Could a leap year matter so much to GDP accounting?

My good friend Vipul Mathur has finally started blogging. This is like inviting competition for oneself and threaten yourself to oblivion.

His first post is on this leap year effect on Japan’s GDP:

Sometimes news can make your head spin. Just this week, Japan’s GDP numbers were announced and they report that the GDP has expanded by an annualized 1.9% and about 0.5% on a quarter-on-quarter basis. Previous to these announcements, Japan was struggling to avert a recession, which is not surprising considering how it has been struggling to barely keep itself afloat for the last decade.

So you will think that a positive growth should really be a good news for Japan, right? Wrong. Instead of rejoicing in the growth numbers the economists seem worried. Well, we are all too familiar with their quibbles and quarrels but this time around the reason for their worry has got nothing to do with economics! 

Rather a queer phenomenon seems to have inflated these growth numbers: leap-year effect.

So, what explains this? You either earn an extra income on 29th or pay an extra bill on 29th. These extras show in the numbers. If we remove this leap year effect, GDP annual declines to 0.92%…

But for a moment think about this: what really changes on 29th Feb? If you are a regular employee, do you get paid more? Do you pay an extra rental for the apartment? Do you pay extra on the monthly travel pass, membership cards? No, not really. But then do you pay for an extra day of gas, electricity bills? Do you buy groceries for that extra day? Yes!

So arguably, there are some portions of GDP which are insulated from the extra day effect, and some which will get increased. A per-day GDP estimate has both these portions embedded. In order to disentangle the portion which really gets affected by an extra day, we follow a rough fraction, say, 25%. Empirically, this number will be different, but for our immediate purpose this is a start.

So now our job is almost done. All that we have to do is to calculate a per-day GDP number and 25% of this is what we will deduct from the Jan-Mar GDP levels to adjust for the leap-year effect. Here are the sample calculations based on the actual numbers for Japan.

# Item Value Comments
a GDP in Oct-Dec 2015 4.4515 Japan’s GDP in trillion $
b Q-o-Q Growth Rate 0.50% Official Figures
c GDP in Jan-Mar 2016 4.47 a*(1+b)
d Annualized Growth Rate 2.02% (1+b)^4-1
e GDP per day in Oct-Dec 0.05 a/(31 Oct+ 30 Nov+31 Dec)
f GDP Increment on Leap Day 0.01 25% of e
g GDP in Jan-Mar without Leap Day 4.46 c-e
h Modified Q-o-Q growth rate 0.23% (c/a)-1
i Modified Annualized Growth Rate 0.92% (1+h)^4
j Difference in q-o-q growth 0.27% b-h
k Difference in annualized growth 1.10% d-k

Well, the numbers do turn out to be similar to what Japanese have been suggesting: the difference in GDP growth rate on a q-o-q basis is around 0.27% and a difference of 1.1% on an annualized basis! Voila! Who would have thought that an innocuous day could make such a difference! 

For a country like Japan, where the q-o-q growth numbers are <0.5%, this makes a huge difference. What about India? Well, the leap year effect will definitely be there, but will it matter enough? Well that depends on how much portion of GDP really gets affected by an extra day. For our above calculations that portion was 25%. However, this will vary, country by country – and this number is really the crucial number here. The higher it is, the higher will be the leap year adjustment. 

Hmm.

This is like the anomaly literature in finance. Interesting to note the same in macro too..

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