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Pension ratios as “correlates” of municipal pension underfunding
RESEARCH
NOTE
Pension Ratios as “Correlates” of Municipal Pension Underfunding Barry R. Marks and K. K. Raman* Unlike the corporate sector, detailed estimates of unfunded pension liabilities for most local governments are not available. Thus, prior research on the association between unfunded pension liabilities and municipal creditor decisions (Copeland and Ingram 1983; Marks and Raman 1985) has implicitly assumed that certain pension ratios are good surrogates for municipal pension underfunding. In this paper, we rely on a theoretical model by Ehrenberg (1980) to test empirically the appropriateness of pension ratios as “correlates” of municipal pension underfunding. These ratios were found to be correlated with pension underfunding, although they accounted for only about 30 percent of the variance in the underfunding variable.
Many local government pension plans are substantially underfunded (GAO, 1970; ACIR, 1980). ’ Underfunded pension obligations represent a potential reallocation of cash flow away from debt service and may be expected to have an impact on creditor decisions and interest costs. 2 Prior research (Copeland and Ingram 1983; Marks and Raman 1985) has implicitly assumed that pension ratios are good proxies for municipal pension underfunding. In this article, we empirically test the appropriateness of pc :,sion surrogates.
Prior Research In a recent article in this journal, Copeland and Ingram (1983) examined the association between current municipal pension accounting disclosures and bond ratings and secondary-market yields for a sample of U.S. cities. Given the many deficiencies in municipal pension reporting practices as noted by Ernst and Whinney (1979), Copeland and Ingram (1983) utilized three financial ratios as surrogates for pension attributes: pension fund receipts/current pension fund *Names are arranged in alphabetical order. Address reprint requests to: Professor K. K. Raman, Department of Accounting, College of Business Administration, North Texas State University, Denton, TX 76203. ’ State and local government pension plans are exempt from the funding and other regulatory requirements of the Employee Retirement Income Security Act (ERISA). ‘We note that prior research in the corporate sector has demonstrated an association between underfunded pensions and corporate security measures (Oldfield 1976; Feldstein and Seligman 1981; D&y, 1984). Journal of Accounting and Public Policy. 4. 14%157(1985) 0 1985 Elsevier Science Publishmg Co., Inc.
149 0278‘l254/85/$3.30
150
B. R. Marks and K. K. Raman
payments; pension fund assets/current pension fund payments; and pension costs/total salaries. 3 The advantage in using these pension ratios is that the necessary data can be obtained from most municipal accounting systems. The rationale that they offer for the use of the first surrogate is that the ratio of receipts to payments is a measure of pension funding growth. A ratio smaller than one (funding less than expenditures) may indicate a deteriorating plan financial condition. The second surrogate (pension fund assets divided by current payments) indicates the number of years for which pension payments equal to the current level can be made, assuming the receipt of no new contributions. Some authorities have suggested that a value for this ratio greater than the median would represent a “safe” accumulation of assets (Copeland and Ingram, p. 155). Information on the first two ratios was obtained from the U.S. Bureau of the Census’ 1977 Census of Governments. The data for the third surrogate (ratio of pension expenditures to total salaries for police and fire departments) were obtained from the 1978 Municipal Year Book. Copeland and Ingram (1983) indicate that this third ratio may be better than the first two ratios largely because the Municipal Year Book data may be more complete and comparable. However, it was found that none of these three pension ratios had any information content for municipal bond risks and returns. They suggest that the “results probably stem from current practices that reduce the relevance and reliability of pension accounting numbers” (p. 147). Subsequently, Marks and Raman (1985) extended Copeland and Ingram’s research by examining the importance of the Bureau of the Census’ pension data for both municipal (city) and state borrowing costs in the new issue (primary) market. They ran their regression models both with and without bond ratings. The pension ratios were not significant in both the city models and in the state model with ratings; however, one ratio (pension plan assets/plan benefit payments) was significant in the state model without ratings, suggesting that this ratio may have been impounded in the bond rating. In a recent survey of the annual reports of 115 municipalities possessing the MFOA Certificate of Conformance, Engstrom (1984) found that only 68 cities reported unfunded pension liabilities. His research cannot be generalized to all U.S. municipalities, as pension disclosures for governmental units with the MFOA Certificate are likely to be considerably superior to those without the Certificate. At this time, only a small fraction of all the municipalities in the U.S. possess the MFOA Certificate. Hence, it is probably fair to state that detailed estimates of unfunded pension liabilities for most governmental units are not available. The availability of appropriate pension ratios as surrogates for municipal pension underfunding thus remains an important issue at this time.
3 Unlike the corporate sector, the state and local government sector of the economy is not subject to the financial disclosure regulations of the Securities and Exchange Commission (SEC). Under the U.S. Constitution, the states are sovereign entities and retain sole legal authority to prescribe the accounting and reporting practices of local governments. Thus, only 43 of the 100 cities surveyed by Ernst and Whinney (1979) reported the amount of unfunded pension liabilities.
151
Pension Ratios
Model Development To test the appropriateness of pension surrogates, we relied on a theoretical model of a public sector retirement system by Ehrenberg (1980). The model seeks to measure the extent of pension underfunding as a function of a number of variables (‘ ‘observable correlates”) that can be calculated for governmental retirement systems. It should be stressed that the model is based on assumptions that are not representative of any given retirement system and that the formula cannot be used to calculate the actual extent of underfunding of a given pension plan. Nevertheless, Ehrenberg claims that the model is sufficiently robust and that in his own empirical research on public sector labor markets these correlates “perform” as satisfactory proxies for underfunding in the anticipated manner. In this paper, we investigate whether these correlates are related to direct measures of pension underfunding. By analyzing the R-square of our regression models, we will also be able to investigate the strength of the relationship between these correlates and pension underfunding. The specific model investigated in this paper is: F=a,,
* (PAPB)a’
* (PCPB)a2 . (EMRET)”
where F is a measure of pension underfunding; PAPB, the ratio of pension fund assets to pension fund payments; PCPB, the ratio of pension fund contributions to pension fund payments; and EMRET, the ratio of active employees to retired employees. The three independent variables in equation (1) were shown by Ehrenberg to be theoretical correlates of pension underfunding. Both PAPB and PCPB were included in Copeland and Ingram’s as well as Marks and Raman’s models. Furthermore, the Advisory Commission on Intergovernmental Relations (ACIR 1973, p. 54) has indicated that a substantial deviation in the PAPB and PCPB ratios from the national averages may indicate inadequate retirement funding. The ACIR, however, did not offer any empirical evidence to substantiate this statement. The dependent variable F is a direct measure of pension plan underfunding. Since the amount of unfunded pension liabilities is probably associated with the size of the governmental unit, the dependent variable in equation (1) is unfunded pension liabilities divided by a scaling variable. The literature on municipal bonds (Lamb and Rappaport 1980; PSA 1981) states that debt burden is an important factor relevant to general obligation credit analysis. In this context, debt burden is measured by the amount of bonded debt outstanding scaled by some size variable such as population (POP), market value of real estate (MV), or general revenues (GR) (Lamb and Rappaport 1980; PSA 1981; Raman 1981, 1982). While unfunded pension liabilities are not bonded debt, they do represent potential claims on the cash flows of the governmental unit. In this study, we measure the burden of unfunded pensions by scaling the amount of unfunded pension obligations (UFL) by each of the three size variables. Therefore, the three dependent variables investigated are unfunded pension liabilities divided
152
B. R. Marks
and K. K. Raman
by population (UNF/POP), unfunded pension liabilities divided by the market value of real estate (UNF/MV), and unfunded pension liabilities divided by general revenues (UNF/GR) . 4 Data for our study were obtained from the Act 293 Report of the Public Employee Retirement Study Commission of the State of Pennsylvania. This act requires the commission to collect certain financial data (including unfunded liabilities) in standardized form for all the pension plans established by Pennsylvania local governments. 5 Total unfunded pension obligations are estimated currently to exceed $2.9 billion. Considerable variation exists among the pension plans; many of these plans are fully funded, while about one quarter of the plans are reportedly being funded substantially below the level necessary to meet minimum actuarial funding requirements. In utilizing Act 293 Report data, we included only nonuniformed employee pension plans for two reasons: 1) policemen and firemen pension plans have unique characteristics that make them different from nonuniformed employee pension plans (Tilove 1976), and 2) data for policemen and firemen plans were not available for all governmental units. Also, we included only those plans that reported unfunded liabilities. Usable data were available for a total of 117 plans. Descriptive statistics for each dependent and independent variable are presented in Table 1.
4 In the economics literature, there have been other attempts (using models and data different from ours) to identify empirically surrogates for pension underfunding. For example, the dependent variable Fin Grosskopf et al. (1983) is the ratio of pension plan assets to pension plan liabilities. While this formulation of the dependent variable may be useful in the context of labor economics, our formulation (as discussed in the text) is more directly relevant to examining the impact of unfunded pension obligations (as a form of debt) on creditor decisions. As for the independent variables, only EMRET was included in Grosskopf s equations. The two ratios (PAPB and PCPB) that are at the heart of our study (and as financial ratios directly relevant to accountants) were not included in any of Grosskopfs equations. Also, Inman (1981) developed models for police and tire department labor budgets. None of our three independent variables (PAPB, PCPB, EMRET) entered any of his equations. 5 Both Ehrenberg and Smith (1981) and Epple and Schippcr (1981) have demonstrated the importance of Act 293 data in the context of research in the labor and housing markets, respectively. Ehrenberg and Smith (1981) report that unfunded pension promises are perceived as being risky by public employees, who then react by demanding some degree of compensation in the form of higher current wages. Epple and Schipper (1981) provide some evidence that unfunded pension obligations are capitalized into local land and housing values.
Table 1. Variable
UFLIPOP
Description
of Data Mean
Std. Dev
Min.
0.371
Median
12.245
Max
36.333
54.365
UFLIMV
0.005
0.007
O.oool
0.0013
287.805
UFL/GR
0.137
0.154
0.004
0.074
0.696
PAPB
22.056
26.681
0.101
13.667
159.000
PCPB
4.844
10.066
0.200
2.882
105.000
EMRET
5.293
4.699
0.156
4.OQO
0.0409
27.000
Pension Ratios
153
Table 2. Pairwise Correlation Coefficients ln(PAPB)
ln(PAPB) 1n(PCPB) ln(EMRET)
1.000
ln(PCPB)
,575 1.000
ln(EMRET)
,580 ,442 1.000
Results Although equation
(1) is nonlinear, it may be estimated by ordinary least squares (OLS) regression analysis. Taking the natural logarithm of both sides of equation (1) yields: lnQ=ln(aa)
+ al * ln(PAPB) +a2 * ln(PCPB) + a3 * ln(EMRET).
(2)
Equation (2) is a log-linear equation where both the dependent variable and the independent variables are expressed in the logarithmic form. The pairwise correlation coefficient between each pair of independent variables is shown in Table 2. Table 3 presents the regression coefficients for each of our three models. Each regression equation is significant at the 0.0001 level. The constant ln(a,,) is significant at the 0.01 level in each equation. In the first equation, ln(aa) is positive, implying that a0 is a positive number greater than one (the antilog of 4.05071 is 57.43822). In the other two equations, ln(ao) is negative implying that a0 is a positive number less than one. For instance, in the equation with UFL/MV as the dependent variable, ln(ao) is - 4.72611, i.e., a0 is equal to the antilog, which is 0.00886. In each equation, al (which represents the power of PAPB in equation (1)) is significant at the 0.01 level with a negative sign. Hence, as one would anticipate, an increase in PAPB is associated with a decrease in unfunded pension obligations. In two of the models, a2 (which represents the power of PCPB in equation (1)) is significant at the 0.05 level with a negative sign. Once again, an increase in PCPB is associated with a decrease in unfunded pension obligations, which is as one would expect. The coefficient of ln(EMRET), i.e., a3, was not significant at the 0.05 level in any of the equations. The highest pairwise correlation between the independent variables was 0.58. According to Farrar and Glauber (1967), multicollinearity is a significant problem only when the pairwise correlation coefficients exceed 0.80. Another test of multicollinearity is the variance inflation factor.6 The highest variance
6 The variance inflation factor (VIF) measures the interrelationship between the independent variables in the model. The VIF is usually calculated for each independent variable. For a given independent variable, the VIF is the inverse of (1 minus R-square), where the R-square is obtained from the regression of the other independent variables on that independent variable (Gunst and Mason, 1980, p. 295).
154
Table 3. Regression
B. R. Marks
and K. K. Raman
Equations Dependent
Coefficients
1n(a0)
ln(UFL/POP) 4.05071 (15.244)b
variables
ln(UFL/MV)
In(UFL/GR)
- 4.72611 (- 16.765)b
- 1.41521 (-6.320)b
aI
-0.54163 (-4.460)*
- 0.61308 (- 4.759)b
- 0.47010 (- 4.594)b
(12
- 0.35773 (- 2.449)’
- 0.35363 (-2.282)C
-0.19547 (-1.588)
a3
0.23436 (1.278)
0.15254 (0.784)
0.13226 (0.856)
N
117 0.32565 0.30775 18.190”
117 0.35607 0.33897 20.828”
117 0.30210 0.28358 16.305”
R2 Adjusted R2 Overall F
t-statistics are in parentheses. u Statistically significant at the 0.0001 level. b Statistically significant at the 0.01 level. c Statistically significant at the 0.05 level.
inflation factor for any of the independent variables in our three models was only 1.86. According to Gunst and Mason (1980), multicollinearity is troublesome only when the variance inflation factor is greater than 10.0. We also ran the models using only one of the ratios at a time but the significance of the independent variables did not change. Finally, we examined the impact on each of our three models of entering the independent variables in a stepwise manner. The coefficients and their significance levels did not materially change from one regression to the next. The results from these various tests suggest that multicollinearity is not a significant problem in our data. The regression equations in Table 3 were estimated by using ordinary least squares (OLS). Heteroscedasticity occurs when the residuals of the regression equation are correlated with the explanatory variables. We applied both a parametric and a nonparametric test for heteroscedasticity. The parametric test that was used was the Glejser test (Maddala 1977, p. 262). This test is performed by regressing the absolute value of each residual on the corresponding value for each of the three independent variables. The other test was to calculate the Spearman’s rank correlation coefficient between the absolute value of each residual and the absolute value of the corresponding independent variable
155
Pension Ratios
(Maddala 1977, p. 263). The null hypothesis that the residuals are not correlated with the independent variables was accepted at the .05 level in each case. Another assumption under OLS regression is that the residuals are normally distributed. The normal probability plots of the standardized residuals were analyzed and the plots in each case appeared to follow a normal distribution. The equations in Table 3 appeared to satisfy the assumptions underlying ordinary least squares analysis. We also compared our log-linear model (equation (2)) with a linear model. The linear model was: F= b. + b,(PAPB) + &(PCPB) + &(EMRET).
(3)
We analyzed equation (3) for each of our three dependent variables. The Rsquare for the linear model was always substantially lower than the R-square for the corresponding log-linear model in equation (2). For example, the R-square for the linear model with (UFL/GR) as the dependent variable was only 0.13885, while the R-square for the corresponding log-linear model (Table 3) is 0.30210. Moreover, for each of the three linear models the normality and homoscedasticity assumptions were strongly rejected. The null hypothesis that the residuals are not correlated with the independent variables was rejected at the 0 .O1 level for each of the three linear models. Furthermore, the probability plots of the standardized residuals indicated that the residuals were not normally distributed. Besides having a lower explanatory power, the linear model in equation (3) did not appear to satisfy the assumptions underlying ordinary least squares.
Summary and Conclusions Prior research (Copeland and Ingram 1983; Marks and Raman 1985) on the association between pension data and municipal bond ratings and returns has implicitly assumed that certain pension ratios are good proxies for pension underfunding. Since detailed estimates of unfunded pension liabilities for most governmental units are not available (Engstrom 1984), the availability of pension ratios as surrogates for municipal pension underfunding remains an important issue. We relied on a theoretical model by Ehrenberg (1980) to select two financial ratios and one nonfinancial ratio that may be expected to be appropriate “correlates” for municipal pension underfunding. We relied on the municipal finance literature to develop three alternative measures of the burden of unfunded pension obligations, by scaling the amount of unfunded liability by three different size variables. Using pension data for local governments in the state of Pennsylvania, we found the two financial ratios (pension assets to pension benefit payments and pension contributions to pension benefit payments) to “perform” as appropriate correlates of pension plan underfunding.
156
Overall,
B. R. Marks and K. K. Raman
the pension
ratios
possess
explanatory
power
but are
not entirely
sufficient surrogates for pension underfunding. The highest R-square in any of our models was only 0.35607. Thus, a major portion of the variance in pension underfimding was not explained by the surrogate variables. Also, our log-linear model had greater explanatory power than a linear model.
References Emergen-
Advisory Commission cies, ACIR.
on Intergovernmental
Relations.
1973. City Financial
Advisory Commission Systems. ACIR.
on Intergovernmental
Relations.
1980. State and Local Pension
Copeland, R., and Ingram, R., Fall 1983. Municipal bond market recognition of pension reporting practices. Journal of Accounting and PubIic Policy 2: 147-166. Daley, L. April 1984. The valuation of reported pension measures for firms sponsoring defined benefit plans. The Accounting Review 177-198. Ehrenberg,
R. July 1980. Correlates of underfunding
of public sector retirement systems.
Economic Inquiry 493-500. Ehrenberg, R., and Smith, R. 1981. A framework for evaluating state and local government pension reform. In Public Sector Labor Markets (P. Mieszkowski and G. Peterson, eds.) Washington, DC: Urban Institute. Engstrom,
J. Spring 1984. Pension reporting by municipalities.
Journal of Accounting,
Auditing and Finance 197-2 11. Epple, D., and Schipper, K. 1981. Municipal evidence. Public Choice 141-178. Ernst and Whinney. and Whinney.
pension
funding:
A theory and some
1979. How Cities Can Improve Their Financial Reporting. Ernst
Farrar, D., and Glauber, R. Feb. 1967. Multicollinearity in regression analysis: problem revisited. The Review of Economics and Statistics 92-107. Feldstein, M., and Seligman, S. 1981. Pension savings. Journal of Finance 801-824.
funding,
share prices
The
and national
Office. 1979. Funding of State and Local Government Pension Plans: A National Problem. GAO.
General Accounting
Grosskopf, S., Hayes, K., and Sivan, D. Mar. 1983. Municipal pensions, wage capitalization. National Tax Journal 115- 12 1.
funding and
Gunst, R., and Mason, R. 1980. Regression Analysis and Its Application: Oriented Approach. New York: Marcel Dekker Inc.
A Data
Inman, R. 1981. Wages, pensions and employment in the local public sector. In Public Sector Labor Markets (P. Meiszkowski and G. Peterson, eds.) Washington, DC: Urban Institute. Lamb, R., and Rappaport,
S. 1980. Municipal Bonds. New York: McGraw-Hill.
Maddala, G. 1977. Econometrics.
New York: McGraw-Hill.
Marks, B., and Raman, K. 1985. The importance of pension data for municipal and state creditor decisions. Journal of Accounting Research (forthcoming).
Pension Ratios
Oldfield,
157
G., July 1976. Financial
aspects of the private pension system. Journal of
Money, Credit and Banking 48-55. Public Securities Association. 1981. Fundamentals Raman, K. Oct. 1981. Financial Reporting
Accounting
of Municipal Bonds. PSA.
and Municipal Bond Rating Changes.
The
Review 910-926.
1982. Financial reporting and municipal bond ratings. Journal of Auditing and Finance 144-153. Tilove, R. 1976. PubIic Employee Pension Funds. New York: Columbia University
Raman, K. Winter
Accounting, Press.
NOTE
Pension Ratios as “Correlates” of Municipal Pension Underfunding Barry R. Marks and K. K. Raman* Unlike the corporate sector, detailed estimates of unfunded pension liabilities for most local governments are not available. Thus, prior research on the association between unfunded pension liabilities and municipal creditor decisions (Copeland and Ingram 1983; Marks and Raman 1985) has implicitly assumed that certain pension ratios are good surrogates for municipal pension underfunding. In this paper, we rely on a theoretical model by Ehrenberg (1980) to test empirically the appropriateness of pension ratios as “correlates” of municipal pension underfunding. These ratios were found to be correlated with pension underfunding, although they accounted for only about 30 percent of the variance in the underfunding variable.
Many local government pension plans are substantially underfunded (GAO, 1970; ACIR, 1980). ’ Underfunded pension obligations represent a potential reallocation of cash flow away from debt service and may be expected to have an impact on creditor decisions and interest costs. 2 Prior research (Copeland and Ingram 1983; Marks and Raman 1985) has implicitly assumed that pension ratios are good proxies for municipal pension underfunding. In this article, we empirically test the appropriateness of pc :,sion surrogates.
Prior Research In a recent article in this journal, Copeland and Ingram (1983) examined the association between current municipal pension accounting disclosures and bond ratings and secondary-market yields for a sample of U.S. cities. Given the many deficiencies in municipal pension reporting practices as noted by Ernst and Whinney (1979), Copeland and Ingram (1983) utilized three financial ratios as surrogates for pension attributes: pension fund receipts/current pension fund *Names are arranged in alphabetical order. Address reprint requests to: Professor K. K. Raman, Department of Accounting, College of Business Administration, North Texas State University, Denton, TX 76203. ’ State and local government pension plans are exempt from the funding and other regulatory requirements of the Employee Retirement Income Security Act (ERISA). ‘We note that prior research in the corporate sector has demonstrated an association between underfunded pensions and corporate security measures (Oldfield 1976; Feldstein and Seligman 1981; D&y, 1984). Journal of Accounting and Public Policy. 4. 14%157(1985) 0 1985 Elsevier Science Publishmg Co., Inc.
149 0278‘l254/85/$3.30
150
B. R. Marks and K. K. Raman
payments; pension fund assets/current pension fund payments; and pension costs/total salaries. 3 The advantage in using these pension ratios is that the necessary data can be obtained from most municipal accounting systems. The rationale that they offer for the use of the first surrogate is that the ratio of receipts to payments is a measure of pension funding growth. A ratio smaller than one (funding less than expenditures) may indicate a deteriorating plan financial condition. The second surrogate (pension fund assets divided by current payments) indicates the number of years for which pension payments equal to the current level can be made, assuming the receipt of no new contributions. Some authorities have suggested that a value for this ratio greater than the median would represent a “safe” accumulation of assets (Copeland and Ingram, p. 155). Information on the first two ratios was obtained from the U.S. Bureau of the Census’ 1977 Census of Governments. The data for the third surrogate (ratio of pension expenditures to total salaries for police and fire departments) were obtained from the 1978 Municipal Year Book. Copeland and Ingram (1983) indicate that this third ratio may be better than the first two ratios largely because the Municipal Year Book data may be more complete and comparable. However, it was found that none of these three pension ratios had any information content for municipal bond risks and returns. They suggest that the “results probably stem from current practices that reduce the relevance and reliability of pension accounting numbers” (p. 147). Subsequently, Marks and Raman (1985) extended Copeland and Ingram’s research by examining the importance of the Bureau of the Census’ pension data for both municipal (city) and state borrowing costs in the new issue (primary) market. They ran their regression models both with and without bond ratings. The pension ratios were not significant in both the city models and in the state model with ratings; however, one ratio (pension plan assets/plan benefit payments) was significant in the state model without ratings, suggesting that this ratio may have been impounded in the bond rating. In a recent survey of the annual reports of 115 municipalities possessing the MFOA Certificate of Conformance, Engstrom (1984) found that only 68 cities reported unfunded pension liabilities. His research cannot be generalized to all U.S. municipalities, as pension disclosures for governmental units with the MFOA Certificate are likely to be considerably superior to those without the Certificate. At this time, only a small fraction of all the municipalities in the U.S. possess the MFOA Certificate. Hence, it is probably fair to state that detailed estimates of unfunded pension liabilities for most governmental units are not available. The availability of appropriate pension ratios as surrogates for municipal pension underfunding thus remains an important issue at this time.
3 Unlike the corporate sector, the state and local government sector of the economy is not subject to the financial disclosure regulations of the Securities and Exchange Commission (SEC). Under the U.S. Constitution, the states are sovereign entities and retain sole legal authority to prescribe the accounting and reporting practices of local governments. Thus, only 43 of the 100 cities surveyed by Ernst and Whinney (1979) reported the amount of unfunded pension liabilities.
151
Pension Ratios
Model Development To test the appropriateness of pension surrogates, we relied on a theoretical model of a public sector retirement system by Ehrenberg (1980). The model seeks to measure the extent of pension underfunding as a function of a number of variables (‘ ‘observable correlates”) that can be calculated for governmental retirement systems. It should be stressed that the model is based on assumptions that are not representative of any given retirement system and that the formula cannot be used to calculate the actual extent of underfunding of a given pension plan. Nevertheless, Ehrenberg claims that the model is sufficiently robust and that in his own empirical research on public sector labor markets these correlates “perform” as satisfactory proxies for underfunding in the anticipated manner. In this paper, we investigate whether these correlates are related to direct measures of pension underfunding. By analyzing the R-square of our regression models, we will also be able to investigate the strength of the relationship between these correlates and pension underfunding. The specific model investigated in this paper is: F=a,,
* (PAPB)a’
* (PCPB)a2 . (EMRET)”
where F is a measure of pension underfunding; PAPB, the ratio of pension fund assets to pension fund payments; PCPB, the ratio of pension fund contributions to pension fund payments; and EMRET, the ratio of active employees to retired employees. The three independent variables in equation (1) were shown by Ehrenberg to be theoretical correlates of pension underfunding. Both PAPB and PCPB were included in Copeland and Ingram’s as well as Marks and Raman’s models. Furthermore, the Advisory Commission on Intergovernmental Relations (ACIR 1973, p. 54) has indicated that a substantial deviation in the PAPB and PCPB ratios from the national averages may indicate inadequate retirement funding. The ACIR, however, did not offer any empirical evidence to substantiate this statement. The dependent variable F is a direct measure of pension plan underfunding. Since the amount of unfunded pension liabilities is probably associated with the size of the governmental unit, the dependent variable in equation (1) is unfunded pension liabilities divided by a scaling variable. The literature on municipal bonds (Lamb and Rappaport 1980; PSA 1981) states that debt burden is an important factor relevant to general obligation credit analysis. In this context, debt burden is measured by the amount of bonded debt outstanding scaled by some size variable such as population (POP), market value of real estate (MV), or general revenues (GR) (Lamb and Rappaport 1980; PSA 1981; Raman 1981, 1982). While unfunded pension liabilities are not bonded debt, they do represent potential claims on the cash flows of the governmental unit. In this study, we measure the burden of unfunded pensions by scaling the amount of unfunded pension obligations (UFL) by each of the three size variables. Therefore, the three dependent variables investigated are unfunded pension liabilities divided
152
B. R. Marks
and K. K. Raman
by population (UNF/POP), unfunded pension liabilities divided by the market value of real estate (UNF/MV), and unfunded pension liabilities divided by general revenues (UNF/GR) . 4 Data for our study were obtained from the Act 293 Report of the Public Employee Retirement Study Commission of the State of Pennsylvania. This act requires the commission to collect certain financial data (including unfunded liabilities) in standardized form for all the pension plans established by Pennsylvania local governments. 5 Total unfunded pension obligations are estimated currently to exceed $2.9 billion. Considerable variation exists among the pension plans; many of these plans are fully funded, while about one quarter of the plans are reportedly being funded substantially below the level necessary to meet minimum actuarial funding requirements. In utilizing Act 293 Report data, we included only nonuniformed employee pension plans for two reasons: 1) policemen and firemen pension plans have unique characteristics that make them different from nonuniformed employee pension plans (Tilove 1976), and 2) data for policemen and firemen plans were not available for all governmental units. Also, we included only those plans that reported unfunded liabilities. Usable data were available for a total of 117 plans. Descriptive statistics for each dependent and independent variable are presented in Table 1.
4 In the economics literature, there have been other attempts (using models and data different from ours) to identify empirically surrogates for pension underfunding. For example, the dependent variable Fin Grosskopf et al. (1983) is the ratio of pension plan assets to pension plan liabilities. While this formulation of the dependent variable may be useful in the context of labor economics, our formulation (as discussed in the text) is more directly relevant to examining the impact of unfunded pension obligations (as a form of debt) on creditor decisions. As for the independent variables, only EMRET was included in Grosskopf s equations. The two ratios (PAPB and PCPB) that are at the heart of our study (and as financial ratios directly relevant to accountants) were not included in any of Grosskopfs equations. Also, Inman (1981) developed models for police and tire department labor budgets. None of our three independent variables (PAPB, PCPB, EMRET) entered any of his equations. 5 Both Ehrenberg and Smith (1981) and Epple and Schippcr (1981) have demonstrated the importance of Act 293 data in the context of research in the labor and housing markets, respectively. Ehrenberg and Smith (1981) report that unfunded pension promises are perceived as being risky by public employees, who then react by demanding some degree of compensation in the form of higher current wages. Epple and Schipper (1981) provide some evidence that unfunded pension obligations are capitalized into local land and housing values.
Table 1. Variable
UFLIPOP
Description
of Data Mean
Std. Dev
Min.
0.371
Median
12.245
Max
36.333
54.365
UFLIMV
0.005
0.007
O.oool
0.0013
287.805
UFL/GR
0.137
0.154
0.004
0.074
0.696
PAPB
22.056
26.681
0.101
13.667
159.000
PCPB
4.844
10.066
0.200
2.882
105.000
EMRET
5.293
4.699
0.156
4.OQO
0.0409
27.000
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153
Table 2. Pairwise Correlation Coefficients ln(PAPB)
ln(PAPB) 1n(PCPB) ln(EMRET)
1.000
ln(PCPB)
,575 1.000
ln(EMRET)
,580 ,442 1.000
Results Although equation
(1) is nonlinear, it may be estimated by ordinary least squares (OLS) regression analysis. Taking the natural logarithm of both sides of equation (1) yields: lnQ=ln(aa)
+ al * ln(PAPB) +a2 * ln(PCPB) + a3 * ln(EMRET).
(2)
Equation (2) is a log-linear equation where both the dependent variable and the independent variables are expressed in the logarithmic form. The pairwise correlation coefficient between each pair of independent variables is shown in Table 2. Table 3 presents the regression coefficients for each of our three models. Each regression equation is significant at the 0.0001 level. The constant ln(a,,) is significant at the 0.01 level in each equation. In the first equation, ln(aa) is positive, implying that a0 is a positive number greater than one (the antilog of 4.05071 is 57.43822). In the other two equations, ln(ao) is negative implying that a0 is a positive number less than one. For instance, in the equation with UFL/MV as the dependent variable, ln(ao) is - 4.72611, i.e., a0 is equal to the antilog, which is 0.00886. In each equation, al (which represents the power of PAPB in equation (1)) is significant at the 0.01 level with a negative sign. Hence, as one would anticipate, an increase in PAPB is associated with a decrease in unfunded pension obligations. In two of the models, a2 (which represents the power of PCPB in equation (1)) is significant at the 0.05 level with a negative sign. Once again, an increase in PCPB is associated with a decrease in unfunded pension obligations, which is as one would expect. The coefficient of ln(EMRET), i.e., a3, was not significant at the 0.05 level in any of the equations. The highest pairwise correlation between the independent variables was 0.58. According to Farrar and Glauber (1967), multicollinearity is a significant problem only when the pairwise correlation coefficients exceed 0.80. Another test of multicollinearity is the variance inflation factor.6 The highest variance
6 The variance inflation factor (VIF) measures the interrelationship between the independent variables in the model. The VIF is usually calculated for each independent variable. For a given independent variable, the VIF is the inverse of (1 minus R-square), where the R-square is obtained from the regression of the other independent variables on that independent variable (Gunst and Mason, 1980, p. 295).
154
Table 3. Regression
B. R. Marks
and K. K. Raman
Equations Dependent
Coefficients
1n(a0)
ln(UFL/POP) 4.05071 (15.244)b
variables
ln(UFL/MV)
In(UFL/GR)
- 4.72611 (- 16.765)b
- 1.41521 (-6.320)b
aI
-0.54163 (-4.460)*
- 0.61308 (- 4.759)b
- 0.47010 (- 4.594)b
(12
- 0.35773 (- 2.449)’
- 0.35363 (-2.282)C
-0.19547 (-1.588)
a3
0.23436 (1.278)
0.15254 (0.784)
0.13226 (0.856)
N
117 0.32565 0.30775 18.190”
117 0.35607 0.33897 20.828”
117 0.30210 0.28358 16.305”
R2 Adjusted R2 Overall F
t-statistics are in parentheses. u Statistically significant at the 0.0001 level. b Statistically significant at the 0.01 level. c Statistically significant at the 0.05 level.
inflation factor for any of the independent variables in our three models was only 1.86. According to Gunst and Mason (1980), multicollinearity is troublesome only when the variance inflation factor is greater than 10.0. We also ran the models using only one of the ratios at a time but the significance of the independent variables did not change. Finally, we examined the impact on each of our three models of entering the independent variables in a stepwise manner. The coefficients and their significance levels did not materially change from one regression to the next. The results from these various tests suggest that multicollinearity is not a significant problem in our data. The regression equations in Table 3 were estimated by using ordinary least squares (OLS). Heteroscedasticity occurs when the residuals of the regression equation are correlated with the explanatory variables. We applied both a parametric and a nonparametric test for heteroscedasticity. The parametric test that was used was the Glejser test (Maddala 1977, p. 262). This test is performed by regressing the absolute value of each residual on the corresponding value for each of the three independent variables. The other test was to calculate the Spearman’s rank correlation coefficient between the absolute value of each residual and the absolute value of the corresponding independent variable
155
Pension Ratios
(Maddala 1977, p. 263). The null hypothesis that the residuals are not correlated with the independent variables was accepted at the .05 level in each case. Another assumption under OLS regression is that the residuals are normally distributed. The normal probability plots of the standardized residuals were analyzed and the plots in each case appeared to follow a normal distribution. The equations in Table 3 appeared to satisfy the assumptions underlying ordinary least squares analysis. We also compared our log-linear model (equation (2)) with a linear model. The linear model was: F= b. + b,(PAPB) + &(PCPB) + &(EMRET).
(3)
We analyzed equation (3) for each of our three dependent variables. The Rsquare for the linear model was always substantially lower than the R-square for the corresponding log-linear model in equation (2). For example, the R-square for the linear model with (UFL/GR) as the dependent variable was only 0.13885, while the R-square for the corresponding log-linear model (Table 3) is 0.30210. Moreover, for each of the three linear models the normality and homoscedasticity assumptions were strongly rejected. The null hypothesis that the residuals are not correlated with the independent variables was rejected at the 0 .O1 level for each of the three linear models. Furthermore, the probability plots of the standardized residuals indicated that the residuals were not normally distributed. Besides having a lower explanatory power, the linear model in equation (3) did not appear to satisfy the assumptions underlying ordinary least squares.
Summary and Conclusions Prior research (Copeland and Ingram 1983; Marks and Raman 1985) on the association between pension data and municipal bond ratings and returns has implicitly assumed that certain pension ratios are good proxies for pension underfunding. Since detailed estimates of unfunded pension liabilities for most governmental units are not available (Engstrom 1984), the availability of pension ratios as surrogates for municipal pension underfunding remains an important issue. We relied on a theoretical model by Ehrenberg (1980) to select two financial ratios and one nonfinancial ratio that may be expected to be appropriate “correlates” for municipal pension underfunding. We relied on the municipal finance literature to develop three alternative measures of the burden of unfunded pension obligations, by scaling the amount of unfunded liability by three different size variables. Using pension data for local governments in the state of Pennsylvania, we found the two financial ratios (pension assets to pension benefit payments and pension contributions to pension benefit payments) to “perform” as appropriate correlates of pension plan underfunding.
156
Overall,
B. R. Marks and K. K. Raman
the pension
ratios
possess
explanatory
power
but are
not entirely
sufficient surrogates for pension underfunding. The highest R-square in any of our models was only 0.35607. Thus, a major portion of the variance in pension underfimding was not explained by the surrogate variables. Also, our log-linear model had greater explanatory power than a linear model.
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