Interpreting Social Accounting Matrix (SAM) as an Information Channel

Information theory, and the concept of information channel, allows us to calculate the mutual information between the source (input) and the receiver (output), both represented by probability distributions over their possible states. In this paper, we use the theory behind the information channel to provide an enhanced interpretation to a Social Accounting Matrix (SAM), a square matrix whose columns and rows present the expenditure and receipt accounts of economic actors. Under our interpretation, the SAM's coefficients, which, conceptually, can be viewed as a Markov chain, can be interpreted as an information channel, allowing us to optimize the desired level of aggregation within the SAM. In addition, the developed information measures can describe accurately the evolution of a SAM over time. Interpreting the SAM matrix as an ergodic chain could show the effect of a shock on the economy after several periods or economic cycles. Under our new framework, finding the power limit of the matrix allows one to check (and confirm) whether the matrix is well-constructed (irreducible and aperiodic), and obtain new optimization functions to balance the SAM matrix. In addition to the theory, we also provide two empirical examples that support our channel concept and help to understand the associated measures.