<p>The Laspeyres and Paasche indices are two widely used empirical indices. One of their key features is their ability to provide upper and lower bounds, respectively, for the cost-of-living index, which is the representative theoretical consumer price index. In this paper, we demonstrate that the Laspeyres and Paasche indices can also provide bounds in the context of productivity measurement. However, their role changes such that the Laspeyres and Paasche productivity indices provide the lower and upper bounds, respectively, for the Malmquist and Hicks-Moorsteen productivity indices, which are the representative theoretical productivity indices. This offers a compelling justification for interpreting true productivity growth as occurring between the Laspeyres and Paasche productivity indices, thereby supporting the use of empirical indices that lie between these bounds. Furthermore, we prove that the Laspeyres productivity index is necessarily lower than the Paasche index under Hicks-neutral technological change.</p>