3 ms·

Could you explain this please?

jerf 12y ago
"If every quarter this year was the same as this one, it would be a 2.9% decline for the year." sp332 uses the ~= symbols for approximately equal because technically you can't just divide the percentage by four like that. 2.9%/4 = .725% (exactly), but technically four quarters at .725% shrink each would produce 100%-((100%-.725%)^4) for the year, which is a 2.869...% decrease, not exactly 2.9%. But for small percents being compounded a small number of times it is a decent approximation, in this case thoroughly dominated by measurement inaccuracies and noise levels; the small percentage and the small number of compoundings work together to keep the error very small.
- sp332 12y ago
  Do you really think it's being compounded like that? I hadn't thought of that.
  - jerf 12y ago
    Uh... are you sure you didn't think of that? ;) Anyways, for the reasons given above, it's indistinguishable. If the economy was changing rapidly enough for it to matter, well, since it can pretty much only shrink at sufficient rates to make a difference we'd probably all have better things to do than argue about compounding correctly... But it is worth reminding people you can't do than in general, because it is easy to forget. See also the Rule of 72: http://en.wikipedia.org/wiki/Rule_of_72 http://en.wikipedia.org/wiki/Rule_of_72
deleted 12y ago
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kinghajj 12y ago
Meaning that if the rate of decline experienced in Q1 continued throughout the year, then the annual shrinkage would be about 3%. 1.0074^4 is about 1.03, so the actual shrinkage for the quarter in question was 0.74%.
logicallee 12y ago
if the economy shrinks by 0.05% on the Sunday before thanksgiving, you could annualize that by multiplying by 365 and getting an 18.25% shrink in the size of the American economy on that day. It would be an extremely false statement to write, "The U.S. Economy contracted by 18.25% on Sunday before Thanksgiving", which is how our title reads. ("The economy shrank almost 3 percent in Q1"). The number 3% doesn't appear anywhere, just as the number 18.25% doesn't appear anywhere. sp332's very good point is that it should include the word "annualized" or read "0.7%". A huge difference!

jerf 12y ago

"If every quarter this year was the same as this one, it would be a 2.9% decline for the year." sp332 uses the ~= symbols for approximately equal because technically you can't just divide the percentage by four like that. 2.9%/4 = .725% (exactly), but technically four quarters at .725% shrink each would produce 100%-((100%-.725%)^4) for the year, which is a 2.869...% decrease, not exactly 2.9%. But for small percents being compounded a small number of times it is a decent approximation, in this case thoroughly dominated by measurement inaccuracies and noise levels; the small percentage and the small number of compoundings work together to keep the error very small.

sp332 12y ago
Do you really think it's being compounded like that? I hadn't thought of that.
- jerf 12y ago
  Uh... are you sure you didn't think of that? ;) Anyways, for the reasons given above, it's indistinguishable. If the economy was changing rapidly enough for it to matter, well, since it can pretty much only shrink at sufficient rates to make a difference we'd probably all have better things to do than argue about compounding correctly... But it is worth reminding people you can't do than in general, because it is easy to forget. See also the Rule of 72: http://en.wikipedia.org/wiki/Rule_of_72 http://en.wikipedia.org/wiki/Rule_of_72

deleted 12y ago

[deleted]

kinghajj 12y ago

Meaning that if the rate of decline experienced in Q1 continued throughout the year, then the annual shrinkage would be about 3%. 1.0074^4 is about 1.03, so the actual shrinkage for the quarter in question was 0.74%.

logicallee 12y ago

if the economy shrinks by 0.05% on the Sunday before thanksgiving, you could annualize that by multiplying by 365 and getting an 18.25% shrink in the size of the American economy on that day. It would be an extremely false statement to write, "The U.S. Economy contracted by 18.25% on Sunday before Thanksgiving", which is how our title reads. ("The economy shrank almost 3 percent in Q1"). The number 3% doesn't appear anywhere, just as the number 18.25% doesn't appear anywhere. sp332's very good point is that it should include the word "annualized" or read "0.7%". A huge difference!