Hostname: page-component-78c5997874-t5tsf Total loading time: 0 Render date: 2024-11-14T23:00:35.920Z Has data issue: false hasContentIssue false
  • English
  • Français

REGRESSOR DIMENSION REDUCTION WITH ECONOMIC CONSTRAINTS: THE EXAMPLE OF DEMAND SYSTEMS WITH MANY GOODS

Published online by Cambridge University Press:  16 August 2012

Stefan Hoderlein  and
Arthur Lewbel
Stefan Hoderlein
Affiliation:
Boston College
Arthur Lewbel*
Affiliation:
Boston College
*
*Address correspondence to Arthur Lewbel, Department of Economics, Boston College, 140 Commonwealth Ave., Chestnut Hill, MA 02467, USA; e-mail: lewbel@bc.edu.
Get access Rights & Permissions [Opens in a new window]

Abstract

Microeconomic theory often yields models with multiple nonlinear equations, nonseparable unobservables, nonlinear cross equation restrictions, and many potentially multicolinear covariates. We show how statistical dimension reduction techniques can be applied in models with these features. In particular, we consider estimation of derivatives of average structural functions in large consumer demand systems, which depend nonlinearly on the prices of many goods. Utility maximization imposes nonlinear cross equation constraints including Slutsky symmetry, and preference heterogeneity yields demand functions that are nonseparable in unobservables. The standard method of achieving dimension reduction in demand systems is to impose strong, empirically questionable economic restrictions such as separability. In contrast, the validity of statistical methods of dimension-reduction such as principal components has not hitherto been studied in contexts like these. We derive the restrictions implied by utility maximization on dimension-reduced demand systems and characterize the implications for identification and estimation of structural marginal effects. We illustrate the results by reporting estimates of the effects of gasoline prices on the demands for many goods, without imposing any economic separability assumptions.

Type
Articles
Information
Econometric Theory , Volume 28 , Issue 5 , October 2012 , pp. 1087 - 1120
Copyright
Copyright © Cambridge University Press 2012

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Altonji, J.G. & Matzkin, R.L. (2005) Cross section and panel data estimators for nonseparable models with endogenous regressors. Econometrica 73, 1053–1102.CrossRefGoogle Scholar
Berry, S., Levinsohn, J., & Pakes, A. (1995) Automobile prices in market equilibrium. Econometrica 63, 841–890.CrossRefGoogle Scholar
Blackorby, C., Primont, D., & Russell, R.R. (1978) Duality, Separability, and Functional Structure: Theory and Economic Applications. North-Holland.Google Scholar
Blundell, R.W. & Powell, J.L. (2004) Endogeneity in semiparametric binary response models. Review of Economic Studies 71, 655–679.Google Scholar
Blundell, R. & Robin, J.M. (2000) Latent separability: Grouping goods without weak separability. Econometrica 68, 53–84.CrossRefGoogle Scholar
Brown, R. & Walker, M. (1989) The random utility hypothesis and inference in demand systems. Econometrica 57, 815–829.Google Scholar
Browning, M. & Chiappori, P.A. (1998) Efficient intra-household allocations: A general characterization and empirical tests. Econometrica 66, 1241–1278.Google Scholar
Christensen, M. (2004) Integrability of Demand Accounting for Unobservable Heterogeneity: A Test on Panel Data. Manuscript. Centre of Applied Microeconomics, University of Copenhagen.Google Scholar
Davis, G.C. (2003) The generalized composite commodity theorem: Stronger support in the presence of data limitations. Review of Economics and Statistics 85, 476–480.Google Scholar
Deaton, A. & Muellbauer, J. (1980) An almost ideal demand system. American Economic Review 70, 312–326.Google Scholar
Gorman, W.M. (1959) Separable utility and aggregation. Econometrica 27, 469–481.Google Scholar
Gorman, W.M. (1976) Tricks with utility functions. In Artis, M.J. & Nobay, A.R. (eds.), Essays in Economic Analysis: Proceedings of the 1975 AUTE Conference, Sheffield, pp. 211–243. Cambridge University Press.Google Scholar
Haag, B., Hoderlein, S., & Pendakur, K. (2009) Testing and imposing Slutsky symmetry in nonparametric demand systems. Journal of Econometrics 153, 33–50.Google Scholar
Hicks, J.R. (1936) Value and Capital. Oxford University Press.Google Scholar
Hoderlein, S. (2005) Nonparametric Demand Systems, Instrumental Variables and a Heterogeneous Population. Manuscript, Brown University.Google Scholar
Hoderlein, S. & Mammen, E. (2007) Identification of marginal effects in nonseparable models without monotonicity. Econometrica 75, 1513–1518.CrossRefGoogle Scholar
Imbens, G.W. & Newey, W.K. (2009) Identification and estimation of triangular simultaneous equations models without additivity. Econometrica 77, 1481–1512.Google Scholar
Jorgenson, D.W., Lau, L.J., & Stoker, T.M. (1982) The transcendental logarithmic model of aggregate consumer behavior. In Basmann, R.L. & Rhodes, G. (eds.), Advances in Econometrics, vol. 1, pp. 97–238. JAI Press.Google Scholar
Judge, G.G., Griffiths, W.E., Hill, R.C., Lütkepohl, H., & Lee, T. (1985) The Theory and Practice of Econometrics, 2nd ed.Wiley.Google Scholar
Leontief, W. (1936) Composite commodities and the problem of index numbers. Econometrica 4, 39–59.CrossRefGoogle Scholar
Lewbel, A. (1991) The rank of demand systems: Theory and nonparametric estimation. Econometrica 59, 711–730.Google Scholar
Lewbel, A. (1996) Aggregation without separability: A generalized composite commodity theorem. American Economic Review 86, 524–543.Google Scholar
Lewbel, A. (2001) Demand systems with and without errors. American Economic Review 91, 611–618.Google Scholar
Lewbel, A. & Ng, S. (2005) Demand systems with nonstationary prices. Review of Economics and Statistics 87, 479–494.CrossRefGoogle Scholar
Newey, W.K., Powell, J.L., & Vella, F. (1999) Nonparametric estimation of triangular simultaneous equations models. Econometrica 67, 567–603.CrossRefGoogle Scholar
Tripathi, G. & Kim, W. (2003) Nonparametric estimation of homogeneous function. Econometric Theory 19, 640–663.Google Scholar
White, H. (1980) Heteroskedasticity-consistent covariance matrix estimator and a direct test for heteroskedasticity. Econometrica 48, 817–836.CrossRefGoogle Scholar
Wooldridge, J.M. (2002) Econometric Analysis of Cross Section and Panel Data. MIT Press.Google Scholar