## Footnote 8, Chapter 5, Page 123:

This version of the paragraphs provided on page 123 gives more detail concerning the manner by which this project’s specific form of regression analysis was chosen. If an analysis of this sort of data is not performed in a way which “controls” for its cross-sectional time series nature, the accuracy of the conclusions will not be optimized. In any statistical model, if phenomena influencing the hypothesis being assessed are not represented through independent variables, the roles of other variables may be misinterpreted. This “omitted variable bias” is quite common in studies using cross-sectional time series data but its detrimental influence on statistical results can be minimized. The precision of statistical models with this sort of data is heightened by controlling for omitted variables that vary between cases but not over time, as well as those which differ over time but are constant between cases. Three types of cross-sectional time series analysis exist, which control for “fixed effects” for omitted variables that are constant over time, “between effects” for those which are constant between cases, and “random effects” for those models in which some omitted variables vary across time and others between cases. The best variant to use on one’s data can be ascertained through a Hausman Test, that examines which means of analysis will produce the most efficient, explanatory model with consistent, optimally reliable results. The Hausman Test for this database indicates that the random effects cross-sectional time series variant of multiple regression analysis should be used, to achieve the most accurate results. The models analyzed with GLS random effects regression tests included independent variables corresponding to consociational components and controlling independent variables, regressed on the dependent variable corresponding to stability. It should be remembered that, although the dependent variable is being analyzed in order to find out which factors contribute to stability, higher values for this variable actually correspond to higher levels of instability, as it is manifested by protests and rebellions. Appendix C lists all variables and the means by which their data were collected. Appendix D describes the manner by which the dependent variable and data were designated, and Appendix F explains the process by which controlling independent variables were chosen and operationalized. Table G.1 in Appendix G presents the results of the statistical regression analyses performed with this data. The role that each consociational component plays independently should be explored because the components often operate on their own and understanding each one’s function will facilitate greater comprehension of which institutions and practices are more conducive to stability in plural societies. The regression analyses show that the somewhat inclusive grand coalition variable (SGC) is not significant when the dependent variable is regressed on it, in models with it as the only independent variable and in models incorporating all independent variables. However, in a test using only the independent variables representing consociational components, this SGC variable is found to be exerting a statistically significant impact. While this set of analyses suggests that some other variables explain the variance in the dependent variable better than SGC, they also indicate that this variable exerts an influence in plural societies in the same direction as instability. Therefore, this project finds that somewhat inclusive grand coalitions exert a detrimental effect in these places, ostensibly because they exclude potentially antagonistic groups from executive power. Examination of this variable actually suggests that coalitions which do not contain representatives from a country’s MARs are more conducive to stability than those including members of some, rather than all, such groups. This phenomenon might conceivably result from some, potentially destabilizing groups’ belief that they may be permanently excluded from such somewhat inclusive coalitions. In contrast, the variable corresponding to highly inclusive grand coalition executives (HGC) is found to have a positive influence on stability, of a high magnitude, that is statistically significant in every regression test in which it is included. The results obtained using these models corroborate Lijphart’s belief that high levels of potentially antagonistic groups’ inclusion in executives is necessary for promotion of stabilization in plural societies. Reference to this website in Chapter 5, Page 125: The following charts include the results of this project’s regression analyses. Multiple Regression Using GLS Random Effects Independent Variables Test 1 Test 2 Test 3 Test 4 Test 5 Test 6 Test 7 Test 8 Test 9 Somewhat Inclusive .327 .067 Grand Coalition (.289) (.292) Highly Inclusive -1.688* -1.019** Grand Coalition (.797) (.312) Minority Veto .944** .325 (.330) (.227) Segmental Autonomy -.016 .069 (.649) (.344) PR .478 .521* (.374) (.227) Democracy .039* .045** (.017) (.010) Geographical .201 .595 Concentration of (.725) (.318) Segments External Threats .032 .396** (.228) (.136) Moderate Multiparty -.054 (.088) Population Size 2.60e-06 (2.14e-06) Socioeconomic Equality -.003 (.194) ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- Overall R-Squared 0.140 .012 .008 .007 .001 .021 .017 .011 .066 N 362 1506 1506 1088 1506 698 1425 1506 1058 Sigma_u 1.658 1.490 1.493 1.566 1.495 1.511 1.441 1.451 1.437 Sigma_e .872 1.372 1.367 1.326 1.372 .950 1.338 1.372 1.347 Rho .783 .541 .544 .583 .543 .717 .537 .528 .532 Note: The dependent variable is allocated higher values for higher levels of instability, as manifested by protest and rebellion. Entries are coefficients and numbers in parentheses are standard errors. The coefficients of those variables with P-values .05 or lower are allocated one asterisk and those with P-values .01 or lower are allocated two asterisks. All figures are rounded to three decimal places. Independent Variables Test 10 Test 11 Test 12 Test 13 Test 14 Somewhat Inclusive .506* .394 Grand Coalition (.244) (.272) Highly Inclusive -3.440** -1.771** Grand Coalition (.513) (.650) Minority Veto .735** .873** (.260) (.303) Segmental Autonomy .883* .015 (.456) (.511) PR .857** .522 (.257) (.334) Democracy .037** (.015) Geographical Concentration of Segments External Threats .061 (.210) Moderate Multiparty .121 System (.098) Population Size 2.99e-06 (1.62e-06) Socioeconomic Equality .158 (.103) -------------------------------------------------------------------------------------------------------------------------------------------------------------------- Overall R-Squared .007 .028 .031 .067 .099 N 1395 1506 1485 566 429 Sigma_u 1.450 1.465 1.486 1.590 1.499 Sigma_e 1.398 1.372 1.371 .877 .828 Rho .518 .533 .540 .767 .766 Footnote 10, Chapter 5, Page 129: Here are the scatterplot results: The following is a more detailed discussion of the scatterplots. Regression tests referred to are included in the results provided on the website, mentioned on page 125 of the book. Figure H.2 plots instability along the “segmental autonomy” component of consociation. In regression Test 13, a statistically significant, detrimental influence of segmental autonomy is identified. However, when the democracy control variable is included in Test 14, the segmental autonomy variable’s influence becomes statistically insignificant so it could be that the aspect of segmental autonomy rendering its variable destabilizing in Test 13 is actually better represented through the democracy variable, which focuses on general levels of democracy versus autocracy. Intriguingly, Figure H.2’s scatterplot suggests that segmental autonomy’s role is more nuanced than is suggested by these regression tests. This scatterplot does show a substantial concentration of cases which exhibit lower levels of instability and were recognized as exhibiting “segmental autonomy.” The line fitting the scatterplot is so close to being flat that it is difficult to interpret its meaning. This project’s quantitative and qualitative analysis collectively suggest that more data representing segmental autonomy, and perhaps its discrimination through multiple variables indicating segmental autonomy, are necessary for objective demonstration of this consociational component’s impact on stability. The qualitative case studies comprising Part 2 inspire one to wonder whether segmental autonomy is most conducive to stability when combined with beneficial widespread attitudes and incentives for intergroup moderation, both of which could not be operationalized here. Figures H.3 and H.4 present scatterplots indicating the influences of “minority veto power” and “PR” on instability. Regression analyses indicate that these variables both exert a statistically significant, detrimental effect. The scatterplots for both relationships indicate the largest concentration of cases lies neither in the lowest nor the higher levels of instability. The lines fitted to the scatterplots’ cases do very slightly slope down, corroborating the regression analyses’ findings that each of these variables exerts a detrimental effect on this dataset’s dependent variable. However, the scatterplots also emphasize and confirm that these detrimental effects are less pronounced than the positive influence exerted by the variable corresponding to highly inclusive executive coalitions. These scatterplots illustrate that a large proportion of cases indicating the presence of these two components were observed to enjoy relatively low amounts of instability. Perhaps more detailed data, indicating factors such as exertion, rather than availability, of MV and particular PR systems, will yield more valuable quantitative insights regarding consociation in the future. The qualitative case analyses presented in Part 2 suggest that perhaps particular types of PR, such as the Single Transferable Vote (STV) system, promote incentives which are more conducive to stability in divided societies. The variables corresponding to the system’s components were not regressed on democracy. The impact of democracy was controlled for through an additional independent variable. However, scatterplots including democracy were conducted here because of their potential insights concerning other scholars’ commentaries involving the extent to which consociation is democratic. Figure H.5, plotting grand coalition and democracy, confirms that most cases are not governed by executives falling into the categories represented by this project’s grand coalition variable. However, the scatterplot and fitted line emphasize that those which are governed by highly inclusive executives are more democratic. Figure H.6, plotting segmental autonomy and democracy, suggests that places using the elements of segmental autonomy which could be represented quantitatively here are fairly evenly spread along the continuum indicating levels of democracy. This is consistent with most of the regression analyses’ inability to detect a statistically significant impact of segmental autonomy on stability. The scatterplot and fitted line presented in Figure H.7 suggest an intriguing hypothesis concerning the data used for representation of the consociational component of minority veto power. It would appear that more cases with minority veto power are undemocratic, than democratic. The data used to represent this consociational component were the first ever compiled to do so but, due to a lack of data necessary for indication of the exertion of such veto power, the variable is represented through information indicating whether countries’ constitutions seemed to provide an opportunity for such exertion. This scatterplot suggests that a concentration of country cases exists in which a lack of democracy is present alongside constitutional provisions that appear to enable minority veto. Lijphart envisions this power as an element of democratic systems so it would appear that additional data indicating its exertion is necessary for comprehension of its role. Some critics of consociation argue that the system is insufficiently democratic so the implication of this scatterplot is not incompatible with all scholarly analysis. However, the contrast between the scatterplot and Lijphart’s consociational theory inspires one to speculate that perhaps the association between minority veto power and democracy is in some way related to the destabilizing effect of the variable corresponding to this consociational component in regression analyses. If data can be compiled documenting the exertion of this power, it may yield much greater comprehension of the nature of this component’s role in plural societies. The scatterplots with fitted lines shown in Figures H.8 and H.9 corroborate the regression analyses conducted with the variables on which they focus. Figure H.8 confirms that PR electoral systems are much more associated with democracy, but also reminds us that PR systems are sometimes used in less democratic countries. Figure H.9 shows that democracies are very slightly more associated with instability, thus reminding one again of the ability of undemocratic regimes to deter protests and rebellion. In general, the only finding derived through scatterplots which is surprising considering this project’s regression analyses is the revelation that more cases coded positively for minority veto power are coded as autocratic, rather than democratic.