I was using R to calculate the annualized quarterly growth rate of real GDP by 400*diff(log(rgdp)).

If I perform in this way some of the percentage change is big.

However, if I calculate as 100*diff(log(rgdp)) than results seems to be accurate as what shows up on the most of the website.

Why is this happening? follow by the growth formula it should be multiplied by 400, not 100.

  • $\begingroup$ Is the data you have in GDP annual or quarterly? if it is annual, then the 100 is appropriate. $\endgroup$
    – Regio
    Commented Apr 22, 2019 at 17:25

2 Answers 2


Perhaps quarterly growth should be multiplied by 400, but not annualized quarterly growth?

  • $\begingroup$ is this not more appropriately a comment than an answer? $\endgroup$ Commented Apr 11, 2021 at 19:11
  • $\begingroup$ @JesperHybel I felt like this answered the question in full, but if you disagree you can raise a flag to have this converted into a comment. And of course you are encouraged to post a better answer. $\endgroup$
    – Giskard
    Commented Apr 11, 2021 at 19:37
  • 1
    $\begingroup$ I dont really know so I dont disagree. I was just reacting to the use of »perhaps« and »?« thinking you perhaps misposted. $\endgroup$ Commented Apr 12, 2021 at 1:07

I usually take the 4th difference for annualized quarterly data.

x2 <- diff(log(x1), lag=4) * 100 

Indeed, you need to see the difference with the same quarter the past year, thus 4 periods before !

With your data, you would have

annualized_gdp = diff(log(rgdp), 4)*100

and it should give the good series ! In addition, it should withdraw any saisonnality in your data


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