Download Optimal Control, Expectations and Uncertainty by Sean Holly PDF

By Sean Holly

The rational expectancies revolution and different advancements in economics (notably video game idea) have essentially altered the applying of optimum keep an eye on idea to monetary forecasting and making plans. specifically, they've got proven that fiscal structures can't be modeled simplistically on actual platforms. in spite of the fact that, because the authors exhibit, those advancements have vastly superior our realizing of ways an financial system features, and now guarantee that optimum keep an eye on conception to be utilized even more successfully to financial modeling and making plans.

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1 Dynamic equivalences The equivalence between the various forms of econometric model representation can be seen from the dynamic structure. , are the matrix multipliers of the econometric model. Thus n 0 = Dx, A o = De are the impact multipliers of the policy instruments and exogenous variables respectively. Similarly the 23 The final form 19 matrices Tlh Ah Ti9 i = 2 , 3 , . . are the dynamic matrix multipliers at lag i. So each element describes the impulse response of the endogenous variables to a one-off shock to the policy instruments, exogenous variables and random disturbances.

Moreover, there is a class of macroeconomic models which, under certain assumptions about the formation of expectations by private agents, is not always controllable. This class of model is examined later, in chapter 7. 1 Static controllability Suppose there are m targets yt (a subset of all the endogenous variables in yt), and n instruments xt9 in each decision period t = 1 , . . , T. A naive strategy is 22 2 THEORY OF ECONOMIC POLICY AND THE LINEAR MODEL to pick xt to reach the desired yt values period by period, each time taking all lagged variables and expected values of other exogenous variables as temporarily fixed.

A more tractable formulation can be derived if we consider the ancillary problem of transferring the value of an endogenous variable from any initial point to any other point. 10) is of rank t (the number of endogenous variables) where t>g. 10) reduces to rank(P*) = g. 3). Indeed this controllability condition for the non-minimal realisation advocated by Chow (1975) makes explicit exactly this point. 12) where now and and (without loss of generality) all uncontrollables have been set to zero again.

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