TOTEX Malmquist index for RPI-X regulation: Does it correctly estimate the true frontier shift?

The factor X in the RPI-X regulation aims to adjust price or revenue allowances to changes in total factor productivity and input prices. A cost Malmquist index can be applied to determine the efficient cost change (ECC). However, regulators typically do not have the necessary data on input quantities and prices. Instead, a TOTEX Malmquist allows for calculating the total cost change (TCC). We study under which conditions the TCC of a TOTEX Malmquist correctly estimates the true ECC. We have two main findings. TCC is an undistorted estimate of ECC if (1) the frontier firms are either fully efficient, or if their inefficiency remain constant over time, and (2) if input prices either stay constant or change by the same proportion for all firms.