INTEREST-RATE RULES: The Welfare Loss from Price-Level Instability 3

We show in the Appendix that, under these assumptions, a second-order approximation for W is given by
where the suppressed final terms are either independent of the evolution of the endogenous variables, or of third order or smaller in the size of the exogenous disturbances. Note that this welfare measure depends solely upon the allocation of real resources, summarized by the pattern of levels of production {yt{z)} at each point in time. However, equation (1.30) indicates that welfare depends not only upon the degree to which aggregate output deviates from the natural level of output F5, but also upon the degree of (inefficient) dispersion of output levels across the different varieties of goods being produced at each point in time. You can now get an amazingly affordable fast easy payday loan without leaving the comfort of your home and embarrassing yourself in front of anyone. You just need to apply with us here to get your financial problems solved in an instant. Trust us today and get your money in a few hours.
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INTEREST-RATE RULES: The Welfare Loss from Price-Level Instability 2

Linearization around this particular (optimal) steady state is extremely convenient, since our approximate measure of W takes an especially simple form in that case. In particular, in this case our second-order approximation for W depends only upon a first-order approximation to the equilibrium responses of inflation and output to the exogenous shocks. This means that we can solve a log-linear approximation to the model’s equilibrium conditions using standard linear methods, as sketched in the previous subsection, and obtain an approximation to W that neglects only terms of third order and higher in the deviations from the steady state. This result depends upon the absence of any first-order contribution to our welfare measure from changes in the average level of output under alternative rules (as a result of the optimality of the level Y relative to which we consider deviations); for if W contained a term of first order in the average level of output, then second-order terms in the equations determining output would matter for a second-order approximation to W. If quick loans cash can fix your financial problems right now, then you should get that money from a lender you can trust without waiting any further. We will be glad to help you by offering a loan for as long as you need. Come and find our offer at Link and see how affordable those loans are.
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INTEREST-RATE RULES: The Welfare Loss from Price-Level Instability

One of the primary advantages of our derivation of our structural equations from explicit optimizing foundations is that we are able to evaluate alternative monetary policy rules in terms of their welfare effects. Specifically, we consider the effects upon the average level oi welfare
in the stationary equilibrium associated with one or another policy rule within the class that we consider.
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INTEREST-RATE RULES: Framework for Analysis 8

Note that because the elements of Z\ refer to exogenous states (underlying states for the dynamics of the real disturbances s*)} unlike the elements of Zt (which correspond to endogenous variables of our model), this specification does not imply the existence of any feedback from the evolution of the endogenous variables to the exogenous disturbance processes st. What this construction does guarantee is that the empirical impulse response functions of inflation, output and interest rates to the two VAR disturbances orthogonal to the monetary policy shock are identical to the impulse responses predicted by our theoretical model.
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