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
quarteronquarter 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: leapyear effect.
What could be this leap
year effect? Well, as the name suggests, it has got to do with an extra day in
February. A JanMar quarter in 2016 will have to be adjusted for this one day
before we compare it with a JanMar quarter of 2015. But how much can just one
extra day of spending, (not of earning, mind you) really change the growth numbers?
A lot
apparently, as the Japanese economists seem to point out and this is where the
story starts to get interesting.
According to some
estimates:
“The effect of the extra day from the leap year
may have magnified firstquarter growth by about 0.9 percentage points on an
annualized basis and by 0.3 percentage points on a qoq basis” Reuters
“Excluding the impact of leap year, which added
an extra day to February, GDP probably expanded around 0.2 percent [on a qoq
basis, instead of the reported 0.5%]” Reuters
Economists are infamous
with their craft, but a 0.3% error on a 0.5% estimate is just too much trickery for even the economists! So, what is really going on in here?
To understand the
intricacies, let’s just brush up our concepts on GDP calculations. A typical year is
divided into four quarters. While a calendar year starts with JanMar quarter,
a fiscal year starts with the AprJun quarter. A quarteronquarter growth rate
is measured as the GDP growth in the current quarter over the preceding
quarter. For example, a qoq growth rate for Q4 201516 (fiscal year), would
be the growth that happened in the months of JanMarch 2016 over that happened
in OctDec 2015.
From this qoq growth rate, an annualized growth rate is
derived. This annualized growth rate is a hypothetical number which
extrapolates the qoq growth rate over the next three quarters to arrive at an
annual figure, with the assumption that the next three quarters will behave
exactly same as the current quarter.
With these definitions under the belt, let’s proceed to
frame our problem here. Consider an economy where within a quarter, each day is
exactly identical in terms of economic activities. People wake up, work,
produce, consume, save and sleep in exactly the same amount and fashion each
day of that quarter. Once every day in a quarter is identical, we can calculate "per day GDP" by simply dividing the GDP in a quarter with the total days in a quarter. We can then postulate that this per day GDP is what would have been counted for 29th Feb, and then simply deduct this from the quarterly numbers to get the leapyear adjusted number for GDP in the JanMar quarter.
But for a moment think
about this: what really changes on 29^{th} 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 perday 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 perday GDP number and 25% of this is what we will deduct
from the JanMar GDP levels to adjust for the leapyear effect. Here are the
sample calculations based on the actual numbers for Japan.
#

Item

Value

Comments

a

GDP in OctDec 2015

4.4515

Japan's GDP in trillion $

b

QoQ Growth Rate

0.50%

Official Figures

c

GDP in JanMar 2016

4.4737

a*(1+b)

d

Annualized Growth Rate

2.02%

(1+b)^41

e

GDP per day in OctDec

0.0484

a/(31 Oct+ 30 Nov+31 Dec)

f

GDP Increment on Leap Day

0.0121

25% of e

g

GDP in JanMar without Leap
Day

4.4616

ce

h

Modified QoQ growth rate

0.23%

(h/a)1

i

Modified Annualized Growth Rate

0.92%

(1+h)^4

j

Difference in qoq growth

0.27%

bh

k

Difference in annualized growth

1.10%

di

Well, the numbers do turn out to be similar to what Japanese have been suggesting: the difference in GDP
growth rate on a qoq 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 qoq 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.
All that said and done, the basic dilemma remains: why should we work when we don't get paid extra! Well, unsurprisingly, we are not alone in this thought. Infact there is a Petition to make leap day a holiday!
Well written and so simplistically explained. Kudos to the author.
ReplyDeleteThe portion of GDP that gets affected by an extra day, it must have a causal association with the population of the country?
In that case, India's claim of the fastest growing economy for the last fiscal year, should that be taken on face value?
Great start. Finally someone has got going after many days of asking him to start a blog. But then this is like creating problems for onself. :)
ReplyDeleteLook forward to more such gyan. AS have been off these topics for a while, will rely on this one. Hope it remains regular.
Won't such an effect exist for holidays or even differing number of weekends?
ReplyDelete