Skip to main content
×
Home

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

  • Ryan S. Mattson (a1) and Philippe de Peretti (a2)
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.

Copyright
Corresponding author
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: philippe.de-peretti@univ-paris1.fr.
Footnotes
Hide All

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.

Footnotes
References
Hide All
Afriat Sydney (1967) The construction of a utility function from expenditure data. International Economic Review 8, 6777.
Afriat Sydney (1973) On a system of inequalities on demand analysis: An extension of the classical model. International Economic Review 14, 460472.
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, 325359.
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.
Barnett William A. (1978) The user cost of money. Economic Letters 1, 145149. Reprinted in Barnett William A. and Serletis Apostolos (2000) The Theory of Monetary Aggregation. Chapter 2, Amsterdam: North Holland.
Barnett William A. (1979) The joint allocation of leisure and goods expenditure. Econometrica 47, 539563.
Barnett William A. (1980) Economic monetary aggregates: An application of index number and aggregation theory. Journal of Econometrics 14, 1148. Reprinted in Barnett William A. and Serletis Apostolos (2000) The Theory of Monetary Aggregation. Chapter 2, Amsterdam: North Holland.
Barnett William A. (2004) Multilateral aggregation-theoretic monetary aggregation over heterogeneous countries. Journal of Econometrics 136, 457482,
Barnett William A. and Choi Seungmook (1989) A Monte Carlo study of tests of blockwise weak separability. Journal of Business and Economic Statistics 7, 363377. Reprinted in Barnett William A. and Binner Jane (2004) Functional Structure and Approximation in Econometrics. Chapter 12, Amsterdam: North Holland.
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, 317334.
Barnett William A. and Wu Shu (2005) On user costs of risky monetary assets. Annals of Finance 1 (1), 3550.
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, 101124.
Blackorby Charles, Primont Daniel, and Russell Robert R. (1977) On testing separability restrictions with flexible functional forms. Journal of Econometrics 5, 195209.
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. 4992. Kluwer: Dordrecht.
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), 129141.
Deaton Angus and Muellbauer John (1980) Economics and Consumer Behavior. Cambridge: Cambridge University Press.
de Jong Piet and Shephard Neil (1995) The simulation smoother for time series models. Biometrika 82, 339350.
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. 322. Amsterdam: Elsevier.
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, 404418.
Diewert Walter E. (1974) Intertemporal consumer theory and the demand for durables. Econometrica 42, 497516.
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, 679683.
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.
El Himdi Khalid and Roy Roch (1997) Tests for noncorrelations for two multivariate ARMA series. Canadian Journal of Statistics 25, 233256.
Elger Thomas and Jones Barry E. (2008) Can rejections of weak separability be attributed to random measurement errors in the data. Economics Letters 99, 4447.
Feenstra Robert C. (1986) Functional equivalence between liquidity costs and the utility of money. Journal of Monetary Economics 22, 271291.
Fisher Douglas and Fleissig Adrian R. (1997) Monetary aggregation and the demand for assets. Journal of Money, Credit and Banking 29, 458475.
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, 133144.
Fleissig Adrian R. and Whitney Gerald A. (2005) Testing the significance of violations of Afriat's inequalities. Journal of Business and Economic Statistics 23, 355362.
Gorman William M. (1961) On a class of preference fields. Metroeconomica 13, 5356.
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, 14951519.
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, 612629.
Leontief Wassily (1947) Introduction to a theory of the internal structure of functional relationships. Econometrica 15, 361373.
Offenbacher Edward Akiva and Shemesh Shachar (2011) Divisia Monetary Aggregates for Israel: Background Note and Metadata. Bank of Israel, Research Department: Monetary/Finance Division.
Patterson Kerry D. (1991) A non-parametric analysis of personal sector decisions on consumption, liquid assets and leisure. Economic Journal 101, 11031116.
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. 219240. New York: Cambridge University Press.
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, 458464.
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, 241246
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.
Varian Hal (1982) The nonparametric approach to demand analysis. Econometrica 50, 945973.
Varian Hal (1983) Nonparametric tests of consumer behavior. Review of Economic Studies 50, 99110.
Varian Hal (1985) Non-parametric analysis of optimizing behavior with measurement error. Journal of Econometrics 30, 445458.
Varian Hal (1990) Goodness-of-fit in optimizing models. Journal of Econometrics 46, 125140.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Macroeconomic Dynamics
  • ISSN: 1365-1005
  • EISSN: 1469-8056
  • URL: /core/journals/macroeconomic-dynamics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×

Keywords:

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 8 *
Loading metrics...

Abstract views

Total abstract views: 86 *
Loading metrics...

* Views captured on Cambridge Core between 10th August 2017 - 23rd November 2017. This data will be updated every 24 hours.