Reduced-form Approach Research Articles

Entry Costs & Increasing Trade

Using confidential microdata from the US Census, we find that the fraction of manufacturing plants that export rose from 21% in 1987 to 39% in 2006. It has been suggested that similar trends in other countries may have been caused by declining costs of entering foreign markets. Our study tests this hypothesis for the first time. Both reduced form and structural estimation approaches find little evidence that the entry costs declined significantly in the US over this period. We instead argue that changes in other factors that determine export status are sufficient to explain these trends.

Does Modeling Framework Matter? A Comparative Study of Structural and Reduced-Form Models

This study provides a rigorous empirical comparison of structural and reduced-form credit risk frameworks. As major difference we focus on the discriminative modeling of default time. In contrast to previous literature, we calibrate both approaches to bond and equity prices. By using same input data, applying comparable estimation techniques, and assessing the out-of-sample prediction quality on same time series of CDS prices we are able to judge whether empirically the model structure itself makes an important difference. Interestingly, the models' prediction power is quite close on average. Still, the reduced-form approach outperforms the structural for investment-grade names and longer maturities.

Dissecting Corporate Bond and CDS Spreads

In this article, the authors propose a new method to estimate the components of corporate bond and CDS spreads. They develop a CDS pricing model with default and nondefault factors and a corporate bond pricing model with default, tax, and liquidity factors using the reduced-form approach, and they jointly estimate parameters of both models from the pooled data. By formulating default intensity as a common factor in the prices of the CDS and reference bonds, the authors are able to identify the default and nondefault components of yield spreads more precisely. They find that, on average, the liquidity premium accounts for about 20–25% of corporate yield spreads across ratings and the size of the liquidity premium increases as the rating decreases. Furthermore, they find that the CDS spread contains a nontrivial nondefault component. Ignoring this component in the CDS spread thus results in a serious bias in the estimate of spread components when using the CDS information to aid in decomposition of corporate yield spreads.

HAZARD PROCESSES AND MARTINGALE HAZARD PROCESSES

In this paper, we build a bridge between different reduced‐form approaches to pricing defaultable claims. In particular, we show how the well‐known formulas by Duffie, Schroder, and Skiadas and by Elliott, Jeanblanc, and Yor are related. Moreover, in the spirit of Collin Dufresne, Hugonnier, and Goldstein, we propose a simple pricing formula under an equivalent change of measure.Two processes will play a central role: the hazard process and the martingale hazard process attached to a default time. The crucial step is to understand the difference between them, which has been an open question in the literature so far. We show that pseudo‐stopping times appear as the most general class of random times for which these two processes are equal. We also show that these two processes always differ when τ is an honest time, providing an explicit expression for the difference. Eventually we provide a solution to another open problem: we show that if τ is an arbitrary random (default) time such that its Azéma's supermartingale is continuous, then τ avoids stopping times.

Dissecting Corporate Bond and CDS Spreads

In this paper, we propose an alternative approach to estimate the components of corporate bond and CDS spreads. We develop a CDS pricing model with default and nondefault factors, and a corporate bond pricing model with default, tax and liquidity factors using the reduced-form approach, and jointly estimate parameters of both models from pooled data. By formulating default intensity as a common factor in the prices of the CDS and reference bonds, we are able to identify the liquidity and other components of yield spreads more precisely. We find that on average the liquidity premium accounts for about 23% of the corporate yield spread and the size of the liquidity premium increases as the rating decreases. Furthermore, the CDS spread contains a significant nondefault component. Results show that ignoring the nondefault component in the CDS premium results in biased estimates of corporate yield spread components when using the CDS information to aid in decomposition of yield spreads.

Obesity, smoking, and cigarette taxes: Evidence from the Canadian Community Health Surveys

Recent studies suggest an ambiguous relationship between obesity and cigarette taxes. We employ Canadian data to evaluate the effects of cigarette taxes on smoking and obesity. We use a simple reduced form approach and exploit the significant cross-province differences that exist between Eastern and Western Canada to estimate the effects of higher cigarette taxes using aggregate health region and individual level data from the 2003 and 2005 waves of the Canadian Community Health Surveys (CCHS). OLS estimates based on health regions data suggest that a 10% increase in cigarette taxes is significantly correlated with a 4-5% increase in the percentage of obese population. We also find cigarette tax elasticities of between -0.2 and -0.4 with respect to the percentage of smokers. Estimates from individual level data are similar. In tandem, these results offer support to the possibility that health benefits from higher cigarette taxes and lower smoking, might be partially offset by a corresponding increase in obesity levels.

A Reexamination of the Relationship between Organizational Forms and Distribution Channels in the U.S. Property Liability Insurance Industry

How do property liability insurance companies choose their organizational forms and distribution channels? Prior studies have not yet provided a consistent conclusion. In this paper, we propose a reduced form approach to reexamine the relationship between organizational forms and distribution channels in the insurance industry, using cross-sectional data pertaining to U.S. property liability insurance companies in 2004. We adopt a conditional dependence test, which can overcome the sensitivity problem of the structural form setting. The results show that after we control for all explanatory variables, the relationship between organizational forms and distribution channels is conditionally uncorrelated. The result is consistent with Regan and Tzeng (1999), but contradicts the findings of Baranoff and Sager (2003) and Kim et al. (1996).

Time Varying and Dynamic Models for Default Risk in Consumer Loans

SummaryWe review the incorporation of time varying variables into models of the risk of consumer default. Lenders typically have data which are of a panel format. This allows the inclusion of time varying covariates in models of account level default by including them in survival models, panel models or ‘correction factor’ models. The choice depends on the aim of the model and the assumptions that can be plausibly made. At the level of the portfolio, Merton-type models have incorporated macroeconomic and latent variables in mixed (factor) models and Kalman filter models whereas reduced form approaches include Markov chains and stochastic intensity models. The latter models have mainly been applied to corporate defaults and considerable scope remains for application to consumer loans.

Pricing Defaultable Bonds: A New Model Combining Structural Information with the Reduced-Form Approach

We propose a new model to price defaultable bonds which incorporates features of both structural and reduced-form models of credit risk. The main novelty of the model is that the default intensity is described by an additional stochastic differential equation coupled with the process of the firm's asset value. Such an approach allows to incorporate structural information as well as to capture the complex dynamics of unexpected default due to not firm-specific variables. From the practical standpoint, the model proposed offers great flexibility to describe credit spreads and allows to correctly reproduce important stylized facts. In particular yield-spread curves of many different shape can be obtained, including double humped term curves, which reveals to be crucial in order to accurately fit realized market data. Finally the model is also mathematically tractable, as a closed-form approximate solution can be obtained using a perturbation approach in conjunction with the Laplace transform. Extensive numerical simulation is presented showing that this formula is accurate and computationally efficient.

Reduced-form valuation of callable corporate bonds: Theory and evidence

We develop a reduced-form approach for valuing callable corporate bonds by characterizing the call probability via an intensity process. Asymmetric information and market frictions justify the existence of a call-arrival intensity from the market's perspective. Our approach both extends the reduced-form model of Duffie and Singleton (1999) for defaultable bonds to callable bonds and captures some important differences between call and default decisions. A comprehensive empirical analysis of callable bonds using both our model and the more traditional American option approach for valuing callable bonds shows that the reduced-form model fits callable bond prices well and that it outperforms the traditional approach both in- and out-of-sample.

Sufficient Statistics for Welfare Analysis: A Bridge Between Structural and Reduced-Form Methods

The debate between structural and reduced-form approaches has generated substantial controversy in applied economics. This article reviews a recent literature in public economics that combines the advantages of reduced-form strategies—transparent and credible identification—with an important advantage of structural models—the ability to make predictions about counterfactual outcomes and welfare. This literature has developed formulas for the welfare consequences of various policies that are functions of reduced-form elasticities rather than structural primitives. I present a general framework that shows how many policy questions can be answered by estimating a small set of sufficient statistics using program-evaluation methods. I use this framework to synthesize the modern literature on taxation, social insurance, and behavioral welfare economics. Finally, I discuss problems in macroeconomics, labor, development, and industrial organization that could be tackled using the sufficient statistic approach.

Bank Size and Small- and Medium-sized Enterprise (SME) Lending: Evidence from China

Using panel data collected in 2005, we evaluate how bank size, discretion over credit, incentive schemes, competition, and the institutional environment affect lending to small- and medium-sized enterprises in China. We deal with the endogeneity problem using instrumental variables, and a reduced-form approach is also applied to allow for weak instruments in estimation. We find that total bank asset is an insignificant factor for banks' decision on small- and medium-enterprise (SME) lending, but more local lending authority, more competition, carefully designed incentive schemes, and stronger law enforcement encourage commercial banks to lend to SMEs.

MODELING THE RECOVERY RATE IN A REDUCED FORM MODEL

This paper provides a model for the recovery rate process in a reduced form model. After default, a firm continues to operate, and the recovery rate is determined by the value of the firm's assets relative to its liabilities. The debt recovers a different magnitude depending upon whether or not the firm enters insolvency and bankruptcy. Although this recovery rate process is similar to that used in a structural model, the reduced form approach is maintained by utilizing information reduction in the sense of Guo, Jarrow, and Zeng. Our model is able to provide analytic expressions for a firm's default intensity, bankruptcy intensity, and zero‐coupon bond prices both before and after default.

Liquidity Premia in the Credit Default Swap and Corporate Bond Markets

This paper employs a new approach to estimating the size of liquidity premia in the credit default swap (CDS) and corporate bond markets. We develop a CDS pricing model with liquidity and default, and a corporate bond pricing model with default, taxes, and liquidity using the reduced-form approach, and jointly estimate parameters of both pricing models from pooled data using the generalized method of moments. By formulating default intensity as a common factor of the spreads of the CDS and reference bonds, we are able to identify the liquidity and other components of spreads more precisely. We find that both CDS and corporate bond spreads contain significant liquidity components. On average, the liquidity premium accounts for 13% of the CDS spread and 23% of the corporate yield spread. The size of the liquidity premium increases as the rating decreases. Estimates of liquidity premia in the CDS and corporate bond markets are highly correlated, and closely linked to bond-specific and aggregate liquidity measures. Results show that liquidity is important for CDS and corporate bond pricing. Ignoring CDS illiquidity results in a significant bias in estimation of corporate yield spread components when using the CDS information to aid in decomposition of spreads.

Money and Capital: A Quantitative Analysis

We study the effects of money (anticipated inflation) on capital formation. Previous papers on this topic adopt reduced-form approaches, putting money in the utility function or imposing cash in advance, but use otherwise frictionless models. We follow a literature that is more explicit about the frictions making money essential. This introduces several new elements, including a two-sector structure with centralized and decentralized markets, stochastic trading opportunities, and bargaining. We show how these elements matter qualitatively and quantitatively. Our numerical results differ from findings in the reduced-form literature. The analysis reduces the previously large gap between mainstream macro and monetary theory.

Money and Capital as Competing Media of Exchange in a News Economy

We study the effects of money (anticipated inflation) on capital formation. Previous papers on this adopt reduced-form approaches, putting money in the utility function or imposing cash in advance, but use otherwise frictionless models. We follow a literature that is more explicit about the frictions that make money essential. This introduces several new elements, including a two-sector structure with centralized and decentralized markets, stochastic trading opportunities, and bargaining. We show how these elements matter qualitatively and quantitatively. Our numerical results differ from findings in the reduced-form literature. The analysis also reduces the gap between monetary theory and mainstream macro.

Modelling Simultaneous Defaults: A Top-Down Approach

This paper provides a new approach in modelling dependent defaults within a top-down approach. First, a general framework to map the default of a set of obligors is developed by using a marked Poisson Process. Then, a characterization of the default intensity for a set of obligors is derived, which allows to incorporate elements of structural models into the intensity modelling framework. As a result the approach combines the advantages of reduced-form and structural approaches in modelling dependent defaults. Using the smart construction of our default model, valuation formulas for the three major payment blocks are easily derived and applied to credit derivative pricing. Furthermore, based on adequate dependency measures the ability of the top-down construction is pointed out. The dependencies induced by this approach are compared to the ones obtained within basic multi-entity structural and reduced-form models. Finally, the impact of a variation of the main dependency drivers on the fair spreads of credit derivatives are illustrated and compared to the selected benchmark models.

Caste discrimination and transaction costs in the labor market: Evidence from rural North India

This paper is an empirical attempt to quantify caste-based discrimination in the labor market using household data taken from rural North India. In the regression analysis, transaction costs associated with entry into the labor market and reservation wages are estimated simultaneously along with market wages. The estimation results provide evidence of the existence of transaction costs in the labor market and discrimination against backward classes with regard to access to regular employment. In line with previous studies, the results suggest that the achievements of India's reservation policy so far have at best been limited. In addition, a comparison between the estimates from the model employed in this paper and conventional (reduced-form) approaches shows that discrimination in labor market entry is likely to be underestimated in the conventional reduced-form approaches.

Credit Spreads und ihre Determinanten: Eine empirische Analyse für Deutschland

Credit Spreads and their Determinants: An Empirical Analysis for Germany Analyses of credit spreads, i. e. the difference between the returns on corporate loans and on no-risk investments for periods equivalent in length, can provide useful information to both business managers and to external observers. In this article, fundamental determinants of such credit spreads have been defined in theoretical terms and been subjected to empirical review on the basis of fixed-rate loan issues of non-financial DAX enterprises. At the micro-econometrics level, a new set of data for Germany has been used for taking account of empirically observable market characteristics in adequate panel methods. In this context, a structural model has been combined with a reduced form approach. Compared to traditional approaches, the result is a significantly better explanation based on economically provable variables.

Credit Risk and the Term Structure of Lease Rates: A Reduced Form Approach

Previous research either assumes default free leases or leases subject to default risk using a structural approach. However, structural credit risk models suffer from a common criticism that the firm’s asset value process is unobservable. We develop a reduced form credit risk model for leases that avoids making assumptions regarding unobservable asset valuation processes. Furthermore, we assume a correlated market and credit risk that provides us with a simple analytic formula for valuing defaultable lease contracts. Numerical analysis reveals that tenant credit risk can have a substantial impact on the term structure of leases. Finally, we use the model to demonstrate the implied lease term structure for a set of retail and financial firms in the Fall of 2000.