Religious change preceded economic change in the 20th century

Religious change predicted economic change in the 20th century, across the world.


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Section S1. WVS and EVS Section S2. Exploratory factor analysis Section S3. Cultural factor loadings Table S1. Participation in the different waves of the WVS and EVS. Table S2. Participating countries in the WEVS. Table S3. Questions common to all eight waves of the WVS and EVS.  Table S12. Openness to extrinsic differences. Table S13. Independence of birth decade, t, versus WEVS phase, p, for secularization, S t , p , and tolerance, V t , p . Table S14. Multilevel time-lagged linear models (see Materials and Methods) demonstrating that secularization predicts GDP and not vice versa (models 1 to 6); tolerance predicts GDP better than secularization (models 7 to 12) and education predicts future GDP, but not secularization (models 13 to 18). Table S15. Time-lagged models, models 1 to 6 (see Materials and Methods), of S versus GDP for cohorts in their first decade or childhood (y = 0 decades, top row), teenage years (y = 1 decade, middle row), and twenties (y = 2 decades, bottom row). Table S16. Multilevel time-lagged models, but with secularization (S alt ) measured using the average of six indicators, which are subjectively associated with religiosity. Table S17. Language categories assigned to WEVS countries, using Ethnologue data. Fig. S1. The ordered factor loadings on WEVS survey questions, following EFA analysis with oblique rotation.

WVS and EVS
The WVS and EVS were administered in waves. There have been five waves of the WVS and three of the EVS since 1990 (see able S1 for participation figures). A WVS and an EVS wave from the early eighties were excluded because the questions did not sufficiently overlap with those from later waves and they were only administered in a few, mainly Western, countries. The total number of participants since 1990 is 475,342.
In total the survey was carried out in 109 unique countries representing over 90% of the worlds population and all geographical regions (a list of the participating countries can be found in table S13). In order to set the data in a form amenable to the EFA regime, all categorical response data were removed, leaving just data of continuous and ordinal types (e.g. binary and Likert scales). All of the variables were transformed to zero mean and unit variance. Finally, missing values were mean imputed. We are able to aggregate the World Value Survey (WVS) and the European Value Survey (EVS) together -we refer to the combined data as WEVS -because the 64 core questions, which are common to the later five waves of the WVS, are present in the later three waves of the EVS. These questions are contained in Exploratory Factor Analysis (EFA) is an unsupervised method to uncover any underlying structure in large multivariate dataset. EFA assumes each observed variable in the dataset is a weighted linear combination of some set of hidden factors that are to be predicted. This procedure is put more formally in Equation S1; where y n is variable n, F m is hidden factor m, w n,m is the contribution of factor F m to variable y n and n is the error term for variable n. We fit this model using maximum likelihood (41): The second part of the EFA regime is an oblique rotation. Rotation acts to improve the interpretability of factors by approaching a simple structure in the factor loading matrix. A factor loading matrix has a perfect simple structure if the following criteria are met (42) 1. Each factor has a small subset of variables with a large factor loadings.
2. The remaining factor loadings should be vanishingly small.
3. Each variable should have a large factor loading on one factor only.
The approximate simple structure, obtained using the WEVS data, is illustrated in Figure 1 where each factor is highly loaded by a small set of variables with a bulk having small loadings. We use an "oblimin" rotation, an oblique rotation, rather than an orthogonal rotation. An oblique rotation relaxes the orthogonality constraint implicit in EFA, so it allows greater freedom when obtaining simple structure. Plus, the orthogonal assumption does not correspond with the real world, where definable cultural values are often correlated.
A Section S . Exploratory Factor Analysis (EFA) where Σ is the real correlation matrix of the WEVS data and S is the simplified factor loading matrix. The VSS score can take values between one and zero; it takes a value of one when simple structure is present and zero when not. VSS is defined for a given "complexity," c, which is the number of factor loadings retained when defining S; for example, if c = 5, then all but the highest five factor loadings are set to zero. Σ res is the error created when the simplified correlation matrix SS T is compared to the real one (Σ). If σ can be recreated using just the c highest factor loadings, then this is the definition of a simple structure and VSS will be close to one. All aspects of the EFA regime were implemented in R using the 'psych' package (http://personalityproject.org/r/psych/).
Tables S4-S12 below list the most significant sets of WEVS questions, and their factor loadings, for Factors 1-9 respectively.

Secularization
Section S . Cultural factor loadings  Table S14. Multilevel time-lagged linear models (see Materials and Methods) demonstrating that secularization predicts GDP and not vice versa (models 1 to 6); tolerance predicts GDP better than secularization (models 7 to12) and education predicts future GDP, but not secularization (models 13 to 18). Row labels are abbreviated as follows: "dep" is the dependent variable, GDP is historical GDP, S is effect of past secularization, E is historical education, V is historical tolerance, y is time lag in decades, N is the number of data points, n is the number of unique countries, i is variance explained by the country random effect, h is variance explained by cultural-history and R 2 is total variance explained. Standard errors are in parentheses. Bonferroni corrected significance: * p < 0.1; ** p < 0.05; *** p < 0.01.   Table S15. Time-lagged models, models 1 to 6 (see Materials and Methods), of S versus GDP for cohorts in their first decade or childhood (y = 0 decades, top row), teenage years (y = 1 decade, middle row) and twenties (y = 2 decades, bottom row). In each row, "dep" is the dependent variable, GDP is historical GDP, S is effect of past secularization, y is time lag in decades, N is number of data points, n is number of unique countries, i is variance explained by the country random effect, h is variance explained by cultural-history and R 2 is total variance explained. Standard errors are in parentheses. Bonferroni corrected significance: * p < 0.1; ** p < 0.05; *** p < 0.01. Significance: ** p < 0.01; *** p < 0.001.  Table S16. Multilevel time-lagged models, but with secularization (S alt ) measured using the average of six indicator which are subjectively associated with religiosity. The results are similar to those using the secularization S derived using EFA: Secularization predicts development and not vice-versa. In each row, "dep" is the dependent variable, GDP is historical GDP, S is effect of past secularization, y is time lag in decades, N is number of data points, n is number of unique countries, i is variance explained by the country random effect, h is variance explained by cultural-history and R 2 is total variance explained. Standard errors are in parentheses. Bonferroni corrected significance: * p < 0.1; ** p < 0.05; *** p < 0.01.  y  1  2  3  1  2  3  N  478  387  289  559  512  427  n  101  98  86  98  101  101  i 0.05*** 0.14*** 0.3*** 0.08*** 0.21*** 0.37*** h 0.04** 0.11** 0.25*** 0.02 0.13** 0.