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Pension funds' asset allocation and participant age: a test of the life-cycle model.

ABSTRACT

This article examines the impact of participants' age distribution on the asset allocation of Dutch pension funds, using a unique data set of pension fund investment plans for 2007. Theory predicts a negative effect of age on (strategic) equity exposures. We observe that a 1-year higher average age in active participants leads to a significant and robust reduction of the strategic equity exposure by around 0.5 percentage point. Larger pension funds show a stronger age-equity exposure effect. The average age of active participants influences investment behavior more strongly than the average age of all participants, which is plausible as retirees no longer possess any human capital.

INTRODUCTION

The main aim of this article is to assess whether Dutch pension funds' strategic investment policies depend on the age of their participants. A pension fund's strategic investment policy reflects its objectives, presumed to be optimizing return, given the risk aversion of its participants, while the actual asset allocation may depart from the objective as a result of asset price shocks, since pension funds do not continuously rebalance their portfolios (Bikker, Broeders, and De Dreu, 2010). In this article, we focus particularly on the strategic allocation of assets to equities and bonds as representing, respectively, risky and safe assets. The argument for age-dependent equity allocation stems from optimal life-cycle saving and investing models (e.g., Bodie, Merton, and Samuelson, 1992; Campbell and Viceira, 2002; Cocco, Gomes, and Maaenhout, 2005; Ibbotson et al., 2007). An important outcome of these models is that the proportion of financial assets invested in equity should decrease over the life cycle, thereby increasing the proportion of the relatively safer bonds. The key argument is that young workers have more human capital than older workers. As long as the correlation between labor income and stock market returns is low, a young worker may better diversify away equity risk with their large holding of human capital.

Dutch pension funds effectively are collective savings arrangements, covering almost the entire population of employees. This article verifies whether pension funds take the characteristics of their participants on board in their decision-making on strategic investment allocation, and to what extent. We investigate whether--in line with the life-cycle saving and investing model--more mature pension funds pursue a more conservative investment policy, that is, whether they hold less equity in favor of bonds.

For pension funds' strategic asset allocation in 2007, we find that a rise in participants' average age reduces equity holdings significantly, as the theory predicts. A cross-sectional increase of active participants' average age by 1 year appears to lead to a significant and robust drop in strategic equity exposure by around 0.5 percentage point. As a pension fund's asset allocation is determined by many other factors, this awareness of the optimal age-equity relationship and its incorporation in their strategic equity allocation is remarkable. We also find that the equity-age relationship is stronger for active participants than for retired and deferred participants. (1) This is in line with the basic version of the life-cycle model where retirees should hold a constant fraction of their wealth in equities, as they no longer possess any human capital. We also observe that other factors, viz. pension fund size, funding ratio, and participants' average pension wealth, influence equity exposure positively and significantly, in line with expectations. Pension plan type and pension fund type, however, do not have significant impact.

The negative equity-age relationship has been found in other studies as well. For pension funds in Finland, Alestalo and Puttonen (2006) report that a 1-year average age increase reduced equity exposure in 2000 by as much as 1.7 percentage points. Similarly, for Switzerland in 2000 and 2002, Gerber and Weber (2007) report a negative relation between equity exposure and both short-term liabilities and age. The effect they find is smaller yet significant, as equity decreases by 0.18 percentage point if the average active participant's age increases by I year. For the United States, Lucas and Zeldes (2009) did not observe a significant relationship between the equity share in pension assets and the relative share of active participants.

The setup of this article is as follows. The second section highlights the theoretical relationship between the participant's age and equity investments, stemming from the life-cycle saving and investing model. The third section describes important characteristics of pension funds in the Netherlands. The fourth section investigates the age dependency of asset allocation empirically using a unique data set of 472 Dutch pension funds at end-2007. The fifth section presents a number of variants of our model, which act as robustness tests. The sixth section concludes.

LIFE-CYCLE SAVING AND INVESTING

In the late 1960s economists developed models which put forward that individuals should optimally maintain constant portfolio weights throughout their lives (Samuelson, 1969; Merton, 1969). A restrictive assumption of these models is that investors have no labor income (or human capital). However, as most investors do in fact have labor income, this assumption is unrealistic. If labor income is included in the portfolio choice model, the optimal allocation of financial wealth of individuals changes over their life cycle (for an overview, see Bovenberg et al., 2007).

The basic version of the life-cycle model with risk-free human capital (see Campbell and Viceira, 2002) can be summarized by the following equation for the optimal fraction of stock investment, denoted by w

w = H + F/F [micro] - [R.sup.f]/[gamma][[sigma].sup.2] (1)

Here H is the human capital, that is, the total of current and discounted future wages, of an individual, and F is the person's current financial capital. The risk premium of the stock market is given by [mu]-[R.sup.f], while y and [[sigma].sup.2] denote, respectively, the individual's constant relative risk aversion and the variance of stock market returns. The preferred allocation to risky assets should be based on total wealth, being the sum of financial wealth and human capital. As can be seen from (1), more human capital leads to a higher optimal investment in stocks. Furthermore, it follows that retirees should invest a constant fraction of their financial wealth in equities, as their human capital is depleted. (2)

Not only do young workers have more human capital, they also have more flexibility to vary their labor supply--that is, to adjust the number of working hours or their retirement date--in the face of adverse financial shocks. Flexible labor supply acts as a form of self-insurance for low investment returns. Bodie, Merton, and Samuelson (1992) show that this reinforces the optimality result, that is, that younger workers should have more equity exposure. Teulings and De Vries (2006) calculate that young workers should even go short in bonds equal to no less than 5.5 times their annual salary in order to invest in stock. (3) The negative age dependency of asset holdings corresponds to the rule of thumb that an individual should invest (100-age)% in stocks (see Malkiel, 2007).

The negative relationship between age and equity exposure in the portfolio is usually derived under the assumption that human capital is close to risk free, or at least is not correlated with capital return. Benzoni, Collin-Dufresne, and Goldstein (2007) put forward that the short-run correlation is low indeed, while in the longer run, labor income and capital income are cointegrated, since the shares of wages and profits in national income are fairly constant. This finding implies that the risk profile of young workers' labor income is equity-like and that they should therefore hold their financial wealth in the form of safe bonds to offset the high-risk exposure in their human capital. For that reason, Benzoni, Collin-Dufresne, and Goldstein (2007) suggest that the optimal equity share in financial assets is hump-shaped over the life cycle: cointegration between human capital and stock returns dominates in the first part of working life, whereas the decline in human capital accounts for the negative age dependency of optimal equity holdings later in life.

This article focuses on the investment behavior of pension funds. One may ask whether the pension fund should be responsible for optimal age-dependent equity allocation, as participants may adjust their privately held investments so that their total assets, including those managed by the pension fund, reflect their optimal allocation. There are four arguments in favor of optimal investment behavior by the pension fund on behalf of its participants. First, not all participants have privately held assets permitting the required adjustment where the pension fund is suboptimal. Second, and probably more important, most participants of course have neither sufficient financial literacy nor the willingness to carry out such an adjustment (Lusardi and Mitchell, 2007; Van Rooij, 2008). For these reasons, most pension plans take care of investment decisions, often by default. Third, insurance companies are a very cost-inefficient alternative for private offsetting of pension funds' suboptimal investment behavior (Bikker and De Dreu, 2007). And fourth, pension funds are able to broaden the risk-bearing basis by distributing risk across generations. This option is not available to individuals.

CHARACTERISTICS OF DUTCH PENSION FUNDS

As in most developed countries, the institutional structure of the pension system in the Netherlands is organized as a three-pillar system. The first pillar comprises the public pension scheme financed on a pay-as-you-go base. It offers a basic flat-rate pension to all retirees. The benefit level is linked to the statutory minimum wage. The second pillar is that of fully funded "supplementary" pension schemes managed by pension funds. The third pillar comprises tax-deferred personal savings, which individuals undertake on their own initiative. The Dutch pension system is unique in that it combines a state run pay-as-you-go scheme in the first pillar with funded occupational plans in the second pillar. The first pillar implies that young individuals cede part of their human capital to older generations in exchange for a claim on part of the human capital of future generations. Given the life-cycle hypothesis, this type of intergenerational risk sharing reinforces the preference of younger people to invest in equity (Heeringa, 2008).

The supplementary or occupational pension system in the Netherlands is organized mainly in the form of funded defined benefit (DB) plans. The benefit entitlement is determined by years of service and a reference wage, which may be final pay or the average wage over the years of service. Most Dutch pension plans are based on average wage. Because corporate sponsors have no legal obligation to cover any shortfall in the pension funds, the residual risk is borne by the participants themselves. (4) This type of plan may also be labeled as hybrid, having characteristics of both DB and defined contribution (DC) plans. It is partly DB by nature in that the yearly accrual of pension rights is specified in the same way as in a traditional DB plan, and partly DC because the yearly indexation is linked to the financial position of the fund and therefore related to the investment returns (Ponds and Van Riel, 2009). (5)

The DB formula takes the public scheme into account. The DB pension funds explicitly base their funding and benefits on intergenerational risk sharing (Ponds and Van Riel, 2009). Shock-induced peaks and troughs in the funding ratio are smoothed over time, thanks to the long-term nature of pension funds. Pension funds typically adjust contributions and indexation of accrued benefits as instruments to restore the funding ratio. Whereas higher contributions weigh on active participants, lower indexation hurts older participants most. (6) The less flexible these instruments are, the longer it takes to adjust the funding level, and the more strongly will shocks be shared with future (active) participants. Effectively, intergenerational risk sharing extends the risk-bearing basis in terms of human capital. The literature on optimal intergenerational risk sharing rules in pension funding concludes that intergenerational risk sharing within pension funds should generally lead to more risk taking by pension funds compared to individual pension plans (e.g., Gollier, 2008; Cui, De Jong, and Ponds, 2011). Thus Dutch pension funds, with their strong reliance on intergenerational risk sharing, may be expected to invest relatively heavily in risky assets.

There are three types of pension funds in the Netherlands. The first is the industry-wide pension fund, organized for a specific sector of industry (e.g., construction, health care, transport). Participation in an industry-wide pension fund is mandatory for all firms operating in the sector. A corporate can opt out only if it establishes a corporate pension fund that offers a better pension plan to its employees than the industry-wide fund. Where a supplementary scheme exists, either as a corporate pension fund or as an industry-wide pension fund, participation by workers is mandatory and governed by collective labor agreements. The third type of pension fund is the professional group pension fund, organized for a specific group of professionals such as physicians or notaries.

The Dutch pension fund system is massive, covering 94 percent of the active labor force. But whereas all employees are covered, the self-employed need to arrange their own retirement plans. As reported by Table 1, the value of assets under management at the end of 2007 amounted to 690 billion [euro], or 120 percent of Dutch gross domestic product (GDP). More than 85 percent of all pension funds are of the corporate pension fund type. Of the remaining 15 percent, most are industry-wide funds, besides a small number of professional group funds. The circa 95 industry-wide pension funds are the dominant players, both in terms of their relative share in total active participants (> 85%) and in terms of assets under management (> 70%). Almost 600 corporate pension funds encompass over a quarter of the remaining assets, serving 12 percent of plan participants. Professional group pension funds are mostly very small.

In the post-WW2 period, pension plans in the Netherlands were typically structured as final-pay DB plans with (de facto) unconditional indexation. After the turn of the century, pension funds in the Netherlands, the United States, and the United Kingdom suffered a fall in funding ratios. In order to improve their solvency risk management, many pension funds switched from the final-pay plan structure to average-pay plans with conditional indexation. In many cases, indexation is ruled by a so-called policy ladder, with indexation and contribution tied one-to-one to the funding ratio (Ponds and Van Riel, 2009). Under an average-pay plan, a pension fund is able to control its solvency position by changing the indexation rate.

Figure 1 documents that Dutch pension funds increased their exposure to equities over time. Between 1995 and 2007 the median equity exposure tripled from 10.8 percent to 31.8 percent. This increase over time is a combined effect of more pension funds choosing a positive equity exposure (see [P.sub.10] and [P.sub.25] indicating, respectively, the 10th and 25th percentile), and pension funds increasing their exposure.

[FIGURE 1 OMITTED]

EMPIRICAL RESULTS

Our data set provides information on pension fund investments and other characteristics for the year 2007. The figures are taken from supervisory reports to De Nederlandsche Bank, the pension funds' prudential supervisor. Pension funds in the process of liquidation--that is, about to merge with another pension fund or to reinsure their liabilities with an insurer--are exempt from reporting to DNB. The original data set covers 569 (reporting) pension funds, of which 472 (or 83%) invest on behalf of the pension fund beneficiaries, while the remainder are fully reinsured and do not control the investments themselves. Nineteen pension funds do not report the average age of their participants and 54 do not report their strategic asset allocation. Three pension funds with funding ratios above 250 percent were disregarded. These are special vehicles designed to shelter savings from taxes and therefore not representative of the pension fund population we are interested in. Another three pension funds with assets worth over one million euros per participant were excluded for the same reason, as these are typically special funds serving a small number of company board members. These funds, as well as 15 others for which one or more explanatory model variables were unavailable, were omitted from the regressions, so that our analysis is based on the remaining 378 pension funds, including all of the largest pension funds.

Table 2 presents descriptive statistics of our data set, with age and strategic equity allocation as key variables. One possible age measure, the average age of all participants in a pension fund, including active and deferred participants and retirees, equals 50, ranging widely across pension funds between 35 and 79. An alternative definition of age is the average age of active participants, which equals 45, varying across pension funds from 35 to 63. The proportion between retired and deferred participants also varies strongly across pension funds, reflecting the various positions these pension funds occupy in the life cycle or the dynamic development of their industry sector or sponsor firm. The share of equity in fund's strategic asset allocation averages 32.9 percent but ranges from 0 percent to 91 percent. Actual equity allocation differs from the strategic asset allocation due to free-floating (meaning that asset allocation is not constantly rebalanced after stock-price changes) and appears to average 33.2 percent. Furthermore, Table 2 presents statistics on other pension fund characteristics, many of which act as control variables in the regression (see below). The 10 and 90 percent percentiles reveal that these characteristics tend to vary strongly. In our analysis we distinguish between the age of active and the age of total participants.

Average Age of Active Participants

Most life-cycle theories suggest that the relationship between average age and equity allocation is negative (Equation (1); see also Malkiel, 2007), while others postulate a hump-shaped relationship (Benzoni et al., 2007). Lucas and Zeldes (2009) investigate a relationship between the share of active participants and the equity allocation, also assuming a nonlinear age pattern: a (constant) effect during the active years and zero during the retirement years. Gerber and Weber (2007) regarded two definitions of average age: age of all participants and age of active participants, where the latter implies a nonlinear functional form of average age, due to the truncation at retirement age. (7) Instead of choosing one of the various specifications found in the literature, we follow the theoretical life-cycle model expressed in Equation (1): equity investment declining with the age of participants during their active years and remaining constant after retirement. In Dutch regulation deferred participants are treated equal to retirees. As such it is fair to assume a constant equity exposure. Hence, our key age-dependent model for pension funds' strategic equity allocation reads as

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (2)

where i represents the pension fund and age active stands for the average age of each pension fund's active participants. (8) In theory, the full age distribution of all participants matters for the asset allocation, but that data set is not available. Therefore, as a first step, we take average age as a summary statistic. Percentages of both retired and deferred participants (denoted by, respectively, share retired and share deferred) incorporate the (different) constant effect of each group on the equity allocation.

A control variable size is included as larger pension funds tend to invest more in equity (Bikker and De Dreu, 2009; De Dreu and Bikker, 2009). One argument may be that the size of a pension fund will go hand-in-hand with its degree of professionalism, investment expertise and willingness to exploit return-risk optimization. The pension fund's size is defined as its total number of participants, where we take logarithms of size to reduce possible heteroskedasticity. The funding ratio is a determinant of equity allocation as a higher funding ratio provides a larger buffer against equity risk and thus may encourage risk taking. A higher risk margin for equity is required under the Dutch supervisory regime (Bikker and Vlaar, 2007). Note that--unlike the actual equity allocation--strategic equity allocation is not affected directly by price shocks, although gradually, over time, it may be influenced somewhat by trends in the stock market (Bikker, Broeders, and De Dreu, 2010). A set of dummy variables may reflect different behavior patterns related to different types of pension plan (DB versus DC) or pension fund (professional group pension funds (PGPF) and industrywide pension funds (IPF) versus corporate pension funds). (9) Finally, [u.sub.i] denotes the error term.

The left-hand panel of Table 3 presents the estimation results of Equation (2), based on the average age of active participants. A 1-year increase in the average age of active participants is associated with a drop in equity exposure of around 0.4 percentage point (first column in Table 3). (10) Unweighted estimation attaches equal informational value to each observation of a pension fund, irrespective of whether it has 10 participants or 2.5 million. By contrast, a regression weighting each pension funds proportionally according to its size (measured by numbers of participants), assigns equal importance to each participant. Such a weighting regression would yield results that are more closely in line with economic reality. (11) The negative coefficient of age increases to 0.5 in the weighted regression case, while its statistical significance rises sharply. This result confirms the negative relationship between age and risky assets as the life-cycle hypothesis supposes, while it rejects the "100-age" rule of thumb, as our estimate is at -0.5 significantly lower (in absolute terms) than -1. Our results are similar in direction but not in size to the findings of Gerber and Weber (2007, for Switzerland) and Alestalo and Puttonen (2006, for Finland), who find "active-age" coefficients of, respectively, -0.18 and -1.73 percent.

In Equation (2), the coefficient of retirees is not significant. Only in the weighted regression case do we find a small but statistically significant reduction of the equity share for pension funds having relatively many deferred participants. One percentage point more retirees implies a 0.25 percentage point reduction in equity allocation. The absence of this effect in the unweighted regression implies that only the larger pension funds take the optimal equity allocation associated with deferred participants into account. (12) This is confirmed when we drop, as a robustness test, the two largest pension funds (30% of all participants): the two dependency ratios drop to near or total insignificance (results not shown here). (13) Remarkably, in that case, the absolute value of the age effect increases further to 0.66.

Note that it is difficult to compare the coefficients of the average age of active participants on the one hand and those of retirees and deferred participants ratios on the other, as their units are different. From a time-series perspective, the age impact of active participants on equity allocation is stronger than that of deferred participants: 0.51 versus 0.25 (for the weighted regression). Moreover, the average age impact accumulates (as age increases each year), where the ratio effects are one-off: one joins the groups of deferred or retired participants only once. The cross-section perspective also uses the variation in the explanatory variables across pension funds. Here the outcomes are inconclusive. Therefore, we will not draw definite conclusions on the treatment of active versus inactive participants until we obtain results based on the average age of all participants in the next section "Average Age of All Participants," which are easier to interpret. (14)

Turning to the other determinants of the equity allocation in Table 3, we observe that the effect of (the logarithm of) size appears to be positive and sizable (with values around 1), which tallies with the stylized fact that large pension funds invest more in equity. The marginal effect of size--number of participants--on equity exposure is itself dependent on size, due to its logarithmic specification. An increase in the number of participants from 10,000 to 100,000 is associated with an increase of equity allocation by 2.5 percentage points. One reason may be that because larger funds are in a better position to invest in a more elaborate risk management functions, they can accept riskier investments. Another may be that the largest pension funds are "too big to fail" (major problems cannot be ignored by the government), which engenders a moral hazard. We measure size as the total number of participants. (15) The variable total assets would be an alternative size measure but a drawback of total assets might be that this measure cannot safely be regarded as exogenous, because high-equity returns would--for pension funds with a high-equity allocation--enlarge both their size and their equity exposure. This is the more important given that pension funds do not continuously rebalance their asset portfolios (see Bikker, Broeders, and De Dreu, 2010). As a robustness check, we replace the number of participants by total assets as size measure and estimate the model using instrumental variables. The size coefficient does not change much, and remains significant (see Table A1 in Appendix A).

Pension funds with higher funding ratios invest more in equity, because their buffers are able to absorb mismatch risk. This is supported by regulation, which requires that the probability of underfunding be less than 2.5 percent on a 1-year horizon (see Broeders and Propper, 2010). This permits better funded pension funds to take more risks. The coefficient of around 0.25 implies that an increase of the funding ratio by 1 percent translates into an increase of the equity allocation by one-quarter percentage point. Note that the funding ratio does not suffer from endogeneity problems, as the dependent variable is strategic--not actual---equity allocation. Indeed, the actual equity exposure would be affected, as high stock returns simultaneously increase both the funding ratio and the equity allocation (at least under "free-floating"). Because the strategic equity allocation may nevertheless have been adjusted to stock market developments, albeit gradually, we alternatively lag the funding ratio (i.e., take 2006 figures) in our robustness analyses (see the fifth section). As expected, the results hardly change. The dummy variables for pension plan type or pension fund category do not have significant coefficients, except the dummy indicating industrywide pension funds, which points to less equity holdings. Over time, the border line between DB and DC pension plans is increasingly blurring, as DB plans often show also some characteristics of DC plans (see the third section). Furthermore, the number of DC plans is at 10 percent quite low while strong a priori assumptions about equity allocation across plan types are absent.

The goodness of fit of basic Equation (2), measured by the adjusted [R.sup.2], rises from 0.16 for the unweighted model to 0.50 for the weighted specification, confirming that the weighted model explanation is superior.

In order to take the possible impact of changes in risk aversion into account, we add the average pension wealth of the participants in a pension fund to our equity allocation model as an extra explanatory variable. This variable is defined as total pension fund wealth per participant and reflects the average (intended) level of the pension benefits (16) and the pension plan's maturity. We assume a similar average duration of a participant's relationship with their pension fund across all pension funds, the duration being the sum of the endured employment contract and the endured retirement period, so that wealth reflects the (intended) level of a participant's pension benefits. We take logarithms of this variable to reduce possible heteroskedasticity. (17)

The results are presented in the right-hand panel of Table 3. The coefficient of (the logarithm of) personal pension wealth is statistically significant and varies from 4 (unweighted) to 2.2 (weighted). The marginal effect of an increase in personal wealth depends on its level, due to the logarithmic specification. Starting from the average value of 81,000, an increase by one standard deviation of 78,000 is associated with an increase of equity allocation by 1.5 percentage points. These results indicate that pension funds with higher wealth per participant invest relatively more in equity, thereby accepting more risk. The active participants' age effect is slightly stronger in this specification than in the model without the wealth variable. Notably, the share of retirees now also has a significant impact on the equity allocation. For retirees, pension funds invest relatively less in equity, just as has been observed for deferred participants. The coefficients of size and funding ratio do not change after inclusion of the wealth variable. None of the dummy variables for pension plan type or pension fund category carry statistically significant coefficients. Apparently, no systematic differences remain across types of pension plan or pension fund after the incorporated model variables have been taken into account. In fact, the alternative model including the wealth variable has a slightly better goodness of fit than basic Equation (2).

Average Age of All Participants

So far, we have assumed that the average age of active participants is the key variable in explaining the equity allocation ratio and that, as retirees no longer possess any human capital anymore, they hold a constant fraction of their financial wealth in equities. An alternative specification of our model involves equal treatment of all participant categories, where the impact of age on equity allocation is concerned. This model has been used by Malkiel (2007) and Gerber and Weber (2007). Therefore, we replace the three age-related variables in Equation (2) by one average age of all participants ("age total"), resulting in

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (3)

Table 4 reports the estimation results of Equation (3). The age coefficient of the average age of all participants is now insignificant for both the unweighted and the weighted regressions (left-hand panel). If personal wealth is added to Equation (3), the age coefficient becomes significant at -0.17 and -0.38 for, respectively, the unweighted and the weighted regression (right-hand panel). The all participants' average age plays a role but with smaller (negative) magnitudes and lower levels of significance than the active participants' average age in Table 3. All these outcomes point to a limited role for the all participants' average age compared to the active participants' average age. The results confirm that in reality, the age of active participants has been taken into account, while retirees contribute to the equity allocation with a constant, age-independent share of equities, each of which is in line with the lifecycle hypothesis.

Other model coefficients are roughly in line with what we have observed before. We consider the results of Table 3 as the most convincing estimates, for three reasons. First, from an economic point of view, Equation (2) reflects a richer specification of the age-equity relationship, in line with the life-cycle hypothesis. Second, if the average ages both of all participants and of active participants are included in our models of Tables 3 and 4, the coefficient of active age is larger than that of total age in all eight cases (in absolute terms), the coefficient of active age is significantly negative in all eight cases (as expected), and the coefficient of total age is never significantly negative. Third, formal testing of Tables 3 and 4 against a general model encompassing both Equations (2) and (3) provides evidence in favor of Table 3 (i.e., Equation (2)) (see Appendix B). (18) Therefore, we take Equation (2) as our basic model specification and Table 3 as the most relevant estimates.

Other model coefficients are roughly in line with what we have observed before. We consider the results of Table 3 as the most convincing estimates, for three reasons.

First, from an economic point of view, Equation (2) reflects a richer specification of the age--equity relationship, in line with the life-cycle hypothesis. Second, if the average ages both of all participants and of active participants are included in our models of Tables 3 and 4, the coefficient of active age is larger than that of total age in all eight cases (in absolute terms), the coefficient of active age is significantly negative in all eight cases (as expected), and the coefficient of total age is never significantly negative. Third, formal testing of Tables 3 and 4 against a general model encompassing both Equations (2) and (3) provides evidence in favor of Table 3 (i.e., Equation (2)) (see Appendix B). (19) Therefore, we take Equation (2) as our basic model specification and Table 3 as the most relevant estimates.

ROBUSTNESS CHECKS

The specification in the previous section rests on several assumptions regarding relevant covariates, variable definition and functional form. This section considers various departures from the assumptions underlying Equation (2), using weighted regression.

As a first approximation, we have so far assumed the effect of the average age of (active) participants on the equity allocation to be linear. However, Benzoni, Collin-Dufresne, and Goldstein (2007) suggest that the relation between age and equity exposure may be hump-shaped rather than linear. They suggest that the age effect is positive in the younger age cohorts, due to the positive long-term correlation between capital returns and return on human capital (i.e., the wage rate). Benzoni's age-equity relation reaches a maximum around a certain point (7 years before retirement), after which it is downward sloping, as the long-term correlation of wages and dividends loses relevance. A simple but effective way to allow for a nonlinear relationship is the inclusion of a quadratic age term in the regression, known as a second-order Taylor-series expansion, approximating an unknown, more complex relationship. The respective weighted regression model results show that the age coefficients are not in line with the assumption of Benzoni, Collin-Dufresne, and Goldstein about the investment behavior of pension funds (Table 5, first column), as the squared term coefficient is not significant and economically has the "wrong" sign. Hence, we find no support for Benzoni's theory.

With regard to the dependent variable "strategic equity allocation," several robustness checks may be considered. First, shocks in equity prices affect the funding ratio, but as observed in the fourth section, they may also have a certain impact on a fund's strategic equity allocation, which could create an endogeneity problem. For this reason we here lag the funding ratio (see Table 5, second column). Although the sample is somewhat smaller, the results hardly change, especially in terms of significance. The magnitude of the (lagged) funding ratio coefficient is slightly smaller here than in the unlagged specification.

Second, four pension funds have zero equity exposure. This runs counter to the OLS assumption that the dependent variable is of a continuous nature. In practice, equity exposure is censored at 0 percent and 100 percent. One may further argue that moving from zero equity allocation to a positive fraction requires an intrinsically different decision than raising an already positive equity exposure. One way to address this is to omit zero observations for equity, restricting attention to funds with positive equity allocations. This does not alter the essence of the results (not shown here). A more elegant alternative approach is the Tobit model that takes some degree of censoring into account. Table 5, third column, reports the Tobit outcomes. The effect of age and the other OLS results from Table 3 do not change substantially.

Third, where pension funds do not constantly rebalance their portfolio after stock price changes, the actual equity exposure of pension funds may differ from their strategic equity allocation. Bikker, Broeders, and De Dreu (2010) document that pension funds' assets are indeed partially free-floating. As strategic asset allocation reflects a fund's actual decision, it is better suited for determining the decision-making and conscious behavior of pension funds. On the downside, however, this may affect comparability with other studies, such as Alestalo and Puttonen (2006) and Gerber and Weber (2007). Also, while the strategic asset allocation reflects a fund's intention, it does not give its actual behavior. Table 5, right-hand column, documents a regression results for the actual stock allocation. To avoid endogeneity, we lag the funding ratio by 1 year. Sign and size of the coefficients hardly change, though the magnitude of the (lagged) funding ratio coefficient is slightly smaller than it is in the other regressions. Table A2 in Appendix A repeats the Table 5 results but with personal wealth as an extra explanatory variable. The results are quite similar, confirming the robust nature of the investigation.

Finally, we also applied our model to strategic bond allocation instead of strategic equity allocation, where we expect a positive rather than a negative sign for age dependency. The results (not shown here) deviate slightly, as bonds are not the exact complement of equity, due to other investment categories. These estimates confirm the age-bond relationship: the strategic bond exposure is significantly higher when the average age of active participants is higher.

CONCLUSION

This article addresses the effect of the average age of pension funds' participants on their strategic equity allocation. Our first and key finding is that Dutch pension funds with higher average participant age have significantly lower equity exposures than pension funds having younger participants. This negative age-dependent equity allocation may be interpreted as an (implicit) application of the optimal life-cycle saving and investing theory. The basic version of this theory assumes a low correlation between wage growth and stock returns. It predicts that the vast amount of human capital of the young has a strong impact on asset allocation because of risk diversification considerations, as human capital has a different risk profile than financial capital. This awareness of the optimal age-equity relationship for pension funds, and its incorporation in the strategic equity allocation, is notable.

A second finding is that the average age of active participants has a much stronger impact on investments than the average age of all participants. This is in line with the standard version of lifecycle theory which suggests that retirees with depleted human capital should invest a constant fraction of their financial wealth in equities.

A third result is that the age effect is much stronger in larger pension funds than in smaller ones. Apparently, larger funds' investment behavior is more closely aligned with the age dependency from the life-cycle hypothesis. A nonlinear age effect allowing a hump-shaped pattern, as suggested by Benzoni, Collin-Dufresne, and Goldstein (2007), could not been confirmed. However, other factors significantly influencing the strategic equity allocation are pension fund's size, funding ratio, and average personal pension wealth of participants, which all have positive coefficients. If we include personal wealth in our model, we do not observe any effect of pension fund type or pension scheme type on funds' equity exposure.

This research provides valuable insights for contemporary policy issues to do with the aging of society. As society grows older, pension funds will adapt their investment strategies to the needs of the average active participant who will get older over time. This may result in a safer investment strategy. According to the life-cycle saving and investing theory, this is less than optimal for younger participants with low-risk human capital, who will not be able to fully utilize the diversification between human and financial capital. At the same time, this policy may be too aggressive for retirees, whose interests are not weighted that heavily by the pension fund boards. This leads to the recommendation that it might be optimal policy for pension funds to replace the average age-based policy by a cohort-specific investment policy as has been suggested by Teulings and De Vries (2006), Ponds (2008), and Molenaar and Ponds (Forthcoming).

APPENDIX A. ALTERNATIVE ESTIMATIONS

This appendix tests an alternative specification of Equations (2) and (3). The left-hand panel of Table A1 reports the impact of the average age of active participants on strategic equity allocation where the log of total assets has been added as an explanatory variable. This variable replaces the number of participants as a measure of size. Note that the coefficient of total assets is highly significant, implying that large pension funds have higher equity exposures. The fact that we use strategic equity allocation as the dependent variable reduces possible endogeneity effects. (20) Similarly, the right-hand panel of Table A1 shows the results for the model with the age of all participants and total assets as size measure. Table A2 repeats the robustness tests of Table 5, but based on a model including personal wealth. The conclusion remains that our analyses are robust for these kinds of changes in the specification.

APPENDIX B. TESTING ALTERNATIVE MODEL SPECIFICATIONS FOR THE IMPACT OF DEMOGRAPHIC VARIABLES

Table B1 presents estimation results for a more general model of the impact of demographic variables on pension funds' strategic equity allocation, which encompasses both Equations (2) and (3). This specification allows testing of the models of these equations. Equation (2) results when the coefficients of the average ages of retired and deferred participants and the three interaction terms are jointly set to zero, while Equation (3) is obtained when the coefficients of the three average ages and the shares of retired and deferred participants are all set to zero while at the same time, the coefficients of the three interaction terms are assumed identical. Note that Equations (2) and (3) are not nested, so that we cannot test the two alternatives against each other.

Using an F-test for restrictions, only one model, Equation (2) with personal wealth (unweighted), is not rejected at the 5 percent significance level, while a second model, Equation (2) without personal wealth (unweighted), is not rejected at the 1 percent significance level. All four Equation (3) models considered, with and without personal wealth and weighted as well as unweighted, are rejected, even at the 1 percent significance level. For all four models, the F-test statistic is higher for Equation (3) than for Equation (2), reflecting that Equation (3) is rejected more strongly (in three cases) or rejected instead of not rejected (one case). This confirms our empirical evidence and theoretical arguments in favor of Equation (2). Apart from the restrictions, the coefficients in Table A3 are informative as well: the consistent and significant coefficient of the average age of active participants, and the nonsignificance of the other demographic coefficients is noteworthy and adds to the evidence favoring Equation (2) over Equation (3).
TABLE A1
Impact of the Average Age on the Strategic Equity Allocation of
Pension Funds With Total Assets as a Measure of Size (2007)

                                             Equation (2)

                                     Unweighted          Weighted

                                  Coeff.   t-value   Coeff.   t-value

Average age of active             -0.35     -2.39    -0.52     -5.84
  participants
Share of retired participants      0.06      1.17    -0.08     -1.97
Share of deferred participants     0.05      1.22    -0.20     -6.60
Average age of all participants
Total assets (in logs)             1.62      4.68     1.07      4.75
Funding ratio                      0.20      6.84     0.27      9.56
Dummy: Defined benefit             1.03      0.29     6.05      1.27
  plans
Dummy: Professional group          0.75      0.19    -0.73     -0.14
  funds
Dummy: Industry-wide              -3.92     -2.27    -0.73     -0.58
  pension funds
Constant                          -2.09     -0.21     9.84      1.17
[R.sup.2] adjusted                 0.19               0.51
Number of observations              381                381

                                            Equation (3)

                                    Unweighted           Weighted

                                  Coeff.   t-value   Coeff.   t-value

Average age of active
  participants
Share of retired participants
Share of deferred participants
Average age of all participants    -0.02    -0.28     -0.18    -2.72
Total assets (in logs)              1.62     4.89      2.14    12.74
Funding ratio                       0.20     6.57      0.31     9.90
Dummy: Defined benefit             -0.11    -0.03      3.54     0.69
  plans
Dummy: Professional group          -0.71    -0.17      0.74     0.13
  funds
Dummy: Industry-wide               -3.11    -1.95     -4.18    -3.60
  pension funds
Constant                          -12.46    -1.70    -31.76    -4.25
[R.sup.2] adjusted                  0.16               0.42
Number of observations               389                389

TABLE A2
Alternative Specifications of the Weighted Regression Model as
Robustness Tests (2007)

                                      Strategic Equity Allocation

                                           Incl.       Funding Ratio
                                      Squared Age          Lagged

                                   Coeff.   t-value   Coeff.   t-value

Average age of active              -0.58     -6.34    -0.38     -2.91
participants
Ditto, squared (b)                  0.01      1.28
Share of retired participants      -0.12     -2.61    -0.19     -3.53
Share of deferred participants     -0.17     -4.85    -0.23     -5.17
Total number of participants (in    0.78      3.00     1.18      4.03
logs)
Funding ratio                       0.27      9.23
Funding ratio, lagged (2006)                           0.19      5.72
Personal pension wealth (in         2.35      3.91     1.86      2.64
logs)
Dummy: Defined benefit plans        5.88      1.24     3.41      0.60
Dummy: Professional group          -1.44     -0.27    -0.95     -0.18
funds
Dummy: Industry-wide funds          0.91      0.62     0.89      0.60
Constant                           10.72      1.28     9.48      1.13
  [R.sup. 2], adjusted              0.52               0.43
Number of observations               378                362

                                    Tobit Regression

                                   (Censored at 0) (a)

                                   Coeff.      t-value

Average age of active              -0.56        -6.22
participants
Ditto, squared (b)
Share of retired participants      -0.12        -2.62
Share of deferred participants     -0.17        -4.75
Total number of participants (in    0.79         3.03
logs)
Funding ratio                       0.27         9.50
Funding ratio, lagged (2006)
Personal pension wealth (in         2.22         3.76
logs)
Dummy: Defined benefit plans        5.95         1.26
Dummy: Professional group          -0.91        -0.17
funds
Dummy: Industry-wide funds          0.9          0.62
Constant                            9.35         1.13
  [R.sup. 2], adjusted              0.08 (c)
Number of observations               378

                                     Actual Equity

                                      Allocation

                                   Coeff.   t-value

Average age of active               -0.42    -3.61
participants
Ditto, squared (b)
Share of retired participants       -0.21    -4.38
Share of deferred participants      -0.23    -5.79
Total number of participants (in     0.88     3.37
logs)
Funding ratio
Funding ratio, lagged (2006)         0.16     5.31
Personal pension wealth (in          2.37     3.84
logs)
Dummy: Defined benefit plans         5.10     1.09
Dummy: Professional group          -14.23    -2.93
funds
Dummy: Industry-wide funds          -0.11    -0.07
Constant                            24.16     2.49
  [R.sup. 2], adjusted               0.48
Number of observations                367

(a) There are four censored observations, that is, four
observations with zero equity exposure.

(b) Expressed as the deviation from the average age of
participants (as in the Taylor series expansion), allowing for
easier interpretation of the coefficients.

(c) This is the pseudo [R.sup. 2].

TABLE B2
A General Model for the Impact of Demographic Variables on
Pension Funds' Strategic Equity Allocation (2007)

                                            General Model

                                      Unweighted         Weighted

                                  Coeff.   t-value   Coeff.   t-value

Average age of active             -0.50     -1.92    -0.50     -2.70
  participants
Average age of retired             0.02      0.09    -0.20     -1.00
  participants
Average age of deferred            0.12      0.28     1.04      2.32
participants
Share retired participants         1.96      3.21     0.72      0.87
Share deferred participants        0.00      0.01    -0.31     -0.76
Interaction age and share          0.00      0.20    -0.01     -0.87
  active
Interaction age and share         -0.02     -2.56    -0.02     -1.29
  retired
Interaction age and share          0.00      0.27    -0.01     -0.73
  deferred
Total number of participants       0.96      2.43     1.21      4.51
  (in logs)
Funding ratio                      0.21      7.00     0.29      9.92
Personal pension wealth (in
  logs)
Dummy: Defined benefit plans       1.82      0.49     5.51      1.12
Dummy: Professional group funds   -1.23     -0.28    -4.53     -0.78
Dummy: Industry-wide funds        -3.15     -1.56    -2.44     -1.66
Constant                          -1.44     -0.05     7.61      0.26
[R.sup.2], adjusted                0.17               0.53
Number of observations              377                377

                                   Idem, Including "Personal Wealth"

                                      Unweighted         Weighted

                                  Coeff.   t-value   Coeff.   t-value

Average age of active             -0.60     -2.38    -0.79     -4.02
  participants
Average age of retired            -0.10     -0.57    -0.61     -2.71
  participants
Average age of deferred            0.05      0.12     1.00      2.28
participants
Share retired participants         0.78      1.21    -0.46     -0.53
Share deferred participants        0.05      0.11     0.13      0.30
Interaction age and share          0.00      0.40     0.00      0.19
  active
Interaction age and share         -0.01     -0.81     0.00      0.34
  retired
Interaction age and share          0.00      0.58    -0.01     -0.74
  deferred
Total number of participants       1.00      2.60     1.11      0.27
  (in logs)
Funding ratio                      0.19      6.55     0.27      9.41
Personal pension wealth (in        4.01      4.68     2.66      3.83
  logs)
Dummy: Defined benefit plans       1.77      0.49     7.08      1.47
Dummy: Professional group funds   -2.07     -0.49    -4.20     -0.74
Dummy: Industry-wide funds         0.68      0.32    -0.27     -0.17
Constant                          -8.63     -0.31     4.63      0.16
[R.sup.2], adjusted                0.22               0.55
Number of observations              377                377


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(1) Deferred participants are former members who are entitled to future benefits, but who are no longer in the service of the employer.

(2) After retirement human wealth is depleted (H = 0), so that the optimal equity allocation equals w = ([mu] - [R.sup.f])/[gamma][[sigma].sup.2]. This reveals that the retiree still has equity exposure based on his risk aversion parameter [gamma].

(3) A variant of this approach is to buy a house financed by a mortgage loan, as happens much more frequently. However, this does not reflect a well-diversified portfolio.

(4) Although there is no legal obligation, a corporation might experience a moral obligation to participate in sharing losses of its pension fund. Also note that the Netherlands has no pension guarantee fund as opposed to, for example, the United States, the United Kingdom, and Germany. Instead Dutch pension funds are exposed to solvency regulation (see, e.g., Broeders and Propper, 2010).

(5) In recent years a few corporate pension plans were designed as collective DC plans in which the pension promise is still based on average wage but where the contribution rate is fixed for an extended, typically a 5-year, period. Although employers can treat such schemes as DC for accounting purposes, from a legal and therefore regulatory point of view they are treated as DB schemes. Our data do not allow the distinction between DB and CDC plans.

(6) In an average wage DB scheme, the accrued pension rights of the active members are often also subject to conditional indexation.

(7) Alestalo and Puttonen (2006) had data available on active participants only.

(8) Concerning the impact of age on asset allocation, we cannot distinguish between the life-cycle effect, on the one hand and age-dependent risk aversion on the other. However, as that the equity allocation is determined by the pension fund board, the life-cycle effect is more likely to dominate than the risk aversion of the elderly who are not represented in the board.

(9) Willingness of the sponsor company to compensate investment losses could be a relevant explanatory variable also. In practice, however, we hardly observe this willingness, except for a few corporate pension funds. Industry-wide pension funds service multiple corporations and it is unlikely that losses can be fairly distributed among those corporations.

(10) The Goldfeld-Quandt test indicates that the model's heteroskedasticity does not increase with pension fund size.

(11) For instance, dropping the largest two pension funds from the unweighted sample would not noticeably affect the regression results (representing less than 1 percent of the number of observations; result not shown here), whereas they include no less than 30 percent of participants.

(12) To some extent, as the age impacts of active and deferred participants in Equation (2) diverge. Equation (3) in the next section "Average Age of All Participants" is an alternative with equal treatment of both categories.

(13) All results in this article marked "not shown here" are available by request from the authors.

(14) Note that when we include both average age of active participants and average age of all participants in Equations (2) and (3), we only obtain significant negative coefficients for the former explanatory variable. The coefficient of the former variable is also always larger (in absolute terms) than that of the latter variable. This indicates that the effect of active participants is larger than that of inactive participants.

(15) The question may arise whether the number of participants is truly exogenous. If pension funds with higher equity allocation earned higher returns (or, better, a higher risk-return trade-off), employees might be persuaded to join the firms related to these pension funds. Over the last decade, however, Dutch pension funds' equity portfolios did not perform better than their bond portfolios. Note that where participants are linked to a certain industry, they cannot change pension funds, due to the mandatory industry-wide pension regime. And even in a wider context, pension plans turn out to have only limited impact on job choice.

(16) The average intended level of the pension benefits is proportionally to the product of the participant's average salary level and its replacement rate.

(17) Note that privately hold assets may also affect the overall optimal asset allocation of participants. However, due to lack of available data, pension funds cannot take privately hold assets of participants into account.

(18) The logarithms of model likelihood in Table 3 are substantially higher than those in Table 4. Likelihood ratio tests reject the Equation (3) models (Table 4) in favor of the Equation (2) models (Table 3). We take the difference in degrees of freedom into account as Equation (3) has two additional explanatory variables compared to Equation (2). The test is not a pure test on restrictions, as one explanatory variable is different: average age of all participants versus average age of active participants. For this test we exclude the additional five observations in Table 3 (concerning pension funds without active participants), so that we use the same sample for both models.

(19) The logarithms of model likelihood in Table 3 are substantially higher than those in Table 4. Likelihood ratio tests reject the Equation (3) models (Table 4) in favor of the Equation (2) models (Table 3). We take the difference in degrees of freedom into account as Equation (3) has two additional explanatory variables compared to Equation (2). The test is not a pure test on restrictions, as one explanatory variable is different: average age of all participants versus average age of active participants. For this test we exclude the additional five observations in Table 3 (concerning pension funds without active participants), so that we use the same sample for both models.

(20) An alternative is estimating using instrumental variables. Since the variable total assets is highly correlated with number of participants (0.87), the latter may be considered as a relevant and valid instrumental variable for the former. Estimation results hardly differ.

DOI: 10.1111/j.1539-6975.2011.01435.x

Jacob A. Bikker and Dirk W. G. A. Broeders are associated with De Nederlandsche Bank (DNB), Supervisory Policy Division, Strategy Department, Amsterdam, the Netherlands. Jacob A. Bikker can be contacted via e-mail: j.a.bikker@dnb.nl. Bikker is also Professor of "Banking and Financial Regulation," School of Economics, Utrecht University, the Netherlands. David A. Hollanders is a postdoc researcher at Tias Nimbas Business School, University of Tillburg. Eduard H. M. Ponds is Professor of "Economics of Pensions," Tilburg University. He is also associated with All Pensions Group (APG). All four authors are also affiliated with Netspar. The authors would like to thank Jack Bekooij for excellent research assistance, and two anonymous referees, Lans Bovenberg, Paul Cavelaars, Willem Heeringa, Klaas Knot, Theo Nijman, Frans de Roon, Bert Stroop, and participants in lunch seminars of Netspar (University of Tilburg, April 16, 2009), DNB (April 21, 2009), "Amsterdams Instituut voor Arbeidsstudies" (AIAS, April 23, 2009), SEO (University of Amsterdam, July 6, 2009), and Netspar Pension Day (November 13, 2009) for helpful comments. The views expressed in this article are personal and do not necessarily reflect those of DNB or APG.
TABLE 1
Pension Funds in the Netherlands (End-2007)

                Number                  Active
                of Funds   Assets    Participants   DB (a)   DC (a)
                                         In %

Corporate          85        27           12          90       10
pension funds

Industry-wide      13        71           87          96        4
pension funds

Professional        2         3           1           83       17
group pension
funds

                      In Absolute Numbers

Total           713        690 bln    5,559,677
                           [euro]

Source: De Nederlandsche Bank (DNB).

(a) Figures as per begin-2006.

TABLE 2
Descriptive Statistics of Our Data Set Including 378 Pension Funds

                                                           Other
                                                        Percentiles

Variable                            Mean     Median     10%       90%

Average age of active                45.2     44.6     39.9      50.1
  participants
Average age of all participants      50.2     49.7     41.7      59.6
Strategic equity exposure (in        32.9     33.0     16.4      46.4
  % of total investments)
Actual equity allocation (in %)      33.2     33.6     17.6      46.9
Average assets of participants       81.2     58.4     11.7     155.4
  (in thousand [euro])
Share of retired (in %)              20.9     17.4      4.0      41.5
Share of deferred participants       42.3     40.8     23.3      65.7
  (in %)
Share of active participants         36.8     36.5     15.3      59.8
  (in %)
Funding ratio (in %)                139.4    135.4    120.2     163.9
Total assets (in million            1,791      150     20.3     2,153
  [euro])
Total number of participants         42.3      2.5      0.4      43.3
  (in thousands)
Defined benefit schemes (in %)        0.97     1        1         1
Defined contribution schemes          0.03     0        0         0
  (in %)
Industry-wide pension funds           0.20     0        0         1
  (in %)
Corporate pension funds (in %)        0.78     1        0         1
Professional group pension            0.02     0        0         0
  funds (in %)

Note: The 378 pension funds are the minimum number of pension funds
included in the various regression analyses.

Source: DNB calculations.

TABLE 3
Impact of the Average Age of Active Participants on the Strategic
Equity Allocation of Pension Funds (2007)

                                           Equation (2)

                                     Unweighted          Weighted

                                 Coeff.   t-value   Coeff.   t-value

Average age of active            -0.39     -2.50    -0.51     -5.54
participants
Share of retired participants     0.09      1.91    -0.06     -1.33
Share of deferred participants    0.03      0.71    -0.25     -9.68
Total number of participants      1.07      2.74     0.94      3.57
  (in logs)
Funding ratio                     0.20      6.86     0.28      9.51
Personal pension wealth (in
  logs)
Dummy: Defined benefit            1.62      0.45     6.51      1.35
  plans
Dummy: Professional group         1.68      0.41    -1.17     -0.22
  funds
Dummy: Industry-wide             -4.14     -2.09    -0.74     -0.51
  funds
Constant                          9.30      0.96    15.71      1.89
[R.sup.2], adjusted               0.16               0.50
Number of observations             380                380

                                  Idem, Including "Personal Wealth"

                                    Unweighted         Weighted

                                 Coeff.   t-value   Coeff.   t-value

Average age of active            -0.44     -2.88    -0.56     -6.20
participants
Share of retired participants     0.04      0.89    -0.12     -2.60
Share of deferred participants    0.09      2.09    -0.17     -4.73
Total number of participants      1.07      2.79     0.78      2.98
  (in logs)
Funding ratio                     0.20      6.89     0.27      9.46
Personal pension wealth (in       4.03      5.21     2.23      3.74
  logs)
Dummy: Defined benefit            0.37      0.10     6.00      1.27
  plans
Dummy: Professional group         0.56      0.14    -0.95     -0.18
  funds
Dummy: Industry-wide              0.37      0.18     0.89      0.60
  funds
Constant                         -5.02     -0.51     9.48      1.13
[R.sup.2], adjusted               0.21               0.52
Number of observations             378                378

TABLE 4
Impact of the Average Age of All Participants on Pension Funds'
Strategic Equity Allocation (2007)

                                             Equation (3)

                                     Unweighted          Weighted

                                  Coeff.   t-value   Coeff.   t-value

Average age of all participants   -0.04     -0.48      0.07     0.92
Total number of participants       1.51      4.05      2.45     9.37
  (in logs)
Funding ratio                      0.21      7.10      0.33     9.89
Personal pension wealth (in
  logs)
Dummy: Defined benefit plans       0.76      0.21      3.69     0.66
Dummy: Professional group funds    0.59      0.14      1.62     0.26
Dummy: Industry-wide funds        -5.22     -2.79     -7.11    -4.79
Constant                          -6.63     -0.92    -41.67    -5.00
[R.sup.2], adjusted                0.15                0.33
Number of observations              385                 385

                                   Idem, Including "Personal Wealth"

                                      Unweighted          Weighted

                                  Coeff.   t-value   Coeff.   t-value

Average age of all participants    -0.17    -2.00     -0.38    -4.65
Total number of participants        1.59     4.33      1.22     4.45
  (in logs)
Funding ratio                       0.20     6.83      0.29     9.55
Personal pension wealth (in         3.67     5.02      3.79     8.93
  logs)
Dummy: Defined benefit plans       -0.60    -0.17      3.97     0.78
Dummy: Professional group funds    -1.81    -0.46     -0.57    -0.10
Dummy: Industry-wide funds         -0.12    -0.06      0.46     0.29
Constant                          -13.21    -1.86    -18.50    -2.31
[R.sup.2], adjusted                 0.20               0.45
Number of observations               383                383

TABLE 5
Alternative Specifications of the Weighted Regression Model as
Robustness Tests (2007)

                                      Strategic Equity Allocation

                                                        Funding Ratio
                                   Incl. Squared Age        Lagged

                                   Coeff.   t-value   Coeff.   t-value

Average age of active              -0.51     -5.56     -0.39    -2.95
participants
Ditto, squared (b)                  0.01      0.59
Share of retired participants      -0.05     -1.29     -0.13    -2.71
Share of deferred participants     -0.26     -9.39     -0.31   -10.19
Total number of participants (in    0.95      3.59      1.30     4.44
  logs)
Funding ratio                       0.28      9.37
Funding ratio, lagged (2006)                            0.19     5.65
Dummy: Defined benefit plans        6.47      1.34      4.05     0.71
Dummy: Professional group          -1.40     -0.26    -15.76     0.00
  funds
Dummy: Industry-wide funds         -0.77     -0.53     -2.13     0.18
Constant                           16.46      1.95     26.61     0.01
[R.sup.2], adjusted                 0.50                0.41
Number of observations               380                 363

                                    Tobit Regression:
                                   (censored at 0) (a)

                                   Coeff.      t-value

Average age of active              -0.50        -5.54
participants
Ditto, squared (b)
Share of retired participants      -0.06        -1.34
Share of deferred participants     -0.25        -9.71
Total number of participants (in    0.95         3.62
  logs)
Funding ratio                       0.28         9.54
Funding ratio, lagged (2006)
Dummy: Defined benefit plans        6.46         1.35
Dummy: Professional group          -1.12        -0.21
  funds
Dummy: Industry-wide funds         -0.72        -0.50
Constant                           15.57         1.88
[R.sup.2], adjusted                 0.07 (c)
Number of observations               380

                                     Actual Equity
                                       Allocation

                                   Coeff.   t-value

Average age of active               -0.44    -3.69
participants
Ditto, squared (b)
Share of retired participants       -0.14    -3.13
Share of deferred participants      -0.33   -12.02
Total number of participants (in     1.05     3.97
  logs)
Funding ratio
Funding ratio, lagged (2006)         0.16     5.15
Dummy: Defined benefit plans         7.31     1.55
Dummy: Professional group          -14.01    -2.83
  funds
Dummy: Industry-wide funds          -1.95    -1.36
Constant                            34.24     3.61
[R.sup.2], adjusted                  0.46
Number of observations                368

(a) There are four censored observations, that is, four
observations with zero equity exposure.

(b) Expressed as the deviation from the average age of
participants (as in the Taylor series expansion), allowing for
easier interpretation of the coefficients.

This is the so-called pseudo [R.sup.2].
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Article Details
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Author:Bikker, Jacob A.; Broeders, Dirk W.G.A.; Hollanders, David A.; Ponds, Eduard H.M.
Publication:Journal of Risk and Insurance
Article Type:Report
Geographic Code:4EUNE
Date:Sep 1, 2012
Words:11174
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