4.1 The Example Once Again

摘要

This can be illustrated using the analysis in Preston (2004) of alternative approaches to implementation of the optimal target criterion (3.3) in the basic new-Keynesian model. Preston shows that under arbitrary (subjective) private-sector expectations, the aggregate-supply relation takes the form π_t = κx_t + E_t ∑~(∞)_(T = t+1) (αβ)~(T-t)[κx_T + (1-α)/α π_T + u_T] +u_t (4.1) where the notation is the same as in (2.1) above, but now the operator E_t[·] indicates the conditional expectation under the (common) probability beliefs of private agents at date t, which may or may not correspond to the true conditional expectation (i.e., "rational expectations"). This inflation equation results from log-linearization of the optimal price-setting rule for firms in a model with monopolistic competition and Calvo staggering of price changes; 0 < α < 1 is the probability that any firm's price will not be revised in a given period. Note that under the assumption of rational expectations - so that subjective forecasts of future inflation are consistent with inflation's being determined by this equation in all future periods - this equation implies the relation (2.1) used by Clarida et ai. (1999); but more generally, subjective forecasts of both inflation and output for more than one period in the future affect the location of the current inflation/output tradeoff.