Essays in multivariate duration models
Effraimidis, Georgios
URL:
|
https://madoc.bib.uni-mannheim.de/32588
|
URN:
|
urn:nbn:de:bsz:180-madoc-325882
|
Document Type:
|
Doctoral dissertation
|
Year of publication:
|
2012
|
Place of publication:
|
Mannheim
|
University:
|
Universität Mannheim
|
Evaluator:
|
Berg, Gerard J. van den
|
Date of oral examination:
|
19 July 2012
|
Publication language:
|
English
|
Institution:
|
School of Law and Economics > Alexander v. Humboldt Professor in Econometrics and Empirical Economics (van den Berg 2009-2016)
|
Subject:
|
330 Economics
|
Subject headings (SWD):
|
Ereignisdatenanalyse , Multivariate Analyse
|
Keywords (English):
|
Multivariate Duration Analysis
|
Abstract:
|
Duration analysis, which is also known as survival analysis, is a core
subject of applied statistics and econometrics. Application of duration
analysis techniques can be found in actuarial science, demography,
economics, finance, marketing, and many other scientific fields. In the
univariate case, the tools of duration analysis are used for the study of
the distribution of a certain duration variable which is possibly associated
with a set of explanatory covariates. This variable measures the time to the
occurrence of an event of interest such as transition from unemployment to
employment, retirement time, onset of a disease, purchase of a product. The
main difference between duration analysis and standard regression analysis
is that sometimes the duration variable is right-censored, namely, the only
available information we have is that its realization exceeds a certain
value.
Multivariate duration analysis is the natural extension of the univariate
analysis. In this set up, multiple duration variables, which specify the
time to the occurrence of multiple events, are considered and their joint
distribution is analyzed for describing the association among them. These
variables can be either parallel or sequential. Parallel duration variables
refer to cases in which the multiple duration variables are measured by
using the same reference point of time. On the other hand, sequential
duration variables refer to cases in which the measurement of each duration
variable starts after the realization of some other duration variable. Death
times of twins or the corresponding time of onset of several diseases are
multivariate examples with parallel duration variables. On the other hand,
unemployment duration and the subsequent employment duration is an example
with sequential durations.
The current PhD dissertation deals with multivariate duration models. In
particular, it consists of three independent essays on multivariate duration
models. In the next three paragraphs, a synopsis of each essay is given.
The first essay, written jointly with Gerard J. van den Berg, considers bivariate frailty models in which the frailty
terms enter multiplicatively on the corresponding hazard rates. The frailty
terms capture unobserved or nonmeasurable characteristics that affect the
duration outcomes. We assume that the joint distribution of the frailty
terms is characterized by gamma marginals. In particular, the gamma
distribution is widely used in empirical analysis for modelling the
distribution for the unobserved heterogeneity terms. Both analytical and
graphical arguments have been developed in the past which rationalize this
specific choice. First, the focus of the paper is on the concepts of
negative quadrant dependence and positive quadrant dependence between the
duration variables. Second, two measures of association between the duration
variables are considered; the Pearson's correlation coefficient and the
Kendall's tau. In particular, (sharp) bounds for these measures are derived
and the necessary conditions are discussed discussion is provided about the
conditions which should be satisfied so that the bounds are approached very
well.
The second essay, written jointly with Carlos Hernandez Mireles and Gerard Tellis, is concerned with a new trivariate hazard rate model which
can be applied to study the relationship among the timing of the
corresponding events. The suggested model allows for three types of
dependence among the timing of the underlying events: due to unobserved
heterogeneity, lagged dependence, and due to causality. As shown in the
paper, this model can be nonparametrically identified and as consequence the
three different types of dependence are disentangled. The new model is
adopted to study the endogenous relationship between the timing of three
important events in the sales and prices of new products. Specifically, we
investigate the causal relationship between the sales crash, price crash,
and sales recovery. A sales crash is a significant and permanent cut in the
sales of a new product. On the other hand, the sales recovery is a sales
peak which is realized after the crash. Finally, the price crash is a deep
and permanent reduction in the price of a new product.
The last essay deals with competing risks models which are very popular in
the scientific field of duration analysis. Such models deal with cases in
which we observe only the minimum duration among several multiple durations
for each individual unit under study. The goal of this paper is the
development of statistical properties of the cumulative incidence function.
This function, which is common in the empirical practice, specifies the
probability that a particular duration variable will be realized by a
certain point of time and before the other duration variables. The proposed
estimator is nonparametric, that is, no parametric assumptions are made
regarding the data generating process. In addition, the estimator allows for
Missing At Random observations. More precisely, for some observations we
have information about the value of the minimum duration variable, but not
information about which duration variable is the one smallest value of
realization.
|
| Dieser Eintrag ist Teil der Universitätsbibliographie. |
| Das Dokument wird vom Publikationsserver der Universitätsbibliothek Mannheim bereitgestellt. |
Search Authors in
You have found an error? Please let us know about your desired correction here: E-Mail
Actions (login required)
|
Show item |
|