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Jackman: Multiple
Regression II 
The Predictability of Coups d'etat: A Model with African Data American Political Science Review, 72 (December 1978), pp. 12621275. 



where M is Social Mobilization, and C is Cultural Pluralism. The earlier discussion implies ß1 > 0, but provides contradictory expectations concerning ß2 and ß3, which incorporate the effects of ethnic dominance. If, as most analysts argue, ethnic heterogeneity is destabilizing, then we would expect ß2 < 0, while ß2 > 0 would be consistent with the countervailingpowers hypothesis that sees ethnic dominance as the destabilizing force. Note that joint effects are also specified in this equation (estimated by ß1) that allow the effects of mobilization to vary according to the degree of cultural pluralism. This is clearly necessary if we are to assess the validity of the arguments of Deutsch and others that were reviewed earlier. The top two rows of Table 1 report the leastsquares estimates for two versions of equation (1), one with additive effects only (i.e., with ß1 constrained to a value of zero) and the other with both additive and multiplicative terms. It is clear that mobilization and ethnicity do not have nonadditive (or joint) effects on coups. This result is obvious from the fact that the estimate of ß1 is not effectively different from zero (the tratio is l.29).[8] Moreover, a comparison of the corrected coefficients of determination shows that the full equation accounts for no more variance than does the truncated version with additive effects only. We can therefore conclude initially that the effect of mobilization on coups does not depend on the degree of cultural heterogeneity, which means that we can confine our attention to the estimates for the additive model in the top row of the table.
^{a}Main
table entries are the parameter estimates, and numbers below
them in parentheses are their standard errors. 
The estimate for ß1 in the additive model is positive and almost three times the size of its standard error. That is, mobilization increases the probability of coups d'etat, as was anticipated. Such an outcome is consistent with the arguments put forward by Deutsch and Huntington, among others, that in the absence of political capacity or institutionalization, mobilization is likely to be destabilizing. Remember that this interpretation of the estimate for ß1 is predicated on the assumption that both the recency of national independence and the decolonization process imply a generally low degree of institutional longevity in black Africa. 
Table 2.
Regressions of Coups d'etat, 1960 to 1975, on Party Strength and
Participation
at Time of Independence (N =29)^{a}
Continuous Version of Participation Binary Variable Version of Participation^{b}
(P)
R^{2}
^{a}Ethiopia
is excluded from this analysis. Main table entries are
the parameter estimates, and numbers below them in
parentheses are their standard errors.
^{b}This variable equals 1 if turnout was 21
percent or more, and zero otherwise.

Table 3.
Regressions of Coups d'etat, 1960 to 1975,
on Mobilization, Pluralism, Party Strength, and Turnout
(N=29)^{a}
M Social Mobilization C Size of Largest Ethnic Group D Percent Vote to Winning Party P Electoral Turnout D.P Winning Party Vote * Turnout C.D Ethnic Group Size * Winning Party Vote C.P Ethnic Group Size Turnout C.D.P Ethnic Group Size * Winning Party Vote * Turnout Constant R^{2} Adjusted R^{2}
^{a}Ethiopia
is excluded from this analysis. Main table entries are
the parameter estimates, and numbers below them in
parentheses are their standard errors.
These estimates also reveal that there is no support for the more complex version of equation (3) that specifies a secondorder interaction: the estimate of ß8 in the second column of Table 3 is smaller than its standard error and the corrected coefficient of determination in the same column is slightly smaller than it was in the first column. This means that party dominance has no special effects in countries with both high turnout and a dominant ethnic group. We can therefore confine our attention to the estimates of equation (3) in the first column of Table 3. In Figure 1, estimated Coup scores from this model are plotted against actual Coup scores.[13] Only the Sudan has a residual (12.959) that is larger than the standard deviation of the coup d'etat index (12.510), and even this difference is slight. In general, then, this scatterplot suggests no obvious biases in the model, but rather reinforces the earlier impression that the model fits well. 
^{a}Estimated coup d'etat scores are from the estimates in the first column of Table 3. Country numbers are provided in the Appendix.
Briefly, the estimates in the first column of Table 3 suggest that each of the four variables has a pronounced effect on elite instability. All of the eight parameter estimates are precise (including 69, in that three of them have tratios larger than 3.0, while the smallest (that for ß5) is close to 2.0 (1.68).[14] In addition, these estimates indicate that none of the effects from the analyses reported in Tables 1 and 2 is spurious. The additive positive effects of mobilization and ethnic dominance on elite instability persist, while the separate and joint effects of participation and party dominance described in Table 3 are of form similar to (if slightly weaker than) those reported in Table 2.. . . . [Text omitted] Summary and Implications
This paper has centered on coups d'etat those illegal efforts by insurgent elites (typically the military) to bypass normal or constitutional channels of executive succession that are accompanied by actual or threatened resorts to physical violence. In particular, we focused on an index covering 16 years that is a weighted sum of successful, unsuccessful, and plotted coups, respectively.
For students of African affairs, one clear inference to be drawn from this study is that instability of this kind is not random with respect to political and social structure. Assuming that I have excluded no important independent variables and (even) that my measures are perfectly reliable, this study shows that the idiosyncratic (i.e., random) factors to which Zolberg (1968, p. 71), Decalo (1976, p. 22) and others have alluded cannot account for more than onefifth of the variance in coups d'etat (the presence of unreliability would, of course, further lower the residual variance that we might attribute to idiosyncratic factors).16
Instead, the fit of this model that casts coups as a function of structural factors is striking. Far from pointing to a random process, these estimates suggest a rather deterministic pattern. It is evident from Figure 1 that the volume of elite instability in the countries of black Africa from 1960 to 1975 can be estimated with a remarkable degree of accuracy, given four straightforward and distinct conditions that are central to the theoretical literature on political instability. Three of these conditions clearly predate the dependent variable, while the fourth (measured c. 1965 to 1966) is a variable that probably underwent little pronounced change in the preceding six years.
. . . . [Text omitted] In short, the analysis suggests that both social mobilization and the presence of a potentially dominant ethnic group have destabilizing consequences, at least in the context of the new nations of black Africa. The first of these variables is one that changes relatively slowly, while the second is even less responsive to conventional political action. However, the results indicate that the destabilizing results of these two "social" variables, especially ethnic dominance, are substantially reduced. by two "political" factors (mass participation and party strength). My emphasis on the role of strong political parties is hardly original. More novel is the clear implication of this analysis that the stabilizing impact of mass political participation may generally be as important as is the consolidation of political parties (an activity that is primarily in the hands of political elites). This suggests that besides its uncomfortable normative implications, the common argument that restricted participation brings stability may be more myth than fact,
Appendix: List of Countries
1
Burundi
16
Mali
2
Cameroon
17
Mauritania
3
Central African Republic
18
Niger
4
Chad
19
Nigeria
5
CongoBrazzaville
20
Rwanda
6
Dahomey (Benin)
21
Senegal
7
Ethiopia
22
Sierre Leone
8
Gabon
23
Somalia
9
Gambia
24
Sudan
10
Ghana
25
Tanzania
11
Guinea
26
Togo
12
Ivory Coast
27
Uganda
13
Kenya
28
Upper Volta
14
Liberia
29
Zaire
15
Malawi
30
Zambia
Footnotes 1. Recent empirical studies include those by Morrison and Stevenson (1972), Wells (1974), and Barrows (1976). Of these analysts, only Wells provides evidence on the fit of his model (in the form of multiple correlation coefficients), but, as Phillips and BarYunus (1976) have pointed out, his models actually account for between zero and 12 percent of the variance in coups d'etat. Indirect evidence in the other two papers suggests a similar degree of fit.2. Note that a concern with the problem of leadership succession is central to the literature on political development. See, for example, Weiner and LaPalombara (1966) and Huntington (1968). In this paper, I use the terms coups d'etat and political or elite instability interchangeably, although I recognize that political instability can manifest itself in forms other than the coup d'etat.
3. Morrison and Stevenson (1971, pp. 36164) provide an analysis of the dimensional properties of their similarly weighted index. I follow their weighting since it results in smaller residual sums of squares in the models to follow than do a series of plausible alternative weights (see Tufte, 1969 for a discussion of this procedure). For the 30 countries listed in the Appendix, values on my measure range from zero to 46 (Dahomey [Benin]), with a mean of 13.967 anda standard deviation of 12.294. Thus, this variable is somewhat skewed, although not substantially so (since the mean is larger than the standard deviation). Country values are plotted on the vertical axis of Figure 1 below. For a comparison of the different sources used in the collection of my data on coups, see Jackman and Boyd (1979).
4. Data on the agricultural component of the labor force are from the United States Agency for International Development (1968), and are the same as those reported two years later in the same publication and those listed by Morrison, et al. (1972, p. 40). I have reversed the AID scores so that this variable reflects the percentage of the labor force in nonagricultural (rather than agricultural) occupations. For the 30 countries in this study, values on this variable range from 4 to 44, with a mean of 16.333 and a standard deviation of 9.320. Data on literacy rates are from Morrison, et al. (1972, p. 70). and values on this component of social mobilization range from 3 to 40, with a mean of 14.533 and a standard deviation of 10.692 (N 30). For the same countries, values on the social mobilization index range from 7 to 74, with a mean of 30.867 and a standard deviation of 17.087.
5. I have treated the "other" category as a separate (and single) ethnic group. C (the percentage of the population in the largest group) ranges from 19 to 95, with a mean of 46.017 and a standard deviation of 19.292. The correlation of this variable with the total number of ethnic groups is .794 (this second variable ranges from 2 to 9). In general, the relative size of ethnic groups is a variable that exhibits substantial temporal stability (the political and social relevance of ethnicity to individuals may, of course, be much less stable).
6. Space considerations preclude a full treatment of the definition and measurement of ethnicity here, but Morrison, et al. (1972, pp. 16670, 41533) provide a lengthy discussion of the term and of issues surrounding the validity and reliability of the data used below.
7. [omitted]
8. Statistical tests of significance help distinguish estimates based on these data from estimates derived from a randomly generated set of data. The precision of an estimate increases with its tratio (i.e., the ratio of an estimate to its standard error). A tratio of 2.0 indicates that the results are significant at the .05 level, while a tratio of 1.7 indicates signilicance at the .10 level. Note that standard errors of estimate are sensitive to the number of observations, which in the present case is small (30).
9. 1t is also possible that the binary variable version of ethnic dominance provides a better fit because it is more reliable than the continuous version. In particular, the dichotomous version of this variable is probably less sensitive to the unreliability thit arises from the more detailed reliance on the various ethnographies required to construct the continuous variable (cf., Morrison, et al., 1972, p. 169). Note incidentally that the binaryvariable versions of C and P are retained in equation (3), since they provided optimal estimates. Thus, this equation constitutes a rather detailed analysis of covariance.
10. This variable ranges from 16 to 100, with a mean of 66.724 and a standard deviation of 22.000 (N=29). I have modified two of the original scores. First, since Ethiopia has no political parties (and given also that it was an "ancient kingdom" in 1960), 1 have excluded it from further analysis, which reduces the N to 29. Second, I have given the Sudan a score of 63 percent, on the grounds that even though Morrison and his colleagues do not use Ibis va]ue, they do suggest this as the best estimate (since the National Unionist Party won 60 percent of the seats). For discussion of the reliability of this and the following measure, see Morrison, et at. (1972, pp. 9697).
11. This variable ranges from 1 to 46, with a mean of 22.483 and a standard deviation of 11.825 (N 29).
12. [omitted]
13. To check on the assumption of homoskedastic disturbances for this model, I followed two procedures. First, as suggested by Anscombe and Tukey (1963), I plotted the fitted values (Coups) against the residuals (Coups  Coups). Second, as suggested by Johnston (1972, p. 219), I computed Speannan coefficients of rank correlation between the absolute values of the residuals and each of the independent variables in equation (3). Neither of these constitutes a formal 'test' for homoskedasticity, but because they are nonparametric, both procedures have the advantage that they do not require (unavailable) information on the precise form of the process generating any heteroskedastic disturbances. Neither of these procedures provides evidence of heteroskedasticity in the estimates in the first column of Table 3.
14. The fact that ßs has a tratio slightly less than 2.0 does not warrant its exclusion from the model, since reestimating equation k3) subject to the constraint that ß1 ß8 0 produces estimates for ß1 and ß1 that are approximately half the size of those reported in the first colsann of Table 3. In addition, this revised estimate of ß1 has a trario of 1.55. This means that [~ should be retained in the model so tInt the nonadditive effects of party dominance and electoral turnout are not suppressed.
15. This judgment depends on the size of the coefficients weighted by the range of the relevant variable. Party dominance (D) ranges from 16 to 100, while electoral participation P) is either 0 or 1. Thus, in societies with no dominant ethnic group, the effect of D (.202*l00 = 20.2) is similar to the effect of P (23.047).
16. Of course, I am not claiming that these measures are perfectly reliable: as I have already noted, potential sources of unreliability are extensively discussed by Morrison, et at. (1972). The fit of the model does suggest, however, that unreliability is not a major problem (simply because its presence would be reflected in attenuated correlations). In conjunction with the parameter estimates, the fit of the model can also be viewed as evidence favoring the validity of the measures I have used.
References
Anscombe, F., and J. W. Tukey (1963). 'The Examination and Analysis of Residuals." Tecnnometrics 5:141 60.
Barrows, Walter L. (1976). 'Ethnic Diversity and Political Instability in Black Africa." Comparative Political Studies 9:13970.
Coleman, James S. (1960). 'The Politics of SubSaharan Africa." In Gabriel A. Almond and lames S. Coleman (cdi), The Politics of the Developing Areas. Princeton: Princeton University Prrss,
Dahl, Robert A. (1956). A Preface to Democratic Theory. Chicago: University of Chicaco Press,
Decalo, Samuel (1976). Coups and Army Rule iinAfrica. New Haven: Yale University Press.
Deutsch, Karl W. (1957). Political Community in the North Atlantic Area. Princeton: Princeton University Press.
Deutsch, Karl W. (1961), "Social Mobilization and Political Development." American Political Science Review, 55:493514.
Finer. Samuel E. (1962). The Man on Horseback: The Role of the Military in Politics. London: Pall Mall Press.
Fossum, Egil (1967). "Factors Influencing the Occurrence of Military Coups D'Etat in Latin America." Journal of Peace Research 4:22851.
Geertz, Clifford (1963). "The Integrative Revolution: Primordial Sentiments and Civil Politics in the New States." In Clifford Geertz (ed.), Old Societies and New States: The Quest for Modernity in Asia and Africa. New York: Free Press.
Greenberg, Joseph H. (1956). 'The Measurement of Linguistic Diversity." Language 32:109  IS.
Hayward, Fred M. (1973). "Political Participation and its Role In Development: Some Observations Drawn from the African Context." Journal of Developing Areas 7:591611.
Huntington, Samuel P. (1968). Political Order in Changing Societies. New Haven: Yale University Press.
Jackman, Robert W., and William A. Boyd (1979). "Multiple Sources and the Collection of Data on Political Conflict." American Journal of Political Science 23 :in press.
Johnston, J. (1972). Econometric Methods. 2nd ed. New York: McGrawHill
Kuper, Leo, and M. G. Smiih. eds. (1969). Pluralism in Africa. Berkeley and Los Angeles: University of California Press.
Morrison, Donald G., R. C. Mitchell, J. N. Paden and H.M. Stevenson (1972). Black Africa: A Comparative Handbook. New York: Free Press.
Morrison, Donald G., and Hugh M. Stevenson (1971). "Political Instability in Independent Black Africa: More Dimensions of Conflict Behavior within Nations." Journal of Conflict Resolution, 15:34768.
 Morrison, Donald G., and Hugh M. Stevenson (1972). "Cultural Pluralism, Modernization, and Conflict: An Empirical Analysis of Sources of Political Instability in African Nations." Canadian Journal of Political Science 5:82103.
 Naroll, Raoul (1970). "The CultureBearing Unit in CrossCultural Surveys." In Raoul Naroll and Ronald Cohen (eds.), Handbook of Method in Cultural Anthropology. New York: Natural History Press.
 Phillips, John, and Ilyas BaYunus (1976). "Commenton Alan Wells's 'The Coup D'Etat in Theory and Practice.' " American Journal of Sociology, 82:68485.
 Rabushka, Alvin, and Kenneth A. Shepsle (1972). Politics in Plural Societies: A Theory of Democratic instability. Columbus, Ohio: Charles Merrill.
 Rae, Douglas W., and Michact Taylor (1970). The Analysis of Political Cleavages. New Haven: Yale University Press.
 Shils, Edward (1957). "Primordial, Personal, Sacred and Civil Ties." British Journal of Sociology 8:13046.
 Tufte, Edward R. (1969). "Improving Data Analysis in Political Science." World Polities 21:64154.
 United States Agency for International Development (1968). AID Economic Data Book: Africa, Oftice of Proeram and Policy Division. Washington, D.C.: Clearinghouse.
 Weiner, Myron, and Joseph LaPatombara (1966). "The Impact of Parties on Political Development.' In Joseph LaPalombara and Myron Weiner (eds.), Political Parties and Political Development. Princeton: Princeton University Press.
 Wells, Alan (1974). "The Coup d'etat in Theory and Practice: lndepessdent Black Africa in the 1960's." American Journal of Sociology' 79:871  87.
 Zolberg, Aristide R. (1968). "Military Intervention in the New States of Africa." In Henry Bienen (ed.), The Military Intervenes. Case Studies in Political Development. New York: Russell Sage.