Econometrics

Download Discrete Time Dynamic Economic Models: Theory and Empirical by Brian Ferguson, Guay Lim PDF

By Brian Ferguson, Guay Lim

Monetary habit is inherently dynamic. whereas issues switch continually through the years, a lot of financial research is predicated on discrete time, comparable to a month, region or a 12 months reflecting the periodic nature of data-collecting and decision-making.

This e-book introduces and develops the concepts of discrete time modelling beginning with first order distinction equation types and increase to platforms of distinction equations, alongside the best way overlaying such subject matters as:

* Non-linear distinction equation modles * Random walks and chaotic techniques * Optimisation in discrete time versions

This well-written and straightforward to persist with booklet should be essentially of curiosity to higher point scholars undertaking monetary modelling. the character of the book--bridging a niche among economics and econometric literature--will suggest that also is of curiosity to all teachers with an curiosity in econometrics and mathematical economics.

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Additional info for Discrete Time Dynamic Economic Models: Theory and Empirical Applications

Example text

Unit roots We can extend these results to add one which will be of importance when we discuss econometric applications of difference equations. 31) is obviously violated. 37) In other words, we have established a condition under which a SODE will have a root equal to 1; a unit root. Repeated roots Another special case arises when the discriminant (β12 − 4β2 ) = 0. 38) that is, we have repeated roots. 39) that is multiply each λ term by a value equal to the power on λ. 39) indeed holds. 40) The reason this result is useful is because it will let us solve for expressions for the unknown constants A1 and A2 even when we have a repeated root.

The case where the roots of our characteristic equation are complex numbers actually turns out to be very important in economic applications. We will deal with this issue shortly – for the moment, we shall assume that (β12 − 4β2 ) is positive and that both of our roots are real. Even when we restrict ourselves to the state where λ1 and λ2 are real, we still have four cases to deal with. Either of the two roots could be positive or negative, and either could be greater or less than 1 in absolute value.

95) is the same as the equilibrium price from a static demand and supply model. We have established, then, that so long as α1 > β1 , the price which the cobweb model eventually settles down to is the same as the static equilibrium price – that is, that once again the value of the equilibrium is not affected by the introduction of a dynamic element. The dynamic element does add something new to the model, though. Beyond the possibility that the equilibrium might be unstable, and the individual period market prices never converge on the long-run equilibrium value is the fact that this is one of the few economic models in which the root of the characteristic equation is negative.

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