S U RV I VA L A N A LY S I S O F E M P L O Y E E
T U R N O V E R
An empirical study
ru b e n s p ru i t 1 0 4 4 7 4 8 2
A Master’s Thesis to obtain the degree in e c o n o m e t r i c s
Supervisor: Dr. M.J.G. Bun Second reader: Dr. J.C.M van Ophem
"Man selects only for his own good: Nature only for that of the being which she tends."
S TAT E M E N T O F O R I G I N A L I T Y
This document is written by Student Ruben Spruit who declares to take full responsi-bility for the contents of this document.
I declare that the text and the work presented in this document are original and that no sources other than those mentioned in the text and its references have been used in creating it.
The Faculty of Economics and Business is responsible solely for the supervision of com-pletion of the work, not for the contents.
Ruben Spruit
A B S T R A C T
For firms is it beneficial to maintain good performing employees. In this paper, the turnover decision is modeled and the effects of determinants on the employment dura-tion are estimated. Using data from a Dutch field marketing company, the effects of performance, and pay on the employment duration and turnover decision are estimated using two econometric models. Also the effects of two different wage schemes on the employment duration are modeled. Survival analysis show higher turnover probabilities for low performing employees. Increased expected pay is shown to have a positive effect on employment duration.
Keywords: Employee turnover, Performance, Pay, Survival analysis, Corre-lated random effects
A C K N O W L E D G E M E N T S
I would like to take this opportunity to show my gratitude to a number of people who have made it possible for me to write my master’s thesis successfully. First of all, I would like to express my special thanks to my university supervisor Dr. Maurice Bun for his support and guidance during the entire process of writing my thesis. Our meetings were valuable and provided insight whenever I was struggling with my research. This stimu-lated me to go on, and for that, I am very grateful.
Special thanks go to Luuc Steltenpool who provided the dataset used in this thesis and was kind enough to provide insight in the company.
Ruben Spruit
C O N T E N T S
1 i n t ro d u c t i o n 1
2 b ac kg ro u n d l i t e r at u r e 5
2.1 Defining Turnover . . . 6
2.2 Economic Theories Related to Turnover . . . 7
2.2.1 Equity Theory . . . 7
2.2.2 Human Capital Theory . . . 8
2.2.3 Matching Theory . . . 9
2.3 Psychological Frameworks of Turnover . . . 9
2.3.1 March and Simon’s Model of Participation . . . 10
2.3.2 Mobley’s Intermediate Linkages Model . . . 11
2.3.3 Price’s and Meuller’s Model of Turnover. . . 11
3 r e s e a rc h d e s i g n 13 3.1 Data Collection . . . 13 3.2 Compensation schemes . . . 14 3.3 Descriptive Statistics . . . 15 3.4 Data Transformation . . . 19 3.5 Variable Selection . . . 21 3.6 Modeling Strategy . . . 22 4 e c o n o m e t r i c m o d e l s 25 4.1 Survival Analysis . . . 25 4.1.1 Basic concepts . . . 26 4.1.2 Kaplan-Meier . . . 26
4.1.3 Proportional Hazard Framework . . . 27
4.1.4 Heterogeneity . . . 28
4.2 Binary Choice Model . . . 29
5 r e s u lt s 33 5.1 Survival Analysis Results . . . 33
5.1.1 Subsets . . . 35
5.1.2 Heterogeneity . . . 37
5.2 Probit Correlated Random Effects Regression Results . . . 38
6 c o n c l u s i o n 41
b i b l i o g r a p h y 43 a a p p e n d i x a : d e s c r i p t i v e s tat i s t i c s s u b - s e t s 49 b a p p e n d i x b : g e n e r a l i z e d r e s i d u a l s 51 c a p p e n d i x c : m i x e d p ro p o t i o n a l h a z a r d s p e c i f i c at i o n s 53 d a p p e n d i x d : m a rg i n a l e f f e c t s p ro b i t c o r r e l at e d r a n d o m e f f e c t s m o d e l . 55
1
I N T R O D U C T I O N
Jobs in industries such as retailing, food services, call centers, and sales companies are popular among students and known for their high employee turnover rates. Studies have found excessive turnover associated with higher direct cost due to the recruitment and
training of new employees (e.g. Staw, 1980; Hinkin & Tracey, 2000; Glebbeek & Bax,
2004). At the same time, employee turnover bears indirect costs caused by a loss of
human capital (Mobley, 1982). Therefore, these industries can suffer severe economic
damage from high turnover.1 From a firm’s perspective, it is desired to maintain
expe-rienced and good performing employees. For managers, two questions that arise from the excessive turnover phenomenon are; what causes turnover in an organization and how can excessive turnover be reduced? Employees who are likely to leave can be iden-tified by determinants of employee turnover within an organization. Managers can use retention strategies to prevent these employees from leaving the company.
In sales companies, performance related pay schemes are often introduced to attract
and maintain good performing employees2 (Lazear,1999). Sorting theory suggests that
performance related pay attracts better performing and risk-averse employees. These employees can capture ’rents’ on their wage that they could not obtain in a fixed time
wage job.Lazear(1999) suggest that performance related pay fosters the sorting of more
capable employees into these kind of jobs.
While performance pay could benefit high performers, performance pay could lead
to a decrease in perceived job satisfaction for less performing employees (Green &
Hey-wood, 2008). First, performance pay could cause a pay dispersion within the firm, in
1 According to an article of the Economist (2000) even the cost of replacing fast-food joint employees,
which are considered as easily replaceable, is estimated at $500.
2 Besides the sorting effect, performance related pay create productivity incentives. It has been shown by several authors that performance related pay can increase the effort, earnings and risk of employees (Booth and Frank, 1999, Lazear 2000 Lemieux et al., 2009; Oettinger, 2001; Paarsch and Shearer, 2000; Parent, 1999; Shearer, 2004). This paper in not concerned about the effects of performance pay on productivity.
which high performing employees earn considerably more than low performing employ-ees. Consequently, this pay dispersion may reduce perceptions of morale and motivation among lower performing workers. Second, pay schemes related to performance may not
only increase efforts but could also bring peer pressure.Kandel & Lazear(1992)
empha-size that this peer pressure can be so severe as to actually lower job satisfaction even as
average earnings rise. Case studies of call centers byDrago(1996) andFernie & Metcalf
(1999) show that intensively monitoring employees and compensating them for their
results can worsen the workplace due to low wages and high stress. The possible pay dispersion and pressure may also foster a selection effect during employment besides the sorting of employees into these jobs. This selection effect could cause lower performing employees, yet still cost-effective employees, to sort out of performance pay jobs.
One of the difficulties in analyzing the turnover decision in a performance related pay setting lies in the fact that it is unclear whether job satisfaction is caused by low earnings or low performance. Previous studies on performance pay generally use aggregated data per employee or compare employment duration data among different pay schemes or industries. Employee specific data is usually gathered by conducting surveys which may be subject to subjective measures on performance. Using per employee aggregated data, as opposed to shift data which monitors employees over time, makes it impossible to capture the effects of short term poor performances on the turnover consideration under the pressure of a performance related pay scheme. Another challenge in analyzing the employee turnover is the complex decision dynamics that play a part in the decision to quit, e.g. there may be juridical constrains forcing an employee to stay with a firm for a certain time period. Few or none studies have been conducted that use objectively measured performance data which is collected at multiple time periods during the course of employment.
This paper studies the relationships between performance and turnover in a Dutch
field marketing company. As for most studies on turnover (Mitchell et al.,2001), this
thesis focuses on voluntary turnover in which the employee itself decides to leave the organization. The dependent variable, whether someone left or stayed after a shift, will be analyzed using different econometric models. The main focus of this thesis is the relationship between pay, performance, and turnover. This thesis aims to answer the main question:
How does employee turnover depend on pay and performance under two different performance related pay schemes?
Understanding the determinants of turnover in a firm can help identifying employees that are likely to leave. Firms can design retention strategies, such as increased pay, to prevent these employees to turnover.
i n t ro d u c t i o n 3
By empirically analyzing employee data working at a Dutch field marketing company the effects of short term as well as an overall performance measure on the probability to quit are estimated. This company, founded in 2002, offers face to face marketing and sales activities. Employees of this company operate in shifts and their compensation consist of two parts. In the first part, employees earn a fixed time-rate pay. Second, employees can earn a variable pay related to their sales performance. This variable pay consists of sales commissions (or piece rates) and target bonuses for individual and team performances. For each shift, data are available on the number of sales and the earnings of the employee. In January 2014 the company was forced to change their compensation scheme to comply with the Dutch minimum wage regulations. Because of this change in compensation scheme, the fixed-time rate pay for certain groups of employees were cut back. For others, this change imposed an increase of the fixed-time rate pay. The new compensation scheme caused earnings to become less tied to performance.
A unique aspect of this paper is the dataset used for the analysis. Because of the change in compensation schemes, situations could occur in which two employees of dif-ferent age performed equally but earned difdif-ferently. This change in the compensation scheme can help to identify the effects of earnings and performance on the turnover deci-sion. Also, the employees working for this sales company are mostly students doing this as a part time job. Their barriers to leave may be lower making effects of performance and pay on turnover more clearly observed. One of the reasons could be that there are few juridical constrains to leave in this job. A lower barrier to exit may simplify the complex decision to quit and could make performance to be more directly linked to turnover.
In the analysis, the employment duration is modeled using survival analysis consider-ing right-hand censorconsider-ing of the data. Employment duration at this company is hard to define because employees work shifts at highly different times intervals. For this reason, also a binary choice model is used to model the turnover decision after each shift given the performance of previous shifts. The binary choice model, however, does not take into account the right-hand censoring of the data. Another way of measuring employment duration would be to count the number of shifts. A count model could be used to model the number of shifts. However, this appoach is not executed because of the aggregation of the data which is required to use the count data model. The short term performance effects and other covariates could dissolve by the aggregation of the data, which is what lacked in previous methods.
This paper is structured as follows, Chapter 2provides insights into the literature on
voluntary employee turnover. This chapter starts with a definition of voluntary turnover
provides information on the data used in the empirical analysis. Chapter4discusses the econometric models and the modeling challenges related to employee turnover. Chapter
5 summarizes the empirical results and findings of this paper and Chapter 6 offers a
2
B A C K G R O U N D L I T E R AT U R E
Because of its psychological dimension, its economic aspect, and its organizational sig-nificance, the turnover phenomenon has caught the interest of researchers from different
fields (Morrell et al.,2001). Past research offers different theoretical models that
concep-tualize the dynamics of turnover.1 The large amount and variety of papers on voluntary
turnover, offering various causal frameworks and inducing different relationships, shows the importance and complexity of the issue.
While this thesis takes an economic approach to modeling the turnover probability of an employee, the psychological aspect should be discussed as well. The economic approach has received criticism from sociologists who claim that a numerical analysis, that tries to model turnover using a mathematical framework, can lose sight of the
complexity of individual employment decisions.2 Moreover, the psychological literature
may provide a further understanding of observed effects and could help HR-managers to develop retention strategies.
This chapter discusses relevant background literature on employee turnover which helps to justify the empirical modeling and to interpret the results. First, a definition of voluntary turnover is given. Second, economic theories related to turnover are presented. Furthermore, psychological conceptual models of turnover are discussed. At last, studies on the effects of performance related pay on turnover are reviewed.
1 The model of March & Simon (1958) been the first and probably gained the most attention from
researchers. After theMarch & Simon(1958) model many other models have been published by other
authors, (e.g.Mobley,1977;Price,1977;Porter & Steers,1973;Mowday,1981;Whitmore,1979)
2 For an example, take a look atBlakemore et al.(1987) for a rather numerical analysis
2.1 d e f i n i n g t u r n ov e r
Price(2001) defines turnover as "the individual movement across the membership bound-ary of an organization". Here the "individual" refers to the employee within an organi-zation and "movement" can be interpreted as either the accession to or the departure from a company. In turnover literature, authors also use definitions as quits, attrition, exits, mobility, churn, migration or succession when referring to turnover. This thesis is concerned with analyzing voluntary, avoidable and dysfunctional turnover. This paper considers this kind of turnover because only for this type of turnover preventive mea-sures can be effective and worth considering. The characteristics of this type of turnover are further discussed below.
First, voluntary turnover is described as the decision in which the employee itself chooses to leave the company. Reasons for voluntary turnover could be a more appeal-ing job offer, more satisfaction from leisure, staff conflicts or a lack of promotional opportunities within the firm. Involuntary turnover, as opposed to voluntary turnover, is defined as the turnover caused by the employer’s decision to discharge an employee.
The avoidability of turnover considers the question whether turnover could have been
prevented by the intervention of the company (Abelson, 1987). A common example
of unavoidable turnover in the literature is the reallocation of the spouse, forcing an employee to find another job. If a company identifies that turnover is unavoidable it
is useless to put in an effort for retention measures for those employees (Morrell et al.,
2001). However, avoidable turnover could, in theory, be prevented by retention measures
such as increased pay.
Functional turnover is defined as turnover from which the company benefits (Dalton
et al.,1981). Turnover is beneficial if it concerns low performing and not profitable
em-ployees (Staw,1980;Mobley,1982). Whereas dysfunctional turnover is described as the
loss of productive employees. By definition, it is not worth to prevent functional turnover using retention measures. Certain retention techniques aimed a preventing dysfunctional turnover could actually encourage functional turnover (e.g. a pay dispersion could lead to a lower morale for dysfunctional employees). To distinguish between functional and dysfunctional turnover requires a thorough definition of these two types of turnover. It is beyond the scope of this thesis to define whether turnover is functional or not.
At last, it should be noted that this thesis doesn’t distinguish between different moti-vations of voluntary, avoidable and dysfunctional turnover. The effects of covariates on turnover may differ for these different motivations. Turnover because of a more appeal-ing job offer has a different origin than turnover because of job dissatisfaction.
2.2 economic theories related to turnover 7
2.2 e c o n o m i c t h e o r i e s r e l at e d t o t u r n ov e r
In this section, relevant economic theories are discussed in which turnover is approached from a labor market perspective. Labor market economics, in the context of employee turnover, seeks to understand the relations between turnover motives as more appealing job opportunities, perceived alternatives, effort and rewards in a rational or subjective
expected utility setting.3 Theories have been developed aimed to provide plausible or
rational explanations of turnover relationships.
Economic theories related to turnover that will be presented in this section include neoclassical microeconomic model, equity theory, human capital theory, and matching theory. These theories are further discussed.
2.2.1 Equity Theory
Equity theory, also known as justice theory, proposes that individuals determine whether
the distribution of resources is fair to both relational partners (Adams,1965)
In organizations, equity theory presumes that employees compare their inputs, such as effort, ability, personal sacrifice or enthusiasm and outputs, such as salary, benefits or sense of achievement to those of others and respond to reduce their perceived inequities. Employees want to feel that their contributions and work performance are rewarded with their pay. When inputs and outputs are fairly distributed among the workers, they feel more motivated. Whereas, inequities can have a negative impact on employees’ morale (Carrell & Dittrich,1978).
It should be noted that each person’s assessment of fairness compared to other can be measured differently and is highly subjective. Employees may value their inputs and outputs differently and hence employees do not measure their contributions in the
same way. Ross & Sicoly (1979) suggest that the evaluation of input may suffer from
availability bias, since one’s own effort or input is more readily available. The judgment of effort can therefore suffer from an egocentric bias. As a result, higher compensation may be perceived as unfair among lower performing workers.
Equity theory states that it may be acceptable for better performing employees to receive a higher compensation, although excessively high compensation differences may have a negative impact on the perceived justice. Subsequently, policies as performance re-3 Studies include the investigation of perceived alternatives (Griffeth & Hom,1988;Gerhart,1990;Hulin
et al.,1985); performance (Jackofsky,1984;Jackofsky et al.,1986;McEvoy & Cascio,1987;Martin et al.,1981); expected utility (Bedeian et al.,1991) and pay satisfaction (Sirola,1998).
lated pay may have implications for employee morale, efficiency, and voluntary turnover. Also, Equity theory could explain the acceptance of a minimum wage. If firms are forced to implement a minimum wage, employees could compare their wages only to colleagues within the same age category.
2.2.2 Human Capital Theory
Becker(1962) developed the human capital theory. This paper describes how investment in an individual’s education and training is similar to business investments in equipment. According to the human capital theory, the use of a human his knowledge and capabil-ities are comparable to the utilization of natural resources involved in the production process. The human capital theory claims not all work is equal and employees’ value
can be increased by training and education (Becker,1993). Education, experience, and
skills of a worker have economic value for employers and for the economy as a whole. Learning capacity, education and knowledge are closely related to earnings, thus it can
raise a person’s income (Card,1999).
The human capital theory (Becker, 1962) distinguishes two main forms of human
capital investment. First, the theory considers schooling as an investment and defines a school (such as a university or high school) as an "institution specializing in the production of training". Human capital theory proclaims that education is an investment
in human capital and increases productivity (Becker,1993). It is often assumed that the
level of general education has a negative effect on turnover since better education is often
associated with increased labor-market alternatives (Hulin et al.,1985). Second,
on-the-job training relates to increasing the productivity of employees by learning new skills
or extending capacities and knowledge on-the-job (Becker, 1993). On-the-job training
can be categorized into two types of on-the-job training. General training is entitled when the acquired competence can also be applied in other work. For example, sales skills learned at one company may be beneficial when working at another sales company. whereas specific training is defined as "training that has no effect on the productivity
of trainees that would be useful in other firms" (Becker,1993).
For employees who possess a high amount of company-specific training, finding an alternative job which meets their expectations, such as wages, will be harder. Based on this theory, it is presumed that company-specific training has an inverse relationship
to turnover.Gritz (1993) used continuous time duration models to model the influence
of training on the number and length of employment episodes. The estimation results showed that participation in a training program improves the duration of employment
2.3 psychological frameworks of turnover 9
spells. Also, if an employee possesses a high amount of general schooling more attractive alternatives were more easily found.
2.2.3 Matching Theory
In economics, matching theory is used to describe the dynamics in the transitions be-tween jobs. It gives an understanding of the engagement and termination of an employ-ment contract. The matching theory provides a mathematical framework that focuses
on modeling the transitions in and out of employment (Pissarides,2000).
The matching theory presumes that employees strive for jobs that match their ca-pabilities and for jobs that associate with an appropriate wage and status. Employees
perform these jobs to maximize their benefit (Sousa-Poza & Henneberger,2002). At the
start of a career, an employee’s productivity in a particular job is not known in advance
but rather appears as job tenure increases (Jovanovic, 1979). Therefore, younger
em-ployees are exposed to an experimental stage. At the beginning of their professional life, they gain experiences and diminish lack of information. Eventually, this experimental stage results in a "match" at a point during the course of the career.
Because this paper considers a sales job which is typically done by students, high turnover rates could be explained by the experimental stage as described by the the matching theory. One of the reasons for students to perform this job could be to try-out a sales job to see whether that job matches their expectations. One of the results could be that performance and pay are a less important factor in the turnover decisions during the early stages of the career.
2.3 p s y c h o l o g i c a l f r a m e wo r k s o f t u r n ov e r
This section presents relevant theories related to turnover from a psychological perspec-tive. Turnover is a decision-making process involving a psychological aspect. To gain a broader understanding of this decision, also the psychological perspective is examined. A number of studies developed and estimated causal models to specify the factors of
voluntary turnover.March & Simon(1958) were the first to conceptualize the
decision-making process. Most of the current theory and research on voluntary turnover springs from the ideas of their work. Theoretical frameworks are often used to provide a possible explanation for how job perceptions, such as job satisfaction, pay, performance and job alternatives influence voluntary turnover. Although there is a variety of models, most
of these models have in common that they presume turnover to be a multistage process
that includes behavioral, attitudinal, and decision components (Barak et al.,2001).
Three turnover models are presented below. These principal models have shaped the research on turnover behavior and are therefore discussed. Because there is a large
body of literature on different models,4 a distinction is made to select the most relevant
frameworks for this research. First, the leading model ofMarch & Simon(1958) will be
highlighted. Furthermore, the models ofPrice & Mueller(1986) and Mobley(1977) are
presented.
2.3.1 March and Simon’s Model of Participation
March & Simon(1958) are one of the first the conceptualize determinants of turnover in a framework. This framework specifies that an employees’ decision to leave the company is shaped by two factors. These factors are the "perceived ease of movement", which refers to the perceived alternatives or opportunities outside the company and the "perceived desirability of movement", which is influenced by job satisfaction. This model describes turnover as a utility consideration process that balances both the benefits of the job, such as pay and the sacrifices, such as effort. When benefits are increased by the company,
this will lower the propensity of the worker to leave. (Morrell et al.,2001).
Only a few studies tested March and Simon’s model empirically.Mayer & Schoorman
(1998) have been one of the few to test the model by using survey data and a structural
equation modeling technique. Findings of this research supported the patterns of
rela-tionships regarding turnover as proposed by the framework by March & Simon (1958).
Many other frameworks on voluntary turnover have been inspired by or are descendants
of this framework (e.g. Mobley,1977;Lee & Mitchell,1994).
As any model trying to capture the complex decision-making process regarding turnover,
the model of March & Simon (1958) suffers from limitations. One limitation is their
model presents a static rather than a procedural view on turnover. The structural equa-tion model which is used to test the framework is also not able to capture the dynamic nature of the turnover process. Also, several important variables influencing the turnover
process, such as stress (Gupta & Beehr,1979) or organizational commitment (Mowday
et al.,2013), are not considered in the original model of March and Simon. Subsequently,
4 The following models have been published; Met expectation model (Porter & Steers, 1973), Hom &
Griffeth (1991) Alternative Linkages Model of Turnover, Whitmore (1979) Inverse Gaussian Model
for Labour Turnover Turnover Model, Porter & Steers (1973) Turnover Model, Sheridan & Abelson
(1983) Cusp Catastrophe Model of Employee Turnover,Jackofsky(1984) Integrated Process Model,Lee
& Mitchell (1991) Unfolding Model of Voluntary Employee Turnover, Aquino et al. (1997) Referent
2.3 psychological frameworks of turnover 11
several authors have developed new models. Mobley’s Intermediate Linkage model pro-poses a more dynamic decision-making process. At last, using survey data to test the model could lacks because of the subjective measures on performance.
2.3.2 Mobley’s Intermediate Linkages Model
Mobley (1977) suggests a turnover model presuming a series of causal relationships af-fecting turnover. This model relates to several preceding models including the model of
March & Simon (1958). This framework proposes that lower job satisfaction leads to thoughts of quitting, followed by an evaluation of the utility of searching for alterna-tives and leaving the job. If this evaluation is positive, intentions to quit follow, which can finally result in the actual turnover. As opposed to the March and Simon model,
Mobley’s model has been tested and extended with different variables (e.g.Hom et al.,
1984;Bannister & Griffeth,1986;Hom & Griffeth,1991).Hom et al.(1984) used survey data of 192 hospital employees to measure of all components in Mobley’s model. In this study, each component of Mobley’s was regressed on causally prior components. Later
models added variables as organizational commitment (e.g. Kim et al., 1996), or took
inspiration from specific elements of the Mobley model (such asHom & Griffeth(1991),
andMowday(1981)). The model component that remains central in these turnover
stud-ies is the job satisfaction evaluation. Although, the original Mobley (1977) model has
influenced work on psychological approaches to turnover, empirical tests of the original
model found weak support for the proposed relations (Hom & Griffeth,1995).
2.3.3 Price’s and Meuller’s Model of Turnover.
Initially,Price(1977) proposed a model of turnover assuming exogenous variables affect
job satisfaction which influences turnover. Reduced job satisfaction increases turnover, moderated by the perceived opportunity for alternatives. This model was later expanded byPrice & Mueller(1981) by adding "intention to leave" as a mediating variable between
job satisfaction and turnover. Finally,Price & Mueller (1986) extended the model.
Fig-ure1shows the extended model in which commitment is added as a mediating variable
between job satisfaction and "intent to leave".
Unlike the March & Simon (1958) model, the Price (1977) model has been tested
and refined extensively.Price & Mueller (1981) tested this framework using data from
questionnaires filled in by registered nurses. Multiple regression and path analysis has been used to analyze the proposed relations. A shortcoming of this model is that its
explanatory ability remains low. The empirical studies in Price & Mueller (1981) and
Price & Mueller(1986) found that the model explained only 18 percent and 13 percent respectively of the variance in turnover. Also, many of the hypothesized relations were not supported.
Figure 1. Conceptual Framework of Price and Meuller (1986)
source: Price & Mueller(1986)
c o n c l u s i o n
Despite the numerous studies on turnover, there is not a universally acknowledged
frame-work for understanding why employees choose to leave (Lee et al., 1999). Due to the
complexity of the turnover decision, a general model does not exist. Most studies use survey data on employee level to test frameworks of turnover. Using survey data lacks because of the subjective measures on performance. Most empirical modeling techniques are not able to capture the dynamic nature of the turnover process. Also, attempts of modeling turnover often lacked in the explained variability of observations.
3
R E S E A R C H D E S I G N
In this chapter, the employee data provided by the Dutch marketing company is de-scribed. The choice of the variables is based on the literature study of the previous sections. First, background information on the data source is given. Second, the
differ-ent compensation schemes used by the company are explained. Section 3.3provides an
overview of descriptive statistics. In section 3.4 the data transformation is explained
and discussed. Section 3.5 discusses the variables used in the empirical model. Section
3.6explains the modeling strategy.
3.1 data c o l l e c t i o n
A dataset is provided by a Dutch field sales and marketing company. The company has been founded in 2002 and offers face to face marketing and sales projects for businesses like retailers, publishers, charities, and energy providers. These businesses hires the field marketing to do projects, which typically are sales campaigns. During a sales project employees perform shifts within a team. The team will go out to a crowded public area or go door to door within a neighborhood. Employees usually try to sell subscriptions or try to raise money for charities. Currently, the company is operating in multiple countries in the European Union. The company provided their data on employees in the Netherlands for the analysis in this paper.
The dataset is an unbalanced panel with individual employees performing multiple shifts at different moments in time. The dataset includes shifts over a period ranging from January 3rd, 2011 to May 8th, 2016. In total, 270084 observations are included in the dataset. Each data point represents a shift performed by an employee. 8972 unique employees are found in the data set. For each shift an employee gets assigned to a team to work on a project. In total, 784 different projects have been worked on during the time span of the dataset. Data on the employee is collected before, during and after
the shift. It should be noted that the data suffers from left and right censoring. The left-hand censoring of employment spells occurs because for some employees only data from a later point during employment is known. Right censored employment spells are caused by employees who are registered as still employed.
The shifts are organized as follows. An employee is working for 5 hours on each shift. Shifts are performed in teams of various sizes and can be composed by three different ranks of employees; talents, promoters and captains. When you start working at the company the first four shifts you operate as a talent. If you perform well you can get promoted to the rank of a promoter and be offered a contract. By monitoring these new employees the company filters out poor performing employees.
The pay of employees consists of fixed wage, commissions, individual bonuses and team bonuses. The fixed wage is a predetermined amount which, unlike the commissions and bonuses, does not depend on performance. The commission is a piece rate which is constant for each sale. An individual bonus is rewarded if an employee reaches a certain sales target. When the team reaches a minimum average of sales, each team member obtains a team bonus. Captains are paid an extra bonus by doing organizational activities, such as accompanying and monitoring newly entered employees. The rates of the commissions and the amounts of the bonuses can differ per project.
3.2 c o m p e n s at i o n s c h e m e s
The Dutch marketing company has used different compensation schemes over the course of the years. Due to government regulations the company was obligated to change their pay structure in the year 2014. Prior to January 2014, the fixed wage was tied to the ranks of the employee. Talents and promoters earned a fixed wage of e23.40 and cap-tains earned e39.00 per shift. The variable wages consisted of commissions, individual bonuses, and team bonuses. The rates of these commissions and bonuses were different per project.
After the wage change the individual bonuses dropped. Talents and promoters earned five times the minimum hourly wage and captains earned seven times the minimum wage per shift. These minimum wages are based on the minimum wage tables provided
by the Dutch Tax Authority. Table1shows the minimum wages for different age groups
and how the compensation change affected the fixed wages. 16-year-old captains were most severely set back in their fixed wage by a decrease of e18.28 of their fixed wage per shift. The fixed wage of 23+-year-old captains increased most from this new wage
3.3 descriptive statistics 15
scheme. The wage change caused the fixed wage to increase by e20.99 per shift for this group.
Table 1. Change in Fixed Wages for Different Ages and Positions
Before 2014 After 2014
Age Minimum wage Talents/promotors Captains Talents/promotors Captains
23+ 8.57 23.40 39.00 42.85 (+19.45) 59.99 (+20.99) 22 7.29 23.40 39.00 36.45 (+13.05) 51.03 (+12.03) 21 6.21 23.40 39.00 31.05 (+ 7.65) 43.47 (+ 4.47) 20 5.27 23.40 39.00 26.35 (+ 2.95) 36.89 (− 2.11) 19 4.50 23.40 39.00 22.50 (− 0.90) 31.50 (− 7.50) 18 3.90 23.40 39.00 19.50 (− 3.90) 27.30 (−11.70) 17 3.39 23.40 39.00 16.95 (− 6.45) 23.73 (−15.27) 16 2.96 23.40 39.00 14.80 (− 8.60) 20.72 (−18.28)
A 13% holiday allowance is added in the pay but is neglected in these amounts.
The stoppage of bonuses and the increase in pay for older captains could lead to fewer performance incentives. Therefore, the company decided in July 2014 to change the fixed wage for captains to 5 times the hourly minimum wage and to reintroduce
individual bonuses for captains.1
3.3 d e s c r i p t i v e s tat i s t i c s
This section provides an overview of descriptive statistics to understand the employment duration and the developments of employees over time. Summary statistics on all the
shifts performed by the employees are reported in Table2. Descriptive statistics on the
unique employees which were in the data set are reported in Table3.
Table 2. Descriptive Statistics of All Shifts
Before 2014 After 2014
Mean Std.Dev. Mean Std.Dev.
Fixed wage + commissions 59.78 28.9 59.54 27.1
Individual bonus 7.68 13.3 2.53 7.9
Team bonus 3.57 8.1 4.84 10.9
Total payments 71.04 45.1 66.91 38.5
Age 20.13 2.3 20.85 2.3
Total shifts 100881 109109
Table2 shows descriptive statistics of the shifts performed before and after the 2014
wage change. An average total payment of e71.04 per shift before the change in the 1 Because this second shift change affected few employees, the descriptive analysis the descriptive statistics
compensation scheme. After the change in compensation scheme, the average total pay-ment dropped to e66.91 per shift. There can be two causal factors identified for this observation. First, the change in compensation scheme could have affected the perfor-mance incentives for employees. This could have changed the culture of the firm in a way that employees felt less pressure to perform. Another reason for the drop of payments could be due due to the fact that good performing employees stopped working at the firm because they were set back by the new wage scheme. Besides the drop of payments, there appears to be a slight increase in the average age of the employee performing a shift after the wage change.
Table 3. Descriptive Statistics of Employees
Started before 2014 Started after 2014
Mean
Total shifts performed 50.9 (84.8) 29.5 (39.0)
Age 20.0 (2.4) 20.1 (2.3) Tenure in days 267.1 (411.5) 135.6 (166.5) Tenure in weeks 38.5 (58.8) 19.8 (23.8) Total Right-censored 234 751 Left-censored 566 22 Male 1870 1344 Female 1551 1103 Talent 1137 1147 Promotor 1649 1098 Captain 635 202 Training 1 completed 98 224 Training 2 completed 107 203 Training 3 completed 109 149 Training 4 completed 91 74 Training 5 completed 76 11
Total unique employees 3421 2447
Table3 describes the composition of the workforce before and after the wage change.
Before the wage change employees performed a total of 50.9 shifts during employment. The average number of shifts performed seems to be decreased after the wage change. It should be noted that the drop of tenure could be largely due to the right-hand censoring of the data. Remarkably, rven in the subset of those who started after 2014 there are several employment spells which suffer from left-censoring. Possibly, the first shift for these 22 employees weren’t registered in the system.
The data showed 573 unique employees started employment at the company before January 3rd, 2011. Therefore, for the first month the number of employees is set to 573. The number of employees for all other months is recursively determined by the formula
3.3 descriptive statistics 17
turnover over time the monthly turnover ratio is calculated. Figure2shows the monthly
turnover ratio over time in the dataset. The monthly turnover ratio in month m is calculated recursively as
Monthly Turnover Ratiom =
Quitsm
Employeesm−1− Quitsm+Startsm (1)
In which Quitsm = number of quits in month m, Employeesm−1 = number of
em-ployees in month m − 1, Startsm = number of new employees in month m.
Figure 2 plots the monthly turnover ratios. The graph shows high peaks of turnover
clustered around the 8th month of the year which coincides with the start of schools and universities. Because many employees are still in school, it is very likely that this outflow of employees is due to the start of the academic year.
Figure 2. Monthly Turnover Ratios
To explore the development of pay during employment, Figure ?? (A) shows the
av-erage total payments per shift. The figure shows an increase of payments when more shifts are performed. The first shift, employees earn on average 48.52 (Standard devia-tion is 23.67) Standard deviadevia-tion in of those that worked for the 100th shift earn 75.46 (Standard deviation is 40.09) on average. This increase in average total payments may have several causes. First, lower performing and therefore lower earning employees are more likely to quit. This selection mechanism could be one of the reasons the average total payments is lower among the first shifts. Second, the increase in average total payments could be due to a learning process. By performing more shifts employees gain experience which will enhance performance. Because payment is linked to performance, this learning process could be one of the reasons behind the increase in average total payments. Third, tenure and performance are related to the promotion of employees. Because the promotion to captain yields better pay, it could result in a higher average total payments.
Figure 3. Total payments when shift count increases
(a) Mean total payments
(b) Mean total payments compared be-tween two groups of total shift count
To compare these effects, the data are split into two groups of employees. The first group consists of employees who worked more than 100 shifts. The second of those who stayed at the company for less than 100 shifts. Considering different groups of employ-ees mitigates the selection effect. Employemploy-ees still in employment (and therefore right censored), who have performed less than 100 shifts, are dropped from this descriptive analysis.
Figure ??(B) shows the average payments per shifts of the first 95 shifts for the two
groups. Those who performed more than 100 shifts during their employment spell were already, on average, earning more in the beginning of their career. This suggests that those who earn more are likely to stay with the company longer.
To examine the development of performance during employment, Figure5(A) shows
the mean relative shift score by shift number. This figure shows a steep increase of the relative score in the beginning of the career indicating a learning effect. This learning curve seems to marginally decrease as more shifts are performed. The fluctuation around higher shifts is due to a diminishing number of observations of workers who stayed at the firm for more shifts.
Figure 5 (B) shows the mean relative score by shift number for the two groups
con-sidered. This figure shows that those who stayed with the company for more than 100 shifts already performed better on average in the beginning of their career. Both groups show a steep increase of relative score during the first couple of shifts. Comparing these graphs suggests that the increase in performance caused by the experience effect mainly affects the performance in the beginning of the career.
The observed increasing average performance at a later stage of employment may be due to a selection effect. A remarkable observation is the decline of average relative
3.4 data transformation 19
scores after the 80th shift for the group of employees who performed less than 100 shifts in total. These employees will soon leave the company. One explanation for a drop in performance could be that a series of poor performance increases the probability of turnover. A second explanation is that during the turnover consideration process or when an employee considers to leave, the employee has a lower incentive to perform. For example, an employee may not feel the urge to perform to avoid being fired causing the employee to perform worse.
Figure 5. Performance over time
(a) Mean relative score
(b) Mean relative score compared be-tween two groups of total shift count
To illustrate the course of promotions among employee figure7shows the ratio of the
three different positions when for the number of shifts performed. The promotion from talent to promoter can happen after 4 shifts Being promoted from talent to promoter does not bring any financial gains. Being promoted to captain does include a monetary gain in the fixed wage and the possibility to obtain captain bonuses. In the July 2014 compensation scheme change, this increase in fixed wage has been replaced by
reintro-ducing individual bonuses for captains. As shown in the figure7, of those who performed
105 shifts about half has been promoted to captains. More than half of the employees who performed more than 105 shifts are earning the captain fixed wage.
3.4 data t r a n s f o r m at i o n
Because this thesis is focused on only analyzing voluntary, avoidable and dysfunctional turnover, employees not satisfying these conditions have been filtered out. When an employee leaves, the company reports the reason the employee left. In the dataset, there are 32 different motivations found for the end of the contract. To filter out involuntary
Figure 7. Positions of employees over the course of employment
turnover, the employees with the following motivations for the end of a contract are dropped:
• "Fired because of fraud" • "Fired because of behavior" • "Fired because of misconduct" • "Fired because of theft"
• "Fired because of physical violence" • "Fired because of not showing up".
To filter out functional turnover, the following reasons are dropped: • "Fired because of poor performance"
• "Didn’t reach target"
To filter out unavoidable turnover, the following end of contract motives are dropped: • "Quit because of health considerations"
• "Not able to work for more than 2 months"
After these employees are dropped, a total of 209990 shifts and 5868 unique employees are still in the dataset.
The number of sales is an important indicator of how well employees perform within a project. Because each project has its own characteristics and compensation scheme, the number of sales can only be compared within projects. To illustrate this, it may be easier to perform a sale on a project to sell cheap and discounted newspaper subscriptions
3.5 variable selection 21
than to perform a sale on a project to sell relatively expensive energy contracts.2 In
order to compare overall performance of an individual working different projects, the performances of employees are ranked within a project. A more comparable measure of performance is obtained by assigning a performance score of each shift based on the cumulative distribution of sales per shift within projects. The relative score takes value between 0 and 1 inclusive. For this relative score measure to be an accurate measure of performance requires the set of employees who worked for a project to be representative for the entire workforce. This assumption would be violated if, for example, good performing employees are picked to work for a certain project. A manager at the firm stated to not explicitly select employees for certain projects based on their performance. It is therefore assumed that the population of employees working on a project is representative of the entire population.
To make the data suitable for analysis, the date of someone quitting is set to 1 day after someone’s last shift. It should be noted that the data contain right-hand censored employees. These employees are still in employment at the end of the data timespan be-cause they haven’t quit. Survival analysis can deal with this type of censoring, however, binary choice models do not explicitly handle this type of censoring. As a result, the effects of covariates on the turnover decision could be biased because turnover for these employees is (not yet) observed. Especially if the number of censored observations show different characteristics as the uncensored observations, the estimation can lead to erro-neous inference. Removing these observations will also lead to biased estimation when different characteristics of censored and uncensored observations are assumed. Again, this advocates the use of survival analysis. The results between the survival analysis and the binary choice approach could be explained by the censored nature of the data (Farewell,1977). To illustrate this, consider the following hypothetical situation: If it is assumed that high performance increases the employement duration, it could occur that these high performance are still in employment. These high performing and long term employees are therefore right-censored. Turnover is not observed for several of these employees and parameter estimates for performance in a binary choice model could give biased results under this assumptions.
3.5 va r i a b l e s e l e c t i o n
Because pay is related to performance, the total amount of payments obtained on a shift is likely to vary significantly over shifts. The mean total payment of previous shifts is used as a proxy for the monetary value an employee expects to gains from working. The 2 This is also the reason why piece-rates differ per project.
proposition is that high expected pay will increase the survival probability. Reversely, the lower the pay for an employee, the less utility an employee gains from working.
In most psychological frameworks, performance is considered to affect turnover. Dummy variables are used to distinguish high and low performers. The mean relative score in the data set is 0.53 (Standard deviation is 0.166). Each group is formed by taking one standard deviation from this mean. Therefore, low expected performers are defined as those whose expected relative score is lower than 0.35. High expected performers are defined as those whose average relative score exceeds 0.70.
The Dutch field marketing offered five types of training. These trainings are generally focused on lecturing about marketing and sales. Human capital theory suggests that general and company specific training may affect the turnover propensities of employees. Dummy variables for each of the training. The dummy variable is assigned value 1 from the moment an employee received a training.
The level of education known to the company is divided into four 4 categories accord-ing to the Dutch education system. The categories are high school, secondary vocational education (SVE), intermediate vocational education (IVE), and university. University level is considered to be the highest education level followed by IVE, SVE and high school.
At last, dummy variables are included in the model indicating the different positions talent, promoter, and captain. To control for other exogenous effects weather condition as rain (mm) and temperature of previous shifts are included. Also, dummy variables for gender, age, months, offices locations and recruitment sources are included as additional control variables.
3.6 m o d e l i n g s t r at e g y
Both survival analysis and the binary choice approach have their pro’s and con’s. Sur-vival analysis in this application may lead to an erroneous inference of the effects of covariates on employment duration. To illustrate this, consider two employees, one who performed 12 shifts in one month before deciding to quit and another employee who also performed 12 shifts before deciding to quit but over the course of one year. In this sense, both employees performed 12 shifts but their employment duration measured in days differs. For the employer, the number of shifts is more important than the time duration of employment. This would be reason to use a binary choice model instead of a survival model to model turnover. Binary choice models, on the other hand, lack in their ability to handle censored data. A justification for the use of a survival model in this
applica-3.6 modeling strategy 23
tion is a high correlation between time employed and total shifts performed during the spell. A correlation of 0.93 is found between the number of days in employment and the
number of shifts performed.3
First, the full sample is used to capture the effects of the pay, performance, educa-tion, and training on the employment duration. Survival analysis is used to estimate these effects using different model specifications. An extended model is estimated which included weather and recruitment variables to test the sensitivity of the parameters. Because the data contain quite a lot of employees with a short employment spells, the model is also estimated by only considering employees who performed more than 10 shifts. There may be a different effect of poor performance for employees who have a longer duration of employment. There are quite some employment spell in which only a few shift are performed. Because of the learning curve in the beginning of employment, the effects of poor performances could amplify the effects of poor performance for those who have been working at the firm for longer. Disregarding the short employment spells will mitigate the effects of the learning curve in the beginning and may improve the parameter estimations for long term employees.
The robustness of these effects under the different compensation schemes is validated by estimating this model using shift data from before and after the wage change. Second, the effects of the financial set back and financial gain caused by the wage change for two subsets are considered. These models can analyze the consequences for the wage change for different groups. Survival analysis estimates the effect of the wage on two subsets of employees who started working before the wage change. The first subset contains employees under 19. These employees were financially set back by the wage change. The second subset contains 22+-year-old employees. For these employees, the fixed wage was raised and gained financially.
A significant challenge in investigating potential effects on turnover is the impos-sibility in observing all the personal characteristics and circumstances that might be relevant. Although the data consists of precise reports on all shifts results and detailed characteristics about the employees, the complex consideration process of the turnover decision makes it inevitable to miss relevant aspects regarding this decision. As a result, the unobserved heterogeneity could lead to improper interpretation if not corrected for. For both econometric models, this source of unobserved heterogeneity is dealt with. In the survival analysis, a multiplicative unobserved heterogeneity term is included in the model. The binary choice deals with the unobserved heterogeneity by using a corre-lated random effects term in the model. It should also be noted that it is not sure if 3 This correlation neglects temporary layoffs, defined as being absent for more than 90 days. Including
lower performance causes turnover or whether turnover propensities are causing lower performance. Employees in the turnover consideration process could feel less pressure to perform once they already decided to quit soon. Most theories suggests that perfor-mance is a causal factor for turnover and not the other way around. Therefore, in this thesis, it is assumed that performance is an independent variable.
Two econometric methods used in the analysis are discussed in chapter4. This chapter
discusses the formal functional forms of these models, fundamental assumptions, and endogeneity problems.
4
E C O N O M E T R I C M O D E L S
This section describes and formulates the econometric models which are used to estimate the effects of covariates on the duration of employment and on the turnover decision of an employee. For modeling the duration of employment, proportional hazard (PH)
models, and mixed proportional hazard (MPH) models are used.1 These econometric
models of duration have been used in different academic disciplines to model the length of time spent in a given state before transitioning to another state. In economics probably the most studied application of duration models have been on unemployment duration
data (e.g.Kiefer,1988a;McCall,1996). Besides the hazard model, a binary choice (BC)
model is used to model the turnover decision. In Section4.1the specification of the PH
model is described and in Section 4.2the BC model is formulated.
The specification of the PH model is presented in section 4.1. The BC model is specified in section 4.2. Both sections discuss the specification of the model, the issue of heterogeneity, and the assumptions of the respective models.
4.1 s u rv i va l a n a ly s i s
The first part of the econometric modeling strategy focuses on modeling the transitions of employees from employment to termination. Methods from the literature on economic duration are used to analyze the employment duration and to account for the
right-censoring of the data.2
1 Stata 13 is used to perform the estimations.
2 Examples of economic duration models can be found inKalbfleisch & Prentice(1980),Kiefer(1988b),
Pudney(1989), and, in particular,Han & Hausman(1990) on Cox regressions
4.1.1 Basic concepts
First some basic concepts should be discussed. Let T be a random variable measuring
the duration of employment of an employee with a probability distribution F(t) =
Pr[T < t] and a density function f(t) = dFdt(t). The survivor function is defined as the
probability that an employee has survived beyond a certain time and is formulated as
S(t) =1 − F(t) =Pr[T ≥ t]. The dates that correspond with the time being employed
can be different for employees. In this sense, t corresponds to the relative employment duration and not a fixed point (or date) in time.
Employment duration data can be characterized in terms of a hazard function, that is, the conditional probability that the employee quits in a short time interval following period t, given being in employment up to period t
λ(t) = f(t)
S(t). (2)
The hazard function specifies the distribution of T . In particular for the continuous case,
by integrating λ(t)and using the normalization S(0) =1 it can be shown that
S(t) =exp − Z t 0 λ(u)du . (3) 4.1.2 Kaplan-Meier
Initially, the employment durations are estimated nonparametrically using the
Kaplan-Meier estimator (Kaplan & Meier,1958), which accounts for the right-hand censoring of
the data set. Let T1, ..., Tn denote the time of employment for all employees i=1, ..., n
till either turnover or censoring occurred in the sample. Suppose the discrete turnover times are ordered T(1) <... < T(r). Let hj be the number of employees that left after
T(j) months, while mj is the number of employees censored between months T(j) and
T(j+1). If nj = P T(J)
i≥T(j)(mi+hi) then the nonparametric Kaplan-Meier estimator for
the employees’ hazard rate per unit of time is given by
ˆλ(t) = hj
τjnj. (4)
for T(j)< T < T(j+1) where τj =T(j+1)− T(j). The Kaplan-Meier estimator provides
4.1 survival analysis 27
4.1.3 Proportional Hazard Framework
Because interest lies in the effects of covariates (X) on the employment duration a
model with regressors is needed. As a starting point, the proportional hazard model is
considered in which the conditional hazard rate λ(t|x) can be factored into separate
functions (Cameron & Trivedi,2005):
λ(t|x(t)) =λ0(t)φ(x(t), β) (5)
the function λ0(t) is the baseline hazard and is a function of t. The baseline hazard
may contain distribution parameters if the baseline hazard has a parametric specification.
The function φ(x(t), β)is a function of the variables x(t) alone and a common
specifica-tion in duraspecifica-tion analysis, which is also used in this thesis, is φ(x(t), β) =exp(x(t)0β)3.
Different parametric specifications of the baseline hazard can be considered. Because interested solely lies in the effects of the covariates on survival, this paper considers the
Cox PH model which does not place restrictions on the baseline hazard (Cox, 1992).
The Cox PH model does not need to specify the form of λ0(t). Variables are allowed to
be time-varying. Time-varying regressors should be taken into consideration. For exam-ple, during employment earnings may change, an employee might get promoted or job specific training may be provided at some point in time.
There are two modeling challenges imposed by introducing these time-varying regres-sors. First, it is erroneous to treat these time-varying regressors as fixed within each time interval. The previous values of a regressor may be relevant for explaining the turnover transition. Therefore, it may be required to incorporate lagged values of re-gressors. Second, time-varying regressors may exhibit feedback. This means that the value of regressors may be explained by previous values of the dependent variable. As a result, the regressors are not strictly exogenous. To illustrate this, consider an employee who gets promoted, this promotion evidently depends on previous performances and is
therefore up to a certain extent internally determined.Kalbfleisch & Prentice(2011)
sug-gest that if covariates are assumed to be weakly exogenous, then the parameters of the internally determined regressors need not be taken into consideration when estimating the hazard model. In this paper, it is assumed that covariates are weakly exogenous.
3 In principle, the parameter β can be time-varying, resulting in the specification λ(t|x) =
4.1.4 Heterogeneity
As mentioned previously, to make proper statements about the dependence of duration, the model requires unobserved heterogeneity to be incorporated in the model
specifi-cation. Lancaster (1979) suggests the parametric mixture proportional hazard (MPH)
model to deal with this unobserved heterogeneity. These models consider a multiplicative unobserved heterogeneity term that, after being integrated out, leaves the conditional mean unchanged but does inflate the conditional variance and changes the conditional hazard function. This approach uses functional form assumptions on the hazard function, which are not required by the Cox PH model. Distributional assumptions on the error
term are required to identify the model.4 The proportional hazard model in equation
(5) is extended by introducing a multiplicative error term ε
λ(t|x(t), εt) =λ0(t)exp(x(t)0β)εt, εt>0 (6)
An expression for the baseline hazard is obtained by integrating out this multiplicative error λ0(t) =λ(t|x(t), εt)exp(−x(t)0β)ε−1t Z λ0(u)du=exp(−x(t)0β)ε−1t Z λ(u|x(u), εt)du lnZ λ0(u)du =−x0β −ln εt+ν (7) where ν = lnR
λ(u|x, ε)du, and ε is assumed to be independent of the covariates and
censoring time and is normalized by the restriction E[] =1. When εt >1 the hazard
rate is greater than the average subject and smaller otherwise. The decision to involve a multiplicative error term instead of a additive error term is due to its mathematical attractiveness. This approach involves assumptions on the distribution for ε such that the marginal distribution of t can be derived.
The independence assumption of ε is a strong assumption because it assumes individ-uals to differ randomly. It can be argued that certain groups of individindivid-uals may have similar unobserved characteristics influencing turnover. A solution to this is to correct for discrete heterogeneity using latent class analysis. This technique has its downside since choosing the optimal number of latent classes is computationally demanding and
convergence of the likelihood to a single unique maximum is not guaranteed (Cameron
4 Hausman et al.(2005) managed to derive an estimator for the mixed proportional hazard model (with heterogeneity) that allows for a nonparametric baseline hazard and uses time-varying regressors. In their model no parametric specification of the heterogeneity distribution nor parametric estimation of the heterogeneity distribution is necessary. However this approached is quite involved and because of the scope of this thesis the decision is made to apply Lancaster’s approach.
4.2 binary choice model 29 & Trivedi, 2005). For these reasons, the decision is made to apply MPH models as a comparison to the Cox PH model.
The fit of the model and the presence of unobserved heterogeneity is examined by looking at the generalized Cox-Snell residuals. Cox-Snell residuals are a certain type of residuals used in reliability analysis. The residual is the difference between an observed data point and the fitted/predicted value. The Cox-Snell residual considers a defined distribution and the estimated parameters from the survival analysis model. The Cox-Snell residuals are equal to the negative of the natural log of the survival probability for each observation. The residuals of a correctly specified model should follow the unit exponential distribution. Therefore, if a model is correctly specified, the generalized residuals and theirs respective cumulative hazard should follow a straight line with slope 1. The model fits of the Cox PH and the different specified MPH models can be compared by these graphs.
The gamma and the inverse Gaussian densities are used for the choice of the hetero-geneity distribution. The gamma model is quite flexible and can lead to closed form marginal of the hazard function which makes it mathematically attractive. The inverse-Gaussian density has thicker tails compared to the gamma density making heterogeneity corrections more conservative. The following three different forms of baseline hazard dis-tributions are considered; Exponential, Weibull, and Gompertz. In total, six models are estimated using different combinations of baseline hazard and heterogeneity distribu-tions.
4.2 b i n a ry c h o i c e m o d e l
As an alternative to the survival analysis, a binary choice model is considered to model the turnover decision on a shift basis and to function as a comparison to the PH model. Series of binary variables, Yi1, ..., YiJi, are constructed for each employee i. Each variable,
Yij, is assigned the value 0 if the employee decides to stay after shift j and value 1 if the
employment spell is terminated after this shift. The total amount of shifts Ji differs per
individual. A Probit model is used to estimate the probability of staying
Pr[Yij =1|xij] =Φ(x0ijβ) (8)
The model should take into account possible unobserved heterogeneity. According to Wooldridge (2010) in the probit analysis, neglected heterogeneity is a more serious
problem than in a linear model. Even if the omitted heterogeneity is independent of
x, the probit coefficients are inconsistent. A favorable approach in dealing with this
unobserved heterogeneity issue is to include fixed effects in the model specification. However, due to the fact that some employees have a rather short employment duration, this approach suffers from the "incidental parameters problem" which can result in a
flat likelihood function (Cameron & Trivedi,2005).
Covariates are likely to be correlated with the unobserved heterogeneity, e.g. overall better performance might lead to a higher unobserved perception of job satisfaction which in turn affects turnover. The strong independence assumption that comes with
random effects seems not appropriate. Mundlak (1979) proposed a correlated random
effect model for panel models which solves this limitation.Wooldridge(2010) provides a
extension to nonlinear models in which an unobserved heterogeneity ci term enters the
equation. Following Wooldridge’s approach the probability of turnover is now defined as
Pr[Yij =1|xij, ci] =Φ(x0ijβ+ci). (9)
This unobserved heterogeneity term ci may be correlated with x (corr(ci, xij)6=0) and
can be expressed as a function of the averages of the covariates ¯xi =PJj=i1xij
ci = ¯xiξ+αi, αi|xi∼ N(0, σα2) (10)
Note that if ξ = 0 this is the traditional random effects probit model. Assuming strict
exogeneity of xij
Pr[Yij =1|xi1, ...xiJ, ci] =Pr[Yij =1|xij, ci], j =1, ..., J (11)
and conditional independence of distribution Yit
f(Yi1, ..., YiJ|xi, ci) =f(Yi1|xi, ci)...f(YiJ|xi, ci) (12)
Then equation (10) can be substituted in (9)
Pr[Yij =1|xij] =Φ(xij0 β+ ¯xiξ+αi). (13)
The resulting concentrated log-likelihood function for the random effects model becomes:
ln LRE(β, ξ, σα) = N X i=1 Z Ji Y j=1 f(yit|xij, αi, β, ξ) g(αi|σα)dαi (14)
4.2 binary choice model 31
is then maximized with respect to β, σα and ξ.
To analyze the effects of the unobserved heterogeneity this model is compared to the standard random effects probit model.
