The Annals of Applied Statistics

Multilevel models with stochastic volatility for repeated cross-sections: An application to tribal art prices

Silvia Cagnone, Simone Giannerini, and Lucia Modugno

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

In this paper, we introduce a multilevel specification with stochastic volatility for repeated cross-sectional data. Modelling the time dynamics in repeated cross sections requires a suitable adaptation of the multilevel framework where the individuals/items are modelled at the first level whereas the time component appears at the second level. We perform maximum likelihood estimation by means of a nonlinear state space approach combined with Gauss–Legendre quadrature methods to approximate the likelihood function. We apply the model to the first database of tribal art items sold in the most important auction houses worldwide. The model allows to account properly for the heteroscedastic and autocorrelated volatility observed and has superior forecasting performance. Also, it provides valuable information on market trends and on predictability of prices that can be used by art markets stakeholders.

Article information

Source
Ann. Appl. Stat., Volume 11, Number 2 (2017), 1040-1062.

Dates
Received: February 2016
Revised: February 2017
First available in Project Euclid: 20 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.aoas/1500537734

Digital Object Identifier
doi:10.1214/17-AOAS1035

Mathematical Reviews number (MathSciNet)
MR3693557

Zentralblatt MATH identifier
06775903

Keywords
Multilevel model hedonic regression model dependent random effects stochastic volatility autoregression

Citation

Cagnone, Silvia; Giannerini, Simone; Modugno, Lucia. Multilevel models with stochastic volatility for repeated cross-sections: An application to tribal art prices. Ann. Appl. Stat. 11 (2017), no. 2, 1040--1062. doi:10.1214/17-AOAS1035. https://projecteuclid.org/euclid.aoas/1500537734


Export citation

References

  • Agnello, R. and Pierce, R. (1996). Financial returns, price determinants, and genre effects in American art investment. J. Cult. Econ. 20 359–383.
  • Ballesteros, T. (2011). Efficiency tests in the art market using cointegration and the error correction model. Social Science Research Network. DOI:http://dx.doi.org/10.2139/ssrn.1696785.
  • Bartolucci, F. and De Luca, G. (2001). Maximum likelihood estimation of a latent variable time-series model. Appl. Stoch. Models Bus. Ind. 17 5–17.
  • Baumol, W. (1986). Unnatural value: Or art investment as floating crap game. Am. Econ. Rev. 76 10–14.
  • Biordi, M. and Candela, G. (2007). L’arte etnica: Tra cultura e mercato. Skira.
  • Bocart, F. Y. R. P. and Hafner, C. M. (2012). Econometric analysis of volatile art markets. Comput. Statist. Data Anal. 56 3091–3104.
  • Bocart, F. Y. R. P. and Hafner, C. M. (2015). Volatility of price indices for heterogeneous goods with applications to the fine art market. J. Appl. Econometrics 30 291–312.
  • Bound, J., Jaeger, D. and Baker, R. (1995). Problems with instrumental variables estimation when the correlation between instruments and the endogenous explanatory variable is weak. J. Amer. Statist. Assoc. 90 443–450.
  • Box-Steffensmeier, J. M., De Boef, S. and Lin, T.-M. (2004). The dynamics of the partisan gender gap. Am. Polit. Sci. Rev. 98 515–528.
  • Browne, W. and Goldstein, H. (2010). MCMC sampling for a multilevel model with nonindependent residuals within and between cluster units. J. Educ. Behav. Stat. 35 453–473.
  • Cagnone, S. and Bartolucci, F. (2017). Adaptive quadrature for maximum likelihood estimation of a class of dynamic latent variable models. Comput. Econ. 49 599–622.
  • Cagnone, S., Giannerini, S. and Modugno, L. (2017). Supplement to “Multilevel models with stochastic volatility for repeated cross-sections: An application to tribal art prices.” DOI:10.1214/17-AOAS1035SUPP.
  • Candela, G., Castellani, M. and Pattitoni, P. (2012). Tribal art market: Signs and signals. J. Cult. Econ. 36 289–308.
  • Candela, G., Castellani, M. and Pattitoni, P. (2013). Reconsidering psychic return in art investments. Econom. Lett. 118 351–354.
  • Chanel, O. (1995). Is art market behaviour predictable? Eur. Econ. Rev. 39 519–527.
  • Chanel, O., Gérard-Varet, L. and Ginsburgh, V. (1996). The relevance of hedonic price indices. The case of paintings. J. Cult. Econ. 20 1–24.
  • Collins, A., Scorcu, A. and Zanola, R. (2009). Reconsidering hedonic art price indexes. Econom. Lett. 104 57–60.
  • Deaton, A. (1985). Panel data from time series of cross sections. J. Econometrics 30 109–126.
  • DiPrete, T. and Grusky, D. (1990). The multilevel analysis of trends with repeated cross-sectional data. Sociol. Method. 20 337–368.
  • Durbin, J. and Koopman, S. J. (2012). Time Series Analysis by State Space Methods, 2nd ed. Oxford Statistical Science Series 38. Oxford Univ. Press, Oxford.
  • Fridman, M. and Harris, L. (1998). A maximum likelihood approach for non-Gaussian stochastic volatility models. J. Bus. Econom. Statist. 16 284–291.
  • Giannerini, S. (2015). tseriesEntropy: Entropy Based Analysis and Tests for Time Series. R package version 0.5-13.
  • Giannerini, S., Maasoumi, E. and Bee Dagum, E. (2015). Entropy testing for nonlinear serial dependence in time series. Biometrika 102 661–675.
  • Ginsburgh, V. and Jeanfils, P. (1995). Long-term comovements in international markets for paintings. Eur. Econ. Rev. 39 538–548.
  • Goetzmann, W. (1993). Accounting for taste: Art and financial markets over three centuries. Am. Econ. Rev. 83 1370–1376.
  • Goetzmann, W. (1995). The informational efficiency of the art market. Manage. Finance 21 25–34.
  • Goetzmann, W., Mamonova, E. and Spaenjers, C. (2014). The economics of aesthetics and three centuries of art price records. Working Paper 20440, National Bureau of Economic Research.
  • Goldstein, H. (2010). Multilevel Statistical Models, 4th ed. Wiley, Chichester.
  • Granger, C. W., Maasoumi, E. and Racine, J. (2004). A dependence metric for possibly nonlinear processes. J. Time Series Anal. 25 649–669.
  • Hodgson, D. and Vorkink, K. (2004). Asset pricing theory and the valuation of Canadian paintings. Canadian Journal of Economics/Revue canadienne déconomique 37 629–655.
  • Joanes, D. and Gill, C. (1998). Comparing measures of sample skewness and kurtosis. J. R. Stat. Soc., Ser. D Stat. 47 183–189.
  • Jones, R. H. (1993). Longitudinal Data with Serial Correlation: A State-Space Approach. Monographs on Statistics and Applied Probability 47. Chapman & Hall, London.
  • Kitagawa, G. (1987). Non-Gaussian state-space modeling of nonstationary time series. J. Amer. Statist. Assoc. 82 1032–1063.
  • Lebo, M. and Weber, C. (2015). An effective approach to the repeated cross-sectional design. Amer. J. Polit. Sci. 59 242–258.
  • Levene, H. (1960). Robust tests for equality of variances. In Contributions to Probability and Statistics (I. Olkin, ed.) 278–292. Stanford Univ. Press, Stanford, CA.
  • Locatelli Biey, M. and Zanola, R. (2005). The market for picasso prints: A hybrid model approach. J. Cult. Econ. 29 127–136.
  • MacKuen, M., Erikson, R. and Stimson, J. (1992). Peasants or bankers? The American electorate and the U.S. economy. Am. Polit. Sci. Rev. 86 597–611.
  • Modugno, L., Cagnone, S. and Giannerini, S. (2015). A multilevel model with autoregressive components for the analysis of tribal art prices. J. Appl. Stat. 42 2141–2158.
  • Modugno, L. and Giannerini, S. (2015). The wild bootstrap for multilevel models. Comm. Statist. Theory Methods 44 4812–4825.
  • Moffitt, R. (1993). Identification and estimation of dynamic models with a time series of repeated cross-sections. J. Econometrics 59 99–123.
  • Rosen, S. (1974). Hedonic prices and implicit markets: Product differentiation in pure competition. J. Polit. Econ. 82 34–55.
  • Scott, A. J. and Smith, T. M. F. (1974). Analysis of repeated surveys using time series methods. J. Amer. Statist. Assoc. 69 674–678.
  • Skrondal, A. and Rabe-Hesketh, S. (2004). Generalized Latent Variable Modeling: Multilevel, Longitudinal, and Structural Equation Models. Chapman & Hall/CRC, Boca Raton, FL.
  • Tanizaki, H. and Mariano, R. (1998). Nonlinear and nonnormal state-space modeling with Monte-Carlo stochastic simulations. J. Econometrics 83 263–290.
  • Wooldridge, J. M. (2010). Econometric Analysis of Cross Section and Panel Data, 2nd ed. MIT Press, Cambridge, MA.
  • Xu, R. (2003). Measuring explained variation in linear mixed effects models. Stat. Med. 22 3527–3541.

Supplemental materials

  • Supplement to “Multilevel models with stochastic volatility for repeated cross-sections: An application to tribal art prices”. The online supplement contains six technical Appendices with detailed material on the following topics: 1. Recursive algorithm for computing the likelihood; 2. Filtering, Smoothing, and Prediction; 3. Application to Tribal Art prices: full table of the estimates; 4. Application to Tribal Art prices: choice of the quadrature based method; 5. Application to Tribal Art prices: entropy based diagnostic tests for serial independence and nonlinearity; 6. Software implementation.