Maximum likelihood estimation framework for table-balancing adjustments

Balancing problems in national accounts and similar applications may be addressed by optimization methods that aim to maximize preservation of specific characteristics of the unadjusted data, for example, levels or time-series movements. However, published methods do not always indicate the assumptions that underpin these methods, making it hard to identify when those assumptions might be violated or how to generalize them to complex cases. Previous authors have observed that least-squares estimation methods correspond to maximum likelihood estimation (MLE) under normality assumptions. This paper explores this relationship in the context of published movement preservation/level preservation methods, showing how the MLE interpretation identifies implicit assumptions made by these methods and, hence, helps inform decisions about their use. It also notes a case where the MLE and preservation approaches diverge, and gives a framework for generalizing MLE approaches to complex scenarios.