# Quarterly GDP growth terminology: YoY vs QoQ

Quarterly GDP growth can be calculated either in terms of YoY change or — in the case of seasonally adjusted data — in terms of QoQ change. (A third option would be to annualize the QoQ rate.)

To start with a current example: In the U.S., GDP in Q1 2018 grew by 2.9% compared to Q1 2017 (= YoY), whereas it grew by 0.7% compared to Q4 2017 (= QoQ).

In Q4 2017, however, YoY growth was at 2.6%, whereas QoQ growth was at 0.7%. So GDP growth in Q1 2018 was higher compared to the previous quarter in terms of YoY (2.6% -> 2.9%), whereas it was slightly lower compared to the previous quarter in terms of QoQ (0.7% -> 0.6%).

Now in judging an economy's growth momentum, analysts typically focus on changes in QoQ growth rates - in the example above coming to a conclusion like "growth in the U.S. slightly lost momentum in Q1 2018".

My question is: Is there a different term to express changes in the YoY rate? To stay with the example above, if I comment on the fact that the U.S. YoY rate is up to 2.9% from 2.6%, concluding that there was a “strengthening of growth momentum” might be misleading (especially given the diverging picture based on changes in the QoQ rate).

• There are many correct ways to say it. It should definitely be clear whether you're referring to YoY growth or the (annualized) growth rate in Q1 2018 compared to Q4 2017. If it arises many times in the text, then you could define some shorthand that would be used, unless using different indicators which could require to be more explicit each time. Jun 15 '18 at 17:29

I have to highlight a flaw in the premise of your question.

For the quarterly NIPA statistics published and reported by the Bureau of Economic Statistics (bea.gov) under the U.S. Dept. of Commerce, the real growth rate shown in Table 1.1.1 in an annualized statistic based on the estimate of the QoQ level change in the real/constant-dollar value of the economy.

Current dollar quarterly values are given in Table 1.1.5. Real dollar quarterly values are given in Table 1.1.6. The growth rate reported in Table 1.1.1 is calculated from the values in Table 1.1.6 as follows: $$100\% * \left( \left( \frac{V_{q}}{V_{q-1}} \right)^4 - 1 \right).$$

This gives you the annualized growth rate.

The annual growth rate is YoY: $$100\% * \left( \left( \frac{V_{q}}{V_{q-4}} \right) - 1 \right).$$

And the quarterly growth rate is QoQ: $$100\% * \left( \left( \frac{V_{q}}{V_{q-1}} \right) - 1 \right).$$

As long as you clearly label what you are doing, there’s probably a lot of ways of phrasing the change in the year-on-year growth rate. However, anyone with experience will take those changes with a large grain of salt, as a result of “base effects.”

For relatively low growth rates, the annual rate of change is roughly equal to the sum of non-annualised quarterly growth rates over the last four quarters (or the average of annualised growth rates for 4 quarters). The change in the annual growth rate on quarter is therefore driven by the difference between the latest quarter, and the quarter that dropped out of the annual average. If that previous period was abnormally low, the current annual growth rate will jump higher, even if the quarterly growth rate is unchanged.

Since that hardly represents new information about the economy, that jump is not providing a lot of new information - we knew about that weak quarter for a long time.

Year-on-year changes are a great for time series plots, but you need to dig further if you want to discuss acceleration/deceleration.

• First of all, many thanks for your response! You say that "For relatively low growth rates, the annual rate of change is roughly equal to the sum of non-annualised quarterly growth rates over the last four quarters (...) The change in the annual growth rate on quarter is therefore driven by the difference between the latest quarter, and the quarter that dropped out of the annual average." Just to clarify: "Annual rate of change" and "annual growth rate" here refers to YoY growth in a certain quarter, right? (and not to, say, growth in full year 2018 compared to full year 2017) Jun 18 '18 at 8:05
• Yes, that’s quarter versus the quarter 4 quarters ago. A full year versus full year would be the percentage change of the 4 quarter moving average. Jun 18 '18 at 13:36
• Can you recommend any literature that specifically addresses things like these and related topics? Oct 22 '18 at 7:48
• @Thorsten The sort of observations I gave are what I picked up when creating charts for publication in industry. At most, the definitions might appear in a book on econometrics, but it would jump to more complicated things immediately. So there’s no particular books I used to pick it up. Oct 23 '18 at 11:56