Introduction

Thus far, the economy has been given by a set of national accounts with unquestioned precision, but confidentiality, reporting, and measurement problems attach error components to economic data and render the derived constructs – multipliers, (potential) GNP, TFP, etc. – imprecise as well. There are two ways to analyze the transmission of errors. A pure error analysis, without imposition of any stochastic structure, involves the calculation of upper and lower bounds. For example, if GNP is to be determined on the basis of sectoral value-added data, the lower bound would be the sum of the lower bounds of the data and the upper bound of GNP would be the sum of the upper bounds of the sectoral value-added figures. A more interesting way to analyze the transmission of errors is by means of a stochastic framework; the errors are considered random variables, with given probability distributions. The worst-case and best-case scenarios may still occur, but with low probability, because it is unlikely that all (value-added) components assume their lower or upper values simultaneously. Errors tend to cancel out and hence sharper bounds can be derived for the economic variables of interest.

Stochastics

List data or underlying variables listed in vector a, estimated by random variable â with mean E(â) = a and variance V(â). The former locates the levels of the data and the latter measures their precision. List the economic variables of interest in a vector b. They will be a function of the data: b = β(a).