VC - A Method For Estimating Time-Varying Coefficients in Linear Models

Schlicht, Ekkehart (November 2019): VC - A Method For Estimating Time-Varying Coefficients in Linear Models. Münchener Wirtschaftswissenschaftliche Beiträge (VWL) 2019-3

Abstract

This paper describes a moments estimator for a standard state-space model with coefficients generated by a random walk. A penalized least squares estimation is linked to the GLS (Aitken) estimates of the corresponding linear model with time-invariant parameters. The VC estimator is a moments estimator that does not require the disturbances be Gaussian, but if they are, its estimates are asymptotically equivalent to maximum likelihood estimates. In contrast to Kalman filtering, no specification of an initial state or an initial covariance matrix is required. While the Kalman filter is one- sided, the VC filter is two-sided and uses more of the available information for estimating intermediate states.. Further, the VC filter has a clear descriptive interpretation.

The final Version appeared in the Journal of the Korean Statistical Society volume 50, pages 1164–1196 (2021), available at https://link.springer.com/article/10.1007/s42952-021-00110-y

• Dokumententyp: Paper
• Publikationsform: Submitted Version
• Keywords: Time-series analysis; linear model; state-space estimation; time-varying coefficients; moments estimation; Kalman filtering; penalized least squares.
• Fakultät: Volkswirtschaft ; Volkswirtschaft > Munich Discussion Papers in Economics ; Volkswirtschaft > Munich Discussion Papers in Economics > Mathematische Methoden ; Volkswirtschaft > Munich Discussion Papers in Economics > Statistische Methoden ; Volkswirtschaft > Lehrstühle > Seminar für Theorie und Politik der Einkommensverteilung (aufgelöst)
• Themengebiete: 300 Sozialwissenschaften > 300 Sozialwissenschaft, Soziologie ; 300 Sozialwissenschaften > 330 Wirtschaft
• JEL Classification: C2, C22, C51, C52
• Sprache: Englisch

Literaturliste

Athans, Michael (1974). “The Importance of Kalman Filtering Methods for Economic Systems”. In: Annals of Economic and Social Measurement, Volume 3, number 1. NBER Chapters. National Bureau of Economic Research.

Cooley, Thomas F and Edward C Prescott (1973). “An Adaptive Regression Model”. In: International Economic Review 14.2, pp. 364–371.

Dijkstra, Theo (1995). “Pyrrho’s lemma, or have it your way”. In: Metrika: International Journal for Theoretical and Applied Statistics 42.1, pp. 119–125.

Gilchrist, W. G. (1967). “Methods of Estimation Involving Discounting”. In: Journal of the Royal Statistical Society. Series B (Methodological) 29.2, pp. 355–369. ISSN: 00359246.

Green, P.J. and B.W. Silverman (2000). Nonparametric Regression and Generalized Linear Models. a Roughness Penalty Approach. Boca Raton, Fla.: Chapman & Hall. ISBN: 0412300400

Hodrick, Robert J and Edward C Prescott (1997). “Postwar U.S. Business Cycles: An Empirical Investigation”. In: Journal of Money, Credit and Banking 29.1, pp. 1–16.

Keynes, John Maynard (1939). “Professor Tinbergen’s Method”. In: Economic Journal 49.195, pp. 558–68.

Keynes, John Maynard (1973). The General Theory and After, Part II: Defense and Development. Ed. by Moggridge. Vol. xiv. The Collected Works of John Maynard Keynes. London: Macmillan.

Leser, C. E. V. (1961). “A Simple Method of Trend Construction”. In: Journal of the Royal Statistical Society. Series B (Methodological) 23, pp. 91–107.

Leser, C. E. V. (1963). “Estimation of Quasi-Linear Trend and Seasonal Variation”. In: Journal of the American Statistical Association 58, pp. 1033–43.

Lucas, Robert (1976). “The Econometric Policy Evaluation: A Critique”. In: Phillips Curve and Labor Markets. Ed. by K. Brunner and A. H. Meltzer. Amsterdam: North Holland, pp. 19–46.

Ludsteck, Johannes (2004). VC Package for Mathematica.

Ludsteck, Johannes (2018). VC Packages for Estimating Time-Varying Coefficients with Mathematica 8 -11.

Rouhiainen, Juhani (1978). “The problem of changing parameters in demand analysis and forecasting”. In: European Review of Agricultural Economics 5.3-4, pp. 349–359.

Schlicht, Ekkehart (1973). Forcasting Markov Chains. A Theoretical Foundation for Exponential Smoothing. Working paper B 13, Department of Economics, University of Regensburg.

Schlicht, Ekkehart (1977). Grundlagen der ökonomischen Analyse. Reinbek: Rowohlt.

Schlicht, Ekkehart (1981). “A Seasonal Adjustment Principle and a Seasonal Adjustment Method Derived from This Principle”. In: Journal of the American Statistical Association 76(374).

Schlicht, Ekkehart (1985). Isolation and Aggregation in Economics. Annotated electronic reprint.

Schlicht, Ekkehart (1989). “Variance Estimation in a Random Coef?cients Model”. In: Munich Discussion Paper. 2006-12. Paper presented at the Econometric Society European Meeting Munich 1989.

Schlicht, Ekkehart (1990). “Local aggregation in a dynamic setting”. In: Journal of Economics 51.3, pp. 287–305.

Schlicht, Ekkehart (2005a). VC -A Program for Estimating Time-Varying Coefficients.

Schlicht, Ekkehart (2005b). VCC -A Program for Estimating Time-Varying Coef?cients. Console Version With Source Code in C.

Schlicht, Ekkehart and Johannes Ludsteck (2006). “Variance Estimation in a Random Coef?cients Model”. In: Munich Discussion Paper 2006-12.

Schlicht, Ekkehart and Ralf Pauly (1983). “Descriptive Seasonal Adjustment by Minimizing Perturbations”. In: Empirica 1983(I), 15-28. . Tinbergen, Jan (1940). “On a Method of Statistical Business-Cycle Research. A Reply”. In: Economic Journal 50.197, pp. 141–54.

Whittaker, E. T. (1923). “On a New Method of Graduation”. In: Proceedings of the Edinburgh Mathematical Society 41, pp. 63–75.

II CONTRIBUTIONS THAT HAVE EMPLOYED VC

Afonso, Antonio, Pedro Gomes, and Davide Furceri (2011). “Sovereign Credit Ratings and Financial Markets Linkages: Application to European data”. In: Working Paper Series 1347.

Afonso, Antonio and Joao Tovar Jalles (2015). “Economic Volatility and Sovereign Yields’ Determinants: A Time-Varying Approach”. In: Working Papers Department of Economics, University of Lisboa.

Afonso, Antonio and Joao Tovar Jalles (2017a). “Euro Area Time-Varying Fiscal sustainability”. In: International Journal of Finance & Economics 22.3, pp. 244–254.

Afonso, Antonio and Joao Tovar Jalles (2017b). “Sovereign Debt Composition and Time-Varying Public Finance Sustainability”. In: The North American Journal of Economics and Finance 42.C, pp. 144–155.

Afonso, Antonio and Joao Tovar Jalles (2017c). (2017c).“Sovereign Debt Effects and Composition:Evidence From Time-Varying Estimates”. In: Working Papers Department of Economics 2017/03, University of Lisboa.

Afonso, Antonio and Joao Tovar Jalles (2019). “Decomposing and Analysing the Determinants of Current Accounts’ Cyclicality: Evidence from the Euro Area”. In: Open Economies Review.

Baxa, Jaromir, Roman Horvath, and Borek Vasicek (2011). “Time Varying Monetary Policy Rules and Financial Stress”. In: ed. by S. Eijffinger and Donato Masciandaro. Edward Elgar Publishing. Chap. Time Varying Monetary Policy Rules and Financial Stress, pp. 268–312.

Baxa, Jaromir, Roman Horvath, and Borek Vasicek (2014). “How Does Monetary Policy Change? Evidence on In?ation-Targeting Countries”. In: Macroeconomic Dynamics 18.3, pp. 593–630.

Cohen, Gail et al. (2017). “Emissions and Growth: Trends and Cycles in a Globalized World”. In: IMF Working Paper WP17/191.

Conway, P., R. Herd, and T. Chalaux (2010). “Reforming China’s Monetary Policy Framework to Meet Domestic Objectives”. In: 6th NIPFP DEA Research Program Conference.

Cournede, Boris, Rudiger Ahrend, and Robert Price (2008). “Have Long-Term Financial Trends Changed the Transmission of Monetary Policy?” In: OECD Economic Department Working Papers 634, 0_1.

Cournede, Boris and Frederic Gonand (2006). “Restoring Fiscal Sustain-ability in the Euro Area: Raise Taxes or Curb Spending?” In: Working Paper.

Flaschel, P. et al. (2008). Topics in Applied Macrodynamic Theory. Berlin-Heidelberg: Springer-Verlag. DOI: 10.1007/978-3-540-72542-8.

Flaschel, Peter (2008). “Linking Goods with Labor Markets: Okun’s Law and Beyond”. In: Topics in Applied Macrodynamic Theory. Berlin, Heidelberg: Springer Berlin Heidelberg, pp. 213–283.

Flaschel, Peter and Ekkehart Schlicht (2006). “The New Keynesian Theory and the New Phillips Curves: A Competing Approach”. In: Quantitative and Empirical Analysis of Nonlinear Dynamic Macromodels. Ed. by Carl Chiarella et al. Elsevier. Chap. The New Keynesian Theory and the New Phillips Curves: A Competing Approach, pp. 113–145.

Franke, Reiner (2006). Themes on Okun’s Law and Beyond. Tech. rep. SCEPA.

Furceri, Davide and Joao Tovar Jalles (2017). “Fiscal Stabilization and Productive Investment: Evidence from Advanced Economies”. In: Working Paper.

Furceri, Davide and Joao Tovar Jalles (2018). “Fiscal counter-cyclicality and productive investment: evidence from advanced economies”. In: The B.E. Journal of Macroeconomics.

Furceri, Davide, Joao Tovar Jalles, and Aleksandra Zdzienicka (2017). “China Spillovers: New Evidence from Time-Varying Estimates”. In: Open Economies Review 28.3, pp. 413–429.

He, Qizhi (2012). “Research on the Dynamic Relationship between Prices of Agricultural Futures in China and Japan”. In: Journal of Computers 7(9).

Jalles, Joao Tovar (2018). “On the Time-Varying Relationship between Unemployment and Output: What shapes it?” In: Scottish Journal of Political Economy.

Jalles, Joao Tovar (2019). Explaining Africa’s Public Consumption Procyclicality: Revisiting Old Evidence. Working Papers REM 2019/0100. ISEG - Lisbon School of Economics and Management, REM, Universidade de Lisboa.

Jalles, Joao Tovar (2019) Onthe Cyclicality of Social Expenditure: NewTime-Varying Evidence from Developing Economies. Working Papers REM2019/82. ISEG-LisbonSchool of Economics and Management, REM, Universidade de Lisboa.

Jalles, Joao Tovar (2019). Polluting Emissions and GDP: Decoupling Evidence from Brazilian States. Working Papers REM 2019/0104. ISEG - Lisbon School of Economics and Management, REM, Universidade de Lisboa.

López-Herrera, Francisco, Humberto Valencia-Herrera, et al. (2016). “Hacia un Modelo de Valuación de Activos de Capital para México: Análisis de Activos Individuales con Coe?cientes Variantes en el Tiempo”. In: Panorama Económico 11.22, pp. 75–103.

Madsen, Michael Walter (2012). “Does Financial Stress Have an Impact on Monetary Policy?: An Econometric Analysis Using Norwegian Data”. PhD thesis. Department of Economics, University of Oslo.

Nogueira, Reginaldo Pinto (2009). “Testing credibility with time-varying coefficients”. In: Applied Economics Letters 16.18, pp. 1813–1817.

Rodriguez, Cesar M. (2014). “Financial development, Fiscal policy and volatility: Their effects on growth”. In: The Journal of International Trade & Economic Development 23.2, pp. 223–266.