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Per US media, the US economy grew 3.1% in 2018 Q4/Q4 and 2.9% in 2018 Y/Y. 2.9% seems the reference number in various databases (World Bank, Reuters, Bloomberg, etc) but what exactly does Q4/Q4 mean and which measures changes from Jan 1 2017 to Dec 31 2017 compared to Jan 1 2018 to Dec 31 2018

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If you could include the source(s) you were talking about that would be great. Without further info, my initial guess is that the Q4/Q4 means you compare GDP in 2018Q4 to GDP in 2017Q4. Y/Y means you compare GDP in the whole year of 2018 to that of 2017.

Upon further inspection, if you take a look at the US's real GDP, you'd get the following:

  • Growth in 2018Q4 compared to 2017Q4: 2.52%
  • Growth in 2018Q3 compared to 2017Q3: 3.13% [Link]
  • Growth in 2018 compared to 2017: 2.93% [Link]

So I think your Y/Y number is right... but the number for "2018Q4/Q4" might have been growth in Q3?


Update

It seems like the number reported was the initial estimate (which gives YoY growth of 2018Q4 to be 3.1% and 2018 to be 2.9%) in February 2019. The third estimate (which is what FRED uses) was released in December 2019 and yields YoY growth as calculated above.

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As mentioned, if you can identify the sources used for the reported figures, that should solve the problem. Art is correct in terms of the the unit of time with Q4/Q4 comparing growth from the same quarter from the prior year, and that the Y/Y based on the according calendar year.

His calculations appear to be correct as well, and my guess is that it was either misreported as Q4 growth annualized rate or misinterpreted as Q3/Q3. I got the same numbers from the same source, and I also compared the actual volume in chained 2012 dollars as a rough check. The volume measurement is likely an inflation baseline that I didn't verify to be the case.

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The difference between Q4/Q4 and yearly GDP growth is explained in a blog post by the New York Fed, Data Insight: Which Growth Rate? It’s a Weighty Subject; quoting the basic points:

The growth rate in real gross domestic product (GDP) is a conventional indicator of the economy’s health. But the two ways of measuring annual GDP growth can give very different answers. In 2013, GDP grew 2.2 percent on a year-over-year basis, but at a faster 3.1 percent rate on a Q4-over-Q4 basis. So, which measure is more meaningful? We show in this post that the Q4/Q4 metric is better since it only considers quarterly growth rates during the current year, while the Year/Year measure depends on quarterly growth rates in both the current and previous year and puts considerable weight on growth around the turn of the year.

A standard method for reporting annual growth in economic variables (as used by the Bureau of Economic Analysis) is to take the average level for the whole year and compare that with the average level in the previous year, which in our example would be 2012. This calculation results in the Year/Year growth rate:

The alternative measure of annual growth is to calculate Q4/Q4 growth: enter image description here

The Q4/Q4 measure is, for example, used by the Federal Reserve presidents and Board members in their economic projections. These two measures can give very different values for annual growth rates. The chart below shows them both from 1950 through 2013.

enter image description here

The next chart shows that the difference in the two measures has been over 4.0 percentage points at times, with the standard deviation of the difference being a fairly high 1.7 percentage points. The key insight from the illustration is that the difference between the two measures tends to be extreme right before and right after National Bureau of Economic Research-dated recessions, represented by the grey shaded areas.

enter image description here

[...]

The Q4/Q4 measure is approximately just an average of the four quarterly growth rates in a given year. Meanwhile, the Year/Year annual measure is a weighted average of the previous and current year’s quarterly growth rates, with the weights shaped like a tent. In fact, the most weight is placed on growth rates around the turn of the year. This feature is an unappealing one as we should care about all growth rates equally. Moreover, the quarterly growth rates from the previous year affect the Year/Year measure, which explains why it is relatively smoother than Q4/Q4 growth. This difference also explains why the gap in the two measures is particularly pronounced around turning points in the business cycle. The Q4/Q4 measure “picks up” any change in GDP growth faster than the Year/Year growth measure.

Despite the appeal of the Q4/Q4 measure, economic forecasters often report GDP growth in Year/Year terms with the notable exception of the Summary of Economic Projections by the Federal Open Market Committee. But, those looking for an alternative can always approximate the Q4/Q4 measure by simply averaging the quarterly growth rates, as we show in this post.

Some forecasters report both Q4/Q4 and yearly/annual changes; here is for example Northern Trust forecasts (March 2023):

enter image description here

In other expert forecasts, it may be not clear if the reported value refers to Q4/Q4 or to annual change; in such cases, averaging the forecasts for the individual quarters (when available), as explained in the quoted blog post above, gives an indication of the Q4/Q4 growth forecast.

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