over all the goods and services produced in the economy of that country, whereas in the case of CPI it loops over a well defined basket of goods that are identified as consumer goods.

This distinction is important for quite a few reasons. Inflation can be calculated both as the rate of change of deflator or as the rate of change of CPI, but the purpose for which that inflation estimate is required determines which of the two methods to use. For example, policy decisions often take CPI into account as it is a better indicator of inflation as it is felt by the general population. 

Secondly, CPI is much more volatile than Deflator. You would expect that to be the case since statistically the Deflator calculation seems to average (weighted-average, to be precise) a whole lot more quantities, and you'd expect the law of large numbers to kick in. But there's also an intuitive explanation on top of that: CPI has a large percentage presence of some of the most volatile sectors, such as, housing, energy and food.

For this reason there is another important measure, commonly called "core inflation", which when considering the rate of change of CPI excludes its volatile components like energy and food which vary a lot merely as a result of short term vagaries of weather, yields etc while not representing any structural change in economic trends.

A word of caveat. Both these measures are hard to estimate with precision, the GDP deflator more so because it has so many more moving parts. CPI estimations, although relatively simpler, have long been tainted with accusations of manipulation by government bodies that estimate them, and often have agendas that outweigh the pursuit of precision. Recently, the startup premise dot com has employed crowdsourcing principles to estimate food inflation from the ground up by having people send prices to them of food they buy everyday while their engine does the almost real time number crunching. You would be surprised at how much their estimates of food inflation differ from the "official" figures, especially for developing, populous countries like Brazil and India. 

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