PwC The Netherlands
Master Thesis
Testing, adjusting and underpinning
the Sustainable Business Modeling
methodology
Author:
Mila Harmelink
Supervisors:
Dr. J.C.M. van Ophem
Prof. dr. J.B. de Swart
MBA
M.M.R. van der Plas Ma.
MSc.
Second reader:
Dr. N.P.A. van
Giersbergen
List of Tables . . . 4
List of Figures . . . 6
1 Introduction 1 2 Background 4 2.1 Sustainable Business Modeling . . . 4
2.2 Mediation and Moderation . . . 7
2.2.1 Mediation . . . 7
2.2.2 Testing for mediation . . . 10
2.2.3 Moderation . . . 18
2.2.4 Testing for moderation . . . 19
3 Data driven approach 22 3.1 Literature study . . . 23
3.2 Data set . . . 24
3.2.1 Client perception . . . 25
3.2.2 Employee perception . . . 26
3.2.3 Financial performance . . . 26
3.2.4 Exploring the data . . . 27
3.3 Models for testing mediation . . . 29
3.3.1 Continuous outcome variable . . . 29
3.3.2 Categorical outcome variables . . . 33
3.3.3 Reversed causality . . . 39
3.3.4 Justification client satisfaction variable . . . 40
3.4 Models for testing moderation . . . 42
3.5.1 Continuous outcome variable . . . 44
3.5.2 Categorical outcome variable . . . 46
3.5.3 Results moderation analysis . . . 58
4 Sensitivity analysis 60 4.1 Steps sensitivity analysis . . . 61
4.2 Results . . . 66
4.2.1 Increase or decrease with a maximum of ten percent in the coefficients 66 4.2.2 Increase or decrease of 40 percent in the coefficients . . . 67
5 Non data driven approach 68 5.1 Framework . . . 68
6 Implementation scenarios in SBM 70 7 Conclusion 72 8 Recommendation 75 A Appendix 77 A.1 Standard errors of the Sobel test . . . 77
A.2 Surface plots . . . 79
A.3 Confusion matrices . . . 81
A.4 Correlation matrices for client satisfaction . . . 83
A.5 Kernel density estimates . . . 85
A.6 Questionnaires client satisfaction . . . 87
2.1 Mediation tests . . . 17
3.1 Definitions of variables . . . 27
3.2 Participated organizations over the years . . . 28
3.3 Overview three approaches . . . 30
3.4 Confusion matrix . . . 39
3.5 Results OLS estimates approach 1 . . . 44
3.6 Results OLS estimates approach 2 . . . 44
3.7 Results OLS estimates approach 3 . . . 45
3.8 Tests for the performance of the models investigating the effect of ES on CS 45 3.9 Diagnostic tests two outliers removed . . . 46
3.10 Percentage of correct predictions . . . 46
3.11 Results approach 1 . . . 47
3.12 Results approach 2 . . . 48
3.13 Results approach 3 . . . 48
3.14 Marginal effects . . . 49
3.15 Brant test. . . 51
3.16 Percentage of correct predictions . . . 51
3.17 Endogeneity . . . 52
3.18 Results 2SLS . . . 52
3.19 Definitions of abbreviations. . . 53
3.20 Results of the principal component analysis for health care type 1 . . . 53
3.21 Regression analysis CS on components . . . 54
3.22 Results principal component analysis health care type 2 . . . 54
3.23 Regression analysis CS on components . . . 55
3.25 Regression analysis CS on components . . . 55
3.26 Established conditions to perform mediation . . . 56
3.27 Correlation coefficient residuals . . . 56
3.28 Confidence intervals for the product of coefficients. . . 57
3.29 Results t-test, AIC and BIC. . . 57
3.30 Summary mediation analysis . . . 57
3.31 Summary statistics . . . 58
3.32 Results moderation analysis approach 1 . . . 58
3.33 Results moderation analysis approach 2 . . . 59
4.1 Overview estimates approach 1, approach 2.1 and approach 3 . . . 61
4.2 Parameters sensitivity analysis approach 1, approach 2.1 and approach 3 . 61 4.3 Values of the discrete probability density of year . . . 64
4.4 Values of the discrete probability density of healthcare type . . . 64
4.5 Results Jarque-Bera test . . . 66
4.6 Results sensitivity analysis . . . 67
5.1 Statistics obtained from previous research . . . 69
6.1 Overview scenarios . . . 71
A.1 Confusion matrix approach 1, FP on CS and ES . . . 81
A.2 Confusion matrix approach 2.1, FP on CS and ES . . . 81
A.3 Confusion matrix approach 2.2, FP on CS and ES . . . 81
A.4 Confusion matrix approach 2.3, FP on CS and ES . . . 82
A.5 Confusion matrix approach 3, FP on CS and ES . . . 82
A.6 Correlation coefficients among all the underlying variables of client satis-faction for healthcare type 1 . . . 83
A.7 Correlation coefficients among all the underlying variables of client satis-faction for healthcare type 2 . . . 84
A.8 Correlation coefficients among all the underlying variables of client satis-faction for healthcare type 3 . . . 84
2.1 Schematic overview SBM . . . 7
2.2 Mediation effect. . . 8
2.3 Direct effect of employee satisfaction on net margins. . . 8
2.4 Possible scenarios. . . 10
2.5 Types of moderation effects. . . 19
3.1 Mediation. . . 22
3.2 Direct effect within mediation framework. . . 22
3.3 Service-Profit Chain. . . 23
3.4 Heterogeneity across organizations, CS variable. . . 28
3.5 Heterogeneity across organizations, ES variable. . . 28
3.6 Mediation effect. . . 33
3.7 Direct effect of employee satisfaction on financial performance. . . 33
3.8 Underlying variables of client satisfaction for healthcare type 1 and 2. . . . 41
3.9 Underlying variables of client satisfaction for healthcare type 3. . . 41
3.10 Surface plots approach 3. . . 50
4.1 Schematic overview sensitivity analysis. . . 62
5.1 Mediation effect. . . 68
5.2 Direct effect independent variable on dependent variable. . . 68
5.3 Decision tree. . . 69
A.1 Surface plots approach 1. . . 79
A.2 Surface plots approach 2.1. . . 80
A.3 Surface plots approach 2.2. . . 80
A.5 Approach 2.1. . . 85 A.6 Approach 3. . . 85 A.7 Approach1. . . 86 A.8 Approach 2.1. . . 86 A.9 Approach 3. . . 86 A.10 Approach1. . . 86 A.11 Approach 2.1. . . 86 A.12 Approach1. . . 87 A.13 Approach 2.1. . . 87
This thesis is submitted in partial fulfilment of the requirements for the degree of Master of Science in Econometrics at the University of Amsterdam. This thesis has been written during an internship at the Data Analytics department of PwC at the Amsterdam office.
First, I would like to thank my supervisor from the UvA dr. J.C.M van Ophem for his feedback and guidance, and in particular for supporting me in my efforts to write my thesis in combination with an internship. Secondly, I would like to thank PwC and especially prof dr. Jacques J.B. de Swart MBA for giving me the opportunity to write my thesis within PwC. It has been a great experience to be part of the Data Analytics team for the past six months. Further, I would like to thank Myrthe van der Plas MSc. MA for her continuous support and valuable feedback during my internship, and for her enthusiasm as a supervisor and colleague. Besides my supervisor, I would like to thank the entire Data Analytics team for their help and for giving me the opportunity of being part of such an amazing team. Finally, I would like to thank ActiZ for using their data for my research.
The purpose of this thesis is to test, adjust and underpin the Sustainable Business Model-ing (SBM) methodology econometrically. A mediation and moderation approach is used to structure the causality relations present within SBM. To test for mediation and mod-eration effects within SBM, two approaches are considered: a data driven and a non data driven approach. A data driven approach for conducting mediation and moderation ana-lysis is presented based on an application in the Dutch healthcare sector. In this example, mediation analysis is performed to find out whether the effect of employee satisfaction on the financial performance of an organization is direct, indirect via client satisfaction or both. Three approaches are considered as the client satisfaction variable can be construc-ted in several ways. The results show, that in case of a continuous outcome variable, no mediation analysis can be performed. However, in case the outcome variable is categor-ical, mediation analysis can be performed and different types of mediation occurred for the three different approaches. Moreover, sensitivity analysis for the indirect effect showed that the significance of the indirect effect within the mediation framework is very sensit-ive to changes in the coefficients within the mediation framework. Moderation analysis in the Dutch healthcare sector showed that the degree of interaction between employee and client moderates the effect of employee satisfaction on client satisfaction. Based on the data driven approach a non data driven approach for conducting mediation analysis is developed. Finally, several ways to account for mediation and moderation effects within SBM are proposed to PwC based on the results of the data driven approach.
Introduction
“Sustainability will become a key driver for all our investment decisions” (Kreutzer, 2010)
For many organizations, sustainability has become increasingly important in their decision making process. Sustainable decision making can be supported by Sustainable Business Modeling.
Ten years ago, most of the organizations did not even recognize the importance of the Dow Jones Sustainability Index (DJSI), while nowadays their decision making processes is based on how to get in the top ranking of this index. According to the United Nations, “sustainable development is development that meets the needs of the present without compromising the ability of future generations to meet their own needs” (“Brundland Commission Report,” 1987).
Although organizations recognize the importance of integrating sustainability into their business processes, most of them still think of sustainable decision making as a cost item rather than a possibility that might deliver financial benefits in the near future. Therefore, most organizations treat sustainable decision making as a corporate social responsibility separated from their business goals. Their purpose is to keep stakeholders satisfied in the short term without worrying about the long term. However, as Porter and Kramer (2011) mention in their article about creating shared value, social objectives do not have to be in conflict with economic objectives. Instead they could be complementary. Porter and Kramer believe that an organization is able to create value which is relevant for society as
well as for the shareholders. In this way, sustainable decision making is not only costly, but also contributes to the profit side. To illustrate, if an organization decides to invest in education, this requires an initial investment. However, in the long run employees gain knowledge and thereby add value to the organization and eventually benefits will exceed costs.
If organizations want to be sustainable decision makers, they should integrate people, planet and profit (PPP) aspects equally into their entire decision making process. SBM is not based on the idea that people and planet aspects are only used in order to gain more profit. For instance, when the decision to invest in solar panels is based on getting positive media attention instead of contributing to a better world. Therefore, proponents of sustainable decision making believe that it is crucial that organizations evaluate both financial and non-financial goals. Only then, shared value is created and hence sustainable decision making takes place.
Organizations that focus on sustainability often implement sustainable decision making into their business processes based on gut feeling rather than quantitative substantiation. Moreover, when implementing sustainable decision making they are struggling with a couple of things. First of all, it is not clear how people and planet related investments influence the performance of their organization. Secondly, they seek a way to compare the impacts of financial and non-financial investments on their objectives. Subsequently, they want to know which combination of people, planet and profit related investments is optimal given their objectives. PwC and Nyenrode Business Universiteit cooperatively developed Sustainable Business Modeling (SBM) to gain insights in the effects of people, planet and profit (PPP) related investments on the objectives of an organization (Roo-beek and De Swart, 2013).
Sustainable Business Modeling (SBM) is a methodology that organizations can use to integrate sustainable decision making into their entire business processes. SBM is based on the idea that if an organization wants to be sustainable, it should integrate the PPP aspects into their entire decision making. The SBM methodology provides a transparent way to quantify the impact of strategic decisions on the people, planet and profit Key Performance Indicators (KPIs) (Roobeek and De Swart, 2013).
The business simulator is the arithmetic unit of SBM and is programmed in AIMMS, a software tool developed for solving optimization problems. The business simulator makes it possible to evaluate the impact of different strategies on the KPIs. Although the busi-ness simulator already does some advanced calculating, its econometric justification is still open for theoretical improvement. In this thesis the SBM methodology is tested, adjusted and underpinned. The following research question is formulated:
How does the Sustainable Business Modeling methodology perform economet-rically and which improvements can be implemented?
This research question is divided in two sub questions:
1. How do causality relations occur in SBM?
2. How can reliability of the values of the coefficients be ensured when obtained from literature study?
The purpose of this thesis is to underpin the Sustainable Business Modeling methodo-logy scientifically and to develop an application such that causality relations in SBM are accounted for. This is done by first investigating the Sustainable Business Modeling meth-odology and the causality relations in SBM. Secondly, a data driven as well as non data driven analysis of the causality relations in the Dutch healthcare sector are conducted. Lastly, a sensitivity analysis is applied to the indirect effects present in SBM.
The structure of this thesis is as follows. First an outline is given on the Sustainable Business Modeling methodology and concepts for analyzing the causality structure within SBM are presented. In the third chapter, these concepts are used in a practical application. Subsequently, in chapter four a sensitivity analysis is applied to the indirect effects present in SBM. Thereafter, in chapter five, a suggestion is provided to test for causality relations in case no data is available. In the last chapter, the results of the thesis are summarized and several recommendations are proposed to PwC.
Background
2.1
Sustainable Business Modeling
“The complexity and persistent nature of sustainability issues pose new chal-lenges on business, which requires new conceptual models for researching in relation between firms and the natural environment” (Loorbach et al., 2009)
Sustainable Business Modeling quantifies what the impact of people, planet and profit related investments is on the objectives of an organization. This section reviews the SBM methodology. First, the use of KPIs is explained. Thereafter, the input variables of SBM are discussed. Finally, a way to get from the input to the output is explained.
Key Performance Indicators
KPIs are used worldwide to measure the performance of organizations. Using KPIs can help an organization to define and measure progress towards organizational goals. In SBM, KPIs are the output of the model and they are used to measure the impact of strategic de-cisions on PPP KPIs. Within the SBM methodology framework it is of great importance that strategic decisions are based on both financial and nonfinancial ambitions. Forming the KPIs consists of two steps. In the first step, all stakeholders and the decision maker are identified and their main goals are taken into consideration. Based on these goals, the appropriate KPIs are defined. A distinction is made between three types of KPIs: profit-related KPIs, people-related KPIs and planet-related KPIs. Profit-related KPIs are the easiest to determine. Examples of frequently used profit-related KPIs are: Breakeven
Point, Net Present Value, and Total Investment (Roobeek and De Swart, 2013). In prac-tice, people and planet ambitions turn out to be much harder to translate to KPIs and difficult to quantify. For instance, what is the effect of stimulating employees to eat more vegetables and fruit on absenteeism? Client satisfaction and employee satisfaction are ex-amples of people-related KPIs and carbon footprint is an example of a planet-related KPI.
After the PPP objectives of an organization are translated into KPIs, different strategies to achieve these objectives are determined. In order to construct several strategies, the input variables of SMB are defined. There are two kinds of variables that form the input of the model: internal variables and external variables. The next sections explain these types of variables in more detail.
Internal variables
Internal variables are variables that the decision maker has direct influence on, by for instance: investments in nutrition, salary, non-smoking programs and work life balance. By assigning different values to the internal variables, potential strategies are defined.
External variables
Input variables, which the decision maker cannot completely influence but do affect the KPIs, are called external variables. The effect of employee satisfaction on client satisfac-tion and the effect of employee satisfacsatisfac-tion on productivity are two examples of external variables. First, the external variables are defined based on expert opinion. Thereafter, values are assigned to the external variables based on literature study, expert opinion, historical data and Monte Carlo simulations. Assigning values to external variables is much harder compared to assigning values to the internal variables, because of the uncer-tainty in external variables. For this reason, different scenarios are obtained by assigning different values to external variables. SBM distinguishes three types of scenarios: the optimistic scenario, the neutral scenario and the pessimistic scenario.
First of all, the absolute expected effects (base case) of external variables on the different KPIs are defined based on literature study, expert opinion, historical data and Monte Carlo simulations. In the optimistic case, the base case effects are multiplied with a factor larger than one. In the neutral scenario, all the effects are assumed to be identical
the base case, i.e. the base case effects are multiplied by a factor of one. In the worst case scenario, the base case effects of the external variables on the different KPI’s are multiplied with a factor smaller than one. This way, three external scenarios for the external variables are modeled.
Appreciation functions
Currently, within SBM the influence of different strategies on a specific KPI under different scenarios is calculated. It is hard to compare the different KPIs, because they are not all measured in the same unit. Therefore, appreciation functions are used to make KPIs comparable to each other. Every KPI has its own appreciation function which assigns a value between 0 and 100 to every possible outcome of the KPI. SBM distinguishs three types of appreciation functions:
1. Smaller the better (STB): the larger the negative effect, the more desired the out-come.
2. Larger the better (LTB): the larger the positive effect, the more desired the outcome.
3. Nominal the best (NTB): the smaller the effect, the more desired the outcome.
From input to output
The business simulator, the arithmetic unit of SBM, relates all internal and external variables to the KPIs and each other and calculates what the impact of all internal and external variables on the KPIs is. All the values of the parameters are obtained from combining information from literature study, expert opinion, historical data and Monte Carlo simulations. For every strategy and scenario the business simulator calculates the effects of both internal and external variables on all KPIs. A schematic overview of the SBM methodology is presented in figure 2.1.
Figure 2.1: Schematic overview SBM
2.2
Mediation and Moderation
Causality relations can be explained by using a mediation and moderation approach.
Mediation and moderation are concepts that can help to get a better understanding of the causality structure between variables. These concepts are often used in behavioral science, but are also useful in structuring and modeling econometric models. The two concepts are taken into account when performing econometric analysis for SBM.
This section consists of two parts. In the first part mediation effects and tests are dis-cussed. In the second part of this chapter, moderation effects are explained and tests for different kinds of moderation effects are given.
2.2.1
Mediation
An independent variable can affect a dependent variable in three ways: 1. directly, 2. indirectly via the mediator variable or 3. both. A mediator variable intermediates in the relation between an independent variable and a dependent variable (Baron and Kenny,
1986). A mediator variable answers the question of how and through which relations an independent variable influences the outcome of the dependent variable. Figure 2.2 shows an example of mediation. In this case, X has a direct effect, denoted by c0, on Y , the dependent variable, but also has an indirect effect on Y (denoted by path a and path b in figure 2.2) via Me, the mediator variable.
Figure 2.2: Mediation effect.
Figure 2.3: Direct effect of employee satis-faction on net margins.
Further, two types of mediation are distinguished: partial mediation and full mediation. In the case of full mediation, the direct effect within the mediation framework has be-come 0 (c0 = 0 in figure 2.2). The mediator variable has taken over the direct effect of the independent variable on the dependent variable. Negligence of full mediation in SBM (c’=0) leads to an overestimate or underestimate of the KPIs, because the direct as well as the indirect effect are assumed to both influence the KPI while the direct effect has become insignificant. If the mediator variable partially absorbs the direct effect of the independent variable on the dependent variable, partial mediation occurs.
Summarizing, mediation can only occur when the following conditions are established:
Condition 1: Correlation between the mediator variable and the independent variable, i.e. a is significant (figure 2.2).
Condition 2: Correlation between the mediator variable and the dependent variable, i.e. b is significant (figure 2.2).
Condition 3: The direct effect of the independent variable on the dependent variable decreases when a mediator variable is included, i.e. c0 < c (figure 2.2 and figure 2.3). In case of full mediation the following condition is added:
Condition 4a: Mediator variable dominates the independent variable, i.e. c0 = 0 (figure 2.2).
In case of partial mediation the following condition is added:
Condition 4b: Co-domination of the independent variable and the mediator variable, i.e. c0 6= 0 and c0 is significant (figure 2.2).
If one of the three first conditions is violated, mediation is not performed. However, if all three conditions are established, mediation is performed and several possible scenarios can occur. Figure 2.4 shows an overview of all possible scenarios.
In section 2.2.2 mediation tests, which are used to detect which scenario is applicable to the suspected mediation framework, are discussed. In chapter 3.2 mediation analysis is tested in a practical application. Subsequently, a non data driven approach is given to conduct mediation analysis, i.e. using expert opinion and past research to perform mediation analysis.
Figure 2.4: Possible scenarios.
2.2.2
Testing for mediation
Mediation tests are carried out to validate the suspected mediation effect and to find out what type of mediation occurs (partial or full mediation). An article of MacKinnon (2002) gives an overview of fourteen mediation tests. In this thesis, two of these mediation tests are used:
2. Sobel test (Sobel, 1982).
Moreover, a bootstrap approach to construct a 95% confidence interval of the product of (standardized) coefficients (a ∗ b) is proposed (Preacher and Hayes, 2008).
In the next section, the three proposed mediation tests are explained in more detail. Table 2.1 summarizes the purpose and imposed assumptions of the mediation tests.
The Baron and Kenny approach
To be able to test for mediation, some conditions need to be complied with.
The most commonly used approach in past research to evaluate these conditions, is the approach proposed by Baron and Kenny. Three regression equations are formulated by Baron and Kenny to investigate the relations within the mediation framework.
The three regression equations are:
Y = α + cX + e, (2.1)
Me = γ + aX + η, (2.2)
Y = υ + c0X + bMe+ ω, (2.3)
where Y is the dependent variable, Methe mediator variable and X the independent
vari-able. If the dependent variable, Y , is continuous, all the coefficients within the mediation framework can be estimated by OLS. If, on the other hand, the dependent variable, Y, is categorical , the coefficients of equation 2.1 and equation 2.3 are fitted via ordered logistic regression and equation 2.2 via OLS regression.
According to Baron and Kenny, mediation occurs if all of the following null hypotheses are rejected :
H0: c = 0 (i.e. the independent variable is not correlated with the dependent
variable).
H0: a = 0 (i.e. the independent variable is not correlated with the mediator).
H0: b = 0 (i.e. the mediator variable is not correlated with the independent variable
If H0 : c0 = 0 is rejected then the independent variable has a direct effect in addition to
the indirect effect. On the other hand, full mediation occurs if H0 : c0 = 0 is not rejected.
Note that the Baron and Kenny approach is a good tool for exploring whether there might be mediation or not, but in this thesis it is only used to determine whether the conditions for the applicability of mediation analysis are established or not.
Sobel test
When an indirect effect is detected the Sobel test is used to test whether the indirect effect is significant or not. Sobel constructs a confidence interval of the product of coefficients to test whether the indirect effect is significant or not. A distinction between a continuous outcome variable and a categorical outcome variable needs to be made when constructing these confidence intervals. First, the confidence interval for the product of coefficients with a continuous outcome variable is presented. Thereafter, the confidence interval for the indirect effect when the outcome variable is categorical is presented.
Continuous outcome variable
Sobel constructs a 95% confidence interval for the product of coefficients (a ∗ b). The coefficient a is obtained from regression equation 2.2 and coefficient b is obtained from regression equation 2.3. The delta method is used to obtain the standard errors for the product of coefficients, which are needed for constructing the confidence interval. In ap-pendix 8 the derivation of the standard errors of the product of coefficients (equation 2.4) is given, using the delta method.
ˆ sˆaˆb = q ˆ a2∗ ˆs2 b + ˆb2∗ ˆs2a (2.4)
The 95% confidence interval for a ∗ b is therefore:
Categorical outcome variable
In this section a confidence interval for the indirect effect, when the outcome variable is categorical, is constructed. Coefficient a is estimated by OLS and the t-test is performed to test for the significance of the relationship between the independent variable and the outcome variable. On the other hand, coefficient b is obtained from the ordered logistic regression equation 2.3. The Wald test statistic is used to determine the significance of the effect of the independent variable on the outcome variable and is compared against a central Chi-Square distribution with one degree of freedom. To state this more clearly:
Significance of independent variable OLS regression is based on t-test statistic; t =
ˆ a ˆ
sa ∼ tn−k.
Significance of independent variable ordered logistic regression is based on the Wald test statistic; W = (ˆsˆb
b)
2
∼ χ2(1).
In the following steps it is showed that the test statistics determining the significance of coefficient a and coefficient b follow approximately the same distribution if both coeffi-cients are in standardized form (Iacobucci, 2012).
W = (ˆb ˆ sb)
2
∼ χ2(1) −−−−−−−−−−→taking square root √W = (ˆb ˆ
sb) ∼ N (0, 1)
For samples larger than 30, the t-test statistic follows approximately a standard normal distribution. t= ˆsˆa
a ∼ N (0, 1).
The standardized coefficients a and b are comparable to each other. For this reason, confidence intervals for the standardized indirect effect are used to determine whether the indirect effect is significant or not. Under the assumption that sb
b and
a
sa are independent,
the expectation and the variance1 of the product of standardized coefficients are:
E[b sb × a sa ] = ˆb ˆ sˆb × ˆa ˆ sˆa (2.6) V ar[b sb × a sa ] = (ˆb ˆ sˆb ) 2 + (ˆa ˆ sˆa ) 2 + 1 (2.7)
In equation 2.8 the standard error of the product of standardized coefficients is given:
1Given that X and Y are independent V ar(XY ) = [E(X)]2
V ar(Y ) + [E(Y )]2V ar(X) + V ar(X) ∗ V ar(Y ) for standardized variables V ar(X) = 1 and V ar(Y ) = 1
ˆ saˆ ˆ sˆa ˆ b ˆ sˆb = s (ˆa ˆ sˆa ) 2 + ( ˆb ˆ sˆb ) 2 + 1 (2.8)
The standard error in 2.8 resembles the standard error in 2.4, with the exception of the last term.
The 95% confidence interval for the product of standardized coefficient is:
ˆ a ˆ saˆ ∗ ˆb ˆ sˆb ± 1.96 ∗ s (ˆa ˆ sˆa ) 2 + ( ˆb ˆ sˆb ) 2 + 1 (2.9)
For both confidence intervals holds that if zero is not in the confidence interval, the me-diation effect is significant according to Sobel. A major weakness of Sobel’s test is that the product of (standardized) coefficients is asymptotically normal distributed. Hence, in small samples the product of (standardized) coefficients might not be normally distributed as we cannot rely on asymptotic theory. Therefore, the Sobel test is not reliable for small samples. For this reason, a bootstrap approach for obtaining the confidence interval of the product of coefficients might be relevant when using small samples.
Another weakness of the Sobel test is that the error terms of the two regression equations are assumed to be independent. If this assumption is violated, the results of the Sobel test are not reliable. For this reason, a correlation test between the two residual vectors needs to be performed, to check whether this assumption holds or not, before the Sobel test can be performed. Obtaining the vector of OLS residuals of regression of Y on X is quite straightforward. However, obtaining the residuals of the ordered logistic model is impossible as the latent variable Y* in the ordered logistic model is not directly observed. For this reason, the generalized residuals are obtained instead. However, the results of the correlation test based on these generalized residuals can only be used as an indication that there is no correlation between the disturbances of the two regression equations. In section 3.3.2 it is described how to obtain the generalized residuals of the ordered logistic model.
Bootstrap approach
In the case of small samples, asymptotic theory cannot be relied upon. Therefore a boot-strap approach to construct the percentile method 95% confidence interval of the product
of (standardized) coefficients (a ∗ b) is proposed. This method to construct confidence intervals does not provide asymptotic refinement. However, it allows confidence intervals to be asymmetric. The percentile-t method can be used in case asymptotic refinement is a requirement. In this thesis, only the percentile-method is used as it requires less computation.
The bootstrap approach consists of the following steps:
1. Given data (w1,..,wn) with wi =(yi,xi,M ei) draw B bootstrap samples of size N.
2. (a) Estimate for each bootstrap sample ˆa∗ and ˆb∗ and calculate ˆa∗ ∗ ˆb∗ if the
outcome variable is continuous.
(b) Estimate for each bootstrap sample aˆˆs∗∗ ˆ a and ˆb∗ ˆ s∗ˆ b and calculate ˆasˆ∗∗ ˆ a∗ ˆ b∗ ˆ s∗ˆ b if the out-come variable is categorical.
3. (a) Order the products of coefficients in ascending order: ˆa∗ˆb∗1,...,ˆa∗ˆb∗B.
(b) Order the products of standardized coefficients in ascending order: (ˆaˆs∗∗ ˆ a ∗ˆb∗ ˆ s∗ ˆ b ) 1 ,...,(ˆaˆs∗∗ ˆ a ∗ˆb∗ ˆ s∗ ˆ b ) B
4. (a) The percentile method 95% confidence interval if the outcome variable is con-tinuous is: ˆa∗ˆb∗0.025B,...,ˆa∗ˆb∗0.975B.
(b) The percentile method 95% confidence interval if the outcome variable is cat-egorical is: (ˆasˆ∗∗ ˆ a ∗ˆb∗ ˆ s∗ˆ b ) 0.025B ,...,(aˆˆs∗∗ ˆ a ∗ ˆb∗ ˆ s∗ˆ b ) 0.975B
If zero is not in the confidence interval, a significant mediation effect is detected. The advantage of using the bootstrap approach instead of the Sobel test is that the assump-tion of normality of the product of (standardized) coefficients is relaxed and this allows confidence intervals to be asymmetric. In other words, the Baron and Kenny approach is a pragmatic way to investigate the presence of mediation effects. However, in mediation analysis an independent variable X is by definition correlated with a mediator variable Me
resulting into multicollinearity problems in equation 2.3. Due to multicollinearity prob-lems the Baron and Kenny approach has low power. For this reason, depending on the distribution of the product of (standardized) coefficients, the Sobel test or the percentile bootstrap method is used to test whether the indirect effect is significant or not.
Testing for partial mediation and full mediation
Based on the previous section, the Baron and Kenny approach is used to check if the conditions of the applicability of mediation analysis are established. The Sobel test and
the bootstrap approach are used to determine whether the indirect effect is significant or not. This section describes briefly how it can be determined whether partial or full mediation occurs in case the outcome variable is categorical. As mentioned before, full mediation occurs when c0 = 0. The coefficients in two ordered logistic models presented in equation 2.10 and 2.11 are estimated by maximum likelihood. Moreover the two models are nested, i.e. model 2.11 is a restricted version of model 2.10. Full mediation occurs if model 2.11 is preferred over model 2.10 and partial mediation occurs if model 2.10 is preferred over model 2.11.
Y = υ + c0X + bMe+ ω, (2.10)
Y = υ + bMe+ ω, (2.11)
A t-test, Aikaike Information Criterion (AIC) (Aikaike, 1973) and the Bayesian Informa-tion Criterion (BIC) (Schwarz, 1978) are used to determine which model is preferred. The significance of coefficients in ordered logistic models is determined by using the Wald test statistic, which follows a Chi Squared distribution with one degree of freedom (2.12). This test statistic is used to determine whether c0 in model 2.10 is significant or not.
W = (ˆc 0− c0 0)2 ˆ se(ˆc0)2 ∼ χ 2 (2.12)
The square root of the Wald test statistic is identical to the t-test statistic, because the square root of a χ2(1) distribution is asymptotically standard normal distributed:
t-test statistic =√W = cˆ0−c00
ˆ
se( ˆc0) ∼ N (0, 1)
H0 : c0 = c00 = 0
Ha : c0 6= 0
So, if H0 is rejected the t-test presents evidence that partial mediation occurs. On the
other hand, if the null hypothesis can not be rejected at the 0.05 level, the t-test statistic presents evidence that full mediation occurs.
An approach to determine which model is preferred in terms of fit is the AIC and BIC, they are presented in equation 2.13 and 2.14, respectively.
AIC(p) = −2Ln(L) + 2p, (2.13) BIC(p) = −2Ln(L) + pLn(N ), (2.14)
where Ln(L) the maximized log-likelihood of the model, p the number of independent variables in the model and N the size of the sample.
Increasing the number of parameters in the models, results always in an increase in the log-likelihood. For this reason, both the AIC and BIC sets a penalty for adding parameters to the model. The penalty for adding parameters to the model is in the AIC formula represented by the term 2p and in the BIC formula represented by the term pLN (L). Hence, for both the AIC and the BIC, there is a trade off between the fit of the model and the number of parameters in the model. The difference between the AIC and the BIC is that the BIC sets a higher penalty for adding parameters to the model than the AIC does. The lower the AIC and the BIC the better. Finally, taking into account the outcome of the t-test, AIC and BIC, it is determined which model is preferred. Full mediation occurs if model 2.11 is preferred and partial mediation occurs if model 2.10 is preferred.
The purpose and imposed assumptions of the several mediation tests are summarized in table 2.1.
Table 2.1: Mediation tests
Mediation test Purpose Assumptions/limitations Baron and Kenny check if conditions are established can not be used to test
significance of indirect effect Sobel test test if indirect effect is significant only reliable if the sample
is large enough
Bootstrap approach test if indirect effect is significant less practical than Sobel test t-test test full or partial mediation test for significance of c’ AIC test full or partial mediation fully based on data BIC test full or partial mediation fully based on data
2.2.3
Moderation
A moderation model explains how under different scenarios and for different kind of groups the independent variable affects the dependent variable. A moderator variable influences the strength of the effect of the independent variable on the dependent variable (Baron and Kenny, 1986). A moderator variable answers the question for whom and when an independent variable affects the dependent variable. The moderator variable can affect the relationship between the independent variable and the dependent variable in several ways. In this thesis, the following three ways are considered:
1. The moderator variable affects the relation between the dependent variable and the independent variable linearly (figure 2.5, left).
2. The moderator variable affects the relation between the dependent variable and the independent variable quadratically (figure 2.5, middle).
3. The effect of the independent variable on the dependent variable differs among groups. In this case the moderator variable explains for which group the effect is the strongest (figure 2.5, right).
Figure 2.5: Types of moderation effects.
Tests for the presence of different types of moderation effects are described in section 2.2.4.
2.2.4
Testing for moderation
In this section several tests for moderation effects are described. As mentioned in section 2.2.3, a distinction between three types of moderation effects is made in this thesis. First, moderation tests in case the moderator variable is continuous are described. Next, mod-eration tests in case the moderator variable is categorical are discussed.
In the case of a continuous moderator variable, regression equation 2.15 is used to test whether a moderation effect is linear or quadratic.
Y = c + β1∗ X + β2 ∗ Mo+ β3∗ XMo+ β4Mo2+ β5∗ XMo2 (2.15)
In equation 2.15, X is the independent variable, Y the dependent variable and Mo the
moderator variable. XMo indicates the moderator effect while controlling for X and Mo.
Linear moderation occurs if β3 differs significantly from zero. Quadratic moderation
oc-curs if β5 differs significantly from zero. A positive value of an interaction term implies
that the higher the moderator variable, the stronger the effect of X on Y .
To test for moderation effects of type 3, two tests are considered. In the first test, moderation effects of type 3 are tested by testing the effect of the independent variable on the dependent variable separately for the two groups. In the first step, a distinction is made between individuals. The individual are divided into two groups:
1. Group 1
For both groups the effect of the independent variable on the dependent variable is es-timated. The moderation effect is given by the difference in slope coefficients. To test whether the difference in slope coefficients differs significantly from zero, confidence in-tervals for the difference in slope coefficients are obtained as follows:
In the first step, β1 and β2 are estimated by OLS.
Yi = c + β1Xi+ i group 1 (2.16)
Yi = c + β2Xi+ i group 2 (2.17)
Under the assumption that the error terms are normally distributed, the estimates for β1
and β2 are also normally distributed:
ˆβ1 ∼ N (β1, σ2I)
ˆβ2 ∼ N (β2, σ2I)
The linear combination of two normally distributed parameters is also normally distrib-uted with:
E( ˆβ1− ˆβ2)= β1− β2
Under the assumption that ˆβ1 and ˆβ2 are uncorrelated, i.e. ρβˆ1, ˆβ2 = 0 the variance
of ˆβ1− ˆβ2 is given by: Var( ˆβ1− ˆβ2) = Var( ˆβ1) + Var( ˆβ2) 2
The 95% confidence interval for β1− β2 is therefore:
β1− β2 ∈ ˆβ1− ˆβ2± 1.96
q
V ar( ˆβ1− ˆβ2) (2.18)
If zero is not in the confidence interval the moderation effect differs significantly from zero at a significance level of 0.05. Hence, the moderator variable significantly influences the strength of the relation between the independent variable and the dependent variable.
In the second test, moderation effects of type 3 are tested using regression equation 2.19.
Yi = c + β1Xi+ β2δi+ β3δiXi+ i (2.19)
2Var( ˆβ
In this equation, Y is the dependent variable, X the independent variable and δi is a
dummy variable which equals one if the group is one. If β3 differs significantly from zero
than the effect of X on Y differs among the two groups. Equation 2.19 reduces to:
Yi = (c + β2) + (β1+ β3)Xi+ i if δi = 1, (2.20)
Yi = c + β1Xi+ i if δi = 0, (2.21)
The differences between the two moderation tests for type three is that in the first ap-proach the effect on X on Y is estimated for every group separately, while in the second approach only one sample is used to estimate the effect of X on Y and interaction terms are added to check whether there is an interaction effect or not.
Data driven approach
In this section, a data driven approach for conducting mediation and moderation analysis is given based on an application in the Dutch healthcare sector. Mediation analysis is performed to find out whether the effect of employee satisfaction on financial performance is direct, indirect via client satisfaction or both (i.e partial mediation). A schematic overview is presented in figure 3.1 and 3.2. In this example, employee satisfaction has a direct effect, denoted by c on the financial performance of an organization, but also has an indirect effect on the financial performance of an organization (denoted by path a and path b in figure 3.1) via client satisfaction, the mediator variable. In order to test for mediation effects, different models are explored to estimate the direct and indirect effects within the mediation framework. In other words, the parameters a, b, c0 in figure 3.1 and c in figure 3.2 are estimated. Before different models are fitted to the data, existing economic theory is used to underpin the relations within the mediation framework. Thereafter, the data set is described and the models to estimate the several parameters are given. In section 3.5 the models are reviewed and the outcomes of the different mediation tests are discussed. After mediation analysis is performed to the Dutch healthcare sector, a moderation analysis is performed to check whether healthcare type moderates the effect of employee satisfaction on client satisfaction.
Figure 3.1: Mediation.
Figure 3.2: Direct effect within mediation framework.
3.1
Literature study
The healthcare sector is a people-driven industry, which ensures that human capital has a great impact on creating value to the organization. A worldwide study conducted by Towers Watson showed that excellent HR management was one of the main drivers for excellent financial performance (Towers Watson, 2000). They found that a harmonious and flexible workplace was one of the HR-practices with the greatest impact on finan-cial performance, therefore employee satisfaction might directly be related to finanfinan-cial performance. Moreover, employees who like their job tend to stay longer at the organiz-ation, which results in a decline in turnover. A decline in turnover leads to a reduction in hiring and training costs (Waldman et al., 2010). Although some literature suggest a direct relation between employee satisfaction and financial performance, some researchers argue that the direct relation between employee satisfaction and financial performance is not significant due to the fact that employee satisfaction influences financial performance indirectly via client satisfaction (Bernhardt et al., 2000).
Figure 3.3 shows the service-profit chain which explains how employee satisfaction affects financial performance via client satisfaction (Heskett, 1994). Essential for this theory is that employee satisfaction directly influences client satisfaction and that client satisfac-tion directly influences financial performance. Although some controversy exists whether the effect of employee satisfaction on financial performance is direct or not, all research reveals strong evidence that employee satisfaction positively influences client satisfaction. Intuitively, this makes sense. Employees who like working for their organization are will-ing to work harder, which is likely to influence the quality of service positively, which in turn leads to a higher client satisfaction (Kaur and Mukherjee, 2013; Brooks, 2000). The service-profit chain claims that client satisfaction positively influences financial perform-ance which is supported by research conducted by Nelson (1992).
Figure 3.3: Service-Profit Chain.
of the relation between employee satisfaction and client satisfaction (Peltier and Dahl, 2009). In this thesis, three types of healthcare are distinguished:
1. Healthcare type 1: nursing and care services.
2. Healthcare type 2: geriatric care.
3. Healthcare type 3: home care.
For all three types of care, there is a lot of interaction between employees and clients but it is expected that the most interaction is in the geriatric care and the least interaction in home care. Hence, it is expected that the effect of employee satisfaction on client sat-isfaction is greater for geriatric care than for home care.
Based on the literature study, employee satisfaction, client satisfaction, healthcare type and financial performance might be suitable variables to explain and test the mediation and moderation framework within SBM as the following causal relations can be explored:
Direct effect of employee satisfaction on financial performance in the healthcare sector.
Indirect effect of employee satisfaction on financial performance via client satisfac-tion in the healthcare sector.
Direct effect of client satisfaction on financial performance in the healthcare sector. The strength of the effect between client satisfaction and employee satisfaction for
different healthcare types.
The following sections describe the data set and the models that are used to estimate the coefficients belonging to the hypotheses within the mediation and moderation framework.
3.2
Data set
The direct and indirect effects within the mediation framework and the strength of the effect between client satisfaction and employee satisfaction for different healthcare types are estimated based on an (unbalanced) panel data set obtained from ActiZ. ActiZ is the association for healthcare providers in the Netherlands. Data of employment perception,
client perception and business operations from 146 organizations and their business units is cooperatively collected by ActiZ and PwC between 2010 and 2013. Therefore, the (unbalanced) panel data set contains the following modules:
Client data, collected between 2010-2013 for three different healthcare types. Employee data, collected between 2010-2013.
Financial data, collected between 2010-2013.
The data set has a large cross sectional dimension and a small time dimension. Client data is collected for three healthcare types:
1. Healthcare type 1: nursing and care services.
2. Healthcare type 2: geriatric care.
3. Healthcare type 3: home care.
Several types of care can be delivered by one organization. The client data as well as the employee data are obtained from employee perception questionnaire and client perception questionnaires. The following sections explain in more detail how certain variables are extracted from the data set of ActiZ to measure employee satisfaction, client satisfaction and financial performance. In this thesis, mediation and moderation analysis is conducted on organizational level only, as the several variables can not be linked to each other on the business unit level.
3.2.1
Client perception
A large number of clients from all organizations completed a questionnaire describing their experiences of receiving healthcare. Different questionnaires are constructed for the several care types. The three different questionnaires are outlined in the attachment (see Appendix A.6). The clients could rate the questions/indicators on a scale of 1 (dissatisfied) to 10 (satisfied). Based on all completed questionnaires, the indicator scores for the organizations are calculated. The indicator scores of the organizations are the average of the indicator scores per business unit, weighted over the number of respondents within each business unit1. The total scores are the average scores of all indicators within an
1Score per indicator = P
business unit
Si∗Ni
P
business unit
Ni , where Si is the average score of the indicator for business unit
organization, which are based upon the unweighted average indicator scores per business unit and the average number of respondents per business unit. 2 The client satisfaction
variable of an organization is given by Total score client satisfaction of an organization and is rated on a scale of 1 to 10, where 10 is being really satisfied and 1 is being dissatisfied.
3.2.2
Employee perception
The questionnaire designed to measure employee perception consists of indicators of the potential to change, workload, entrepreneurship and attractiveness of work (see Appendix A.7). The employees could rate the questions/indicators on a scale of 1 (dissatisfied) to 10 (satisfied). One questionnaire is used to measure employee perception. Analogously, the indicator scores and the total employee satisfaction scores are calculated. The employee satisfaction variable is given by Total score employee satisfaction of an organization and is rated on a scale of 1 to 10, where 10 being really satisfied and 1 is being dissatisfied.
3.2.3
Financial performance
Two variables are derived from the data set of ActiZ which represent financial perform-ance. The first variable representing financial performance are the net margins of the organization, which is a continuous variable. However, capturing financial performance by net margins might be a problem as net margins alone do not represent the financial performance of an organization well enough. For this reason, a categorical variable is con-structed which not only captures financial performance via net margins, but also takes into account liquidity and budget ratios.
Liquidity and budget ratios are, besides net margins, available for every organization in the data set of ActiZ. The categorical variable is constructed based on three measures:
1. Net margins = Net ProfitRevenue.
2. Liquidity (current ratio) = Current LiabilitiesCurrent Asset . 3. Budget ratio = Total RevenueEquity .
2Total score client satisfaction = P business unit ¯ Si∗ ¯Ni P business unit ¯
Ni , where ¯Si is the average of all indicator scores for
Based on how well the organizations score on the three items mentioned above, they are divided into 4 categories:
1. Category one: financial unsustainable.
2. Category two: early warning on two focus areas.
3. Category three: early warning on one focus area.
4. Category four: financially healthy.
An organization is financially healthy if the organization has a net margin of more than 2.5 percent, a liquidity of more than 1 and a budget ratio of more than 153. An organ-ization is placed in category three; early warning on one focus area, if an organorgan-ization is not fulfilling one of the three requirements. If two out of three requirements are not met, an organization gets an early warning on two focus areas. An organization is financial unsustainable if non of the requirements are met.
Hence, the following variables are derived from the data set of ActiZ:
Table 3.1: Definitions of variables
Variable Explanation scale/range
CS1i Total client satisfaction score for care type 1 of organization i 1-10
CS2i Total client satisfaction score for care type 2 of organization i 1-10
CS3i Total client satisfaction score for care type 3 of organization i 1-10
¯
CSi Average of the three total client satisfaction scores of organization i 1-10
ESi Total employee satisfaction score of organization i 1-10
N Mi Net margins of organization i (0,1)
F Pi Categorical variable based on net margins, budget ratios and liquidity (1,2,3 or 4)
δs Year dummy variable δs=1 if t = s and zero otherwise, t=2011, 2012 and 2013
δh Healthcare type dummy variable δh=1 if type=h and zero other wise , h=1,2 or 3
3.2.4
Exploring the data
The data set of ActiZ is extremely unbalanced as only a few organizations participated twice in the benchmark, none of them three times and most of the organizations only participated once (table 3.2).
Table 3.2: Participated organizations over the years Period Number of organizations
2011,2012 0 2011,2013 13 2012,2013 2 2011 36 2012 56 2013 39
total number of organizations 146
Moreover, figure 3.4 and figure 3.5 show that there is heterogeneity across organizations. To sum up, the important characteristics of the data are:
1. Large heterogeneity across organizations.
2. Most organizations only participated once in the benchmark.
3. Time-series dimension of three.
For this reason, a cross sectional analysis is performed and dummy variables for the years are added to take into account that the observations are obtained at several points in time.
Figure 3.4: Heterogeneity across organiza-tions, CS variable.
Figure 3.5: Heterogeneity across organiza-tions, ES variable.
3.3
Models for testing mediation
Different models are fitted to the data to estimate the coefficients within the mediation framework. Simple OLS regression is performed when the financial performance variable is continuous. An ordered logistic regression is fitted to the data when the financial per-formance variable is categorical.
In the first section the linear regression models are discussed and three different ap-proaches are used to estimate the coefficients within the mediation framework. Next, the ordered logistic regression models are obtained. Again, models for all three approaches are presented.
3.3.1
Continuous outcome variable
In order to test for the presence of mediation effects, the paths in figure 3.1 and figure 3.2 are estimated with linear regression models. As mentioned in the description of the data, there are three types of care and for each type there is a different client satisfaction questionnaire. Hence, the client satisfaction variable can be constructed in several ways. For this reason, a distinction between three approaches is made to take the different types of care into account. The three approaches are summarized in table 3.3. In the first approach (model 3.1, 3.2 and 3.3), ¯CSi is used as the client satisfaction score. The second
approach treats every type of care separately (model 3.4, 3.5 and 3.6). Hence, for every care type different models are used to obtain the coefficients. In the third approach, CSiis
used as the client satisfaction variable, but a dummy variable is submitted to distinguish between the different types of care (model 3.7, 3.8 and 3.9). OLS regression is used to estimate the models.
Table 3.3: Overview three approaches
Approach Client satisfaction variable Healthcare type Approach 1 CS¯ i, average of the three is not taken into account
total client satisfaction scores
Approach 2 for every healthcare type different estimate models separately client satisfaction scores are used for every healthcare type 2.1 CS1i, total client satisfaction
score for care type 1
2.2 CS2i, total client satisfaction
score for care type 2
2.3 CS3i, total client satisfaction
score for care type 3
Approach 3 CSi, total client satisfaction score healthcare type dummy is added to the models
Approach 1: Client satisfaction variable is ¯CSi.
¯ CSi = τ + aESi+ 3 X s=2 γsδs,i+ ui, (3.1) N Mi = τ + b ¯CSi+ c0ESi+ 3 X s=2 γsδs,i+ ui, (3.2) N Mi = τ + cESi+ 3 X s=2 γsδs,i+ ui, (3.3)
with, ¯CSi the average client satisfaction score of the three healthcare types of
organiza-tion i, ESi the employee satisfaction score of organization i and δs,i = 1 if t = s and zero
otherwise.
Approach 2: Client satisfaction variable is CShi.
CShi = τ + aESi+ 3 X s=2 γsδs,i+ ui, (3.4) N Mi = τ + bCShi+ c 0 ESi+ 3 X s=2 γsδs,i+ ui, (3.5) N Mi = τ + cESi+ 3 X s=2 γsδs,i+ ui, (3.6)
employee satisfaction score of organization i and δs,i = 1 if t = s and zero otherwise.
Approach 3: Client satisfaction variable is CSi.
CSi = τ + aESi+ 3 X s=2 γsδs,i+ 3 X h=2 ρhδh,i+ ui, (3.7) N Mi = τ + c0CSi+ bESi+ 3 X s=2 γsδs,i+ 3 X h=2 ρh,δh,i+ ui, (3.8) N Mi = τ + cESi+ 3 X s=2 γsδs,i+ 3 X h=2 ρhδh,i+ ui, (3.9)
with, CSi the client satisfaction score of organization i, ESi the employee satisfaction
score of organization i, δs,i = 1 if t = s and zero otherwise and δh,i = 1 if the healthcare
type = h and zero otherwise. Note that h equals two or three. In section 3.5 the results of the OLS regressions are presented.
Diagnostic tests continuous models
Several tests are applied to equations 3.1, 3.4 and 3.7 to check if the models suffer from non-normal error terms, misspecification and whether the error terms are heteroskedastic or not. Moreover, it is investigated whether the models suffer from multicollinearity or not. They are described subsequently.
Jarque-Bera test
Non-normal error terms result in OLS estimators that are also not normally distributed. Although the estimates are still unbiased and efficient, hypothesis tests are modified. For this reason the Jarque-Bera test is conducted to test whether the skewness and the kurtosis of the error terms, correspond to the skewness and the kurtosis of the normal distribution, i.e. whether the error terms are normal distributed or not. The Jarque-Bera test statistic is given, JB=n6(S2 + 14(K − 3)2), with n the number of observations, S the skewness of the error terms and K the kurtosis of the error term. Under the null hypothesis the error terms are normally distributed, and the Jarque-Bera test statistic approximately follows a χ2(2) distribution.
Ramsey-reset test
The Ramsey-reset test is conducted, to test whether the relation between the dependent and independent variables is linear or not. The auxiliary regression equation to test whether this relation is linear or not is presented below.
yi = x0iβ + γ ˆyi2+ i (3.10)
Under the null hypothesis, γ = 0 and the model is correctly specified. A simple t-test is used to determine whether γ differs significantly from zero. Under the alternative hypo-thesis, the model is misspecified.
White test
In case the error terms are heteroskedastic, the standard errors are not reliable which makes hypothesis testing more difficult as the standard errors can not be used. For this reason, robust standard errors will be used if the error terms tend to be heteroskedastic. The White test is performed to check for heteroskedasticity. In the first step, the linear regression model is estimated by OLS and the squared residuals are collected (see 3.11). In the next step, the auxiliary regression model of equation 3.12 is estimated. In other words, the squared residuals of step one are regressed on the regressors, the crossproducts of the regressors and the squared regressors.
Yi = β0+ β1x1i+ β2x2i+ ei, (3.11)
i2 = γ1+ γ2x1i+ γ3x2i+ γ3x1i∗ x2i+ γ4x1i2+ γ5x2i2+ ηi (3.12)
In the final step, the Lagrange Multiplier test statistic is calculated, LM = nR2 which
follows asymptotically a χ2(p) distribution under the null hypothesis of homoskedasticity,
with p the number of variables in the auxiliary regression. If the null hypothesis of ho-moskedasticity is rejected, the White test presents evidence that the error terms are not constant, i.e. V(i) 6= σ2.
Multicollinearity
In the presence of multicollinearity, the standard errors of the model turn out to be ex-tremely large resulting in large confidence intervals. Consequently, the null hypothesis are
too often wrongly accepted. For this reason, it is important to detect multicollinearity. To detect multicollinearity, the variance inflation factor (VIF) is used. In the first step, one of the regressors is regressed on the other regressors and the R-squared is saved. Next, the VIF is calculated, VIF=1−R1
i2, with Ri
2 the R-squared of the regression of X
i on the
other regressors. A VIF higher than 10 is often used as an indication of multicollinearity (Hair et al., 1995).
The p-values of the several tests and the VIF for the models in 3.1, 3.4 and 3.7 are summarized in the results section in table 3.8.
3.3.2
Categorical outcome variables
In the description of the data it is explained how a categorical variable, which not only captures financial performance via net margins, but also takes into account liquidity and budget ratios, is constructed. The FP variable is defined as an ordered categorical outcome variable, because the financial performance of an organization is rated from un-sustainable (1) to financially healthy (4). This implies that the coefficients within the mediation framework cannot all be estimated by OLS. Instead, ordered logistic models are fitted to the data to estimate path b, path c and path c0 within the mediation frame-work presented in figure 3.6 and figure 3.7. To estimate the effect of employee satisfaction on client satisfaction (path a in figure 3.6), OLS models are fitted to the data, because the mediator variable and the independent variable are both continuous. Again, because the variable representing client satisfaction can be constructed in several ways, three ap-proaches are proposed to estimate the coefficients within the mediation framework (see table 3.3). The equations for every approach are presented below.
Figure 3.6: Mediation effect.
Figure 3.7: Direct effect of employee satis-faction on financial performance.
Approach 1: Client satisfaction variable is ¯CSi. ¯ CSi = τ + aESi+ 3 X s=2 γsδs,i, +ui (3.13) F Pi = τ + b ¯CSi+ c0ESi+ 3 X s=2 γsδs,i, +ui (3.14) F Pi = τ + cESi+ 3 X s=2 γsδs,i+ ui, (3.15)
Approach 2: Client satisfaction variable is CShi .
CShi = τ + aESi+ 3 X s=2 γsδs,i+ ui, (3.16) F Pi = τ + bCShi+ c 0 ESi+ 3 X s=2 γsδs,i+ ui, (3.17) F Pi = τ + cESi+ 3 X s=2 γsδs,i+ ui, (3.18)
Approach 3: Client satisfaction variable is CSi.
CSi = τ + aESi+ 3 X s=2 γsδs,i+ 3 X h=2 ρhδh,i+ ui, (3.19) F Pi = τ + c0CSi+ bESi+ 3 X s=2 γsδs,i+ 3 X h=2 ρhδh,i+ ui, (3.20) F Pi = τ + cESit+ 3 X s=2 γsδs,i+ 3 X h=2 ρhδh,i+ ui, (3.21)
Ordered logistic models
To estimate the coefficients in equations 3.14, 3.15, 3.17, 3.18, 3.20 and 3.21, ordered logistic models are fitted to the data (Cameron and Trivedi, 2011). For instance, to estimate the coefficients in equation 3.17, the index model presented in equation 3.22 is used. F Pi∗ = bCShi+ c 0 ESi+ 3 X s=2 γsδs,i+ ui (3.22)
A very low F Pi* corresponds to an unsustainable financial performance, while a very large
F Pi* corresponds to a financially healthy organization. Subscript j is used to indicate
what the financial performance of the organization is. To state this more clearly:
F Pi = j if αj−1 < F Pi∗ ≤ αj, with j = 1,2,3,4 α0 = −∞ and α4 = ∞ F Pij = 1 if F Pi = j 0 if F Pi 6= j Then pij = P r[F Pi = j] = P r[αj−1 < F Pi∗ ≤ αj] = P r[αj−1 < bCShi + c 0 ESi+ 3 X s=2 γsδs,i+ ui ≤ αj] = F (αj− bCShi− c 0 ESi− 3 X s=2 γsδs,i) − F (αj−1− bCShi − c 0 ESi− 3 X s=2 γsδs,i)
In the last step it is used that u is logistic distributed such that F (z) = 1+eezz. Under the
assumption that the observations are independently distributed, maximum likelihood es-timation is used to estimate α1, α2, α3, b, γ2, γ3 and c’. Analogously, the parameters in the
other ordered logistic models are obtained. To sum up, for every approach the estimates of model 3.13, 3.16 and 3.19 are obtained by OLS while coefficients of the other models for every approach are estimated by ordered logistic regression.
Interpretation coefficients ordered logistic models
After the betas of the ordered logistic models are estimated, their coefficients can be in-terpreted as follows. An increase of one in one of variables leads to an increase of beta in the latent variable F Pi∗. Hence, the beta coefficients in ordered logistic models are
only used to see whether an increase in a variable increases or decreases the probability of an organization being in a higher category of financial performance. For this reason, marginal effects are used to give an interpretation to the results. The marginal effect for
client satisfaction and employee satisfaction in model 3.17 are calculated as follows: ∂P r[F Pi = j] ∂CSi = (f (αj−1− bCShi− c0ESi− 3 X s=2 γsδs,i) − f (αj − bCShi− c0ESi− 3 X s=2 γsδs,i)) ∗ b ∂P r[F Pi = j] ∂ESi = (f (αj−1− bCShi− c0ESi− 3 X s=2 γsδs,i) − f (αj − bCShi− c0ESi− 3 X s=2 γsδs,i)) ∗ c0,
where f (.) the derivative of F (.)
The marginal effect for the client satisfaction variable is interpreted as follows: a one unit increase in client satisfaction leads to an increase of 100 ∗∂P r[F Pi=j]
∂CSi % in the likelihood of
announcing a financial performance of j. The marginal effects for every category can be calculated and they are reported in section 3.5.2.
Generalized residuals
As the latent variable F Pi* is not directly observed, it is not possible to obtain the
resid-uals of the underlying regression equation. However, it is possible to predict Pr[F Pi=j|
CSi,ESi, YEAR] for all the organizations in the sample.
Pr[F Pi=j|CSi,ESi, YEAR] = F[aj-bCSi-c’ESi-γ2δ2,i-γ3δ3,i]-F[aj−1-bCSi-c’ESi-γ2δ2,i-γ3δ3,i],
where F(.) is the cumulative distribution function of the logistic distribution.
The generalized residuals, denoted by ri,j, of the ordered logistic model are calculated
conditional on the maximum likelihood parameters (see 3.23).
ri,j =
f (Zi,j−1) − f (Zi,j)
F (Zi,j− F (Zi,j−1)
, (3.23)
with Zi,j = ˆaj − ˆc0ESi− ˆbCSi− ˆγ2δ2,i− ˆγ3δ3,i and
Zi,j−1= ˆaj−1− ˆc0ESi− ˆbCSi− ˆγ2δ2,i− ˆγ3δ3,i , where aj and aj−1 are the cut-off points in
the ordered logistic model and f(.) and F(.) the logistic probability density function and logistic cumulative density function, respectively.
Diagnostic tests categorical models
In this section, the Brant test and the Confusion matrix are explained and they are used to test the performance of the ordered logistic models.
Brant test
Ordered logistic regression models assume that the betas across categories are the same. This underlying assumption of the model is referred to as the parallel regression as-sumption. Brant (1990) constructed a test to determine whether the parallel regression assumption holds or not. In this section, the Brant test statistic is derived for model 3.17. For all the other models for which the outcome variable is categorical, the Brant test statistic can be obtained analogously. In the first step, k − 1 binary logistic regressions are performed,where k is the number of categories. In other words, (k − 1) binary logistic regressions are performed for the financial performance variables separately, F Pi1, F Pi2
and F Pi3: F Pij = 1 if F Pi > j 0 if F Pi ≤ j pij = P r[F Pij = 1], with j = 1, 2, 3
To test whether the betas are the same across categories, the following null and alternat-ive hypotheses are formulated:
H0 = R ∗ β0 = 0
