What brings persistence into the macroeconomy? This is one of the big unresolved issues in current macroeconomic theory. Economic models, in fact, typically struggle to imply levels of persistence comparable to those observed in the data. Most of the persistence is therefore introduced by highly autocorrelated exogenous stochastic shocks. Other solutions consist of introducing various sorts of nominal and real rigidities or adjustment costs. Standard DGE models of monetary policy analysis share this difficulty. The workhorse in this area, the New-Keynesian model, does not deliver realistic degrees of inflation and output inertia. Therefore, additional features like rule-of-thumb firms and consumers, indexation to past inflation, habits are often brought into the analysis. This paper evaluates the potential for learning as a source of persistence in macroeconomic models. We start from microfoundations, allowing for inflation indexation and (internal) habit formation in consumption. But, differently from most previous literature, we drop the assumption of rational expectations (RE). We assume, instead, that agents behave as econometricians, using economic models to form their forecasts. But in contrast to almost all the literature on learning, we do not start from the equations obtained under RE and introduce learning from that point. Instead, we consider agents that solve multi-period decision problems and have to learn the relevant state variables. Consumers and firms do not know the correct model of the economy when making their optimal spending and pricing decisions and they cannot consequently infer the true probability laws describing the evolution of the economy. Therefore, they learn them using simple econometric models. Learning has important implications for aggregate dynamics: the standard Euler equations characterizing output and inflation dynamics under RE will no longer hold. Current aggregate variables under learning will not depend just on one-period-ahead expectations but also on the path of long-term expectations of macroeconomic conditions infinitely into the future. The aggregate dynamics will be therefore different from the RE case and from the framework considered by E-H (2003) and Bullard-Mitra (2002). Our modeling choice is, instead, in the same spirit of Preston (2003). Differently from the latter, however, we allow for real rigidities like price indexation and habit formation in consumption. This framework includes different sources of persistence. We estimate the whole system by Bayesian methods. An interesting question is whether after having introduced learning, the coefficients on lagged inflation and output gap (inflation indexation and habit formation parameters), are still large and positive. We also obtain an estimate of the time-varying beliefs of the private sector and of the constant gain coefficient. The results are compared to those we obtain by estimating the model under RE. We can test RE against adaptive learning by using the tools of Bayesian model comparison. By estimating a monetary model with learning, this paper represents an initial step towards what Ireland (2003) terms "Irrational Expectations Econometrics"
