PPP Rules, Macroeconomic (In)stability and Learning

Governments in emerging economies have pursued real exchange rate targeting through Purchasing Power Parity (PPP) rules that link the nominal depreciation rate to either the deviation of the real exchange rate from its long run level or to the difference between the domestic and the foreign CPI-inflation rates. In this paper we disentangle the conditions under which these rules may lead to endogenous fluctuations due to self-fulfilling expectations in a small open economy that faces nominal rigidities. We find that besides the specification of the rule, structural parameters such as the share of traded goods (that measures the degree of openness of the economy) and the degrees of imperfect competition and price stickiness in the non-traded sector play a crucial role in the determinacy of equilibrium. To evaluate the relevance of the real (in)determinacy results we pursue a learnability (E-stability) analysis for the aforementioned PPP rules. We show that for rules that guarantee a unique equilibrium, the fundamental solution that represents this equilibrium is learnable in the E-stability sense. Similarly we show that for PPP rules that open the possibility of sunspot equilibria, a common factor representation that describes these equilibria is also E-stable. In this sense sunspot equilibria and therefore aggregate instability are more likely to occur due to PPP rules than previously recognized.