The Effect of Bundling on Pension Fund
X-efficiencies: An Analysis of the Complexities
of the Administrative Market
Bernadette Baron S2687879
Supervisor: Dr. P. Heijnen Researched at ACM
Master Thesis Economics & Finance EBM877A20, 2018-2019
Abstract
This thesis examines the effect of bundling and complexity on pension funds efficiencies in the period 2007-2017. We analyse these effects by focusing on the supply side of the market. We find that bundling has a significant and positive effect on the efficiencies of pension funds. Discounts on bundled asset management and administration management result in lower costs for pension funds. The effect of bundling is higher for asset management than for administration, 20.6% and 6.6% respectively. Moreover, we show that an increase in complexity of the regulations of the pension fund also leads to a significant increase in administration and total cost.
2
1. Introduction
Currently there is a growing debate about the increase in the retirement age. Due to a rise in life expectancy, pension payouts will not be sufficient for the population to provide for themselves until death, and this has led to changes in the retirement age in an attempt to postpone the payouts (Bhattacharya et al., 2014). Moreover, due to the low returns on asset allocations over the last couple of years, pension funds have seen a decrease in the obtained returns. These developments make pension funds more vulnerable to misallocations and rising operating costs.
People do not like uncertainty in relation to payouts. These payouts are (partly) determined by the costs incurred by pension funds. Costs are deducted from the payouts, which means that an increase in efficiency may imply a lower deduction. The large differences in efficiencies between pension funds show that there are potential improvements for some funds, which will lead to increased efficiency and lower costs (Alserda et al., 2018).
A pension fund’s performance in terms of efficiency can be analysed by the use of different concepts (i.e. allocative, technical, productive and X-efficiency). While technical and allocative efficiencies are based on costs, productive efficiency is based on combining different inputs to reach an optimal mix. X-efficiency is based on the difference between estimated minimum costs and the actual costs (Alserda et al., 2018).
Apart from efficiencies, economies of scale can also display potential improvements for pension funds. When economies of scale are present, this implies that cost advantages are also present as pension funds grow. Larger pension funds may benefit from cost advantages in comparison to smaller pension funds. These advantages are not always incorporated in to funds, and will therefore not be applicable to all. Diseconomies of scale, on the other hand, imply cost disadvantages once pension funds grow.
3
According to Bikker and De Dreu (2009), an increase of 1% in the annual operating costs (i.e. investments and administrative costs) of pension funds’ assets implies an overall reduction of 27% in the pensions benefits. Although administration costs are only a minor proportion of the total costs of a pension fund, small efficiency gains can lead to large advantages. This paper analyses the efficiencies of pension funds for the period 2007-2017 using data from the Dutch Central Bank (DNB). This paper examines the potential relationship between bundling asset and administration management, and the efficiency of the pension funds. This research focuses on administration management and its complexity but also includes asset management to make conclusions regarding total costs.
The complexity of pension schemes may influence the level of administration costs of pension funds. Complex pension schemes involve different rules and calculations, which for instance influence the time spent on communication. This increases the involved costs. Therefore, complexity is assumed to determine administration costs to a large extent. However, there has not yet been much research about this assumption.
Results show evidence that bundling, and complexity influence the administration costs of pension funds. The analysis shows that complexity significantly increases the costs. This is assumed to be due to less time spent on communication, which lowers the associated personnel costs. Bundling, on the other hand, significantly lowers the costs. Research shows that this may hold due to a discount which is given when a pension funds takes advantage of bundling administration and asset management.
4
2. Literature review
Pension funds have an important role in the economy. The costs that they create have considerable effects on the benefits received by pensioners. Administrative costs include all expenses to operate the pension fund except investment costs. That is, personnel costs, costs charged by third parties, rent, depreciation, and many more (Bikker et al., 2012). Investment costs, on the other hand, are not easily definable. There is a lack of knowledge surrounding the investment costs of pension funds, as they may be hidden in the net return of the pension funds (Bikker and De Dreu, 2009). The degree of efficiency is based on these costs.
Alserda et al. (2018) observe the efficiency of pension funds using X-efficiencies and economies of scale. Firstly, X-inefficiencies represent the managerial ability to choose the input set, given input prices and the output mix, which minimises costs for all given scales (Alserda et al., 2018). X-efficiency depends on the difference between the actual costs and the estimated minimum costs. The higher the difference between the two, the lower the X-efficiency. In addition to X-efficiencies, pension funds may also encounter economies of scale. If there are economies of scale, costs will be lower per member once the pension funds grow. However, should costs rise upon the increased number of members, this can be seen as diseconomies of scale. Alserda et al. (2018) find that there are economies of scale in administrative costs.
Moreover, for investment costs there are higher cost elasticities, meaning that diseconomies of scale are present. This can be due to the fact that large pension funds will invest in more complex and expensive assets classes (Alserda et al., 2018). Smaller pension funds are more likely to invest in ‘easier’ assets, instead of the more extensive financial instruments (e.g. hedge funds, derivatives). More extensive financial instruments may induce higher costs levels for investment management. However, since investment costs are difficult to measure, it is difficult to establish if this is true.
5
There has no research been done about the relationship between bundling administration and asset management and the efficiency of the pension. However, much research is done about bundling (i.e. Nalebuff (2004), Nalebuff (2005), Guiltinan (1987), etc.). This research primarily concerns systems where the demand side has some negotiation power. This research focuses on a system in which the consumers do not have much influence on the offered products. Bundling is the practice of marketing two or more products and/or services in a single ‘package’ for a special price (Guiltinan, 1987). There is mixed and pure bundling. Mixed bundling is the practice of selling the products and/or services combined and separately, while pure bundling means they are only provided together (Nalebuff, 2004).
When there is a degree of bundling in the market, this may lead to implications for the degree of competition and consumer welfare. The main anti-trust concern about bundling is that it may restrict competition in the market (Zhou, 2017). Fumagalli et al. (2018) refer to this as the ‘leverage’ theory. They argue that bundling provides a mechanism through which a firm with market power in one market can leverage it to gain market power in another market. Zhou (2017) argues the leverage theory suggests that bundling can be used by a multiproduct firm to deter the entry of potential single product. When efficiency is significantly affected by such aspects in the market, this indicates that competition is affected (Nalebuff, 2004). This may lead to a higher concentration in the market.
6
3. Institutional background
All citizens in the Netherlands who are working for an employer are paying a pension premium. A small part of the income is paid to a pension fund, which will provide a pension benefit to the citizens in return once they retire. In this paper, we will refer to the pension funds as the demand side while the administrators are on the supply side of the market. These two parties will be discussed separately.
This thesis uses data from the DNB, which contains information about Dutch pension funds over the period 2007-2017. These pension funds must report their costs and organizational structure to the DNB, which they may use for research and monitoring. The provided data from the DNB to the ACM is different than those reported on the DNB website. This is due to the fact that the dataset is based on the pension funds which are the survivors. Liquidated and merged pension funds are excluded from this dataset which DNB provided to the ACM. Next, we will discuss the demand and supply side separately and give a description of the market and the data.
3.1
Demand
3.1.1 Market description
7
Figure 1. Number of pension funds from 2007-2017.
Within the pension sector, there are different types of pension funds, which have all seen a drop in membership over this time period (e.g. company funds, professional funds, mandatory industry-wide funds, and non-mandatory industry-industry-wide funds). The differences between these funds are based on the members who are enrolled for the fund. A company fund has members who are part of the same company. A professional fund is based on members who are part of a specific profession, such as dentists, doctors, or pharmacists. The industry-wide funds are based on industries and include employees from different companies which are operating in the same industry (Alserda et al., 2018). These funds can either be mandatory or non-mandatory, meaning that members do not have the ability to choose for a different pension fund than the one linked to their industry. DNB (2017a) shows the drop in the pension sector for the different types of pension fund. The number of professional funds has stayed practically the same over the years. However, the largest drop has been in the industry-wide funds (mandatory and non-mandatory). In 1997 there were 967 industry-wide funds, while there were only 192 left in 2017. So, the industry-wide funds have been affected the most by the consolidation and liquidation.
A pension fund faces several tasks. Two important tasks of the pension fund are the asset and administration management. To increase efficiencies or productivity these tasks can be outsourced to different companies. This is where the suppliers step in. It is assumed that pension funds are likely to profit from outsourcing due to technological advances. New technologies provide the
8
opportunity to outsource with lower costs than before, increasing the demand on the market. The size of the pension fund determines the purchasing and bargaining power.
Pension funds have to report to several national institutions, such as the DNB and Authority of Financial Markets (AFM). According to the DNB (2017b), the pension funds have to conform to international directives from the European Union (EU), which includes several laws. Nationally they must conform to the ‘Pensioenwet’ among other laws, which is an agreement between the employer and employee. The Ministerial arrangements, supervisor schemes and the policy rules of the DNB must also be complied with. Thus, pension funds have several schemes and rules that they must abide during their operations.
3.1.2 Data description
The data of the DNB provides all information about the organisational structure and costs of the different pension funds over the period 2007-2017. These data did not contain information about the administrative and investment management organisations for 2007. Therefore, our focus is on the period from 2008-2017.
To prevent biases, the data are analysed for outliers and some assumptions must be made to designate the correct determinants for the analysis. For example, Alserda et al. (2018) argue that pension funds with fewer than 10 members should be omitted from the dataset. They note that funds with less than 10 members are not representing collective pension arrangements. Therefore, they have a different aim and should be analysed differently than the funds including more than 10 members. Thus, these funds are excluded from the dataset. Furthermore, the DNB provides information about different costs1. There are two different reported costs of administration and
asset management which differ in accuracy and the reported time period. While one method is more accurate, it is only reported for a subsection of the analysed period. Considering the reliability of the time period analysed, this research is based on the costs reported for the entire time period.
During the period 2008-2017, pension funds often switched investors and administrators. The data show that switching investors is more frequently done than switching administrators. This can be explained by the higher switching costs associated with administration management, as there is a large amount of information which has to be transferred between the different administrators.
1 For more information about the different costs provided by the DNB, we refer to the reporting framework of the
9
Moreover, long-term relationships between different operators and the pension fund may lead to advantages in terms of interests and know-how. Therefore, parties can become more dependent on each other. Thus, the total switching costs can be based on direct costs and indirect costs, such as long-term relationships.
Although switching from an administrator is done less frequently, switching behavior is observed in the data. This means that the extent of bundling varies over time. The bundle we examine is the bundle between administration and asset management. However, there are bundles which also include advisory service. In this sample, we excluded the effect of the bundles including asset management, administration management, and advisory service. Table 1 provides information about the level of bundling in the market. The average varies around 30%. This is based on the total observations and not on the pension funds individually. Note that the total number of observations is lower in table 1 than in figure 1, which is due to missing observations according to administration and asset management.
Year Unbundled Bundled % Bundled Total
2008 164 82 33,33% 246 2009 169 76 31,02% 245 2010 172 77 30,92% 249 2011 173 74 29,96% 247 2012 154 51 24,88% 205 2013 168 75 30,86% 243 2014 167 65 28,02% 232 2015 145 67 31,60% 212 2016 134 67 33,33% 201 2017 125 60 32,43% 185 Total 1574 694 30,60% 2268
Table 1. Frequencies of the degree of bundling for the pension funds for the period 2008-2017.
Moreover, this sector2 stresses the importance of the complexity of pension regulations to explain
their administration costs. The pension regulation is a document every pension fund has to publish to communicate how the pension fund works, as well as establishing the rights of the members of
10
the pension fund. We use the number of pages of these pension regulations as a proxy for complexity. We assume that pension funds who refer to relatively easy pension regulation are able to write their regulation down in a concise way. Therefore, a variable which contains information about the number of pages of the pension regulations of the different pension funds has been generated. This implies an assumption that the number of pages for the pension regulation indicates the complexity associated with it. The variable varies between a minimum of 14 pages, to a maximum of 271 pages. This shows to what extent pension funds differ in the length of their regulations.
Each pension fund has an individual pension regulation document and the complexity varies between the different pension funds. Figure 2 displays the position of pension funds based on complexity. The associated scatterplot is located in Appendix A, figure 1A. The figure distinguishes between pension funds above and below the mean value of complexity (51.30). It shows a clear distinction between the two groups. Once pension funds become larger, we start to see a difference between the pension funds with a higher degree of complexity compared to those with a lower degree of complexity. This may signify that there may be some inefficiency stemming from the degree of complexity of the pension regulation. It provides a clear signal that those with lower complexity are able to provide services at a lower cost based on a given number of members.
11
When considering efficiencies of pension funds, we need to distinguish between the two different costs associated with this fund. We start by looking at the administration costs. The costs of administration are highly correlated with the number of members of the pension fund (a correlation of 0.9396). Investment costs have a high correlation with the total assets (a correlation of 0.8232). Since the number of members and the total assets are important determinants of the costs, administration, and investment respectively, we summarize the investment costs per total assets and administration costs separately in the next subsections.
There may be some reporting errors in the data, such as incomplete data, incorrect data and underreporting. An example is a jump in administrative costs per member in 2015. Furthermore, some pension funds have reported several investment management providers in the report by DNB. However, this report’s focus is to report to the provider only when more than 30% of the investment management was handed over to this company. Several pension funds have reported more than 3 providers, which seems to be a reporting error. These pension funds have probably reported all providers instead of those managing more than 30% of the asset management. Including more rather than less are not expected to lead to large biases, which is why these are not deleted from the dataset.
3.2 Supply
3.2.1 Administration
3.2.1.1 Market description
12
Figure 3. Number of administrative operators from 2008-2017.
The concentration of the market is analysed through the use of the Hirschman-Herfindahl Index (HHI). The HHI sums the squared market shares of firms in the relevant market (Akomea and Adusei, 2013). The market share is dependent on the number of members served by the administrator. The HHI is shown in table 2. A market with an HHI between 1500 and 2500 is seen to be moderately concentrated and a market with an HHI above 2500 is assumed to be a concentrated market (Akomea and Adusei, 2013). The C4 concentration shows the market share of the four top administrators and is used as a tool for measuring concentration. The C4 is based on the number of mandates of the administrator. This gives a C4 concentration value of 60.227% in 2017.
Year 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017
HHI 1811.307 2403.164 1882.713 1820.905 1752.879 1740.533 1745.231 1742.591 1765.622 1769.935
C4 58.173% 64.975% 64.019% 64.486% 63.212% 66.239% 64.563% 65.263% 62.921% 60.227%
Table 2. Hirschman-Herfindahl Index (HHI) and C4 measurement over the period from 2008-2017 for the administrators. Market share is based on the total members served. The C4 is based on the number of mandates of the administrator.
Table 2 shows that the concentration in the market for subsidiaries and external administrators is high, taking into account the C4 measurement technique, meaning that a large part of the market is served by a small number of administrators. The tasks performed by administrators are less cost-effective than asset management, which implies that the profit margin is low. To overcome this issue, administrators try to offer administration management together with asset management.
13
Operators claim to prefer to provide both services, instead of only administration management due to the low profitability of this activity. According to Nayyar (1993), administrators may seek potential benefits from economies of scope when they diversify. However, these benefits are not always realised.
Administrators are highly monitored when providing services to pension funds. For example, the retirement federation prepared a document called ‘Code pensioenfondsen’. This is a code for the board of the pension fund with the aim to supervise, control and let pension funds be accountable. This ‘Code pensioenfondsen’ of the monitoring committee stresses the importance of outsourcing and its supervision. Moreover, the DNB provides guidelines for outsourcing which are also applicable for pension funds. This implies substantial rules for administrators and pension funds.
Independent of bundling, some administrators are vertically integrated with the pension fund they offer a service to. This means that the pension funds own the supply chain, being the administrator. This holds for the pension funds of MN Services, Delta Lloyd, Blue Sky Group, APG, Mercer, Allianz, DSM, AZL, and Achmea. These administrators are also serving other pension funds.
3.2.1.2 Data description
14
Figure 4. Locally linear plot of pension funds distinguished between different administrators (operators).
15
Figure 5. Mean of administration costs (left axis) and mean of members (right axis) of operators.
The cost dispersion between the different operators is €10,621.70, and €14,542.83 within the operators. This dispersion is based on the lowest and highest costs and is equal to the standard deviation. These values are based on the administrative costs since members are an important determinant of the administrative costs. It can be said that there are remarkable differences between the different operators. The dispersion ranges from a maximum of €52,410.470 to a minimum of €160.304. When we observe the dispersion between the share of costs per member, we find that this varies between operators at a value of 0.472. Within operators for the different pension funds, the dispersion is 19.661. This shows that the shares are mostly determined by the pension funds, instead of the administrator. This may imply that the complexity of regulation imposed by the pension funds has a large impact on these costs dispersions.
16
which change by the number of members. However, these existing fixed costs give the opportunity to take advantage of economies of scale which is shown in figure 6.
Figure 6. Administrative cost per member in different member classes, based on different percentiles.
The sector states the fact that switching costs are substantial in the supply side of the market. This means that switching to another administrator will impose a large burden on administration costs. These switching costs are mostly high due to the difficulties of transferring the information and the tendering process. The tendering process takes almost 1.5 years. During this tendering process, there are many meetings, resulting in a large fraction of costs for the switchers associated with these meetings. Suppliers may impose discounts to solve for these switching costs, resulting in pension funds switching to another investor or administrator. However, administrators are only willing to impose a discount when the pension fund has substantial potential to grow. This would be a prerequisite for offering the discount.
3.2.2 Asset management
3.2.2.2 Market description
Investors provide the asset management of the pension fund. This also can be done by the pension fund itself, a subsidiary or an external investor. Investment costs are based on asset management, which is associated with the specific assets invested and the extensiveness of the allocations. For example, large pension funds may have a higher degree of investment costs due to more extensive allocations of assets and other financial instruments (Alserda et al. 2018). Investments are made with the capital available in the fund. Therefore, changes in the stock exchange may lead to
17
significant changes in the market value of pension funds. After the financial crisis, the stock exchange market dropped remarkably, which led to a massive drop in market value.
For asset management, the vertical integration is lower than for administration. While there are 9 pension funds which face vertical integration based on administration, there are only 5 based on asset management. Pension funds facing vertical integration are ABP, PME, PFWZ, ‘BPF bouw’ and ‘Koopvaardij’. These investors are also allowed to serve other pension funds.
Switching from an investor has been done more often than switching from an administrator. This is more than likely down to switching costs associated with investors being smaller than those of administrators. The amount of information which has to be transferred is smaller. However, switching costs are still present.
3.2.2.2 Data description
Figure 7 shows the investment costs as a share of total assets based on different asset classes for different percentiles. In the figure, there is no clear picture of economies of scale. Alserda et al. (2018) found diseconomies of scale for investment costs. This means that there are cost disadvantages present that are obtained by larger pension funds. This may hold since larger pension funds have a more extensive allocation of assets and other complex financial instruments. This may increase the costs associated with asset management, entailing diseconomies of scale.
18
19
4. Analysis
For estimating the efficiencies we have considered both non-parametric and parametric models as a replication of the analysis of Alserda et al. (2018). However, this analysis focuses on more recent data and includes more determinants explaining administration and investment costs. Non-parametric models are mathematical techniques to estimate the efficiency frontier (Alserda et al., 2018). These models do not define a specific cost function and are therefore mostly dominated by parametric models that do define a cost function. In this section, we discuss the parametric models and five different cost functions. We will start by analysing the administration costs and later we will discuss investment costs and total costs. For an analysis of the non-parametric models, we refer to Appendix C.
4.1
Administration
4.1.1 Parametric models
For the parametric models, we distinguish between the Linear Regression Model (LRM) and the Stochastic Cost Frontier Analysis (SCFA). The LRM does not show the degree of efficiency but does contain information about economies of scale. Additionally, the LRM provides the opportunity to verify whether the model is specified correctly. The SCFA model does contain information about efficiencies. In this model, the efficiencies are based on a specific cost model.
Table 3 shows the estimates of these two different methods. The LRM model is a linear regression model based on the listed variables. The SCFA model is an estimated frontier regression based on the listed variables. su2 represents the inefficiency estimate and sv2 represents the random shocks.
The X-efficiencies are predicted based on the frontier analysis and represent the differences between the estimated minimum costs and actual costs of all pension funds (Alserda et al., 2018). The average X-efficiency is 0.107, meaning that the average efficiency for pension funds is very low. 75% of the pension funds score an efficiency score below 0.138, while 25% of the pension funds scores below 0.012. This low level of efficiency shows that the level of efficiencies between the pension funds vary a great deal.
20
analysis. In the next subsection, five different models based on the SCFA model, showing the best model to fit the data are discussed.
Variables (1) LRM (2) SCFA Bundle -0.103 (0.079) -0.073** (0.032) Complexity 0.004*** (0.002) 0.017*** (0.002) Total members (ln) 0.667*** (0.035) 0.726*** (0.052) Total members2 (ln, mean deviation) 0.012 (0.002) -0.032*** (0.012) Amount of regulations 0.041** (0.020) 0.280*** (0.042) Industry fund Mandatory -0.266 (0.307) 1.988*** (0.327) Non-mandatory 0.110 (0.312) 2.067*** (0.336) Company fund -0.017 (0.293) -0.063 (0.144) Professional fund 0.339 (0.314) 2.988*** (0.364) Defined Contribution 0.075 (0.090) 1.550*** (0.273) Outsourcing Admin. 0.151 (0.106) 0.070 (0.051)
Asset per member (€) 0.001*** (0.000) 0.001*** (0.000)
Pensioners (%) 0.206 (0.317) 0.597** (0.268) Inactive members (%) -0.380 (0.318) -0.363*** (0.132) Constant 0.940** (0.468) -4.547*** (0.482) su2 11.897 (1.912) sv2 0.049 (0.002) AIC 2118.554 704.655 R2 0.857 0.244 Observations 1339 1339 X-efficiency: Average 0.107 25% percentile 0.012 Median 0.024 75% percentile 0.138
21
4.2 Functional Forms
4.2.1 Method
This section reports the outcomes of the five different functional forms based on the SCFA model. We took the SCFA model for further analysis due to the outcome of the previous subsection. Alserda et al. (2018) consider five functional forms based on the SCFA to evaluate the costs of pension funds. The variables containing information about bundling and complexity are included in the models to estimate the relationship between the administration costs and the different determinants. The following model is used:
(1) 𝐿𝑛(𝑎𝑑𝑚𝑖𝑛𝑖𝑠𝑡𝑟𝑎𝑡𝑖𝑜𝑛 𝑐𝑜𝑠𝑡𝑠) = 𝛽1+ 𝐹(𝑥5) + 𝛽6∗
(𝑝𝑒𝑛𝑠𝑖𝑜𝑛 𝑓𝑢𝑛𝑑 𝑐ℎ𝑎𝑟𝑎𝑐𝑡𝑒𝑟𝑖𝑠𝑡𝑖𝑐𝑠) + 𝛿 ∗ 𝑏𝑢𝑛𝑑𝑙𝑒 + 𝛾 ∗ 𝑐𝑜𝑚𝑝𝑙𝑒𝑥𝑖𝑡𝑦 + 𝜃 ∗ 𝑡𝑜𝑡𝑎𝑙 + 𝜀5,E
In this model, 𝑥5 is the number of members of the pension fund and 𝑏𝑢𝑛𝑑𝑙𝑒 is the variable based
on the relationship between the administration and asset management. 𝐶𝑜𝑚𝑝𝑙𝑒𝑥𝑖𝑡𝑦 represents the complexity of the regulation pension funds, which is based on the total number of pages of the regulations of the specific pension fund. 𝑇𝑜𝑡𝑎𝑙 contains the number of regulations available for the pension fund, correcting for the fact that some pension funds have several different regulations. 𝐹(𝑥5) differentiates between the different cost functions and is a function of members.
The differences between the cost function will be explained below.
First of all, we would like to consider the quadratic spline costs function (QSF). This model distinguishes a break point in the data. The QSF is similar to the Translog cost function (TCF), except that the variable based on the quadratic logarithm of members is split into two different variables instead of one for the TCF. The specifics of these variables are based on the breakpoint in the model. The breakpoint may be different for different datasets and is found by the selection of the value with the highest loglikelihood. The QSF cost function is specified as follows:
(2) 𝐹(𝑥5) = 𝛽6∗𝑙𝑛 (𝑥5) + 𝛽H∗ I𝑙𝑛 (𝑥5 − 𝑥̅)|1MNO P + 𝛽Q∗ I𝑙𝑛 (𝑥5 − 𝑥̅)|1RNO P
Here, 𝑥̅ is the mean of the members and 𝑥6 represents the breakpoint. Secondly, we have the
quadratic Translog cost function (TCF). This cost function is specified as follows:
22
Thirdly, we have the unrestricted Laurent function (ULF), which is based on the following specification: (4) 𝐹(𝑥5) = 𝛽6∗𝑙𝑛 (𝑥5) + 𝛽H∗𝑙𝑛 ( 𝑥5− 𝑥̅)H+ 𝛽Q∗ST (N6 U) + 𝛽V ∗ 6 ST (NU)W
Fourthly, we introduce a simplified unrestricted Laurent function, which is the same as the ULF cost function with 𝛽V = 0.
(5) 𝐹(𝑥5) = 𝛽6∗𝑙𝑛 (𝑥5) + 𝛽H∗𝑙𝑛 ( 𝑥5− 𝑥̅)H+ 𝛽Q∗ST (N6
U)
Lastly, we consider the hyperbolically adjusted Cobb Douglas cost function (HACD):
(6) 𝐹(𝑥5) = 𝛽6∗𝑙𝑛 (𝑥5) + 𝛽H∗ (N6
U)
4.2.2 Results
Table 4 provides the estimates of the five functional forms. The coefficients of the variables do not differ to a large extent between the models, which gives an impression of the robustness of the estimation. To decide on which model to use in further analysis, the AIC is used as a tool to select the model that fits the data in the best manner. Table 4 shows that the QSF has the lowest AIC and is therefore used as the base model for our analysis.
Based on model (1) this section analyses the following hypothesis;
𝐻1: 𝛿 = 0
𝐻6: 𝛿 ≠ 0
23 Variables (2) QSF Breakpoint = 13.5 (3) TCF (4) ULF (5) SULF (6) HACD Bundle -0.066* (0.035) -0.066* (0.035) -0.065* (0.035) -0.065* (0.035) -0.068* (0.035) Complexity 0.026*** (0.004) 0.019*** (0.003) 0.023*** (0.004) 0.023*** (0.003) 0.017*** (0.002) Members (ln) 0.997*** (0.172) 0.731*** (0.056) 3.476 (3.398) 2.162*** (0.523) 0.811*** (0.070) Members2 (ln, mean dev.) 0.002 (0.017) -0.195 (0.176) -0.129** (0.050) 1/(ln members) 300.908 (509.388) 102.141*** (37.132) 1/(ln members2) -428.651 (1095.577) 1/ members 267.960* (139.807) Members2 (ln, x dev. |p≤ x) 0.027 (0.018) Members2 (ln, x dev. |p> x) -1.479*** (0.389) Number of regulations 0.429*** (0.055) 0.441*** (0.055) 0.434*** (0.055) 0.432*** (0.055) 0.445*** (0.055) Outsourcing Admin. (0.054) 0.052 (0.054) 0.059 (0.055) 0.053 (0.054) 0.053 (0.054) 0.052 Asset per member 0.001*** (0.000) 0.001*** (0.000) 0.001*** (0.000) 0.001*** (0.000) 0.001*** (0.000) Pensioners (%) 0.738** (0.293) 0.719** (0.293) 0.658** (0.295) 0.669** (0.294) 0.669** (0.293) Inactive members (%) -0.496*** (0.144) -0.482*** (0.144) -0.498*** (0.144) -0.499*** (0.144) -0.491*** (0.144) Constant -7.740*** (1.860) -4.543*** (0.484) -57.499 73.756 -28.851*** (8.849) -5.231*** (0.587)) su2 12.860 14.007 13.320 13.340 13.703 sv2 0.057 0.057 0.057 0.057 0.057 AIC 908.296 920.812 917.1046 915.2577 917.148 R2 0.322 0.380 0.332 0.337 0.387 Wald 38.010*** 22.980*** 31.960*** 30.810*** 26.800***
24 Percentiles (2) QSF Breakpoint = 13.5 (3) TCF (4) ULF (5) SULF (6) HACD X-efficiencies Average 0.053 0.042 0.048 0.047 0.044 25th percentile 0.016 0.015 0.015 0.016 0.015 Median 0.025 0.021 0.023 0.023 0.023 75th percentile 0.045 0.033 0.037 0.037 0.033
Table 5. X-efficiencies of the five functional forms divided into percentiles. These X-efficiencies are predicted from the frontier regression of the five functional forms. Low X-efficiencies explain large differences in administration costs between pension funds.
The estimated functional forms are inefficiency models, which means that a negative sign in the estimation shows a negative effect on the inefficiency. The estimation results show that integration between the administrator and investor has a negative effect on the inefficiency. Having administration and asset management provided by the same company results in lower administration costs of 6.6%.
The second hypothesis analysed, based on model (1), is the following; 𝐻1: 𝛾 = 0
𝐻6: 𝛾 ≠ 0
Here, 𝛾 is the effect of complexity on the administration costs. Table 4, column 1 shows that 𝛾 is significantly different from zero at the 1% significance level. The null hypothesis that 𝛾 is equal to zero is rejected and we can conclude that complexity does result in an increase in the inefficiency of a pension fund. This means that having a more complex regulation (measured by the number of pages of the regulation) will lower the degree of efficiency. Having 1 page less in the regulation will lead to a drop of 2.6% in the administration costs. The significance of the variable explaining the total number of regulations shows that it is beneficial for pension funds to lower the number of separate regulations as this will increase efficiency.
25
regulation. The variables of the model remain similar and for average complexity, the bundle variable remains the same. Thus, on average the costs in a bundle do not depend on the complexity of a regulation.
Cost elasticities based on the estimates in table 4 are below 1, which indicates that the pension funds benefit from economies of scale. When cost elasticities are above 1, this would have indicated diseconomies of scale. The distance from 1 shows the degree of unused economies of scale (Alserda et al., 2018). The economies of scale of the five functional forms are consistent with the outcomes of the Wald tests shown in table 4 and can be found in figure 8. The TCF and QSF cost elasticity functions are quite different from the other functional forms. The QSF line shows that there are large unused economies of scale for the smaller pension funds and small unused economies of scale for the larger pension funds. However, since the QSF does not exceed the value of 1, there are no diseconomies of scale visible.
Figure 8. Histogram of the number of pension funds divided into different member classes. The line graph represents the cost elasticities of the different functional forms. These cost elasticities are calculated by the first derivative of the five functional forms with respect to the number of members. Cost elasticities below 1 represent economies of scale.
26
is worth noting that the bundle variable is varying largely over time. Furthermore, for 2013-2015 the average X-efficiency is 0.003, while the X-efficiency for 2008-2009 is 0.656. The highest average X-efficiency is stated in the first years. This is remarkable since there are no clear indicators why efficiency would have been higher in these years.
The period between 2013-2015 seems to be the period with the largest difference of estimates in comparison with the other periods. When comparing this information with the change in the number of pension funds between the different periods, we see that after 2013 there has been a decrease in the number of pension funds in the market. The decrease in X-efficiency may have led to pension funds failures, meaning that these pension funds went bankrupt and merged with another pension fund. In this period there is a decrease in the number of administrators in the market, which may be the reason that the bundle variable is highly significant in this period. There is clear drop in the number of administrators in the period after 2013, which would result in a higher concentration of the market. This could have intensified the incentive to attract pension funds by the use of discounts and would be a reason for the negative coefficient of 𝑏𝑢𝑛𝑑𝑙𝑒. This mechanism could have been more present in this period and could be the explanation that this effect is only significant in this period of time. When considering the period from 2008-2012 and 2012-2017 separately, the bundle variable remains significant for the last period. We can thus conclude that the effect of bundling started to become visible in the most recent years.
27 X-efficiencies Average 0.656 0.270 0.320 0.003 0.019 25th percentile 0.606 0.074 0.100 0.001 0.012 Median 0.663 0.178 0.242 0.001 0.015 75th percentile 0.728 0.422 0.480 0.002 0.018
Table 6. Estimation based on the QSF functional model for different subperiods. The Wald test refers to a test for constant returns to scale, for which the null hypothesis states that there are constant returns to scale.. These X-efficiencies are predicted from the frontier regression for the different time periods. Low X-efficiencies explain large differences in administration costs between pension funds.
28
There may be biases in the data when considering subperiods. The sector explains that switching costs will be high for some pension funds, while other pension funds will receive a discount since these are large enough to be interesting for the supplier. This means that the pension funds that are expected to grow substantially or have a high degree of profitability will have lower switching costs.. This difference in switching costs may lead to biases in the data when considering these subperiods. Therefore, it is assumed that the estimation over the period as a whole is more reliable than the estimation of the subperiods.
4.3 Asset management costs
4.3.1 Method
Another aspect of a pension fund are the costs of the asset management, i.e. investment costs. To draw conclusions on the total costs of the pension funds, we must analyse the investment costs first. The outcomes of the non-parametric models can be found in Appendix D.
29 Variables (1) LRM (2) SCFA Total assets (ln) 1.014*** (0.043) 1.086*** (0.037) Total assets2 (ln, mean deviation) -0.019 (0.012) -0.031*** (0.009) Bundle -0.425*** (0.118) -0.308*** (0.068) Industry fund Mandatory -0.020 (0.801) 1.235*** (0.366) Non-mandatory 0.186 (0.799) 1.512*** (0.455) Company fund -0.005 (0.796) 0.763** (0.340) Professional fund 0.747 (0.810) 1.973*** (0.403) Defined Contribution 0.017 (0.119) 0.159 (0.153)
Asset per member (€) -0.000 (0.000) 0.000 (0.000)
Pensioners (%) -0.439 (0.360) 0.170 (0.296) Inactive (%) 0.594* (0.319) 0.258 (0.233) Private equity 6.135* (3.144) 1.446 (1.398) Real estate 2.489** (0.993) 2.987*** (0.633) Fixed income 0.159 (0.416) 0.101 (0.216) Constant -7.012*** (0.951) -9.986*** (0.585) su2 1.702 (0.250) sv2 0.303 (0.012) AIC 3627.704 3052.064 R2 0.842 0.830 Observations 1547 1547 X-efficiency: Average 0.369 25% percentile 0.199 Median 0.295 75% percentile 0.502
Table 7. Estimates of parametric methods. P>|t| = *<0.10, **<0.05, ***<0.01. The Wald test refers to a test for constant returns of scale, for which the null hypothesis states that there are constant returns to scale.
30
The functional forms for investment costs are different from the functional forms for administration costs. The number of members is not included in the estimation of the cost function for investment costs, and the complexity of the regulations and the number of regulations is assumed to have no effect on the investment costs by itself. The base model is as follows:
(7) 𝐿𝑛(𝐼𝑛𝑣𝑒𝑠𝑡𝑚𝑒𝑛𝑡 𝑐𝑜𝑠𝑡𝑠) = 𝛽1+ 𝐹(𝜑5) + 𝛽6∗ (𝑝𝑒𝑛𝑠𝑖𝑜𝑛 𝑓𝑢𝑛𝑑 𝑐ℎ𝑎𝑟𝑎𝑐𝑡𝑒𝑟𝑖𝑠𝑡𝑖𝑐𝑠) +
𝛿 ∗ 𝑏𝑢𝑛𝑑𝑙𝑒 + 𝜀5,E
in which 𝑓(𝜑5) represents a function of total assets. This function differs between the different
cost functions. These are shown below.
The ULF cost function will be estimated as follows:
(8) 𝐹(𝜑5) = 𝛽6∗𝑙𝑛 (𝜑5) + 𝛽H ∗𝑙𝑛 ( 𝜑5 − 𝜑`)H+ 𝛽Q∗ST (a6
U) + 𝛽V∗
6 ST (aU)W
in which 𝜑` is the mean of the assets. Secondly, the TCF function is considered to be the following:
(9) 𝐹(𝜑5) = 𝛽6∗𝑙𝑛 (𝜑5) + 𝛽H ∗𝑙𝑛 ( 𝜑5 − 𝜑`)H
Thirdly, we also introduce a simplified unrestricted Laurent function, which is the same as the ULF function with 𝛽V = 0.
(10) 𝐹(𝜑5) = 𝛽6∗𝑙𝑛 (𝜑5) + 𝛽H ∗𝑙𝑛 ( 𝜑5 − 𝜑`)H+ 𝛽Q∗ST(a6
U)
Fourthly, we consider the HACD cost function:
(11) 𝐹(𝜑5) = 𝛽6∗𝑙𝑛 (𝜑5) + 𝛽H ∗ 6 (aU)
Lastly, we consider the QSF cost function, which is specified as follows:
31
4.3.2 Results
Table 8 shows the estimates of the five functional forms for investment costs. The preferred model based on the AIC is the ULF model. Thus, the ULF model is used in further analysis of the investment costs.
Considering model (8) this section analyses the following hypothesis;
𝐻1: 𝛿 = 0
𝐻6: 𝛿 ≠ 0
in which 𝛿 is the effect of the bundle on the investment costs. The first column of table 8 shows that the coefficient of 𝑏𝑢𝑛𝑑𝑙𝑒, 𝛿, is significantly different from zero at the 1% level, which implies that we are able to reject the null hypothesis. This means that bundling administration and asset management together results in lower investment costs for pension funds. The coefficient shows that being in a bundle results in a decrease in investment costs by 20.6%. In comparison to the administration estimation, this effect is very substantial.
The cost elasticities in the model show diseconomies of scale. This means that there are cost disadvantages once pension funds grow. This outcome corresponds to the outcome of Alserda et al. (2018) who find diseconomies of scale for investment costs. This leads to the conclusion that pension funds face diseconomies of scale for asset management, while they face economies of scale for administration management.
32 Variables (8) ULF (9) TCF (10) SULF (11) HACD (12) QSF Breakpoint = 19.5 Bundle -0.206*** (0.065) -0.162** (0.068) -0.188*** (0.065) -0.149** (0.068) -0.160** (0.068) Total assets (ln) -10.295*** (2.854) 1.106*** (0.026) 4.732*** (0.393) 1.334*** (0.096) 1.120*** (0.094) Total assets2 (ln, mean dev.) 0.330*** (0.116) -0.000*** (0.008) -0.279*** (0.034) 1/(ln total assets) -4127.867*** (891.473) 582.695*** (63.760) 1/(ln total assets2) 13996.48*** (2651.010) 1/ total assets 38.869** (15.826) Total assets2 (ln, x dev. |p≤ x) (0.008) 0.001 Total assets2 (ln, x dev. |p> x) -15.300** (6.094) Asset per member (0.000) -0.000 (0.000) 0.000 (0.000) -0.000 (0.000) -0.000 (0.000) 0.000 Pensioners (%) -0.381 (0.325) -0.238 (0.313) -0.509 (0.337) -0.283 (0.334) -0.230 (0.314) Inactive members (%) (0.208) -0.074 (0.220) 0.187 (0.212) -0.012 (0.219) 0.254 (0.220) 0.192 Private equity 1.613 (1.439) 0.491** (1.467) 2.276 (1.446) -0.328 (1.441) 0.741 (1.466) Real estate 1.608*** (0.574) 0.899 (0.596) 1.182** (0.579) 0.7092 (0.593) 0.886 (0.595) Fixed income -0.034 (0.189) -0.346*** (0.190) -0.158 (0.188) -0.315* (0.190) -0.355* (0.190) Constant 373.953*** (90.020) -9.182*** (0.355) -101.013*** (10.005) -15.318*** (0.587)) -9.437*** (2.531)) su2 2.320 (0.306) 2.537 (0.355) 2.557 (0.334) 2.690 (0.358) 2.569 (0.359) sv2 0.320 (0.012) 0.338 (0.012) 0.321 (0.012) 0.330 (0.012) 0.336 (0.012) AIC 3908.674 4019.878 3932.647 3990.175 4015.594 R2 0.104 0.132 0.072 0.143 0.129 Wald 154.19*** 17.720*** 110.90*** 61.100*** 37.760***
33
Percentiles ULF TCF SULF HACD QSF
Breakpoint = 19.5 X-efficiencies Average 0.297 0.268 0.285 0.252 0.265 25th percentile 0.165 0.149 0.150 0.134 0.147 Median 0.242 0.214 0.231 0.195 0.211 75th percentile 0.359 0.322 0.377 0.314 0.316
Table 9. X-efficiencies of the five functional forms divided into percentiles. These X-efficiencies are predicted from the frontier regression of the five functional forms. Low X-efficiencies explain large differences in investment costs between pension funds.
4.4 Total costs
We have discussed investment costs and administration costs separately to investigate different effects on different costs. Now we consider the effect on the total costs, which is the combination of investment and administration costs. Total costs provide the opportunity to observe economies of scope, which indicates the benefits of providing more than one service.
According to Giannakas et al. (2003), finding the appropriate functional form for analysis is not trivial. This means that the best model depends on the data and the specific model. Traditional used functional forms are the TCF and Cobb-Douglas model. Therefore, we impose the TCF model to combine the two separate models for administration and investment into one model for the total costs. Combining the two best models we used in the individual analysis of administration and investment cost would have a higher probability of estimation errors.
Since the two costs have different economies of scale and different determinants, combining the two models together without adding an interaction term may lead to a bias. To solve this problem we introduced an interaction term, which multiples members with total assets.
The interaction variable is set up as follows:
𝐼𝑛𝑡𝑒𝑟𝑎𝑐𝑡𝑖𝑜𝑛Ebc= 𝑙𝑛 (𝑥5) ∗ 𝑙𝑛 (𝜑5)
34 Percentiles TCF X-efficiencies Average 0.354 25th percentile 0.218 Median 0.297 75th percentile 0.447
Table 10. X-efficiencies of total costs divided into percentiles. These X-efficiencies are predicted from the frontier regression of TCF of total costs. Low X-efficiencies explain large differences in total costs between the pension funds.
The estimates can be found in table 11. 𝐵𝑢𝑛𝑑𝑙𝑒 remains significant in the estimation of the total costs. The coefficient shows that being in a bundle will result in a reduction in total costs of 9.8% at the 10% significance level. The complexity variable shows a lower coefficient on the total costs than it did on the administration costs alone. This can be explained by the fact that complexity has no effect on the investment costs. Therefore, the effect on total costs is estimated to be lower. Table 11 shows that adding one page to the regulation of the pension fund, increasing the complexity, will lead to an increase in the total costs of 0.6%. The number of regulations show that decreasing the number of separate regulations will lead to a decrease in total costs of 14.2%, which is significant at the 1% level. This higher value for the number of regulation is understandable since most pension funds already have only one regulation, resulting in the fact that they are not always able to lower the number of regulations.
The cost elasticity of the total costs at the mean is equal to 0.902, which indicates that economies of scale are present. The investment costs show diseconomies of scale, whereas administration costs exhibit economies of scale. Total costs can not be plotted against total members since it is based on the members and the total assets together. This outcome is in contrast with the outcome of Alserda et al. (2018), who find a constant return to scale for total costs. The interaction term shows a negative coefficient, which implies economies of scope. However, this term is not significantly different from zero.
35 Variables TCF Bundle -0.098* (0.054) Complexity 0.006*** (0.002) Total members (ln) 1.111** (0.482) Total Members2 (ln, mean dev.) 0.025 (0.021) Total assets (ln) 0.844** (0.427) Total assets2 (ln, mean dev.) 0.025 (0.025) Interaction term -0.048 (0.041) Total 0.142*** (0.038) Outsourcing Adm. 0.134* (0.075)
Asset per member 0.000
(0.000) Pensioners (%) 1.121*** (0.351) Inactive members (%) -0.615*** (0.203) Private equity (%) -1.380 (1.198) Real estate (%) 0.164 (0.536) Fixed income (%) -0.214 (0.170) Constant -9.170** (4.989) su2 1.611 (0.250) sv2 0.137 (0.006) AIC 1628.69 R2 0.221 Wald 1061.41***
Cost elasticity at mean 0.902
36
5. Discussion
The results for administration costs, investment costs, and total costs all provide statistically and economically significant results for the bundling variable. Complexity is estimated to have a significant effect on administration costs and total costs. This implies that the null hypotheses are rejected, and we can conclude that there is a significant effect of bundling and complexity on the efficiency of pension funds.
This paper finds significant evidence that mixed bundling, which implies that two products are offered together as well as separately (Evans and Salinger, 2005), has a positive effect on administration costs. This effect can be caused by different factors.
First of all, Nalebuff (2005) stated that bundles may entail bundle discounts. This implies that prices will drop when the suppliers provide a bundle. These discounts are referred to as bundled rebates. Bundled rebates occur when a firm offers a discount conditional on the sales growth on a set of products (Fumagalli et al., 2018). In this case, it would mean that the costs for the pension funds are lower than they would have been when they would have bought the two services separate. This would mean that costs would be 6.6% and 20.6% lower for administration costs and investment costs respectively. Since the bundle has a significant effect on investment costs and administration costs, this indicates that the discount should be divided between the two. This means that the pension funds receive a discount on the administration costs and the investments costs due to the bundle bought.
However, since the effect on administration and asset management is remarkably different, these effects should be explained differently. The effect on administration is small in comparison with the effect on asset management. This could infer that most discounts are debited from the investment costs, which means that the effect on administration could have a different cause. Since the administration is less profitable than asset management, the administrator has less freedom of movement than the investor. There may be a lower profit margin available for the administrator to give a discount, which would imply that the given discount on administration could not be higher.
37
pension funds imposing lower costs to deter competition from the market. For substantial evidence, there should be extended research about discounts in the market.
According to Nalebuff (2004), the concentration of the market is important to impose bundling as an entry barrier. This would imply that bundling would result in a theory of harm. To detect whether there is enough evidence for this statement, we analysed the concentration of the market for administration. These outcomes show that the market faces a moderate level of concentration of 1800 according to the HHI. However, the C4 measurement shows that the top 4 has a large market share of around 60.227% in 2017 based on the mandates of the administrator.
Moreover, Knoll (2008) argued that there may be synergies associated with the bundle, which implies that these synergies may be the reason the costs are lower for the pension funds which are part of a bundle. He provides two reasons for this. Firstly, growth synergies may lead to higher revenues and lower costs. The supplier has the ability to differentiate which may increase the efficiency and innovative offerings of the firm, leading to differentiation advantages over the more focused firms. Secondly, bundling may ease the search of individual components of a solution. This would imply that the pension fund will spend less time searching for the right operator for their service.
Fumagalli et al. (2018) discuss different efficiency rationales for bundling, which may occur once a company decides to bundle products. Most rationales are based on technological products which bundle systems and codes together, which do not all comply with the bundled services of administration and asset management. However, some rationales are also applicable to this industry, e.g. the solution to reputation problems. Bundling products together may increase certainty amongst consumers about the quality of one of the components (Fumagalli et al., 2018).
The second hypothesis tested by this paper shows significant evidence that complexity has a negative effect on the administration costs of pension funds. This implies that the increase of the complexity by one, which is measured by the pages included in the regulation, will lead to an increase in the administration costs of 2.6%, and an increase of 0.6% of the total costs.
38
39
6. Conclusion
Pension funds contain more than the GDP of the Netherlands, showing the importance of efficiencies associated with it. Small efficiency gains may lead to large benefit increases for the members of the pension fund and this will even increase once efficiency continues to grow over a longer period of time. This study researches the market of administrators and investors within the pension funds, analysing the efficiencies of administration and investment costs on pension funds. The costs are analysed separately and combined at a later stage to analyse the effects of total costs, for which we replicate the analysis of Alserda et al. (2018).
This study finds a significant and positive effect of bundling on administration costs, investment costs and total costs. This implies that it is profitable for pension funds to do business with an administrator and investor who bundle their services. This may be caused by synergies, such as cohesive communication, growth advantages and the lower amount of time involved in searching components. Another cause may be discounting. An administrator could impose a discount on asset management once a pension fund agrees to outsource asset management and post it at the same company as administration. This would explain the lower costs associated with the bundle variable.
Since the effect of bundling on administration (6.6%) is significantly smaller than the effect on asset management (20.6%), these effects should be explained differently. Asset management has higher profitability, which implies that the margin on this industry is higher than on administration. Therefore, discounts provided can be more substantial than for administration. The effect shown on administration may imply small discounts but could contain information about imposing lower prices and bundling as an entry barrier. Total costs show a similar effect of bundling, but the robustness test shows insignificant estimates. This implies that conclusions made from this model are questionable.
40
Efficiencies of the pension funds show larger inefficiencies for administration (0.052). Due to high switching costs, pension funds are more tended to stay at the administrator instead of switching to a more efficient competitor. This could explain why inefficient parties remain in the market, lowering the efficiency based on administration costs. For asset management, these X-efficiencies are equal to 0.286. This means that the differences between different pension funds based on asset management are smaller than for administration. For total costs, the X-efficiency is equal to 0.354. This indicates that the difference between the pension funds becomes smaller once we look at the total costs instead of at the costs separately.
The aim of this paper is to analyse the efficiency of pension funds and to consider recommendations for improvement. Economies of scale indicate the relevance of consolidation between different pension funds and the significant effect of bundling shows the importance of a different allocation of administration and asset management on pension funds’ costs. Assuming these outcomes are the result of given discounts, this may push players out of the market. Therefore, control and monitoring discounts and the effect on small players in the market are important. Substantial research about vertical integration may give more information about the efficiency gains for administrators and investors. The effect on complexity raises questions about the pension regulations within pension funds and their efficiency and conciseness. Pension funds should consider decreasing their pension regulations in order to lower costs. This may lead to reduced switching costs, improving competition in the market for administration management.
41
Appendices
Appendix A
42
Appendix B
43
Appendix C
Non-parametric models are based on mathematical techniques which calculate the input-oriented or output-oriented efficiencies. These models calculate efficiencies based on the differences between different pension funds by looking at the best-in-practice funds.
The Free Disposal Hull (FDH) model is based on weak dominance. This means that the funds are compared to those that produce at least the same output as the other fund. The FDH looks at the share of efficient funds and the mean and median of the total funds. However, this model is extremely vulnerable to outliers. Order-a, on the other hand, chooses a percentile (i.e. 95% or 99% ) which is a minimum/maximum benchmark. FDH can be approached as an order-a level of 100%. Order-a gives the possibility to distinguish between efficient and super-efficient funds. Meaning that the lower the percentile the higher the degree of super-efficient funds estimated by the model. For estimation, we considered the order-a for the 95% and 99% percentile and the FDH model.
Table 1C shows the results of the estimation of the three non-parametric models. This shows that the efficiencies of the three models are remarkably different. For the FDH model, we see that the average efficiency is based on 0.132. However, for the order-(95) estimates, this average efficiency is equal to 0.710. This is due to the fact that the order-(95) model assigns more pension funds the label of super-efficient. The order-a model assigns more pension funds the label of super-efficient than the order-(99) model. Therefore, the mean efficiency level of the order-(99) model is equal to 0.431, which is lower than the efficiency of the order-(95) model.
44 Variables (1) Order-(99) (2) Order-(95) (3) FDH Members (ln) 0.030*** (0.005) -0.038*** (0.005) 0.027*** (0.003) Members2 (ln, mean dev.) -0.012*** (0.001) -0.004*** (0.001) 0.003*** (0.001) Complexity 0.000 (0.000) -0.000** (0.000) -0.000 (0.000) Amount of regulations -0.021*** (0.006) -0.025*** (0.006) -0.000 (0.004) Bundle 0.012 (0.015) 0.040*** (0.014) -0.002 (0.009) Industry fund Mandatory 0.029 (0.085) 0.081 (0.080) 0.220*** (0.052) Non-mandatory -0.127 (0.089) -0.079 (0.083) 0.092* (0.054) Company fund -0.037 (0.083) -0.014 (0.078) 0.015 (0.051) Professional fund -0.170* (0.087) -0.176** (0.082) 0.002 (0.053) Defined Contribution -0.034** (0.016) -0.014 (0.015) -0.020** (0.010) Outsourcing Admin. -0.101*** (0.018) -0.098*** (0.017) -0.040*** Asset per member -0.000*** (0.000) -0.001*** (0.000) -0.000 (0.000)
Pensioners (%) -0.017 (0.052) -0.051 (0.047) -0.010 (0.032) Inactive members (%) -0.028 (0.051) 0.090* (0.047) -0.011 (0.031) Constant 0.357*** (0.097) 1.211*** (0.090) -0.130 (0.031) Adjusted R2 0.230 0.321 0.546 Observations 1339 1339 1339 X-efficiencies Average 0.431 0.710 0.132 25th percentile 0.220 0.512 0.014 Median 0.395 0.713 0.039 75th percentile 0.590 1.000 0.166
45
Appendix D
Variables (1) Order-(99) (2) Order-(95) (3) FDH Total assets (ln) 0.001 (0.011) -0.040*** (0.013) 0.016*** (0.004) Total assets2 (ln, mean dev.) 0.003 (0.003) 0.014*** (0.005) 0.007*** (0.001) Bundle 0.112*** (0.035) 0.137*** (0.038) -0.053*** (0.016) Industry fund Mandatory 0.067 (0.142) 0.217* (0.088) -0.128 (0.163) Non-mandatory -0.035 (0.141) 0.139 (0.089) -0.181 (0.163) Company fund 0.057 (0.139) 0.206* (0.077) -0.122 (0.162) Professional fund -0.123 (0.142) -0.054 (0.088) -0.184 (0.163) Defined Contribution 0.013 (0.028) 0.024 (0.046) -0.001 (0.010)Asset per member -0.000** (0.000) -0.000 (0.000) 0.000* (0.000)
Pensioners (%) 0.075 (0.092) 0.072 (0.128) 0.048 (0.051) Inactive members (%) -0.135 (0.082) -0.027 (0.122) -0.051 (0.033) Private equity -1.391** (0.653) -2.509** (0.000) -0.366 (0.000) Real estate -0.483* (0.277) -0.803** (0.000) -0.287* (0.000) Fixed income -0.121 (0.107) -0.081 (0.000) -0.054 (0.000) Constant 0.310 (0.192) 1.009*** (0.182) -0.012 (0.031) Adjusted R2 0.091 0.172 0.201 Observations 1547 1547 1547 X-efficiencies Average 0.250 0.638 0.071 25th percentile 0.105 0.392 0.014 Median 0.161 0.604 0.029 75th percentile 0.285 1 0.062
46
References
Akomea S.Y., Adusei, M. (2013). Bank recapitalization and market concentration in Ghana’s banking industry: A Herfindahl-Hirshman Index analysis. Global Journal of Business Research, 7(3), 31-45.
Alserda, G.A., Bikker, J.A., Van Der Lecq, F.S. (2018). X-efficiency and economies of scale in pension fund administration and investment. Applied Economics, 50(48), 5164-5188.
Alhborn, C., Evans, D.S., Padilla, A.J. (2003). The Antitrust Economics of Tying: A farewell to Per Se Illegality. The Antitrust Bulletin, 49(1-2), 287-341.
Bikker, J.A., De Dreu, J. (2009). Operating Costs of Pension Funds: The Impact of Scale, Governance and Plan Design. Journal of Pension Economies & Finance, 8(1), 63-89.
Bikker, J.A., Steenbeek, O.W., Torracchi, F. (2012). The Impact of Scale, Complexity, and Services Quality on the Administrative Costs of Pension Funds: A Cross-Country Comparison.
The Journal of Risk and Insurance, 79(2), 477-514.
Bhattacharya, J., Hyde, T., Tu, P. (2014). Health Economics (1st ed.). London, United Kingdom:
Palgrave MacMillan.
DNB (2017a). DNBulletin: Pension funds consolidation continues – general pension funds are gaining market share. Retrieved 6 March 2019 from
www.dnb.nl/en/news/news-and-archive/dnbulletin-2017/dnb362426.jsp
DNB (2017b). Open boek toezicht. Retrieved 6 March 2019 from www.toezicht.dnb.nl/2/6/50-232355.jsp
Evans, D.S., Salinger, M. (2005). Why Do Firms Bundle and Tie? Evidence from Competitive Markets and Implications for Tying Law. Yale Journal of Regulation, 22(3), 37-89.
47
Giannakas, K., Tran, K.C., Tzouvelekas, V. (2003). On the choice of functional form in stochastic frontier modeling. Empirical Economics, 28(1), 75-100.
Guiltinan, J. P. (1987). The Price Bundling of Services: A Normative Framework. Journal of
Marketing, 51, 74-85
Knoll, S. (2008). Cross-Business Synergies: A Typology of Cross-business Synergies and a Mid-range Theory of Continuous Growth Synergy Realization (1st ed.). Springer Science & Business
Media.
Nalebuff, B. (2004). Bundling as an Entry Barrier. The Quarterly Journal of Economics, 119(1), 159-187.
Nalebuff, B. (2005). Exclusionary Bundling. The Antitrust Bulletin, 50(3), 321-370.
Nayyar, P.R. (1993). Performance Effects of Information Asymmetry and Economies of Scope in Diversified Service Firms. Academy of Management Journal, 36(1), 28-57.
