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TESTING FOR WEAK SEPARABILITY USING STOCHASTIC SEMI-NONPARAMETRIC TESTS: AN EMPIRICAL STUDY ON US DATA

Published online by Cambridge University Press:  10 August 2017

Ryan S. Mattson  and
Philippe de Peretti
Ryan S. Mattson
Affiliation:
West Texas A&M
Philippe de Peretti*
Affiliation:
Université Paris1 Panthéon-Sorbonne
*
Address correspondence to: Philippe de Peretti, Centre d'Economie de la Sorbonne (CES), Université Paris1 Panthéon-Sorbonne, 106-112 Boulevard de l'Hôpital, 75013 Paris, France; e-mail: [email protected].
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Abstract

In this paper, we use the weak separability criterion to check for the existence of six different monetary aggregates reported by the Center of Financial Stability (CFS). We implement an extended version of the semi-nonparametric tests introduced by Barnett and de Peretti on US monthly data from January 1967 to December 2012. The test, first, checks for the necessary existence conditions of an overall utility function and a monetary subutility function, and then tests for the separability of the latter. On different subsamples, our results suggest that only the DM1 aggregate meets the separability criterion. Implemented on macroeconomic data, we have tested a joint assumption about separability and the existence of a representative agent. Thus, the rejection of the null could also be due to the rejection of stringent Gorman's conditions. More advanced tests for weak separability are clearly required to confirm the results found in this paper.

Keywords

Weak Separability CriterionSemi-Nonparametric TestsCFS Data
Type
Articles
Information
Macroeconomic Dynamics , Volume 22 , Issue 6 , September 2018 , pp. 1510 - 1534
Copyright
Copyright © Cambridge University Press 2017 

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Footnotes

The research leading to these results has received funding from the European Union Seventh Framework Programme (FP7-SSH/2007-2013) under grant agreement no. 320270 SYRTO. This work was achieved through the Laboratory of Excellence on Financial Regulation (Labex ReFi) supported by PRES heSam under the reference ANR10LABX0095. It benefited from French government support managed by the National Research Agency (ANR) within the project Investissements d'Avenir Paris Nouveaux Mondes (investments for the future Paris New Worlds) under the reference ANR11IDEX000602.

References

REFERENCES

Afriat, Sydney (1967) The construction of a utility function from expenditure data. International Economic Review 8, 67–77.Google Scholar
Afriat, Sydney (1973) On a system of inequalities on demand analysis: An extension of the classical model. International Economic Review 14, 460–472.Google Scholar
Anderson, Richard A. and Jones, Barry E. (2011) A comprehensive revision of the US Monetary Services (Divisia) Index. Federal Reserve Bank of St. Louis Review 93, 325–359.Google Scholar
Andreoni, James, Gillen, Benjamin J., and Harbaugh, William T. (2013) The Power of Revealed Preference Tests: Ex-post Evaluation of Experimental Design. Working paper. University of California, San Diego.Google Scholar
Barnett, William A. (1978) The user cost of money. Economic Letters 1, 145–149. Reprinted in Barnett, William A. and Serletis, Apostolos (2000) The Theory of Monetary Aggregation. Chapter 2, Amsterdam: North Holland.Google Scholar
Barnett, William A. (1979) The joint allocation of leisure and goods expenditure. Econometrica 47, 539–563.Google Scholar
Barnett, William A. (1980) Economic monetary aggregates: An application of index number and aggregation theory. Journal of Econometrics 14, 11–48. Reprinted in Barnett, William A. and Serletis, Apostolos (2000) The Theory of Monetary Aggregation. Chapter 2, Amsterdam: North Holland.Google Scholar
Barnett, William A. (2004) Multilateral aggregation-theoretic monetary aggregation over heterogeneous countries. Journal of Econometrics 136, 457–482,Google Scholar
Barnett, William A. and Choi, Seungmook (1989) A Monte Carlo study of tests of blockwise weak separability. Journal of Business and Economic Statistics 7, 363–377. Reprinted in Barnett, William A. and Binner, Jane (2004) Functional Structure and Approximation in Econometrics. Chapter 12, Amsterdam: North Holland.Google Scholar
Barnett, William A. and Peretti, Philippe de (2009) Admissible clustering of aggregator components: A necessary and sufficient stochastic seminonparametric test for weak separability. Macroeconomic Dynamics 13, 317–334.Google Scholar
Barnett, William A. and Wu, Shu (2005) On user costs of risky monetary assets. Annals of Finance 1 (1), 35–50.Google Scholar
Barnett, William A., Lu, Jia, Mattson, Ryan S., and van den Noort, Jeff (2013) The new CFS divisia monetary aggregates: Design, construction, and data sources, manuscript. Open Economies Review 24, 101–124.Google Scholar
Blackorby, Charles, Primont, Daniel, and Russell, Robert R. (1977) On testing separability restrictions with flexible functional forms. Journal of Econometrics 5, 195–209.Google Scholar
Blackorby, Charles, Primont, Daniel, and Russell, R. Robert (1998) Separability: A survey. In Barbera, Salvador, Hammond, Peter, and Seidl, Christian (eds.), The Handbook of Utility Theory, vol. 1, pp. 49–92. Kluwer: Dordrecht.Google Scholar
Cherchye, Laurens, Demuynck, Thomas, De Rock, Bram, and Hjerstrand, Per (2015) Revealed preference tests for weak separability: An integer programming approach. Journal of Econometrics 186 (1), 129–141.Google Scholar
Deaton, Angus and Muellbauer, John (1980) Economics and Consumer Behavior. Cambridge: Cambridge University Press.Google Scholar
de Jong, Piet and Shephard, Neil (1995) The simulation smoother for time series models. Biometrika 82, 339–350.Google Scholar
de Peretti, Philippe (2007) Testing the significance of the departures from weak separability. In Barnett, William A. and Serletis, Apostolos (eds.), International Symposia in Economic Theory and Econometrics: Function Structure Inference, pp. 3–22. Amsterdam: Elsevier.Google Scholar
Denny, Michael and Fuss, Melvyn (1977) The use of approximation analysis to test for separability and the existence of consistent aggregates. American Economic Review 67, 404–418.Google Scholar
Diewert, Walter E. (1974) Intertemporal consumer theory and the demand for durables. Econometrica 42, 497–516.Google Scholar
Drake, Leigh (1997) Nonparametric demand analysis of U.K. personal sector decisions on consumption, leisure, and monetary assets: A reappraisal. The Review of Economics and Statistics 79, 679–683.Google Scholar
Durbin, James and Koopman, Siem Jan (2001) Time series analysis by state space methods. In Oxford Statistical Science Series Book vol. 38. Oxford: Oxford University Press.Google Scholar
El Himdi, Khalid and Roy, Roch (1997) Tests for noncorrelations for two multivariate ARMA series. Canadian Journal of Statistics 25, 233–256.Google Scholar
Elger, Thomas and Jones, Barry E. (2008) Can rejections of weak separability be attributed to random measurement errors in the data. Economics Letters 99, 44–47.Google Scholar
Feenstra, Robert C. (1986) Functional equivalence between liquidity costs and the utility of money. Journal of Monetary Economics 22, 271–291.Google Scholar
Fisher, Douglas and Fleissig, Adrian R. (1997) Monetary aggregation and the demand for assets. Journal of Money, Credit and Banking 29, 458–475.Google Scholar
Fleissig, Adrian R. and Whitney, Gerald A. (2003) New PC-Based test for Varian's weak separability conditions. Journal of Business and Economic Statistics 21, 133–144.Google Scholar
Fleissig, Adrian R. and Whitney, Gerald A. (2005) Testing the significance of violations of Afriat's inequalities. Journal of Business and Economic Statistics 23, 355–362.Google Scholar
Gorman, William M. (1961) On a class of preference fields. Metroeconomica 13, 53–56.Google Scholar
Hjertstrand, Per and Swofford, James L. (2014) Are the choices of people stochastically rational? A stochastic test of the number of reveals preference violations. Empirical Economics 46, 1495–1519.Google Scholar
Jones, Barry E. and de Peretti, Philippe (2005) A comparison of two methods for testing the utility maximization hypothesis when quantity data is measured with error. Macroeconomic Dynamics 9, 612–629.Google Scholar
Leontief, Wassily (1947) Introduction to a theory of the internal structure of functional relationships. Econometrica 15, 361–373.Google Scholar
Offenbacher, Edward Akiva and Shemesh, Shachar (2011) Divisia Monetary Aggregates for Israel: Background Note and Metadata. Bank of Israel, Research Department: Monetary/Finance Division.Google Scholar
Patterson, Kerry D. (1991) A non-parametric analysis of personal sector decisions on consumption, liquid assets and leisure. Economic Journal 101, 1103–1116.Google Scholar
Poterba, James M. and Rotemberg, Julio J. (1987) Money in the utility function: An empirical implementation. In Barnett, William A. and Singleton, Kenneth J. (eds.), New Approaches to Monetary Economics, pp. 219–240. New York: Cambridge University Press.Google Scholar
Swofford, James L. and Whitney, Gerald A. (1987) Non-parametric tests of utility maximization and weak separability for consumption, leisure, and money. Review of Economic Studies 69, 458–464.Google Scholar
Swofford, James L. and Whitney, Gerald A. (1988) A comparison of nonparametric tests of weak separability for annual and quarterly data on consumption, leisure, and money. Journal of Business & Economic Statistics 6, 241–246Google Scholar
Swofford, James L. and Whitney, Gerald A. (1994) A revealed preference test for weakly separable utility maximization with incomplete adjustment. Journal of Econometrics 60, 235–49.Google Scholar
Varian, Hal (1982) The nonparametric approach to demand analysis. Econometrica 50, 945–973.Google Scholar
Varian, Hal (1983) Nonparametric tests of consumer behavior. Review of Economic Studies 50, 99–110.Google Scholar
Varian, Hal (1985) Non-parametric analysis of optimizing behavior with measurement error. Journal of Econometrics 30, 445–458.Google Scholar
Varian, Hal (1990) Goodness-of-fit in optimizing models. Journal of Econometrics 46, 125–140.Google Scholar