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Table 2 Global Polynomial Regression Coefficients: Share of Equity Assets related to the Funding Ratio

From: Swiss pension funds: funding ratio, discount rate, and asset allocation

Year Intercept, \(\alpha\) Difference, \(\tau\) Slope left, \(\beta _1\) Slope right, \(\gamma _1\) n Polynomial \(R^2\)
2006 24.74*** − 5.29* − 0.25 0.79*** 1838 1, 2 0.08
(2.31) (2.54) (0.36) (0.10)    
2007 28.45*** − 7.9*** 0.27 0.61*** 1777 1, 2 0.06
(1.74) (1.89) (0.37) (0.09)    
2008 20.11*** − 0.88 − 0.46*** − 0.28* 1769 1, 2 0.09
(0.50) (0.80) (0.06) (0.12)    
2009 26.56*** − 4.15*** − 0.23 0.69*** 1768 1, 3 0.02
(0.89) (1.21) (0.20) (0.20)    
2010 27.94*** − 2.08* 0.01 − 0.02 1688 1, 1 0.01
(0.87) (0.97) (0.17) (0.03)    
2011 26.91*** − 3.02*** 0.05 − 0.05 1669 1, 1 0.02
(0.68) (0.78) (0.14) (0.03)    
2012 28.49*** − 3.22* 0.1 0.01 1558 1, 1 0.01
(1.27) (1.30) (0.25) (0.04)    
2013 25.71*** − 3.32 − 0.97*** 1.02*** 1485 1, 3 0.04
(1.55) (1.82) (0.25) (0.21)    
2014 28.13*** − 5.12* − 0.18 0.53*** 1411 1, 2 0.04
(1.94) (2.23) (0.36) (0.11)    
2015 30.57*** − 5.98*** − 0.27 0.47*** 1388 1, 2 0.03
(1.34) (1.54) (0.35) (0.10)    
2016 30.94*** − 5.37* 0.15 0.47*** 1344 1, 2 0.03
(2.04) (2.23) (0.28) (0.10)    
2017 25.66*** − 3.73 − 0.71 0.83*** 1279 1, 2 0.09
(3.15) (3.32) (0.60) (0.12)    
2006–2017 25.54*** − 3.46*** − 0.09 0.65*** 18,974 1, 3 0.03
(0.32) (0.41) (0.05) (0.05)    
  1. Coefficients for global polynomial regression for share of total assets invested in equities (in %), depending on funding ratio (in %) and polynomial terms. Table columns only show the estimates for the intercept (\(\alpha\)), for the difference left and right of the cut-off (\(\tau\)), and slopes (first polynomial terms, \(\beta _1\), and \(\gamma _1\)). Estimates from global polynomial regressions with separate polynomials to the left and right of a funding ratio of 100%. Selected number of polynomials based on the BIC selection criterion. Bootstrapped standard errors in parentheses (500 iterations). The last three columns show the number of observations (n), the number of selected polynomial terms (left, p, and right, q), and the \(R^2\). Significance levels at 0.05 \(^{*}\), 0.01 \(^{**}\) and 0.001 \(^{***}\). Estimates for \(\tau\) show a negative and significant difference between unfunded and funded funds in almost all years (excluding 2008, 2013, 2017). In the pooled regression (last row), the difference is 3.46 percentage points. For sufficiently funded funds, the share of equity assets is positively related to the funding ratio (\(\gamma _1 > 0\)) in almost all years (excl. 2010–2012). The samples include only private and public funds without state guarantees, and includes only funds with a funding ratio between 81.5 and 152.3% (0.5th–95th percentile range)