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As I understand it, economic downturn means that economic growth is significantly slowing down or entering into recession. (If anyone wants to correct me, please do so). i.e. Growth rate is decreasing.

But what if the country is already in recession, but its growth rate is increasing? i.e. -5% one year, -3% the next, -2.5% the next, etc. Is this still classed as downturn (since the economy is still shrinking) or is it not since the growth rate is actually increasing despite being negative?

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I'm no macroeconomist, so other will correct me if I am wrong, but I would use the following definition:

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More formally, if $Y(t)$ is GDP at time $t$, one could express this as

Recession: $Y'(t)<0$ for 6+ months

downturn: $Y''(t)<0$

recovery: $Y''(t)>0$.

The definition of recession (2 quarters of negative growth) is widely standardised. I think the definition of downturn and recovery is less standard, and therefore more subject to debate.

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    $\begingroup$ At the top of your recovery period you have still not reached the middle GDP level of the downturn period. Perhaps the recovery is longer? $\endgroup$ – Giskard Oct 19 '16 at 20:01
  • $\begingroup$ Historically GDP growth has had a positive long-term trend $\endgroup$ – Henry Oct 19 '16 at 20:25
  • $\begingroup$ What the historical trend has been is irrelevant. If you have a good definition for downturn then it should apply to any profile of growth, whether empirical or fictitious. $\endgroup$ – Ubiquitous Oct 20 '16 at 7:01
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By any reasonable definition a period of economic downturn has to mean that the slope of GDP vs time is negative. If the second derivative (i.e. rate of change of slope) is positive then we could say that the downturn is becoming less severe, but its still a downturn until the slope goes positive again.

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