MONOTONICITY OF THE FISHER INFORMATION AND THE KULLBACK-LEIBLER DIVERGENCE MEASURE

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.