The cyclical behavior of work effort is rather puzzling. One would expect that people would work harder during a recession to avoid getting laid off, yet measures of labor productivity (per worker or per hour) are consistently positively correlated with GDP. This also runs counter to the argument that the least productive workers are laid off first in a recession, which should improve the productivity of the remaining ones through a composition effect. Survey data is much more mixed, though, but that is often based on perceptions rather than facts.
One reason why labor productivity may vary could also come from counterproductive efforts from the workforce: stealing, sabotaging, annoying co-workers. Aniruddha Bagchi and Siddhartha Bandyopadhyay fold all these activities under the crime label and ask whether this is linked to the business cycle. There is no data about this, unless you think like the authors that this is only dimension that makes labor productivity vary. So you are left with purely theoretical exercises. The authors highlight here to contradictory effects. First, pretty much everyone gets a job in a boom, including those "criminals," which would lead to a negative correlation of labor productivity with output. But this effect could go the other way if labor market prospects are likely to weaken and jeopardize re-employment. Second, they assume that deviancy requires a setup cost, which one is less likely to bear when the labor market weakens. This would even reinforce this negative correlation.
This possible ambiguity would need to be sorted out with a tight calibration exercise at least, or some structural estimation with hidden variables. But the authors just wave hands and claim things can go either way. In any case, they are probably right not to pursue. Using a two-period model to study business cycles is silly anyway.