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# First-order difference equations

DOI link for First-order difference equations

First-order difference equations book

# First-order difference equations

DOI link for First-order difference equations

First-order difference equations book

## ABSTRACT

Introduction The simplest type of difference equation is a linear, ﬁrst-order equation, of the general form:

Yt = αYt−1 + g (2.1) In an equation like this one, the time subscript, ‘t’, should be thought of not as representing calendar time, but rather elapsed time – the amount of time which has passed since the dynamic process, which we are studying, began. As written, when the term g is non-zero, Equation (2.1) is called a non-homogeneous equation; when g is equal to zero, Equation (2.1) is called a homogeneous equation. Furthermore, since α is a constant, Equation (2.1) is also an example of a linear, constant coefﬁcient ﬁrst-order difference equation (FODE). Most economic applications of FODE involve constant coefﬁcient models, although this is not a requirement.