Fig 1.
Dynamics of the structural variables 1938–2019 (EMP, MMP, SFD) and trajectory of the political stress indicator predicted by the structural-demographic theory (PSI).
A) Fiscal stress indices (SFD.fb [black line] & SFD.pd [red line]). B) Population Mobilization Potential (MMP). C) Intra-elite tension (EMP). D) Political Stress Index (PSI). Numbers are representative of the main events of conflict: 1- Coup d’état of 73 (blue), 2- Popular mobilizations of the 80s (green), 3- Social Outbreak 2019 (violet). Smooth with loess method (span = 0.25). Shaded area represents confidence interval (95%). All data were normalized to a scale between 1–2.
Fig 2.
Correspondence between the observed political instability index and the political stress indicator predicted by the structural-demographic theory (PSI) (1938–2019).
A) Comparison of the dynamics of the PSI indicator (firm line) and the observed political instability index (dotted line). Regression between PSI* (PSI* = SFDa*MMPb*EMPc ) and observed political instability index in Chile (1938–2019). NLS Parameter values: a = 0.54 (p-value = 1.86e-11*), b = 0.36 (p-value = 2.60e-08*), c = 0.07 (p-value = 0.421), pseudo-R2 = 0.41. Residual: Test Shapiro-Wilk. 0.913, p-value = 0.48 B) GLS Regression between rate of change of PSI* (PSI* = SFDa*MMPb*EMPc) and rate of change of observed political instability index in Chile (1938–2019). (ARIMA (4,0,0), β = 1.25. CI-95%: 0.57–1.93, p-value = 0.0005*).C) Prediction through the Cross-Validation method (prediction one step ahead) of the dynamics of political instability in Chile from the PSI* model (1938–2019). Predicted series (green) and Observed series (red). RMSE = 0.15. All data were normalized to a scale between 1–2.
Fig 3.
Analysis of the interactions of the EMP and MMP components.
A) Antithetic trend between the relative income of the population (w; black) and the relative number of people that make up the elites (e, red). B) Relationship between demographic variables and the relative income of the population. Multiple linear regression between w (black series), and e & proportion of youth population (blue series) (R2 = 0.48; β1 = -0.82; β2 = -0.28; p-value< 2.81 e-12*). Multiple linear regression between w, and e & proportion of urban population (violet series) (R2 = 0.82; β1 = -0.11; β2 = -0.80; p-value< 2.2 e-16*).
Fig 4.
Relationship between rate of change of w (rw) and rate of change of e (re) mediated by demographic variables.
A) Relationship between rate of change of w (r.w) and the interaction of rate of change of e (r.e) and youth proportion (r.youth): (ARIMA (2,0,2); β = −5.62. C.I-95% = (-8.35,-2.88), p-value = 1e-3*. Residual: Shapiro-Wilk test = 0.9291, p-value = 3e-4). B) Relationship between r.w and the interaction of r.e and r.Nurb. (β = −20.02; C.I-95% = (-38.8,-1.23), p-value = 0.04*. Residual: Shapiro-Wilk test = 0.8485, p-value<0.01). Shaded area represents confidence interval (95%). All data were normalized to a scale between 1–2.