A Bayesian nonparametric approach to modeling market share dynamics
We propose a flexible stochastic framework for modeling the market share dynamics over time in a multiple markets setting, where firms interact within and between markets. Firms undergo stochastic idiosyncratic shocks, which contract their shares, and compete to consolidate their position by acquiring new ones in both the market where they operate and in new markets. The model parameters can meaningfully account for phenomena such as barriers to entry and exit, fixed and sunk costs, costs of expanding to new sectors with different technologies, competitive advantage among firms. The construction is obtained in a Bayesian framework by means of a collection of nonparametric hierarchical mixtures, which induce the dependence between markets and provide a generalization of the Blackwell-MacQueen Polya urn scheme, which in turn is used to generate a partially exchangeable dynamical particle system. A Markov Chain Monte Carlo algorithm is provided for simulating trajectories of the system, by means of which we perform a simulation study for transitions to different economic regimes. Moreover, it is shown that the infinite-dimensional properties of the system, when appropriately transformed and rescaled, are those of a collection of interacting Fleming-Viot diffusions.
|Date of creation:||2011|
|Date of revision:|
|Contact details of provider:|| Postal: Via Real Collegio, 30, 10024 Moncalieri (To)|
Web page: http://www.carloalberto.org/
More information through EDIRC
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Lau, John W. & Siu, Tak Kuen, 2008. "On option pricing under a completely random measure via a generalized Esscher transform," Insurance: Mathematics and Economics, Elsevier, vol. 43(1), pages 99-107, August.
- De Iorio, Maria & Muller, Peter & Rosner, Gary L. & MacEachern, Steven N., 2004. "An ANOVA Model for Dependent Random Measures," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 205-215, January.
- Jovanovic, Boyan, 1982. "Selection and the Evolution of Industry," Econometrica, Econometric Society, vol. 50(3), pages 649-70, May.
- Jason A. Duan & Michele Guindani & Alan E. Gelfand, 2007. "Generalized Spatial Dirichlet Process Models," Biometrika, Biometrika Trust, vol. 94(4), pages 809-825.
- Paolo Dai Pra & Wolfgang J. Runggaldier & Elena Sartori & Marco Tolotti, 2007. "Large portfolio losses: A dynamic contagion model," Papers 0704.1348, arXiv.org, revised Mar 2009.
- Griffin, J. E. & Steel, M. F. J., 2004.
"Semiparametric Bayesian inference for stochastic frontier models,"
Journal of Econometrics,
Elsevier, vol. 123(1), pages 121-152, November.
- Jim E. Griffin & Mark F.J. Steel, 2002. "Semiparametric Bayesian Inference for Stochastic Frontier Models," Econometrics 0209001, EconWPA, revised 18 Sep 2002.
- Vaillancourt, Jean, 1990. "On the scaling theorem for interacting Fleming-Viot processes," Stochastic Processes and their Applications, Elsevier, vol. 36(2), pages 263-267, December.
- Walker, Stephen & Muliere, Pietro, 2003. "A bivariate Dirichlet process," Statistics & Probability Letters, Elsevier, vol. 64(1), pages 1-7, August.
- Burda, Martin & Harding, Matthew & Hausman, Jerry, 2008.
"A Bayesian mixed logit-probit model for multinomial choice,"
Journal of Econometrics,
Elsevier, vol. 147(2), pages 232-246, December.
- Martin Burda & Matthew Harding & Jerry Hausman, 2008. "A Bayesian mixed logit-probit model for multinomial choice," CeMMAP working papers CWP23/08, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
- David B. Dunson & Ju-Hyun Park, 2008. "Kernel stick-breaking processes," Biometrika, Biometrika Trust, vol. 95(2), pages 307-323.
- Griffin, J.E. & Steel, M.F.J., 2006. "Order-Based Dependent Dirichlet Processes," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 179-194, March.
- Vaillancourt, Jean, 1990. "Interacting Fleming-Viot processes," Stochastic Processes and their Applications, Elsevier, vol. 36(1), pages 45-57, October.
- Ramsés H. Mena & Stephen G. Walker, 2005. "Stationary Autoregressive Models via a Bayesian Nonparametric Approach," Journal of Time Series Analysis, Wiley Blackwell, vol. 26(6), pages 789-805, November.
- Griffin, J.E. & Steel, M.F.J., 2011. "Stick-breaking autoregressive processes," Journal of Econometrics, Elsevier, vol. 162(2), pages 383-396, June.
- Lorenzo Trippa & Peter Müller & Wesley Johnson, 2011. "The multivariate beta process and an extension of the Polya tree model," Biometrika, Biometrika Trust, vol. 98(1), pages 17-34.
When requesting a correction, please mention this item's handle: RePEc:cca:wpaper:217. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Giovanni Bert)
If references are entirely missing, you can add them using this form.