Question

Consider the model y<sub>t</sub> = a y<sub>t-1</sub> + ?<sub>0</sub>x<sub>t</sub> + ?<sub>1</sub>x<sub>t-1</sub> + ?<sub>t</sub>, where |a| < 1, ?<sub>t</sub> ~ NID (0, ?<sup>2</sup>), (a) Put the model in error correction form. What is the co-integrating vector? (b) Show that if x<sub>t</sub> is stationary in first differences, then x<sub>t</sub> and y<sub>t</sub> are co-integrated of order (1, 1). (c) Suppose that y and x are, respectively, the logarithm of Y and the logarithm of X. If the long-run elasticity of Y with respect to X is known to be unity, how does this affect the specification of the model?

          Consider the model
y<sub>t</sub> = a y<sub>t-1</sub> + ?<sub>0</sub>x<sub>t</sub> + ?<sub>1</sub>x<sub>t-1</sub> + ?<sub>t</sub>, where |a| < 1, ?<sub>t</sub> ~ NID (0, ?<sup>2</sup>),
(a) Put the model in error correction form. What is the co-integrating vector?
(b) Show that if x<sub>t</sub> is stationary in first differences, then x<sub>t</sub> and y<sub>t</sub> are co-integrated of order (1, 1).
(c) Suppose that y and x are, respectively, the logarithm of Y and the logarithm of X. If the long-run
elasticity of Y with respect to X is known to be unity, how does this affect the specification of the
model?

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Consider the model
y<sub>t</sub> = a y<sub>t-1</sub> + ?<sub>0</sub>x<sub>t</sub> + ?<sub>1</sub>x<sub>t-1</sub> + ?<sub>t</sub>, where |a| < 1, ?<sub>t</sub> NID (0, ?<sup>2</sup>),
(a) Put the model in error correction form. What is the co-integrating vector?
(b) Show that if x<sub>t</sub> is stationary in first differences, then x<sub>t</sub> and y<sub>t</sub> are co-integrated of order (1, 1).
(c) Suppose that y and x are, respectively, the logarithm of Y and the logarithm of X. If the long-run
elasticity of Y with respect to X is known to be unity, how does this affect the specification of the
model?

Added by Mary N.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

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Solved by Expert Jerelyn Nevil

Step 1

Let's denote the stationary components of Yt and xt as Yt* and xt*, respectively. We can express Yt as the sum of its stationary component Yt* and the error correction term (Yt - Yt*): Yt = Yt* + (Yt - Yt*) Similarly, we can express xt as the sum of its Show more…

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Consider the model: Yt = Î²Yt-1 + Î²0xt + Î²1xt-1 + Îµt where |Î²| < 1, Îµt ~ NID(0,Ïƒ^2) Put the model in error correction form. What is the co-integrating vector? Show that if xt is stationary in first differences, then xt and Yt are co-integrated of order (1,1). (c) Suppose that Y and X are, respectively, the logarithm of Y and the logarithm of X. If the long-run elasticity of Y with respect to X is known to be unity, how does this affect the specification of the model?

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