# Annual, Annualized, q4/q4 Growth Rates: A Graphical Depiction

Why do reported growth rates differ for the same variable? Refer to the last three years of GDP data to see…

Figure 1: Quarterly GDP, SAAR, FRED series GDPC1 (dark red line), annual, FRED series GDPCA (green bars), in billions of Chained 2009\$. 2017 q4/q4 growth rate (red arrow); annual 2017 y/y growth rate (green arrow); 2017Q4 q/q SAAR growth rate (blue arrow); 2016Q1 y/y SAAR growth rate (black arrow). Source: BEA, 2017Q4 3rd release via FRED, and author’s calculations.

So, there are several ways to calculate the growth rate over the course of the year. They will almost invariably differ, perhaps substantially, when GDP is either growing very rapidly or shrinking very rapidly. And there is no “right” way. If one wants to calculate the most recent growth experience, one might stress q/q. If one wants to look at a longer horizon, then one might want to use the quarterly y/y. If one thinks quarterly series are very noisy, one might want to look at annual y/y.

Note: SAAR denotes Seasonally Adjusted at Annual Rates.

Additional Note: One could average the q/q annualized growth rates over the four quarters of 2017 to try to get 2017 q4/q4 growth rate. This calculation leads to an approximation, which gets worse the more variable growth rates are (unless growth rates are calculated as log-differences — which is part of the reason economists like to express variables in logs and log differences…).

## 10 thoughts on “Annual, Annualized, q4/q4 Growth Rates: A Graphical Depiction”

1. Moses Herzog

@ Menzie
I have kind of a “philosophical” question for you. This is getting back to the chain-index discussion. And if this comes across as being hypercritical or judgmental of economists, that is not what I mean. More of a curiosity about human beings in general. Irving Fisher came up with his “Ideal Fisher” method in 1922. It was only really used or “adapted” into official stats in 1996. That is 74 years later, correct?? Isn’t that kind of weird when you think about it??—especially if we consider economists are a pretty cerebral lot overall. Why the delay there??

1. Menzie Chinn Post author

Moses Herzog: There’s more computation with the Fisher ideal indices, and with Paasche and Laspeyres indices, can refer to a bundle in a specific year. With relatively small changes in relative prices, the issues with fixed base year were minimal…which stopped being the case with the advent of rapid decreases in (quality adjusted) computer equiptment prices.

2. Moses Herzog

I saw a paper that argued using t-3 as a weight was slightly better than using t-2 as a weight. Curious if you had any thoughts on that. I mean if we’re using all these weird ways to get a number ahead of time (such as Atlanta Fed’s GDPNow) wouldn’t the idea be to get the most accurate number as possible??

2. Moses Herzog

Drinking Monster drink and popping aspirin while I wait for a relative to come back from cataract surgery. I really f’ing hate living in a dry house.

3. Moses Herzog

If anyone knows or is aware of a FREE link or FREE pdf download version of the Vavares, Prakken, Guirl paper on Chain-Indexes and the particulars thereof, that would be, like, super awesomely cool if you could put that in this comment thread someplace. Allow me to pre-emptively say thank you to anyone who can do that.

4. Not Trampis

We down under and in almost every other country always use SAAR. the OECD and the IMF use it or variations of it.

Simply get rid of annualised rates they are useless IMHO

5. Moses Herzog

Warning: off-topic of post
I thought this was a terrific post by “EconoFact”. They are discussing how US legislators are “forgetting” (forgetting, or being bribed not to recall??) the economic crisis of 2007–’08, which was caused largely by financial derivatives/swaps and banks taking exorbitant amounts of debt instruments on their balance sheets, with little equity to cover the bets.