Learning Dynamics with Data (Quasi-) Differencing

The paper studies learning with data (quasi-)differencing where agents need to (quasi-)difference data and then use an otherwise standard least squares learning procedure. It (1) establishes that the E-stability Principle is still valid for analyzing the convergence of the learning with (quasi-) differencing data process to the Rational Expectations Equilibrium (REE), (2) provides new perspectives on the stability of the Rational Expectations bubble solutions, and equilbrium selection under adaptive learning, (3) demonstrates the importance of consideringagents' uncertainty and learning about the long-run growth of endogenous variables in dynamic macroeconomic models, (4) provides recommendations and a caveat on addressing model misspecifications in econometric practice, and (5) showslearning with (quasi-) differencing data helps understand some salient features of fluctuations in asset prices, inflation and aggregate economic activities.