Peter Zadrozny, Bureau of Labor Statistics
Project Description/Abstract
A linear rational-expectations model (LREM) is specified in terms of a structural equation that determines how endogenous variables are generated and a separate process that determines how exogenous variables are generated. The structural equation is solved for a rational expectations solution (RES) equation, which, for an assumed exogenous VAR process, reduces to a reduced-form (RF) equation. The paper contributes by deriving linear identification 1 of structural coefficients from RES coefficients and linear identification 2 of RES coefficients from RF coefficients. The RF equation and exogenous VAR process combine to form a larger RF-VAR process of all variables that is identified from data moments under standard least-squares assumptions, whereupon identified RES and structural coefficients are sequentially identified from data moments. Identifications 1-2 as estimation yield: (i) a consistently unrestrictedly linearly estimated LREM that can be compared in terms of in-sample fit and out-of-sample prediction with a commonly estimated LREM, nonlinearly in terms of restricted deep parameters; (ii) an estimated RES equation that can be used for making out-of-sample predictions (forecasts and policy evaluations) that are consistent with Lucas’s critique; and, (iii) the estimated LREM can serve as an unrestricted (purely data based) benchmark for developing a commonly nonlinearly-restricted estimated LREM or modifying an existing estimated LREM.