An empirical evaluation of the determinants of the return on investments and risk-taking in pension plans

(1)

1

An empirical evaluation of the determinants

of the return on investments and risk-taking

in pension plans

Bas ten Dam

Amsterdam School of Economics, University of Amsterdam (UvA), the Netherlands

Abstract.

In this study, I examine the effect of the size, type, funding ratio and characteristic of participants of pension plans on their return and risk-taking. Using Form 5500 data from 2000-2012, I estimate the effects with a fixed effects vector decomposition model as proposed by Plümper and Troeger (2007). As expected, diseconomies of scale in the income from investments dominate the economies of scale in operating costs, defined contribution plans have a higher return and invest in more risky assets and plans with more retired participants have a lower return and engage in less risk-taking. The lower return and less risk-taking in multiemployer plans is also in line with expectations, but deserves special attention for its relatively large impact. Contrary to the expectations, underfunded plans have a higher return and engage in more risk-taking.

(2)

2

1 Introduction

Pensions are worldwide under discussion. Ageing population, the fact that people live longer, puts pressure on the pension system and the financial crisis of 2008 has intensified questions about the affordability of pensions. An expression of the growing concern over pensions, is the fact that the Dutch government has asked the Social and Economic Council to advise on the future of the pension system with special attention to the challenges of solid capital growth, freedom of choice and solidarity (SER, 2015). Similar policy-oriented issues are debated in other countries as well (OECD, 2014).

A government nurtures the size and type of plans and regulates how the funding ratio and characteristic of participants effect the risk-taking. For example, governments encourage the existence of larger pension plans if these plans have a higher return on investment. Furthermore, the Dutch Ministry of Social Affairs and Employment (2014) recently proposed that pension plans could invest the money of retired participants instead of changing it into a fixed income stream. 1_An

underlying assumption of this proposal is that plans with more retired participants act in line with economic theory by decreasing their risk-taking. However, for these kind of decisions the government needs to have information on how the characteristic of participants, size, type and funding ratio affect the risk-taking and return of plans. The effect on the return of investment is even more important since the return is a yearly flow and can have relatively large consequences over time. For example, Bikker, Steenbeek and Torracchi (2012) state that a cost reduction of 0.25 percentage point leads to an increase in pension assets of 7.5% in forty years.2

Empirical results from recent literature on the effect of size, type, funding ratio and characteristic of participants on the return and risk-taking, however, are inconclusive. Rauh (2009) and An, Huang and Zhang (2013) conclude that underfunded plans invest in safer assets whereas Andonov, Bauer and Cremers (2014) and Mohan and Zhang (2014) provide evidence for the opposite. The literature on how size effects return is also ambivalent. Most authors find that larger pension plans reach a higher return on investments due to economies of scale (Bikker & Dreu, 2009; Tapia & Yermo, 2008; Dyck & Pomorski, 2011; Bikker et al., 2012). Moreover, the Melbourne Mercer Global Pension Index uses size as a proxy for lower costs, because they see the presence of economies of scale as self-evident (Australian Centre for Financial Studies, 2013). However, Bikker and Dreu (2009) and Bikker et al. (2012) use operating costs as proxy for the return on investments. A proxy which is criticized by the study of Andonov, Bauer and Cremers (2012) who show that the diseconomies of

1_{The effects are measured using a dataset with US private plans. However, apart from the regulation which}

could influence the effect of the funding ratio on risk-taking, there is no reason to believe that the effects are different.

2_{This calculation assumes a “base” nominal annual return of 13-14% whereas the average nominal return of US}

(4)

4

scale in the income from investments dominate the economies of scale in the operating costs.3_This

study allows for analyzing return on investments directly without having to use proxies and uses a dataset with over three million pension plan filings. The empirical evidence of this study is therefore better than for example Bikker and Dreu (2009), Bikker et al. (2012) and Tapia and Yermo (2008).

For governments to nurture the size and type of plans and regulate the funding ratio and characteristic of participants, knowing how these factors affect the return and risk-taking is a prerequisite. The aim of this thesis is to contribute to this necessarily stock of knowledge. In order to do this, I will answer two key questions. First, what is the effects of the size, characteristic of participants, type and funding ratio of a pension fund on its return on investments? Second, what is the effect of the same determinants on risk-taking in investments? Both questions will empirically be answered by looking at the Form 5500 data, which consists of information on all private pension plans in the United States from 2000-2012.

This study is structured in the following way. In section 2, I will start by outlining the state of the art of the literature on the effects of size, characteristic of participants, type and funding ratio on return and risk-taking. Section 3 consists of a description and adjustments of the dataset. In section 4, the methodology on how these effects will be estimated is described. The results of this study are presented and discussed in section 5. Finally, section 6 consists of a summary of the main findings and suggestions for further research.

(5)

5

2 Literature

2.1 Relation between return on investments and risk-taking

The return on investments refers to the net income of a pension plan divided by its amount of assets. A pension plan who governs 100 dollar and a net income of 10 dollar has therefore a return on investments of 10%. A pension plan’s income is derived from investing in bonds and equities whereas the operating costs are interest and administrative expenses. The risk-taking refers to the amount of risk associated with the investments of pension plans. Equities are assumed to be more risky than bonds, because bondholders will sooner receive their money in the case of default.

The return on investment and risk-taking in investments are a trade-off since higher returns are generally accompanied by more risk-taking (Fama & French, 2004). This trade-off is captured in the Capital Asset Pricing Model (CAPM). In this model investors are assumed to be risk-averse. When faced with two possible investments with the same expected return, they will choose the one with the lowest associated risk. Risky investments should therefore offer a higher expected return to attract investors. The trade-off is empirically confirmed by Walker and Iglesias (2007) who find that pension plans with riskier assets have a larger return on investments. On the other hand, Andonov et al (2014) show that this does not always hold. They find that US public pension plans with riskier assets actually underperformed during 1990-2010.

Pension plans differ from other mutual funds by their focus on long-term objectives (Antolin, 2008, pp. 16-18). The time horizon for the evaluation of the returns should be the lifetime of participants, because they do not receive any money until retirement. This long-term objective has important consequences for the comfortable amount of risk-taking. Pension plans are therefore able to invest in more risky assets than other mutual funds. On the other hand, there are characteristics of pension plans such as defined benefits which decrease the comfortable amount of risk-taking. In the following subsections I will discuss the effects of the various characteristics on risk-taking and return.

2.2 Effect of the size on return and risk-taking

The most mentioned reason why size can have a positive effect on the return is the costs advantage of large plans. Bikker, Steenbeek and Torracchi (2010) explain this by arguing that overhead and other fixed costs are spread over a larger pool of participants and are therefore effectively lower. Andonov et al. (2012) agree with this, but emphasize that larger plans do also have lower investment costs due to their ability to negotiate lower fees. The costs advantage argument is supported by several studies (e.g.Bauer, Cremers, & Frehen, 2010; Bikker & De Dreu, 2009; Dyck & Pomorski, 2011; Tapia & Yermo, 2008). Another reason why larger plans have a higher return is mentioned by Dyck

(6)

6

and Pomorski (2011). They find evidence that larger plans are able to attract superior managers who outperform the managers of smaller plans.

Size can also have a negative effect on the return of investment. One reason for this phenomenon is mentioned by Chen, Hong, Huang and Kubik (2004) who study mutual funds. They argue that managers in larger plans need to find more stock ideas than in smaller plans and therefore invest in not-so-good ideas. In theory, this is not a problem since larger plans can have the same amount of assets and thereby the same workload per manager. However, Chen et al. argue that larger plans could behave different in practice. They empirically support this argument by observing that the underperformance of large plans who invest in small stocks is larger than in other large plans. Large plans who invest in small stocks need relatively more stock ideas, because increasing the position in small stocks will result in a price impact which decreases the return of this position. Their estimation therefore shows that large plans perform worse when they need relatively more investment ideas. This argument is supported by Andonov et al. (2012) and Bauer et al. (2010) for US pension plans. In addition, Bauer et al. (2010) argue that smaller plans have higher returns because large plans often offer jobs to well performing small cap managers. These managers have more expertise in managing a small than a large pension plan which results in relatively worse performances of large plans. A final reason for a negative effect of size on return can, according to Chen et al. (2004), be that larger organizations are more complex and have therefore a lower return. However, this argument has not been evaluated for pension plans.

In most of the above mentioned studies the overall effect of size on return are empirically estimated. Whereas some authors conclude that the effect is positive (Bikker & De Dreu, 2009; Bikker et al, 2010; Dyck & Pomorski, 2011; Tapia & Yermo, 2008), others conclude the opposite (Andonov et al, 2012; Bauer et al, 2010). The positive effect is, according to Bikker and De Dreu (2009) and Bikker et al. (2010), in the order of 0.8% meaning that a 1% increase in the number of participants decreases the operating costs by 0.85%. Dyck and Pomorski (2011) do also estimate that the largest plans have 0.4 percentage point lower costs than the smallest plans. On the other hand, Andonov et al. (2012) estimates a negative effect of 0.11-0.15 which implies that increasing the size with 1% decreases the return by 0.11-0.15 percentage points.4_{Bauer et al. (2010) estimate that}

smaller plans outperform other plans by 1.3-3%. Although there is also some empirical literature on the effect in mutual funds which both finds diseconomies and economies of scale, these studies are less relevant since pension plans have different characteristics than other funds.

At this point it is important to note that the effect of return on investment is difficult to estimate, because most datasets do not consist of information on the return or amount of assets.

4_{Whether the effect is measured in percentages or percentage points depends on whether the return is}

(7)

7

This is why most authors measure the effect by taking a proxy for these variables. Of the above mentioned authors, only Dyck and Pomorski (2011), Bauer et al. (2010) and Andonov et al. (2012) include the size in assets and return on investment in their estimation. Tapia and Yermo (2008) do also have information on the amount of assets, but use the proxy fees paid by participants to measure the return. Finally, Bikker and De Dreu (2009) and Bikker et al (2010) use proxies for both measures by estimating the effect of amount of participants on operating costs. Especially the latter proxy is highly debatable since most positive effects of the size on the return on investment are through the cost-channel whereas most negative effects are through the income-channel. This is further emphasized by authors who find a negative effect of size on return, but a positive on operating costs (Andonov et al., 2012; Bauer et al., 2010). The different findings between most authors could therefore presumably be explained by the use of proxies. To test this hypothesis, I will include an estimation with costs as proxy in this study (see subsection 2.6).

In Table 1 the most important features of the studies discussed above are presented. The difference between the estimated effects can, among others, be due to the number of observations, measures or countries.

Table 1 : Empirical literature on the effect of size of pension plans on the return

_observationsNumber of Country Measure for Return on

Investments Measure for size Effect of size on return Bikker and Dreu (2009) 8.515 Netherlands Operating costs _participantsAmount of Positive Bikker, Steenbeek and Torracchi

(2010) 450 Cross country Operating costs participants Amount of Positive Tapia and Yermo (2008) 15 Cross country Fees Assets Positive Andonov, Bauer and Cremers (2012) 11.697 US _investmentsReturn on Assets Negative Dyck and Pomorski (2011) 5.008 Multiple _investmentsReturn on Assets Positive Bauer, Cremers and Frehen (2010) 2.484 US _investmentsReturn on Assets Negative

Finally, there is literature on the effect of the size on the risk-taking of pension plans. Mohan and Zhang (2014) argue that larger pension plans have relatively lower transaction fees and are therefore able to invest more in equities and alternative investments. They estimate that an increase in the size of 1% increases the allocation to equities with 0.5 percentage points. Dyck and Pomorski (2011) do also find a positive relationship in the order of 0.6, but explain this by emphasizing that larger plans get preferential access to equity or real estate. Boon, Brière and Rigot (2014) and Rauh (2009) do also empirically estimate a positive effect of size on risk-taking, but do not offer a theoretical

(8)

8

explanation. Boon et al. (2014) estimate that an increase in pension assets of one billion increases the allocation to risky assets by 0.2% whereas Rauh (2009) estimates that increasing the size of plans with 1% leads to an increase of allocation to risky assets of 2-5 percentage points.

2.3 Effect of the type of a pension plan on its return and risk-taking

A pension plan can be characterized as a defined contribution (DC) or a defined benefit (DB) scheme. Contributions are the payments of participants to a pension plan whereas benefits are the money that participants receive when retired. DC schemes have a fixed contribution and pay a benefit which depends upon the return on assets. DB schemes, on the other hand, have a fixed benefit and demand a contribution necessary to pay this benefit (Blake, 2001; Bikker & De Dreu, 2009). Bikker and de Dreu (2009) estimate that DB schemes have 0.20% higher administration costs than DC schemes. They argue that this is because DC schemes are easier to manage. They also argue that DC could have higher marketing costs and costs of education in risk awareness. However, they find no empirical evidence for this argument and state that this is because participants have limited freedom in choosing their DC plan (which reduces marketing costs) and have no investment choices (which reduces costs of education). Blake (2001) and Benartzi and Thale (1999) theoretically study the effect of the type of scheme on risk-taking and come to the conclusion that DB schemes are less flexible in risk taking because DB schemes are required to pay a specific benefit. Distinguishing between the two schemes is not always possible according to Blake (2001), who shows that DB schemes are in reality sometimes DC schemes which are managed in such a way that it has fixed benefits.

Plan types can also be grouped in single-employer (SE), multiemployer (ME) and multiple employer (MPE) plans. Single-employer plans are plans where participants have only one employer whereas multiemployer and multiple employer plans have more than one employer. Before 2008, all three types of plans had some flexibility in choosing their assumptions with regard to the discount rate and mortality tables (Kisser, Kiff, & Soto, 2014, pp. 8-9; Munnell & Aubry, 2014, pp. 4-5; GAO, 2014, pp. 9-10). However, this changed with the US Pension Protection Act of 2006 stating that single-employer plans should be treated different, because of the risks associated with having only one sponsor. This act came into force in 2008 and required single-employer and multiple employer plans to use specified mortality tables and discount rates.

Another difference between multiemployer, multiple employer and single-employer plans is that the first is a union plan which is collectively bargained while the others are not (26 US Code §414). Participants who engage in a collectively bargained plan do usually have more bargaining power than participants in other plans (Allen & Clark, 1986; Even & Macpherson, 2010). Allen and Clark (1986) argue that this results in a distribution of wealth from younger to older participants,

(9)

9

because older participants are more actively involved. However, this does not influence the estimated effects of this study, because the distributions are not regarded as expenses. This issue will be further clarified in the next section. Furthermore, Allen and Clark (1986) and Even and Macpherson (2010) mention another characteristic of a collectively bargained plan. They argue that participants have more collective resources to monitor their pension plans which results in a more desired plan for the participants. However, these authors differ in the practical implications of a more desired plan. Allen and Clark argue that participants would then have a higher demand for pension benefits, which increases the size of a pension plan. Collectively bargained plans, such as the multiemployer plans, could therefore be larger than other plans. However, Even and Macpherson make the argument that this results in the allocation of a plan’s resources towards union members’ goals. A plan could for example sponsor loans of participants which are below market value. The authors support this argument by observing from Form 5500 data that multiemployer plans have a lower return on investments of 0.5-0.7 percentage points.

2.4 Effect of the funding ratio on return and risk-taking

The third determinant of return on investment and risk-taking is the financial position of a pension plan. The authorities measure the financial position of a plan by looking at their funding ratio. The funding ratio is calculated as the current value of the assets of a plan divided by its liabilities. The liabilities of a plan are equal to the present value of the future benefit payments. The present value is calculated using a specific discount rate. A higher discount rate results in a lower present value and vice versa. The discount rate is specified by legislation and differs among different type of plans and countries. For example, US public plans can use a different discount rate than US private plans. This will be further explained later on in this subsection. The effect of the funding ratio is only present in DB plans, since DC plans promise participants specified retirement benefits and have therefore, by definition, a funding ratio of 100% (Atanasova & Gatev, 2009; Cooper & Ross, 2003). A pension plan is called underfunded if the funding ratio is lower than 100%.

From an underfunded perspective there is a trade-off in risk-taking. A pension plan can decrease their risk-taking so the situation will not worsen further (An et al. 2012; Novy-Marx & Rauh, 2009). However, decreasing risk-taking also lowers the possibility of higher returns which can improve the situation.5_{From an overfunded perspective, the situation is slightly different. If}

participants of a plan will not profit from the surplus of assets, then an overfunded plan would act in the interest of its participants by decreasing its risk-taking and thereby lowering its downside risk

5_{In for example the Netherlands, regulating authorities limit the risk-taking of underfunded plans during their}

(10)

10

(Bodie, Light & Morck, 1987, p. 17). This is however not always the case for US plans who can distribute the surplus to participants if they have a funding ratio of 125% or higher (Yermo & Severinson, 2010).

Several studies have shown that underfunded plans decrease their risk-taking. Rauh (2009) estimates that decreasing the funding ratio with one percentage point decreases risk-taking with 0.05-0.07 percentage points. Atanasova and Gatev (2009) study the effect using Form 500 data and conclude that decreasing the funding ratio with one percentage point decreases volatility with 0.7%. However, they also show that very well-funded pension plans engage in less risk-taking. Crossley and Jametti (2008) and Brown (2008) argue that the negative effect of the funding ratio on risk-taking is reduced by the moral hazard problems which arise from the Pension Benefit Guaranty Corporation (PBGC). The Pension Benefit Guaranty Corporation guarantees a limited retirement income of participants of private US pension plans. The negative consequences of underfunding will therefore be borne by the Pension Benefit Guaranty Corporation which reduces the incentive of individuals to improve the plan’s funding status. The authors test this hypothesis empirically for US, Canadian and UK pension plans and conclude that insured plans invest 2.2% more in risky assets than uninsured plans.

While the studies carried out estimate a positive effect of the funding ratio on risk-taking in the US private sector, the opposite appears to be true in the US public sector. Andonov et al. (2014) and Mohan and Zhang (2012) find that underfunded US public plans increase their risk-taking in order to camouflage their underfunding with a higher discount rate. The underlying idea is that US public plans use the expected return in order to choose a discount rate. More risky assets have a higher expected return which results in a higher discount rate. A higher discount rate decreases the liabilities of a pension plan and thereby improves the funding ratio. The estimated effect of Andonov et al. (2014) is in the order of -0.08 meaning that a decrease of one percentage point in the funding ratio increases the allocation to risky assets by 0.08 percentage point. The estimated effect of Mohan and Zhang (2012) is -0.04.

2.5 Effect of the characteristic of participants on return and risk-taking

The final determinant of return on investment and risk-taking is the characteristic of the participants in a pension plan. Participants can be categorized as active, retired or sleepers. Active participants are contributing to the plan and do not yet receive benefits. Retired (or separated) participants are not contributing and receive benefits. Sleepers are retired or separated participants entitled to future benefits. Bikker and De Dreu (2009) show that the characteristics of participants effects the return on investment through the administrative and investment costs. They conclude that

(11)

11

increasing the share of retired participants by one percentage point increases administrative costs by 0.6% whereas increasing the share of sleepers lowers administrative costs by 0.3%. The negative effect of sleepers on administrative costs is neutralized by the positive effect on investment costs of 0.3%. They do not offer an explanation for these results. Other authors argue that the characteristic of participants influences return through risk-taking (Basu & Drew, 2007; Mohan & Zhang 2014; Rauh, 2009). The main argument is that pension plans can increase risk-taking and thereby the return on investments when participants are young, because the pay-out time lies further ahead. Mohan and Zhang (2014) estimate that increasing the share of retired participants with one percentage point decreases allocation to equity with 0.02 percentage points whereas Rauh (2009) estimates that the effect is in the order of 0.04 percentage points. Andonov et al. (2014) come to the same conclusion for US private pension plans, but find that the opposite holds for US public plans. They estimate that increasing the share of retired participants with one percent increases allocation to risky assets by 0.2 percent. Their explanation is that public plans with older participants invest in riskier assets, because they have a shorter maturity of their promised benefits which limits their ability to camouflage their underfunding. These pension plans want to improve their funding ratio by using a higher discount rate and justify a higher discount rate by engaging in more risk-taking.

2.6 Disentangle the effect on income and operating costs

In the previous subsections, I explained two different channels in which the determinants effect the return. The return on investment consists of income minus operating costs. Some authors (e.g. Bauer et al. 2010; Chen et al. 2004) argue that the size, funding ratio, type and characteristic of participants effect the return through income whereas others (e.g. Andonov et al. 2012; Bikker et al. 2010) argue that these variables effect the return through operating costs. Andonov et al. (2012) tries to disentangle these two effects by estimating what the effects are on the return on investment and on the operating costs. For example, if the effect of size on the return is positive while the effect on the operating costs is zero, then the effect on the return is through income. Vice versa, if the effect of size on the return is 0.2 and the effect of size on operating costs is -0.2, then the effect on the return is through operating costs. Apart from Andonov et al. (2012) there is no literature which tries to disentangle the effects on income and operating costs. This is probably because of the limited availability of data. I will follow the approach of Andonov et al and include a regression with operating costs as dependent variable.

Another reason for including a regression with operating costs as dependent variable is described in the subsection 2.2. In this subsection I showed that some authors estimate a positive effect on the return whereas other authors estimate a negative effect. I argued that this is probably

(12)

12

caused by the use of proxies for the return on investment. For example, Bikker et al. (2010) estimate economies of scale using operating costs as dependent variable. On the other hand, Bauer et al. (2010) estimate diseconomies of scale using the return on investments. Including a regression with operating costs as dependent variable can support or weaken the argument that proxies cause these different results.

(13)

13

3 Data

3.1 Form 5500 Data

The data that will be used in this study for answering the research questions consists of the Form 5500 Private Pension Plan Research Files datasets ranging from 2000 to 2012. Every year all private pension plans in the United States are required to declare general, financial and actuarial information. Each year the Employee Benefits Security Administration’s Office of Policy Research prepares a summary of the general and financial information in which it corrects for duplicates and unfiled plans. I follow their corrections by deleting the observations which they identified as duplicates. Furthermore, I drop 56 ‘missed’ duplicates and 1,639 pension plans which cannot be identified as defined contribution or benefit. After dropping these plans, I end up with an unbalanced dataset of 3,165,773 pension plan filings.

The thus prepared datasets comprises of information on the return on investments, risk-taking in investments, size, characteristics of participants and type. However, the available data from Employee Benefits Security Administration’s Office of Policy research does not include information about the funding ratio. I therefore combine this dataset with the raw, unedited Form 5500 Schedule B, MB and SB filings. Unfortunately, these Schedules are neither filed by all pension plans from 2000-2012 nor have uniform measures. From 2000-2007 all defined benefit plans (and certain money purchase defined contribution plans) were required to file Schedule B. This changed with the Pension Protection Act of 2006 which came into force in 2008 and replaced Schedule B by Schedule MB and SB. From 2008-2012 filing of Schedule MB was required by all multiemployer defined benefit plans (and certain money purchase defined contribution plans) whereas filing of Schedule SB was required by all single-employer and multiple employer defined benefit plans. The 2008’s Schedule MB and SB, however, are not available for public use.

As mentioned previously, the Schedules also differ in terms of measures. Schedule B and MB contain the Current Liability (CL) of a pension plan whereas Schedule SB contains the Funding Target (FT). The Current Liability and Funding Target are similar concepts and capture the present value of a plan’s benefits payable (Kisser et al., 2014). However, the Current Liabilities is based on RPA 94 legislation while the Funding Target uses the methods and assumptions of ERISA sections 303(h) and (i). The Current Liabilities use therefore a weighted average of 30-year constant-maturity Treasury bond yields and the GAM-83 mortality table whereas the Funding Target uses a 24-month average of high quality corporate bonds of varying maturities and the RP-2000 mortality table. The RP-2000 mortality values are generally 2-11 percent higher for males than the GAM-83 values and 3-5 percent lower for females (Society of Actuaries, 2001).

Apart from the differences between measures, the assumptions on which measures are based do also change over the years. In 2012 the US government signed the MAP-21 Act (Kisser et

(14)

14

al., 2014). This changed the calculation of the Funding Target by installing a corridor for the discount rate using a long-term average of 25 years. Pension plans could use the corridor’s (higher) discount rate when the discount rate falls below this corridor. A higher discount rate decreases a plan’s liabilities and thereby increases the funding ratio. Pension plans in the US could either adapt this new discount rate in 2012 or 2013. The result is that some pension plans already adapted the discount rate in 2012 whereas others did not. The Funding Targets of different plans in 2012 are therefore not comparable unless it is possible to determine which plans adopted the new legislation. I determine this by following Kisser et al. (2014) who identify pension plans with the new discount rate by estimating whether the discount rate changed significantly over the last three years.

Since the Funding Target and Current Liability are different measures, I intend to include a balanced panel dataset from 2000-2007 using Schedule B, 2000-2012 using Schedule B and MB and 2009-2012 using Schedule SB and MB. In order to match these datasets with the Form 5500 Private Pension Plan Research Files, I use the filing ID from 2000 to 2007 and the acknowledgement ID from 2009 to 2012. To enable this, I drop all pension plan filings with filing ID’s which could not be uniquely identified. This resulted in the loss of 21,318 observations in the 2000-2007 dataset and 52.592 observations in the 2000-2012 dataset. After each correction, I rebalance the dataset. The result is that all pension plans need to be deleted which had a plan filing with no unique filing ID. Fortunately, all acknowledgement ID’s are unique.

Apart from the corrections necessary to merge the datasets, I also exclude plans with less than 121 participants and drop outliers and missing observations. A reason for excluding plans with less than 121 participants is mentioned by Bikker, Knaap and Romp (2014) who argue that small pension plans could be distinguished tax vehicles. Furthermore, I exclude the following outliers. I do not include pension filings which filed a return on investments under -100% or over 50%.6_The

returns over 50% (or under -100%) are mainly caused by a very high (low) unrealized return of assets or in some cases a typing error and do therefore not represent the income during the particular year. I do also not include plans which experienced an increase in assets of 100% or higher since these are most likely the result of a merger and could bias the results. Moreover, I exclude plans which filed an allocation to risky assets under 0% or over 100% since these plans are clearly not intended to provide a safe but affordable stream of income after retirement. Furthermore I only include filings with a funding ratio between 20% and 300%. Besides these outliers, I drop pension plans which have a year in which they did not file any information on the return on investment, amount of assets or funding ratio. The datasets that have been established in the above manner, make a thorough analysis of the return on investment possible.

6_{This return on investment is, contrary to the measure used in the estimation, based on the total income}

(15)

15

3.2 Explanatory variables

For answering the research questions, I define the following explanatory variables: size of assets, characteristic of participants, type of plan and funding ratio. The size of assets is the current value of total assets at the beginning of the year as filed in Schedule H of the Form 5500. In order to determine the size of assets, pension plans use the fair market value (26 US Code §430). Information on whether participants are active, retired or sleepers and whether a plan is single-employer, multiemployer or multiple employer as well as the existence of defined benefit or defined contribution can be identified from the dataset. The funding ratio is obtained from Schedule B, SB and MB and calculated as the current value of total assets at the beginning of the year divided by the current liability or funding target. The interest rate used to compute the current liability must be in accordance with guidelines issued by IRS and can vary among different plans. The instructions of the Form 5500 state that the current value of assets in Schedule B, SB and MB should not be different from Schedule H. In practice these amounts do slightly differ, but less than 1%.

3.3 Dependent variables

Apart from the independent variables I also define the following dependent variables: return on investment and risk-taking. The return on investment is the total income from investments minus the operating costs divided by the total assets multiplied by 100. In the literature section I described that the determinants can have an effect on the return through the income or operating costs. This is emphasized by the return on investment which consists of the income minus the operating costs. The operating costs consist of interest and administrative costs. Unlike Kisser et al. (2014) I do not include benefit payments or distributions among participants in operating costs since these do not reflect any change in the sum of value for the participants of a plan. For example, imagine two pension plans with the same income and interest and administrative costs: one with a high share of retired participants and one with a low share. Including benefit payments in operating costs would imply that the plan with more retired participants would have a lower return on investment, because it will have to pay the necessary benefits. In my view this does not measure the investment performance of a plan and I therefore exclude these costs. The total income from investments includes interest; dividends; rents; net gain (loss) on sale of assets; unrealized appreciation (depreciation) of assets; all net investment gains (losses) from common collective trusts, pooled separate accounts, master trust investment accounts, 103-12 investment entities and registered investment companies and other income. The total income from investments does not consist of contributions by participants or transfers in or out the plan.

(16)

16

The variable risk-taking in investments is the percentage allocated to risky assets at the beginning of the year. I define risky assets as allocations to equity and non-risky assets as cash and fixed income investments. This definition is in line with Kisser et al. (2014) who use the same measure in their Form 5500 dataset. An alternative definition is the one used by Andonov et al. (2014) who differ by including non-preferred corporate debt in the share of risky assets. They therefore make a distinction between risky and non-risky fixed income investments. Risky fixed income investments include non-preferred corporate debt instruments and construction, securities, commercial, residential mortgage and participation loans whereas non-risky fixed income assets include U.S. government securities and preferred corporate debt instruments. I include the estimations of the effects on both measures to check whether this makes a difference.

3.4 Balanced datasets

Using the Form 5500 data as a starting point, I constructed three different balanced panel datasets. Table 2.1, 2.2 and 2.3 consist of summaries of the balanced dataset 2000-2007, 2000-2012 and 2009-2012. Observations from 2008 are missing in all three datasets due to reasons mentioned above. The information is split among the different type of the pension plans in which SE stand for single-employer, ME for multiemployer and MPE for multiple employer. The number of observations show that the majority of plans are single-employer plans. Single-employer and multiple employer plans are more often characterized as a defined contribution plan whereas multiemployer plans are more often characterized as a defined benefit plan.

The return on investments (ROI) and risk-taking varies both among the type of plans in terms of employer status as whether the plans are characterized as DC or DB. The return and risk-taking are generally lower in multiemployer plans than in single-employer and multiple employer plans. A lower return on investment in plans is also observed by Evan and Macpherson (2010) who argue that this is the result of the allocation of a plan’s resources towards unprofitable union goals. Following the reasoning of Evan and Macpherson (2010) and Allen and Clark (1986), the lower risk-taking could also be explained by the preferences of participants. However, this could also be caused by underlying reasons such as a higher share of retired participants. The next section will clarify how these effects will be identified. Apart from the type of employer, it also matters for the return and risk-taking whether a plan is DC or DB. Defined contribution plans have a higher return on investment. This is in line with the findings that defined contribution plans are more flexible in risk-taking and have lower administration costs (see e.g. An et al., 2012; Bikker & De Dreu, 2009; Blake, 2001;).

(17)

17

Table 2.1 : Summary variables of DB & DC Balanced Set 2000-2007

_DB _DC SE ME MPE SE ME MPE Observations 27,501 3,558 741 129,712 3,091 4,135 ROI _{(-4.84 | 23.69)}10.32 _{(-3.10 | 18.00)}8.45 _{(-3.97 | 23.35)}10.12 _{(0.38 | 28.60)}15.54 _{(3.35 | 23.06)}13.39 _{(0.91 | 29.40)}16.42 %Risky Assets _{(56.72 | 100)}84.97 _{(46.21 | 98.09)}69.62 _{(59.09 | 100)}83.10 _{(83.57 | 100)}94.02 _{(30.65 | 99.23)}77.33 _{(84.10 | 100)}93.94 %Risky Assets Andonov Method (66.83 | 100) 87.93 (53.81 | 98.07) 76.78 (69.49 | 100) 87.60 (84.42 | 100) 94.36 (43.43 | 99.25) 81.33 (85.15 | 100) 94.42 Assets _{(3,118,137 | 208,000,000)}176,000,000 _{(10,700,000 | 560,000,000)}275,000,000 _{(5,867,705 | 648,000,000)}419,000,000 _{(1,496,386 | 62,600,000)}54,900,00 _{(3,770,655 | 169,000,000)}64,900,000 _{(2,127,228 | 173,000,000)}118,000,000 Funding Ratio CL _{(74.02 | 126.35)}97.77 _{(59.74 | 104.29)}81.18 _{(77.84 | 131.07)}101.22 - - - %Retired _{(2.33 | 43.96)}20.88 _{(22.53 | 47.81)}32.00 _{(2.46 | 39.85)}19.06 _{(0 | 1.5)}0.8 _{(0 | 5.74)}2.97 _{(0 | 1.70)}0.86 %Sleeping _{(9.51 | 46.72)}26.61 _{(6.93 | 36.93)}20.40 _{(8.98 | 43.07)}24.97 _{(3.16 | 31.06)}15.72 _{(0 | 45.57)}13.25 _{(3.35 | 32.09)}16.18 %Active _{(21.17 | 80.03)}52.52 _{(26.02 | 67.25)}47.60 _{(29.34 | 78.82)}55.97 _{(67.78 | 96.21)}83.47 _{(48.21 | 100)}83.78 _{(66.77 | 96.09)}82.96 Excluded: Outliers in ROI, FR, RA, Size and Participants and missing observations in ROI, RA, Size & FR

(18)

18

_DB _DC SE ME MPE SE ME MPE Observations 29,579 4,000 1,017 147,320 4,427 5,417 ROI _{(-8.21 | 23.81)}9.41 _{(-7.12 | 19.31)}7.53 _{(-5.51 | 23.69)}9.92 _{(-4.49 | 28.16)}13.38 _{(-0.15 | 22.65)}11.61 _{(-3.53 | 28.86)}14.03 %Risky Assets _{(57.51 | 100)}85.26 _{(48.75 | 98.03)}72.89 _{(55.47 | 100)}82.77 _{(84.64 | 100)}94.58 _{(34.45 | 99.40)}80.52 _{(84.26 | 100)}94.46 %Risky Assets Andonov Method (68.00 | 100) 88.23 (57.56 | 98.02) 79.30 (67.42 | 100) 87.87 (85.27 | 100) 94.85 (50.37 | 99.41) 84.37 (85.56 | 100) 94.83 Assets _{(3,988,138 | 239,000,000)}162,000,000 _{(11,600,000 | 626,000,000)}286,000,000 _{(7,344,831 | 916,000,000)}662,000,000 _{(2,017,040 | 85,300,000)}69,700,000 _{(4,650,834 | 215,000,000)}84,600,000 _{(3,113,574 | 213,000,000)}152,000,000 Funding Ratio CL _{(74.59 | 126.61)}98.09 _{(43.00 | 100.40)}71.34 _{(78.63 | 125.83)}99.58 - - - Funding Ratio FT _{(75.35 | 115.88)}93.82 - _{(75.19 | 118.63)}95.25 - - - %Retired _{(3.15 | 46.16)}22.90 _{(16.49 | 49.25)}33.44 _{(3.07 | 41.86)}20.60 _{(0 | 1.71)}0.86 _{(0 | 5.79)}2.75 _{(0 | 1.81)}0.85 %Sleeping _{(10.68 | 48.03)}27.89 _{(7.42 | 37.53)}21.10 _{(11.95 | 46.17)}27.15 _{(3.70 | 32.04)}16.39 _{(0 | 50.05)}14.27 _{(4.22 | 33.22)}17.15 %Active _{(34.19 | 77.16)}49.21 _{(25.29 | 64.58)}45.46 _{(24.26 | 77.09)}52.25 _{(66.67 | 95.71)}82.75 _{(46.13 | 100)}82.98 _{(66.00 | 95.10)}82.00 Excluded: Outliers in ROI, FR, RA, Size and Participants and missing observations in ROI, RA, Size & FR

The first number is the mean whereas the numbers between brackets represent the 10% and 90% percentile

Note that the Current Liability is filed by all DB plans before 2008 and only by DB ME plans after 2008 whereas the Funding Target is only filed by DB SE and MPE plans after 2008

(19)

19

_DB _DC SE ME MPE SE ME MPE Observations 18,272 2,099 705 161,256 3,740 5,417 ROI _{(6.08 | 25.79)}15.94 _{(4.21 | 21.92)}13.79 _{(5.37 | 25.23)}14.68 _{(6.59 | 31.83)}19.14 _{(2.93 | 24.63)}13.45 _{(7.47 | 32.27)}20.13 %Risky Assets _{(61.70 | 100)}87.40 _{(56.72 | 98.14)}79.61 _{(50.88 | 100)}81.65 _{(87.54 | 100)}95.73 _{(45.26 | 99.47)}83.95 _{(88.52 | 100)}96.06 %Risky Assets Andonov Method (73.33 | 100) 90.26 (66.57 | 98.12) 84.69 (65.45 | 100) 87.79 (87.84 | 100) 95.90 (61.47 | 99.47) 87.69 (88.73 | 100) 96.25 Assets _{(4,123,285 | 323,000,000)}225,000,000 (11,400,000 | 333,000,000 698,000,000) 600,000,000 (7,052,905 | 1,150,000,000) 52,700,000 (1,312,333 | 143,000,000) (353,507 | 320,000,000) 85,100,000 (1,903,066 | 111,000,000) 108,000,000 Funding Ratio CL - _{(36.03 | 68.13)}51.48 - - - - Funding Ratio FT _{(75.23 | 118.28)}95.26 - _{(75.43 | 115.67)}94.59 - - - %Retired _{(3.61 | 52.61)}27.02 _{(18.31 | 52.77)}36.59 _{(4.75 | 42.84)}23.69 _{(0 | 1.69)}0.92 _{(0 | 6.74)}3.43 _{(0 | 1.54)}0.83 %Sleeping _{(12.40 | 53.16)}31.78 _{(9.08 | 40.81)}23.73 _{(13.64 | 51.76)}32.14 _{(3.95 | 35.86)}17.98 _{(0 | 53.73)}16.54 _{(4.41 | 32.96)}17.23 %Active _{(8.65 | 73.13)}41.20 _{(18.15 | 64.46)}39.68 _{(20.09 | 71.80)}44.16 _{(62.84 | 95.45)}81.10 _{(41.15 | 100)}80.11 _{(65.84 | 95.02)}81.94 Excluded: Outliers in ROI, FR, RA, Size and Participants and missing observations in ROI, RA, Size & FR

The first number is the mean whereas the numbers between brackets represent the 10% and 90% percentile

(20)

20

The amount of assets does also strongly vary among the type of plans. The largest difference is between defined contribution and benefit pension plans in which the latter is generally larger. There are also differences between single-employer, multiemployer and multiple employer plans in terms of size. Multiple employer plans are on average larger than multiemployer plans. This is contrary to the belief of Allen and Clark (1986) who argue that the presence of a union increases the size of multiemployer plans. Furthermore, both multiple employer and multiemployer plans are larger than single-employer ones. This makes sense, because there is a limit to the amount of employees employed under the same employer.

The funding ratio is only filed for defined benefit plans since defined contribution plans have no fixed future obligations towards participants and their liabilities are therefore by definition equal to their assets. Furthermore, starting in 2009 the funding ratio is filed using the Current Liability (CL) for multiemployer plans and using the Funding Target (FT) for single-employer and multiple employer plans. The means of the funding ratio show that multiemployer pension plans are more poorly funded than the others, even though they have more freedom in choosing their assumptions necessary to determine their Current Liability. There is no solid explanation for this in the literature. In addition , the funding ratios of multiemployer plans significantly worsened after the crisis of 2008. This did not happen for single-employer and multiple employer plans. However, it is important to note that single-employer and multiple employer plans filed their funding ratio using the Funding Target instead of Current Liability after 2008. These measures are therefore not easily comparable.

The last explanatory variable is the shares of retired, sleeping and active participants. Defined contribution pension plans have almost no retired participants which indicates that the assets of a participant are changed into a fixed income stream at retirement (Australian Centre for Financial Studies, 2013; United States Department of Labor, 2015). Moreover, multiemployer plans have a higher share of retired participants. This can either reflect the argument of Allen and Clark (1986) that plans are friendlier towards older participants or that multiemployer plans grow out of fashion. Furthermore, the share of retired participants slightly increases over time, which is probably due to the ageing population which can be seen in the upcoming graphs.

Graph 1 shows the means and the 10th_{and 90}th_{percentiles of the return on investment,}

allocation to risky assets, size, funding ratio (CL) and the share retired participants over the years in the balanced set 2000-2012. The trend in the return on investment, size and funding ratio consist of two significant drops. The first drop is around 2001 and represents the burst of the dot com bubble whereas the second drop is larger and represents the crisis of 2008. These drops are also present in the allocation to risky assets which is less self-evident, but also makes sense. The allocation to risky assets is compromised as the percentage of assets allocated in equities valued at market prices. These market prices drop during a crisis which makes the percentage goes down. Other interesting

(21)

21

features are the general time trends of different variables. Over time there is an increase in size, share of retired participants and allocation to risky assets. The increase in size is explained by inflation and population growth whereas the increase in retired participants is a reflection of the ageing population and higher life expectancy. However, the increase in allocation to risky assets is more interesting and shows that plans increased their risk-taking during the last couple of years. This is even more remarkable since the funding ratio decreased and share of retired participants increased: two effects which should decrease the risk-taking. The last observation from these graphs is that the funding ratio of defined benefit plans has not quite recovered from the last crisis.

Graph 1: Means and 10th_{and 90}th_{percentiles of return, allocation to risky assets, size, funding ratio and}

(22)

22

3.5 Variants

As mentioned above, I have three different balanced panel datasets: 2000-2007, 2000-2012 and 2009-2012. It is not possible to estimate the effect of the size, funding ratio, type and characteristic of participants using all data within these datasets, because the funding ratio differs in measure and assumptions for different types of plans and years and is not filed at all by defined contribution plans. The datasets are therefore split into the following variants, which are shown in Table 3.

Table 3 : Variants of datasets

_{Defined Benefit Plans} Defined Contribution Plans with Funding _{Ratio = 100}

SE ME MPE SE ME MPE

Balanced 2000-2007 DB only yes yes yes no no no

Balanced 2000-2007 DB & DC yes yes yes yes yes yes

Balanced 2000-2012 DB (ME) only no yes no no no no

Balanced 2000-2012 DB (ME) & DC no yes no yes yes yes

Balanced 2009-2012 DB only (ME) no yes no no no no

Balanced 2009-2012 DB (ME) & DC no yes no yes yes yes

Balanced 2009-2012 DB only (SE & MPE) yes no yes no no no

Balanced 2009-2012 DB (SE & MPE) & DC yes no yes yes yes Yes

The 2000-2007 dataset will be split into two variants: one with only defined benefit plans and one using defined benefit and contributions plans in which the funding ratio for the latter is set equal to 100. Setting the funding ratio equal to 100 for defined contribution plans is done because these plans have no fixed obligations and are therefore fully funded by definition. The 2000-2012 dataset will not be estimated using single-employer and multiple employer defined benefit plans since these plans changed their liabilities measure from Current Liability to Funding Target in 2008. Instead, this dataset will be split into an estimation with multiemployer defined benefit plans only and one with multiemployer defined benefit and all defined contribution plans (in which the funding ratio is set equal to 100). The last 2009-2012 dataset is split into four different variants. The first variant only includes multiemployer defined benefit pension plans while the second only includes single-employer and multiple single-employer defined benefit plans. This distinction is made, because multiemployer plans filed the Current Liability whereas single-employer and multiple employer plans

(23)

23

used the Funding Target. 7_{In the third and fourth variant the multiemployer defined benefit and}

single-employer and multiple employer defined benefit plans will be appended by defined contribution plans in which the funding ratio is set equal to 100. After splitting al variants, I rebalanced the datasets which results in dropping around 0,5% of the observations. This is because some plans changed their status from defined benefit to defined contribution or from single-employer to multi-single-employer or multiple single-employer and vice versa.

7_{I will drop all single-employer and multiple employer plans in 2012 who adopted the new legislation. This}

results in the loss of 3.807 out of 18.977 observations in 2012. Since I rebalance the dataset, the total amount of dropped observations is 15.228. Furthermore, I also drop some multiple employer observations which did not file a Funding Target.

(24)

24

4 Methodology

In all variants of the datasets used, I estimate the effect of the size, characteristics of participants, type and funding ratio on the return, and risk-taking of pension plans. The first estimation is therefore the following in which 𝑖𝑖𝑖𝑖𝑖𝑖 stands for the return on investments; 𝑠𝑠𝑖𝑖𝑖𝑖 is the size of a pension fund which is estimated by taking the logarithm8_{; 𝑝𝑝𝑝𝑝}

𝑖𝑖𝑖𝑖 refers to the percentage of retired participants and 𝑝𝑝𝑠𝑠𝑖𝑖𝑖𝑖 to the percentage of sleepers in a pension fund; 𝑓𝑓𝑝𝑝𝑖𝑖𝑖𝑖 is the funding ratio of the pension fund. The 𝐷𝐷𝐷𝐷𝑖𝑖𝑖𝑖, 𝑀𝑀𝑀𝑀𝑀𝑀𝑖𝑖𝑖𝑖 and 𝑀𝑀𝑀𝑀𝑖𝑖𝑖𝑖 are three dummy variables which define whether a plan is a defined contribution or benefit plan and whether it is a single-, multiple employer (MPE) or multiemployer (ME) plan. If the variable of the defined contribution plan is zero then the plan has a defined benefit status. If the variables for multiple employer and multiemployer plan are zero, then the plan is a single-employer plan. The second estimation differs only in the dependent variable which is the risk-taking (𝑝𝑝𝑖𝑖𝑖𝑖) instead of the return (𝑖𝑖𝑖𝑖𝑖𝑖). All estimations include dummies for the year effects (𝑦𝑦𝑖𝑖) to measure the effects of stock markets and interest rates in given year. The subscript t indicates the year and the subscript i indicates the fund, So 𝑥𝑥𝑖𝑖𝑖𝑖 is the value of a variable x in a pension plan during a certain year.

(1) 𝑖𝑖𝑖𝑖𝑖𝑖= 𝛼𝛼𝑖𝑖+ 𝛽𝛽1∙ log(𝑠𝑠𝑖𝑖𝑖𝑖) + 𝛽𝛽2∙ 𝑝𝑝𝑝𝑝𝑖𝑖𝑖𝑖+ 𝛽𝛽3∙ 𝑝𝑝𝑠𝑠𝑖𝑖𝑖𝑖+ 𝛽𝛽4∙ 𝐷𝐷𝐷𝐷𝑖𝑖𝑖𝑖+ 𝛽𝛽5∙ 𝑀𝑀𝑀𝑀𝑀𝑀𝑖𝑖𝑖𝑖+ 𝛽𝛽6∙ 𝑀𝑀𝑀𝑀𝑖𝑖𝑖𝑖+ 𝛽𝛽7∙ 𝑓𝑓𝑝𝑝𝑖𝑖𝑖𝑖+ 𝛽𝛽6∙ 𝑦𝑦𝑖𝑖+ 𝑣𝑣𝑖𝑖𝑖𝑖+ 𝑒𝑒𝑖𝑖

(2) 𝑝𝑝𝑖𝑖𝑖𝑖= 𝛼𝛼𝑖𝑖+ 𝑥𝑥1∙ log(𝑠𝑠𝑖𝑖𝑖𝑖) + 𝑥𝑥2∙ 𝑝𝑝𝑝𝑝𝑖𝑖𝑖𝑖+ 𝑥𝑥3∙ 𝑝𝑝𝑠𝑠𝑖𝑖𝑖𝑖+ 𝑥𝑥4∙ 𝐷𝐷𝐷𝐷𝑖𝑖𝑖𝑖+ 𝑥𝑥5∙ 𝑀𝑀𝑀𝑀𝑀𝑀𝑖𝑖𝑖𝑖+ 𝑥𝑥6∙ 𝑀𝑀𝑀𝑀𝑖𝑖𝑖𝑖+ 𝑥𝑥7∙ 𝑓𝑓𝑝𝑝𝑖𝑖𝑖𝑖+ 𝑥𝑥8∙ 𝑦𝑦𝑖𝑖+ 𝑜𝑜𝑖𝑖𝑖𝑖+ 𝑞𝑞𝑖𝑖

To estimate these equations, I use three different estimation methods. The first method is a fixed effects model which is regarded as a solution to the bias which results from omitted variables which vary over entities but stay constant over time (Stock & Watson, 2012, pp. 396-403). The second model is a fixed effects vector decomposition model (fevd) as proposed by Plümper and Troeger (2007). The advantage of the Plümper and Troeger’s fevd procedure compared to ordinary fixed effects models is that the fevd procedure can estimate the effect of variables with no within variance (i.e. time invariant variables) or only a little. A standard fixed effects model will not correctly estimate the effect of a time invariant variable, because the model only measures the effect of changes in a given entity over the years. Since the time invariant variables do not change or change only a little, the fixed effects model will only measure the effect of these little changes. It can therefore not correctly estimate the effect of the difference between a pension plan of $1,000,000,000 and $500,000. Using the fevd procedure is supported by Bikker et al. (2012, p. 16) who argue that a standard fixed effects model will wipe out the size of a pension plan and thereby

8_{Taking the logarithm of the size results in approximately 150 missing observations, because some plans filed 0}

(25)

25

affect the estimation of economies of scale. I therefore assume that the size and type of pension plans are the time-invariant variables.

I will proceed by taking the following steps. I start by explaining Plümper and Troeger’s fevd procedure and the conditions under which this model outperforms standard fixed effects models. These conditions are that the between variation is sufficiently larger than the within variation and the correlation between the rarely changing variables and unit effects is sufficiently low. After describing the procedure and the conditions, I calculate the between/within variation and estimate the correlation between the rarely changing variables and unit effects to determine whether the fevd procedure is applicable for a certain variable.

4.1 The FEVD model

The first step in obtaining the time invariant effects is to estimate the entity effects 𝑢𝑢�𝑖𝑖 and 𝑐𝑐̂𝑖𝑖. The entity effects include all time-invariant variables, the overall constant term and the mean effects of the time-varying variables. In other words, it includes all effects which differ among pension plans but not over time and thereby excludes all time-varying effects. To obtain this entity effect Plümper and Troeger (2007) start by estimating a standard fixed effects model without the time-invariant variables. The fixed effects transformation can be derived by first averaging equation (1) and (2) over time:

(3) 𝚤𝚤̅𝑖𝑖= 𝛼𝛼𝑖𝑖+ 𝛽𝛽1∙ log(𝑠𝑠𝑖𝑖) + 𝛽𝛽2∙ 𝑝𝑝𝑝𝑝��𝑖𝑖+ 𝛽𝛽3∙ 𝑝𝑝𝑠𝑠��𝑖𝑖+ 𝛽𝛽4∙ 𝐷𝐷𝐷𝐷𝑖𝑖𝑖𝑖+ 𝛽𝛽5∙ 𝑀𝑀𝑀𝑀𝑀𝑀𝑖𝑖𝑖𝑖+ 𝛽𝛽6∙ 𝑀𝑀𝑀𝑀𝑖𝑖𝑖𝑖+ 𝛽𝛽7∙ 𝑓𝑓𝑝𝑝��𝑖𝑖+ 𝛽𝛽8∙ 𝑦𝑦� + 𝑣𝑣̅𝑖𝑖+ 𝑒𝑒𝑖𝑖

(4) 𝑝𝑝̅𝑖𝑖= 𝛼𝛼𝑖𝑖+ 𝑥𝑥1∙ log(𝑠𝑠𝑖𝑖) + 𝑥𝑥2∙ 𝑝𝑝𝑝𝑝��𝑖𝑖+ 𝑥𝑥3∙ 𝑝𝑝𝑠𝑠��𝑖𝑖+ 𝑥𝑥4∙ 𝐷𝐷𝐷𝐷𝑖𝑖𝑖𝑖+ 𝑥𝑥5∙ 𝑀𝑀𝑀𝑀𝑀𝑀𝑖𝑖𝑖𝑖+ 𝑥𝑥6∙ 𝑀𝑀𝑀𝑀𝑖𝑖𝑖𝑖+ 𝑥𝑥7∙ 𝑓𝑓𝑝𝑝��𝑖𝑖+ 𝑥𝑥8∙ 𝑦𝑦� + 𝑜𝑜̅𝑖𝑖+ 𝑞𝑞𝑖𝑖

Where the variables are the fund specific averages over time. As in a standard fixed effects model, the entity averages are subtracted from each variable. This results in equation (5) and (6). Note that herein the time-invariant variables, entity specific error terms 𝑒𝑒𝑖𝑖and 𝑞𝑞𝑖𝑖and constant terms

are wiped out, because they do not change over time.

(5) 𝑖𝑖𝑖𝑖𝑖𝑖− 𝚤𝚤̅𝑖𝑖= 𝛽𝛽2𝐹𝐹𝐹𝐹∙ (𝑝𝑝𝑝𝑝𝑖𝑖𝑖𝑖− 𝑝𝑝𝑝𝑝��𝑖𝑖) + 𝛽𝛽3𝐹𝐹𝐹𝐹∙ (𝑝𝑝𝑠𝑠𝑖𝑖𝑖𝑖− 𝑝𝑝𝑠𝑠��𝑖𝑖) + 𝛽𝛽7𝐹𝐹𝐹𝐹∙ (𝑓𝑓𝑝𝑝𝑖𝑖𝑖𝑖− 𝑓𝑓𝑝𝑝��𝑖𝑖) + 𝛽𝛽8𝐹𝐹𝐹𝐹∙ (𝑦𝑦_𝑡𝑡−𝑦𝑦�) + (𝑣𝑣𝑖𝑖𝑖𝑖− 𝑣𝑣̅𝑖𝑖)

(6) 𝑝𝑝𝑖𝑖𝑖𝑖− 𝑝𝑝̅𝑖𝑖= 𝑥𝑥2𝐹𝐹𝐹𝐹∙ (𝑝𝑝𝑝𝑝𝑖𝑖𝑖𝑖− 𝑝𝑝𝑝𝑝��𝑖𝑖) + 𝑥𝑥3𝐹𝐹𝐹𝐹∙ (𝑝𝑝𝑠𝑠𝑖𝑖𝑖𝑖− 𝑝𝑝𝑠𝑠��𝑖𝑖) + 𝑥𝑥7𝐹𝐹𝐹𝐹∙ (𝑓𝑓𝑝𝑝𝑖𝑖𝑖𝑖− 𝑓𝑓𝑝𝑝��𝑖𝑖) + 𝑥𝑥8𝐹𝐹𝐹𝐹∙ (𝑦𝑦_𝑡𝑡−𝑦𝑦�) + (𝑜𝑜𝑖𝑖𝑖𝑖− 𝑜𝑜̅𝑖𝑖)

Remember that the purpose of this standard fixed effects model is to estimate the entity effects 𝑢𝑢�𝑖𝑖 and 𝑔𝑔�𝑖𝑖. Furthermore, remember that the entity effects include all time-invariant variables, the overall constant term and the mean effects of the time-varying variables. By using the coefficients from the standard fixed effects model, it is possible to derive these entity effects. This is done by subtracting all time-varying effects from the mean of the dependent variable.

(26)

26

(7) 𝑢𝑢�_𝑖𝑖 = 𝚤𝚤̅𝑖𝑖− 𝛽𝛽2𝐹𝐹𝐹𝐹∙ 𝑝𝑝𝑝𝑝��𝑖𝑖− 𝛽𝛽3𝐹𝐹𝐹𝐹∙ 𝑝𝑝𝑠𝑠��𝑖𝑖− 𝛽𝛽5𝐹𝐹𝐹𝐹∙ 𝑓𝑓𝑝𝑝��𝑖𝑖− 𝛽𝛽6𝐹𝐹𝐹𝐹∙ 𝑦𝑦� − 𝑣𝑣̅

(8) 𝑔𝑔�_𝑖𝑖 = 𝑝𝑝̅𝑖𝑖− 𝑥𝑥2𝐹𝐹𝐹𝐹∙ 𝑝𝑝𝑝𝑝��𝑖𝑖− 𝑥𝑥3𝐹𝐹𝐹𝐹∙ 𝑝𝑝𝑠𝑠��𝑖𝑖− 𝑥𝑥5𝐹𝐹𝐹𝐹∙ 𝑓𝑓𝑝𝑝��𝑖𝑖− 𝑥𝑥6𝐹𝐹𝐹𝐹∙ 𝑦𝑦�−𝑜𝑜̅

Equation (7) and (8) provide an estimate of the entity effects 𝑢𝑢�𝑖𝑖 and 𝑔𝑔�𝑖𝑖. It is now necessary to divide the entity effects in two parts: an unexplained part and a part explained by the time-invariant variables. This is possible by regressing the entity effects on the time-invariant variables as in equation (9) and (10). The residuals 𝑧𝑧𝑖𝑖and 𝑙𝑙𝑖𝑖denote the entity effects which cannot be explained by

the time-invariant variables.

(9) 𝑢𝑢�𝑖𝑖 = 𝑎𝑎1∙ log(𝑠𝑠𝑖𝑖) + 𝑎𝑎4∙ 𝐷𝐷𝐷𝐷𝑖𝑖𝑖𝑖+ 𝑎𝑎5∙ 𝑀𝑀𝑀𝑀𝑀𝑀𝑖𝑖𝑖𝑖+ 𝑎𝑎6∙ 𝑀𝑀𝑀𝑀𝑖𝑖𝑖𝑖+ 𝑧𝑧𝑖𝑖

(10) 𝑔𝑔�_𝑖𝑖 = 𝑏𝑏1∙ log(𝑠𝑠𝑖𝑖) +𝑏𝑏4∙ 𝐷𝐷𝐷𝐷𝑖𝑖𝑡𝑡+ 𝑏𝑏5∙ 𝑀𝑀𝑀𝑀𝑀𝑀𝑖𝑖𝑡𝑡+ 𝑏𝑏6∙ 𝑀𝑀𝑀𝑀𝑖𝑖𝑡𝑡+ 𝑙𝑙𝑖𝑖

I now have a part of the entity effects which is explained by the time-invariant variables and a part which is unexplained. In the last step I estimate the original equations (1) and (2) in which I include the unexplained entity effects. This advantage of this approach is that the unexplained entity effects are no longer correlated with the invariant variables. The estimation of these time-invariant variables is therefore consistent. At the same time, this method resolves the problem of estimating the time-invariant variables, because it no longer demeans these and fully captures their effect on the return and risk-taking. The final model is displayed in equations (11) and (12) and can be estimated using pooled OLS:

(11) 𝑖𝑖𝑖𝑖𝑖𝑖= 𝛼𝛼𝑖𝑖+ 𝛽𝛽1∙ log(𝑠𝑠𝑖𝑖𝑖𝑖) + 𝛽𝛽2∙ 𝑝𝑝𝑝𝑝𝑖𝑖𝑖𝑖+ 𝛽𝛽3∙ 𝑝𝑝𝑠𝑠𝑖𝑖𝑖𝑖+ 𝛽𝛽4∙ 𝐷𝐷𝐷𝐷𝑖𝑖𝑖𝑖+ 𝛽𝛽5∙ 𝑀𝑀𝑀𝑀𝑀𝑀𝑖𝑖𝑖𝑖+ 𝛽𝛽6∙ 𝑀𝑀𝑀𝑀𝑖𝑖𝑖𝑖+ 𝛽𝛽7∙ 𝑓𝑓𝑝𝑝𝑖𝑖𝑖𝑖+ 𝛽𝛽8∙ 𝑦𝑦𝑖𝑖+ 𝛽𝛽9∙ 𝑧𝑧 + 𝑣𝑣𝑖𝑖𝑖𝑖𝑖𝑖

(12) 𝑝𝑝𝑖𝑖𝑖𝑖= 𝛼𝛼𝑖𝑖+ 𝑥𝑥1∙ log(𝑠𝑠𝑖𝑖𝑖𝑖) + 𝑥𝑥2∙ 𝑝𝑝𝑝𝑝𝑖𝑖𝑖𝑖+ 𝑥𝑥3∙ 𝑝𝑝𝑠𝑠𝑖𝑖𝑖𝑖+ 𝑥𝑥4∙ 𝐷𝐷𝐷𝐷𝑖𝑖𝑖𝑖+ 𝑥𝑥5∙ 𝑀𝑀𝑀𝑀𝑀𝑀𝑖𝑖𝑖𝑖+ 𝑥𝑥6∙ 𝑀𝑀𝑀𝑀𝑖𝑖𝑖𝑖+ 𝑥𝑥7∙ 𝑓𝑓𝑝𝑝𝑖𝑖𝑖𝑖+ 𝑥𝑥8∙ 𝑦𝑦𝑖𝑖+ 𝑥𝑥9∙ 𝑙𝑙𝑖𝑖+ 𝑜𝑜𝑖𝑖𝑖𝑖

The first condition under which the fevd procedure outperforms standard fixed effects (FE) models is that the between variation is sufficiently larger than the within variation (Plümper & Troeger, 2007). This means that the variables vary relatively more between different pension plans than within a pension plan. In other words, the assets should differ more when looking at different plans in a given year than looking at a given plan in different years.

The second condition is that the correlation between the rarely changing variables and unit effects is sufficiently low (Plümper & Troeger, 2007). This refers to the inability of the pooled OLS final model (equation (11) and (12)) to distinguish the effects from time-invariant variables and unit effects when these are correlated. A high correlation will therefore bias the estimation of the time-invariant variables. Graph 2 displays the relation between these two conditions and shows when the

(27)

27

fevd outperforms the standard fixed effects (FE) model. The graph is taken from Plümper and Troeger (2007, p. 137) in which they show at which underlying assumptions the fevd procedure outperforms the standard fixed effects model. The vertical axis shows the between/within ratio whereas the horizontal axis shows the correlation between time-invariant variables and entity effects. Under the graph, they outline the other assumptions with regard to the amount of observations, time periods, 𝑅𝑅2_{, correlation between unit effects and time-varying variable and} between unit effects and time-invariant variable and the standard deviations of the time-invariant variable.

Graph 2: Plümper and Troeger’s estimation in which they show when the fevd outperforms the FE model.

Table 4.1 and 4.2 show the between/within-ratio of all proposed time-invariant variables and the correlation between these variables and the unit effects in all variants of the datasets. The proposed time-invariant variables are the size and dummies for the type of a plan. Note that the type of the pan is sometimes missing. This is because some variants do not include all types of a plan. The variant with only defined benefit plans does for example not include defined contribution plans which makes it impossible to estimate the correlation and between/within ratio of this plan. Whether the fevd procedure outperforms the standard fixed effects (FE) model is answered by comparing the results of the tables with graph 2. The size has a mild, mostly negative, correlation with the entity effects. Furthermore, it has a sufficiently larger between than within variance which indicates that the size in assets does not change as much over years as it differs among different plans. The combination of the correlation and the between/within ratio indicates that the fevd outperforms the standard fixed effects model. The between variance of multiple employer plans is larger than the within variance. However, the ratio is not as large as with the size or multiemployer

(28)

28

plans. This means that plans shift relatively often between having a single-employer and multiple employer status whereas plans do not shift as much from a single-employer to multiemployer status. The reason is probably that it is easier to switch from one to multiple employers than to switch from one employer to having multiple employers and a union plan. However, due to the low correlation between a dummy for multiple employer plans and the unit effects, the fevd still outperforms the standard fixed effects model. The same accounts for the multiemployer variable, though this variable has a slightly higher and negative correlation with the entity effects. Finally, the between/within of a dummy for DC schemes is very large compared to the others which implies that plans do not regularly shift between a DC and DB status. The DC status of a plan has, depending on the dataset, a relatively large correlation with the entity effects. However, the combination between the correlation and between/within ratio of this variable indicates that the fevd outperforms the standard fixed effects model. In sum, I will use the fevd procedure to estimate the effects of these variable.

An empirical evaluation of the determinants of the return on investments and risk-taking in pension plans