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.     

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.     

Analysis of failure time using threshold regression with semi‐parametric varying coefficients

Many new statistical models may enjoy better interpretability and numerical stability than traditional models in survival data analysis. Specifically, the threshold regression (TR) technique based on the inverse Gaussian distribution is a useful alternative to the Cox proportional hazards model to analyse lifetime data. In this article we consider a semi‐parametric modelling approach for TR and contribute implementational and theoretical details for model fitting and statistical inferences. Extensive simulations are carried out to examine the finite sample performance of the parametric and non‐parametric estimates. A real example is analysed to illustrate our methods, along with a careful diagnosis of model assumptions.     

A disaster response model driven by spatial–temporal forecasts

In this research, we propose a disaster response model combining preparedness and responsiveness strategies. The selective response depends on the level of accuracy that our forecasting models can achieve. In order to decide the right geographical space and time window of response, forecasts are prepared and assessed through a spatial–temporal aggregation framework, until we find the optimum level of aggregation. The research considers major earthquake data for the period 1985–2014. Building on the produced forecasts, we develop accordingly a disaster response model. The model is dynamic in nature, as it is updated every time a new event is added in the database. Any forecasting model can be optimized though the proposed spatial–temporal forecasting framework, and as such our results can be easily generalized. This is true for other forecasting methods and in other disaster response contexts.     

The importance of flexible hazard functions in the analysis of organizational survival data -- experiences from a cohort of Swedish commercial banks

The survival pattern of Swedish commercial banks during the period 1830--1990 is studied by parametric and non-parametric event-history methods. In particular we study the sensitivity of the conclusions reached with respect to the model used. It is found that the hazard is inversely U-shaped, which means that models that cannot allow for this type of hazard run into difficulties. Thus two of the most popular approaches in the analysis of event history data, the Gompertz and the Weibull models produce misleading results regarding the development of the death risk of banks over time. As regards the effect of explanatory variables on survival, on the other hand, most models are found to be robust and even in cases of misspecified baseline hazards, the estimated effects of the explanatory variables do not seem to be seriously wrong.     

Discrete time duration models with group-level heterogeneity

Dynamic discrete choice panel data models have received a great deal of attention. In those models, the dynamics is usually handled by including the lagged outcome as an explanatory variable. In this paper we consider an alternative model in which the dynamics is handled by using the duration in the current state as a covariate. We propose estimators that allow for group-specific effect in parametric and semiparametric versions of the model. The proposed method is illustrated by an empirical analysis of job durations allowing for firm-level effects.     

‘Nobody is perfect’: Asset pricing and long-run survival when heterogeneous investors exhibit different kinds of filtering errors

In this paper we analyze an economy with two heterogeneous investors who both exhibit misspecified filtering models for the unobservable expected growth rate of the aggregated dividend. A key result of our analysis with respect to long-run investor survival is that there are degrees of model misspecification on the part of one investor for which there is no compensation by the other investor's deficiency. The main finding with respect to the asset pricing properties of our model is that the two dimensions of asset pricing and survival are basically independent. In scenarios when the investors are more similar with respect to their expected consumption shares, return volatilities can nevertheless be higher than in cases when they are very different.     

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.     

Reparameterized inverse gamma regression models with varying precision

In this article, we propose a mean linear regression model where the response variable is inverse gamma distributed using a new parameterization of this distribution that is indexed by mean and precision parameters. The main advantage of our new parametrization is the straightforward interpretation of the regression coefficients in terms of the expectation of the positive response variable, as usual in the context of generalized linear models. The variance function of the proposed model has a quadratic form. The inverse gamma distribution is a member of the exponential family of distributions and has some distributions commonly used for parametric models in survival analysis as special cases. We compare the proposed model to several alternatives and illustrate its advantages and usefulness. With a generalized linear model approach that takes advantage of exponential family properties, we discuss model estimation (by maximum likelihood), black further inferential quantities and diagnostic tools. A Monte Carlo experiment is conducted to evaluate the performances of these estimators in finite samples with a discussion of the obtained results. A real application using minerals data set collected by Department of Mines of the University of Atacama, Chile, is considered to demonstrate the practical potential of the proposed model.     

Smoothed binary regression quantiles

This paper extends results regarding smoothed median binary regression to general smoothed binary quantile regression, discusses the interpretation of the resulting estimators under alternative assumptions, and shows how they may be used to obtain semiparametric estimates of counterfactual probabilities. The estimators are applied to a model of labour force participation of married women in the USA. We find that the elasticity with respect to non‐labour income is significantly negative only for women that belong to the middle of the conditional willingness‐to‐participate (WTP) distribution. In comparing the quantile models with parametric logit and semiparametric single‐index specifications, we find that the models agree closely for women around the centre of the WTP distribution, but there are considerable disagreements as we move towards the tails of the distribution. Copyright © 2006 John Wiley & Sons, Ltd.     

The duration of homelessness: evidence from a national survey

This paper provides evidence on the determinants of the duration of homelessness. We use newly available data from a large-scale, comprehensive microeconomic survey to estimate a parametric survival model of the length of a spell of homelessness. We find that homeless spells are longer for persons with certain demographic characteristics (such as older men) and behavioral histories (for example, previous incarceration and a history of drug and alcohol abuse). Our results suggest that current eligibility criteria for receiving housing assistance, which give preference to drug-free, single women with young children, are unlikely to reduce homelessness substantially and in a cost-effective manner.     

Semiparametric econometrics: A survey

Semiparametric econometric models contain both parametric and nonparametric components, reflecting in some fashion what has been learned from economic theory and previous empirical experience, and what remains unknown. They raise such questions as how well the parametric component can be estimated, and how to construct rules of inference with good statistical properties. The paper attempts to survey the econometric and most relevant statistical literature on semiparametric inference, and includes a partial bibliography.     

Endogenous censoring in the mixed proportional hazard model with an application to optimal unemployment insurance

We examine the sensitivity of estimates of the MPH model with respect to assumptions on the censoring mechanism in the context of an economic model of optimal unemployment insurance. We assume a parametric model for the duration of interest and leave the distribution of censoring unrestricted, allowing it to be correlated with observed and unobserved characteristics. We provide a practical characterization of the identified set with moment inequalities and suggest methods for estimating this set. We apply this approach to estimate the elasticity of unemployment exit rate with respect to unemployment benefit. Finally, we investigate welfare consequences of our estimates.     

Nonparametric estimation of conditional distribution functions with longitudinal data and time-varying parametric models

Nonparametric estimation and inferences of conditional distribution functions with longitudinal data have important applications in biomedical studies. We propose in this paper an estimation approach based on time-varying parametric models. Our model assumes that the conditional distribution of the outcome variable at each given time point can be approximated by a parametric model, but the parameters are smooth functions of time. Our estimation is based on a two-step smoothing method, in which we first obtain the raw estimators of the conditional distribution functions at a set of disjoint time points, and then compute the final estimators at any time by smoothing the raw estimators. Asymptotic properties, including the asymptotic biases, variances and mean squared errors, are derived for the local polynomial smoothed estimators. Applicability of our two-step estimation method is demonstrated through a large epidemiological study of childhood growth and blood pressure. Finite sample properties of our procedures are investigated through simulation study.     

Statistical Decision Problems and Bayesian Nonparametric Methods

This paper considers parametric statistical decision problems conducted within a Bayesian nonparametric context. Our work was motivated by the realisation that typical parametric model selection procedures are essentially incoherent. We argue that one solution to this problem is to use a flexible enough model in the first place, a model that will not be checked no matter what data arrive. Ideally, one would use a nonparametric model to describe all the uncertainty about the density function generating the data. However, parametric models are the preferred choice for many statisticians, despite the incoherence involved in model checking, incoherence that is quite often ignored for pragmatic reasons. In this paper we show how coherent parametric inference can be carried out via decision theory and Bayesian nonparametrics. None of the ingredients discussed here are new, but our main point only becomes evident when one sees all priors—even parametric ones—as measures on sets of densities as opposed to measures on finite-dimensional parameter spaces.     

Semi‐parametric Regression under Model Uncertainty: Economic Applications

Economic theory does not always specify the functional relationship between dependent and explanatory variables, or even isolate a particular set of covariates. This means that model uncertainty is pervasive in empirical economics. In this paper, we indicate how Bayesian semi‐parametric regression methods in combination with stochastic search variable selection can be used to address two model uncertainties simultaneously: (i) the uncertainty with respect to the variables which should be included in the model and (ii) the uncertainty with respect to the functional form of their effects. The presented approach enables the simultaneous identification of robust linear and nonlinear effects. The additional insights gained are illustrated on applications in empirical economics, namely willingness to pay for housing, and cross‐country growth regression.     

The Lognormal Distribution as a Model for Survival Time in Cancer, With an Emphasis on Prognostic Factors

Despite their long history, parametric survival-time models have largely been neglected in the modern biostatistical and medical literature in favour of the Cox proportional hazards model. Here, I present a case for the use of the lognormal distribution in the analysis of survival times of breast and ovarian cancer patients, specifically in modelling the effects of prognostic factors. The lognormal provides a completely specified probability distribution for the observations and a sensible estimate of the variation explained by the model, a quantity that is controversial for the Cox model. I show how imputation of censored observations under the model may be used to inspect the data using familiar graphical and other technques. Results from the Cox and lognormal models are compared and shown apparently to differ to some extent. However, it is hard to judge which model gives the more accurate estimates. It is concluded that provided the lognormal model fits the data adequately, it may be a useful approach to the analysis of censored survival data.     

A flexible parametric selection model for non‐normal data with application to health care usage

I examine the effects of insurance status and managed care on hospitalization spells, and develop a new approach for sample selection problems in parametric duration models. MLE of the Flexible Parametric Selection (FPS) model does not require numerical integration or simulation techniques. I discuss application to the exponential, Weibull, log‐logistic and gamma duration models. Applying the model to the hospitalization data indicates that the FPS model may be preferred even in cases in which other parametric approaches are available. Copyright © 2002 John Wiley & Sons, Ltd.     

Google data in bridge equation models for German GDP

Interest in the use of “big data” when it comes to forecasting macroeconomic time series such as private consumption or unemployment has increased; however, applications to the forecasting of GDP remain rather rare. This paper incorporates Google search data into a bridge equation model, a version of which usually belongs to the suite of forecasting models at central banks. We show how such big data information can be integrated, with an emphasis on the appeal of the underlying model in this respect. As the decision as to which Google search terms should be added to which equation is crucial —- both for the forecasting performance itself and for the economic consistency of the implied relationships —- we compare different (ad-hoc, factor and shrinkage) approaches in terms of their pseudo real time out-of-sample forecast performances for GDP, various GDP components and monthly activity indicators. We find that sizeable gains can indeed be obtained by using Google search data, where the best-performing Google variable selection approach varies according to the target variable. Thus, assigning the selection methods flexibly to the targets leads to the most robust outcomes overall in all layers of the system.     

Measuring the costs of children: parametric and semiparametric estimators1

How much additional income does a family with four children need to attain the same welfare level as a family with two children? And how much does a single person need compared to a childless couple? These questions are important in applied micro-economics and underlie public policy on, for example, social benefits and child allowances. In microeconomics, this is known as the problem of measuring equivalence scales. We estimate these scales using two types of subjective survey information. First, we use answers to survey questions on the income required to attain a given utility level. We compare the results for the usual linear model with semiparametric estimates, in which the functional form of the relationship between required income and family size and actual income is left unspecified. Second, we use answers to the question: how satisfied are you with actual household income? We present parametric and semiparametric estimates for ordered response models explaining this discrete variable. We find that according to the second type of information, costs of children are much larger than according to the first.