MULTIPLE EVENT INCIDENCE AND DURATION ANALYSIS FOR CREDIT DATA INCORPORATING NON‐STOCHASTIC LOAN MATURITY

Applications of duration analysis in economics and finance exclusively employ methods for events of stochastic duration. In application to credit data, previous research incorrectly treats the time to predetermined maturity events as censored stochastic event times. The medical literature has binary parametric ‘cure rate’ models that deal with populations that never experienced the modelled event. We propose and develop a multinomial parametric incidence and duration model, incorporating such populations. In the class of cure rate models, this is the first fully parametric multinomial model and is the first framework to accommodate an event with predetermined duration. The methodology is applied to unsecured personal loan credit data provided by one of Australia's largest financial services organizations. This framework is shown to be more flexible and predictive through a simulation and empirical study that reveals: simulation results of estimated parameters with a large reduction in bias; superior forecasting of duration; explanatory variables can act in different directions upon incidence and duration; and variables exist that are statistically significant in explaining only incidence or duration. Copyright © 2013 John Wiley & Sons, Ltd.     

A class of binary response models for grouped duration data

This paper explores the relationship between conventional models for binary response such as the probit and logit, and the proportional hazard (PH) and related specifications for grouped duration data. I outline a general class of hazard models for grouped duration data based upon the choice of period-specific distribution functions, facilitating a thorough analysis of the implications of various specifications and consideration of various issues of model identification. This class of models nests, among others, the proportional hazard, probit, and logit specifications for interval survival. I consider the implications of various specifications for hazard behaviour, focusing on familiar specifications. While the specifications will generally yield results that are quite similar along a number of dimensions, there are significant differences. The probit model generates non-proportional effects of variables on the discrete hazard, while the logit and PH tend to show only slight non-proportionality. Furthermore, while the effects of variables on the derivatives are considerably larger for the probit specification, the time-pattern of the probit effects is relatively insensitive to changes in explanatory variables. I illustrate these issues by providing an example taken from Katz's (1986) unemployment data from the Panel Study of Income Dynamics.     

Temporary jobs and job search effort in Europe

Using longitudinal data on individuals from the European Community Household Panel (ECHP) for eleven countries during 1995-2001, I investigate temporary job contract duration and job search effort. The countries are Austria, Belgium, Denmark, Finland, France, Greece, Ireland, Italy, the Netherlands, Portugal and Spain. I construct a search model for workers in temporary jobs which predicts that shorter duration raises search intensity. Calibration of the model to the ECHP data implies that at least 75% of the increase in search intensity over the life of a 2+ year temporary contract occurs in the last six months of the contract. I then estimate regression models for search effort that control for human capital, pay, local unemployment, and individual and time fixed effects. I find that workers on temporary jobs indeed search harder than those on permanent jobs. Moreover, search intensity increases as temporary job duration falls, and roughly 84% of this increase occurs on average in the shortest duration jobs. These results are robust to disaggregation by gender and by country. These empirical results are noteworthy, since it is not necessary to assume myopia or hyperbolic discounting in order to explain them, although the data clearly also do not rule out such explanations.     

Generalised residuals and heterogeneous duration models: With applications to the Weilbull model

This paper deals with models for the duration of an event that are misspecified by the neglect of random multiplicative heterogeneity in the hazard function. This type of misspecification has been widely discussed in the literature [e.g., Heckman and Singer (1982), Lancaster and Nickell (1980)], but no study of its effect on maximum likelihood estimators has been given. This paper aims to provide such a study with particular reference to the Weibull regression model which is by far the most frequently used parametric model [e.g., Heckman and Borjas (1980), Lancaster (1979)]. In this paper we define generalised errors and residuals in the sense of Cox and Snell (1968, 1971) and show how their use materially simplifies the analysis of both true and misspecified duration models. We show that multiplicative heterogeneity in the hazard of the Weibull model has two errors in variables interpretations. We give the exact asymptotic inconsistency of M.L. estimation in the Weibull model and give a general expression for the inconsistency of M.L. estimators due to neglected heterogeneity for any duration model to O(σ²), where σ² is the variance of the error term. We also discuss the information matrix test for neglected heterogeneity in duration models and consider its behaviour when σ²>0.     

Estimated Precision for Predictions from Generalized Linear Models in Sociological Research

In this paper I present a general method forconstructing confidence intervals for predictionsfrom the generalized linear model in sociologicalresearch. I demonstrate that the method used forconstructing confidence intervals for predictions inclassical linear models is indeed a special case ofthe method for generalized linear models. I examinefour such models – the binary logit, the binaryprobit, the ordinal logit, and the Poissonregression model – to construct confidence intervalsfor predicted values in the form of probability,odds, Z score, or event count. The estimatedconfidence interval for an event prediction, whenapplied judiciously, can give the researcher usefulinformation and an estimated measure of precisionfor the prediction so that interpretation ofestimates from the generalized linear model becomeseasier.     

The Extended Generalized Gamma Model and its Special Cases: Applications to Modeling Marriage Durations

The paper demonstrates how various parametric models for duration data such as the exponential, Weibull, and log-normal may be embedded in a single framework, and how such competing models may be assessed relative to a more comprehensive one. To illustrate the issues addressed, the survival patterns of marriages among 1203 Swedish men born 1936–1964 are studied by parametric and non-parametric survival methods. In particular, we study the sensitivity of model-choice with respect to level of aggregation of the time variable; and of covariate-effects with respect to the model chosen. In accordance with previous works our empirical results indicate that the choice of a parametric model for the duration variable is affected by the level of time aggregation. In contrast to previous results, however, our analysis shows that estimates of covariate effects are not always robust to distributional assumptions for the duration variable.     

A comparison of financial duration models via density forecasts

Using density forecast evaluation techniques, we compare the predictive performance of econometric specifications that have been developed for modeling duration processes in intra-day financial markets. The model portfolio encompasses various variants of the Autoregressive Conditional Duration (ACD) model and recently proposed dynamic factor models. The evaluation is conducted on time series of trade, price and volume durations computed from transaction data of NYSE listed stocks. The results show that simpler approaches perform at least as well as more complex methods. With respect to modeling trade duration processes, standard ACD models successfully account for duration dynamics while none of the models provides an acceptable specification for the conditional duration distribution. We find that the Logarithmic ACD, if based on a flexible innovation distribution, provides a quite robust and useful framework for the modeling of price and volume duration processes.     

Econometric analysis of jump-driven stochastic volatility models

This paper introduces and studies the econometric properties of a general new class of models, which I refer to as jump-driven stochastic volatility models, in which the volatility is a moving average of past jumps. I focus attention on two particular semiparametric classes of jump-driven stochastic volatility models. In the first, the price has a continuous component with time-varying volatility and time-homogeneous jumps. The second jump-driven stochastic volatility model analyzed here has only jumps in the price, which have time-varying size. In the empirical application I model the memory of the stochastic variance with a CARMA(2,1) kernel and set the jumps in the variance to be proportional to the squared price jumps. The estimation, which is based on matching moments of certain realized power variation statistics calculated from high-frequency foreign exchange data, shows that the jump-driven stochastic volatility model containing continuous component in the price performs best. It outperforms a standard two-factor affine jump–diffusion model, but also the pure-jump jump-driven stochastic volatility model for the particular jump specification.     

Financial incentives to postpone retirement and further effects on employment — Evidence from a natural experiment

This paper examines the effect of the introduction of permanent benefit reductions for early retirees (i) on the duration until benefit claiming and (ii) on the duration until exit from gainful employment. I estimate discrete time duration models using different error term specifications. Administrative data containing the full earnings history of the individuals are used. Since the reform implementing the benefit reductions was a natural experiment, under some assumptions a causal effect can be identified. The permanent reduction of retirement benefit amounts causes a postponement of claiming benefits by about 14 months and a delay of employment exit by about 10 months on average.     

Unemployment insurance and subsequent job duration: job matching versus unobserved heterogeneity

The relationship between Unemployment Insurance (UI) benefit duration, unemployment duration and subsequent job duration is investigated using a multi‐state duration model with state specific unobserved heterogeneity. I examine two potential explanations for the negative correlation between unemployment and job spell durations; UI benefits increase job matching quality (the ‘Matching’ effect) versus unobserved heterogeneity (‘Adverse Selection’). The Matching effect is found to be weak. Although new jobs accepted within 5 weeks of benefit termination seem to have a higher dissolution rate, the negative correlation between unemployment and job duration is mostly explained by unobserved heterogeneity. Various simulations indicate that increasing the maximum benefit duration by one week will raise expected unemployment duration by 1.0 to 1.5 days but will raise expected job duration by 0.5 to 0.8 day only. Copyright © 2001 John Wiley & Sons, Ltd.     

Duration dependence in US business cycles: An analysis using the modulated power law process

The modulated power law process is used to analyze the duration dependence in US business cycles. The model makes less restricting assumptions than traditional models do and measures both the local and global performance of business cycles. The results indicate evidence of positive duration dependence in the U.S. business cycles. Structural change after WWII in both expansion and contraction phases of business cycles is also documented. Hypothesis tests confirm that the model fits US business cycles.      

Can indeterminacy resolve the cross-country correlation puzzle?

Are productivity shocks the only driving force of international business fluctuations? In this paper I argue that another source of uncertainty—changes in market expectations or ‘sunspots’ – is also important. One major shortcoming of existing IRBC models is the ‘cross-country correlation puzzle’: models tend to generate cross-country consumption correlations that are too high and output, investment and employment correlations that are too low when compared to the data. I show that with empirically supported level of increasing returns, an otherwise standard model possesses multiple, indeterminate convergent paths to the steady state, which allow for sunspots to influence the economy. The model displays time series properties that in many ways match the data better than the conventional model. It is especially successful in generating realistic consumption and output correlations.     

A Tutorial on Multilevel Survival Analysis: Methods,Models and Applications

Data that have a multilevel structure occur frequently across a range of disciplines, including epidemiology, health services research, public health, education and sociology. We describe three families of regression models for the analysis of multilevel survival data. First, Cox proportional hazards models with mixed effects incorporate cluster‐specific random effects that modify the baseline hazard function. Second, piecewise exponential survival models partition the duration of follow‐up into mutually exclusive intervals and fit a model that assumes that the hazard function is constant within each interval. This is equivalent to a Poisson regression model that incorporates the duration of exposure within each interval. By incorporating cluster‐specific random effects, generalised linear mixed models can be used to analyse these data. Third, after partitioning the duration of follow‐up into mutually exclusive intervals, one can use discrete time survival models that use a complementary log–log generalised linear model to model the occurrence of the outcome of interest within each interval. Random effects can be incorporated to account for within‐cluster homogeneity in outcomes. We illustrate the application of these methods using data consisting of patients hospitalised with a heart attack. We illustrate the application of these methods using three statistical programming languages (R, SAS and Stata).     

Broad Cross‐License Negotiations

In many industries, broad cross‐license agreements are considered a useful method to obtain freedom to operate and to avoid patent litigation. In this paper, I study firm incentives to sign a broad cross‐license as well as the duration of broad cross‐license negotiations. I develop a model of bargaining with learning, which predicts that two firms will enter a broad cross‐license agreement only if their capital intensities are large enough. The model also predicts faster negotiations when firms have high capital intensities and when the frequency of future disputes is low. I confirm these predictions empirically using a novel data set on cross‐licensing and litigation in the US semiconductor industry.     

Time aggregation and the distributional shape of unemployment duration

This paper reports empirical evidence on the sensitivity of unemployment duration regression estimates to distributional assumptions and to time aggregation. The results indicate that parameter estimates are robust to distributional assumptions, while estimates of duration dependence are not. Time aggregation does not seem to have drastic effects on the estimates in a simple parametric model like the Weibull, but can produce dramatic changes in the more complicated extended generalized gamma model. Semiparametric models for grouped data produce stable estimates, and perform much better than continuous-time models in terms of significance at high levels of time aggregation.     

Bond immunization for additive interest rate shocks

This paper explores bond immunization for additive term structure models. This class of term structures contains many models that are commonly used in the duration and immunization literature. We establish the necessary and sufficient conditions for immunization and prove the existence of a bond portfolio that satisfies the immunization condition. Based upon the immunization condition, we develop a general definition of duration that applies to any additives term structure model.     

Binary choice models with discrete regressors: Identification and misspecification

This paper explores the inferential question in semiparametric binary response models when the continuous support condition is not satisfied and all regressors have discrete support. I focus mainly on the models under the conditional median restriction, as in Manski (1985). I find sharp bounds on the components of the parameter of interest and outline several applications. The formulas for bounds obtained using a recursive procedure help analyze cases where one regressor’s support becomes increasingly dense. Furthermore, I investigate asymptotic properties of estimators of the identification set. I describe a relation between the maximum score estimation and support vector machines and propose several approaches to address the problem of empty identification sets when the model is misspecified.     

MODEL AVERAGING IN ECONOMICS: AN OVERVIEW

Standard practice in empirical research is based on two steps: first, researchers select a model from the space of all possible models; second, they proceed as if the selected model had generated the data. Therefore, uncertainty in the model selection step is typically ignored. Alternatively, model averaging accounts for this model uncertainty. In this paper, I review the literature on model averaging with special emphasis on its applications to economics. Finally, as an empirical illustration, I consider model averaging to examine the deterrent effect of capital punishment across states in the USA.     

Structural VAR and financial networks: A minimum distance approach to spatial modeling

In this paper, I interpret a time series spatial model (T-SAR) as a constrained structural vector autoregressive (SVAR) model. Based on these restrictions, I propose a minimum distance approach to estimate the (row-standardized) network matrix and the overall network influence parameter of the T-SAR from the SVAR estimates. I also develop a Wald-type test to assess the distance between these two models. To implement the methodology, I discuss machine learning methods as one possible identification strategy of SVAR models. Finally, I illustrate the methodology through an application to volatility spillovers across major stock markets using daily realized volatility data for 2004–2018.