I was investigating the deviation of real GDP is from its HP trend, expecting it to be negative from 2008 until now. I found real GDP has actually been above trend since about 2012. If I managed to get the HP filter to work correctly (as we all know how easy it is to make excel errors), a couple graphs may help demonstrate how trends can be misleading:
This first graph shows a vague but nice picture. No crazy spikes or downturns. Of course, time series data tend to smooth things out. Additionally, the trend tends to smooth out the small number of kinks that do exist.
The next graph is the same series, just chopped off at the 2007-2013 range. Here, it appears the 2008 financial crash was just a deviation from the trend and about 2012 is when real GDP started operating above trend.
The graph above looks like a positive picture. But, we have to keep in mind the trend was based off of all of the data, 1947 until the present. This means the trend was able to capture the dip in real GDP and adjust accordingly to make real GDP a little bit below trend sometimes and a little bit above trend sometimes. In other words, if we summed up all the deviations from the trend, we'd get zero.
I don't know too much about the theory of real business cycles but when I do hear about it, I always hear it in the context of "output fluctuating around a long-term trend". But in this case, being above the trend doesn't mean the economy is doing well or we are in a time of expansion, it just means in order for the deviations to equal zero, the deviation from trend must be positive now.
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