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A Common-Feature Approach for Testing Present-Value Restrictions with Financial Data

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  • Hecq, Alain
  • Issler, João Victor

Abstract

It is well known that cointegration between the level of two variables (labeled Yt and yt inthis paper) is a necessary condition to assess the empirical validity of a present-value model(PV and PVM, respectively, hereafter) linking them. The work on cointegration has been soprevalent that it is often overlooked that another necessary condition for the PVM to hold isthat the forecast error entailed by the model is orthogonal to the past. The basis of this resultis the use of rational expectations in forecasting future values of variables in the PVM. If thiscondition fails, the present-value equation will not be valid, since it will contain an additionalterm capturing the (non-zero) conditional expected value of future error terms. Our article has a few novel contributions, but two stand out. First, in testing for PVMs,we advise to split the restrictions implied by PV relationships into orthogonality conditions(or reduced rank restrictions) before additional tests on the value of parameters. We showthat PV relationships entail a weak-form common feature relationship as in Hecq, Palm, andUrbain (2006) and in Athanasopoulos, Guillén, Issler and Vahid (2011) and also a polynomialserial-correlation common feature relationship as in Cubadda and Hecq (2001), which representrestrictions on dynamic models which allow several tests for the existence of PV relationships tobe used. Because these relationships occur mostly with nancial data, we propose tests based ongeneralized method of moment (GMM) estimates, where it is straightforward to propose robusttests in the presence of heteroskedasticity. We also propose a robust Wald test developed toinvestigate the presence of reduced rank models. Their performance is evaluated in a Monte-Carlo exercise. Second, in the context of asset pricing, we propose applying a permanent-transitory (PT)decomposition based on Beveridge and Nelson (1981), which focus on extracting the long-runcomponent of asset prices, a key concept in modern nancial theory as discussed in Alvarez andJermann (2005), Hansen and Scheinkman (2009), and Nieuwerburgh, Lustig, Verdelhan (2010).Here again we can exploit the results developed in the common cycle literature to easily extractpermament and transitory components under both long and also short-run restrictions.The techniques discussed herein are applied to long span annual data on long- and short-term interest rates and on price and dividend for the U.S. economy. In both applications we donot reject the existence of a common cyclical feature vector linking these two series. Extractingthe long-run component shows the usefulness of our approach and highlights the presence ofasset-pricing bubbles.

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Bibliographic Info

Paper provided by FGV/EPGE Escola Brasileira de Economia e Finanças, Getulio Vargas Foundation (Brazil) in its series Economics Working Papers (Ensaios Economicos da EPGE) with number 728.

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Date of creation: 24 Feb 2012
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Handle: RePEc:fgv:epgewp:728

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  1. Campbell, John Y & Deaton, Angus, 1989. "Why Is Consumption So Smooth?," Review of Economic Studies, Wiley Blackwell, vol. 56(3), pages 357-73, July.
  2. Athanasopoulos, George & Guillén, Osmani Teixeira de Carvalho & Issler, João Victor & Vahid, Farshid, 2010. "Model selection, estimation and forecasting in VAR models with short-run and long-run restrictions," Economics Working Papers (Ensaios Economicos da EPGE) 704, FGV/EPGE Escola Brasileira de Economia e Finanças, Getulio Vargas Foundation (Brazil).
  3. Issler, Joao Victor & Vahid, Farshid, 2001. "Common cycles and the importance of transitory shocks to macroeconomic aggregates," Journal of Monetary Economics, Elsevier, vol. 47(3), pages 449-475, June.
  4. Engle, Robert F & Kozicki, Sharon, 1993. "Testing for Common Features," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(4), pages 369-80, October.
  5. Candelon, Bertrand & Hecq, Alain & Verschoor, Willem F.C., 2005. "Measuring common cyclical features during financial turmoil: Evidence of interdependence not contagion," Journal of International Money and Finance, Elsevier, vol. 24(8), pages 1317-1334, December.
  6. Vahid, Farshid & Issler, João Victor, 2001. "The Importance of Common Cyclical Features in VAR Analysis: A Monte-Carlo Study," Economics Working Papers (Ensaios Economicos da EPGE) 417, FGV/EPGE Escola Brasileira de Economia e Finanças, Getulio Vargas Foundation (Brazil).
  7. Johansen, Soren, 2000. "Modelling of cointegration in the vector autoregressive model," Economic Modelling, Elsevier, vol. 17(3), pages 359-373, August.
  8. Proietti, Tommaso, 1997. "Short-Run Dynamics in Cointegrated Systems," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 59(3), pages 405-22, August.
  9. Johansen, Soren, 1995. "Likelihood-Based Inference in Cointegrated Vector Autoregressive Models," OUP Catalogue, Oxford University Press, number 9780198774501.
  10. Hecq, Alain & Palm, Franz C & Urbain, Jean-Pierre, 2000. " Permanent-Transitory Decomposition in VAR Models with Cointegration and Common Cycles," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 62(4), pages 511-32, September.
  11. Christensen Timothy & Hurn Stan & Pagan Adrian, 2011. "Detecting Common Dynamics in Transitory Components," Journal of Time Series Econometrics, De Gruyter, vol. 3(1), pages 1-28, February.
  12. Centoni, Marco & Cubadda, Gianluca & Hecq, Alain, 2003. "Common Shocks, Common Dynamics, and the International Business Cycle," Economics & Statistics Discussion Papers esdp03007, University of Molise, Dept. SEGeS.
  13. Engsted, Tom, 2002. " Measures of Fit for Rational Expectations Models," Journal of Economic Surveys, Wiley Blackwell, vol. 16(3), pages 301-55, July.
  14. Campbell, John Y, 1987. "Does Saving Anticipate Declining Labor Income? An Alternative Test of the Permanent Income Hypothesis," Econometrica, Econometric Society, vol. 55(6), pages 1249-73, November.
  15. Johansen, Soren & Swensen, Anders Rygh, 1999. "Testing exact rational expectations in cointegrated vector autoregressive models," Journal of Econometrics, Elsevier, vol. 93(1), pages 73-91, November.
  16. Fernando Alvarez & Urban J. Jermann, 2005. "Using Asset Prices to Measure the Persistence of the Marginal Utility of Wealth," Econometrica, Econometric Society, vol. 73(6), pages 1977-2016, November.
  17. Lettau, Martin & Ludvigson, Sydney, 1999. "Consumption, Aggregate Wealth and Expected Stock Returns," CEPR Discussion Papers 2223, C.E.P.R. Discussion Papers.
  18. B. Ravikumar & Surajit Ray & N. Eugene Savin, 2000. "Robust Wald Tests in SUR Systems with Adding-up Restrictions," Econometrica, Econometric Society, vol. 68(3), pages 715-720, May.
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Cited by:
  1. Hecq Alain & Laurent Sébastien & Palm Franz C., 2012. "On the Univariate Representation of BEKK Models with Common Factors," Research Memorandum 018, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).

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