Abstract
Applying a probabilistic causal approach, we define a class of time series causal models (TSCM) based on stationary Bayesian networks. A TSCM can be seen as a structural VAR identified by the causal relations among the variables. We classify TSCMs into observationally equivalent classes by providing a necessary and sufficient condition for the observational equivalence. Applying an automated learning algorithm, we are able to consistently identify the data-generating causal structure up to the class of observational equivalence. In this way we can characterize the empirical testable causal orders among variables based on their observed time series data. It is shown that while an unconstrained VAR model does not imply any causal orders in the variables, a TSCM that contains some empirically testable causal orders implies a restricted SVAR model. We also discuss the relation between the probabilistic causal concept presented in TSCMs and the concept of Granger causality. It is demonstrated in an application example that this methodology can be used to construct structural equations with causal interpretations.
References
Aaronson, D. (2001). Price pass-through and the minimum wage. The Review of Economic Studies, 83:158–169.Search in Google Scholar
Bach, F. R. and Jordan, M. I. (2004). Learning graphical models for stationary time series. IEEE Tansmitions on signal processing, 52:2189–2199. Further information10.1109/TSP.2004.831032Search in Google Scholar
Cartwright, N. (2001). What is wrong with bayes nets? MONIST, 84:242–264. Further information10.5840/monist20018429Search in Google Scholar
Chen, P., Chiarella, C., Flaschel, P., and Semmler, W. (2005). Keynesian macrodynamics and the phillips curve. an estimated baseline macromodel for the U.S. economy. Quantitative and Empirical Analysis of Nonlinear Dynamic Macromodels. Further information in IDEAS/RePEcSearch in Google Scholar
Clark, T. (1997). Do producer prices help to predict consumer prices? Federal Reserve Bank of Kansas City Research Paper, No.97-09. Further information in IDEAS/RePEcSearch in Google Scholar
Dahlhaus, R. (2000). Graphical interpretation for multivariate time series. Metrika, 51:157–172.Search in Google Scholar
Demiralp, S. and Hoover, K. (2004). Searching for the causal structure of a vector autoregression. Oxford Bulletin of Economics and statistics, 65:745–767. Further informationSearch in Google Scholar
Dhrymes, P. J. (1993). Topics in Advanced Econometrics. Springer-Verlag, 1st edition.Search in Google Scholar
Eichler, M. (2003). Granger causality and path diagrams for multivariate time series. Discussion papers, Department of Statistics, the University of Chicago. Further information in IDEAS/RePEcSearch in Google Scholar
Freedman, D. and Humphreys, P. (1998). Are there algorithms that discover causal structure? http://www.stanford.edu/class/ed260/freedman514.pdfSearch in Google Scholar
Ghali (1999). Wage growth and the inflation process: A multivariate cointegration analysis. Journal of Money, Credit and Banking, 31:417–431.Search in Google Scholar
Glymour, S. and Spirtes, G. (1988). Latent variables, causal model and overidentifying constraints. Journal of Econometrics, 39:175–198. Further information in IDEAS/RePEc10.1016/0304-4076(88)90044-9Search in Google Scholar
Heckerman (1995). A tutorial on learning with bayesian networks. Microsoft Research, MSR-TR-95-06. ftp://ftp.research.microsoft.com/pub/tr/tr-95-06.pdfSearch in Google Scholar
Heckerman, D., Geiger, D., and Chickering, D. (1995). Learning bayesian network: The combination of knowledge and statistical data. Machine Learning, 20:197–243.Search in Google Scholar
Hess, G. and Schweitzer, M. (2000). Does wage inflation cause price inflation? Federal Reserve Bank of Cleverland Policy Discussion Paper No.10. Further information in IDEAS/RePEcSearch in Google Scholar
Hogan, V. (1998). Explaining the recent behavior of inflation and unemployment in the united states. IMF working paper No. 98/145. Further information in IDEAS/RePEc10.5089/9781451856514.001Search in Google Scholar
Hoover, K. (2005). Automatic inference of the contemporaneous causal order of a system of equations. Econometric Theory, 21:69–77. Further information in IDEAS/RePEc10.1017/S026646660505005XSearch in Google Scholar
Jonsson, M. and Palmqvist, S. (2004). Do higher wages cause inflation? SVERIGES RISKBANK, Working Paper Series 159. Further information in IDEAS/RePEcSearch in Google Scholar
Mehra, Y. (1993). Unit labor costs and the price level. Federal Reserve Bank of Richmond Economic Review, 79:25–53. Further information in IDEAS/RePEcSearch in Google Scholar
Pearl, J. (2000). Causality. Cambridge University Press, 1st edition. Further informationSearch in Google Scholar
Pearl, J. and Verma, T. (1991). A theory of inferred causation. In J.A. Allen, R. Fikes, and E. Sandewall (Eds.), Principles of Knowledge Representation and Reasoning: Procedings of the 2nd International Conference, San Mateo, CA: Morgan Kaufmann.:441-52.Search in Google Scholar
Phillips, A. (1958). The relation between unemployment and the rate of change of money wage rates in the united kingdom 1861–1957. Economica, 25:283–299.Search in Google Scholar
Rissman, E. (1995). Sectoral wage growth and the inflation. Federal Reserve Bank of Chicago, Economic Perspevtives, July/August:16–28. Further information in IDEAS/RePEcSearch in Google Scholar
Spirtes, P., Glymour, C., and Scheines, R. (2001). Causation, Prediction and Search. Springer-Verlag, New York / Berlin / London / Heidelberg / Paris, 2nd edition. Further information10.7551/mitpress/1754.001.0001Search in Google Scholar
Staiger, D., Stock, J. H., and Watson, M. W. (1997). The nairu, unemployment and monetary policy. Jounal of Economic Perspectives, 11:33–49. Further information in IDEAS/RePEc10.1257/jep.11.1.33Search in Google Scholar
Swanson, N. and Granger, J. (1997). Impulse response functions based on causal approach to residual orthogonalization in vector autoregressions. Journal of the American Statistical Association, 92:357–367. Further information in IDEAS/RePEc10.1080/01621459.1997.10473634Search in Google Scholar
© 2007 Pu Chen et al., published by Sciendo
This work is licensed under the Creative Commons Attribution 4.0 International License.
