Reduced-form Model Research Articles

Synchronization of endogenous business cycles

Business cycles tend to comove across countries. However, standard models that attribute comovement to propagation of exogenous shocks struggle to generate a level of comovement that is as high as in the data. In this paper, we consider models that produce business cycles endogenously, through some form of non-linear dynamics—limit cycles or chaos. These models generate stronger comovement, because they combine shock propagation with synchronization of endogenous dynamics. In particular, we study a demand-driven reduced-form model in which business cycles emerge from strategic complementarities within countries, synchronizing their oscillations through international trade linkages. We develop an eigendecomposition that explores the interplay between non-linear dynamics, shock propagation and network structure, and use this theory to understand the mechanisms of synchronization. Next, we calibrate the model to data on 24 countries and show that the empirical level of comovement can only be matched by combining endogenous business cycles with exogenous shocks. Despite the limitations of using a stylized model, our results support the hypothesis that business cycles are at least in part caused by underlying non-linear dynamics.

Valuing Vulnerable Basket Options with Stochastic Liquidity Risk in Reduced-form Models

Valuing Vulnerable Basket Options with Stochastic Liquidity Risk in Reduced-form Models

Comparative Analysis of the Reduced form Model and the Structural Model in Credit Risk Modelling

Credit risk models are statistical tools to infer the future default probabilities and loss distribution of values of a portfolio of debts. Credit risk modelling is prevalent in today’s financial decision-making process. It turns out that both models of modelling credit risk contribute to explaining the default risk of listed firms, however, reduce-form model outperformances the structural model. Structural models are used to calculate the probability of default for a firm based on the value of assets and liabilities. The basic idea is that a company (with limited liability) defaults if the value of its assets is less than the debt of the company. The causal driver of defaults in structural model will choose to work with variables that help us explain what causes defaults. Default risk is endogenous in the structural model, this is so because the factors that causes defaults within a path are predictable. The structural model is an economic model with focus on options pricing, call option and put option. It provides clarity about the nature of defaults and how the various economic features that are chosen to relate with each other when defaults occur. The reduced form model is mostly concerned with prediction of when does defaults occurs? Default risk is exogenous to the reduced form model, can be caused by random events and most often comes as a surprise. Statistical models are used to observe the variables and help maximise the reduced form model. The empirical result suggests that reduce-form model can better predict the firm’s default risk.

Credit default swap pricing with counterparty risk in a reduced form model with Hawkes process

Credit default swap pricing with counterparty risk in a reduced form model with Hawkes process

IPlan: A Platform for Constructing Localized, Reduced-Form Models of Land-Use Impacts

To help young people understand socio-environmental systems and develop the confidence that meaningful action can be taken to address socio-environmental problems, young people need interactive simulations that enable them to take consequential actions in a familiar context and see the results. This can be achieved through reduced-form models with appropriate user interfaces, but it is a significant challenge to construct a system capable of producing educational models of socio-environmental systems that are localizable and customizable but accessible to educators and learners. In this paper, we present iPlan, a free, online educational software application designed to enable educators and middle- and high-school-aged learners to create custom, localized land-use simulations that can be used to frame, explore, and address complex land-use problems. We describe in detail the software application and its underlying computational models, and we present robust evidence that the accuracy of iPlan simulations is appropriate for educational contexts and preliminary evidence that educators are able to produce simulations suitable for their pedagogical goals and learner populations.

Merging Structural and Reduced-Form Models for Forecasting

Abstract Recent economic crises have posed important challenges for forecasting. Models estimated pre-crisis may perform badly when normal economic relationships have been disrupted. Meanwhile, forecasting, especially in central banks, is increasingly based on a suite of models, following two main approaches: structural (DSGE) and reduced form. The challenge remains to identify which model – or combination of models – is likely to make better forecasts in a changing environment. We explore this issue by assessing the forecasting performance of combinations of a medium-scale DSGE model with standard reduced-form methods applied to the Spanish economy and a reference period that includes both the great recession and the sovereign debt crisis. Our findings suggest that: (i) the mean reverting properties of the DSGE model cause it to underestimate the growth of real variables following the inclusion of crisis episodes in the estimation period; (ii) despite this, reduced-form VARs benefit from the imposition of an economic prior from the structural model; but (iii) pooling information in the form of variables extracted from the structural model with (B)VAR methods does not improve forecast accuracy. By analysing the quantiles of the predictive distributions, we also provide evidence that merging models can help improve the forecast in a context including crisis episodes.

Local Competition, Multimarket Contact, and Product Quality: Evidence From Internet Service Provision

AbstractI investigate the effect of competition on quality in the internet service provision industry: I examine both local competition within markets and multimarket contact among firms across markets. This industry offers an ideal setting, as quality is both objective and measurable. I use data from speedtest.net from 2008 to 2014 to estimate a reduced-form model of the effects of local competition and multimarket contact on realized consumer download speeds. I find that increased multimarket contact leads to decreased download speeds, which is consistent with the mutual forbearance hypothesis. I also find that duopolies lead to faster download speeds than do monopolies, but that further increases in the number of competitors decrease speeds.

A reduced-form model for lease contract valuation with embedded options

A reduced-form model for lease contract valuation with embedded options

Optimal investment and consumption strategies for an investor with stochastic economic factor in a defaultable market

This paper considers the issue of optimal investment and consumption strategies for an investor with stochastic economic factor in a defaultable market. In our model, the price process is composed of a money market account and a default-free risky asset, assuming they rely on a stochastic economic factor described by a diffusion process. A defaultable perpetual bond is depicted by the reduced-form model, and both the default risk premium and the default intensity of it rely on the stochastic economic factor. Our goal is to maximize the infinite horizon expected discounted power utility of the consumption. Applying the dynamic programming principle, we derive the Hamilton–Jacobi–Bellman (HJB) equations and analyze them using the so-called sub-super solution method to prove the existence and uniqueness of their classical solutions. Next, we use a verification theorem to derive the explicit formula for optimal investment and consumption strategies. Finally, we provide a sensitivity analysis.

Wrong Way Risk corrections to CVA in CIR reduced-form models

In this paper we provide an efficient methodology to compute the credit value adjustment of a European contingent claim subject to some default event concerning the issuer solvability, when the underlying and the default event are correlated. In particular, in a Black and Scholes market/CIR intensity-default model, we consider a second order expansion around the origin of a vulnerable call option with respect to a correlation parameter rho, which may be used to describe the wrong way risk of the contract, measuring the dependence between the underlying asset price and the option’s issuer default intensity. Numerical implementations of this approach are compared with the benchmark Monte Carlo simulations.

Identifying structural asymmetries by jointly estimating tourism expenditure intensity and extensity

This article proposes a structural framework for the joint estimation of tourists’ daily personal expenditures (intensity) and length of stay (extensity). We reconceptualize commonly accepted exogeneous determinants of both outcomes into a set of exogenous antecedents pre-existing the travel decision and a set of endogenous mediators that capture the role of market exchange after the travel decision and corresponding choices are made. Findings reveal that the effects of some exogenous factors, such as gender, income, and motives on total spending are fully mediated within the intensity and extensity components, absent of any direct impacts. Other factors, such as nationality, appear not to influence spending due to offsetting mediated effects. As these forces are difficult to discern via reduced-form modeling, the proposed structural framework provides tourism managers with deeper insight into the footprints of established expenditure determinants, potentially improving upon the efficacy of marketing strategies.

The Social Cost of Ozone-Related Mortality Impacts From Methane Emissions.

Atmospheric methane directly affects surface temperatures and indirectly affects ozone, impacting human welfare, the economy, and environment. The social cost of methane (SC-CH4) metric estimates the costs associated with an additional marginal metric ton of emissions. Current SC-CH4 estimates do not consider the indirect impacts associated with ozone production from changes in methane. We use global model simulations and a new BenMAP webtool to estimate respiratory-related deaths associated with increases in ozone from a pulse of methane emissions in 2020. By using an approach consistent with the current SC-CH4 framework, we monetize and discount annual damages back to present day values. We estimate that the methane-ozone mechanism is attributable to 760 (95% CI: 330-1200) respiratory-related deaths per million metric tons of methane globally, for a global net present damage of $1800/mT (95% CI: $760-$2800/Mt CH4; 2% Ramsey discount rate); this would double the current SC-CH4 if included. These physical impacts are consistent with recent studies, but comparing direct costs is challenging. Economic damages are sensitive to uncertainties in the exposure and health risks associated with tropospheric ozone, assumptions about future projections of NOx emissions, socioeconomic conditions, and mortality rates, monetization parameters, and other factors. Our estimates are highly sensitive to uncertainties in ozone health risks. We also develop a reduced form model to test sensitivities to other parameters. The reduced form tool runs with a user-supplied emissions pulse, as well as socioeconomic and precursor projections, enabling future integration of the methane-ozone mechanism into the SC-CH4 modeling framework.

An observation-based, reduced-form model for oxidation in the remote marine troposphere

The hydroxyl radical (OH) fuels atmospheric chemical cycling as the main sink for methane and a driver of the formation and loss of many air pollutants, but direct OH observations are sparse. We develop and evaluate an observation-based proxy for short-term, spatial variations in OH (ProxyOH) in the remote marine troposphere using comprehensive measurements from the NASA Atmospheric Tomography (ATom) airborne campaign. ProxyOH is a reduced form of the OH steady-state equation representing the dominant OH production and loss pathways in the remote marine troposphere, according to box model simulations of OH constrained with ATom observations. ProxyOH comprises only eight variables that are generally observed by routine ground- or satellite-based instruments. ProxyOH scales linearly with in situ [OH] spatial variations along the ATom flight tracks (median r2 = 0.90, interquartile range = 0.80 to 0.94 across 2-km altitude by 20° latitudinal regions). We deconstruct spatial variations in ProxyOH as a first-order approximation of the sensitivity of OH variations to individual terms. Two terms modulate within-region ProxyOH variations-water vapor (H2O) and, to a lesser extent, nitric oxide (NO). This implies that a limited set of observations could offer an avenue for observation-based mapping of OH spatial variations over much of the remote marine troposphere. Both H2O and NO are expected to change with climate, while NO also varies strongly with human activities. We also illustrate the utility of ProxyOH as a process-based approach for evaluating intermodel differences in remote marine tropospheric OH.

Empowering environmental change: role of green bonds in shaping green e-commerce and sustainable business.

This research aims to investigate the impact of green bonds on the development of sustainable and environmentally friendly e-commerce businesses, with a focus on promoting environmental empowerment. Recognizing the necessity of preparing for economic changes and strengthening institutional frameworks, this study addresses the shortcomings identified in previous research, including statistical limitations, insufficient inclusion of variables, and a lack of diversity. By bridging these gaps, the research explores the interconnections between economic expansion, sustainability, profitability, and effective governance. To account for country-specific variations, a robust reduced-form modeling strategy is employed, supplemented by generalized method of moments estimates to address potential variability. The study analyzes survey data spanning the years 1990 to 2019. The research findings confirm the significant role of organizational excellence and economic growth in fostering sustainability, lending support to the presence of the environmental Kuznets curve hypothesis. Additionally, the study underscores the potential adverse consequences for the natural environment if economic liberalization proceeds without robust governance structures. By providing original empirical evidence on the effectiveness of green bonds in driving the growth of sustainable e-commerce businesses, this research contributes to the field of environmental empowerment and emphasizes the importance of well-designed frameworks to guide economic transitions. The insights derived from this study have implications for policymakers, businesses, and organizations aiming to align economic growth with sustainability goals, ultimately facilitating a more environmentally conscious and resilient future.

Minimally capturing heterogeneous complier effect of endogenous treatment for any outcome variable

Abstract When a binary treatment D D is possibly endogenous, a binary instrument δ \delta is often used to identify the “effect on compliers.” If covariates X X affect both D D and an outcome Y Y , X X should be controlled to identify the “ X X -conditional complier effect.” However, its nonparametric estimation leads to the well-known dimension problem. To avoid this problem while capturing the effect heterogeneity, we identify the complier effect heterogeneous with respect to only the one-dimensional “instrument score” E ( δ ∣ X ) E\left(\delta | X) for non-randomized δ \delta . This effect heterogeneity is minimal, in the sense that any other “balancing score” is finer than the instrument score. We establish two critical “reduced-form models” that are linear in D D or δ \delta , even though no parametric assumption is imposed. The models hold for any form of Y Y (continuous, binary, count, …). The desired effect is then estimated using either single index model estimators or an instrumental variable estimator after applying a power approximation to the effect. Simulation and empirical studies are performed to illustrate the proposed approaches.

Particle MCMC in Forecasting Frailty-Correlated Default Models with Expert Opinion

Predicting corporate default risk has long been a crucial topic in the finance field, as bankruptcies impose enormous costs on market participants as well as the economy as a whole. This paper aims to forecast frailty-correlated default models with subjective judgements on a sample of U.S. public non-financial firms spanning January 1980–June 2019. We consider a reduced-form model and adopt a Bayesian approach coupled with the Particle Markov Chain Monte Carlo (Particle MCMC) algorithm to scrutinize this problem. The findings show that the 1-year prediction for frailty-correlated default models with different prior distributions is relatively good, whereas the prediction accuracy ratios for frailty-correlated default models with non-informative and subjective prior distributions over various prediction horizons are not significantly different.

The impact of concentration among venture capitalists: revisiting the determinants of venture capital

ABSTRACT This article analyzes the impact of the level of concentration among Venture Capitalists (VCs) on the supply of venture capital (VC), through the reduced form model for the equilibrium amount of VC (using a simultaneous equation model on aggregated data from 15 European countries). It is shown that the level of concentration among VCs has a positive effect on VC supply, so creating conditions to increase the level of concentration can stimulate VC supply. The findings reveal the importance of unemployment and personal income rate on VC demand and the positive impact of stock market capitalization on VC supply.

What do contracts do to facilitate relationships?

I demonstrate that transacting parties may expend resources on ex ante contracting, which may not be legally enforceable, to help build and maintain their long-term relationships. I first introduce three legal concepts, namely scaffolding, managerial provisions, and formal relational contracts, which highlight the recent trend towards more detailed contracts. These concepts indicate that the role of detailed contracts is not to improve judicial contract enforcement, but to enhance clarity and alignment of interests and to reduce renegotiation costs, which ultimately support the parties’ relationships. I then proceed to present and analyze a simple reduced-form model, which demonstrates that the parties’ efforts for ex ante contracting are not necessarily monotonic with the level of alignment of their interests. Furthermore, I discuss recent contracting practices in Japan and attempt to provide an explanation for the lack of change observed in these practices.

The role of stickiness, extrapolation and past consensus forecasts in macroeconomic expectations

We estimate a simple reduced-form model of expectation formation with three distinct deviations from full-information rational expectations that combines underreaction with overreaction to new information. In particular, forecasts are sticky, extrapolate the most recent news about the current period, and depend on the lagged consensus forecast about the period being forecast. We find that all three biases are present in the Survey of Professional Forecasters as well as in the Livingston Survey, and that their magnitudes depend on the forecasting horizon. We also stress the point that using the past consensus forecast to form expectations is a reasonable thing to do if a forecaster is not able to come up with full-information rational expectations all by herself. Finally, we show that forecasters that have more sticky expectations generally tend to rely less on the lagged consensus forecast but extrapolate news about the current period more.

A country-specific COVID-19 model

Abstract Objectives To dynamically measure COVID-19 transmissibility consistently normalized by population size in each country. Methods A reduced-form model enhanced from the classical SIR is proposed to stochastically represent the Reproduction Number and Mortality Rate, directly measuring the combined effects of viral evolution and population behavioral response functions. Results Evidences are shown that this e(hanced)-SIR model has the power to fit country-specific empirical data, produce interpretable model parameters to be used for generating probabilistic scenarios adapted to the still unfolding pandemic. Conclusions Stochastic processes embedded within compartmental epidemiological models can produce measurables and actionable information for surveillance and planning purposes.