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. 2024 Feb 16;10(5):e26544. doi: 10.1016/j.heliyon.2024.e26544

Table 2.

Results for the KPSS-PUR Test (Happiness index).

Panel A: Structural Breaks
Countries # of Brks Break 1 Break 2 Break 3 Break 4 Break 5 Break 6 Break 7
Belgium (BE) 6 1978 1986 1990 1998 2011 2015
Denmark (DK) Reference Country
France (FR) 4 1984 1993 1998 2010
Ireland (IR) 4 1987 2003 2012 2016
Italy (IT) 4 1987 2000 2007 2011
Luxembourg (LU) 3 1991 2003 2015
Netherlands (NL) 4 1980 1984 1988 2004
United Kingdom(UK) 4 1985 1989 1999 2015
Panel B: Optimal Frequencyrowhead
Frequency Selection Bootstrap critical values
Countries
Hypotheses
Frequency
F Statistics
10%
5%
1%
Belgium (BE) H0:ρ1 = ρ2 = 0 5 26.560*** 2.860 3.821 5.913
Denmark (DK)
Reference Country




France (FR) H0:ρ1 = ρ2 = 0 2 31.110*** 2.632 3.518 5.600
Ireland (IR) H0:ρ1 = ρ2 = 0 13 2.861* 2.446 3.209 5.204
Italy (IT) H0:ρ1 = ρ2 = 0 18 2.929* 2.461 3.336 5.517
Luxembourg (LU) H0:ρ1 = ρ2 = 0 12 3.982** 2.442 3.291 5.134
Netherlands (NL) H0:ρ1 = ρ2 = 0 14 4.420** 2.465 3.335 5.233
United Kingdom(UK) H0:ρ1 = ρ2 = 0 13 6.924*** 2.441 3.234 5.269
Panel C: Cross-sectional Dependence Testrowhead
Statistic P value
CD Test 4.509*** <0.01
Panel D: KPSS-PUR Test

Cross-section independent
Bootstrap critical values
Panel Stationary Test Statistics P values 10% 5% 1%
Z(λ) Homogeneous 15.374 <0.01 28.536 33.986 46.624
Z(λ) Heterogeneous 36.684 <0.01 63.034 72.000 93.662

Note: “***”, ”**”, and “*” represent 1%, 5%, and 10% significance levels, respectively. The finite sample critical values are computed using the bootstrap method, replicating samples 10,000 times. The maximal number of breaks and frequencies are fixed at 7, and 20, respectively.