Modelling Simultaneous Defaults: A Top-Down Approach

Microfoundations for Performance, Competition and Econometric Implications

The assessment of businesses' credit risk is a difficult and important process in the area of financial risk management. In a classical multivariate model, financial ratios are combined in order to achieve a credit risk score, which signals if a loan application is approved or discarded. Despite their good performance, the developed multivariate models using statistical methods have been widely criticized. They are based on models that use accounting data, which have the disadvantage of being static and so often fail to follow the changes in the economic and business environment. In recent years, market models (structural and reduced form models) have become popular among banks and financial institutions, because of their theoretical background and the use of updated information. The aim of this article is to present an overview of basic market models (structural models, reduced form models and market models used from credit institutions) together with their characteristics in order to outline their development throughout the last decades.

The authors provide a comprehensive and useful review of structural models in marketing (Chintagunta et al. 2006). They evaluate the strengths and limitations of a structural approach and present examples of recent advancements in the development and application of structural models. Their discussion on the directions for future studies is very insightful. Despite the growing trend in the literature to claim contribution by offering structural treatments to research questions, it remains arbitrary and sometimes mysterious as to what constitutes a “structural” model. I agree with the authors that artificial boundaries are commonly imposed in our field between structural and reduced-form models. I believe it is more constructive to classify research studies along a structural/reduced-form continuum than to draw a distinctive line between, or even develop different research paradigms around, them. My objective in this discussion is to provide further insights into the structural/reduced-form continuum. I first argue that this continuum is usually multidimensional, and one can move up the continuum in two directions. Following the argument are some examples of how the studies in the literature can be positioned along the continuum. I also discuss the role of data in developing more structural models. I argue that limited data quality can be a “double-edged sword” for the use of more structural models and that data integration and researcher creativity can be substitutes for limited data quality. Directions for future research on moving up the structural/reduced-form continuum are also identified. The discussion intends to support the complementarity between “structural” and “reduced-form” models, and the need to break the boundary between them.

In order to further empirical study of the performance of structural models in China, this paper empirically tests four structural models of corporate bonds pricing: those of Merton (1974), modified Merton with exogenous recovery rate, Black and Cox (1976) and Leland and Toft (1996). The article implement these models by using a sample of 45 Chinese firms issuing short-term financing bonds in 2006. Empirical results show that the predicted spreads in four models are lower than actual spreads on average, particularly those of Merton model. Comparing the different models we find the spreads from Black and Cox (1976) and Leland and Toft (1996) are higher than the basic structural models, but accuracy is a problem. The modified Merton model can further improve Merton (1974)'s underestimation. The basic structural models including Merton (1974) and modified Merton can more comparatively catch the trend of movement of credit spreads than so-called extended models. The performance of recently developed structural models is not superior to the original Merton models. More accurate structural models must not only avoid underestimation but also improve the accuracy.

Covers credit risk and credit derivatives. This book offers several points of view on credit risk when looked at from the perspective of Econometrics and Financial Mathematics. It addresses the challenge of modeling defaults and their correlations, and results on copula, reduced form and structural models, and the top-down approach.

[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT AUTHOR'S REQUEST.] In this study, I examine effects of financial incentives and non-financial incentives on public school teachers' retirement in Missouri. For financial incentives, existing studies commonly model the retirement in two types, static reduced-form and structural-form. There are two main types of the reduced-form models, linear probability model (e.g., Costrell and McGee, 2010; Brown, 2013), probit or logit model (e.g., Furgeson et al., 2006; Asch et al., 2005; Coile and Gruber, 2007). A prominent structural form model is the Stock and Wise (1990) option value model. In addition, some researchers (Brown and Laschever, 2012; Gustman and Steinmeier, 2000; Dwyer and Mitchell, 1999) suggest that non-financial incentives, such as colleagues, health status, and family, are also important factors to explain retirement decisions. Among these non-financial incentives, peer effects are the focus of my study. The first chapter analyzes peer effects on public school teachers' retirement timing decisions. I use an administrative dataset of the full population of late career Missouri public school teachers during academic years 1994-2007 to construct a model incorporating both financial incentives and non-financial incentives when teachers make retirement decisions. My study mainly differs from previous literature in the controls of financial incentives and the use of data. For controls of financial incentives, instead of using pension wealth and peak value, I propose the simulated "financial benefit of postponing retirement" based on Stock-Wise (hereafter, SW) option value model as a new financial incentive proxy. Besides, I use a much richer dataset so that more detailed information about teachers are available and the schools are more diverse in poverty and urbanicity. Empirically, when the retirement rate of peers in previous year increases 1%, the probability of retirement increases approximately 0.128 percentage points. In addition, I find evidence of heterogeneous peer effects. For example, teachers with different education levels respond to peers retirement differently. Because the reduced-form parameters generally depend on the pension rules, the reduced-form models are unreliable to predict the effects of changes in the pension rules. In contrast, the structural model parameters are independent of pension rules, which makes them useful for policy analysis. The second chapter uses an economic structural model to fit late career Missouri public school teachers' data and study the effects of changing pension rules on the timing of retirement. Ni and Podgursky (2016) show that the SW option value model produces good fit for the Missouri public school teachers during 2002-2008. There are three limitations in their study and other applications of the SW model. First, the SW option value model has only been applied to retirement data when the pension rules are fixed. Second, there is a selection bias in the sample of senior teachers: among the retirement-eligible teachers only the "stayers" are in the sample, while the "early leavers" are absent. This bias has not been adjusted in the previous studies. Third, the SW model is estimated based on the likelihood of panel data of individuals (teachers or salesmen). The cost of computing the likelihood increases in the number of teachers and the length of the sample period. For a larger state, such as Texas, and/or a longer sample period, the computation cost may be prohibitively high. The second chapter solves these problems. First, I model expectations of pension rule changes. Second, I adjust the sample selection bias by using distribution of initial preference errors. Third, I group individual teachers into a fixed number of (age, experience) cells to reduce the time of evaluating the likelihood. I estimate the model under different expectation assumptions and compare their performance by simulation. The estimated SW model exhibits good in-sample and out-of-sample fits. Counterfactual analysis shows that pension enhancements reduce the retirement age by around 0.4 years for the 1994 cohort teachers and by more than one year for teachers in the steady state. Finally, I compare SW option value model with an alternative widely applied structural model of retirement, dynamic programming model. Compared to dynamic programming model, the SW model tends to predict early retirement.

The impact of Wal-Mart in lowering incumbents’ retail prices has been well documented by previous studies using reduced form models. This article uses a structural model to examine the pricing behavior and promotion responses of incumbent supermarkets to a rapid expansion of Wal-Mart Supercenters (WMS) using the Dallas–Fort Worth milk market as a case study. Empirical results verify that WMS expansion disciplines incumbent supermarkets by decreasing oligopoly power and numbing consumer responsiveness to promotion. In addition, WMS expansion lures away price-sensitive consumers, leaving incumbent supermarkets to face more price-inelastic but lower demands for milk.

This chapter summarizes the overall tendering and contracting process in the pharmaceutical industry by providing an overview of the first-sealed price auction theory, auction rules, and drug pricing mechanism of different countries. Comparing procurement systems across Asia, Africa, Europe, and Latin America, the review casts light on various pharmaceutical bidding systems across the world and their impact on drug prices. Then, this review focuses on the empirical estimation of first-price auction models. In terms of model specification, we compare the two most commonly used empirical methods for bidding price estimation: structural models and reduced form approaches to test the auction theory. Maximum likelihood estimation is the most frequently used method for structural estimation in literature and selection bias correction is widely adopted using reduced form models. In addition to parametric model construction, we also provide an extensive introduction of non-parametric testing methodologies, including non-parametric estimation and quantile-based estimation to reduce the computation complexity and further illustrate how auction theory could be validated by real-world applications. Additional thoughts and adjustments on non-parametric testing are brought up based on a real-world tendering use case from a large multi-national pharmaceutical company.

Analysts associated with the Cowles Commission attached great importance to the distinction between structural and reduced-form models: in their view structural models, but not reduced-form models, allow the analysis of causal relations. They did not present clear justification for this view. Here we show that this insight is correct, and make the demonstration of it precise. Causal relations are shown to depend on parameter restrictions that are explicit in the structural form, but not in the reduced form when the coefficients are interpreted as unrestricted constants. The requisite parameter restrictions are those associated with implementation-neutral causation. A graphical procedure is outlined that identifies causal orderings and also the ordering based on implementation-neutral causation. The same procedure applied to reduced form models produces the implementation-neutral causal ordering only if the parameter restrictions are explicitly incorporated in the reduced form. The analysis is applied in investigating the validity of the causal Markov condition.

The VAR and cointegrated VAR model considered in the previous chapters are reduced form models. As argued before, the dynamic properties of the VAR system are often investigated within an impulse response analysis. Because of the reduced form nature of the models considered in Chapters 2 and 3 economic interpretation is often not possible within this framework. In recent years structural VAR models have become a popular modeling tool in empirical macroeconometrics and macroeconomics. Similar to reduced form VAR models, structural VARs have the same problems related to the large number of parameters. Therefore, in this chapter we discuss possibilities to combine the structural restrictions needed to identify the economic shocks and the subset restrictions discussed in Chapter 2. This chapter is structured as follows: Section 4.1 reviews the concept of structural VAR models and provides an overview of the structural models considered. In Section 4.2 we describe the estimation of SVAR models and suggest some estimation algorithms that can be used if subset restrictions are present and, moreover, provide an illustrative example. In Section 4.3 we compare different estimation methods for subset SVAR models and investigate the effects of data based model reduction on the precision of structural parameter estimates, impulse response point and interval estimates. Section 4.4 summarizes the main results.KeywordsImpulse ResponseModel ReductionGeneralize Methodof MomentStructural ShockGeneralize Methodof Moment EstimateThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Purpose This study examined hope, meaning in life (MIL), and religious/spiritual struggle (RSS) as predictors of the quality of life (QOL) in cancer patients. We hypothesized a positive association of QOL with hope and MIL, whereas a negative association with RSS. The stage of cancer was hypothesized as a moderator variable between QOL and hope. Hope and MIL were assumed as positive predictors and RSS as negative predictor of QOL. Methods Data stem from the cross-sectional survey study of 300 cancer patients (Mean age = 50.97 ± 13.50 SD). Herth Hope Index, Meaning in Life Scale, Religious Spiritual Struggle Scale and WHO-QOL-BRIEF were used. The correlation coefficient and partial least square structural equation modeling approach (PLS-SEM) were used for assessing the measurement model and the structural model. Results As hypothesized, QOL was found positively associated with Hope and MIL, but negatively associated with RSS. The stage of cancer was hypothesized as a negative moderator. The three predictors significantly predicted QOL in cancer patients and explained 75.3% of the variance in QOL, and the overall model fit was adequate (SRMR = 0.075). Hope and MIL had a positive impact on QOL (β = .356, p < 0.01; β = .355 p < 0.01, respectively), whereas RSS had a negative impact (β = –.102, p < .05). The Stage of cancer did not moderate the path coefficient between the hope and QOL to a significant degree (β = .097, p > 0.01). Conclusion In cancer patients, hope and MIL are facilitators of QOL. Addressing religious and spiritual concerns and struggles is critical to overall QOL improvement.

Structural Estimation of Decision Making under Natural Hazard Risk

This paper examines three hypotheses using the time-series between 1978 and 1995 of quarterly tourist flows into Japan, Australia and New Zealand. First, whether periodic models can be used to successfully forecast tourism arrival series. Second, whether the Basic Structural Model (BSM) can forecast as accurately as the Box Jenkins (ARIMA) model. Third, whether the integrated seasonal univariate models forecast more accurately than the naive process. The paper concludes that the periodic model does not improve forecast accuracy. The BSM model performs at least as well as the ARIMA model, and the naive process is not a substitute for seasonal integrated models.

This article develops a three-factor defaultable term structure model for the pricing of a wide range of risky debt contracts and derivatives. One of the factors that determine the credit spread is the so-called uncertainty process, which can be understood as an aggregation of all information currently available on the quality of the firm. The authors assume that the spread between a defaultable and a non-defaultable bond is driven to a considerable extent by the uncertainty index, but also that contractual provisions, liquidity, and the premium demanded in the market for similar instruments have a great impact on credit spreads. Credit spreads can be easily related to business cycles by replacing the uncertainty index by some index of macroeconomic variables without any change of the theoretical framework. The analytical solution obtained for defaultable bonds can be implemented easily in practice, as all the variables and parameters can be inferred from market data. The authors demonstrate application of the model to the pricing of a variety of default-related instruments such as credit derivatives.

A four‐factor model (the extended model of Schmid and Zagst) is presented for pricing credit risk related instruments such as defaultable bonds or credit derivatives. It is an advancement of an earlier three‐factor model. In addition to a firm‐specific credit risk factor, a new systematic risk factor in the form of GDP growth rate is included. This new model is set in the context of other hybrid defaultable bond pricing models and empirically compared to specific representatives. We find that a model based only on firm‐specific variables is unable to capture changes in credit spreads completely. However, it is shown that in this model, market variables such as GDP growth rates, non‐defaultable interest rates and firm‐specific variables together significantly influence credit spread levels and changes.