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Table 3 Local linear regression: Technical Discount Rate Related to the Funding Ratio

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

Year   f(85) f(90) f(95) f(100) f(105) f(110) f(115)
2006 f(x) 4.10 4.00 3.91 3.83 3.78 3.74 3.70
C.I. [3.89; 4.31] [3.87; 4.14] [3.82; 4.00] [3.78; 3.88] [3.74; 3.82] [3.71; 3.78] [3.66; 3.75]
h(x) 22.84 17.84 12.84 7.97 4.00 2.45 2.50
2007 f(x) 3.89 3.85 3.81 3.77 3.73 3.69 3.68
C.I. [3.50; 4.28] [3.62; 4.08] [3.71; 3.90] [3.72; 3.82] [3.69; 3.77] [3.64; 3.73] [3.63; 3.72]
h(x) 20.97 15.97 10.97 6.27 3.03 2.34 2.24
2008 f(x) 3.77 3.75 3.67 3.59 3.56 3.58 3.56
C.I. [3.70; 3.84] [3.70; 3.79] [3.63; 3.71] [3.55; 3.64] [3.52; 3.61] [3.53; 3.63] [3.51; 3.62]
h(x) 7.47 3.41 2.23 1.73 3.51 6.52 10.24
2009 f(x) 3.79 3.79 3.76 3.68 3.62 3.58 3.55
C.I. [3.68; 3.90] [3.72; 3.87] [3.71; 3.81] [3.63; 3.72] [3.57; 3.66] [3.53; 3.62] [3.50; 3.60]
h(x) 15.17 10.17 5.36 2.51 1.74 2.56 4.64
2010 f(x) 3.87 3.78 3.71 3.65 3.60 3.48 3.50
C.I. [3.75; 3.99] [3.71; 3.85] [3.66; 3.76] [3.60; 3.70] [3.56; 3.65] [3.43; 3.53] [3.45; 3.55]
h(x) 15.74 10.74 6.02 2.47 1.76 2.64 4.65
2011 f(x) 3.64 3.63 3.56 3.48 3.36 3.33 3.33
C.I. [3.52; 3.76] [3.56; 3.70] [3.50; 3.61] [3.43; 3.53] [3.32; 3.41] [3.28; 3.38] [3.27; 3.39]
h(x) 13.44 8.45 4.36 1.54 1.95 3.63 6.38
2012 f(x) 3.48 3.50 3.44 3.38 3.26 3.21 3.15
C.I. [3.27; 3.70] [3.38; 3.62] [3.36; 3.52] [3.32; 3.44] [3.21; 3.31] [3.15; 3.27] [3.09; 3.20]
h(x) 16.88 11.88 7.05 2.94 1.65 2.37 4.19
2013 f(x) 3.16 3.23 3.30 3.16 3.18 3.07 2.97
C.I. [2.86; 3.46] [3.04; 3.42] [3.19; 3.41] [3.06; 3.27] [3.12; 3.23] [3.02; 3.12] [2.92; 3.03]
h(x) 19.25 14.25 9.31 4.65 2.24 1.97 3.03
2014 f(x) 3.06 3.08 3.13 3.04 2.99 2.91 2.83
C.I. [2.82; 3.30] [2.88; 3.29] [2.91; 3.35] [2.93; 3.15] [2.92; 3.05] [2.86; 2.97] [2.77; 2.89]
h(x) 22.04 17.04 12.04 7.07 3.65 2.27 2.37
2015 f(x) 2.71 2.79 2.88 2.78 2.67 2.61 2.56
C.I. [2.22; 3.20] [2.51; 3.07] [2.77; 3.00] [2.69; 2.87] [2.60; 2.74] [2.55; 2.68] [2.50; 2.62]
h(x) 19.11 14.11 9.15 4.55 2.55 2.07 2.47
2016 f(x) 2.57 2.55 2.50 2.59 2.39 2.30 2.30
C.I. [2.24; 2.90] [2.32; 2.77] [2.35; 2.66] [2.49; 2.70] [2.33; 2.45] [2.24; 2.36] [2.24; 2.37]
h(x) 19.25 14.25 9.34 4.63 2.23 2.16 2.62
2017 f(x) 2.45 2.34 2.22 2.24 2.30 2.13 2.10
C.I. [2.12; 2.78] [2.09; 2.58] [2.02; 2.42] [2.09; 2.39] [2.21; 2.39] [2.07; 2.19] [2.04; 2.17]
h(x) 22.70 17.70 12.70 7.72 3.75 2.46 2.14
  1. Point estimates (f(x)) for local average technical discount rate (in percent), for different funding ratios (in percent). Estimates from local linear regressions with varying local bandwidths h(x) covering the closest 20% of observations and using a tricube kernel. Confidence band (C.I.) in square brackets is from bootstrapped standard errors (500 iterations). The sample includes 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)