Learning to become rational. The case of self-referential autoregressive and non-stationary models (Q1921009)

Consider a macroeconomy which is out of rational expectations equilibrium (REE). A basic (and important) question is, how does such an economy get to an REE? This monograph gives some convincing answers. The first chapter discusses the two main approaches to the basic question, coming down on the side of a boundedly rational learning approach. The main focus of the next chapter is the univariate autoregressive model with forecast feedback, a simple version of which is \[ y(t)= F(y(t-1),y^e(t+1))+\text{noise},\tag{1} \] where \(y^e\) is an expectation and the function \(F\) is unknown. The author gives sufficient conditions for a relative error adjustment process to converge to \(F\) almost surely. Results on rate of convergence, global convergence, and stability are also provided, as well as a fully-worked example of the Cobweb model. Chapter 3 extends the convergence results to include exogenous variables in (1). The author also shows why stability results do not extend -- again, in the context of the Cobweb model. Chapter 4 studies versions of (1) which are nonstationary. The complications resulting from nonstationarity require one to specify more fully the learning process -- here, restricted to ordinary least squares learning. Chapter 5 studies multivariate (mainly two-dimensional) extensions of (1) which are stationary, as well as a fully worked version of the Taylor model for real GDP and the price level. Chapter 6 extends the convergence results to the nonstationary case. The results contained therein have no counterparts in the existing literature.