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This paper aims to provide an overview, a classification of existing research groups for correlated default models using a reduced-form method and an identification of future research opportunities in the field.

A systematic literature review is used for the identification, selection, evaluation and synthesis of relevant literature using keywords regarding the reduced-form default models in the Web of Science database. The authors also add articles from cross-referencing and expert recommendations to the literature. HistCite^™ program is used to generate a citation map of the literature.

The results show that reduced-form correlated default risk models are developing towards modelling credit risk with both observable and unobservable variables. The frailty correlated default model at the firm level is still a potential research field.

This is the first paper systematically reviewing the research on reduced-form models of default timing.

This article surveys available research on the contingent‐claims approach to risky debt valuation. The author describes both the structural and reduced form versions of contingent claims models and summarizes both the theoretical and empirical research in this area. Relative to the progress made in the theory of risky debt valuation, empirical validation of these models lags far behind. This survey highlights the increasing gap between the theoretical valuation and the empirical understanding of risky debt.

This chapter develops a set of two-step identification methods for social interactions models with unknown networks, and discusses how the proposed methods are connected to the identification methods for models with known networks. The first step uses linear regression to identify the reduced forms. The second step decomposes the reduced forms to identify the primitive parameters. The proposed methods use panel data to identify networks. Two cases are considered: the sample exogenous vectors span Rn (long panels), and the sample exogenous vectors span a proper subspace of Rⁿ (short panels). For the short panel case, in order to solve the sample covariance matrices’ non-invertibility problem, this chapter proposes to represent the sample vectors with respect to a basis of a lower-dimensional space so that we have fewer regression coefficients in the first step. This allows us to identify some reduced form submatrices, which provide equations for identifying the primitive parameters.

The purpose of this paper is to explore new reduced form of the (3 + 1)-dimensional generalized B-type Kadomtsev-Petviashvili (BKP) equation by considering its bilinear equations, derived from connection between the Hirota’s transformation and Bell polynomials.

Based on the bilinear form of new reduced form of the (3 + 1)-dimensional generalized BKP equation, lump solutions with sufficient and necessary conditions to guarantee analyticity and rational localization of the solutions are discovered. Also, extended homoclinic approach is applied to considered equation for finding solitary wave solutions.

A class of the bright-dark lump waves are fabricated for studying different attributes of (3 + 1)-dimensional generalized BKP equation and some new exact solutions including kinky periodic solitary wave solutions and line breathers periodic are also obtained by Following the extended homoclinic approach.

The paper presents that the implemented methods have emerged as a promising and robust mathematical tool to manage (3 + 1)-dimensional generalized BKP equation by using the Hirota’s bilinear equation.

By considering important characteristics of lump and solitary wave solutions, one can understand the shapes, amplitudes and velocities of solitons after the collision with another soliton.

The analysis of these higher-dimensional nonlinear wave equations is not only of fundamental interest but also has important practical implications in many areas of mathematical physics and ocean engineering.

To the best of the authors’ knowledge, the acquired solutions given in various cases have not been reported for new reduced form of the (3 + 1)-dimensional generalized BKP equation in the literature. These obtained solutions are advantageous for researchers to know objective laws and grab the indispensable features of the development of the mathematical physics.

The objective of this study is to investigate the simultaneity between farm couples’ decisions on labor allocation and production efficiency. Using an unbalanced panel data set of Norwegian farm households (1989–2008), we estimate off-farm labor supply of married farm couples and farm efficiency in a three-equation system of jointly determined endogenous variables. We address the issue of latent heterogeneity between households. We solve the problem by two-stage OLS and GLS estimation where state dependence is accounted for in the reduced form equations. We compare the results against simpler model specifications where we suppress censoring of off-farm labor hours and endogeneity of regressors, respectively. In the reduced form specification, a considerably large number of parameters are statistically significant. Davidson–McKinnon test of exogeneity confirms that both operator and spouse's off-farm labor supply should be treated as endogenous in estimating farming efficiency. The parameter estimates seem robust across model specifications. Off-farm labor supply of farm operators and spouses is jointly determined. Off-farm work by farm operator and spouses positively affects farming efficiency. Farming efficiency increases with operator's age, farm size, agricultural subsidises, and share of current investment to total farm capital stock.

Recently, it has been suggested that macroeconomic forecasts from estimated dynamic stochastic general equilibrium (DSGE) models tend to be more accurate out-of-sample than random walk forecasts or Bayesian vector autoregression (VAR) forecasts. Del Negro and Schorfheide (2013) in particular suggest that the DSGE model forecast should become the benchmark for forecasting horse-races. We compare the real-time forecasting accuracy of the Smets and Wouters (2007) DSGE model with that of several reduced-form time series models. We first demonstrate that none of the forecasting models is efficient. Our second finding is that there is no single best forecasting method. For example, typically simple AR models are most accurate at short horizons and DSGE models are most accurate at long horizons when forecasting output growth, while for inflation forecasts the results are reversed. Moreover, the relative accuracy of all models tends to evolve over time. Third, we show that there is no support to the common practice of using large-scale Bayesian VAR models as the forecast benchmark when evaluating DSGE models. Indeed, low-dimensional unrestricted AR and VAR forecasts may forecast more accurately.

We examine the roles of sample initial conditions and unobserved individual effects in consistent estimation of the dynamic binary response panel data model. Different specifications of the model are estimated using female welfare and labor force participation data from the Survey of Income and Program Participation. These include alternative random effects (RE) models, in which the conditional distributions of both the unobserved heterogeneity and the initial conditions are specified, and fixed effects (FE) conditional logit models that make no assumptions on either distribution. There are several findings. First, the hypothesis that the sample initial conditions are exogenous is rejected by both samples. Misspecification of the initial conditions results in drastically overstated estimates of the state dependence and understated estimates of the short- and long-run effects of children on labor force participation. The FE conditional logit estimates are similar to the estimates from the RE model that is flexible with respect to both the initial conditions and the correlation between the unobserved heterogeneity and the covariates. For female labor force participation, there is evidence that fertility choices are correlated with both unobserved heterogeneity and pre-sample participation histories.

This chapter contributes to the growing global VAR (GVAR) literature by showing how global and national shocks can be identified within a GVAR framework. The usefulness of the proposed approach is illustrated in an application to the analysis of the interactions between public debt and real output growth in a multicountry setting, and the results are compared to those obtained from standard single country VAR analysis. We find that on average (across countries) global shocks explain about one-third of the long-horizon forecast error variance of output growth, and about one-fifth of the long-run variance of the rate of change of debt-to-GDP. Evidence on the degree of cross-sectional dependence in these variables and their innovations are exploited to identify the global shocks, and priors are used to identify the national shocks within a Bayesian framework. It is found that posterior median debt elasticity with respect to output is much larger when the rise in output is due to a fiscal policy shock, as compared to when the rise in output is due to a positive technology shock. The cross-country average of the median debt elasticity is 1.45 when the rise in output is due to a fiscal expansion as compared to 0.76 when the rise in output follows from a favorable output shock.