ST45_1 Uncertainty measures for economic accounts

Document date: 
Monday, 28 August, 2017

Many macro-economic figures, for instance arising in the context of national economic and social accounting systems, are connected by known constraints. We refer to such identities as accounting equations. The actual input estimates, often based on a variety of sources, usually do not automatically satisfy the relationship due to measurement and sampling errors. The estimation of an accounting equation involves then an adjustment or reconciliation step by which the input estimates are modified to conform to the known identity. In this paper we consider the measurement of uncertainty in such reconciled estimated accounting equations. The initial input uncertainty can in principle be quantified by a joint covariance or mean squared error matrix. However, this does not take into account the adjustment effects. Moreover, a matrix of uncertainty measures like this is not easy to present or digest. We consider an accounting equation as a single entity and develop scalar uncertainty measures that more directly capture the adjustment effect as well as the relative contribution of the various input estimates to the final estimated account. We develop two approaches for defining these scalar measures. For each approach we define two variants of scalar measures and using a simple simulation example demonstrate the application of these measures.