Measurement Error in Monetary Aggregates: A Markov Switching Factor Approach

Barnett, William A. and Chauvet, Marcelle and Tierney, Heather L. R. (2007): Measurement Error in Monetary Aggregates: A Markov Switching Factor Approach.

Abstract

This paper compares the different dynamics of the simple sum monetary aggregates and the Divisia monetary aggregate indexes over time, over the business cycle, and across high and low inflation and interest rate phases. Although traditional comparisons of the series sometimes suggest that simple sum and Divisia monetary aggregates share similar dynamics, there are important differences during certain periods, such as around turning points. These differences cannot be evaluated by their average behavior. We use a factor model with regime switching. The model separates out the common movements underlying the monetary aggregate indexes, summarized in the dynamic factor, from individual variations in each individual series, captured by the idiosyncratic terms. The idiosyncratic terms and the measurement errors reveal where the monetary indexes differ. We find several new results. In general, the idiosyncratic terms for both the simple sum aggregates and the Divisia indexes display a business cycle pattern, especially since 1980. They generally rise around the end of high interest rate phases – a couple of quarters before the beginning of recessions – and fall during recessions to subsequently converge to their average in the beginning of expansions. We find that the major differences between the simple sum aggregates and Divisia indexes occur around the beginnings and ends of economic recessions, and during some high interest rate phases. We note the policy relevance of the inferences. Indeed, as Belongia (1996) has observed in this regard, "measurement matters."

• Item Type: MPRA Paper
• Language: English
• Keywords: Measurement error; monetary aggregation; Divisia index; aggregation; state space; Markov switching; monetary policy; index number theory; factor models
• Subjects: E - Macroeconomics and Monetary Economics > E5 - Monetary Policy, Central Banking, and the Supply of Money and Credit > E58 - Central Banks and Their Policies; E - Macroeconomics and Monetary Economics > E5 - Monetary Policy, Central Banking, and the Supply of Money and Credit > E52 - Monetary Policy; E - Macroeconomics and Monetary Economics > E4 - Money and Interest Rates > E40 - General

References

Anderson, R., B. Jones, and T. Nesmith, 1997a, “Introduction to the St. Louis Monetary Services Index Project,” Federal Reserve Bank of St. Louis Review, January/February, Vol. 79, No.1, 25-30.

Anderson, R., B. Jones, and T. Nesmith, 1997b, “Building New Monetary Services Indexes: Concepts Data and Methods,” Federal Reserve Bank of St. Louis Review, January/February, Vol. 79, No.1, 53-82.

Arrow, K. J. and G. H. Hahn, 1971. General Competitive Analysis, San Francisco: Holden-Day.

Barnett, William A., 1978. "The User Cost of Money." Economics Letter 1 145-149. Reprinted in William A. Barnett and Apostolos Serletis (eds.), 2000, The Theory of Monetary Aggregation, North Holland, Amsterdam, chapter 1, pp. 6-10.

Barnett, William A., 1980. "Economic Monetary Aggregates: An Application of Aggregation and Index Number Theory," Journal of Econometrics 14, 11-48. Reprinted in William A. Barnett and Apostolos Serletis (eds.), 2000, The Theory of Monetary Aggregation, North Holland, Amsterdam, chapter 1, pp. 6-10.

Barnett, William A., 1982. "The Optimal level of Monetary Aggregation," Journal of Money, Credit, and Banking 14, 687-710. Reprinted in William A. Barnett and Apostolos Serletis (eds.), 2000, The Theory of Monetary Aggregation, North Holland, Amsterdam, chapter 7, pp. 125-149.

Barnett, William A., 1983. "Understanding the New Divisia Monetary Aggregate," Review of Public Data Use 11, 349-355. Reprinted in William A. Barnett and Apostolos Serletis (eds.), 2000, The Theory of Monetary Aggregation, North Holland, Amsterdam, chapter 4, pp. 100-108.

Barnett, William A., 1987, “The Microeconomic Theory of Monetary Aggregation, in William A. Barnett and Kenneth Singleton (eds.), New Approaches to Monetary Economics, Cambridge U. Press. Reprinted in William A. Barnett and Apostolos Serletis (eds.), 2000, The Theory of Monetary Aggregation, North Holland, Amsterdam, chapter 3, pp. 49-99.

Barnett, William A., 1997. “Which Road Leads to Stable Money Demand?”, The Economic Journal 107, 1171-1185. Reprinted in William A. Barnett and Apostolos Serletis (eds.), 2000, The Theory of Monetary Aggregation, North Holland, Amsterdam, chapter 24, pp. 577-592.

Barnett, William A., 2007, “Multilateral Aggregation-Theoretic Monetary Aggregation over Heterogeneous Countries,” Journal of Econometrics, vol 136, no 2, February, pp. 457-482.

Barnett, William A. and Marcelle Chauvet, 2008, “A Survey of the Connection between Monetary Aggregation Theory, Bad Data, and the Monetary Policy Puzzles,” working paper.

Barnett, William A. and Philippe de Peretti, 2008. “A Necessary and Sufficient Stochastic Semi-Nonparametric Test for Weak Separability, Macroeconomic Dynamics, forthcoming.

Barnett, W. A. and A. Serletis (eds), 2000, The Theory of Monetary Aggregation, Contributions to Economic Analysis Monograph Series, Elsevier, Amsterdam.

Barnett, William A. and Wu, She. 2005. “On user costs of risky monetary assets.” Annals of Finance 1, 35-50.

Barnett, W., Fisher, D. and Serletis, A. 1992. Consumer theory and the demand for money. Journal of Economic Literature 30, 2086–119. Reprinted in Barnett and Serletis (2000, ch. 18).

Barnett, W. A., Liu, Y. and Jensen, M. 2000. CAPM risk adjustment for exact aggregation over financial assets. Macroeconomic Dynamics 1, 485–512.

Barnett, William A., Edward K. Offenbacher, and Paul A. Spindt, 1984. "The New Divisia Monetary Aggregates," Journal of Political Economy 92, 1049-1085. Reprinted in William A. Barnett and Apostolos Serletis (eds.), 2000, The Theory of Monetary Aggregation, North Holland, Amsterdam, chapter 17, pp. 360-388.

Belongia, M., 1996, “Measurement Matters: Recent Results from Monetary Economics Reexamined,” Journal of Political Economy, v. 104, No. 5, 1065-1083.

Belongia, M. and J. Binner (eds), 2000, Divisia Monetary Aggregates: Theory and Practice. Basingstoke: Palgrave.

Belongia, M. and P. Ireland, 2006, “The Own-Price of Money and the Channels of Monetary Transmission,” Journal of Money Credit and Banking, 38, No. 2, 429-445.

Brock, W. A., W. D. Dechert, J. A. Schenkman, and B. LeBaron, “A Test for Independence Based on the Correlation Dimension,” Econometric Reviews, 15(3), 1996, 197-235.

Bry, G., and C. Boschan, 1971, Cyclical Analysis of Times Series: Selected Procedures and Computer Programs, (New York: National Bureau of Economic Research).

Chauvet, M., 1998, “An Econometric Characterization of Business Cycle Dynamics with Factor Structure and Regime Switches,” International Economic Review, Vol. 39, No. 4, November, 969-96.

Chauvet, M., 2001, “A Monthly Indicator of Brazilian GDP,” in Brazilian Review of Econometrics Vol. 21, No. 1.

Chrystal, A. and MacDonald, R. 1994. Empirical evidence on the recent behaviour and usefulness of simple-sum and weighted measures of the money stock. Federal Reserve Bank of St. Louis Review 76, 73–109.

Diewert, W. 1976. Exact and superlative index numbers. Journal of Econometrics 4, 115–45.

Divisia, F. 1925. L’Indice monétaire et la théorie de la monnaie. Revue d’Economie Politique 39, 980–1008.

Feenstra, R. C., 1986, “Functionial Equivalence between Liquidity Costs and the Utility of Money,” Journal of Monetary Economics 17, 271-291.

Fischer, Stanley, 1974, “Money and the Production Function,” Economic Inquiry 12, 517-533.

Friedman, Milton and Anna Schwartz, 1970, Monetary Statistics of the United States: Estimation, Sources, Methods, and Data, New York, Columbia University Press.

Harrison, P. J. and C. F. Stevens, 1976, “Bayesian Forecasting,” Journal of the Royal Statistical Society Series B 38, 205-247.

Haywood, E., 1973, “The Deviation Cycle: A New Index of the Australian Business Cycle, 1950-1973,” Australian Economic Review, 4th Quarter, 31-39.

Hicks, J. R., 1946, “Value and Capital,” Oxford: Clarendon Press.

Jones, B., Dutkowsky, D. and Elger, T. 2005. Sweep programs and optimal monetary aggregation. Journal of Banking and Finance 29, 483–508.

Kim, C.J. and C. Nelson, 1998, “State-Space Models with Regime-Switching: Classical and Gibbs-Sampling Approaches with Applications,” The MIT Press.

Lucas, Robert E., 2000, “Inflation and Welfare,” Econometrica, vol 68, no. 62, March, pp. 247-274.

Phlips, Louis and Frank Spinnewyn, 1982, “Rationality versus Myopia in Dynamic Demand Systems.” In Advances in Econometrics, R. L. Basmann and G. F. Rhodes (eds.), Greenwich, CT: JAI Press, 3-33.

Poterba, J. and J. Rotemberg, 1987, “Money in the Utility Function: An Empirical Implementation.” In New Approaches to Monetary Economics, W. A. Barnett and K. J. Singleton (eds.), Cambridge: Cambridge University Press, 219-240.

Serletis, A. (ed.), 2006, “Money and the Economy,” World Scientific.

Schunk, D., 2001, “The Relative Forecasting Performance of the Divisia and Simple Sum Monetary Aggregates,” Journal of Money, Credit and Banking, 33, No. 2, 272-283.