While much of the debate has centered on growth prospects of the US economy in the aftermath of the crisis, a slightly overlooked issue is how the potential output has been affected by the crisis.
Admittedly, the measure of potential output is a bit hard to measure (take a look at the Wikipedia article on Macroeconomic Analysis), as is the related output gap variable. Standard measures range from pure statistical filter (like the Hodrick-Prescott Filter, or simply HP, the Band Pass filter), simple economic models (like the production function) or structural models (like state space models or even DSGE models). This is the reason why simple measures of potential output, like the one provided by CBO (Congressional Budget Office), are quite controversial, given their emphasis on the use of simple filters (see also the comments on Econbrowser).
It appears that studying the effects of the crisis is a daunting task. Nevertheless, a few studies discussed this topic. Furceri and Mourougane (2012) used panel data on OECD economies to estimate univariate autoregressive process for output, with a sample between 1960 and 2008. Their main finding was that financial crises tend to decrease potential output by 1.5 to 2.4%. However, the way financial crises impact potential output is much more complex than simple filters can reveal. For example, financial crises can affect the investments in capital, while the effects of labor participation are ambiguous.
A slightly different focus is found in the paper by Haltmaier (“Do Recessions Affect Potential Output?”). Again data panel techniques were used, however, unfortunately, only the HP filter has been applied to determine the trend. The most significant result is that the effects differ for emerging and developed economies. While emerging economies are mostly affected by the length of a recession, developed economies are actually affected by the depth of a crisis.
The number of studies on this topic remains rather low, given the importance of the concept of potential output. There is much work to be done here which could, for example, link austerity or Quantitative Easing policies to potential output.
Macroeconomcis Wikipedia: Potential Output
Macroeconomics Wikipedia: Output Gap