Final answer:
The real business cycle theory can explain employment being procyclical, investment being more volatile than consumption, and average labor productivity being procyclical, but it cannot successfully identify the productivity shocks that have caused business cycle fluctuations.
Step-by-step explanation:
The real business cycle theory explains many of the major facts of business cycles, such as the fact that employment is procyclical (fact B), meaning employment tends to increase during booms and decrease during recessions. It also explains investment being more volatile than consumption (fact C), highlighting how businesses adjust their investment spending more than consumers adjust their consumption in response to economic fluctuations. Furthermore, it accounts for average labor productivity being procyclical (fact D), where productivity increases during expansions and decreases during recessions. However, the theory does not successfully explain identifying the productivity shocks that have caused business cycle fluctuations (fact A), as the source and nature of productivity shocks can be ambiguous and are difficult to measure directly.