Abstract
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.
Highlights
We showed first that a Social Accounting Matrix (SAM) coefficient matrix can be interpreted as an ergodic Markov chain, and extended it as an information channel
We saw that this interpretation as an information channel is fully compatible with the cross entropy and related methods used to obtain missing information to build up the SAM matrix, and shown the relationship between the different objective functions themselves and with the channel quantities
We presented several examples of SAM information channels, computing the different quantities of the channel, as the entropy of the source, the entropy of the channel, and the mutual information and entropy of each row, and given an interpretation to each of these quantities
Summary
Social accounting matrixes (SAM) are used often to study the economy of a country or a region They capture the complete information about all (at the relevant level of resolution) transactions between economic agents in a specific economy for a specific period of time. We show that the SAM coefficients matrix can be thought of as an ergodic Markov chain, and subsequently can be represented as an information (or communication) channel. We add a toy example in Appendix A that follows step by step how to obtain from a toy 3 × 3 SAM matrix a Markov chain and an information channel with all associated mesures
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