# Solution of Linear and Non-Linear Systems

• D. W. Challen
• A. J. Hagger
Chapter

## Abstract

In the previous chapter we defined a macroeconometric system as a set of n numerical relationships linking n endogenous variables and m predetermined variables. Since KK systems are just a special type of macroeconometric system, this definition applies to a KK system. A KK system can thus be viewed as a set of n numerical simultaneous equations in which the n endogenous variables are the ‘unknowns’ and the m predetermined variables the ‘knowns’. Moreover, as with any set of simultaneous equations which has as many equations as unknowns, one can use a KK system, at least in principle, to solve for the unknowns (the n endogenous variables) in terms of the knowns (the m predetermined variables). In other words, with the help of a KK system one can find those values of the n endogenous variables which satisfy the system as a whole for specified values of the m predetermined variables, i.e. for specified values of the lagged endogenous variables and the lagged and unlagged exogenous variables. In this chapter we shall explain the procedures which are commonly used in practice to solve KK systems in this sense. A good understanding of these solution procedures is essential at this stage because in the chapters which follow we shall be dealing with a number of topics relating to the construction, evaluation and use of KK systems in which system solution plays a vital part.

## Preview

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