# Bayesian analysis of structural change in a distributed Lag Model (Koyck Scheme)

• Volume: 34, Issue: 1-2, page 113-126
• ISSN: 1509-9423

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## Abstract

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Structural change for the Koyck Distributed Lag Model is analyzed through the Bayesian approach. The posterior distribution of the break point is derived with the use of the normal-gamma prior density and the break point, ν, is estimated by the value that attains the Highest Posterior Probability (HPP). Simulation study is done using R. Given the parameter values ϕ = 0.2 and λ = 0.3, the full detection of the structural change when σ² = 1 is generally attained at ν + 1. The after one lag detection is due to the nature of the model which includes lagged variable. The interval estimate HPP near ν consistently and efficiently captures the break point ν in the interval HPPₜ ± 5% of the sample size. On the other hand, the detection of the structural change when σ² = 2 does not show any improvement of the point estimate of the break point ν.

## How to cite

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Arvin Paul B. Sumobay, and Arnulfo P. Supe. "Bayesian analysis of structural change in a distributed Lag Model (Koyck Scheme)." Discussiones Mathematicae Probability and Statistics 34.1-2 (2014): 113-126. <http://eudml.org/doc/271044>.

@article{ArvinPaulB2014,
abstract = { Structural change for the Koyck Distributed Lag Model is analyzed through the Bayesian approach. The posterior distribution of the break point is derived with the use of the normal-gamma prior density and the break point, ν, is estimated by the value that attains the Highest Posterior Probability (HPP). Simulation study is done using R. Given the parameter values ϕ = 0.2 and λ = 0.3, the full detection of the structural change when σ² = 1 is generally attained at ν + 1. The after one lag detection is due to the nature of the model which includes lagged variable. The interval estimate HPP near ν consistently and efficiently captures the break point ν in the interval HPPₜ ± 5% of the sample size. On the other hand, the detection of the structural change when σ² = 2 does not show any improvement of the point estimate of the break point ν. },
author = {Arvin Paul B. Sumobay, Arnulfo P. Supe},
journal = {Discussiones Mathematicae Probability and Statistics},
keywords = {distributed lag model; posterior distribution; break point},
language = {eng},
number = {1-2},
pages = {113-126},
title = {Bayesian analysis of structural change in a distributed Lag Model (Koyck Scheme)},
url = {http://eudml.org/doc/271044},
volume = {34},
year = {2014},
}

TY - JOUR
AU - Arvin Paul B. Sumobay
AU - Arnulfo P. Supe
TI - Bayesian analysis of structural change in a distributed Lag Model (Koyck Scheme)
JO - Discussiones Mathematicae Probability and Statistics
PY - 2014
VL - 34
IS - 1-2
SP - 113
EP - 126
AB - Structural change for the Koyck Distributed Lag Model is analyzed through the Bayesian approach. The posterior distribution of the break point is derived with the use of the normal-gamma prior density and the break point, ν, is estimated by the value that attains the Highest Posterior Probability (HPP). Simulation study is done using R. Given the parameter values ϕ = 0.2 and λ = 0.3, the full detection of the structural change when σ² = 1 is generally attained at ν + 1. The after one lag detection is due to the nature of the model which includes lagged variable. The interval estimate HPP near ν consistently and efficiently captures the break point ν in the interval HPPₜ ± 5% of the sample size. On the other hand, the detection of the structural change when σ² = 2 does not show any improvement of the point estimate of the break point ν.
LA - eng
KW - distributed lag model; posterior distribution; break point
UR - http://eudml.org/doc/271044
ER -

## References

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1. [1] G. Casella and R. Berger, Statistical Inference, First Edition (Brookes/Cole Publishing Company, 1990).
2. [2] A. Chaturvedia and A. Shrivastavab, Bayesian Analysis of a Linear Model Involving Structural Changes in Either Regression Parameters or Disturbances Precision (Department of Statistics, University of Allahabad, Allahabad U.P 211002 India, 2012).
3. [3] L.M. Koyck, Distributed lags models and investment analysis (Amsterdam, North-Holland, 1954).
4. [4] J.H. Park, Bayesian Analysis of Structural Changes: Historical Changes in US Presidential Uses of Force (Annual Meeting of the Society for Political Methodology, 2007).
5. [5] A.P. Supe, Parameter changes in autoregressive processes: A Bayesian approach, Philippine Stat. J. 44-45 (1-8) (1996) 27-32.
6. [6] B. Western and M. Kleykamp, A Bayesian Change Point Model for Historical Time Series Analysis (Princeton University, 2004).

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