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.

Here the expectation is over alternative possible histories of the preference shocks (which include the effects of technology shocks, since technological possibilities are implicit in our assumed disutility of supplying output). We only consider the welfare associated with alternative stationary rational expectations equilibria, in which all relative quantities are stationary and all quantities are trend-stationary. Thus we can evaluate an unconditional expectation in (1.29) for each of the equilibria that we consider. These days, getting an online loan does not seem like a big problem anymore. However, it’s very important who you get your speedy cash payday loans online from. We, as a trusted lender, will be happy to offer our help at Just fill out our application and we will get back to you with the number.

We also restrict our attention to monetary policy rules which result in unique stationary rational expectations equilibria (in terms of inflation, all relative prices, detrended output, and all relative quantities); we thus obtain a unique welfare measure for each policy rule in the admissible set. Given that we evaluate the unconditional expectation, rather than conditioning upon the current state of the economy at some particular date at which the policy choice is to be made, the criterion (1.29) is equivalent to comparing equilibria on the basis of the average level of expected utility of the households in our model (for the unconditional expectation of the latter quantity is simply (1 — We evaluate the unconditional expectation in order to obtain a policy evaluation criterion that is not subject to any problem of time consistency.

Following Rotemberg and Woodford (1998), we take a second-order Taylor series approximation of this welfare measure around the steady-state values of the stationary variables that affect utility. The “steady-state values” represent the constant equilibrium values of these variables in the absence of real disturbances, and in the case of a deterministic monetary policy consistent with zero inflation.17 The steady state considered for this purpose also involves a tax rate r which is set so that the steady-state level of output is efficient. (This involves a small output subsidy, in order to counteract the distortion caused by monopoly power.) Consideration of a Taylor series expansion around these values means that our approximate welfare measure will accurately rank alternative policy rules insofar as they result in only a small degree of variability of the relevant state variables, and they result in average values of the state variables that are close to the assumed steady-state values.

Thus our analysis should be most reliable in the case of rules which imply an average rate of inflation not too different from zero and an average level of output near the optimal steady-state level Y, and in which the fluctuations in both inflation and output are small. In fact, the policies that we characterize as optimal within various families of possible policy rules all imply low inflation rates, and also low variability of inflation and output, in the case that the variability of the real disturbances (represented by ft) is small enough.