Many economic variables are often reported only up to intervals, and n
ot up to exact points. This paper proves that as the data information
gets richer in the sense that the data partition gets finer, both the
Fisher information and the Kullback-Leibler divergence measure increas
e monotonically, approaching their continuous counterparts, respective
ly. This monotonicity property offers a valuable insight into designin
g an optimal number of cells to increase the power of specification te
sts based on cell counts.