Benchmarking and movement preservation. Evidences from real-life and simulated series

The benchmarking problem arises when time series data for the same target variable are measured at different frequencies with different level of accuracy, and there is the need to remove discrepancies between annual benchmarks and corresponding sums of the sub-annual values. Two widely used benchmarking procedures are the Modified Denton (Proportional First Differences - PFD) and the Causey and Trager (Growth Rates Preservation - GRP) techniques. The PFD procedure, which looks for benchmarked estimates aimed at minimizing the sum of squared proportional differences between the target and the unbenchmarked values, involves simple matrix operations. The GRP technique is a non-linear procedure based on a `true' movement preservation principle, according to which the sum of squared differences between the growth rates of the target and of the unbenchmarked series is minimized. In the literature it is often claimed that the PFD procedure produces results very close to those obtained through the GRP procedure. In this paper we study the conditions under which this result holds, by looking at an artificial and a real-life economic series, and by means of a simulation exercise.