Alfred Hamerle

Event history analysis : statistical theory and application in the social sciences

Contents: Foreword. Aim and Structure of the Book. Domains and Rationale for the Application of Event History Analysis. The Statistical Theory of Event History Analysis. Data Organization and Descriptive Methods. Semi-Parametric Regression Models: The Cox Proportional Hazards Model. Parametric Regression Models. Appendices: List of Variable Names Used in Examples. Listing of the FORTRAN Program PR3FUN Written by Trond Petersen. Listing of the FORTRAN Program for Episode Splitting Given Discrete Time-Dependent Covariates. Listing of the FORTRAN Program for Episode Splitting Given Continuous Time-Dependent Covariates. Listing of the GLIM Macros to Estimate the Weibull and Log-Logistic Models of Roger and Peacock.

Multiple-spell regression models for duration data

General models for multiple-spell duration data are considered. A general theory which indicates how the successive spells of an individual are generated by an underlying stochastic process is presented. Various special cases of the general model are discussed. The implications of different timescales are investigated: different timescales lead to different underlying stochastic processes such as Markov processes or semi-Markov processes. Occasionally common computer programs for duration data such as SAS, BMDP, GLIM and RATE can be used without further programming. Finally, multiple-spell models are applied to the duration of unemployment, and analysing the data in a single-spell framework is shown to lead to false interpretations and conclusions.

Problems with the estimation of stochastic differential equations using structural equations models

The present paper deals with the identification and maximum likelihood estimation of systems of linear stochastic differential equations using panel data. So we only have a sample of discrete observations over time of the relevant variables for each individual. A popular approach in the social sciences advocates the estimation of the “exact discrete model” after a reparameterization with LISREL or similar programs for structural equations models. The “exact discrete model” corresponds to the continuous time model in the sense that observations at equidistant points in time that are generated by the latter system also satisfy the former. In the LISREL approach the reparameterized discrete time model is estimated first without taking into account the nonlinear mapping from the continuous to the discrete time parameters. In a second step, using the inverse mapping, the fundamental system parameters of the continuous time system in which we are interested, are inferred. However, some severe problems arise wit...

Identification and estimation of continuous time dynamic systems with exogenous variables using panel data

This paper deals with the identification and maximum likelihood estimation of the parameters of a stochastic differential equation from discrete time sampling. Score function and maximum likelihood equations are derived explicitly. The stochastic differential equation system is extended to allow for random effects and the analysis of panel data. In addition, we investigate the identifiability of the continuous time parameters, in particular the impact of the inclusion of exogenous variables.

On the Treatment of Interrupted Spells and Initial Conditions in Event History Analysis

This article deals with some problems of event history analysis that arise in special types of sampling plans where spells in progress at time t0, the start date of the observation period, are sampled. Then, the available data are random samples of interrupted spells, or else may be spells that begin after the start date of the sample. For the interrupted spells, all relevant probability distributions of the elapsed duration until t0 and the duration of the spell after t0 have to account for the condition that the individual is in the state y0 in question at time t0. Relying on results of Ridder (1984) and Heckman and Singer (1986), we discuss the distribution of the “sampled” spells (i.e., conditional on the presence of the individual in state y0 at time t0), in particular the joint distribution of pre-interview and post-interview durations. In general, this distribution depends on the entry rate into the state y0. The distribution of the sampled spells for the special sampling plans differs from the corresponding duration distributions in the population. We then show that, sampling spells in progress, the distribution of the explanatory variables in the sample becomes informative for the parameters of interest. Next, we investigate the distribution of the sampled spells of individuals who enter or leave the state in question. This referred to as “sampling the flow.” We then discuss the special case of a time invariant entry rate. Appropriate likelihood contributions are given depending on which pre-interview, post-interview, and completed durations are observable. We also discuss a conditional likelihood approach due to Lancaster (1979) that does not require any assumptions on the entry rate. Next we derive the appropriate likelihood contributions of right censored observations and both left and right censored observations for the specific sampling plans considered here. Finally, we present the results of some simulation studies that show the usefulness of taking into account the observable part of spells with unknown origin in the estimation procedure.

Unobserved heterogeneity in hazard rate models: a test and an illustration from a study of career mobility

This paper proposes a test for neglected heterogeneity in continuous-time hazard rate models that can be done easily using generally available program packages. It is a score test appropriate for cases in which the variance of the heterogeneity is small and it can be applied quite generally, provided that the generalized residuals can be calculated. The test is demonstrated using data on the career trajectories of German males from the German Life History Study.

Uses and Misuses of Measures for Credit Rating Accuracy

The New Basel Capital Accord will allow the determination of banks’ regulatory capital requirements due to default probabilities which are estimated and forecasted from internal ratings. External ratings from rating agencies play fundamental roles in capital and credit markets. Discriminatory power of internal and external ratings is a key requirement for the soundness of a rating system in general and for the acceptation of a bank’s internal Rating systems under Basel II. Statistics such as the area under a receiver operating characteristic or the accuracy ratio, are widely used in practice as measures for the performance. This note shows that such measures should only be interpreted with caution. Firstly, the outcomes of the measures depend not only on the discrimination power of the rating system but mainly on the structure of the portfolio under consideration. Thus, the absolute values achieved do not measure the performance of a rating system solely. Secondly, comparisons of the outcomes between different portfolios, different time periods or both may be misleading. As a positive result we show that the value achieved by a rating system which predicts all default probabilities correctly can not be beaten.

Unobserved heterogeneity in event history models

This paper demonstrates the effect of unobserved heterogeneity in event history models and discusses parametric methods to include unobserved factors into the models. Using data on career trajectories of German males, the application of models with unobserved heterogeneity is shown.

Using Cox Models to Study Multiepisode Processes

This article shows how Cox models can be used to study multiepisode-multistate processes as well as which computer programs can be used to estimate semiparametric models with multispell data. The application of a multiepisode Cox model is demonstrated using data on career trajectories of German males from the German Life History study.

Modelling Loss Given Default: A “Point in Time”-Approach

In recent years the quantification of credit risk has become an important topic in research and in finance and banking. This has been accelerated by the reorganisation of the Capital Adequacy Framework (Basel II).