The Fundamental Input - Output Identities with Heterogeneous Prices and Imperfect Economic Accounts

The fundamental input-output identities that express the solution for commodity output and price also guarantee that nominal GDP is the same whether measured as the sum of final demand expenditures or as the sum of value added. In the simplified framework in which the identities are usually presented, all relationships hold exactly, and there is one homogenous price for each commodity. However, when constructing a model of a real economy, one usually needs to confront several issues. First, prices may vary across the row. Second, input-output identities often do not hold with available data . Finally, final demand and value added from the input-output table may not be equal to the corresponding figures from the aggregate national accounts. The solution to the first problem is simply to use a more complicated input-output identity. Often, the solution to the last two problems is to introduce discrepancy variables that can be added to final demand, unit value added, or aggregate final demand and value added concepts to force the necessary identities to hold. Such discrepancies are then usually held constant for the forecast interval of the model. This paper first discusses how non-homogenous prices are handled in several Inforum models. Next, we investigate the conditions under which nominal GDP as measured by total final demand or total value added is still equivalent, in the presence of final demand and value added discrepancies. Finally, several other types of discrepancies are discussed, that arise from inconsistent input-output and national accounts data.