THE DETERMINANTS OF PUBLIC PENSION DEBT IN U.S. STATES*1

Abstract State and local governments across the United States of America (USA) were hit hard by the recent recession. The fi scal stress alerted the public to the increasing amount of public pension debt for which, despite snowballing levels of pension debt, the causes are unclear. This article examines the factors contributing to annual changes in unfunded public pension ratios, focusing in particular on public pension management (including investment performance, investment assumptions, and accounting practices). The data on pension debt for state defi ned benefi t plans comes from the Pew Charitable Trusts for the period 2005 to 2015. Two methods (random-effects and general estimating equation) were used to verify the consistency of the results. These results showed that investment return decreases the annual change in the public pension debt while using a project unit credit method, and the implementation of the Government Accounting Standards Board (GASB) Statement 67 increase the annual change in the public pension debt. These fi ndings illustrate the importance of public pension management in explaining public pension debt.


Introduction
When the housing bubble burst in the late 2000s, it devastated state and local governments across the US.  e nationwide fi scal stress this caused drew a ention to the problem of public pension liabilities 1 . Some scholars estimate that state and local pension liabilities are as high as $4.43 trillion (Novy-Marx and Rauh, 2011).
 e gravity of the pension problems aff ecting state and local governments has led to an increase in research on public pensions. However, few studies have directly assessed the factors contributing to the annual change in unfunded public pension ratios at the aggregate state level.  is study therefore examines the factors that might infl uence unfunded public pension liabilities, focusing primarily on dimensions of public pension management.
Data on pension debt for state defi ned benefi t plans from 2005 to 2015 were obtained and two statistical methods were used to verify the consistency of the results (random-eff ects and general estimating equation).  e results show that public pension management plays a sizable role in infl uencing public pension debt across U.S. states. For instance, investment return reduces the annual change in public pension debt while using a project unit credit method to calculate pension costs along with the implementation of the GASB 67 increases the annual change in public pension debt.  is underlines the importance of public pension management, such as investment performance and accounting practices, in explaining public pension debt.
 e presentation of the research is organized as follows: fi rst, I discuss factors that might contribute to public pension debt, focusing on public pension management and, secondly, I discuss the data and specifi c variables used in the model. Finally, I present the empirical results along with a discussion of their implications, followed by several policy recommendations for public offi cials involved in public pension management.

 eory and hypotheses
In recent years, an increasing number of studies have explored public pension issues; this refl ects the growing importance of such pensions in the public arena. From these studies, several themes have emerged. One such theme is the relationship between state politics and public pensions (Coggburn and Kearney, 2010;Kiewiet, 2010;  om, 2013a and 2013b; Anzia and Moe, 2017). Public unions have also been subject to scholarly inquiry (Mitchell and Smith, 1994;Munnell et al., 2011a). A third, fl ourishing arena of research is the management of public pension boards concerned with public pension performance and state bond ratings (Hess, 2005;Andonov et al., 2018;Dove et al., 2018).  e estimation of public pension liabilities with respect to discount rates and their sustainability have also garnered scholarly a ention (Brown and Wilcox, 2009; Novy-Marx and Rauh, 2009, 2011; Waring, 2012; Chen and Matkin, 2017) as has an ideal funding level for public pensions (Bohn, 2011;Munnell et al., 2011a).  e investment pa erns of public pension assets have also raised concerns (Lucas and Zeldes, 2009;Pennacchi and Rastad, 2011). In addition, economists have examined the impact of public pensions on labor markets and practices (Munnell et al., 2007;Schieber, 2011;Goldhaber et al., 2017) along with the political and economic aspects of public pension liabilities (Schneider and Damnanpour, 2002;Glaeser and Ponze o, 2014;Kelley, 2014). Scholars have also studied the impact of fi scal institutions such as budget stabilization funds and fi scal conditions on public pensions (Clair, 2012;Chen, 2018). Several scholars have probed the legal structures of public pensions and the possibilities for pension reform (Monahan, 2010(Monahan, , 2012(Monahan, , 2015(Monahan, , 2017Fitzpatrick and Monahan, 2015;Aubrey and Crawford, 2017).
Despite a growing number of studies researching public pensions, few have examined the factors contributing to public pension debt using the 'annual change in unfunded public pension ratios' measure.  is study does so with a specifi c focus on the dimensions of public pension management. Monahan (2015) argued that it is not easy to compare the costs of pension plans due to diff erences in underlying investment assumptions. Despite being ambiguous and o en mystifying, the investment assumption rate -o en used interchangeably with 'discount rate' -plays a vital role in determining pension costs. For the same pension plan, a stronger discount rate can make future liabilities seem much lower than they actually are (Munnell, 2012). A majority of states and local governments have anticipated the expected return on pension assets to be approximately 7.5%.  is overly optimistic assumption enables states and local governments to put less than their required contribution into the pension pot. Unlike public pension plans, private companies have, in recent years, discounted their pension liabilities at an average rate of 4.7% to account for real-life circumstances ( e Economist, 2013).

Public pension management: Investment return and assumption
Novy-Marx and Rauh (2009, 2011) have argued that the serious shortfall in pension funds facing states and local governments stems in part from optimistic actuarial assumptions over the years. Although these assumptions might have been acceptable in the robust economy of the 1990s, such optimism could lead to a calamity in leaner economic times. With the application of a realistic discount rate, pension liabilities of around $900 billion can jump to $3.2 trillion or even higher to $4.43 trillion (Novy-Marx and Rauh, 2011).  e former assumes that pension liabilities are equivalent to states' general obligation debt; whereas, in the la er, a discount rate is considered a zero-coupon Treasury yield. Regardless of whether states should use a 'risk-free' rate actuarial -because a pension payment is bound to be made in the future -(Novy-Marx and Rauh, 2011; Waring, 2012), an optimistic rate is equated with a decline in pension liabilities.  e close relationship between an assumed rate and pension debt also applies to the relationship between an investment return and pension debt; in fact, a discount rate is a hypothesized rate while an investment return is a realized rate. As such, it is also critical in understanding the dynamics of pension debt. For instance, an improvement in investment yields on pension assets can signifi cantly shrink the size of the pension debt. A healthy economy and accompanying investment returns can hide the size of the public pension debt whereas a poor economy can quickly magnify the problem (Monahan, 2017). Based on reasonable expectations regarding the relationship between investment return, investment assumption rate and public pension debt, the following hypotheses were constructed for empirical testing: • Hypothesis 1: An increase in investment return will be associated with a decrease in the annual change in unfunded pension ratios, and • Hypothesis 2: An increase in investment assumptions will be associated with a decrease in the annual change in unfunded pension ratios.

Public pension management: accounting practices
Accounting practices can signifi cantly infl uence the level of public pension debt. Regarding the accounting method, state plans primarily use the entry age normal while approximately 13% of plans employ the project unit credit method. For the entry age normal, employers 'frontload' future benefi ts; whereas in the project unit credit employers are backloaded with pension obligations as a retirement horizon approaches (Munnell, 2012, p. 52). Assuming that employers fully fund their pension obligations, they would have to set aside fewer pension assets by using the project unit credit.  us, the project unit credit is a less stringent method of funding than using the entry age normal (Munnell, 2012). However, having fewer assets to work with will dampen investment opportunities and eventually lead to larger public pension debt.
It is also important to note any changes to accounting methods that infl uenced the way pensions were calculated during the period from 2005 to 2015.  e Government Accounting Standards Board announced the GASB 67 in 2012 and it took eff ect in 2014 (Farmer and Maciag, 2015).  e GASB 67 requires states to adopt a realistic discount rate.  e change adopted the blend rate whereby states that regularly make their full annual required contributions can use an assumed investment return, whereas those not doing so are forced to use a market rate. An optimistic discount rate with its overly positive assumptions about future investment returns conceals the true state of public pension funding.  e change exposed several states to the grim reality of worsening pension debt. For example, the state of Kentucky had to lower its investment return assumption by 2%, which meant that it suddenly experienced a 6% increase in pension debt from 2013 to 2014.  e change in method could help explain the variations in unfunded ratios across states that occurred in 2014 and 2015 (Farmer and Maciag, 2015). As such, we arrived at: • Hypothesis 3: States using a project unit credit method will experience an increase in the annual change in unfunded pension ratios, and • Hypothesis 4: Implementing the GASB 67 will be associated with an increase in the annual change in unfunded pension ratios.

Explanatory variables
Five variables were employed to explore public pension management: investment return, investment assumption, project unit credit, GASB 67, and active plan members. Because the dependent variable was an aggregate measure, it would have been ideal to have state-level aggregate data available. Unfortunately, however, most states manage multiple pension plans, and it is diffi cult to derive aggregate state-level measures.  us, for each state, I used the largest representative defi ned benefi t plan (in terms of total pension assets) for the variables noted above.
 e investment return is a fi ve-year return and a ratio; the investment return assumption is also a ratio.  e project unit credit was a dummy variable coded as 1 if the representative plan in each state employed the project unit credit method to estimate actuarial pension costs and 0 otherwise. Active plan members were logged to correct for the skewness resulting from large numbers.  e fi nal public pension management variable was the GASB 67, which was a dummy variable coded as 1 if implemented in a given year and 0 otherwise. Table 1 shows the 50 representative plans that were selected to identify plan-specifi c pension management characteristics (Public Plans Data, 2001-2016). For control variables, I relied on the state's fi scal constraints, state politics, and state fi scal conditions. Scholars argue that fi scal constraints such as tax and expenditure limitations (TELs) play a substantial role in explaining a state's fi scal behavior (Poterba, 1994 Kallen (2017).  e data ranged from 0 (states such as Alabama and North Dakota) to 28 (Missouri), and the total score was built on the following six categories: 'Type of TEL,' 'Statutory/Constitutional', 'Growth Restriction', 'Method of Approval', 'Override Provisions', and 'Exemptions'.  is measure of TELs is superior to the simple dummy variable used in many other studies (e.g., Mason, 2005; McGuire and Rueben, 2006) as it refl ects the diversity of TELs measures across states.
State politics and public unions were also accounted for in the model. Scholars have found that states controlled by the Democratic Party tend to spend and tax more, and are more likely to support employee-friendly policies and public unions than the Republican Party (Blais et al., 1993;Poterba, 1996;Shadbegian, 1999;Marschall and Ruhil, 2005). Popular media outlets continue to blame public unions for their outsized pension benefi ts and debt (Lowenstein, 2008;Greenhut, 2009;Malanga, 2010;Erie et al., 2011), although empirical fi ndings on the eff ects of public unions on public pension debt and benefi ts are inconclusive (Mitchell and Smith, 1994;Munnell et al., 2011b).  us, public unions may cut both ways and therefore it was appropriate to see what the data would reveal. State political party variables were lagged at t-1, as decisions regarding current budget outcomes are made in the previous year (Budge and Hoff erbert, 1990).  ese variables included Democratic membership in the state house at t-1 (%), Democratic membership in the state senate at t-1 (%), Democratic governor at t-1 (dummy), unifi ed Democratic control at t-1 (dummy), and unifi ed Republican control at t-1 (dummy).  e public union variable consisted of public union membership (%) (Hirsch and MacPherson, 2003;updated). An interaction term between unifi ed Republican control at t-1 and public union membership was also included in the model to account for potential relationships between politics and public unions. Finally, the model accounted for fi scal conditions that may infl uence public pension debt. Unlike federal governments, states and local governments are constrained by having to balance their budgets, even in the midst of a fi scal crisis, and o en cut spending or raise revenue during economic downturns. As such, it is critical to account for the fi scal conditions of states when accounting for fi scal outcomes such as public pension debt. Well-known variables for identifying fi scal stress include unemployment rates (Mitchell and Smith, 1994), year-end general fund balance (Wilson, 1983;Wilson and Howard, 1984; National Council of State Legislature, 1987; Raman and Wilson, 1990;Chaney et al., 2002), and long-term debt (Wilson, 1983;Denison et al., 2006). Both long-term debt and year-end general fund balance were expressed as a share of total state revenue to avoid severe right skewness due to the large numbers involved. Table 2 shows the measurement and data sources for the variables while Table 3 presents the descriptive statistics.

Findings
 e model was estimated using two methods: random-eff ects (RE) and general estimating equation (GEE).  e two models also controlled for year dummies, whose results are not reported in the table.  e results from the two models were consistent and only a few diff erences were evident in terms of coeffi cients and standard errors. Although the fi xed eff ects model is ideal for eliminating potential sources of omi ed variable bias, a Hausman test result (probabilities= 0.72) indicated that the RE was appropriate in this case.  us, the RE model was used fi rst, rather than a fi xed-eff ects model, with standard errors clustered around states.
 e results from the GEE equation are also shown here as they provide signifi cant advantages for the panel data.  e GEE equation is an extension of a generalized linear model Zeger and Liang, 1986) and was also appropriate, especially given that cross-sectional panels are fraught with correlated data.  is often leads to the violation of homoskedasticity and, consequently, introduces correlated error terms (Kmenta, 1986;Liang and Zeger, 1986;Zeger and Liang, 1986).
Because variance within each panel was likely to be heteroskedastic, Huber-White standard errors were employed to produce a robust estimate as well as correlational error structures of AR(1), assuming that data in the previous year infl uence the current year's data and lead clustered errors (Zorn, 2001). Table 4 shows the results for the two models.  e χ2 statistic was 503.84 for the RE model and 594.20 for the GEE model; both numbers indicate that the two models fi t the data well.  e two models show that the four variables signifi cantly infl uenced the annual change in unfunded pension ratios. In terms of the main explanatory variables, the investment return was negatively associated with the annual change in unfunded pension ratios.  is means that as an investment return increases, it helps slow the annual increase in public pension debt.  is has implications for offi cials responsible for managing public pension assets in that it implies they should derive strategies or mechanisms to improve investment performance (discussed further in the fi nal section).  e two variables were positively associated with the annual change in unfunded pension ratios: project unit credit and the GASB 67. As hypothesized, using the project unit credit method infl ates the unfunded liabilities vis-à-vis the entry age normal, as states put aside fewer assets with which to gain sizable investment returns.  e GASB 67, the implementation of the accounting change that began in 2014, appears to infl uence the way states estimate their unfunded liabilities.  is contributes to an increase in the annual change in unfunded ratios, worsening the level of pension debt.  e negative impact of project unit credit and the GASB 67 raise two key points for offi cials in public pension management. First, they need to avoid using the project unit credit and instead adopt the entry age normal, which is a more robust accounting method for calculating public pension costs at the beginning of public employment. Second, public offi cials need to apply more a realistic investment assumption rate to their pension assets.  e fact that using the GASB 67, which is more honest than the previous unconstrained investment assumption rate used by states, revealed a darker picture of public pension debt and should inform public offi cials of the need to adopt honest accounting methods and practices.
Finally, public union membership was also positively associated with the change in unfunded ratios, albeit at a weak, ten percent level.  is indicates that increased public union membership increases the annual change in public pension debt.  is highlights the need for public offi cials to work with public unions to fi nd ways of dealing with public pension debt.
 e results imply that the annual change in unfunded ratios is heavily infl uenced by dimensions of public pension management such as investment returns and accounting practices. Except for public unions (via public union membership), the lack of signifi cance of other variables shows that fi scal constraints, state politics (except for public unions), and fi scal conditions do not play an important role in controlling the public pension debt aff ecting U.S. states. Although media outlets have decried political meddling with public pension management in the current pension crises, these political factors did not have any impact when combined with public pension management variables in the model.

Implications for public offi cials
 is study sheds some light on factors aff ecting the annual change in unfunded public pension liabilities.  e results show that dimensions of public pension management -such as investment returns, accounting methods (project unit credit), and accounting changes (GASB 67) -heavily infl uence public pension debt.
 e results have important implications for the public offi cials responsible for managing public pension plans, who therefore need to adopt sound policy options. First, the results suggest that public offi cials need to work hard to boost their investment returns by scrutinizing their investment portfolios. One way to accomplish this is to diversify their pension asset investment strategies. In recent years many plans have relied too heavily on alternative investment methods, which entail paying heavy fees to investment fi rms. Moreover, this information is o en hidden from the watchful eyes of the public ( e Pew Charitable Trusts, 2015), eroding the accountability of public pension plans, especially in the eyes of current and retired public employees. If states invest too heavily in risky projects that produce few investment returns, they need to shi their assets to more stable choices such as index funds that correspond to stock market performance and those producing a stable, fi xed income such as a treasury bond. Similarly, public offi cials need to adopt ways to regularly monitor public pension asset management.
If investment returns do not achieve the yields expected in terms of previously-established standards, stakeholders in public pension management need to determine what did not work and devise alternative strategies to improve pension performance. Naturally, there has to be a formal rule specifying this type of activity. Comparing the investment performance of pension plans with that of other states will also be benefi cial for public offi cials aiming to improve pension asset performance. Enacting legislation that covers all these aspects will help bind public offi cials to be er forms of public pension management.
Second, as Monahan (2015) argued, public offi cials need to adopt several enforcement mechanisms to ensure sound public pension management.  is means that major decision makers in the public sector need to adopt state-of-the-art accounting management standards and practices.  ere should also be enforcement mechanisms to prevent public offi cials from utilizing accounting gimmicks for their own political gain. For instance, a practice such as the entry age normal method would ensure that states face larger pension liabilities at the beginning of public employment than would be the case for the project unit method.  is would help states deal with such liabilities and enable them to build large pension assets for the investment of assets. More importantly, by clarifying the true state of their unfunded pension liabilities, sound accounting methods and practices will help states confront where they actually are in terms of numbers and what needs to be done. Adopting an accounting change such as the GASB 67 is also benefi cial for public offi cials; although it generates worse numbers than when states were free to adopt their investment assumption rate, confronting this darker picture will eventually help public offi cials to prepare necessary strategies for dealing with public pension debt. By forcing public offi cials to use honest numbers, optimal accounting methods and practices will provide opportunities for public offi cials to alleviate public pension debt. Using a market rate for investment returns rather than the blended rate suggested by the GASB 67 is one option that can be used to reveal the true condition of the public pension debt and uncover the harsh reality for each state. Legislating enforcement mechanisms that force states to adopt best accounting methods and practices will go a long way in enabling states to identify problems and formulate solutions.
Although this study has several merits, it also has certain limitations. For instance, the model includes a mixture of state-level and individual-level variables. Second, aggregation of the dependent variable at state level means the model might not have explored or accounted for some potentially crucial individual-level variables. Nevertheless, the study minimizes the potential threat of omi ed variable bias by accounting for a comprehensive array of variables. Furthermore, examining the impact of factors on pension debt at the aggregate state level yields valuable macro-level insights that can inform both policymakers and the public regarding the steps that need to be taken.