Reduced-form Approach Research Articles

Inter-industry network and credit risk

As previous literature has documented cross-industry returns and tail risk predictability, especially during a financial crisis, this research investigates the effects of industries' position within an economy, inter-industry connectedness, and industry returns on credit risk using a reduced-form approach. We employ an aggregate measure of tail risk emitted from an industry to capture its outgoing connectedness with other industries, and our empirical results show that the outgoing connectedness of some highly central industries positively impacts all sample firms’ default probabilities, controlling for a variety of firm-specific and macroeconomic variables that are well-known to be related to corporate defaults. In sum, our empirical results support that industry network risk helps explain corporate default and improves default prediction accuracy.

Does geographical exposure to language learning centres affect language skills and labour market outcomes in a bilingual city?

In this paper, we investigate the effects of geographical exposure to local language training centres in a bilingual urban labour market, the Metropolitan Area of Barcelona, exploiting the implementation of a language policy that provided publicly subsidized language courses for adults. Our variable of interest consists in a measure of spatial availability of language schools that captures potential exposure and its expansion over time. First, we focus on the formation of local language skills, adopting a reduced-form approach. Our results indicate that exposure to language learning opportunities has a positive but quantitatively modest effect on local language skills, since individuals residing in neighbourhoods with a higher supply of language centres are more likely to be able to speak and write in Catalan. The effect is very robust to falsification exercises and several sensitivity checks and is driven by younger individuals, and especially by those who were born in Catalonia. Second, we analyse whether accessibility to language centres also affects employment, working hours, employment sector, and occupation. Our results indicate that, although skills in Catalan are positively and significantly associated with improved labour market outcomes, spatial accessibility to language centres is not directly related to any of them. This lack of effect is possibly due to the fact that the impact of geographical exposure on language skills is too small in size to improve performance in the local labour market.

Bayesian persuasion: Reduced form approach

We introduce reduced form representations of Bayesian persuasion problems where the variables are the probabilities that the receiver takes each of her actions. These are simpler objects than, say, the joint distribution over states and actions in the obedience formulation of the persuasion problem. This can make a difference in computational and analytical tractability, which we illustrate with two applications. The first shows that with quadratic receiver payoffs, the worst-case complexity scales with the number of actions and not the number of states. If |A| and |S| denote the number of actions and states respectively, the worst case complexity of the obedience formulation is O(|A||S|(|S|+|A|)1.5L) where L is its input size. The worst-case complexity of the reduced form representation is O(|A|2.5L). In the second application, the reduced form leads to a simple greedy algorithm to determine the maximum value a sender can achieve in any cheap talk equilibrium.

The Best of Both Worlds: Combining Randomized Controlled Trials with Structural Modeling

There is a long-standing debate about the extent to which economic theory should inform econometric modeling and estimation. This debate is particularly evident in the program/policy evaluation literature, where reduced-form (experimental or quasi-experimental) and structural modeling approaches are often viewed as rival methodologies. Reduced-form proponents criticize the assumptions invoked in structural applications. Structural modeling advocates point to the limitations of reduced-form approaches in not being able to inform about program impacts prior to implementation or about the costs and benefits of program designs that deviate from the one that was implemented. In this paper, we argue that there is a new emerging view of a natural synergy between these two approaches, that they can be melded to exploit the advantages and ameliorate the disadvantages of each. We provide examples of how data from randomized controlled trials (RCTs), the exemplar of reduced form practitioners, can be used to enhance the credibility of structural estimation. We also illustrate how the structural approach complements experimental analyses by enabling evaluation of counterfactual policies/programs. Lastly, we survey many recent studies that combine these methodologies in various ways across different subfields within economics. (JEL C21, C52, C53, H24, I38, J13, R38)

A Reduced Form Approach for Modeling Credit Risk Sensitivity to Excessive CO2 Emissions

A Reduced Form Approach for Modeling Credit Risk Sensitivity to Excessive CO2 Emissions

The disaggregated environmental effects of growth and distributional heterogeneity: Evidence from emerging markets economies

The environment-growth literature mainly relies on reduced-form approaches and overlooks the environmental role of technological changes and structural effects of growth. Providing comprehensive evidence on the decomposed environment-growth linkages also demands accounting for the distributional heterogeneity. Accordingly, we examine the decomposed structural effects of economic growth on GHG emissions in the presence of renewable energy and institutional quality in 29 Emerging Market Economies (EMEs) using different panel estimation approaches. Based on the panel MM-Quantile Regression model, which allows for unobserved distributional heterogeneity, our findings invariably confirm that economic growth in EMEs creates positive scale and composition effects—an increase in the scale-and composition-induced economic growth tends to worsen environmental pressures. In contrast, growth appears to reduce emissions through its technique effect. Renewable energy and Institutional quality are also negatively related to GHG emissions, with the impacts being stronger in lower-emitting countries. These results are robust to alternative panel regression models considered in the paper. Further, the impacts of all variables are heterogeneously distributed across different GHG emission levels. The negative moderating role of renewable energy and institutional quality in the growth-GHG emissions linkage strongly suggests that EMEs need to accelerate their green growth transition by expanding the share of renewable energy technologies and improving their institutional frameworks.

A principal–agent approach for estimating firm efficiency: Revealing bank managerial behavior

We consider agency-theory-based structural and reduced form models of bank performance. In the structural models, we take into account the managerial decision-making processes, and reveal underlying managerial efforts and thereby managerial behavior. In an empirical application, we estimate performance of Eurozone banks using our novel structural and reduced form approaches by Markov Chain Monte Carlo techniques. Our findings show, for the first time, that bank underperformance persists in the Eurozone whereas considerable variability across Member States exists. Our agency-theory-based structural modeling would favor cooperation of all interested parties and towards higher financial integration.

Approximate value adjustments for European claims

We consider the problem of computing the Value Adjustment of European contingent claims when the possibility of default of either party is considered, possibly including also funding and collateralization requirements.As shown in Brigo et al. (Brigo, Liu, Pallavicini, and Sloth (2016b), Brigo, Francischello, and Pallavicini (2016a)), this leads to a more articulate variety of Value Adjustments (XVA) that introduce some nonlinear features. When exploiting a reduced-form approach for the default times, the adjusted price can be characterized as the solution to a possibly nonlinear Backward Stochastic Differential Equation (BSDE). The expectation representing the solution of the BSDE is usually quite hard to compute even in a Markovian setting, and one might resort either to the discretization of the Partial Differential Equation characterizing it or to Monte Carlo Simulations. Both choices are computationally quite expensive, In this paper, we suggest an alternative method based on an appropriate change of numéraire and a Taylor polynomial expansion when intensities are represented by affine processes correlated with the asset price. The numerical discussion at the end of this work shows that, at least in the case of the Cox-Ingersoll-Ross (CIR) intensity model, even the simple first-order approximation has a remarkable computational efficiency.

On the measurement of the elasticity of labour

We use a simple theoretical framework, a building block of many macroeconomic models, to study the prominently debated relationship between the model parametrisation of the Frisch elasticity and the reduced-form evidence on the elasticity of labour. Focusing on tax holidays, we show that the elasticity measured with a reduced-form approach is only equal to the Frisch-elasticity parameter if there are no income or general equilibrium effects. Furthermore, for a wide range of standard values of the Frisch-elasticity parameter, the response of labour generated by a tax holiday in the model is aligned with the reduced-form evidence.

Getting into the details: structural effects of economic growth on environmental pollution in Ethiopia

Reduced-form approaches are like a ‘black-box’ which do not explicitly display the possible channels (exact forces) through which growth may influence the environment. Accordingly, this study aims to provide some empirical evidence regarding the underlying structural effects of growth on emissions of carbon dioxide (CO2), Methane (CH4), and Nitrous oxide (N2O) in Ethiopia over 1975–2017. Autoregressive Distributed Lag (ARDL) model is employed and the results confirm that the scale effect of growth increases all types of emissions in both the short run and long run. And, the composition effect has a long-run monotonically increasing relationship with CO2 emissions and a non-increasing pattern with CH4 and N2O emissions. On the other hand, a generally decreasing (for CO2 emissions) and an Inverted-U shaped (for CH4 and N2O emissions) technique effects of growth are obtained. This indicates that while growth through its technique effect reduces CO2 even at a lower level of income, the country needs to achieve a higher income level for the technique effect to be effective in reducing CH4 and N2O emissions. Fossil fuel energy appears to be the main driver of environmental pollution. Furthermore, the Toda-Yamamoto Granger causality test indicates a unidirectional causality from the three structural components of growth to all emissions. The findings, generally, suggest that a self-correcting mechanism in the growth process may not automatically reduce environmental pollution. Quite simply, to achieve environmentally sustainable economic growth, the technique effect should be sufficiently strong to offset the scale effect.

PDE models for the pricing of a defaultable coupon-bearing bond under an extended JDCEV model

We consider a two-factor model for the pricing of a non callable defaultable bond which pays coupons at certain given dates. The model under consideration is the Jump to Default Constant Elasticity of Variance (JDCEV) model. The JDCEV model is an improvement of the reduced form approach, which unifies credit and equity models into a single framework allowing for stochastic and possible negative interest rates. From the mathematical point of view, the valuation involves two partial differential equation (PDE) problems for each coupon. First, we obtain the existence of solution for these PDE problems. In order to solve them, we propose appropriate numerical schemes based on a Crank-Nicolson semi-Lagrangian method for time discretization combined with quadratic Lagrange finite elements for space discretization. Once the numerical solutions of the PDEs are obtained, a post-processing procedure is carried out in order to achieve the value of the bond. This post-processing includes the computation of an integral term which is approximated by using the composite trapezoidal rule. Finally, we present some numerical results for real market bonds issued by different firms in order to illustrate the proper behaviour of the numerical schemes. Moreover, we obtain an agreement between the numerical results from the PDE approach and those ones obtained by applying a Monte Carlo technique and an asymptotic aproximation method.

Optimal Time-Consistent Investment and Reinsurance Strategies with Default Risk and Delay under Heston’s SV Model

Considering the influence of past information on the decision-making of insurers, the correlation between the insurance businesses owned by insurers, and the possible default faced by insurers, we investigate the mean-variance investment and reinsurance problem with the default risk, delay, and common shock dependence. We characterize the insurance market by two-dimensional dependent claims, the financial market by the Heston SV model, and default risk by reduced-form approach and then obtain the evolution equation of the insurer’s wealth. Based on the introduction of time delay, the insurer’s wealth dynamics characterized by a stochastic delay differential equation are obtained. Furthermore, applying stochastic control theory within the game-theoretic framework and stochastic control theory with delay, we derive optimal time-consistent investment and reinsurance strategies, as well as equilibrium value function and equilibrium efficient frontier. Finally, we use a numerical example to analyze the influence of parameters on the time-consistent equilibrium strategies and give an economic explanation.

ON THE FAILURE AND SYSTEMIC RISK OF INNOVATION CLUSTER: COPULA APPROACH

In order to assess and parameterize the risk of innovation activity implemented by innovation clusters, it is necessary to determine the reliable tools of measuring of systemic risk. Purpose – to propose an adequate approach to evaluate the systemic risk with regard to the impact of interlinkages between cluster entities and other external factors. Research methodology – general overview of research papers and documents presenting concepts and methodologies of evaluation of systemic risk and performance of networked structures as approach to evaluate the systemic risk with regard to the impact of interlinkages between cluster entities and other external factors, applied research. Findings – it is suggested to develop the further parameterization of intensity. Modelling of the tail dependence and asymmetric dependence between pairs of networked positions remains an important task. Research limitations – the lack of information concerning the structure and types of interactions and relationship between the members of innovation cluster. There are made some additional assumptions related to reduced-form approach of credit risk modelling. Practical implications – proposed conceptual model of evaluation of systemic risk should be useful for understanding and further treatment of measuring risk in a case of innovation management. Originality/Value – the concept of the measuring the systemic risk in innovation cluster as a joint probability of correlated failure of commercialization of innovative activity results is proposed and analysed in this paper.

A closed formula for illiquid corporate bonds and an application to the European market

How to price illiquid corporate bonds when their prices are not available for several days in the marketplace, but other bonds of the same issuer trade frequently? This situation appears to be quite common in the fixed income market: it is rather usual to find issuers that, besides liquid benchmark bonds, issue some other debt instruments that either are placed to a small number of investors in private placements or have a limited issue size. To answer to this question we propose an option approach for pricing bond illiquidity that is reminiscent of the celebrated work of Longstaff (1995) on the non-marketability of some non-dividend-paying shares in IPOs.Our approach models interest rate and credit risks via a convenient reduced-form approach. We deduce a simple closed formula for illiquid corporate coupon bond prices when liquid bonds with similar characteristics (e.g. maturity) are present in the market for the same issuer. The key model parameter is the time-to-liquidate a position, i.e. the time that an experienced bond trader takes to liquidate a given position on a corporate coupon bond. We show that illiquid bonds present an additional liquidity spread that depends on the time-to-liquidate aside from bond volatility.We provide a detailed application for two financial issuers in the European market.

Commitment Institutions and Electoral and Political Instability: A Reduced-Form Approach

Commitment Institutions and Electoral and Political Instability: A Reduced-Form Approach

Incidence Network, Risk Spillover and Systemic Risk of Financial Institutions

Systemic risk is closely related to the risk contagion of financial institutions. The risk of a single financial institution will spread among financial systems through the complex incidence network among financial institutions, and lead to the outbreak of crisis. However, the risk contagion paths of different financial institutions are different, and the degree of impact is significantly different. The research of using the reduced-form approach mostly focuses on measuring the risk level of a single institution in the system, but there is relatively little literature on the measurement of risk spillover level among financial institutions and different types of financial sectors. The existing research for complex network model analysis is still focused on the construction of multiple symmetric correlation matrix, and the analysis of financial institutions through the construction of asymmetric correlation matrix is still a small number. Based on the classification of commercial banks, securities companies, insurance institutions and other types of financial institutions, this paper measures the impact of specific financial institutions on systemic risk from the perspective of risk spillover degree of financial institutions. Then, according to the nonparametric Granger causality test, the incidence matrix of financial institutions is constructed, and the financial institutions are used as nodes to depict and describe the incidence network indicators and network center properties of financial institutions. At the same time, the risk area is divided by combining the risk spillover index and the input/output value of financial institutions, so as to clearly identify the vulnerability of risk tolerance and the infectivity of risk transmission of financial institutions, in order to judge the risk prevention core and the key of targeted measures. The empirical results show that banking financial institutions are the core of China’s financial incidence network, and they have high stability. Securities financial institutions are at a high level in the level of systemic risk spillover and the degree of financial network connection, and they are the key sectors for China’s systemic risk prevention. The vulnerability and infectivity of different financial institutions are different, and the vulnerability and infectivity of the same financial institution are also different. The increase of capital scale does not mean the increase of risk contagion and vulnerability. Therefore, the risk identification of financial institutions should be comprehensive, not limited to a single standard. On the basis of focusing on the scale of financial institutions, combined with the direction, path and degree of risk impact of specific financial institutions, the risk prevention core is determined. At the same time, according to the different characteristics of risk vulnerability and risk contagion of financial institutions, we should implement targeted regulatory measures.

Revisiting the exchange rate pass through: A general equilibrium perspective

A large literature estimates the exchange rate pass-through to prices (ERPT) using reduced-form approaches, whose results are an important input for Central Banks. We show two shortcomings of these empirical measures for monetary policy analysis, which are quantitatively important and may lead to imprecise and biased inflation predictions. First, while the literature describes a single ERPT, which we will label unconditional, there are different ERPT conditional on each shock that hits the economy. Second, these crucially depend on expected monetary policy, so that empirical ERPT measures should not be taken as given in evaluating policy actions. We use a simple model of a small and open economy to understand the intuition behind these two critiques, showing that these results seem to hold under many alternative specifications. We then highlight the quantitative relevance of these distinctions using a large-scale DSGE model of a small open economy.

INTERBANK CREDIT RISK MODELING WITH SELF-EXCITING JUMP PROCESSES

The credit crunch of 2007 caused major changes in the market of interbank rates making the existing interest rate theory inconsistent. This paper puts forward one way to reconcile practice and theory by modifying the arbitrage-free condition. In this framework, the forward Libor rate is no longer considered as a risk-free rate and the credit and liquidity risks within the interbank market partly drive its dynamics. In a similar manner to the multiple-curve approach, we model the evolution of default-free rates, assimilated to overnight interest swap rates, and the default times of an interbank market segment determined by its tenor. For each segment, we use the reduced form approach to model the arrival rate of defaults with a self-exciting jump-diffusion process. Then, we deduce the dynamics of the spot forward Libor rates and provide closed-form approximation pricing formulae for options on forward Libor rates and swap rates. Even in a context of negative interest rates and compared to other forms of intensity processes such as a CIR, the self-excitation property allows a better understanding of the spread OIS-IRS and provides information about the interbank credit risk. Furthermore, our framework enables to parse the impact of the interbank credit risk on forward Libor as well as on interest rates derivatives like caps, floors, and swaptions.

Information Limits of Aggregate Data

This paper uses a small model in the Cowles Commission (CC) tradition to examine the limits of aggregate data. It argues that more can be learned about the macroeconomy following the CC approach than the reduced form and VAR approaches allow, but less than the DSGE approach tries to do.

Gasoline Price and Competition: New Evidence from Traffic Pattern

Competition is considered as an important factor that influences gasoline prices. In spatial competition, an increased density of competitors has a direct impact on lowering gasoline price. However, prior research omitted an important demand factor: traffic volume. This paper uses a reduced-form approach to test for the relationship between market density and retail gasoline price with and without traffic volume. The omission of traffic volume biases the estimated effect of market density on retail gasoline price and leads to a 61% overstatement. Furthermore, this paper examines the relationship between market density and price dispersion with and without traffic dispersion.