Effect of cyclicality of pension funds on their asset allocation : are non-cyclical pension funds performing better than cyclical funds in difficult economic times?

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Effect of cyclicality of pension funds on their asset allocation. Are non-cyclical pension funds performing better than cyclical funds in difficult economic times?

By Abraham Borst Student ID: 0578177 November 2015

Presented to the Faculty of Economics and Business University of Amsterdam

In Partial Fulfillment of the Requirements for the Degree of Master of Science in Economics Master of Science in Economics – Specialization: Monetary Policy, Banking and Regulation

Supervisor: Dr. W.E. Romp Co-reader: Dr. C.A. Stoltenberg Faculty of Economics and Business

Department of Macro & International Economics Abstract

This thesis studies the relation between the asset allocation of a pension fund and the cyclicality of the sponsor's sector. A balanced dataset consisting of 90155 observations of 6935 U.S. corporate pension plans of the type defined benefits (DB), defined contributions (DC), single-employer (SE), multisingle-employer (ME), and multiple-single-employer (MPE) is constructed for the 2000-2012 period. I compare the asset allocation (return on investments and risky assets) for this period with the financial crisis and find that funds of firms in non-cyclical sectors underperform 1.15 percentage points compared to cyclical ones during normal or upward movements of the business cycles, but they perform 17.39 percentage points better during the financial crisis of 2008. Finally, the results from the Fixed Effects Vector Decomposition (FEVD) model show that pension funds of firms operating in non-cyclical sectors invest DB funds invest 3.57 percentage points more in risky assets compared to cyclical ones during the financial crisis of 2008. These results confirm the importance of the cyclicality of the sponsor's sector as a determinant of the asset allocation of pension funds.

Keywords:

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2 Preface and Acknowledgements

This master thesis would not be possible if my girlfriend, Nahymja, had not always believed in me and that, despite her own busy work obligations, she never left me alone one single second during the master.

Special thanks to my mother and to my father who always support me, and always encouraged me with great enthusiasm during this masters.

Huge thanks to dr. Romp, who pushed me to the limit, even after I almost officially handed in my thesis, he pushed me even further to a higher standard.

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3 Verklaring eigen werk

Hierbij verklaar ik, Abraham Johannes Samuël Borst, dat ik deze scriptie zelf geschreven heb en dat ik de volledige verantwoordelijkheid op me neem voor de inhoud ervan.

Ik bevestig dat de tekst en het werk dat in deze scriptie gepresenteerd wordt origineel is en dat ik geen gebruik heb gemaakt van andere bronnen dan die welke in de tekst en in de referenties worden genoemd.

De Faculteit Economie en Bedrijfskunde is alleen verantwoordelijk voor de begeleiding tot het inleveren van de scriptie, niet voor de inhoud.

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0. List of tables

Table 1 Variable construction of cyclical and non-cyclical pension funds page 14

Table 2 Summary statistics of baseline model page 23

Table 3 Summary statistics of the financial crisis of 2008 page 24

Table 4 Regression results of the FEVD model for the 2000-2012 period page 25

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1. Introduction

In the past decades, pension funds have been confronted with a maturing participant base, increasing demands for transparency and accountability, tightening regulation and financial crises. Most defined benefit (DB) funds, which guarantee a certain level of income security for members after retirement, are underfunded and have less assets than the promises they made (see e.g. Novy-Marx and Rauh (2011) on the US public pension funds).

DB plans are sensitive to the number of years of service, salary, and a multiplier (such as 2 percent for each year of service) of the participants and are sponsored by employers. Consequently they bear the risk of funding and investments. The employers (plan sponsors) also bear the interest rate risk, which is used to calculate the present value of liabilities and therefore affects the mandatory funding requirements. With historically low interest rates, the corporate pension liabilities significantly increased and the sponsor of the DB plan is required to make a contribution (Munnell and Soto, 2007).

On the other hand, in defined contribution (DC) plans employers contribute to employees’ retirement funds (fixed contributions), but offer no guarantees regarding returns or benefits. The accumulation of the pension benefits in DC plans are tied to employees’ salaries or to employer’s profits, hence they depend on the participant's contribution, and on financial market returns. Because of this relationship DC plans expose future retirees to greater risk than DB plans (Poterba, Rauh, Venti and Wise, 2007).

The predictable costs and a low level of regulation of DC plans in comparison to the volatile costs and a high level of regulation of DB plans, make DC plans more attractive to employers. Hence, the future of private pension plans is going in the direction of DC plans, where during their working lives, individuals bear the main risks. The recent crisis, however, has highlighted the risks of a DC pension plan, where individuals are fully exposed to the whims of the financial markets (see Severinson and Yermo, 2010). Likewise, Dvorak (2012) argues that the mechanical nature of contributions to DB plans could be a better option compared to the arbitrary contributions to DC plans.

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Nevertheless, Yermo and Severinson (2010) argue that, by making funding regulations more counter-cyclical the sustainability and security of DB plans could be strengthened. Nowadays, regulators basically force employers to increase their DB pension contributions during an economic downturn while making funding regulations cyclical. This is exactly a time when pension funds cannot afford it and hence this puts pressure on sponsor’s finances. In particular firms operating in cyclical sectors are hit hard in these times, since cyclical firms are usually defined in relation to the overall economy and thus move up and down with the economy (Damodaran, 2009). Hence, some industries are more vulnerable to business cycle phenomena (cyclical industries), while others are relatively immune (non-cyclical industries).

The Financial Stability Forum (FSF, 2009) poses that procyclicality is a positive feedback mechanism between the financial and the real sectors of the economy (see Papaioannou, Park, Pihlman and Van der Hoorn, 2014). Investors are considered procyclical if there are buying risky assets when market prices rise, and selling them when they fall, hereby potentially exaggerating market movements (Boon, Brière and Rigot, 2014). The banking sector, for instance, has a tendency to procyclicality, since a combination of capital requirements, high leverage and rigid market-based risk management, cause credit rationing during financial turbulence.Generally, during peaks of the business cycle with increasing competition, assets can be allocated towards investments with marginally positive or even negative net present value (NPV). Managers of cyclical industries tend to be less risk-averse in these times. In contrast, during an economic downturn with excessive risk aversion, even investments with positive NPV cannot receive financing from investors. With the unfold of the crisis several investors discard long-term investment strategies, reduced risk-exposures, and switched to safer assets.

Since share prices are more stable for pension funds of firms operating in non-cyclical sectors, they profit less from normal or upward movements of the business cycle, but their profits are less susceptible to economic downturns as well. The share prices of cyclical companies are more volatile, and therefore cyclical sectors could suffer more from recessions. In this paper, I examine to what extent the cyclicality of the pension fund's sponsor influences the pension funds’ asset allocation, and I compare normal economic times with the financial crisis of 2008. Hence, the main hypothesis of this study is that pension funds of firms in cyclical sectors are more involved in risk taking in their asset allocation and have higher return on investments. On the other hand, funds operating in non-cyclical sectors outperform cyclical ones during the financial crisis of 2008.

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The obtained results from the econometric model statistically confirm the hypothesis of this study, meaning that the cyclicality of the sponsor's sector is an important indicator for the assets allocation of pension funds. Pension funds of firms operating in non-cyclical pension funds tend to underperform by 1.15 percentage points during normal or upward movements of the business cycle. Also, funds of firms in non-cyclical sectors perform 17.39 percentage points better than their cyclical counterparts in difficult times and invest 3.57 percentage points more in risky assets.

This thesis makes three contributions to the literature. First, I am the first to investigate the cyclicality of the sponsor's sector in relation to the asset allocation of pension funds. Second, I use a large sample of 6935 corporate pension plans with data from the Form 5500 provided by the U.S. Department of Labor (DOL). Third, I use the Fixed Effects Vector Decomposition (FEVD) model of Plümper and Pfloeger (2007) to investigate my research questions.

The remainder of this paper is structured as follows: Chapter 2 reviews the literature on this matter. In chapter 3, I will present the methodology, followed by the dataset in chapter 4, and the empirical results in chapter 5. Chapter 6 concludes.

2. Review of the literature

This chapter starts by briefly reviewing the historical perspective and characteristics of US corporate pension funds. Subsequently, it surveys the literature on the conventional determinants of the asset allocation of pension plans. Finally, the last part of this chapter serves the literature on cyclicality and regulation as determinants of asset allocation of pension plans.

2.1 Characteristics of U.S. corporate pension funds

In order to protect employee benefits, under the 1974 Employee Retirement Income Security Act (ERISA), plan budgeting rules impose minimum standards for funding levels, recovery periods and sponsor contributions. Many subsequent amendments of the ERISA followed. One of the latest is the Pension Protection Act of 2006 (PPA) and came into effect in 2008 after concerns over low levels of private pension funding and the ineffectiveness of minimum funding rules. The PPA of 2006 introduced higher funding targets and quicker remediation of shortfalls from a 30-year to a 7-year period (see Love, Smith and Wilcox, 2011).

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With the U.S. government signing into law Moving Ahead for Progress in the 21st_Century

Act (MAP-21), it allows corporate DB pension plan sponsors to use a higher discount rate when computing the present value of pension liabilities. This give pension funds the possibility to set their discount rates based on the expected rate of return of their asset portfolio, hereby providing them with incentives to take more risk over time in response to declining government bond yields (Andonov, Bauer and Cremers, 2014).

Apart from the two basic types of pensions (DC and DB) mentioned in the introduction,

corporate pension funds are classified by single-employer (SE) plans, multiple employer (MPE) plans or multiemployer (ME) plans. In short, Governmental Accounting Standards Board (GASB) states the following definitions: “Single-employer plans provide pension benefits to the employees of one employer. Multiple employer plans shall be applied as if all employees of each of the employers maintain the plan were employed by a single employer. Multiemployer plans provide pension benefits to the employees of more than one employer.” Multiemployer plans are collectively bargained plans maintained by labor unions and therefore are known as industry funds or “union” funds. This type of plan is common in industries that are typically unionized and characterized by frequent job switching, such as construction, entertainment, trucking, and mining.

2.2 The asset allocation of pension plans: Determinants of risky assets and the return on investment

Pension funds have long investment horizons, of which they can exploit to avoid short-term volatility in asset prices (Papaioannou et al., 2014). Also, pension funds can invest in illiquid equity investments gaining the liquidity premium associated with these investments (Bauer, Cremers and Frehen, 2010). With the globalization of capital markets the significance of such asset classes has increased. The challenge for investors lies in identifying ex-ante (expected) risk-taking and ex-post (realized) returns. It is common, however, to use ex-post market-based measures of risk, such as fluctuations in stock returns, or accounting-based measures of risk, such as fluctuation in accounting earnings (Atanasova and Gatev, 2013).

Finance theories suggest diversification among a broad package of assets (such as equities and U.S. government securities). The decision lies between debt (the low risk asset class) and equity (the high risk asset class). If the assets are mainly allocated towards high-risk instruments, this results in more volatility in the return on investments. If the assets are mainly invested in low-risk instruments, investment loss will be avoided, but the return will be lower (see Jun Peng, 2004).

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In defined contribution (DC) funds, plan sponsors select the available investment options. For the decision which option to select is each plan member individually responsible. Hence, asset allocation outcomes depend on individual decision making (Poterba, Rauh, Venti and Wise, 2007). Moreover, DC funds usually do not include alternative asset classes and these classes are exactly a significant part of the portfolio of a DB fund. The board of a pension fund represents equally employers and employees and together they make the asset allocation decisions and are responsible for the eventual performance. Being responsible for the income of retirees, a poor investment performance of pension funds can reduce the wealth and consumption of current and future retirees (Novy-Marx and Rauh, 2011).

That the main determinants of pension plan risk taking are different for public and private firms has been shown by Atanasova and Gatev (2013). They compare publicly-traded DB sponsors with private DB sponsor plans, by looking at the volatility of the return on plan assets. This is calculated as the prior 5-year standard deviation of the return on plan assets. Their results show a more than two and a half times higher effect of pension liability funding for publicly-traded plan sponsors compared with private plan sponsors. In contrast, the effect of contributions is more than four times higher for private sponsor plans. Since their results show that changes in sponsor’s contributions and funding status are positively related to the future change in volatility of pension returns, but unrelated to the past change in volatility, access to external financing and possible cash constraints are relatively more important for private firms than for public ones. Reason for this is that pension contributions can reduce investment spending and other corporate expenses.

Lucas and Zeldes (2009) and Frank (2002) investigate whether pension plans are used to maximize tax benefits.Frank (2002) investigates what the relationship is between potential tax benefits and a private pension plan’s decision to allocate their DB plan's assets between equity and bonds. He finds that tax benefits are positively and significantly correlated with the percentage of their pension assets invested in bonds. Lucas and Zeldes (2009) find little variation in investment strategies across public pension plans. They conclude that this variation cannot be easily explained by economic factors (for instance the share of active participants). There exists a tradeoff with higher average return on equities and lower average taxes on the one hand, and greater risk of equities and higher expected tax distortions on the other hand. Their model emphasizes distortionary taxes, and since 60 percent is invested in equity, there are other considerations that are equally important in determining the optimal asset allocation. They suggest that the accounting rules create an incentive to invest in high risk asset classes

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with high expected return in order to lower shortfalls, since these rules allow state and local plans to discount liabilities at the expected return on assets.

Bartram (2012) states there is little support of firms using pension plans to maximize tax benefits, but pension plans are used as part of their overall corporate financial strategy. He investigated the financial management of 1439 U.S. non-financial firms and their DB plans before and during the financial crisis of 2008. He measured investment risk by the volatility of the return on plan assets, which is a measure of total risk. His results show that firms invest their pension funds in riskier assets if they are larger and older. Firms also invested less in risky assets during the financial crisis when they had large obligations, lower performance of plan assets, and if they made small contributions. Furthermore, he shows that plan sponsors with smaller pension plans and lower volatility of plan assets contributed more during the crisis.

Since pension funds are restricted to invest in some risky asset classes, they reallocate to other risky assets like high yield bonds, private equity and hedge funds because these classes are non-restricted (see Boon, Brière and Rigot, 2014). Boon, Brière and Rigot (2014) analyzed an unbalanced panel of 589 funds (of which 377 in the US) over the 1991-2011 period and they find that size of the pension fund (measured by assets under management) has a significant impact on the allocation to alternatives (tactical asset allocation, commodities, natural resources, real estate, other real assets, hedge funds, private equity) compared to any other asset class. This result is in line with the fact that larger funds are more sophisticated. On top of that larger pension funds have more resources to hire competent professionals, who have expertise in monitoring complicated assets such as hedge funds and private equity.

Dyck and Pomorski (2011) use a CEM Benchmarking, Inc. (CEM) to investigate the relationship between size and performance in asset management with an unbalanced panel. The CEM dataset provides detailed information on benchmarks, costs and fund-specific returns for all types of pension plans. The returns on the largest plans compared to smaller pension plans are higher by 43-50 basis points per year. A big part of the realized returns comes from the fact that larger DB plans have higher allocations to alternative investments funds' characteristics. Furthermore, economies of scale, superior monitoring and screening of managers and cost savings related to internal management play a significant role.

Contrary to Boon et al. (2014) and Dyck and Pomorski (2011), Bauer, Cremers and Frehen (2010) find that smaller plans perform better. Also using the CEM pension fund dataset, they give two possible explanations for their result. One is that because pension funds can invest in illiquid equity investments and gaining the liquidity premium by doing so, this outperformance

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may be easier achieved in smaller portfolios. The second reason could lie in that pension funds may have some skill in selecting (external) managers that outperform.

2.3 Cyclicality and asset allocation of pension funds

Procyclicality can affect investment strategies. In a bull market, equity prices boom, and pension funds may not always rebalance their portfolio. This leads to growing equity allocations in the portfolio. Especially in a downturn, the inherently procyclical financial system can be harmful. During the financial crisis, for example, pension funds were net sellers of equities (Papaioannou, Park, Pihlman and Van der Hoorn, 2014), and pension funds drove down markets even further by selling these equities and crystallizing losses (Yermo and Severinson, 2010). Papaioannou et al. (2014) state that that the financial system is inherently procyclical, and that as a group institutional investors tend to move with the state of the economy, called ‘institutional herding’. In line with this Boon, Brière and Rigot (2014) find mild evidence that pension funds’ investments are procyclical during normal times, but much stronger evidence of procyclicality during turbulence. Also, Atanasova and Gatev (2013) make an interesting point with respect to ownership stake, because a low-risk pension plan can lower the total risk exposure of owner-managers who are not well diversified.

Dvorak (2012) examines the impact of the cyclicality of contributions of DB and DC plans on ROI. Although contributions to DC plans are uncorrelated to the business cycle, contributions to DB plans are counter-cyclical. During the financial crisis of 2008, contributions in DB plans increase, and at the same time contributions to DC plans show no difference. He concludes that better timing of contributions can lead to the same level of assets with lower total contributions for a given level of retirement benefits. Hence, when a plan sponsor operates in a cyclical industry this is an additional problem on top of the already existing cash flow problems during economic difficult times.

2.4 Regulation and asset allocation of pension funds

Recently the literature started focusing on the impact of regulation on the asset allocation of pension funds. The regulatory environment may also influence the willingness of funds to invest in risky assets. Yermo and Severinson (2010) state that the positive impact of counter- cyclicality should be considered when evaluating the two types of plans (DB and DC) and when

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designing the funding rules of DB plans. As stated earlier, the counter-cyclicality of DB contributions probably dampens the volatility of stock prices, while procyclicality of DC contributions does the opposite. Since more and more firms prefer DC plans, this gradual exodus of DB plans could lead to higher market volatility (Yermo and Severinson, 2012). Therefore, documenting the differences in nature of for example contributions to DB and DC plans could be important for understanding current and future volatility of asset prices (Dvorak, 2012). But also, with potentially higher market volatility the importance of the cyclicality of the sponsor's sector increase, since this could have impact on the asset allocation of pension funds as well.

To bring the pressure down and to increase the sustainability of DB plans, Boon et al. (2014) suggest an appropriate level of risk-taking in the funds’ investments. For example, this exposure towards risky assets led to losses of an estimated $1 trillion dollars following the decline of the stock marketfrom October 2007 to October 2008 (Munnell, Haverstick and Aubry, 2008). Overall, the empirical results of Boon, Brière and Rigot (2014) show that regulatory mechanisms has more influence on asset allocation choices than pension funds’ individual characteristics (maturity of the plan and the size of the plan), but that regulation has little impact on the procyclicality of asset allocations.

3. Methodology

This section outlines the methodological framework used to examine the main questions of this study and describes the features of the used variables.

3.1 The econometric model: baseline specification

Given the main question of this study, whether there exists an effect of cyclicality of the sector of the pension fund on their return on investments and asset allocation towards risky assets, the following two baseline specifications (1) and (2) are estimated:

(𝟏) 𝐑𝐎𝐈 𝐢𝐭= 𝛃𝟎+ 𝛃𝟏𝐧𝐨𝐧𝐜𝐲𝐜𝐥𝐢𝐜𝐚𝐥𝐢+ 𝛃𝟐𝐃𝐁𝐢+ 𝛃𝟑𝐌𝐄𝐢+ 𝛃𝟒𝐌𝐏𝐄𝐢+ 𝛃𝟓𝐥𝐨𝐠𝐒𝐢𝐳𝐞𝐢𝐭+

𝛃𝟔𝐀𝐜𝐭𝐢𝐯𝐞 𝐏𝐚𝐫𝐭𝐢𝐜𝐢𝐩𝐚𝐧𝐭𝐬𝐢𝐭+ 𝛃𝟕(𝐧𝐨𝐧𝐜𝐲𝐜𝐥𝐢𝐜𝐚𝐥 ∗ 𝐃𝐁)𝐢+ 𝛃𝟖(𝐧𝐨𝐧𝐜𝐲𝐜𝐥𝐢𝐜𝐚𝐥 ∗ 𝐌𝐄)𝐢+ 𝛃𝟗(𝐧𝐨𝐧𝐜𝐲𝐜𝐥𝐢𝐜𝐚𝐥 ∗

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(𝟐) 𝐑𝐢𝐬𝐤𝐲 𝐢𝐭= 𝛉𝟎+ 𝛉𝟏𝐧𝐨𝐧𝐜𝐲𝐜𝐥𝐢𝐜𝐚𝐥𝐢+ 𝛉𝟐𝐃𝐁𝐢+ 𝛉𝟑𝐌𝐄𝐢+ 𝛉𝟒𝐌𝐏𝐄𝐢+ 𝛉𝟓𝐥𝐨𝐠𝐒𝐢𝐳𝐞𝐢𝐭+

𝛉𝟔𝐀𝐜𝐭𝐢𝐯𝐞 𝐏𝐚𝐫𝐭𝐢𝐜𝐢𝐩𝐚𝐧𝐭𝐬𝐢𝐭+ 𝛉𝟕(𝐧𝐨𝐧𝐜𝐲𝐜𝐥𝐢𝐜𝐚𝐥 ∗ 𝐃𝐁)𝐢+ 𝛉𝟖(𝐧𝐨𝐧𝐜𝐲𝐜𝐥𝐢𝐜𝐚𝐥 ∗ 𝐌𝐄)𝐢+ 𝛉𝟗(𝐧𝐨𝐧𝐜𝐲𝐜𝐥𝐢𝐜𝐚𝐥 ∗

𝐌𝐏𝐄)𝐢 +𝛉𝟏𝟎(𝐧𝐨𝐧𝐜𝐲𝐜𝐥𝐢𝐜𝐚𝐥 ∗ 𝐥𝐨𝐠𝐒𝐢𝐳𝐞)𝐢𝐭+𝛉𝟏𝟏(𝐧𝐨𝐧𝐜𝐲𝐜𝐥𝐢𝐜𝐚𝐥 ∗ 𝐀𝐜𝐭𝐢𝐯𝐞 𝐏𝐚𝐫𝐭𝐢𝐜𝐢𝐩𝐚𝐧𝐭𝐬)𝐢𝐭+𝛉𝟏𝟐𝛄𝐭+ 𝐯𝐢+ 𝛔𝐢𝐭 In specification (1) the dependent variable is return on investments (ROI) and in specification (2) the dependent variable is the allocation towards risky assets (Risky). Both specifications consist of a dummy variable “noncyclical” that equals one if the pension fund of the firm is operating in a non-cyclical sector and zero otherwise (see also table 1 in the data section). Also included are dummy variables to catch the effect of the type of the plan: “DB” equals one if the fund is of the defined benefits type and zero if the fund is a DC fund, and “ME” and “MPE” equals one if the fund is multiemployer or multiple-employer, compared to single-employer (SE) funds which equal zero. Furthermore, included are the controls for the plan size which is measured as the log of plan assets at the beginning of the year and the share of active participants of the plan. Also interaction terms for “non-cyclical” sectors are added to pick up the effect of cyclicality on the various control variables. Finally γ𝑡 is included for all

the year dummies, u_i and v_i denotes the entity specific effects (fixed effects) and ε_it and σ_it are the i.i.d. error terms.

3.2 The econometric model: the financial crisis of 2008

The unfold of the crisis started in the summer of 2007, but the peak was reached in the autumn of 2008 with the fall of Lehman Brothers and the accelerator effect after this event. Since the U.S. economy experienced a relatively quick recovery during 2009 (see Severinson and Yermo, 2010), I interact the year 2008 with the various independent variables. Consequently, specification (3) and specification (4) are basically the same regressions as specifications (1) and (2) in the previous paragraph. In order to examine if funds of firms in non-cyclical sectors tend to outperform their cyclical counterparts during the financial crisis of 2008, the following two specifications (3) and (4) are estimated:

(𝟑) 𝐑𝐎𝐈 𝐢𝐭= 𝛃𝟎+ 𝛃𝟏𝐧𝐨𝐧𝐜𝐲𝐜𝐥𝐢𝐜𝐚𝐥𝐢+ 𝛃𝟐𝐃𝐁𝐢+ 𝛃𝟑𝐌𝐄𝐢+ 𝛃𝟒𝐌𝐏𝐄𝐢+ 𝛃𝟓𝐥𝐨𝐠𝐒𝐢𝐳𝐞𝐢𝐭+ 𝛃𝟔𝐀𝐜𝐭𝐢𝐯𝐞 𝐏𝐚𝐫𝐭𝐢𝐜𝐢𝐩𝐚𝐧𝐭𝐬𝐢𝐭+ 𝛃𝟕(𝐧𝐨𝐧𝐜𝐲𝐜𝐥𝐢𝐜𝐚𝐥 ∗ 𝐃𝐁)𝐢+ 𝛃𝟖(𝐧𝐨𝐧𝐜𝐲𝐜𝐥𝐢𝐜𝐚𝐥 ∗ 𝐌𝐄)𝐢+ 𝛃𝟗(𝐧𝐨𝐧𝐜𝐲𝐜𝐥𝐢𝐜𝐚𝐥 ∗ 𝐌𝐏𝐄)𝐢+ 𝛃𝟏𝟎(𝐧𝐨𝐧𝐜𝐲𝐜𝐥𝐢𝐜𝐚𝐥 ∗ 𝐥𝐨𝐠𝐒𝐢𝐳𝐞)𝐢𝐭+𝛃𝟏𝟏(𝐧𝐨𝐧𝐜𝐲𝐜𝐥𝐢𝐜𝐚𝐥 ∗ 𝐀𝐜𝐭𝐢𝐯𝐞 𝐏𝐚𝐫𝐭𝐢𝐜𝐢𝐩𝐚𝐧𝐭𝐬)𝐢𝐭+ 𝛃𝟏𝟐(𝐧𝐨𝐧𝐜𝐲𝐜𝐥𝐢𝐜𝐚𝐥 ∗ 𝐲𝟐𝟎𝟎𝟖)𝐢𝐭+ 𝛃𝟏𝟑(𝐃𝐁 ∗ 𝐲𝟐𝟎𝟎𝟖)𝐢𝐭+ 𝛃𝟏𝟒(𝐌𝐄 ∗ 𝐲𝟐𝟎𝟎𝟖)𝐢𝐭+ 𝛃𝟏𝟓(𝐌𝐏𝐄 ∗ 𝐲𝟐𝟎𝟎𝟖)𝐢𝐭+𝛃𝟏𝟔(𝐥𝐨𝐠𝐒𝐢𝐳𝐞 ∗ 𝐲𝟐𝟎𝟎𝟖)𝐢𝐭+ 𝛃𝟏𝟕(𝐀𝐜𝐭𝐢𝐯𝐞 𝐏𝐚𝐫𝐭𝐢𝐜𝐢𝐩𝐚𝐧𝐭𝐬 ∗ 𝐲𝟐𝟎𝟎𝟖)𝐢𝐭+ 𝛃𝟏𝟖(𝐧𝐨𝐧𝐜𝐲𝐜𝐥𝐢𝐜𝐚𝐥 ∗ 𝐃𝐁 ∗ 𝐲𝟐𝟎𝟎𝟖)𝐢𝐭+ 𝛃𝟏𝟗(𝐧𝐨𝐧𝐜𝐲𝐜𝐥𝐢𝐜𝐚𝐥 ∗ 𝐌𝐄 ∗ 𝐲𝟐𝟎𝟎𝟖)𝐢𝐭+ 𝛃𝟐𝟎(𝐧𝐨𝐧𝐜𝐲𝐜𝐥𝐢𝐜𝐚𝐥 ∗ 𝐌𝐏𝐄 ∗ 𝐲𝟐𝟎𝟎𝟖)𝐢𝐭+ 𝛃𝟐𝟏(𝐧𝐨𝐧𝐜𝐲𝐜𝐥𝐢𝐜𝐚𝐥 ∗ 𝐥𝐨𝐠𝐒𝐢𝐳𝐞 ∗ 𝐲𝟐𝟎𝟎𝟖)𝐢𝐭+ 𝛃𝟐𝟐(𝐧𝐨𝐧𝐜𝐲𝐜𝐥𝐢𝐜𝐚𝐥 ∗ 𝐀𝐜𝐭𝐢𝐯𝐞 𝐏𝐚𝐫𝐭𝐢𝐜𝐢𝐩𝐚𝐧𝐭𝐬 ∗ 𝐲𝟐𝟎𝟎𝟖)𝐢𝐭+𝛃𝟐𝟑𝛄𝐭+ 𝐮𝐢+ 𝛆𝐢𝐭

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15 (𝟒) 𝐑𝐢𝐬𝐤𝐲 𝐢𝐭= 𝛉𝟎+ 𝛉𝟏𝐧𝐨𝐧𝐜𝐲𝐜𝐥𝐢𝐜𝐚𝐥𝐢+ 𝛉𝟐𝐃𝐁𝐢+ 𝛉𝟑𝐌𝐄𝐢+ 𝛉𝟒𝐌𝐏𝐄𝐢+ 𝛉𝟓𝐥𝐨𝐠𝐒𝐢𝐳𝐞𝐢𝐭+ 𝛉𝟔𝐀𝐜𝐭𝐢𝐯𝐞 𝐏𝐚𝐫𝐭𝐢𝐜𝐢𝐩𝐚𝐧𝐭𝐬𝐢𝐭+ 𝛉𝟕(𝐧𝐨𝐧𝐜𝐲𝐜𝐥𝐢𝐜𝐚𝐥 ∗ 𝐃𝐁)𝐢+ 𝛉𝟖(𝐧𝐨𝐧𝐜𝐲𝐜𝐥𝐢𝐜𝐚𝐥 ∗ 𝐌𝐄)𝐢+ 𝛉𝟗(𝐧𝐨𝐧𝐜𝐲𝐜𝐥𝐢𝐜𝐚𝐥 ∗ 𝐌𝐏𝐄)𝐢+ 𝛉𝟏𝟎(𝐧𝐨𝐧𝐜𝐲𝐜𝐥𝐢𝐜𝐚𝐥 ∗ 𝐥𝐨𝐠𝐒𝐢𝐳𝐞)𝐢𝐭+𝛉𝟏𝟏(𝐧𝐨𝐧𝐜𝐲𝐜𝐥𝐢𝐜𝐚𝐥 ∗ 𝐀𝐜𝐭𝐢𝐯𝐞 𝐏𝐚𝐫𝐭𝐢𝐜𝐢𝐩𝐚𝐧𝐭𝐬)𝐢𝐭+ 𝛉𝟏𝟐(𝐧𝐨𝐧𝐜𝐲𝐜𝐥𝐢𝐜𝐚𝐥 ∗ 𝐲𝟐𝟎𝟎𝟖)𝐢𝐭+ 𝛉𝟏𝟑(𝐃𝐁 ∗ 𝐲𝟐𝟎𝟎𝟖)𝐢𝐭+ 𝛉𝟏𝟒(𝐌𝐄 ∗ 𝐲𝟐𝟎𝟎𝟖)𝐢𝐭+ 𝛉𝟏𝟓(𝐌𝐏𝐄 ∗ 𝐲𝟐𝟎𝟎𝟖)𝐢𝐭+𝛉𝟏𝟔(𝐥𝐨𝐠𝐒𝐢𝐳𝐞 ∗ 𝐲𝟐𝟎𝟎𝟖)𝐢𝐭+ 𝛉𝟏𝟕(𝐀𝐜𝐭𝐢𝐯𝐞 𝐏𝐚𝐫𝐭𝐢𝐜𝐢𝐩𝐚𝐧𝐭𝐬 ∗ 𝐲𝟐𝟎𝟎𝟖)𝐢𝐭+ 𝛉𝟏𝟖(𝐧𝐨𝐧𝐜𝐲𝐜𝐥𝐢𝐜𝐚𝐥 ∗ 𝐃𝐁 ∗ 𝐲𝟐𝟎𝟎𝟖)𝐢𝐭+ 𝛉𝟏𝟗(𝐧𝐨𝐧𝐜𝐲𝐜𝐥𝐢𝐜𝐚𝐥 ∗ 𝐌𝐄 ∗ 𝐲𝟐𝟎𝟎𝟖)𝐢𝐭+ 𝛉𝟐𝟎(𝐧𝐨𝐧𝐜𝐲𝐜𝐥𝐢𝐜𝐚𝐥 ∗ 𝐌𝐏𝐄 ∗ 𝐲𝟐𝟎𝟎𝟖)𝐢𝐭+ 𝛉𝟐𝟏(𝐧𝐨𝐧𝐜𝐲𝐜𝐥𝐢𝐜𝐚𝐥 ∗ 𝐥𝐨𝐠𝐒𝐢𝐳𝐞 ∗ 𝐲𝟐𝟎𝟎𝟖)𝐢𝐭+ 𝛉𝟐𝟐(𝐧𝐨𝐧𝐜𝐲𝐜𝐥𝐢𝐜𝐚𝐥 ∗ 𝐀𝐜𝐭𝐢𝐯𝐞 𝐏𝐚𝐫𝐭𝐢𝐜𝐢𝐩𝐚𝐧𝐭𝐬 ∗ 𝐲𝟐𝟎𝟎𝟖)𝐢𝐭+𝛉𝟐𝟑𝛄𝐭+ 𝐯𝐢+ 𝛔𝐢𝐭

3.3 The Fixed Effects Vector Decomposition Model

In deciding the most appropriate model, a fixed effects (FE) model would avoid omitted variable bias that vary over entities but stay constant over time. Consequently, the FE model only measures the effect of changes in a given entity over the years. Since these variables show only little changes or no changes at all, the FE model will only measure the effect of these small changes. The fixed effect would have absorbed the non-time-varying explanatory variables “non-cyclical”, “DB”, “ME” and “MPE”. Hence, with the specifications used in this thesis, it would lead to biased results because of the time-invariant variables.

Therefore, I use a balanced dataset that runs from 2000-2012 with a Fixed Effects Vector Decomposition (FEVD) model, by following the steps in a paper by Plümper and Ploeger (2007). The procedure of the FEVD model consists of three stages. In the first stage I run a baseline panel FE model without time-invariant variables. In this way I can estimate the entity fixed effects. In the second stage I decompose the entity effects vector into a part explained by the time-invariant variables and an error term. This is done by running an OLS regression of the fixed effects vector on the time invariant explanatory variables from the baseline models (1) and (2). In the third stage I re-estimate the first stage by pooled-OLS including all explanatory time-variant variables, the time-invariant variables plus the error term (the unexplained part of the fixed effects vector) of stage 2 (see Plümper and Ploeger, 2007).

As mentioned in the introduction of this chapter, I assume the dummy variables “non-cyclical”, defined benefits (“DB”), multiemployer (“ME”), multiple-employer (“MPE”) and the logarithm of the size of the plan to be time-invariant, and the (interaction terms with the) share of active participants to be time-varying. Apart from the interaction terms with the share of active participants, I assume that the other interaction terms are time-invariant.

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16 3.3.1 First stage of the FEVD model

In order to estimate the entity fixed effects, the fixed effects transformation can be found by first averaging the baseline specifications (1) and (2) over time, with e̅_𝑖and s̅_i as the residuals

of the estimated models, followed by subtracting the averages of the time-varying variables from equation (1) and (2):

(𝟓) (𝐑𝐎𝐈 𝐢𝐭− 𝐑𝐎𝐈 ̅̅̅̅̅̅̅̅) = 𝛃𝐢 𝟔𝐅𝐄(𝐀𝐜𝐭𝐢𝐯𝐞 𝐏𝐚𝐫𝐭𝐢𝐜𝐢𝐩𝐚𝐧𝐭𝐬𝐢𝐭− 𝐀𝐜𝐭𝐢𝐯𝐞 𝐏𝐚𝐫𝐭𝐢𝐜𝐢𝐩𝐚𝐧𝐭𝐬̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅𝐢) + 𝛃𝟏𝟏𝐅𝐄((𝐧𝐨𝐧𝐜𝐲𝐜𝐥𝐢𝐜𝐚𝐥 ∗

𝐀𝐜𝐭𝐢𝐯𝐞 𝐏𝐚𝐫𝐭𝐢𝐜𝐢𝐩𝐚𝐧𝐭𝐬𝐢𝐭) − (𝐧𝐨𝐧𝐜𝐲𝐜𝐥𝐢𝐜𝐚𝐥 ∗ 𝐀𝐜𝐭𝐢𝐯𝐞 𝐏𝐚𝐫𝐭𝐢𝐜𝐢𝐩𝐚𝐧𝐭𝐬̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅𝐢)) + 𝛃𝟏𝟐𝐅𝐄(𝛄_𝐭− 𝛄̅) + (𝐞𝐢𝐭− 𝐞̅𝐢)

(𝟔) (𝐑𝐢𝐬𝐤𝐲 𝐢𝐭− 𝐑𝐢𝐬𝐤𝐲 ̅̅̅̅̅̅̅̅̅̅̅ = 𝛉𝐢) 𝟔𝐅𝐄(𝐀𝐜𝐭𝐢𝐯𝐞 𝐏𝐚𝐫𝐭𝐢𝐜𝐢𝐩𝐚𝐧𝐭𝐬𝐢𝐭− 𝐀𝐜𝐭𝐢𝐯𝐞 𝐏𝐚𝐫𝐭𝐢𝐜𝐢𝐩𝐚𝐧𝐭𝐬̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅𝐢) + 𝛉𝟏𝟏𝐅𝐄((𝐧𝐨𝐧𝐜𝐲𝐜𝐥𝐢𝐜𝐚𝐥 ∗

𝐀𝐜𝐭𝐢𝐯𝐞 𝐏𝐚𝐫𝐭𝐢𝐜𝐢𝐩𝐚𝐧𝐭𝐬𝐢𝐭) − (𝐧𝐨𝐧𝐜𝐲𝐜𝐥𝐢𝐜𝐚𝐥 ∗ 𝐀𝐜𝐭𝐢𝐯𝐞 𝐏𝐚𝐫𝐭𝐢𝐜𝐢𝐩𝐚𝐧𝐭𝐬̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅𝐢)) + 𝛉𝟏𝟐𝐅𝐄(𝛄_𝐭− 𝛄̅) + (𝐬𝐢𝐭− 𝐬̅𝐢)

Hence, these transformations take out the individual effects u_i and v_iand the time-invariant variables. By doing so, this fixed effects model gives me estimates of the entity effects, including all time-invariant variables, the overall constant term, and the mean effects of the time-varying variables. Equations (7) and (8) show the entity effects and the explanatory variables for these entity effects:

(7)𝐭̂𝐢 = (𝐑𝐎𝐈)̅̅̅̅̅̅̅̅̅ − 𝛃𝐢 𝟏𝐅𝐄(𝐀𝐜𝐭𝐢𝐯𝐞 𝐏𝐚𝐫𝐭𝐢𝐜𝐢𝐩𝐚𝐧𝐭𝐬)̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅𝐢− 𝛃𝟐𝐅𝐄(𝐧𝐨𝐧𝐜𝐲𝐜𝐥𝐢𝐜𝐚𝐥 ∗ 𝐀𝐜𝐭𝐢𝐯𝐞 𝐏𝐚𝐫𝐭𝐢𝐜𝐢𝐩𝐚𝐧𝐭𝐬)̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅𝐢− 𝛃𝟑𝐅𝐄𝛄̅ − 𝐞̅𝐢

(8)𝐮̂𝐢 = (𝐑𝐢𝐬𝐤𝐲)̅̅̅̅̅̅̅̅̅̅̅ − 𝛉𝐢 𝟏𝐅𝐄(𝐀𝐜𝐭𝐢𝐯𝐞 𝐏𝐚𝐫𝐭𝐢𝐜𝐢𝐩𝐚𝐧𝐭𝐬̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅)𝐢− 𝛉𝟐𝐅𝐄(𝐧𝐨𝐧𝐜𝐲𝐜𝐥𝐢𝐜𝐚𝐥 ∗ 𝐀𝐜𝐭𝐢𝐯𝐞 𝐏𝐚𝐫𝐭𝐢𝐜𝐢𝐩𝐚𝐧𝐭𝐬)̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅𝐢− 𝛉𝟑𝐅𝐄𝛄̅ − 𝐬̅𝐢 With β₁FE, β₂FE, β₃FE, θ₁FE, θ₂FE, and θ₃FE are the pooled OLS estimates of the demeaned model in equations (7) and (8).

3.3.2 Second stage of the FEVD model

In stage 2, I regress the entity effects t̂i and ûi from stage 1 on the observed

time-invariant and rarely changing variables.

(𝟗) 𝐭̂𝐢 = 𝛃𝟏𝐧𝐨𝐧𝐜𝐲𝐜𝐥𝐢𝐜𝐚𝐥𝐢+ 𝛃𝟐𝐃𝐁𝐢+ 𝛃𝟑𝐌𝐄𝐢+ 𝛃𝟒𝐌𝐏𝐄𝐢+ 𝛃𝟓 𝐥𝐨𝐠𝐒𝐢𝐳𝐞 ̅̅̅̅̅̅̅̅̅̅̅̅ + 𝛃𝐢 𝟔(𝐧𝐨𝐧𝐜𝐲𝐜𝐥𝐢𝐜𝐚𝐥 ∗ 𝐃𝐁)𝐢+

𝛃𝟕(𝐧𝐨𝐧𝐜𝐲𝐜𝐥𝐢𝐜𝐚𝐥 ∗ 𝐌𝐄)𝐢+ 𝛃𝟖(𝐧𝐨𝐧𝐜𝐲𝐜𝐥𝐢𝐜𝐚𝐥 ∗ 𝐌𝐏𝐄)𝐢 +𝛃𝟗(𝐧𝐨𝐧𝐜𝐲𝐜𝐥𝐢𝐜𝐚𝐥 ∗ 𝐥𝐨𝐠𝐒𝐢𝐳𝐞 )̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅ + 𝐰𝐢 𝐢

(𝟏𝟎) 𝐮̂𝐢 = 𝛉𝟏𝐧𝐨𝐧𝐜𝐲𝐜𝐥𝐢𝐜𝐚𝐥𝐢+ 𝛉𝟐𝐃𝐁𝐢+ 𝛉𝟑𝐌𝐄𝐢+ 𝛉𝟒𝐌𝐏𝐄𝐢+ 𝛉𝟓 𝐥𝐨𝐠𝐒𝐢𝐳𝐞 ̅̅̅̅̅̅̅̅̅̅̅̅ + 𝛉𝐢 𝟔(𝐧𝐨𝐧𝐜𝐲𝐜𝐥𝐢𝐜𝐚𝐥 ∗ 𝐃𝐁)𝐢+

𝛉𝟕(𝐧𝐨𝐧𝐜𝐲𝐜𝐥𝐢𝐜𝐚𝐥 ∗ 𝐌𝐄)𝐢+ 𝛉𝟖(𝐧𝐨𝐧𝐜𝐲𝐜𝐥𝐢𝐜𝐚𝐥 ∗ 𝐌𝐏𝐄)𝐢 +𝛉𝟗(𝐧𝐨𝐧𝐜𝐲𝐜𝐥𝐢𝐜𝐚𝐥 ∗ 𝐥𝐨𝐠𝐒𝐢𝐳𝐞 )̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅ + 𝐳𝐢 𝐢

The unexplained parts w_i and z_i are obtained by predicting the residuals from equations (9) and (10). Hence, I decompose the estimated entity effects into an explained part by the time-invariant variables and an unexplained part. In stage 3, I use this unexplained part.

(17)

17 3.3.3 Third stage of the FEVD model

Stage 3 is estimated by pooled OLS. I re-run the full model without the entity effects but with the in stage 2 found unexplained parts w_i and z_i:

(𝟏𝟏) 𝐑𝐎𝐈 𝐢𝐭= 𝛃𝟎+ 𝛃𝟏𝐧𝐨𝐧𝐜𝐲𝐜𝐥𝐢𝐜𝐚𝐥𝐢+ 𝛃𝟐𝐃𝐁𝐢+ 𝛃𝟑𝐌𝐄𝐢+ 𝛃𝟒𝐌𝐏𝐄𝐢+ 𝛃𝟓𝐥𝐨𝐠𝐒𝐢𝐳𝐞𝐢𝐭+ 𝛃𝟔𝐀𝐜𝐭𝐢𝐯𝐞 𝐏𝐚𝐫𝐭𝐢𝐜𝐢𝐩𝐚𝐧𝐭𝐬𝐢𝐭+ 𝛃𝟕(𝐧𝐨𝐧𝐜𝐲𝐜𝐥𝐢𝐜𝐚𝐥 ∗ 𝐃𝐁)𝐢+ 𝛃𝟖(𝐧𝐨𝐧𝐜𝐲𝐜𝐥𝐢𝐜𝐚𝐥 ∗ 𝐌𝐄)𝐢+ 𝛃𝟗(𝐧𝐨𝐧𝐜𝐲𝐜𝐥𝐢𝐜𝐚𝐥 ∗ 𝐌𝐏𝐄)𝐢 +𝛃𝟏𝟎(𝐧𝐨𝐧𝐜𝐲𝐜𝐥𝐢𝐜𝐚𝐥 ∗ 𝐥𝐨𝐠𝐒𝐢𝐳𝐞)𝐢𝐭+𝛃𝟏𝟏(𝐧𝐨𝐧𝐜𝐲𝐜𝐥𝐢𝐜𝐚𝐥 ∗ 𝐀𝐜𝐭𝐢𝐯𝐞 𝐏𝐚𝐫𝐭𝐢𝐜𝐢𝐩𝐚𝐧𝐭𝐬)𝐢𝐭+𝛃𝟏𝟐𝛄𝐭+ 𝛃𝟏𝟑𝐰𝐢+ 𝛆𝐢𝐭 (𝟏𝟐) 𝐑𝐢𝐬𝐤𝐲 𝐢𝐭= 𝛉𝟎+ 𝛉𝟏𝐧𝐨𝐧𝐜𝐲𝐜𝐥𝐢𝐜𝐚𝐥𝐢+ 𝛉𝟐𝐃𝐁𝐢+ 𝛉𝟑𝐌𝐄𝐢+ 𝛉𝟒𝐌𝐏𝐄𝐢+ 𝛉𝟓(𝐥𝐨𝐠𝐒𝐢𝐳𝐞)𝐢𝐭+ 𝛉𝟔(𝐀𝐜𝐭𝐢𝐯𝐞 𝐏𝐚𝐫𝐭𝐢𝐜𝐢𝐩𝐚𝐧𝐭𝐬)𝐢𝐭+ 𝛉𝟕(𝐧𝐨𝐧𝐜𝐲𝐜𝐥𝐢𝐜𝐚𝐥 ∗ 𝐃𝐁)𝐢+ 𝛉𝟖(𝐧𝐨𝐧𝐜𝐲𝐜𝐥𝐢𝐜𝐚𝐥 ∗ 𝐌𝐄)𝐢+ 𝛉𝟗(𝐧𝐨𝐧𝐜𝐲𝐜𝐥𝐢𝐜𝐚𝐥 ∗ 𝐌𝐏𝐄)𝐢 +𝛉𝟏𝟎(𝐧𝐨𝐧𝐜𝐲𝐜𝐥𝐢𝐜𝐚𝐥 ∗ 𝐥𝐨𝐠𝐒𝐢𝐳𝐞)𝐢𝐭+𝛉𝟏𝟏(𝐧𝐨𝐧𝐜𝐲𝐜𝐥𝐢𝐜𝐚𝐥 ∗ 𝐀𝐜𝐭𝐢𝐯𝐞 𝐏𝐚𝐫𝐭𝐢𝐜𝐢𝐩𝐚𝐧𝐭𝐬)𝐢𝐭+𝛉𝟏𝟐𝛄𝐭+ 𝛉𝟏𝟑𝐳𝐢+ 𝛔𝐢𝐭 By doing so, w_i and z_i are not correlated with the vector of the time-invariant variables.

3.3.4 The FEVD model with the financial crisis of 2008 shock

The first stage of the FEVD model for the shock of 2008 is estimated with the following regressions: (𝟏𝟑) 𝐨̂𝐢 = (𝐑𝐎𝐈)̅̅̅̅̅̅̅̅̅ − 𝛃𝐢 𝟏𝐅𝐄̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅)(𝐀𝐜𝐭𝐢𝐯𝐞 𝐏𝐚𝐫𝐭𝐢𝐜𝐢𝐩𝐚𝐧𝐭𝐬 𝐢− 𝛃𝟐𝐅𝐄(𝐧𝐨𝐧𝐜𝐲𝐜𝐥𝐢𝐜𝐚𝐥 ∗ 𝐀𝐜𝐭𝐢𝐯𝐞 𝐏𝐚𝐫𝐭𝐢𝐜𝐢𝐩𝐚𝐧𝐭𝐬)̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅𝐢− 𝛃𝟑𝐅𝐄(𝐧𝐨𝐧𝐜𝐲𝐜𝐥𝐢𝐜𝐚𝐥 ∗ 𝐀𝐜𝐭𝐢𝐯𝐞 𝐏𝐚𝐫𝐭𝐢𝐜𝐢𝐩𝐚𝐧𝐭𝐬 ∗ 𝐲𝟐𝟎𝟎𝟖̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅)𝐢− 𝛃𝟒𝐅𝐄(𝐀𝐜𝐭𝐢𝐯𝐞 𝐏𝐚𝐫𝐭𝐢𝐜𝐢𝐩𝐚𝐧𝐭𝐬 ∗ 𝐲𝟐𝟎𝟎𝟖̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅)𝐢− 𝛃𝟓𝐅𝐄𝛄̅ − 𝐞̅𝐢 (𝟏𝟒) 𝐩̂𝐢 = (𝐑𝐢𝐬𝐤𝐲)̅̅̅̅̅̅̅̅̅̅̅ − 𝛉𝐢 𝟏𝐅𝐄̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅)(𝐀𝐜𝐭𝐢𝐯𝐞 𝐏𝐚𝐫𝐭𝐢𝐜𝐢𝐩𝐚𝐧𝐭𝐬 𝐢− 𝛉𝟐𝐅𝐄(𝐧𝐨𝐧𝐜𝐲𝐜𝐥𝐢𝐜𝐚𝐥 ∗ 𝐀𝐜𝐭𝐢𝐯𝐞 𝐏𝐚𝐫𝐭𝐢𝐜𝐢𝐩𝐚𝐧𝐭𝐬)̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅𝐢− 𝛉𝟑𝐅𝐄(𝐧𝐨𝐧𝐜𝐲𝐜𝐥𝐢𝐜𝐚𝐥 ∗ 𝐀𝐜𝐭𝐢𝐯𝐞 𝐏𝐚𝐫𝐭𝐢𝐜𝐢𝐩𝐚𝐧𝐭𝐬 ∗ 𝐲𝟐𝟎𝟎𝟖̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅)𝐢− 𝛉𝟒𝐅𝐄(𝐀𝐜𝐭𝐢𝐯𝐞 𝐏𝐚𝐫𝐭𝐢𝐜𝐢𝐩𝐚𝐧𝐭𝐬 ∗ 𝐲𝟐𝟎𝟎𝟖̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅)𝐢− 𝛉𝟓𝐅𝐄𝛄̅ − 𝐬̅𝐢 With β₁FE_{, β} 2 FE_{, β} 3 FE_{, β} 4 FE_{, β} 5 FE_θ 1 FE_,_θ 2 FE_,_θ 3 FE_{, θ} 4 FE_{, andθ} 5

FE_{are the pooled OLS estimates of the}

demeaned model in equations (13) and (14).

In stage 2, I regress the entity effects ô_i and p̂_i from stage 1 on the observed time-invariant and rarely changing variables:

(𝟏𝟓) 𝐨̂𝐢 = 𝛃𝟏𝐧𝐨𝐧𝐜𝐲𝐜𝐥𝐢𝐜𝐚𝐥𝐢+ 𝛃𝟐𝐃𝐁𝐢+ 𝛃𝟑𝐌𝐄𝐢+ 𝛃𝟒𝐌𝐏𝐄𝐢+ 𝛃𝟓 𝐥𝐨𝐠𝐒𝐢𝐳𝐞 ̅̅̅̅̅̅̅̅̅̅̅̅ + 𝛃𝐢 𝟔(𝐧𝐨𝐧𝐜𝐲𝐜𝐥𝐢𝐜𝐚𝐥 ∗ 𝐃𝐁)𝐢+ 𝛃𝟕(𝐧𝐨𝐧𝐜𝐲𝐜𝐥𝐢𝐜𝐚𝐥 ∗ 𝐌𝐄)𝐢+ 𝛃𝟖(𝐧𝐨𝐧𝐜𝐲𝐜𝐥𝐢𝐜𝐚𝐥 ∗ 𝐌𝐏𝐄)𝐢 +𝛃𝟗(𝐧𝐨𝐧𝐜𝐲𝐜𝐥𝐢𝐜𝐚𝐥 ∗ 𝐥𝐨𝐠𝐒𝐢𝐳𝐞 )̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅ + 𝛃𝐢 𝟏𝟎(𝐧𝐨𝐧𝐜𝐲𝐜𝐥𝐢𝐜𝐚𝐥 ∗ 𝐲𝟐𝟎𝟎𝟖)𝐢𝐭+ 𝛃𝟏𝟏(𝐃𝐁 ∗ 𝐲𝟐𝟎𝟎𝟖)𝐢𝐭+ 𝛃𝟏𝟐(𝐌𝐄 ∗ 𝐲𝟐𝟎𝟎𝟖)𝐢𝐭+ 𝛃𝟏𝟑(𝐌𝐏𝐄 ∗ 𝐲𝟐𝟎𝟎𝟖)𝐢𝐭+𝛃𝟏𝟒(𝐥𝐨𝐠𝐒𝐢𝐳𝐞 ∗ 𝐲𝟐𝟎𝟎𝟖 )̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅ +𝐢 + 𝛃𝟏𝟓(𝐧𝐨𝐧𝐜𝐲𝐜𝐥𝐢𝐜𝐚𝐥 ∗ 𝐃𝐁 ∗ 𝐲𝟐𝟎𝟎𝟖)𝐢𝐭+ 𝛃𝟏𝟔(𝐧𝐨𝐧𝐜𝐲𝐜𝐥𝐢𝐜𝐚𝐥 ∗ 𝐌𝐄 ∗ 𝐲𝟐𝟎𝟎𝟖)𝐢𝐭+ 𝛃𝟏𝟕(𝐧𝐨𝐧𝐜𝐲𝐜𝐥𝐢𝐜𝐚𝐥 ∗ 𝐌𝐏𝐄 ∗ 𝐲𝟐𝟎𝟎𝟖)𝐢𝐭+ 𝛃𝟏𝟖(𝐧𝐨𝐧𝐜𝐲𝐜𝐥𝐢𝐜𝐚𝐥 ∗ 𝐥𝐨𝐠𝐒𝐢𝐳𝐞 ∗ 𝐲𝟐𝟎𝟎𝟖 )̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅ + 𝐚𝐢 𝐢 (𝟏𝟔) 𝐩̂𝐢 = 𝛉𝟏𝐧𝐨𝐧𝐜𝐲𝐜𝐥𝐢𝐜𝐚𝐥𝐢+ 𝛉𝟐𝐃𝐁𝐢+ 𝛉𝟑𝐌𝐄𝐢+ 𝛉𝟒𝐌𝐏𝐄𝐢+ 𝛉𝟓 𝐥𝐨𝐠𝐒𝐢𝐳𝐞 ̅̅̅̅̅̅̅̅̅̅̅̅ + 𝛉𝐢 𝟔(𝐧𝐨𝐧𝐜𝐲𝐜𝐥𝐢𝐜𝐚𝐥 ∗ 𝐃𝐁)𝐢+ 𝛉𝟕(𝐧𝐨𝐧𝐜𝐲𝐜𝐥𝐢𝐜𝐚𝐥 ∗ 𝐌𝐄)𝐢+ 𝛉𝟖(𝐧𝐨𝐧𝐜𝐲𝐜𝐥𝐢𝐜𝐚𝐥 ∗ 𝐌𝐏𝐄)𝐢 +𝛉𝟗(𝐥𝐨𝐠𝐒𝐢𝐳𝐞 ∗ 𝐲𝟐𝟎𝟎𝟖 )̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅ + 𝛉𝐢 𝟏𝟎(𝐧𝐨𝐧𝐜𝐲𝐜𝐥𝐢𝐜𝐚𝐥 ∗ 𝐲𝟐𝟎𝟎𝟖)𝐢𝐭+ 𝛉𝟏𝟏(𝐃𝐁 ∗ 𝐲𝟐𝟎𝟎𝟖)𝐢𝐭+ 𝛉𝟏𝟐(𝐌𝐄 ∗ 𝐲𝟐𝟎𝟎𝟖)𝐢𝐭+ 𝛉𝟏𝟑(𝐌𝐏𝐄 ∗ 𝐲𝟐𝟎𝟎𝟖)𝐢𝐭+𝛉𝟏𝟒(𝐥𝐨𝐠𝐒𝐢𝐳𝐞 ∗ 𝐲𝟐𝟎𝟎𝟖 )̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅ +𝐢 + 𝛉𝟏𝟓(𝐧𝐨𝐧𝐜𝐲𝐜𝐥𝐢𝐜𝐚𝐥 ∗ 𝐃𝐁 ∗ 𝐲𝟐𝟎𝟎𝟖)𝐢𝐭+ 𝛉𝟏𝟔(𝐧𝐨𝐧𝐜𝐲𝐜𝐥𝐢𝐜𝐚𝐥 ∗ 𝐌𝐄 ∗ 𝐲𝟐𝟎𝟎𝟖)𝐢𝐭+ 𝛉𝛉𝟏𝟕(𝐧𝐨𝐧𝐜𝐲𝐜𝐥𝐢𝐜𝐚𝐥 ∗ 𝐌𝐏𝐄 ∗ 𝐲𝟐𝟎𝟎𝟖)𝐢𝐭+ 𝛃𝛉𝟏𝟖(𝐧𝐨𝐧𝐜𝐲𝐜𝐥𝐢𝐜𝐚𝐥 ∗ 𝐥𝐨𝐠𝐒𝐢𝐳𝐞 ∗ 𝐲𝟐𝟎𝟎𝟖 )̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅ + 𝐱𝐢 𝐢

(18)

18

As before, I obtain the unexplained but now for parts ai and xi by predicting the residuals

from equations (15) and (16). Hence, again I decompose the estimated entity effects into an explained and an unexplained part and the unexplained part is used in stage 3.

To tackle stage 3, I re-run the full model without the entity effects but with the in stage 2 found unexplained parts ai and xi:

(𝟏𝟕) 𝐑𝐎𝐈 𝐢𝐭= 𝛃𝟎+ 𝛃𝟏𝐧𝐨𝐧𝐜𝐲𝐜𝐥𝐢𝐜𝐚𝐥𝐢+ 𝛃𝟐𝐃𝐁𝐢+ 𝛃𝟑𝐌𝐄𝐢+ 𝛃𝟒𝐌𝐏𝐄𝐢+ 𝛃𝟓𝐥𝐨𝐠𝐒𝐢𝐳𝐞𝐢𝐭+ 𝛃𝟔𝐀𝐜𝐭𝐢𝐯𝐞 𝐏𝐚𝐫𝐭𝐢𝐜𝐢𝐩𝐚𝐧𝐭𝐬𝐢𝐭+ 𝛃𝟕(𝐧𝐨𝐧𝐜𝐲𝐜𝐥𝐢𝐜𝐚𝐥 ∗ 𝐃𝐁)𝐢+ 𝛃𝟖(𝐧𝐨𝐧𝐜𝐲𝐜𝐥𝐢𝐜𝐚𝐥 ∗ 𝐌𝐄)𝐢+ 𝛃𝟗(𝐧𝐨𝐧𝐜𝐲𝐜𝐥𝐢𝐜𝐚𝐥 ∗ 𝐌𝐏𝐄)𝐢+ 𝛃𝟏𝟎(𝐧𝐨𝐧𝐜𝐲𝐜𝐥𝐢𝐜𝐚𝐥 ∗ 𝐥𝐨𝐠𝐒𝐢𝐳𝐞)𝐢𝐭+𝛃𝟏𝟏(𝐧𝐨𝐧𝐜𝐲𝐜𝐥𝐢𝐜𝐚𝐥 ∗ 𝐀𝐜𝐭𝐢𝐯𝐞 𝐏𝐚𝐫𝐭𝐢𝐜𝐢𝐩𝐚𝐧𝐭𝐬)𝐢𝐭+ 𝛃𝟏𝟐(𝐧𝐨𝐧𝐜𝐲𝐜𝐥𝐢𝐜𝐚𝐥 ∗ 𝐲𝟐𝟎𝟎𝟖)𝐢𝐭+ 𝛃𝟏𝟑(𝐃𝐁 ∗ 𝐲𝟐𝟎𝟎𝟖)𝐢𝐭+ 𝛃𝟏𝟒(𝐌𝐄 ∗ 𝐲𝟐𝟎𝟎𝟖)𝐢𝐭+ 𝛃𝟏𝟓(𝐌𝐏𝐄 ∗ 𝐲𝟐𝟎𝟎𝟖)𝐢𝐭+𝛃𝟏𝟔(𝐥𝐨𝐠𝐒𝐢𝐳𝐞 ∗ 𝐲𝟐𝟎𝟎𝟖)𝐢𝐭+ 𝛃𝟏𝟕(𝐀𝐜𝐭𝐢𝐯𝐞 𝐏𝐚𝐫𝐭𝐢𝐜𝐢𝐩𝐚𝐧𝐭𝐬 ∗ 𝐲𝟐𝟎𝟎𝟖)𝐢𝐭+ 𝛃𝟏𝟖(𝐧𝐨𝐧𝐜𝐲𝐜𝐥𝐢𝐜𝐚𝐥 ∗ 𝐃𝐁 ∗ 𝐲𝟐𝟎𝟎𝟖)𝐢𝐭+ 𝛃𝟏𝟗(𝐧𝐨𝐧𝐜𝐲𝐜𝐥𝐢𝐜𝐚𝐥 ∗ 𝐌𝐄 ∗ 𝐲𝟐𝟎𝟎𝟖)𝐢𝐭+ 𝛃𝟐𝟎(𝐧𝐨𝐧𝐜𝐲𝐜𝐥𝐢𝐜𝐚𝐥 ∗ 𝐌𝐏𝐄 ∗ 𝐲𝟐𝟎𝟎𝟖)𝐢𝐭+ 𝛃𝟐𝟏(𝐧𝐨𝐧𝐜𝐲𝐜𝐥𝐢𝐜𝐚𝐥 ∗ 𝐥𝐨𝐠𝐒𝐢𝐳𝐞 ∗ 𝐲𝟐𝟎𝟎𝟖)𝐢𝐭+ 𝛃𝟐𝟐(𝐧𝐨𝐧𝐜𝐲𝐜𝐥𝐢𝐜𝐚𝐥 ∗ 𝐀𝐜𝐭𝐢𝐯𝐞 𝐏𝐚𝐫𝐭𝐢𝐜𝐢𝐩𝐚𝐧𝐭𝐬 ∗ 𝐲𝟐𝟎𝟎𝟖)𝐢𝐭+𝛃𝟐𝟑𝛄𝐭+ 𝛃𝟐𝟒𝐚𝐢+ 𝛆𝐢𝐭 (𝟏𝟖) 𝐑𝐢𝐬𝐤𝐲 𝐢𝐭= 𝛉𝟎+ 𝛉𝟏𝐧𝐨𝐧𝐜𝐲𝐜𝐥𝐢𝐜𝐚𝐥𝐢+ 𝛉𝟐𝐃𝐁𝐢+ 𝛉𝟑𝐌𝐄𝐢+ 𝛉𝟒𝐌𝐏𝐄𝐢+ 𝛉𝟓𝐥𝐨𝐠𝐒𝐢𝐳𝐞𝐢𝐭+ 𝛉𝟔𝐀𝐜𝐭𝐢𝐯𝐞 𝐏𝐚𝐫𝐭𝐢𝐜𝐢𝐩𝐚𝐧𝐭𝐬𝐢𝐭+ 𝛉𝟕(𝐧𝐨𝐧𝐜𝐲𝐜𝐥𝐢𝐜𝐚𝐥 ∗ 𝐃𝐁)𝐢+ 𝛉𝟖(𝐧𝐨𝐧𝐜𝐲𝐜𝐥𝐢𝐜𝐚𝐥 ∗ 𝐌𝐄)𝐢+ 𝛉𝟗(𝐧𝐨𝐧𝐜𝐲𝐜𝐥𝐢𝐜𝐚𝐥 ∗ 𝐌𝐏𝐄)𝐢+ 𝛉𝟏𝟎(𝐧𝐨𝐧𝐜𝐲𝐜𝐥𝐢𝐜𝐚𝐥 ∗ 𝐥𝐨𝐠𝐒𝐢𝐳𝐞)𝐢𝐭+𝛉𝟏𝟏(𝐧𝐨𝐧𝐜𝐲𝐜𝐥𝐢𝐜𝐚𝐥 ∗ 𝐀𝐜𝐭𝐢𝐯𝐞 𝐏𝐚𝐫𝐭𝐢𝐜𝐢𝐩𝐚𝐧𝐭𝐬)𝐢𝐭+ 𝛉𝟏𝟐(𝐧𝐨𝐧𝐜𝐲𝐜𝐥𝐢𝐜𝐚𝐥 ∗ 𝐲𝟐𝟎𝟎𝟖)𝐢𝐭+ 𝛉𝟏𝟑(𝐃𝐁 ∗ 𝐲𝟐𝟎𝟎𝟖)𝐢𝐭+ 𝛉𝟏𝟒(𝐌𝐄 ∗ 𝐲𝟐𝟎𝟎𝟖)𝐢𝐭+ 𝛉𝟏𝟓(𝐌𝐏𝐄 ∗ 𝐲𝟐𝟎𝟎𝟖)𝐢𝐭+𝛉𝟏𝟔(𝐥𝐨𝐠𝐒𝐢𝐳𝐞 ∗ 𝐲𝟐𝟎𝟎𝟖)𝐢𝐭+ 𝛉𝟏𝟕(𝐀𝐜𝐭𝐢𝐯𝐞 𝐏𝐚𝐫𝐭𝐢𝐜𝐢𝐩𝐚𝐧𝐭𝐬 ∗ 𝐲𝟐𝟎𝟎𝟖)𝐢𝐭+ 𝛉𝟏𝟖(𝐧𝐨𝐧𝐜𝐲𝐜𝐥𝐢𝐜𝐚𝐥 ∗ 𝐃𝐁 ∗ 𝐲𝟐𝟎𝟎𝟖)𝐢𝐭+ 𝛉𝟏𝟗(𝐧𝐨𝐧𝐜𝐲𝐜𝐥𝐢𝐜𝐚𝐥 ∗ 𝐌𝐄 ∗ 𝐲𝟐𝟎𝟎𝟖)𝐢𝐭+ 𝛉𝟐𝟎(𝐧𝐨𝐧𝐜𝐲𝐜𝐥𝐢𝐜𝐚𝐥 ∗ 𝐌𝐏𝐄 ∗ 𝐲𝟐𝟎𝟎𝟖)𝐢𝐭+ 𝛉𝟐𝟏(𝐧𝐨𝐧𝐜𝐲𝐜𝐥𝐢𝐜𝐚𝐥 ∗ 𝐥𝐨𝐠𝐒𝐢𝐳𝐞 ∗ 𝐲𝟐𝟎𝟎𝟖)𝐢𝐭+ 𝛉𝟐𝟐(𝐧𝐨𝐧𝐜𝐲𝐜𝐥𝐢𝐜𝐚𝐥 ∗ 𝐀𝐜𝐭𝐢𝐯𝐞 𝐏𝐚𝐫𝐭𝐢𝐜𝐢𝐩𝐚𝐧𝐭𝐬 ∗ 𝐲𝟐𝟎𝟎𝟖)𝐢𝐭+𝛉𝟐𝟑𝛄𝐭+ 𝛉𝟐𝟒𝐱𝐢+ 𝛔𝐢𝐭

Consequently, ai and xi are not correlated with the vector of the time-invariant variables.

3.4 Summary of hypotheses

As stated and explained in the first chapter, I expect that pension funds of firms operating in non-cyclical sectors underperform compared to cyclical ones during the sample period of 2000-2012. Conversely, because firms operating in non-cyclical sectors are considered recession proof, I expect that their pension funds perform better than the ones from firms in cyclical sectors resulting in a positive ROI during the financial crisis of 2008.

Since cyclical firms move with the upswings and downswings of the economy, I expect that plan sponsors of firms in non-cyclical sectors invest in less riskier assets during normal or upward movements of the business cycle. Contrarily, as a result of the fact that firms operating in cyclical sectors are hit harder compared to non-cyclical sectors during recessions, I expect that plan sponsors of firms in non-cyclical sectors invest in riskier assets compared to funds in cyclical sectors in the financial crisis of 2008.

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Due to the counter-cyclical character of contributions to DB plans (they are lower in normal or upward economic times and higher during recessions), and because in DC plans reductions in contributions translate into lower pension benefits during a financial crisis (see Severinson and Yermo, 2010), I expect that DB plans underperform compared to DC plans during the sample period, and that DB plans outperform DC plans during the financial crisis of 2008 (via the expenses channel, since total earnings on investments does not consist of contributions by employers or participants. Total expenses consist of payments to provide benefits, see also paragraph 4.3). With respect to allocation towards risky assets, DC plans have lower administration costs and they are more flexible in their asset allocation, hence I expect that DB funds invest in less riskier assets compared to DC plans.

Since ME plans historically have great flexibility in the valuation assumptions and on funding methods in comparison with single-employer types (see Boon et al., 2014), I expect that this type of plans perform better than single-employer (SE) plans, because of this discretion. Considering the fact that ME plans are typically unionized and mainly characterized by cyclical industries (construction, entertainment, see table 3 on page 24), I expect that ME funds of firms in non-cyclical sectors underperform compared to their cyclical counterparts.

I am unaware of literature on multiple employer plans, but since MPE plans ‘shall be applied

as if all employees of each of the employers maintain the plan were employed by a single employer’ (see explanation of the GASB in the literature review), I expect no difference between funds of firms serving in SE plans and MPE plans. But, since multiple employers consist of more than one employer, they have the possibility to spread their risk, hence when there exist a relationship in my sample the sign is expected to be positive for both ROI and risky assets.

In line with research by Dvorak (2012), Andonov et al. (2012), and Dyck and Pomorski (2011), I expect that larger plans do better than small plans in normal and difficult economic times, as a result of economies of scale, the resulting lower fees and the more easy access to valuable information. Following a study by Boon, Brière and Rigot (2014) who find that larger plans have higher allocations to alternative investments (equities and other high risk assets), I expect that larger plans invest in riskier assets. For the same line of reasoning as before, I expect larger plans in non-cyclical sectors underperform and invest in less risky assets compared to funds operating in cyclical ones during the sample period, and conversely that they perform better and invest in riskier assets during the financial crisis of 2008.

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Furthermore, if a pension plan has a higher share of active participants, it receives more contributions, has lower operating costs and the duration of payouts is far in the future (see Rauh, 2009), therefore I expect that during the sample period and with the financial crisis of 2008 this results in higher ROI. Contrary to Cocco and Volpin (on the UK pension trusts, 2007) and in line with Rauh (research on the U.S. state pension funds, 2009), I expect that the share of active plan participants is positively correlated with investment into risky securities, since more active participants leaves the possibility to invest in more risky assets.

4. Data and sample

4.1 Form 5500 of the Department of Labor (DOL)

In order to tackle the questions stated in the introduction, I focus on a sample of corporate pension plans data from the Form 5500 series provided by the U.S. Department of Labor (DOL). Every year, pension plan sponsors are required to file a return with the U.S. Department of Labor (DOL). This source contains information about the active participants, assets, contributions, investments, and type of plan of approximately 800.000 retirement and welfare benefit plans. In this way the government is able to monitor compliance with the Employee Retirement Income Security Act (ERISA) and the Internal Revenue Code (IRS). Due to this rich and extensive form there is a significant lag between the data collection and the time in which aggregate numbers are available to the public. Sponsors have up to ten months to file the forms, and it can take up to two or three years to convert the raw forms. The data must be cleaned, analyzed, and tabulated into a manageable and complete dataset. Following the instruction form on the site of the DOL (http://www.dol.gov/ebsa/pdf/2014-5500inst.pdf), the general information on the plan consists of the type of plan, the business code and the total active participants used to determine the share of active participants of the plan. Schedule H contains financial information about the contributions, earnings on investments and expenses to the plan and the total assets of the plan used to determine the size of the plan.

The starting point of my dataset is motivated by the fact that as of 2000 information on important actuarial assumptions are jointly available. The latest year for which the complete data are available is 2012 (http://www.dol.gov/ebsa/foia/foia-5500.html). In order to get the form 5500 in a workable dataset I used the unbalanced dataset of pension plan filingsfrom Bas Ten Dam (2015). In line with Bikker, Knaap and Romp (2014), I exclude small pension plans

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with less than 150 participants, since this could be tax vehicles. Furthermore, I exclude observations with return on investments under the -100% or over the 50%, since this is caused by unrealistic low or high unrealized returns. Also, an allocation towards risky assets under 0% or over 100% are excluded, as are plans which do not include a business code, since in this case I cannot distinguish between cyclical or non-cyclical sectors. Furthermore, pension plans with no information on return on investments, share of active participants, and the size of the plan are excluded. Last, I excluded plans that changed from type during the sample period, since I need these plans to be time-invariant.

4.2 Variable Construction: identification of cyclical and non-cyclical industries

The Form 5500 contains a six-digit industry classification code (North American Industry Classification, NAICS) that best describes the nature of the plan sponsor’s business.

The first two digits designate the largest business sector, which classify plans into 19 different

industries. If more than one employer or employee organization is involved, the business code for the main business activity of the employers and/or employee organizations is filled in (see instruction form page 78-80 of the Department of Labor: http://www.dol.gov/ebsa/pdf/2014-5500inst.pdf).

I categorize industry sectors into cyclical and non-cyclical, based on their projected correlation with GDP and I assume that all firms in the sector share the same characteristics. For instance, construction and real estate sectors have been projected (and are historically considered) to be cyclical, and all firms in these sectors will share that label.This is in line with papers by Boudoukh, Richardson and Whitelaw (1994) and Berman and Pfleeger (1997). Boudoukh et al. (1994) industrial production growth rates of cyclical sectors have high correlation with the aggregate industrial production growth rate. Industrial production growth rates of non-cyclical sectors have low correlation with the aggregate industrial production growth rate. Berman and Pfleeger (1997) support their finding by looking at the correlation between industry employment and GDP and the correlation between industry final demand and GDP. The higher the correlation, the higher the vulnerability of the industry to the state of the economy. I end up with the following list on page 22, with a cut-off score for cyclicality of 0.5 correlation with projected GDP.

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Table 1 Variable construction of cyclical and non-cyclical sectors

Sector Code Projected

correlation Proyclical Non-cyclical

with GDP sectors sectors

Agricultural, Forestry, Fishing and Hunting 11 -.1532 Yes

Mining, Quarrying, and Oil and Gas Extraction 21 .3290 Yes

Utilities 22 .2471 Yes

Construction 23 .9248 Yes

Information 51 .4218 Yes

Finance and Insurance 52 .6195 Yes

Real Estate and Rental and Leasing 53 .8366 Yes

Professional, Scientific and Technical Services 54 .1138 Yes Management of Companies and Enterprises 55 .5583 Yes

Administrative and Support, Waste Management

and Remediation Serv. 56 .5435 Yes

Educational services 61 -.0129 Yes

Health care and Social Assistance 62 .3031 Yes

Arts, Entertainment and Recreation 71 .6335 Yes

Accommodation and Food Services 72 .6203 Yes

Other Services (Except Public Administration) 81 .4427 Yes

4.3 Variable construction of return on investments and the allocation towards risky assets

Asset allocation has been shown to be an important source of performance and thus income for pension fund. I focus on dimensions that has been widely analyzed in theory: the allocation towards risky assets and the return on investment (ROI).The return on investments is the total earnings on investments minus the total expenses divided by total investment multiplied by 100. The total earnings on investments includes interest, dividends, rents, net gain (loss) on sale of assets; unrealized appreciation (depreciation) of assets, net investment gains (losses) from common/collective trusts, pooled separate accounts, master trust investment accounts, 103-12 investment entities and registered investment companies (e.g. mutual funds), and other income. The total earnings on investments does not consist of contributions by employers, participants or transfers in or out the plan. The total expenses consist of payments to provide benefits, corrective distributions, certain deemed distributions of participant loans, interest expense, and administrative expenses.

There are a number of ways to measure the riskiness of the asset allocation, the most direct method being to measure the volatility of the funds’ portfolios. Since I only have access to

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annual data on pension funds’ returns, I am unable to assess the dynamics of risk. Hence I measure the riskiness of the asset allocation in line with Kisser, Kiff and Soto. (2014):

𝑟𝑖𝑠𝑘𝑦 𝑎𝑠𝑠𝑒𝑡𝑠 =1 − (cash – accounts receivable – US treasuries – corporate debt) total investment

4.2 Descriptive statistics

Tables 3 and 4 show descriptive statistics for my sample with the means and standard deviations between brackets. The final sample consists of a total of 90155 observations of 6935 U.S. corporate DB an DC pension plans with further division in SE, ME, MPE, plans over the period 2000 to 2012.

Table 2 Summary statistics of baseline model

SE ME MPE DB DC DB DC DB DC Procyclical Observations 6285 31475 3679 2724 191 668 Sectors ROI 4.34 6.25 0.60 5.53 4.96 8.50 [14.79] [16.25] [12.85] [11.80] [14.00] [16.07] Allocation towards risky

assets 82.62 94.61 72.21 84.99 86.90 94.66

[19.61] [10.28] [18.46] [20.41] [18.09] [13.91]

Share of active participants 53.59 83.15 48.12 84.99 55.63 81.48

[22.89] [12.45] [13.84] [20.41] [19.95] [12.56] log(total assets) 17.31 16.38 18.25 17.41 18.47 16.86 [1.63] [1.55] [1.44] [1.41] [1.55] [1.74] Non-cyclical Observations 10006 33386 607 245 291 598 Sectors ROI 3.80 6.12 0.56 7.04 3.84 6.00 [15.16] [16.36] [14.71] [12.15] [13.76] [15.52] Allocation towards risky

assets 83.52 94.18 71.23 71.48 80.21 95.08

[18.55] [11.05] [20.94] [33.78] [20.62] [7.75]

Share of active participants 54.13 80.63 45.61 83.92 53.49 80.15

[18.46] [12.97] [20.74] [24.25] [18.72] [14.66]

log(total assets) 17.43 16.57 17.83 16.37 18.24 17.81

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Table 3 Summary statistics of the financial crisis of 2008

Proyclical sector SE ME MPE

DB DC DB DC DB DC

Crisis dummy 0 1 0 1 0 1 0 1 0 1 0 1

Observations 5802 483 29050 2425 3396 283 2515 209 177 14 617 51

ROI 6.98 -27.36 9.41 -31.66 3.39 -32.85 7.76 -21.25 7.19 -23.19 11.58 -28.76

[11.14] [16.34] [11.81] [14.19] [8.27] [10.63] [8.49] [13.03] [10.04] [24.09] [12.10] [10.22] Allocation towards risky

assets 82.91 79.06 94.65 94.08 72.16 72.81 79.75 80.89 87.09 84.55 94.68 94.42 [19.48] [20.80] [10.25] [10.56] [18.34] [19.93] [26.64] [25.93] [18.22] [16.83] [13.89] [14.24] Active participants 53.86 50.39 83.22 82.22 48.13 47.97 85.07 84.10 55.80 53.58 81.57 80.42 [22.90] [22.49] [12.42] [12.83] [13.90] [13.20] [20.34] [21.31] [20.05] [19.28] [12.54] [12.84] Log(total assets) 17.29 17.58 16.35 16.74 18.23 18.42 17.39 17.62 18.46 18.69 16.82 17.29 [1.63] [1.61] [1.55] [1.47] [1.43] [1.49] [1.38] [1.70] [1.55] [1.57] [1.75] [1.60]

Non-cyclical sector SE ME MPE

DB DC DB DC DB DC

Crisis dummy 0 1 0 1 0 1 0 1 0 1 0 1

Observations 9234 772 30823 2563 560 47 225 20 269 22 552 46

ROI 6.72 -31.18 9.32 -32.32 3.62 -35.91 9.08 -15.83 6.51 -28.88 9.15 -31.84

[11.09] [13.47] [11.89] [13.54] [10.11] [11.69] [9.55] [14.84] [9.74] [13.78] [11.03] [10.94] Allocation towards risky

assets 83.67 81.73 94.25 93.41 70.99 74.09 71.32 73.28 80.30 79.28 95.15 94.20 [18.36] [20.61] [10.99] [11.75) [21.04] [19.79] [33.93] [32.85] [20.64] [20.84] [7.59] [9.51] Active participants 54.35 51.57 80.72 79.53 45.80 43.35 84.02 82.81 53.83 49.22 80.27 78.64 [18.49] [17.92] [12.94] [13.22] [20.87] [19.23] [24.12] [26.29] [18.66] [19.31] [14.69] [14.59] Log(total assets) 17.41 17.69 16.54 16.93 17.82 18.03 16.33 16.81 18.22 18.53 17.78 18.17 [1.51] [1.49] [1.56] [1.49] [1.52] [1.54] [1.27] [1.20] [1.75] [1.81] [1.91] [1.83]

5. Results

This section analyses the empirical findings obtained from the FEVD model. The main results of the baseline specifications (1) and (2) are reported in table 5 on the next page with between brackets the t-statistics.

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Table 4 Regression results of the FEVD model for the 2000-2012 period

(1) (2)

Return on

Investments Risky assets

coefficient coefficient Non-cyclical sector -1.15** -0.53 [-1.97] [0.70] DB 1.63*** -11.35*** [13.49] [-83.21] DB*noncyclical -0.62*** -0.00 [-3.81] [-0.01] ME -1.25*** -12.90*** [-10.92] [-100.05] ME*noncyclical -0.14 -2.59*** [-0.47] [-7.76] MPE 2.43*** 0.82*** [9.04] [2.69] MPE*noncyclical -1.72*** -1.60*** [-4.57] [-3.76] LogSize -0.73*** 0.19*** [-30.13] [6.77] LogSize*noncyclical 0.11*** 0.07** [3.20] [1.96] Share_of_Active 0.11*** -0.01*** [46.26] [-3.15] Share_of_Active*noncyclical -0.01* -0.01*** [-1.78] [-3.19] Constant 4.75*** 90.34*** [9.85] [165.81] N 90155 90155 0.76 0.67

Year effects yes yes

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26 5.1 Baseline results for return on investments

Column 1 of table 5 shows the baseline results for return on investments. The estimated coefficient 𝛽₁ for the influence of non-cyclicality of the pension fund on the return on investment has the expected negative sign and is statistically significant at a 5 percent level. Pension funds of firms operating in non-cyclical sectors tend to underperform 1.15 percentage points compared to cyclical pension funds between 2000 and 2012.

The result for the comparison between DB plans and DC plans is highly significant. DB funds tend to outperform DC funds by 1.63 percentage points. Regarding the impact of being a DB fund of a firm serving in a non-cyclical sector, 𝛽7 is highly significant at a 1 percent level.

This means that, ceteris paribus, funds in non-cyclical sectors underperform by 0.62 percentage points compared with cyclical DB funds. With respect to further division of the plans, ME plans underperform by 1.25 percentage points compared to SE plans (𝛽3 is highly significant at a 1

percent level). A reason for this result could be found in a paper by Mitchell and Andrews (1981), who state that plan sponsors of SE plans often absorb some or all of the plan’s administrative expenses rather than charging them directly to the pension trust. Thus the reports of SE pension plans are likely to understate actual expenses and misstate scale economies. ME pension plans are administered by separated trusts and therefore charge the major part of all expenses. Furthermore, I find no difference in performing for multi-employer pension funds operating in non-cyclical sectors compared to cyclical ones (𝛽8 shows no significant effect).

Moreover, I find a statistical significant difference at a 1 percent level between SE plans and MPE plans (𝛽₄ > 0). MPE plans tend to outperform SE plans by 2.43 percentage points. With respect to the interaction term 𝛽₉ funds of firms operating in non-cyclical sectors underperform by 1.72 percentage points.

Additionally, bigger plans tend to underperform by 0.007 percentage points if a plan increases by 1 percent, and pension funds of firms operating in non-cyclical sectors perform better by 0.001 percentage points if a plan increases by 1 percent ( 𝛽10 is significant at a 1

percent level). These results are on a yearly basis, hence this could add up to fairly large differences with the usually large horizons of pension funds. The results are exactly the opposite from what is stated in paragraph 3.4. Hence, the line of reasoning according to research by Bauer et al. (2010) who states that small plans perform better is further exploited in the next paragraphs. In line with the finding of a research by Rauh (2009), 𝛽6 shows a significant effect