Consider the Following Model Y_t = β₀ + β₁X_t $\sum _ { i = 1 } ^ { 3 } \beta _ { i } = 1$

question 46

Essay

Consider the following model Y_t = β₀ + β₁X_t + β₂X_t-1 + β₃Y_t-1 + u_t, where X_t is strictly exogenous. Show that by imposing the restriction $\sum _ { i = 1 } ^ { 3 } \beta _ { i } = 1$ , you can derive the following so-called Error Correction Mechanism (ECM)model
△Y_t = β₀ + β₁△X_{t -} θ(Y - X)_t-1 + u_t
where θ = β₁ + β₂. What is the short-run (impact)response of a unit increase in X? What is the long-run solution? Why do you think the term in parenthesis in the above expression is called ECM?

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Definitions:

Conditioned Stimulus

An initially neutral signal that, upon being paired with an unconditioned stimulus, triggers a learned response.

Classical-Conditioning Principles

Fundamental concepts of classical conditioning, such as stimulus generalization, extinction, and spontaneous recovery, that describe how conditioned responses are acquired, maintained, and eliminated.

Unconditioned Response

A naturally occurring reaction to an unconditioned stimulus, such as salivating when smelling food.

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