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The Kalman Foundations of Adaptive Least Squares: Applications to Unemployment and Inflation

  • J. Huston McCulloch

Adaptive Least Squares (ALS), i.e. recursive regression with asymptotically constant gain, as proposed by Ljung (1992), Sargent (1993, 1999), and Evans and Honkapohja (2001), is an increasingly widely-used method of estimating time-varying relationships and of proxying agents’ time-evolving expectations. This paper provides theoretical foundations for ALS as a special case of the generalized Kalman solution of a Time Varying Parameter (TVP) model. This approach is in the spirit of that proposed by Ljung (1992) and Sargent (1999), but unlike theirs, nests the rigorous Kalman solution of the elementary Local Level Model, and employs a very simple, yet rigorous, initialization. Unlike other approaches, the proposed method allows the asymptotic gain to be estimated by maximum likelihood (ML). The ALS algorithm is illustrated with univariate time series models of U.S. unemployment and inflation. Because the null hypothesis that the coefficients are in fact constant lies on the boundary of the permissible parameter space, the usual regularity conditions for the chi-square limiting distribution of likelihood-based test statistics are not met. Consequently, critical values of the Likelihood Ratio test statistics are established by Monte Carlo means and used to test the constancy of the parameters in the estimated models.

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Paper provided by Society for Computational Economics in its series Computing in Economics and Finance 2005 with number 239.

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Date of creation: 11 Nov 2005
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Handle: RePEc:sce:scecf5:239
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  1. Preston, Bruce, 2006. "Adaptive learning, forecast-based instrument rules and monetary policy," Journal of Monetary Economics, Elsevier, vol. 53(3), pages 507-535, April.
  2. Evans, George W. & Honkapohja, Seppo, 2002. "Adaptive learning and monetary policy design," Research Discussion Papers 29/2002, Bank of Finland.
  3. Orphanides, Athanasios & Williams, John C., 2005. "The decline of activist stabilization policy: Natural rate misperceptions, learning, and expectations," Journal of Economic Dynamics and Control, Elsevier, vol. 29(11), pages 1927-1950, November.
  4. Roy, Anindya & Fuller, Wayne A, 2001. "Estimation for Autoregressive Time Series with a Root Near 1," Journal of Business & Economic Statistics, American Statistical Association, vol. 19(4), pages 482-93, October.
  5. Bullard, James & Mitra, Kaushik, 2002. "Learning about monetary policy rules," Journal of Monetary Economics, Elsevier, vol. 49(6), pages 1105-1129, September.
  6. Thomas J. Sargent & Noah William, 2005. "Impacts of Priors on Convergence and Escapes from Nash Inflation," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 8(2), pages 360-391, April.
  7. James H. Stock & Mark W. Watson, 1994. "Evidence on structural instability in macroeconomic times series relations," Working Paper Series, Macroeconomic Issues 94-13, Federal Reserve Bank of Chicago.
  8. Fabio Milani, 2005. "Adaptive Learning and Inflation Persistence," Macroeconomics 0506013, EconWPA.
  9. Timothy Cogley & Thomas J. Sargent, 2003. "Drifts and volatilities: monetary policies and outcomes in the post WWII U.S," Working Paper 2003-25, Federal Reserve Bank of Atlanta.
  10. Perron, P, 1988. "The Great Crash, The Oil Price Shock And The Unit Root Hypothesis," Papers 338, Princeton, Department of Economics - Econometric Research Program.
  11. Klein, Benjamin, 1978. "The Measurement of Long- and Short-Term Price Uncertainty: A Moving Regression Time Series Analysis," Economic Inquiry, Western Economic Association International, vol. 16(3), pages 438-52, July.
  12. Prasad V. Bidarkota & J. Huston McCulloch, 1998. "Optimal univariate inflation forecasting with symmetric stable shocks," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 13(6), pages 659-670.
  13. Sargent, Thomas J, 1971. "A Note on the 'Accelerationist' Controversy," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 3(3), pages 721-25, August.
  14. McCulloch, J Huston, 1997. "Measuring Tail Thickness to Estimate the Stable Index Alpha: A Critique," Journal of Business & Economic Statistics, American Statistical Association, vol. 15(1), pages 74-81, January.
  15. Thomas Sargent & Noah Williams & Tao Zha, 2009. "The Conquest of South American Inflation," Journal of Political Economy, University of Chicago Press, vol. 117(2), pages 211-256, 04.
  16. Cooley, Thomas F & Prescott, Edward C, 1973. "An Adaptive Regression Model," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 14(2), pages 364-71, June.
  17. McGough, Bruce, 2003. "Statistical Learning With Time-Varying Parameters," Macroeconomic Dynamics, Cambridge University Press, vol. 7(01), pages 119-139, February.
  18. McCulloch, J. Huston, 1985. "Interest-risk sensitive deposit insurance premia : Stable ACH estimates," Journal of Banking & Finance, Elsevier, vol. 9(1), pages 137-156, March.
  19. Clarida, R. & Gali, J. & Gertler, M., 1998. "Monetary Policy Rules and Macroeconomic Stability: Evidence and some Theory," Working Papers 98-01, C.V. Starr Center for Applied Economics, New York University.
  20. repec:cup:macdyn:v:7:y:2003:i:1:p:119-39 is not listed on IDEAS
  21. Bullard, James, 1992. "Time-varying parameters and nonconvergence to rational expectations under least squares learning," Economics Letters, Elsevier, vol. 40(2), pages 159-166, October.
  22. Tanaka, Katsuto, 1983. "Non-Normality of the Lagrange Multiplier Statistic for Testing the Constancy of Regression Coefficients," Econometrica, Econometric Society, vol. 51(5), pages 1577-82, September.
  23. Durbin, James & Koopman, Siem Jan, 2001. "Time Series Analysis by State Space Methods," OUP Catalogue, Oxford University Press, number 9780198523543, March.
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