Book contents
- Frontmatter
- Dedication
- Contents
- List of Tables
- List of Figures
- Acknowledgments
- 1 Introduction
- 2 A Theory of Regime Survival and Fall
- 3 Competitive Regimes and Authoritarianism in Latin America
- 4 Regime Survival and Fall
- 5 From Multiple Breakdowns to Stabilization of Democracy: Argentina
- 6 From Persistent Authoritarianism to a Durable Democracy: El Salvador
- 7 International Actors, International Influences, and Regime Outcomes
- 8 Political Regimes after the Third Wave
- 9 Rethinking Theories of Democratization in Latin America and Beyond
- Appendix 3.1 Coding Rules for Political Regimes
- Appendix 3.2 Coding U.S. Foreign Policy toward Democracy in Latin America
- Appendix 4.1 Long-Run Equilibrium for the Proportion of Competitive Regimes
- Appendix 5.1 Qualitative Comparative Analysis
- Appendix 6.1 Coding of Salvadoran Actors, 1979–2010
- Bibliography
- Index
Appendix 4.1 - Long-Run Equilibrium for the Proportion of Competitive Regimes
Published online by Cambridge University Press: 05 June 2014
- Frontmatter
- Dedication
- Contents
- List of Tables
- List of Figures
- Acknowledgments
- 1 Introduction
- 2 A Theory of Regime Survival and Fall
- 3 Competitive Regimes and Authoritarianism in Latin America
- 4 Regime Survival and Fall
- 5 From Multiple Breakdowns to Stabilization of Democracy: Argentina
- 6 From Persistent Authoritarianism to a Durable Democracy: El Salvador
- 7 International Actors, International Influences, and Regime Outcomes
- 8 Political Regimes after the Third Wave
- 9 Rethinking Theories of Democratization in Latin America and Beyond
- Appendix 3.1 Coding Rules for Political Regimes
- Appendix 3.2 Coding U.S. Foreign Policy toward Democracy in Latin America
- Appendix 4.1 Long-Run Equilibrium for the Proportion of Competitive Regimes
- Appendix 5.1 Qualitative Comparative Analysis
- Appendix 6.1 Coding of Salvadoran Actors, 1979–2010
- Bibliography
- Index
Summary
Equation 4.3 summarized the equilibrium conditions for the proportion of democracies D* = pDt bSt/( bDt bSt + pDt bSt + pSt bDt ) and semi-democracies S* = pSt bDt/( bDt bSt + pDt bSt + pSt bDt). This appendix provides proof of those conditions.
Given the transition matrix presented in Figure 4.1, the proportion of democracies observed at time t can be defined as Dt = Dt-1 (1 – bDt – qSt) + St-1 qDt + (1 – Dt-1 – St-1) pDt. Because we are only interested in changes from competitive politics to authoritarianism (and vice versa), and for the sake of consistency between the analytic solution and the empirical models, we shall assume no erosion or deepening, that is qSt = 0 and qDt = 0. The equation then reduces to Dt = Dt-1 (1 – bDt) + (1 – Dt-1 – St-1) pDt. Similarly, the proportion of semi-democracies reduces to St = St-1 (1 – bSt) + (1 – Dt-1 – St-1) pSt.
In equilibrium, the proportion of democracies and semi-democracies must remain steady such that, at the limit, Dt = Dt-1 = D* and St = St-1 = S*. We can reexpress the proportion of democratic regimes in equilibrium as D* = D*(1 – bDt) + (1 – D*– S*) pDt, where for any relevant case in which 0 < D* < 1, bDt > 0 and pDt > 0. It follows that D*bDt = (1 – D*– S*) pDt. For the same reason, S*bSt = (1 – D*– S*) pSt.
As a result, in equilibrium, pDt/ bDt = D*/(1 – D*– S*), and pSt/ bSt = S*/(1 – D*– S*).
Solving the equation for democracies, D* = pDt (1 – S*) / (pDt + bDt), and for semi-democracies we get S* = pSt (1 – D*) / (pSt + bSt).
Substitute the equation for semi-democracies in step 4 into the equilibrium equation for democracies in step 3, such that pDt/bDt = D*/( 1 – D*– (pSt – pSt D*)/(pSt + bSt)).
Solving for D*, we get D* = pDt bSt/( bDt bSt + pDt bSt + pSt bDt ).
Repeating steps 5–6 for semi-democracies, we obtain S* = pSt bDt/( bDt bSt + pDt bSt + pSt bDt ).
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- Democracies and Dictatorships in Latin AmericaEmergence, Survival, and Fall, pp. 303Publisher: Cambridge University PressPrint publication year: 2014