Two Exact, Non-Arbitrary and General Methods of Decomposition Analysis

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Abstract
A common goal in economics is to attribute changes in a variable (Y) between two points in time to various causes, when the only information available is an equation expressing Y as a matrix product of several variables, and the values of all variables at the two dates. Past methods of decomposing temporal changes into various components are found to suffer from one or more problems: the can arbitrary due to the uncertainty concerning whether the expand the initial of final time period; inexact due to a residual term; and specific to cases in which the variable is a product of two matrices. This paper presents two decomposition methods which overcome all these three shortcomings.
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