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Dynamical Analysis of Socio-Economic Oscillations Peter Turchin University of Connecticut To be presented at the Santa

Dynamical Analysis of Socio-Economic Oscillations Peter Turchin University of Connecticut To be presented at the Santa Fe Workshop April-May 2004. Analytical approaches. Graphical analysis: time and phase plots Fitting models: Δ Y t = f( X t ) + e t X t : predictor variable(s)

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Dynamical Analysis of Socio-Economic Oscillations Peter Turchin University of Connecticut To be presented at the Santa

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  1. Dynamical Analysis of Socio-Economic Oscillations Peter Turchin University of Connecticut To be presented at the Santa Fe Workshop April-May 2004

  2. Analytical approaches • Graphical analysis: time and phase plots • Fitting models: ΔYt = f(Xt) + et • Xt : predictor variable(s) • ΔYt = Yt+τ – Yt: rate of change (response) • τ : time lag • more on this in the Turchin-Korotayev supplement, also see Historical Dynamics

  3. Phase shifts between oscillating variables tell us whether their interaction can potentially drive the observed cycles (here illustrated with a predator-prey system) Turchin P. 2003. Nature 424:257

  4. Time-series analysis results • Periodicity is statistically significant • average period of 3.2 centuries • “secular cycle” • Second-order system • with a strong endogenous (deterministic) component • Q: what is the identity of the second-order factor(s) that drive the cycle?

  5. Real wages and epidemics: conclusions • Both variables fluctuate synchronously with population • Act as first-order factors • Cannot drive the secular cycle

  6. Population and sociopolitical instability • Instability as a second-order factor • correct phase shift • Effect very strong • explains 80% of variance in compound annual growth rate (Schofield et al data) • Analysis results are consistent with the hypothesis that interaction between population and instability drives the secular cycle

  7. Table 1. Comparing out-of-sample predictive abilities of the inertial and interactive models (from Turchin-Korotayev Supplement)

  8. Some other analyses • Vital rates (fertility, mortality) • Crime statistics • Climate change

  9. Regression Analysis: r2 versus BD, logW, y, t, N, WAGE r2 = population rate of change, tau = 20 y BD = dummy variable for the Black Death logW = instability, log-transformed y = year (monotonic temporal trend) t = temperature N = population pressure (in relation to K) WAGE = real wage Predictor of r2 Coef SE Coef T P Constant -0.15804 0.03053 -5.18 0.000 BD -0.11646 0.01118 -10.42 0.000 logW -0.030560 0.003385 -9.03 0.000 y 0.00008885 0.00002282 3.89 0.000 t -0.17738 0.05676 -3.13 0.003 N -0.0005824 0.0002043 -2.85 0.006 WAGE 0.003293 0.001572 2.10 0.041 R-Sq = 90.0% R-Sq(adj) = 89.0% R-Sq(pred) = 85.55%

  10. General conclusions: regression analysis of population rate of change • Strong effect of the Black Death • not surprising! • Strong effect of instability • Moderate temporal trend • Moderate effect of temperature • but the sign is negative! (expect positive) • Moderate effect of population pressure • Weak effect of wage • but without pop. pressure in the model, effect of wage strengthens, t = 2.5, P < 0.016

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