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Seminarios académicos y conferencias

Eugenio Bobenrieth, Agronomía PUC

Euler equation with a latent trend

Coautores: Juan Bobenrieth y Brian D. Wright

15 marzo 2018 - 17:00 hrs.

Sala de Postgrado, Facultad de Ciencias Económicas y Administrativas UC

Abstract: Empirical work in economics often involves estimation of Euler equations from data that may include latent trends induced by exogenous dynamics of, for example, productivity or tastes. Consider a market with stationary demand and transient output disturbances around a negative latent deterministic productivity trend, and intertemporal arbitrage of non-negative stocks. There is a latent trend in price. By the Euler equation, when stocks are positive, the spread is equal to the fixed positive interest rate. Otherwise, the spread is a jump to a latent trending threshold. Given data on observed prices only, which are not detrended in a preliminary step, we prove strong consistency of non-linear least squares estimators of the latent price trend, the interest rate, and the time-dependent threshold, taking account of the singular asymptotic behavior of the predictors of the spread. We prove superconsistency of the estimator for the trend parameter, which is a result we use to prove asymptotic normality of the estimators.