A bivariate finite mixture growth model with selection

A model is proposed to analyze longitudinal data where two response variables are available, one of which is a binary indicator of selection and the other is continuous and observed only if the first is equal to 1. The model also accounts for individual covariates and may be considered as a bivariate finite mixture growth model as it is based on three submodels: (i) a probit model for the selection variable; (ii) a linear model for the continuous variable; and (iii) a multinomial logit model for the class membership. To suitably address endogeneity, the first two components rely on correlated errors as in a standard selection model. The proposed approach is applied to the analysis of the dynamics of household portfolio choices based on an unbalanced panel dataset of Italian households over the 1998–2014 period. For this dataset, we identify three latent classes of households with specific investment behaviors and we assess the effect of individual characteristics on households’ portfolio choices. Our empirical findings also confirm the need to jointly model risky asset market participation and the conditional portfolio share to properly analyze investment behaviors over the life-cycle.

[1]  F. Bartolucci,et al.  A latent class growth model for migrants’ remittances: an application to the German Socio‐Economic Panel , 2019, Journal of the Royal Statistical Society: Series A (Statistics in Society).

[2]  Andrea Brandolini,et al.  The Distribution of Personal Income in Post-War Italy: Source Description, Data Quality, and the Time Pattern of Income Inequality , 1999 .

[3]  A. Soest,et al.  Ownership of Stocks and Mutual Funds: A Panel Data Analysis , 2004, Review of Economics and Statistics.

[4]  Leo A. Goodman,et al.  1. On the Assignment of Individuals to Latent Classes , 2007 .

[5]  Paola Giuliano,et al.  Growing up in a Recession , 2014 .

[6]  Robert Tibshirani,et al.  An Introduction to the Bootstrap , 1994 .

[7]  A. Farcomeni,et al.  A Multivariate Extension of the Dynamic Logit Model for Longitudinal Data Based on a Latent Markov Heterogeneity Structure , 2009 .

[8]  Silvia Pandolfi,et al.  A comparison of some criteria for states selection in the latent Markov model for longitudinal data , 2012, Adv. Data Anal. Classif..

[9]  T. Jappelli,et al.  Household Portfolios in Italy , 2000 .

[10]  D. Oakes.  Direct calculation of the information matrix via the EM , 1999 .

[11]  José G. Dias,et al.  A bootstrap-based aggregate classifier for model-based clustering , 2008, Comput. Stat..

[12]  Bengt Muthén,et al.  Latent Variable Analysis: Growth Mixture Modeling and Related Techniques for Longitudinal Data , 2004 .

[13]  Risk Aversion, Wealth and Background Risk , 2008 .

[14]  Kenneth A. Bollen,et al.  Latent curve models: A structural equation perspective , 2005 .

[15]  L. A. Goodman.  The Analysis of Systems of Qualitative Variables When Some of the Variables Are Unobservable. Part I-A Modified Latent Structure Approach , 1974, American Journal of Sociology.

[16]  B. Silverman,et al.  Nonparametric Regression and Generalized Linear Models: A roughness penalty approach , 1993 .

[17]  Katherine E. Masyn,et al.  Covariates and Mixture Modeling: Results of a Simulation Study Exploring the Impact of Misspecified Effects on Class Enumeration , 2016 .

[18]  B. Silverman,et al.  Nonparametric regression and generalized linear models , 1994 .

[19]  L. Guiso,et al.  Risk Aversion, Wealth and Background Risk , 2001 .

[20]  Stephanie T. Lanza,et al.  Eliminating Bias in Classify-Analyze Approaches for Latent Class Analysis , 2015, Structural equation modeling : a multidisciplinary journal.

[21]  Michael Haliassos,et al.  Portfolio Inertia and Stock Market Fluctuations , 2009 .

[22]  Francesco Bartolucci,et al.  A finite mixture latent trajectory model for modeling ultrarunners’ behavior in a 24-hour race , 2015 .

[23]  M. Haliassos.  Stockholding: Recent Lessons from Theory and Computations , 2002 .

[24]  Scott L. Zeger,et al.  Latent Variable Regression for Multiple Discrete Outcomes , 1997 .

[25]  B. Muthén,et al.  Deciding on the Number of Classes in Latent Class Analysis and Growth Mixture Modeling: A Monte Carlo Simulation Study , 2007 .

[26]  V. Atella,et al.  Household portfolio choices, health status and health care systems: A cross-country analysis based on SHARE. , 2012, Journal of banking & finance.

[27]  Patrick A. Puhani,et al.  The Heckman Correction for Sample Selection and Its Critique - A Short Survey , 2000 .

[28]  L. Guiso,et al.  Asset Market Participation and Portfolio Choice Over the Life-Cycle , 2013 .

[29]  Yulia V. Marchenko,et al.  A Heckman Selection-t Model , 2012 .

[30]  Geoffrey J. McLachlan,et al.  Finite Mixture Models , 2019, Annual Review of Statistics and Its Application.

[31]  Laurent E. Calvet,et al.  Fight or Flight? Portfolio Rebalancing by Individual Investors , 2007 .

[32]  Adrian E. Raftery,et al.  Model-Based Clustering, Discriminant Analysis, and Density Estimation , 2002 .

[33]  J. Heckman.  Sample selection bias as a specification error , 1979 .

[34]  D. Rubin.  INFERENCE AND MISSING DATA , 1975 .

[35]  Luigi Guiso,et al.  Household Finance: An Emerging Field , 2012 .

[36]  D. Rubin,et al.  Maximum likelihood from incomplete data via the EM - algorithm plus discussions on the paper , 1977 .

[37]  A. Lusardi,et al.  Financial Literacy and Stock Market Participation , 2007 .

[38]  Appendix for "Fight or Flight? Portfolio Rebalancing by Individual Investors" , 2009 .

[39]  Roger W. Johnson,et al.  An Introduction to the Bootstrap , 2001 .

[40]  G. Schwarz.  Estimating the Dimension of a Model , 1978 .

[41]  Ryan D. Edwards.  Health Risk and Portfolio Choice , 2008 .

[42]  Markus K. Brunnermeier,et al.  Do Wealth Fluctuations Generate Time-Varying Risk Aversion? Micro-Evidence on Individuals' Asset Allocation , 2008 .

[43]  T. Jappelli,et al.  Cognitive Abilities and Portfolio Choice , 2006 .

[44]  M. Haliassos,et al.  Household Stockholding in Europe: Where Do We Stand and Where Do We Go? , 2002, SSRN Electronic Journal.

[45]  Jeroen K. Vermunt,et al.  Latent class modeling with covariates : Two improved three-step approaches 1 , 2012 .

[46]  B. Muthén,et al.  Finite Mixture Modeling with Mixture Outcomes Using the EM Algorithm , 1999, Biometrics.

[47]  H. Akaike,et al.  Information Theory and an Extension of the Maximum Likelihood Principle , 1973 .

[48]  R. C. Merton,et al.  Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case , 1969 .