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 http://www.easyloans-now.com/ to get your financial problems solved in an instant. Trust us today and get your money in a few hours.

The dispersion of output levels directly corresponds, in equilibrium, to the degree of dispersion of output prices. Prices differ across goods, in turn, only because of variation in the overall price level (together with the fact that different suppliers adjust their prices at different times). The £[var2{logyt(2)}] term in (1.30) can accordingly be expressed as a function of the aggregate inflation process, as shown in the Appendix. With this substitution, we obtain

Here 7Г* again denotes the steady-state rate of inflation associated with a given policy rule (the rate of inflation when the shocks ft = 0 for all time); it corresponds, neglecting terms of second order or higher, to the average rate of inflation (or to the unconditional mean of 7r) in the stationary equilibrium. The notation “t.i.p.” refers to the terms that are independent of policy.