Estimation of Conflict Dynamics

Abstract

This chapter develops an econometric methodology to deal with the endogeneity problem in conflict models with contemporaneous interactions. Using the Greek Civil War time-series, a dynamic Lotka-Volterra model with external disturbances is estimated. A stable conflict trap is determined, explaining the prolongation of the civil war and its dire consequences for the country.

This chapter has been written in collaboration with Christos Axioglou.

Appendix

6.1.1 Alternative Estimations

To thoroughly examine the problem of endogeneity, a number of alternative estimates is obtained first and are then compared with the estimation results by using OLS estimation techniques. The following steps are taken:

• Step 1: First, we need to take into account the presence of heteroskedasticity and/or contemporaneous correlation in the errors across equations. The seemingly unrelated regression (SUR) method, also known as the multivariate regression, or Zellner’s method, is applied to estimate the parameters of the system.⁵ Estimates are shown in Table 6.5.

  Table 6.5 Seemingly unrelated regressions estimation

• Step 2: If some of the right-hand side variables are correlated with the error terms, but there is neither heteroskedasticity nor contemporaneous correlation in the residuals, the System Two-Stage Least Squares (S2SLS) estimator is appropriate. Estimation results are shown in Table 6.6.

  Table 6.6 Two stage least squares estimation

• Step 3: If the right-hand side variables are correlated with the error terms, and there is both heteroskedasticity and contemporaneous correlation in the residuals, a more appropriate method is the Three-stage least squares (3SLS) estimation.⁶ This amounts to a two-stage least squares version of the SUR method.⁷ Results are shown in Table 6.7.

  Table 6.7 Three stage least squares estimation

• Step 4: Finally we compare the above estimates with the OLS outcome. Formal endogeneity is examined by employing the Durbin-Wu-Hausman test. The test stands for the existence of significant difference between the estimates obtained via OLS on each individual equation and those via Two Stage Least Squares.

6.1.2 Endogeneity Tests

Following the step highlighted in the previous Section, the system of Eqs. (6.4a, 6.4b) is estimated by applying the SUR method over the two phases. Using battle-deaths as the dependent variable, the following findings are established (results and further details available by the author)⁸:

• (a) Serial correlation is not detected in the residuals; this implies no evidence of permanent effects by unobserved factors incorporated in (ξ ₁, ξ ₂).

• (b) Additional experiments with alternative instrument sets deliver similar results. For example, by including ${R}_{t-1}{S}_{t-1}$ no perceptible difference is noticed.

• (c) The Durbin-Wu-Hausman tests indicate statistically insignificant differences in all cases but for one marginally significant case.

By comparing estimates shown in Tables 6.5, 6.6 and 6.7, it seems that the coefficients are similar with those obtained by using OLS in Table 6.3.⁹ Hence, the consequences of ignoring possible correlation between (ξ ₁, ξ ₂) are not severe. In all cases the explanatory power is satisfactory, and all coefficients but one are found to be statistically significant and correctly signed.

The only exception occurs regarding the firing effectiveness of GNA (β), whose estimate appears to be very sensitive to the choice of estimation method. By using the Seemingly Unrelated regression in Table 6.5, the estimates of (β) become significant and are closer to those obtained by simple OLS methods. However, the estimates obtained in Tables 6.6 and 6.7 are not statistically significant at the 10 % level.