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IV Coefficient Tests for a Unit Root

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We examine the property of the LM coefficient tests using instrumental variables (IV) estimation. As in Im and Lee (2011), we utilize stationary instrumental variables but consider coefficient tests rather than t-tests. Under the null hypothesis,the proposed coefficient statisics converge to the standard normal distribution. This result follws since the score vector in the derivation of the LM statistic from the likelihood function converges to a constant. This makes a contrast from the DF version tests whose distributions are nonstandard.

Abstract

We examine the property of the LM coefficient tests using instrumental variables (IV) estimation. As in Im and Lee (2011), we utilize stationary instrumental variables but consider coefficient tests rather than t-tests. Under the null hypothesis,the proposed coefficient statisics converge to the standard normal distribution. This result follws since the score vector in the derivation of the LM statistic from the likelihood function converges to a constant. This makes a contrast from the DF version tests whose distributions are nonstandard.

참고문헌 (10)

  1. Bhargava, A., "On the theory of testing for unit roots in observed time series", Review of Economic Studies, 52(3), pp.369~384 (1986)
  2. Dickey, D. A,, "Distribution of the Estimators for Autoregressive Time Series with a Unit Root", Journal of the American Statistical Association, 74, pp.427~431 (1979)
  3. Hamilton, J., "Time Series Analysis" (1994), Princeton University Press
  4. Testing for Unit Roots Using Weighted Moment Conditions, "Im, K.", University of Alabama., ~ (2011)
  5. Lee, J., "Minimum LM Unit Root Test with Two Structural Breaks", Review Economics and Statistics, 85(4), pp.1082~1089 (2003)
  6. So, B. S., "Cauchy Estimators for Autoregressive Processes with Applications to Unit Root Tests and Confidence Intervals", Econometric Theory, 15(2), pp.165~176 (1999)
  7. Schmidt, P., "A Modification of the Schmidt-Phillips Unit Root Test", Economics Letters, 36(3), pp.285~289 (1991)
  8. Schmidt, P., "LM Tests for a Unit Root in the Presence of Deterministic Trends", Oxford Bulletin of Economics and Statistics, 54(3), pp.257~287 (1992)
  9. Vougas, D. V., "Reconsidering LM Unit Root Testing", Journal of Applied Statistics, 30(1), pp.727~741 (2003)
  10. White, H., "Asymptotic Theory for Econometricians" (2001), Academic Press

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