# koyck lag - Distributed Lag Models The Koyck Distributed...

• Notes
• beatricemutindi94
• 2

This preview shows pages 1–2. Sign up to view the full content.

Distributed Lag Models The Koyck Distributed Lag Estimator 1. Begin with a model of Y as a function of X and k lags of X: [1] Y t = a + b 0 X t + b 1 X t-1 + b 2 X t-2 + b 3 X t-3 + ... + b k X t-k + e t 2. Restrict the coefficients such that b i = b 0 i Assuming 0 < < 1, the model parameters will be smaller for each successive lag, e.g., if b 0 = .8 and = .5 b 1 = b 0 = (.8)(.5) = .40 b 2 = b 0 2 = (.8)(.5) 2 = .20 b 3 = b 0 3 = (.8)(.5) 3 = .10 [2a] Y t = a + b 0 X t + b 0 X t-1 + b 0 2 X t-2 + b 0 3 X t-3 + ... + b 0 k X t-k + e t Simplify by removing the b 0 factor. [2b] Y t = a + b 0 (X t + X t-1 + 2 X t-2 + 3 X t-3 + ... + k X t-k ) + e t Question: How do we estimate a, b 0 , and ? 3. The "trick" here is to create a new estimating equation as we did in calculating the Cochrane-Orcutt correction for serial correlation. a. Lag equation 2b one time period, [3a] Y t-1 = a + b 0 (X t-1 + X t-2 + 2 X t-3 + 3 X t-4 + ... + k X t-k-1 ) + e t-1 b. Multiply equation 3a by lambda [3b] Y t-1 = a + b 0 ( X t-1 + * X t-2 + * 2 X t-3 + * 3 X t-4 + ... + * k X t-k-1 ) + e t-1 c. Subtract equation 3b from equation 2b.

This preview has intentionally blurred sections. Sign up to view the full version.

This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern