Pension fund investments in infrastructure

Infrastructure investment is increasingly important for institutional investors. This paper focuses on pension fund allocations to infrastructure, using the CEM Benchmarking database. We document that larger pension funds, public pension funds, and pension funds with a higher allocation to other alternative assets are more likely to invest in infrastructure. Pension funds across the globe face infrastructure investment costs that are comparable, but we observe significant scale advantages in infrastructure investments, with larger pension funds exhibiting lower investment costs, and higher net returns. Importantly, infrastructure has been among the best-performing asset classes, as measured by net returns, and we document persistence in pension fund infrastructure investment performance over a one-year horizon.


Introduction
The link between infrastructure investments and long-term economic growth has been well-established (Duclos et al. 2013;Roller and Waverman 2001). Infrastructure is generally defined as the essential physical and organizational structures that facilitate the functioning of a society. It is therefore not surprising that governments spend significant amounts of capital on all sorts of public infrastructure, varying from social infrastructures, such as schools and hospitals to roads, airports, harbors, and energy/utility/water networks. In addition to regular infrastructure spending, infrastructure investments are also used as part of long-term economic stimulus packages, including China's Belt and Road Initiative plan, the recent Biden infrastructure package, and Europe's COVID recovery plan, NextGenerationEU.
Even though government spending on infrastructure is sizeable, the World Bank's Global Infrastructure Outlook (2018) 1 forecasts a global infrastructure investment need of USD97 trillion by 2040, and more importantly, it forecasts a USD15 trillion gap between the projected and needed infrastructure investments. One important reason for the struggle of governments to meet infrastructure needs is that the amount of capital required to close the infrastructure gap far exceeds the resources that countries can raise in a fiscally and macroeconomically responsible manner (Schwartz et al. 2020). As a result, calls for institutional investors, pension funds and insurance companies to invest in public infrastructure projects have intensified. As an example, half of the European Green Deal's USD1.2 trillion investment plan to eliminate or offset all EU greenhouse gas emissions by 2050 is expected to come from institutional capital. 2 While the recent interest in the asset class seems new, infrastructure investment is old. A majority of the first stocks ever listed on stock exchanges were railway and infrastructure companies. For example, the Philadelphia Stock Exchange, which was the first stock exchange in the USA, was essential in raising funds for multiple paramount public work projects. Examples of these initial public projects funded by the stock exchange include the first toll road by the Philadelphia and Lancaster Turnpike company in the year 1796, the Pennsylvania Railroad, the Philadelphia Railway, and the Reading Railway in 1840. 3 This prevalence of infrastructure investments was reflected in the composition of the original stock indices. For example, the original S&P500 index was composed of 425 industrial stocks, 15 rail stocks, and 60 utility stocks. 4 Yet, infrastructure was only recently re-discovered as a distinct asset class, starting in the 1990s in Australia (Inderst 2020). Over the past 2 decades, pension funds, sovereign wealth funds, and insurance companies have started allocating significant resources to infrastructure (Andonov et al. 2021). Institutional interest has been furthered by the lowyield environment over the past decade and the appealing investment characteristics of infrastructure. Supposedly, infrastructure offers long-term stable returns, low risk, low correlation with other asset classes, and a natural fit with long-lasting and often inflation-linked pension liabilities. Furthermore, ESG regulations explain some 25-40% of the higher allocation to infrastructure investments made by public investors (Andonov et al. 2021). However, the empirical foundations for these claims are weak (Wurstbauer and Schäfers 2015), and are mostly limited to listed infrastructure investment, due to lack of credible and accessible performance data for direct investments. For example, Marzuki and Newell (2020) examine the MSCI global infrastructure benchmark series, a composite index of publicly traded infrastructure companies, over the 2008-2019 period and document that infrastructure delivered returns of 6.16% per year with a volatility rate of 10.27%. In addition, the authors document that infrastructure outperformed other asset classes, delivered inflation-linked returns, and found that including infrastructure in a mixed-asset portfolio enhanced performance.
To our knowledge, the only recent paper investigating private infrastructure investments is Andonov et al. (2021), who examined the private infrastructure investments of 650 institutional investors. They find that unlisted infrastructure funds do not provide more stable returns to institutional investors as compared to other "alternative" asset classes, while many institutional investors include infrastructure in their portfolios based on the expectations of stable cash flows. They conclude that investment in infrastructure via the private fund channel does not deliver on the promises often made about infrastructure as an asset class.
This very limited body of research contrasts markedly with the ongoing allocation to infrastructure by pension funds all over the world. Whereas investor characteristics, investment approaches, costs, and performance of alternative assets like real estate, private equity, and hedge funds have been widely researched [see, for example, Andonov et al. (2015), Harris et al. (2014), Capocci and Hübner (2004), Jorion (2021)], this is not the case for infrastructure investments.
This paper provides detailed empirical insight into the choices and consequences of pension funds investing in the infrastructure asset class, including investment strategy, costs, and investment performance.
The results show that in 2018, about 48% of all pension funds in the CEM Benchmarking database 5 invested in infrastructure, with an average allocation of 4.1% of total assets for those who do. Larger pension funds and pension funds with a higher percentage allocation to other alternative assets in their portfolios are more likely to invest in infrastructure. When pension funds decide to invest in infrastructure assets, they must choose an investment approach. Pension funds generally employ five distinct investment approaches to gain exposure to infrastructure assets: internal management, coinvesting, open-end funds, limited partnerships, and fund of funds. 6 We find that in 2018 only 13% of the pension funds in our sample chose to manage infrastructure investments internally. Smaller pension funds are more likely to rely on financial intermediaries, whereas larger pension funds are more likely to invest internally. However, even among the 20% largest pension funds investing in infrastructure, with on average USD174 billion in assets under management, just 30.4% chose to manage their infrastructure investments internally.
The choice of investment approach has significant effects on the investment costs of pension funds' infrastructure holdings. The average fee of a pension fund investment in infrastructure is 110 bps. The fee is substantially higher for investments made through external vehicles (166 bps) as compared to internal channels (46 bps). In comparison to other alternative assets, the average investment costs of infrastructure are considerably lower than private equity (270 bps) and hedge funds (208 bps), and similar to real estate (92 bps). We document economies of scale in the cost of infrastructure investments of pension funds, with 3 https:// phila delph iaenc yclop edia. org/ essays/ phila delph ia-stockexcha nge/#: ~: text= These% 20inc luded% 20The% 20Fir st% 20Ban k,Insur ance% 20Com pany% 20of% 20Nor th% 20Ame rica. 4 https:// globa lfina ncial data. com/ the-sp-compo site-before-1957. 5 For more information on the CEM Benchmarking, please refer to the following source: https:// www. cembe nchma rking. com/. 6 We will provide clarity on CEM's definition of these approaches in the Data section. a doubling of the infrastructure mandate size leading to a reduction in costs by 3.85 bps.
Investigating net returns to infrastructure investments, we document that infrastructure, after private equity, has been the best-performing asset class over the 2007-2018 time period, with a net return of 10.1%. Furthermore, we do not find evidence that financial intermediation leads to significantly lower net returns in comparison to internal management, contrasting much of the literature on intermediation (e.g., Andonov et al. 2015). Larger mandate size leads to better net performance, with a doubling of the infrastructure mandate size increasing net returns by 84 bps.
Clearly, infrastructure has become a well-established component of the institutional mixed-asset portfolio, at least for the larger pension funds across the globe. Our findings support the increased interest, both at the extensive and intensive margin, showing favorable risk/return characteristics for infrastructure investments over the past 12 years, with significant economies of scale in the infrastructure allocation. Of course, like any alternative asset, investing in infrastructure requires skill and local knowledge. For most pension funds this implies a need for intermediaries. Importantly, our results regarding the impact of the investment approach only partially support Stoughton et al. (2011) theory of financial intermediation, according to which highnet-worth institutions do not invest through funds of funds and achieve superior returns because underperforming assets are sold indirectly through these funds. While we document that larger pension funds make less use of funds-of-funds and that funds-of-funds exhibit significantly higher investment costs and marginally lower net returns than alternative investment approaches, we do not find evidence that the use of funds-of-funds leads to significant underperformance compared to internal investment management.
Even though infrastructure seems to develop quite rapidly as an asset class, it still lags behind other "alternatives" such as real estate and private equity, both in terms of overall allocation and from the perspective of institutionalization. There is a dearth of performance data at the infrastructure asset level, and with that a lack of appropriate benchmarks to assess the relative performance of fund managers. 7 Liquid infrastructure offerings can be found in the publicly traded realm, but the universe of infrastructure companies is still limited, and there is no "core," easy-to-access infrastructure offering in the private space as of yet (compared to the openend diversified core equity (ODCE) universe in real estate 8 ). Also, the siren song on the investment characteristics of infrastructure may slowly fade. As the infrastructure industry continues to develop and institutionalize, capital inflows may reduce the relatively attractive returns achieved over the past years (although asset values may inflate further, boding well for existing investors).
Furthermore, this paper contributes to the literature by providing insights into the costs of investing in infrastructure and the return profiles of all investment vehicles. This is a unique feature of the CEM Benchmarking database, as other commonly used data sources (e.g., Preqin) do not have information on cost levels and primarily cover closed-end fund structures.
The remainder of this paper is structured as follows. The next section describes the dataset, which is followed by an investigation of the determinants of infrastructure allocations by pension funds in "Infrastructure allocations and costs" and "Pension fund characteristics and infrastructure investments" sections. "The cost of pension fund infrastructure investments" section shows the analysis of the effect of fund characteristics and investment choices on investment costs. The "Pension fund performance in infrastructure investments" section presents the performance outcomes of pension funds in infrastructure on a net return basis and investigates performance persistence in infrastructure investments. The "Conclusions" section concludes.

Data
We employ the CEM Benchmarking global pension fund database (hereafter referred to as the CEM database), the broadest global database reporting on pension fund asset allocation and investment, which includes detailed information on investment approach, costs, performance, and benchmarking choices for each separate asset class. The CEM database is the only database available for academic research that contains information on costs at the pension fund level and on the (net) performance of internal mandates. To our knowledge, Preqin, a prominent data company on private equity transactions, does not contain any cost information. Furthermore, Preqin does not collect information on the performance of open-end funds and internal mandates. In this way our study builds on Andonov et al. (2021), which only covers limited partnership structures.
The CEM database has been used previously in a variety of studies of pension fund investments (see Carlo et al. 2021 for a discussion). Since reporting to CEM is done on a voluntary basis, the database could be liable to self-reporting bias. Andonov et al. (2012) address this issue and document that there is no evidence that pension funds enter or exit the CEM database based on their performance, yet they note that larger funds are more likely to remain in the database.
The CEM database covers 1132 defined benefit pension funds over the 1991-2018 time period. The total pension fund assets under management included in the CEM database have grown from USD612 billion in 1991 to USD9.9 trillion in 2018, representing almost 25% of total global pension fund assets in 2018. 9 While CEM gathers data on pension funds' investments in several asset classes, this paper concentrates on the infrastructure allocations by pension funds. Pension funds can get exposure to infrastructure in various ways, such as municipal bonds, tax increment bonds (TIF), and listed and unlisted infrastructure equity funds. In the CEM database, infrastructure data solely includes pension fund investments in unlisted infrastructure, distinguishing between internal and external infrastructure holdings. Investments in publicly traded infrastructure assets are not separately captured and are included in public equity mandates. As we do not have asset-level data, we are unable to identify whether the infrastructure investments are economic infrastructure investments (e.g., transportation, communication, and energy assets) or social infrastructure investments (e.g., hospitals, prisons, and administrative buildings); nor do we know if they concern greenfield or brownfield investments, and nor the ex-ante risk profile of the investment (i.e., core versus opportunistic).
CEM started to report on "infrastructure" as a separate asset class in the year 2002. However, before 2007, pension fund allocations to the infrastructure asset class were very limited. The last year for which we have data is 2018. Therefore, we focus our analysis on the 2007-2018 period. We provide descriptive statistics of our sample coverage in Tables 7 and 8 in the Appendix. As the tables show, most of the pension funds in the database are from the North American region, including 534 out of the 782 funds in the sample. There are also many European funds in our sample, with 219 unique pension funds, primarily covering the UK and the Netherlands. Figure 1A shows the percentage of pension funds in the CEM database investing in infrastructure assets. Clearly, infrastructure investment has been rising steadily over time, from 12% of pension funds in 2007 to 47.5% in 2018. To put this into perspective, the percentage of pension funds investing in other alternative, but more established alternative assets, was 88.3% for real estate, 74.2% for private equity, and 57.1% for hedge funds in that same year. When looking at regional differences, Fig. 1A shows that U.S. pension funds are less likely to invest in infrastructure as compared to their peers in Canada, Europe, and the rest of the world.

Infrastructure allocations and costs
For the pension funds that do invest in infrastructure, we observe an increasing trend in average holdings, as illustrated in Fig. 1B. In dollar terms, the total value of pension fund infrastructure holdings in the CEM database increased from less than USD29 billion in 2007 to almost USD245 billion in 2018, illustrating the rapid rise of institutional infrastructure investments worldwide. The solid line depicts the global average infrastructure allocation for the group of pension funds investing in the asset class, as a percentage of total pension fund assets (i.e., weighted average). This rises from 2.4% in 2007 to 4.1% in 2018. In addition, the figure shows that the infrastructure allocations differ significantly across regions, with Canadian pension funds showing the strongest growth and the highest allocations. In 2018, the Canadian pension funds with infrastructure exposure allocated an average of 8.5% of total assets. On the other hand, the more hesitant approach towards infrastructure investments by U.S. pension funds illustrated in Fig. 1A is also apparent for pension funds that decided to invest in infrastructure-on average, allocations were "just" 1.0% of total assets in 2018. The increase in allocation does not seem to come at the cost of other alternative asset classes, which implies that infrastructure forms part of the wider private asset revolution, where pension funds move away from traditional asset classes like public equities and fixed income. Table 1 provides more detailed information about infrastructure allocations, with information on portfolio holdings in U.S. dollars. Panel A provides a regional perspective and panel B provides data across investment approaches. All numbers relate to 2018. Panel A demonstrates that the differences in percentage allocation to infrastructure across regions lead to substantial variation in the average infrastructure holding size of pension funds. For example, Canadian funds with infrastructure exposure have substantially larger average infrastructure holdings than European and U.S. pension funds in 2018, but the table also shows that this is mainly caused by a few very large outliers: in terms of median holdings per pension fund, the U.S. trumps Canada and Europe.

Investment approaches
Pension funds use five distinct investment approaches for their infrastructure investments. CEM Benchmarking reports infrastructure investment either as internal, co-investment, open-end, limited partnership, or fundof-funds. The internal category means that the portfolio of infrastructure investments is managed by a dedicated in-house investment department. On the other hand, the open-end stands for private open-end infrastructure funds, while limited partnerships refer to closed-end funds with a predetermined holding period. Co-investments sit between internal and external, with a pension fund taking a direct stake in an infrastructure investment, but the investment is managed externally. Pension funds can make co-investments only when they are invited to co-invest by their general partners. Thus, the co-investments exist conditional on investing in limited partnerships or funds-of-funds. Pension funds that allocate capital to infrastructure via B Infrastructure as a percentage of total pension fund assets (by region). Note: A presents the percentage of pension funds in the CEM Benchmarking database investing in infrastructure by year and region. B presents pension-fund size weighted infrastructure holdings as a percentage of total pension fund assets for the pension funds that invest in infrastructure fund-of-funds rely on intermediaries to select limited partnerships (i.e., infrastructure funds).
Panel B of Table 1 shows that there are considerable differences in the size of infrastructure holdings by investment approach. As an illustration: the average capital allocated through internal infrastructure investment is approximately twice as much as the other four investment approaches combined (both in terms of mean and median). Funds-of-funds are the least chosen route to acquire infrastructure exposure.
To investigate which investment approaches are taken by pension funds over time, Fig. 2 displays the development of the investment approach used by pension funds for their infrastructure investments over the 2007-2018 period. From Fig. 2 we find that open-end funds were the dominant investment approaches in the early years of infrastructure investing. Contrasting Fig. 2 with Panel B of Table 1, it is apparent that the internal approach is not used often in our sample, however, when used; pension funds have a large mandate allocated. This is not surprising, as only big pension funds have the resources and expertise to have an in-house infrastructure management team (similar to real estate, see Andonov et al. 2015).
Over time, the rise of infrastructure investing has led to the emergence of the fund-of-funds, co-investment vehicles, and especially limited partnerships, which now represent the largest channel to gain infrastructure exposure, rising from 15% in 2007 to approximately 41% of infrastructure investment approaches in 2018. This table provides descriptive statistics on the infrastructure investments of pension funds with an existing allocation to infrastructure in 2018. We present the cross-sectional averages and display the following statistics: median, mean and standard deviation (StDev). The Columns # Funds and # Obs document the number of pension funds investing in infrastructure or through an investment approach as well as the number of observations. Panels A and B show the summary statistics of infrastructure holdings in million US$. In Panel A, the infrastructure assets descriptive statistics are displayed separately for pension funds from Canada, Europe, the U.S. and the Rest of World group. Panel B shows the infrastructure holdings descriptive statistics by investment approach. Finally, we observe that at the beginning of the sample, most pension funds had exposure to infrastructure via one investment vehicle and at the end of the sample, most had exposure via a mix of two or three investments vehicles. Some funds have gone through a lifecycle where they first gain exposure through external managers, and as pension funds have obtained more knowledge of the asset class, they move to internally managed mandates.

Investment costs
CEM provides detailed information about pension funds' investment costs. The investment costs for internal management consist of compensation and benefits for the employees that manage the investments as well as support staff, overhead costs, and research expenses. The investment costs for external management include payment of management fees to external money managers and investment consultants. In addition, the costs for internal employees who oversee the external investments in infrastructure assets are also included. Historically, CEM directly subtracted performance fees, carried interest, and rebates from gross returns and did not incorporate these fees in the overall cost figures. Even though CEM has separately captured and reported performance fees, carried interest and rebates for the past 7 years, we subtract these fees directly from gross returns to ensure consistency for the full sample period. The same applies for funds of funds, where the cost figures pertain only to the base management fee paid to the fund of funds manager as well as the underlying managers, not to the performance fees and carried interest on either of those layers.
Panel A of Fig. 3 shows that pension funds from Europe and the U.S. consistently pay higher fees as compared to their global peers, based on asset-weighted cost numbers. Especially U.S. pension funds face high fees, albeit with a slightly downward trend: 2018 investment fees for infrastructure investments were about 180 bps, compared to 115 bps for European funds, and slightly over 80 bps for Canada. Canadian funds' low fees are consistent over time. When looking at the unweighted investment costs across regions and by investment approach (not shown in the graph), which avoids the dominance of large pension funds in the cost figures, we find that the investment cost levels across regions were much closer to each other and substantially higher, with all funds paying on average 185 bps in infrastructure investment fees in 2018. Pension funds in Europe and the U.S. still have the highest average costs (189 bps and 201 bps respectively), but Canadian funds are not served much more economically when looking at the cost data in this way: unweighted average costs are 169 bps.
As noted in Panel B of Table 1, pension funds invest in infrastructure through five different channels, each having their own distinct cost profiles. Panel B of Fig. 3 illustrates this. The difference in cost levels between investment approaches has been rather consistent over time, apart from the volatility of the investment costs for funds-of-funds, which can be partly explained by the small number of fundof-fund observations at the start of the sample period. The differences can be summed up by noting that more internally focused investment approaches are least expensive, and external approaches are more expensive. That holds especially for limited partnerships and funds-of-funds, with cost levels above 200 bps. Internal investment and co-investment are associated with fees around 40 bps.

Pension fund characteristics and infrastructure investments
This section empirically assesses the decision of pension funds whether to invest in infrastructure, and once they invest, the choice of investment approach. First, we investigate which pension fund characteristics affect the choice to invest in infrastructure, estimating the following logit model: where F is a logit function taking on values between zero and one, with y i,t the dependent binary variable. The probabilities are modeled as a function of pension fund characteristics ( X ), which consists of total pension fund size ( Size ), measured by the natural logarithm of pension fund assets under management in U.S. dollars, and the percentage allocation to other alternative asset classes (%Alter ) of pension fund i in year t (other alternatives include real estate, private equity, hedge funds, commodities and natural resources). We use a dummy variable ( Public ) to control for plan type, which takes a value of one when a pension plan is public and zero when it is corporate. In addition, we also incorporate regional dummies ( Region ), where the base refers to U.S. pension funds, as well as year dummies ( YD ). We cluster the standard errors by pension fund to allow for intragroup correlation of standard errors. Table 2 displays the results. Panel A shows which pension fund characteristics determine whether a pension fund invests in infrastructure or not. Larger pension funds are more likely to invest in infrastructure: a one-unit increase in the logarithm of assets under management-meaning a doubling of the fund size-increases the likelihood that a pension fund invests in infrastructure by 17.8%. Interestingly, public pension funds are also more likely to invest in infrastructure assets, although the effect is not statistically significant. This is in line with Andonov et al. (2021), who find that public institutional investors have exposure to a higher number of infrastructure investments, which is partially explained by the public nature of infrastructure assets and the Environmental, Social, and Governance (ESG) considerations of public investors. Panel A of Table 2 also shows that, based on the regional dummies, pension funds from Canada, Europe, and the Rest of World group are significantly more likely to invest in infrastructure than U.S. pension funds. B Overall infrastructure investment costs by investment approach (in bps). Note: Figure 1A presents the overall infrastructure cost by year and region of the pension funds in the CEM Benchmarking database investing in infrastructure assets. Figure 1B presents the overall infrastructure cost by year and investment approach of the pension funds in the CEM Benchmarking database investing that invest in infrastructure assets Panel B of Table 2 provides results with regards to the characteristics determining the investment channel chosen to gain infrastructure exposure, either through an internal department, a co-investment vehicle, an external manager, a limited partnership structure, or a fund-of-funds. We find that larger pension funds are more likely to manage their infrastructure investments internally. A one-unit increase in the log size (i.e., doubling the fund size) increases the likelihood that a pension fund invests in infrastructure internally by 64.4%. On the other hand, fund-of-funds investment is more strongly associated with smaller pension funds. The likelihood that a pension fund invests through this most "intermediated" channel drops by 47% for every one unit increase in the logarithm of assets. Although the percentage of internal infrastructure investments increases as pension fund size increases, we observe that even among the 20% largest pension funds, 69.6% of investments are made through external vehicles (i.e., open-end funds, limited partnerships structures, and fund-of-funds) in 2018.
Public pension funds are far more likely to choose the internal management route and are less likely to choose external funds for their infrastructure investments. Pension funds from Canada, Europe, and the Rest of World are significantly more likely to invest in infrastructure assets through internal channels than U.S. pension funds, even after controlling for pension fund size, investments in other alternative asset classes, and plan type. In addition, Canadian pension funds are less likely than their U.S. peers to employ funds-of-funds.
In sum, larger pension funds, and public pension funds are significantly more likely to have exposure to infrastructure assets and are more likely to invest in these assets In Panel A, the dependent variable is set up based upon the decision of a pension fund to invest in infrastructure or not. Panel B shows the results of logit regressions that explain whether a pension fund invests in infrastructure internally, through a co-investment vehicle, externally, via a limited partnership structure or through fund-of-funds. The independent variables included are Size -which is the log of total pension fund assets, %Alter-which is the percentage allocation to other alternative assets, Public -a dummy variable that captures whether a pension fund is public (where the base result refers to corporate funds), Canada, Europe, and Rest of World-regional dummy variables (where the base result refers to U.S. pension funds). At the means of the independent variables, we present the marginal effects (elasticities). For discrete changes from 0 to 1, the marginal effects for the dummy variables are estimated. Furthermore, we add year dummies (YD) and the standard errors are clustered by pension fund, in order to allow for intragroup correlation. Standard errors are shown in brackets and the significance levels are reported with *, and **, which match with 0.05, and 0.01, respectively through internal channels. The significant resources required to set up an internal or "at-arms-length" operating division that manages infrastructure investments could drive the choices of pension funds to invest mostly through external vehicles. On the other hand, it is possible that pension funds opt for external vehicles because specialized external managers bring more expertise and years of experience to the table than internal teams and may be able to achieve better results. 10 The next two sections investigate cost and performance differences between internal and external investment approaches.

The cost of pension fund infrastructure investments
This section investigates the relationship between investment approach, mandate size, and investment costs of pension fund infrastructure investments. We estimate pooled panel regressions, similar to Andonov et al. (2015), to disentangle the effects of infrastructure portfolio size and investment approach: (2) where C i,t stands for investment costs in basis points (bps), Mandate represents the logarithm of the dollar value of the infrastructure investment portfolio and Approach captures dummy variables representing the four investment approaches, with the base dummy referring to internal investments. Region i represents dummy variables with the base dummy referring to U.S. pension funds, YD t concerns the year dummies and u i,t are the idiosyncratic errors. The standard errors are double clustered independently at the fund as well as the year level to control for any potential correlation of performance shocks within pension funds and across years. Table 3 shows the results of the pooled panel regressions. The regression including all assets suggests pension funds that allocate more resources to infrastructure realize small but significant scale advantages on their investment costs. While controlling for the chosen investment approach, year, and region, a one-unit increase in the logarithm of the infrastructure mandate (i.e., doubling the mandate size) results in a 3.85 bps reduction in costs. The results from the pooled panel regression on all assets also imply that the use of external and more intermediated investment approaches leads to higher cost levels. Delegating asset management to a general partner within a limited partnership structure increases the investment costs by 162 bps compared to the cost levels in a situation where a pension fund manages its investments internally. Not surprisingly, a pension fund that chooses funds-of-funds, the most layered investment The investment costs in bps are the dependent variables. The investment costs for all infrastructure assets are the dependent variables in the regional regressions. For the investment approach regressions, the investment costs for all infrastructure assets managed internally, through a co-investment vehicle, externally, via a limited partnership structure or through fund-of-funds are the dependent variables. The table shows the results of pooled panel regressions with regional and year dummies (YD). The standard errors are independently double clustered by pension fund and by year in the pooled panel regressions. The following characteristics are included in the regressions: Mandate -log of total infrastructure holdings, log of holdings in one investment approach. Co (Co-Investments), OE (Open-end), LP (Limited Partnership,) and FoF (fund-of-funds) are investment approach dummy variables (where the base result refers to internally managed infrastructure investments). Canada, Europe, and Rest of World are regional dummy variables (where the base result refers to U.S. pension funds). Standard errors are shown in brackets and the significance levels are reported with *, and **, which match with 0.05, and 0.01, respectively. The R 2 column shows the R-square approach, faces the highest cost levels: 222 bps higher as compared to internal investment. At the other end of the spectrum, pension funds engaging in co-investment face costs that do not significantly differ from internal investment. Overall, controlling for investment approach and size, only pension funds from the Rest of World group have significantly lower non-listed infrastructure investment costs as compared to U.S. pension funds (22 bps). When separating the sample into the different regions, we observe that the previously reported relations between financial intermediation and investment costs applies for each region. Although the exact cost levels differ across regions, the more intermediated investment approaches are associated with significantly higher costs. Interestingly, co-investment is associated with lower investment costs in the U.S., with 39 bps lower costs as compared to internal investment.
Overall, these results indicate that pension funds with a larger infrastructure mandate can achieve somewhat lower cost levels. The most obvious finding is that additional layers of financial intermediation are associated with significantly higher investment costs as compared to internal investments. This holds for all four regions in a comparable manner, contrasting the findings of Andonov et al. (2015) for real estate, where U.S. pension funds face substantially higher real investment cost levels than their global peers. When it comes to infrastructure, U.S. pension funds take an approach that is more oriented towards external management, which is more expensive, but the cost levels of the external approach are similar to those in other regions.
Of course, one can argue that additional layers of infrastructure investment expertise are indeed expensive, but that they add value in finding the best assets at the most attractive price, translating into superior net-of-cost returns. Indeed, that is the sales pitch that is invariably given by the purveyors of these investment vehicles. We will now turn to the question of whether there is merit in such arguments.

Pension fund performance in infrastructure investments
In this section, we first analyze whether pension fund infrastructure returns justify the increased allocations to the asset class, and then investigate whether the choice of certain investment vehicles in infrastructure is associated with superior performance. We first address the net returns to infrastructure investments over time, without controlling for pension fund characteristics, comparing pension funds' infrastructure investment performance with other asset classes in their portfolios. After these nonparametric comparisons, we provide the results of pooled panel regressions of net returns, controlling for pension fund characteristics, region, and investment approach. "Net returns" are measured as returns net of costs, not benchmark-adjusted returns. In the CEM database, pension funds report benchmarks against which performance is measured. The main advantage of using these performance benchmarks is that they likely reflect the risk exposure of the infrastructure allocations more precisely. A disadvantage of these self-declared performance benchmarks is that pension funds can strategically select the more easily outperformed benchmarks, especially since the appropriate benchmarks for infrastructure investments are still unclear. This is an inherent problem for investments in private markets. For example, Phalippou (2020) shows that private equity funds engage in "benchmark shopping behavior" over time, to report outperformance with respect to their respective benchmark. To avoid this endogeneity trap, we focus our analysis on returns net of cost, so the return accruing to the pension fund, without a comparison to self-reported benchmarks.
We present volatility as the standard deviation of net returns. However, for infrastructure, as for other sparsely traded private assets, the traditional measure of volatility may be less reliable as compared to liquid assets, which makes a like-for-like comparison between asset classes challenging (de Jong, 2022). Our aim is not to model the returns and volatility of assets for portfolio optimization, and as such we are somewhat less concerned about measurement error in the volatility measure. That said, the evaluation of the performance of infrastructure based on Sharpe ratios should be made with caution, as Sharpe ratios for private assets are likely overstated. Table 4 Panel A shows that infrastructure provided the second-highest net return over the entire sample period-10.1% on average. Only private equity investments delivered higher net returns over the 2007-2018 sample period, with an average net return of 12.6%. Infrastructure assets exhibit lower volatility as compared to other alternative asset classes for the full sample period, with bonds the only asset class showing a lower standard deviation than infrastructure. When we divide the sample into two sub-periods, with the first covering the global financial crisis and the second the subsequent global economic boom, we observe that infrastructure delivered its stellar relative investment performance, especially in the second period.

Descriptive analysis of net returns
Panel B of Table 4 shows substantial variation in infrastructure net returns across regions, with Canada and the Rest of the World group (which includes Australia) exhibiting the highest net returns over the sample period. The infrastructure investments of European and U.S. pension funds tend to deliver lower net returns with higher volatility. Panel C of Table 4 provides net infrastructure performance by investment approach. We observe that the investment approaches that are more externally oriented deliver somewhat lower net returns as compared to internal investment, with a higher standard deviation. Panel C of Table 4 also shows that the recent rise of co-investments seems to be justified by their higher net returns than other investment approaches, while exhibiting similar volatility levels. Over the 2013-2018 time period, co-investments in infrastructure delivered the highest annual net returns as compared to other investment approaches, 13.3% on average, with the lowest standard deviation. It is important to note, however, that the number of observations for co-investments is small. Table 5 reports the results of the pooled panel regressions of the net returns on pension fund characteristics, region, and investment approach. These regressions are comparable to those employed for the investment cost analysis (see Eq. 2), and as before, we double-cluster the standard errors and include time-fixed effects.

Explaining net returns by fund characteristics
The results show a significant and positive relationship between infrastructure mandate size and the infrastructure investment performance of pension funds. A one-unit increase in the log of infrastructure holdings (i.e., doubling the mandate size) increases the net returns by 84 basis points. In addition, investing in infrastructure through coinvestments leads to significantly higher net returns than investing internally. However, the number of observations for co-investments is fairly small, and the results, therefore, need to be interpreted with some caution. The other external investment approaches-limited partnerships and fund of funds-do not lead to significantly lower or higher net returns than internally managed infrastructure investments. Investigating possible regional heterogeneity, we document In Panel A, B, and C, we present the time-series averages of cross-sectional value-weighted net mean returns in percentages over the whole sample period as well as two sub-periods. Underneath the returns, the standard deviations of the returns are displayed no significant differences between the net returns of U.S. pension funds and their global peers. We then split the infrastructure assets by region and study the relation between mandate size, investment approach, and performance for pension funds from the U.S., Canada, Europe, and the Rest of World group separately. Panel B of Table 5 shows statistically significant economies of scale Rest of World pension funds. A doubling of the infrastructure mandate size for Rest of World pension funds increases net returns by 199 basis points, respectively. The results are statistically insignificant in all other regions. Importantly, financial intermediation does not seem to harm net returns significantly in any of the regions.
We also investigate the relation between mandate size, region, and performance for each investment approach separately, and find significant scale economies for infrastructure investments through open-end funds, limited partnerships and fund of funds. For example, doubling the mandate size increases the net returns by 89 basis points for limited partnership investments. As previously mentioned, this paper solely looks at the effect of pension fund characteristics, region, and investment approach on the performance of infrastructure investments by pension funds. The unavailability of data on the underlying infrastructure assets and their risk profile makes that these risk factors are not controlled for. Therefore, differences in the risk profiles of the underlying assets may be driving any difference in the results across regions and by investment approach.
To sum up, we do not observe much heterogeneity across regions regarding net investment performance, but we do find that size matters, with a doubling of the infrastructure mandate size leading to an 84 bps increase in net returns. More importantly, financial intermediation does not seem to lead to significantly lower or higher net returns than Table 5 Regression results infrastructure investment performance and characteristics By subtracting the costs from pension fund infrastructure returns, the net returns are calculated. The net return on all infrastructure assets is used as a dependent variable in all assets and regional regressions. In the regressions by investment approach, the net return on the infrastructure assets invested through the channels internal, co-investment, external, limited partnership, and fund-of-funds is the dependent variable. Panel A shows the results of pooled panel regressions with regional and year dummies (YD). The standard errors are independently double clustered by pension fund and by year in the pooled panel regressions. The following characteristics are included in the regressions: Mandate -log of total infrastructure holdings, log of holdings in one investment approach. Co (Co-Investments), OE (Open-end), LP (Limited Partnership,) and FoF (fund-of-funds) are investment approach dummy variables (where the base result refers to internally managed infrastructure investments). Canada, Europe, and Rest of World are regional dummy variables (where the base result refers to U.S. pension funds). Standard errors are shown in brackets and the significance levels are reported with *, and **, which match with 0.05, and 0.01, respectively. The R 2 column shows the R-square internally managed investments for infrastructure-external infrastructure fund managers deliver a gross performance that compensates for their added costs, but not more than that.

Persistence
Finally, we investigate persistence in the infrastructure investment performance of pension funds. We split pension fund investment performance into five quintiles based on the net benchmark-adjusted returns achieved by these pension funds. Table 6 shows the transition matrixes, which indicate the probabilities that a pension fund ranked in one of the quintiles in year t ends up in any of the five quintiles in year t + 1. In addition, we investigate the difference between returns in year t + 1 of pension funds that are ranked in the lowest and highest quintile in year t. With a null hypothesis of "no persistence," the value representing the difference in returns in year t + 1 is expected to be zero, implying that performance in the past is no prediction for performance in the future. Carpenter and Lynch (1999) demonstrate that a t-test investigating the difference between the bottom and top portfolios ranked by performance in the past is best specified with a null hypothesis of no persistence, as this is the most robust method compared to alternatives considered. Table 6 Panel A shows strong persistence in the infrastructure investment performance of pension funds, using a 1-year horizon. Pension funds are more likely to be among the best performing funds in the next year when performance is good this year. As an illustration, a pension fund that performed among the best-performing pension funds in year t had a 24.74% chance of being among the best-performing funds one year later. Similarly, funds that perform relatively poorly this year are more likely to end up with a low ranking in the next year. Panel A's last columns provide the average net return in year t + 1 for pension funds in the lowest and highest ranked quintiles in year t and the t-statistic for the difference in performance between these two groups. The net return for the lowest quintile is 7.5%, whereas the return for the highest quintile is 9.65%. The difference between these two groups is statistically significant, with a t-statistic of 1.94, implying strong persistence in pension funds' infrastructure investment performance.
We then investigate whether this performance persistence in infrastructure is also visible at a two-year horizon, to mitigate a potential valuation smoothing effect, which is well documented for real estate but not for infrastructure. Over Table 6 Performance persistence in pension fund infrastructure investments: net returns Based on their net returns in infrastructure within a given investment approach, pension funds are categorized into five performance quintiles. The quintile with the highest return is represented by the High row or column. In panel A, the percentages in exhibit the likelihood that a pension fund ranked in one of the five quintiles in year t will be in any of the quintiles in year t + 1. The returns in t + 1 column provide the average net benchmark-adjusted return in year t + 1 for pension funds that are in the lowest and highest ranked quintiles in year t. The Test Diff column shows a t-statistic of the difference in net benchmark-adjusted returns between the low and high quintiles. In Panel B, I look at performance persistence over a two-year timespan in order to control for any potential short-term smoothing of the infrastructure net benchmark-adjusted returns. In panel B, the percentages in exhibit the likelihood that a pension fund ranked in one of the five quintiles in year t will be in any of the quintiles in year t + 2. The returns in t + 2 column provide the average net benchmark-adjusted return in year t + 2 for pension funds that are in the lowest and highest ranked quintiles in year t. The significance levels are reported with *, and **, which match with 0.05, and 0.01, respectively  Table 6 demonstrates that 22.37% of pension funds that belong to the highest-ranked quintile in year t end up in that same best performing quintile two years later. When looking at the difference in returns in year t + 2 between the worst and the best-ranked pension funds in year t, there is no significant difference: the t-statistic is − 1.37, so the persistence is rather short lived or caused by valuation smoothing. These findings are partially in line with earlier results on performance persistence for other alternative investment categories, such as real estate, private equity funds, and hedge funds. Andonov et al. (2015) document substantial persistence in the direct real estate performance of pension funds. Kaplan and Schoar (2005) show performance persistence in venture capital and leveraged buyout fund performance. Fung et al. (2008) document that hedge funds that perform better are less likely to be liquidated and simultaneously have a higher propensity to deliver alpha persistently.

Conclusions
Over the last three decades, institutional investors have increased their exposure to alternative assets, and infrastructure allocations have increased accordingly, albeit belatedly (Andonov et al. 2017;Carlo et al. 2021). Pension funds across the globe increasingly face the choice whether, and if yes, how they can gain exposure to infrastructure. This paper shows that larger pension funds, public pension funds, and pension funds with a higher percentage allocation to other alternative assets are more likely to invest in infrastructure. When making these investments, smaller pension funds are more likely to use external vehicles, while larger funds are more likely to invest in infrastructure internally. Overall, a substantial proportion of infrastructure investments is allocated through intermediaries, even by larger pension funds.
Regarding investment costs in infrastructure investment, pension funds across the globe experience quite similar investment costs, contrasting findings for other alternative asset classes, such as real state. This may reflect the global playing field of infrastructure investments. When looking at the performance of infrastructure over time, we find that, similar to other asset classes, the financial returns of infrastructure investments experienced a significant slump during the Global Financial Crisis, after which returns bounced back. Over the 2007-2018 time period, infrastructure has been one of the best-performing asset classes, exhibiting the second-highest net returns (after private equity). We document persistence in pension fund infrastructure investment performance within a particular investment approach over a one-year, but not over a 2-year time horizon.
We further document that larger pension funds make more limited use of intermediaries such as fund-of-funds, which exhibit significantly higher investment costs. However, and contrasting general wisdom, we do not find evidence that the use of funds of funds leads to significant underperformance as compared to internal or other external investment management approaches. We do observe scale advantages in infrastructure investments, as larger pension funds exhibit lower investment costs, and higher net returns. These economies of scale are partially explained by the choices pension funds make regarding the investment approach, where larger pension funds are more likely to invest internally, and smaller pension funds are more likely to rely on externally oriented investment approaches. However, even when pension funds opt for the most intermediated investment approach, larger pension funds can perform significantly better on a net return basis as compared to smaller pension funds.
The findings of this paper have some implications for institutional investors with an existing allocation to infrastructure and for those contemplating to gain exposure to this rediscovered asset class. First, based on the data presented in this paper, the increase in infrastructure allocations seems to be justified from a risk/return perspective, and pension funds with no infrastructure exposure should consider investing in this alternative asset class. On the other hand, the externally oriented approach through which pension funds mainly invest in infrastructure is more expensive as compared to internally managing infrastructure assets (even though that does not seem to hurt net returns during our sample period). If the reliance on more intermediated external investment vehicles is motivated by the idea that these investment approaches deliver higher returns than internal teams could achieve, pension funds may need to reconsider their investment approach.
Of course, this paper does not provide the complete perspective on infrastructure as an asset class, with limited insight into the risk/return characteristics of individual infrastructure assets, and no insight into the optimal allocation from a portfolio optimization perspective. In addition, infrastructure investments are highly illiquid, and typically quite chunky. In addition to the risk/return profile, these considerations are important for pension funds. Further institutionalization of the asset class, both through the development of publicly traded vehicles and open-end "core" private funds, may lead to increased allocation to infrastructure by pension funds. This development may help governments around the world reach infrastructure investment goals, in both "green" and more traditional sectors.  (2007)(2008)(2009)(2010)(2011)(2012)(2013)(2014)(2015)(2016)(2017)(2018) The CEM Benchmarking database. This table presents the number of pension funds in the CEM Benchmarking database over the entire sample by region (#Funds in data) and the numbers of pension fund-year observations over the entire sample by region (#Observations). The Average Size column shows the average total assets under management (in US$ billion) of the pension funds in the database over the entire sample. The Average Infrastructure Holdings column presents the average net asset value infrastructure holdings of pension funds in the database, over the entire sample.