Mortgage default decisions in the presence of non-normal, spatially dependent disturbances

Abstract We develop a flexible binary choice model for mortgage default decisions that incorporates neighborhood effects in the disturbances. The main advantage of the model lies in its performance in providing improved estimates of the probability of default for risky mortgage loans. In addition, it can be applied to portfolios with a high number of loans. Assuming mortgage decisions with spatially dependent disturbances, the proposed approach uses the generalized extreme value distribution to flexibly model the error terms. To estimate the model on a large sample size, we use a variant of the Geweke-Hajivassiliou-Keane algorithm. We apply the proposed model and its competitors to a large dataset on almost 300,000 mortgages in Clark County, which includes Las Vegas, over 2009–2010. The results show that our proposal greatly improves the predictive accuracy of identifying loans that will default. Moreover, the competitor models underestimate credit Value at Risk.

[1]  Daniel McFadden,et al.  Modelling the Choice of Residential Location , 1977 .

[2]  James P. LeSage,et al.  Models for Spatially Dependent Missing Data , 2004 .

[3]  M. D. Ugarte,et al.  Introduction to Spatial Econometrics , 2011 .

[4]  V. Hajivassiliou,et al.  Smooth unbiased multivariate probability simulators for maximum likelihood estimation of limited dependent variable models , 1993 .

[5]  K. Train.  Discrete Choice Methods with Simulation , 2003 .

[6]  R. Pace,et al.  The Influence of Foreclosure Delays on Borrowers' Default Behavior , 2015 .

[7]  D. McFadden,et al.  The method of simulated scores for the estimation of LDV models , 1998 .

[8]  J. R. DeShazo,et al.  Designing Choice Sets for Stated Preference Methods: The Effects of Complexity on Choice Consistency , 2002 .

[9]  The Political Economy of the US Mortgage Default Crisis , 2010 .

[10]  Li Lin.  Optimal loan-to-value ratio and the efficiency gains of default , 2014 .

[11]  Langche Zeng,et al.  A Heteroscedastic Generalized Extreme Value Discrete Choice Model , 2000 .

[12]  Alan Agresti,et al.  Categorical Data Analysis , 2003 .

[13]  Zvi Griliches,et al.  Specification Error in Probit Models , 1985 .

[14]  B. Arnold,et al.  Measuring Skewness with Respect to the Mode , 1995 .

[15]  Gary King,et al.  Logistic Regression in Rare Events Data , 2001, Political Analysis.

[16]  Mike Rees,et al.  5. Statistics for Spatial Data , 1993 .

[17]  A. W. Kemp,et al.  Univariate Discrete Distributions , 1993 .

[18]  Subprime Mortgages: What, Where, and to Whom? , 2008 .

[19]  Karen,et al.  WORKING PAPER SERIES SUBPRIME MORTGAGES : WHAT , WHERE , AND TO WHOM ? , 2011 .

[20]  S. Shore,et al.  The Effect of Negative Equity on Mortgage Default: Evidence From HAMP’s Principal Reduction Alternative , 2016 .

[21]  J. Davis.  Univariate Discrete Distributions , 2006 .

[22]  Michael Keane,et al.  A Computationally Practical Simulation Estimator for Panel Data , 1994 .

[23]  Shane M. Sherlund,et al.  The Rise in Mortgage Defaults , 2008 .

[24]  R. Duncan Luce,et al.  Individual Choice Behavior , 1959 .

[25]  N. L. Johnson,et al.  Continuous Multivariate Distributions: Models and Applications , 2005 .

[26]  John Geweke,et al.  Efficient Simulation from the Multivariate Normal and Student-t Distributions Subject to Linear Constraints and the Evaluation of Constraint Probabilities , 1991 .

[27]  James P. LeSage,et al.  Fast Simulated Maximum Likelihood Estimation of the Spatial Probit Model Capable of Handling Large Samples , 2011 .

[28]  D. McFadden.  Conditional logit analysis of qualitative choice behavior , 1972 .

[29]  Silvia Angela Osmetti,et al.  Bankruptcy prediction of small and medium enterprises using a flexible binary generalized extreme value model , 2013, J. Oper. Res. Soc..

[30]  Raffaella Calabrese,et al.  Estimating Binary Spatial Autoregressive Models for Rare Events , 2015 .

[31]  Mahendra Sahare,et al.  A Review of Multi-Class Classification for Imbalanced Data , 2012 .

[32]  Florian Heiss,et al.  Discrete Choice Methods with Simulation , 2016 .

[33]  Raffaella Calabrese,et al.  Estimators of Binary Spatial Autoregressive Models: A Monte Carlo Study , 2013, 1302.3414.

[34]  C. Bhat.  A heteroscedastic extreme value model of intercity travel mode choice , 1995 .

[35]  Wim P. M. Vijverberg,et al.  Probit in a Spatial Context: A Monte Carlo Analysis , 2004 .

[36]  Richard L. Smith.  Maximum likelihood estimation in a class of nonregular cases , 1985 .

[37]  Jordan J. Louviere,et al.  Combining sources of preference data , 1998 .

[38]  John P. Harding,et al.  The Contagion Effect of Foreclosed Properties , 2008 .

[39]  Thomas H. Klier,et al.  Clustering of Auto Supplier Plants in the United States , 2008 .

[40]  Dipak K. Dey,et al.  Generalized extreme value regression for binary response data: An application to B2B electronic payments system adoption , 2011, 1101.1373.

[41]  J. Corcoran.  Modelling Extremal Events for Insurance and Finance , 2002 .

[42]  Marianna Kudlyak,et al.  Recourse and residential mortgage default: Evidence from US states , 2011 .

[43]  Ronel Elul.  Securitization and Mortgage Default , 2011 .

[44]  R. Pace,et al.  Modeling Spatially Interdependent Mortgage Decisions , 2011 .

[45]  John M. Quigley,et al.  Mortgage Terminations, Heterogeneity and the Exercise of Mortgage Options , 1999 .

[46]  Eric R. Ziegel,et al.  Generalized Linear Models , 2002, Technometrics.

[47]  J. LeSage.  Bayesian Estimation of Limited Dependent Variable Spatial Autoregressive Models , 2010 .

[48]  Mark J. Garmaise,et al.  Borrower Misreporting and Loan Performance , 2013 .

[49]  Joris Pinkse,et al.  Contracting in space: An application of spatial statistics to discrete-choice models , 1998 .