Learning about which measure of inflation to target

Using a closed economy model with a flexible-price good and a sticky-price good we study the conditions under which interest rate rules induce real determinacy and, more importantly, the MSV solution is learnable in the E-stability sense proposed by Evans and Honkapohja (2001). We show that these conditions depend not only on how aggressively the rule responds to inflation but also on the measure of inflation included in the rule and on whether the flexible-price good and the sticky-price good are Edgeworth complements, substitutes or utility separable. We consider three possible measures of inflation: the flexible-price inflation, the sticky price inflation and the core inflation; and we analyze three different types of rules: a forward-looking rule, a contemporaneous rule and a backward-looking rule. Our results suggest that in order to guarantee a unique equilibrium whose MSV representation is learnable, the government should implement a backward looking rule that responds exclusively to the sticky-price inflation. Forward-looking and contemporaneous rules that respond to either the flexible-price inflation or the core-inflation are more prone to induce multiple equilibria and E-instability of the MSV solution. More importantly backward-looking rules that react to either the flexible-price inflation or the core inflation may guarantee a unique equilibrium but in these cases the fundamental solution (MSV representation) is not learnable in the E-stability sense