Estimation of time series of latent variables in an accounting system

We present an approach for estimating time series of a set of latent variables satisfying accounting identities. We concentrate on a simple case study and comment on possible generalizations. The model consists of three main parts: (i) A system of accounting identities, e.g., a subsystem of the national accounts, which variables are considered latent. (ii) A measurement model connecting the latent variables to indicators from different sources, including micro and macro data. (iii) Stochastic processes of a subset of the latent variables in the accounting system, with stochastic trend and random walk as alternative models. The model is given a state space formulation and the Kalman filter and EM algorithms implemented in the software STAMP, are used to estimate the parameters and the time series of the latent variables. The approach is applied to estimate petrol consumption of the household and nonhousehold sectors in Norway 1973-1995, from observation of macro data on total petrol consumption and survey data of household expenditures for petrol. Satisfactory model properties are obtained. The stochastic trend model gives smooth and plausible estimates of the time series of latent petrol consumption of the household and nonhousehold sectors.