The Disappointing Recovery of Output after 2009
John Fernald, Robert Hall, James Stock, Mark Watson Link
Abstract
U.S. output has expanded only slowly since the recession trough in 2009, even though the unemployment rate has essentially returned to a precrisis, normal level. We use a growth-accounting decomposition to explore explanations for the output shortfall, giving full treatment to cyclical effects that, given the depth of the recession, should have implied unusually fast growth. We find that the growth shortfall has almost entirely reflected two factors: the slow growth of total factor productivity, and the decline in labor force participation. Both factors reflect powerful adverse forces that are largely unrelated to the financial crisis and recession—and that were in play before the recession.
Some weird arbitrary choices in this paper but per @hodrickExplorationTrendCycleDecomposition2020 this is supposedly an example of “gold standard” econometric research, so I’ll try to follow the logic. I do think the use of unemployment to measure the state of the cycle is interesting and potentially applicable to other domains.
Note that they are decomposing the growth rate itself, not the level of the series.
When measuring growth rates they use the annualized Q/Q growth rate, which I’m not used to seeing but perhaps worth thinking about for my purposes. I’d imagine that this would tend to be highly seasonal (EDIT: Likely using seasonally adjusted data so this point is moot). Seems like the key to this is that changes in unemployment period to period have an expected value of zero. Thus a cycle that is a linear combination of various leads and lags of the change in unemployment will also have a zero expected value, though it might fluctuate up and down as we’d hope a cycle would.
Unemployment recovers fairly consistently across recessions, as per @hallWhyHasUS, but output seemed to recover much more slowly in the financial crisis than in prior recessions. This paper posits that the reason lies in the trend level of GDP having slowed substantially during this time, such that the contemporaneous output gap was less pronounced than commonly believed.
Key assumption is that the capital-output ratio should be stationary and reasonably stable over time. Thus increases and decreases can be interpreted as strong signals of either capital surplus and shortfall relative to the “ideal” level.
Good example of a DFM, estimated on detrended growth rates of various economic variables. Here the DFM is used to forecast the cyclical component of each series, while the trend in each series is assumed to be constant at wherever it ended at the 2009 trough:
The 123 series are transformed into growth rates (for activity variables; see the online appendix for the details of other series); low-frequency trends are extracted, as discussed above; and six factors are then estimated using principal components. … In the notation of equation 6, the factor model forecast of is the sum of the trend projection μt and the projection of computed using the detrended factors. Thus, the forecast error is an estimate of the irregular part ; subtracting this forecast error measures the growth shortfall of .
Standard deviation of GDP components 
