What does this equation mean?

The paper checks this with a seeded simulation rather than leaving it asymptotic. A competitive industry of 400 comparably sized firms (HHI = 0.0031, $N_e$ $\approx$ 321 ) and a concentrated industry of 40 Zipf-distributed firms (HHI = 0.1006, $N_e$ $\approx$ 10 ) were each run through 20,000 replicate neutral periods with no selection whatsoever operating. A reading of half a log point of apparent “selection” — the kind of magnitude an Olley-Pakes-style decomposition would report without hesitation as meaningful reallocation — occurred in 4.0 percent of neutral periods in the competitive industry and in 49.7 percent of neutral periods in the concentrated one. In an industry with an effective population of ten, roughly a coin flip’s worth of periods will show economically meaningful “selection” with none present. The paper adds a further caution for anyone tempted to reach for a textbook significance test on a covariance term like this: real firm growth rates are tent-shaped and fat-tailed rather than Gaussian, so a nominal five-percent test can carry a true false-positive rate several times that whenever the effective population is small, and bootstrap or simulated critical values are recommended over normal-theory ones in exactly those settings.