Piecewise Constant Hazard Model Research Articles

Analysing Wage Differences between the USA and Germany Using Proportional Hazards Models

AbstractWe analyse differences between the wage distributions in the USA and Germany in 2001 for both women and men. The empirical analysis is based on the decomposition of differences using Cox's marginal (partial) likelihood. The approach based on rank invariant estimators such as Cox's is borrowed from the literature on failure time data. Donald et al. pioneered this approach in 2000. However, they did not use the full power of the semi‐parametric approach. Instead, they argued for using a piecewise constant hazard rate model. We improve on their work by showing that the semi‐parametric features of Cox's marginal likelihood are as appropriate for the analysis of wage decompositions and as easy to interpret. Moreover, we extend their approach by allowing for non‐linear regression effects. We show empirically that this formulation both increases the flexibility of their approach and improves the discriminatory power between wage regimes.

Bayesian Adjustment of Anticipatory Covariates in Analyzing Retrospective Data

In retrospective surveys, records on important variables such as the respondent's educational level and social class refer to what is achieved by the date of the survey. Such variables are then used as covariates in investigations of behavior such as marriage and divorce in life segments that have occurred before the survey. To what extent can any change in the behavior be attributed to the misclassification of respondents across the various levels of the anticipatory variable? To what extent do they reflect real differences in the behavior across the levels? The connection is obtained by a Bayesian adjustment, by specifying a continuous-time Markov model for the incompletely observed time-varying anticipatory covariates, and by implementing standard Bayesian data augmentation techniques. The issues are illustrated by estimating effects of educational level on risks of divorce in a multiplicative piecewise-constant hazard model. Results show that ignoring the time-inconsistency of anticipatory variables may seriously plague the analyses because the relative risks across the anticipatory educational level are overestimated.

Labor Market Integration and the Transition to Parenthood - A Comparison of Germany and the UK

The aim of this paper is to investigate the hypothesis that after leaving the educational system, labour market integration has a causal effect on first-birth decisions. The analysis focuses on two major research questions: First, how is the timing of first parenthood associated with previous labour market performance‘ Second, can differences in first birth-risks be related to labour market performance‘ In other words, to what extent do the fertility decisions of successfully integrated individuals differ from those who are poorly integrated into the labour force‘ To account for the impact of cross-national differences in institutional settings, I contrast the continental conservative German welfare state with the liberal market economy of the UK. To account for gender-specific differences in opportunity costs, I distinguish between men and women in this analysis. Using longitudinal micro-data from the SOEP and BHPS, I apply a piecewise constant exponential hazard model. The results show a significantly reduced first-birth risk in the case of German men with weak occupational integration, as well as in the case of British and German women with pronounced labour market attachment. Furthermore, regarding the timing of family formation, a lengthy process of occupational integration tends to delay the transition to parenthood for both men and women, especially in Germany.

WHAT HAS FAITH GOT TO DO WITH IT? RELIGION AND CHILD SURVIVAL IN GHANA

Using pooled children data from the 1998 and 2003 Ghana Demographic and Health Surveys, this study examines religious differences in child survival in Ghana. Guided by the particularized theology and selectivity theses, a piecewise constant hazard model with gamma-shared frailty is used to explore if there are denominational differences in child mortality, and whether these could be explained through other characteristics. At the bivariate level, children whose mothers identified as Muslim and Traditional were found to have a significantly higher risk of death compared with their counterparts whose mothers identified as Christians. In the multivariate models, however, the religious differences disappeared after the mediating and confounding influence of socioeconomic factors were controlled. The findings provide support for the selectivity hypothesis, which is based on the notion that religious variations mainly reflect differential access to social and human capital rather than religious theology per se.

Heterogeneity in Consumer Price Stickiness

We examine heterogeneity in price stickiness using a large, original, set of individual price data collected at the retail level for the computation of the French consumer price index. For that purpose, we estimate at a very high level of disaggregation, a piecewise-constant hazard model, as well as competing-risks duration models that distinguish between price increases, price decreases, and product replacements. The main findings are the following: (a) at the product–outlet-type level, the baseline hazard function of a price spell is nondecreasing; (b) cross-product and cross-outlet-type heterogeneity is pervasive, both in the shape and the level of the hazard function as well as in the impact of covariates; (c) there is strong evidence of state dependence, especially for price increases; (d) there is an asymmetry because determinants of price increases differ from those of price decreases.

Model Selection for the Competing-Risks Model With and Without Masking

The competing-risks model is useful in settings in which individuals (or units) may die (or fail) because of various causes. It can also be the case that for some of the items, the cause of failure is known only up to a subgroup of all causes, in which case we say that the failure is group-masked. A widely used approach for competing-risks data with and without masking involves the specification of cause-specific hazard rates. Often, because of the availability of likelihood methods for estimation and testing, piecewise constant hazards are used. The piecewise constant rates also offer model flexibility and computational convenience. However, for such piecewise constant hazard models, the choice of the endpoints for each interval on which the hazards are constant is usually a subjective one. In this article we discuss and propose the use of model selection methods that are data-driven and automatic. We compare three model selection procedures based on the minimum description length principle, the Bayes information criterion, and the Akaike information criterion. A fast-splitting algorithm is the computational tool used to select among an enormous number of possible models. We test the effectiveness of the methods through numerical studies, including a real dataset with masked failure causes.

Replacement rates and labour market behaviour

This paper studies how the replacement rate, defined as the ratio of disposable income when unemployed to expected disposable income if beginning to work, affects individuals’ transition rate from unemployment. Linked register data, representing a local Finnish labour market in 1996, are analysed with piece-wise constant exponential hazard models. Results suggest that the effect of the replacement rate and, thus, of “unemployment traps”, is fairly modest. It does not seem to change with time spent unemployed. The impact on the transition rate into employment is lower than on the transition rate out of the labour force. Unemployment insurance recipients are found to be less sensitive to changes in the replacement rate than are unemployment assistance recipients.

A correlated frailty model for analysing risk factors in bilateral corneal graft rejection for Keratoconus: a Bayesian approach

There are many unknown causes that increase the rate of corneal graft rejection. In bilateral cases, some of these unknown causes are common, and some are individual factors. In this paper, we use a correlated frailty model to analyse risk factors for bilateral corneal graft in Keratoconus. Applying the piecewise constant baseline hazard model, we have performed a Bayesian analysis of the correlated frailty model using the Markov chain Monte Carlo method. The correlated frailty model and the shared frailty model are compared by deviance information criterion. The results show more accurate and better fit for the correlated frailty model.

Age and stage specific prevalence estimate of cancer from population based Cancer Registry using inhomogeneous Poisson process

A multi stage model is described for estimating the age and two stage specific prevalence of cancer. The disease evolution is considered as an inhomogeneous Poisson process in the Lexis diagram. Prevalences are estimated from the basic epidemiological measures (stage specific incidences and survivals). A piecewise constant hazard model is used to estimate the transition rates constructing a finite partition of age and, where it is the case, of duration. Moreover, variance calculations are described. An application to breast cancer in the Hérault (France) population is presented.

Retirement Timing in Germany

:This article examines the timing of retirement in a household context, using longitudinal data on employment and family careers. It investigates the retirement decisions of unmarried and married elderly men and women. Since in (West) Germany, patterns of investment in alternative family and market roles over the life course are highly tendered, a separate analysis is also performed on a subsample of working spouses where both partners were employed at age fifty. The determinants of retirement decisions considered in the models are: early life course employment patterns, employment characteristics in later life, health situation, and household circumstances, including the income level. Data come from the German Socioeconomic Panel Study. An event history analysis is conducted using a piecewise constant hazard model with time-varying covariates. The analysis indicates that there are indeed important differences in retirement behavior between men and women as well as between unmarried and married individuals. The household context does matter in retirement decisions but the study discloses gender asymmetry in response to marital status and displays differences between partnerships in which both spouses are employed in late life and those that portray a traditional division of paid/unpaid labor.

Survival in a Concentrating Industry: The Case of Daily Newspapers in the Netherlands

This paper studies the effects of aggregate, industry-, and firm-specific factors on the exit hazard rates in the market for daily newspapers in The Netherlands from 1950 to 1996. We present a brief overview of the exit literature. On the basis of the existing empirical evidence, we decided to specify and estimate exponential and piecewise constant hazard rate models. We find that exit hazards of daily newspapers depend on the circulation size, ownership, and number of incumbents. Moreover, the effects are time-dependent. We do not find any significant effect of macroeconomic factors.

Delayed childbearing in contemporary Spain: trends and differentials.

Data from the 1985 Spanish Survey of Fertility including 8789 women aged 18-49 years is used to examine the timing of 1st births from marriage. Premarital births are excluded. Life table estimates are used to describe trends and differentials. A piecewise constant hazard model, which assumes a constant transition rate within each duration segment (0-7, 8-12, 13-18, 19-24, 25-36, and 37-48 months), and discrete-time hazard models are used in the analysis. Analysis is devoted to the trends in the timing of 1st birth, differentials in the timing of transition to 1st birth as affected by age at marriage, education, labor force participation before marriage, religiosity, number of siblings, place of residence, and region. Fertility has declined from 2.7 in 1975 to 1.3 in 1990 while the country adapted to a democratic political process, legalization of contraceptives, and relaxation of gender roles. There was rapid family formation during the 1960s and 1970s. Recent marriage cohorts have been delaying the birth of a 1st child and birth control has increased. Premarital conceptions have increased. Differentials in timing of 1st birth did not affect fertility because delayers still had children. Postponement of childbearing is new to Spain and may reflect unstable economic conditions or security of women's position in the labor market. Cultural norms have also changed to define an appropriate time for childbearing as not immediately after marriage. Life table estimates show the median age of women at 1st birth as 25.6 years in the early 1980s compared to 24.6 years in the later 1970s. The interquartile timing of 1st births ranged from 14 months for the 1970-74 birth cohort to 26 months for the 1980-83 cohort. Women who married in the 1960s and early 1970s had their 1st child within the 1st year of marriage. Observations are that motherhood remains unchanged, timing reflects intercohort differences, postponement occurs after 1975, and differentials are not constant across marriage duration. Marriage cohort composition has changed to women with higher education, lower religiosity, smaller families of origin, and increasing labor participation before marriage, which shows in the life table estimates to postponement. The rate differentials between 1965-69 and 1970-74 cohorts are statistically significant in the multivariate model.

Estimation in the piece-wise constant hazard rate model

The piece-wise constant hazard rate is presented along with the resulting piece-wise constant exponential model for the life times. Maximum likelihood estimation is considered for the complete life test and a life test censored at a preset time. The estimators are found along with their expected values and variances. An example from industry illustrates the estimation procedure in the special case where only two pieces are used.