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A note on Wiener-Kolmogorov prediction formulas for rational expectations models

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  • Lars Peter Hansen
  • Thomas J. Sargent

Abstract

A prediction formula for geometrically declining sums of future forcing variables is derived for models in which the forcing variables are generated by a vector autoregressive-moving average process. This formula is useful in deducing and characterizing cross-equation restrictions implied by linear rational expectations models.

Suggested Citation

  • Lars Peter Hansen & Thomas J. Sargent, 1981. "A note on Wiener-Kolmogorov prediction formulas for rational expectations models," Staff Report 69, Federal Reserve Bank of Minneapolis.
    • Handle: RePEc:fip:fedmsr:69
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    References listed on IDEAS

    as
    1. Sargent, Thomas J, 1981. "Interpreting Economic Time Series," Journal of Political Economy, University of Chicago Press, vol. 89(2), pages 213-248, April.
    2. Lars Peter Hansen & Thomas J. Sargent, 1980. "Linear rational expectations models for dynamically interrelated variables," Working Papers 135, Federal Reserve Bank of Minneapolis.
    3. Sargent, Thomas J, 1972. "Rational Expectations and the Term Structure of Interest Rates," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 4(1), pages 74-97, Part I Fe.
    4. Hansen, Lars Peter & Sargent, Thomas J., 1980. "Formulating and estimating dynamic linear rational expectations models," Journal of Economic Dynamics and Control, Elsevier, vol. 2(1), pages 7-46, May.
    5. Salemi, Michael K & Sargent, Thomas J, 1979. "The Demand for Money during Hyperinflation under Rational Expectations: II," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 20(3), pages 741-758, October.
    6. Sargent, Thomas J, 1978. "Rational Expectations, Econometric Exogeneity, and Consumption," Journal of Political Economy, University of Chicago Press, vol. 86(4), pages 673-700, August.
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    Cited by:

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    2. Barro, Robert J., 1987. "Government spending, interest rates, prices, and budget deficits in the United Kingdom, 1701-1918," Journal of Monetary Economics, Elsevier, vol. 20(2), pages 221-247, September.
    3. Guillén, Osmani Teixeira & Hecq, Alain & Issler, João Victor & Saraiva, Diogo, 2015. "Forecasting multivariate time series under present-value model short- and long-run co-movement restrictions," International Journal of Forecasting, Elsevier, vol. 31(3), pages 862-875.
    4. Lars Peter Hansen & Thomas J. Sargent, 1982. "Formulating and estimating continuous time rational expectations models," Staff Report 75, Federal Reserve Bank of Minneapolis.
    5. Chahrour, Ryan & Ulbricht, Robert, 2017. "Information-driven Business Cycles: A Primal Approach," TSE Working Papers 17-784, Toulouse School of Economics (TSE), revised Dec 2017.
    6. Kasa, Kenneth, 2001. "A robust Hansen-Sargent prediction formula," Economics Letters, Elsevier, vol. 71(1), pages 43-48, April.
    7. Charles Engel & Kenneth D. West, 2005. "Exchange Rates and Fundamentals," Journal of Political Economy, University of Chicago Press, vol. 113(3), pages 485-517, June.
    8. Joseph DeJuan & Tony S. Wirjanto & Xinpeng Xu, 2016. "The Adjustment of Consumption to Income Changes Across Chinese Provinces," Annals of Economics and Finance, Society for AEF, vol. 17(2), pages 235-253, November.
    9. Huang, Yu-Lieh & Huang, Chao-Hsi & Kuan, Chung-Ming, 2008. "Reexamining the permanent income hypothesis with uncertainty in permanent and transitory innovation states," Journal of Macroeconomics, Elsevier, vol. 30(4), pages 1816-1836, December.
    10. Bent E. Sorensen & Maria J. Luengo-Prado, 2004. "The Buffer Stock Model and the Aggregate Propensity to Consume," Econometric Society 2004 North American Summer Meetings 457, Econometric Society.
    11. Kristoffer Nimark, 2007. "Dynamic Higher Order Expectations," 2007 Meeting Papers 542, Society for Economic Dynamics.
    12. Ryan Chahrour & Robert Ulbricht, 2023. "Robust Predictions for DSGE Models with Incomplete Information," American Economic Journal: Macroeconomics, American Economic Association, vol. 15(1), pages 173-208, January.
    13. West, Kenneth D., 2012. "Econometric analysis of present value models when the discount factor is near one," Journal of Econometrics, Elsevier, vol. 171(1), pages 86-97.
    14. Emilio Fernandez-Corugedo, 2004. "Consumption Theory," Handbooks, Centre for Central Banking Studies, Bank of England, number 23, April.
    15. Neri, Marcelo Côrtes, 2014. "Brazil's middle classes," FGV EPGE Economics Working Papers (Ensaios Economicos da EPGE) 759, EPGE Brazilian School of Economics and Finance - FGV EPGE (Brazil).
    16. Hyeongwoo Kim & Ippei Fujiwara & Bruce E. Hansen & Masao Ogaki, 2015. "Purchasing Power Parity and the Taylor Rule," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 30(6), pages 874-903, September.
    17. Pischke, Jorn-Steffen, 1995. "Individual Income, Incomplete Information, and Aggregate Consumption," Econometrica, Econometric Society, vol. 63(4), pages 805-840, July.
    18. Campbell, John Y. & Hentschel, Ludger, 1992. "No news is good news *1: An asymmetric model of changing volatility in stock returns," Journal of Financial Economics, Elsevier, vol. 31(3), pages 281-318, June.
    19. Laurence Bloch & Françoise Maurel, 1991. "Consommation-revenu permanent : un regard d'économètre," Économie et Prévision, Programme National Persée, vol. 99(3), pages 113-144.
    20. Jose Luengo-Prado, Maria, 2006. "Durables, nondurables, down payments and consumption excesses," Journal of Monetary Economics, Elsevier, vol. 53(7), pages 1509-1539, October.
    21. Joseph DeJuan & John Seater & Tony Wirjanto, 2006. "Testing the permanent-income hypothesis: new evidence from West-German states ( Länder)," Empirical Economics, Springer, vol. 31(3), pages 613-629, September.
    22. Brock, William A. & Durlauf, Steven N. & Rondina, Giacomo, 2013. "Design limits and dynamic policy analysis," Journal of Economic Dynamics and Control, Elsevier, vol. 37(12), pages 2710-2728.
    23. Jonathan J Adams, 2019. "Macroeconomic Models with Incomplete Information and Endogenous Signals," Working Papers 001004, University of Florida, Department of Economics.
    24. Abdelhak S. Senhadji, 2000. "How Significant are Departures from Certainty Equivalence? Some Analytical and Empirical Results," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 3(3), pages 597-617, July.
    25. Osmani Teixeira de Carvalho Guillén & Alain Hecq & João Victor Issler & Diogo Saraiva, 2013. "Time Series under Present-Value-Model Short- and Long-run Co-movement Restrictions," Working Papers Series 330, Central Bank of Brazil, Research Department.

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