Survival Within the Selectorate Model

Political institutions determine the ease of political survival. There is always a plentiful supply of political rivals that wishes to come to power. If members of the incumbent's coalition believe they would be better off under a rival's leadership, they can defect and depose the incumbent. Small coalition systems, particularly in the presence of a large selectorate, make survival relatively easy, at least once a leader is well established. Although a potential rival might offer a member of the current coalition more rewards than they currently receive from the incumbent, the rival is inherently disadvantaged in her ability to credibly promise private goods in the future. Once established in power a new leader might, and often does, rearrange her coalition and replace some members of the former leader's coalition with those she likes more or thinks will be more loyal. Hence supporters who defect to support a challenger risk losing access to future private goods when the new leader reorganizes her coalition. An incumbent leader does not suffer from this commitment problem, because she has already reorganized her coalition around those with whom she has the greatest affinity. Coalition members can therefore expect to be included for as long as she is leader.

In small coalition systems in which private goods are particularly prominent, a leader's ability to commit to providing future private goods endows her with an incumbency advantage once she is well established in office. While there is also an incumbency advantage in democracies, the incumbent's advantage is not as strong because private goods are relatively less important in large coalition systems.

Protests and Revolution

Revolutions are attempts by those outside the winning coalition to replace the existing political institutions with more inclusive ones and are often preceded by mass protests. Citizens have a greater incentive to protest in small coalition systems than in large coalition systems, as the former provide few public goods. However, such autocratic systems make it difficult for citizens to coordinate and depose the extant regime because communications and political freedoms are restricted. While someone might be prepared to join an anti-government protest in a neighbouring town, they can not express their discontent if they do not know the protest is taking place or if there is no transport to get there. Natural disasters can serve as a coordinating device for citizens, and governments, particularly small coalition ones, fear they may provide a rally point for protest.

Disasters can facilitate coordination by concentrating those who are unhappy with the current system and have little to lose, and thus pose a potential problem to political leaders. In small coalition systems the people outside the coalition want to expand it. While citizens can potentially reach this goal once they are organized into a mass movement, autocratic governments make assembly and coordination difficult, costly and risky. In an argument first advanced by Schelling, Kuran and others conceptualize mass political movements as tipping points:Footnote ³² if enough people participate, then it is hard for the government to single them out for retaliation. Once events gain sufficient momentum, disgruntled people readily join them. However reaching this critical mass is difficult, as the initial participants expose themselves to government retaliation. Unless there is a strong expectation that protests will succeed, few people are willing to initiate them. Earthquakes and other disasters can serve as coordinating devices because they force together large numbers of people, which makes it easier to reach the critical mass. Disaster can also weaken the state's capacity to monitor and punish.

Since natural disasters can facilitate revolutionary movements in small coalition systems, leaders in such systems often try to prevent people from congregating. For instance when Cyclone Nargis struck Burma in 2008, the military junta made no effort to evacuate the people. Afterwards, survivors were prevented from seeking assistance in larger towns and villages. Within a week of the disaster the army started forcibly dispersing survivors from makeshift camps, schools and monasteries.Footnote ³³ By letting people die in outlying areas, the government forestalled the possibility of protest. Dead people cannot revolt.

The extent to which natural disasters serve as coordinating devices depends on where they occur. Disasters that afflict the capital city or other densely populated urban areas are more likely to stimulate protest than those in rural or remote areas. In general small coalition systems are not geared towards disaster relief, but they are more likely to provide some assistance in urban areas than in remote areas. In China, the government only half-heartedly assisted the remote province of Qinghai after an earthquake in 2010 and suffered few political consequences for its inaction. But when an earthquake hit Sichuan in 2008, the Chinese government – wary of protest in this politically and economically powerful centre – undertook relief operations that won the approval of much of the international community.

Data

We tested the predicted relationships between disasters and politics using data on the occurrence and impact of disasters, political institutions, anti-government protests, leader survival and many control variables. Data about disasters were drawn from the Emergency Events Database EM-DAT at the Centre for Research on the Epidemiology of Disasters (CRED).Footnote ³⁴ This database contains information about the occurrence and characteristics of more than 16,000 disasters around the world since 1900. According to CRED, a disaster is a ‘situation or event, which overwhelms local capacity, necessitating a request to national or international level for external assistance’. For the EM-DAT database, an event is considered a disaster event if it caused the deaths of ten or more people, if 100 or more people were affected, if an authority declared a state of emergency or if there is a call for international assistance. When an event fulfills any of these criteria, it is recorded at three different levels: disaster level, country level and source level. In this framework, a unique identifier is assigned to each disaster, and each disaster can be associated with several countries affected by it. For instance, the December 2004 tsunami has a unique identifier, but it is recorded for thirteen different countries. Disasters can be classified into groups, subgroups, types and subtypes. There is also a classification for primary disasters that caused associated disasters. CRED also records the number of people killed, injured, left homeless and affected by the disasters, as well as the economic damage of disasters in US dollars. Information about the occurrence and effect of a disaster is obtained from several sources, such as the United Nations as well as governmental and non-governmental agencies, among others. CRED ranks the reliability of the information produced by these sources, and in the majority of cases a disaster is included in the database only if two sources report the event in terms of casualties or people affected. Once an event is included in the database, it goes through an internal validation process, and is made available to the public once it is validated.

The first part of our study focuses on the variable ln(Deaths), which is the natural logarithm of the count of disaster deaths plus one for all disasters in a particular country-year, and the variable Disasters, which is the count of disasters that takes place in a particular country in a year. Unfortunately the EM-DAT database is still susceptible to reporting biases, as some nations are much more likely to report events than others.Footnote ³⁵ In addition, the Disasters variable cannot distinguish between the scale of different disasters. Such concerns have lead some scholars to focus on earthquakes, for which the Richter scale offers an objective measure of intensity.Footnote ³⁶ Other studies use alternative measures of disaster magnitudes. For example, Chen explores the effect of storm intensity on disaster relief,Footnote ³⁷ while Healy and Malhotra use the Fujita scale to examine the effect of economic losses from tornadoes on electoral outcomes.Footnote ³⁸

However it is important to recognize that this fix for one form of measurement error introduces another type of measurement error. A focus on earthquakes, for instance, provides an objective measure of the magnitude of disasters for a small subset of natural disasters. Yet considering only earthquakes implicitly gives the magnitude of all other forms of disasters a value of zero. Hence unless one believes that earthquakes generate political fallout but storms do not, then an exclusive focus on earthquakes must be seen as a different trade-off in dealing with noisy, poorly measured data rather than as a fix. Reassuringly, we obtain similar results when we examine only earthquakes.

To measure mass protests against the government we used a count of the number of anti-government demonstrations per year obtained from Arthur S. Banks's Cross National Time Series Data Archive.Footnote ³⁹ Banks codes this variable as a peaceful public gathering of more than 100 people to express discontent based upon media reports. We operationalize this variable as both a simple count of the number of protests (AntiGov) and as the natural logarithm of this count variable plus one (ln(AntiGov)). Data on leader survival are obtained from Archigos, a database of political leaders collected by Goemans, Gleditsch and ChiozzaFootnote ⁴⁰ that provides the dates for the entry and exit of political leaders and their age.

The selectorate institutions of winning coalition size (W) and selectorate size (S) are obtained from Bueno de Mesquita et al.Footnote ⁴¹ The estimate of W is a composite index based on institutional variables that reflect the openness of a political system. More specifically, the measurement of the winning coalition is a composite index of Polity IV data on a regime's competitiveness of executive recruitment, openness of executive recruitment and competitiveness of participation. The composition of the winning coalition also includes regime type as defined by Banks's Cross National Time Series Data Archive. Systems with small winning coalitions resemble autocracies, whereas systems with large winning coalitions are similar to democracies. The estimate of the selectorate (S) reflects the selectiveness of a country's legislature, which is a function of the breadth of the selectiveness of the members of each country's legislature and can be interpreted as a logarithmic scale of the magnitude of a polity's selectorate. This variable is also obtained from Polity IV data. Both W and S have a minimum normalized value of 0, and a maximum of 1. As a practical matter the democracies of Western Europe are all classified as having the largest coalition size (W = 1). The next category of coalition size (W = 0.75) includes emerging democracies such as Indonesia and the Philippines. The smallest coalition systems (W = 0) are generally military regimes such as Pakistan following Musharraf's coup in 1999. Middle Eastern monarchies, such as Saudi Arabia and Kuwait, are generally coded as W = 0.25.

Measuring political institutions is a contentious topic. Much of the discipline has focused on differentiating democracies from other political systems. An advantage of selectorate theory is that it allows comparisons both within and across democracies and non-democracies. Of course this is not the only approach to classifying non-democratic regimes. Geddes, for instance, examines whether autocracies are military, personalist or single-party in nature. Yet her typology does not directly relate to the theoretical ideas developed here.Footnote ⁴² All measures have practical limitations, and assessing selectorate institutions is no exception. Clarke and Stone and Morrow et al. debate, for instance, the close correlation between measures of selectorate institutions and Polity IV's measure of democracy.Footnote ⁴³ Given these concerns, in the Appendix we replicate all results replacing measures of W with Polity's −10 to +10 measure of democracy-autocracy rescaled between 0 and 1, a variable we label Demaut. These analyses produce similar results. However given the theoretical focus on selectorate theory, we focus on the impact of W on disasters and their political consequences.

Our analyses also use a number of additional variables related to economic and demographic conditions. The ln(GDPPC) is the natural logarithm of per capita gross domestic product (GDP) in constant dollars. Growth is the annual change in GDPPC. The variable ln(Population) measures a country's population.Footnote ⁴⁴ These variables are taken from the World Bank's World Development Indicators. All data and programs to replicate the analyses are available from the authors. Table 1 presents summary statistics for the key variables.

Table 1

Summary Statistics

Deaths from Disasters

Consistent with existing studies, our analyses showed that fewer people die in disasters in large coalition systems, such as democracies, than in small coalition systems. Figure 1 shows the smoothed density plot of the number of disaster-related deaths in each nation-year according to the size of the winning coalition.

Fig. 1

Difference in disaster deaths by institution

Clearly, there are significant differences in the mean and variance of these distributions. Countries with large winning coalitions have a smaller mean number of deaths and a smaller variance around this number, while countries with small winning coalitions have a larger mean number of deaths and a much larger variance.

Motivated by these initial results, our first set of estimations explored the role of political institutions on the number of deaths caused by disasters. The unit of analysis for this set of models is the country-year. The dataset includes information on nations from 1900–2008. However, due to data restrictions on other variables, GDP in particular, our sample for estimation will be smaller.

Table 2 presents estimates from a least squares regression of the natural logarithm of the number of deaths plus one per nation-year.Footnote ⁴⁵ Political institutions, the number of disasters, GDP per capita, population and their interactions with the size of the winning coalition influence the number of disaster-related fatalities. Model 1 uses region-year fixed effects, while Model 2 uses country fixed effects.Footnote ⁴⁶ As with all analyses, we report robust standard errors clustered by either nation or region-year.

Table 2

Dependent Variable: ln(Deaths)

Unit: country-year.

*p < 0.10, †p < 0.01.

The estimates are consistent with the results produced by the literature on the effect of institutions on disaster-related casualties, and they show support for Hypothesis 1.Footnote ⁴⁷ In Model 1 the negative coefficient estimate on coalition size and the interaction of coalition size and wealth indicate that large coalition systems experience few deaths, and that such systems convert societal resources into better protection against disasters than do small coalition systems. The positive (but insignificant) parameter estimate in Model 1 on the wealth variable indicates that small coalition systems do not successfully use increased societal resources to reduce citizens’ risk from natural disasters. This finding is consistent with the theory's predictions that large coalition leaders spend available resources on public goods while small coalition leaders retain such resources for their coalition rather than protecting their citizens. Although not shown, a similar pattern observed in the analysis is repeated without fixed effects: wealth reduces disaster-related deaths in large, but not small, winning coalition systems.

Model 2 replicates the analysis using a fixed effect for each nation. Unfortunately, since there is relatively little institutional variation between nations, the estimates show a less significant pattern, which is a common problem when variables are relatively invariant within the fixed-effect grouping.Footnote ⁴⁸ As a robustness test we ran Plümper and Troeger's fixed-effect vector decomposition procedure, which accounts for the lack of temporal change within the fixed-effect units, and obtained similar results to those reported in Model 1:Footnote ⁴⁹ institutions affect the number of casualties from natural disasters. Our next analyses delved into the reasons for these institutionally induced differences by testing how the occurrence and impact of disasters affect public protests and leader survival. The negative coefficient estimate on the interaction of coalition size and wealth indicates that large coalition systems experience few deaths, and that such systems also convert societal resources into better protection against disasters.

Anti-Government Protests and Disasters

We now turn to an examination of anti-government protests. In large coalition systems, leaders impose few restrictions on free speech and the right of assembly. Protests thus provide an easy means for citizens of democracies to express their dissatisfaction with government performance. Joining a protest in a small coalition system is a much more risky endeavor. Leaders in such nations restrict the right of assembly, and those who protest often risk arrest, imprisonment or torture. Compared to citizens in large coalition systems, citizens in small coalition systems have much greater cause to protest, but the costs and risks of dissent are much higher. We argue that disasters affect protests in different ways across political systems. In large coalition systems we expect that the occurrence of disasters will have little effect on protests. However, the people will protest if the government performs poorly – that is, if it lets a lot of people die. In contrast, the occurrence of protests in small coalition systems is restricted by citizens’ ability to coordinate and organize rather than by their satisfaction with the government. Disasters facilitate coordination, for example, by concentrating disgruntled people in camps and potentially diminishing the government's repressive capacity. We predict that in small coalition systems, the occurrence of disasters is more important in predicting protests than the government's handling of the crisis.

These predictions are borne out by the analyses in Table 3. In Models 3 through 6, the dependent variable is the natural logarithm of the number of protests plus one, ln(Anti-Gov). Models 7 and 8 examine a direct count of the number of protests. Model 7 is a fixed-effects negative binomial count model. The data exhibit a large number of cases in which there are no protests recorded. To adjust for this skew, Model 8 estimates a zero inflated negative binomial count model.Footnote ⁵⁰ In this framework a first equation determines whether any count is observed, and then the negative binomial is used for the positive outcomes. In the model shown we included only coalition size in this first equation. The regression and count models approaches yield similar results.

Table 3

Dependent Variable: Anti-Government Demonstrations

Unit: country-year.

*p < 0.10; †p < 0.05; ‡p < 0.01.

There is strong temporal dependence in the number of protests; a high level of protests in one year is a strong predictor of protests in the following year, as demonstrated by the highly significant parameter estimate on the lagged dependent variable. The models in Table 3 include variables for political institutions, the number of disasters in a year (Disasters) and the number of disaster-related deaths (ln(Deaths)). The models also include controls for GDP per capita, economic growth and population, and the interactions of these variables with the size of the winning coalition, W. Models 3 and 4 include region-year fixed effects, while Models 5, 6, 7 and 8 have country-specific fixed effects. We report robust standard errors clustered by either nation or region-year.

Models 4 and 6 include lagged values of disasters and disaster deaths. These lagged terms are included as well as the contemporaneous variables because it can often take time for protests to take place and propagate. The need for lags is particularly pertinent if a disaster occurs late in the year. As mentioned before, the models in Table 3 also contain all the disaster and death variables interacted with coalition size, W. Since coalition size is coded between 0 and 1, the impact of deaths and disasters on the level of protest in the smallest coalition systems is given by the non-interacted coefficient estimates. In large coalition systems the impact of disasters and deaths is given by the sum of the non-interacted and interacted coefficient estimates.

In small coalition systems, the occurrence of disasters leads to an increase in the level of protest. For example, in Model 3 the coefficient estimate for disasters is a significant 0.0196, which implies that in the most autocratic systems the occurrence of disasters leads to increased protest. Model 4, which examines effects in both the current and previous periods, yields the same substantive conclusion. Although the coefficient estimate for lagged disasters is statistically insignificant, a joint hypothesis test that the sum of the disaster and lagged disaster coefficients is different from zero is highly significant. Thus in autocracy, each additional disaster increases the level of protest by about 2 per cent.

The occurrence of disasters has no significant effect on the level of protest in democracies. In the analysis the largest coalition systems are coded as W = 1. To evaluate the effect of disasters in these systems we need to examine the coefficient estimates on both the disasters variable and its interaction with W. In Model 3, the sum of these coefficients is 0.0196−0.0208 = −0.0012, which is statistically indistinguishable from zero. In the Appendix we provide tables with hypotheses tests for the sum of coefficients in each of the models in Tables 3 and 4. An examination of the sum of estimated coefficients for the disasters variables and their interaction with W in the other models leads to the same substantive conclusion: disasters produce a small but statistically significant increase in the likelihood of protest in small coalition systems but have no discernible effect in democracies.

When large numbers of people die in disasters, this is an indication that the government has done a poor job of preparing for and responding to a natural disaster. In large coalition systems such poor performance results in a significant increase in the level of protest. Yet in small coalition systems the level of disaster-related fatalities has no significant effect on protest. For instance, the coefficient estimate for deaths in Model 3 is an insignificant −0.0002. Likewise in Model 4, a joint hypothesis test on the deaths variable and the lagged deaths variable is indistinguishable from zero. In small coalition systems, the number of deaths appears to have little impact on the level of protest. Protest in the wake of a large number of disaster-related deaths is more likely in democracies. Assessing the impact of disaster deaths for large coalition systems requires summing the deaths variable and its interaction with W. In Model 3 this sum equals 0.0118, which is significant at the 5 per cent level in a one-tailed test. A similar effect is seen in Models 4, 5 and 6. Deaths have no effect on the level of protest in autocracies, but lead to an increase in protest in democracies; a result that is statistically significant at the 1 per cent level. However, the effects of disaster-related fatalities estimated in the count models (7 and 8) are statistically indistinguishable from zero.

As predicted, the relationship between disasters and anti-government protests is highly dependent on political institutions. In small winning coalitions the occurrence of disasters leads to increased protest, but the number of disaster-related deaths has no significant effect. In large coalition systems, the level of fatalities – not the occurrence of disasters – affects the level of protest. This pattern repeats in analyses of leader survival.Footnote ⁵¹

Leader Survival and Disasters

We explore the effect of disasters and disaster-related deaths on leaders’ tenures in office while controlling for population size, per capita income, economic growth, leader age and the interaction of these terms with coalition size. The unit of analysis is the leader-year. Although the Archigos database has information on about 3,020 leaders from 1800–2008, the inclusion of economic indicators reduces the sample to the years 1961–2004. For the estimation sample (1,111 leaders), median survival time is 2.6 years with a standard error of 0.16 years and a 95 per cent confidence interval of [2.30, 2.93] years. Table 4 presents survival models. Positive coefficients represent an increase in the hazard rate. Standard errors clustered on the leader are presented below coefficients.

Table 4

Dependent Variable: Tenure in Office

Unit: leader-year.

*p < 0.10; †p < 0.05; ‡p < 0.01.

Table 4 contains two forms of survival analysis. Models 9 and 10 are Cox proportional hazard models. Models 11 and 12 use a Weibull parametric method in which the shape parameter, ρ, is modelled as a function of coalition size. Each of the models supports the same substantive conclusion. In small coalition systems, the occurrence of disasters leads to an increased risk of leader removal. The number of deaths caused by these disasters has no statistically significant effect on leader survival in small coalition systems. The pattern is different for large coalition leaders. Their survival is greatly endangered by disaster-related deaths, but the actual occurrence of disasters appears to help them retain office. We start by examining the coefficient estimates in the models. We then turn to technical issues relating to the temporal dependence of the results and explain why we present multiple estimation approaches.

Institutions affect the survival of leaders directly, and also by conditioning the effect of other variables. Models 9–12 each contain coalition (W) and selectorate (S) size. As predicted by selectorate theory, leaders survive longer when they form a coalition from a large pool of potential supporters. The significant negative coefficient estimate on the S variable supports this prediction. The impact of coalition size is more nuanced. The coefficient estimates on W are insignificant, but W significantly modifies the impact of other variables. For instance, the parameter estimate on age is positive in each model, indicating that old autocrats are at a greater risk of deposition than young autocrats. Age is a less important factor in democratic leader survival. The coefficient estimate on the age variable interacted with W is significant and negative. For democratic leaders, the impact of age on survival is given by the sum of the age variable and its interaction with W (0.0062 in Model 9). Democratic leaders are much less sensitive to age than autocrats, which illustrates a common pattern throughout the analyses; coalition size modifies the impact of other variables. For instance, the significant negative coefficient estimate of the growth variable and the positive estimate on growth interacted with W indicate that economic growth helps autocrats remain in office more than democrats.

Disasters affect leader tenure. The positive significant coefficient estimates on the disasters variable in Models 9 and 11 indicate that the occurrence of a disaster will jeopardize a small coalition leader's hold on office. Models 10 and 12 examine the effect of disasters in both the current and previous years. Joint hypothesis tests of the effects across these two years show that disasters increase the risk to autocrats. In contrast, disasters – at least low casualty ones – lower the risk of deposition in large coalition systems. Across the four models, the sum of the estimates of the disasters variables and their interaction with W is negative and generally statistically significant. Disasters help democratic leaders stay in power, but imperil autocrats. This result for democracies is consistent with prior evidence. Abney and Hill, Chen, Healy and Malhotra, and Reeves have shown that US leaders can benefit from the opportunity to disperse benefits and demonstrate competence in the aftermath of disasters;Footnote ⁵² Olson and Gawronski also found evidence in favour of this hypothesis in their analysis of several case studies around the world.Footnote ⁵³ The story is reversed when it comes to evaluating disaster-related fatalities. The small statistically insignificant coefficient estimate on the deaths variable indicates that small coalition leaders are relatively immune to disaster-related deaths. However the estimates of the interactions between W and the deaths variables are larger, and joint hypothesis tests show that increased deaths impose a statistically significant threat to the tenure of large coalition leaders.

Figure 2 illustrates the substantive effects of disasters and deaths on the rate of leader removal. The graph plots estimates of the hazard rate leaders face under different conditions. The hazard rate at any point in time is the rate at which leaders are deposed, and is conditional upon having survived to at least that point in time. The upper panel in Figure 2 reflects the risks autocrats face (W = 0), while the lower panel plots the risks for democratic leaders (W = 1). The estimates are constructed under the premise that S = 1, leaders are aged 55 years, and per capita income and national size are that of the average democracy, around $11,000 and 10 million people. The graphs plot the estimated hazard calculated from Model 9 over ten years under different disaster contingencies. The solid line in each panel assumes that no disasters occur. The dashed line plots the hazard if a nation experiences five natural disasters and no casualties. Five disasters represents approximately the 90^th percentile in terms of the number of disasters per nation-year. The final dot-dash line plots the hazard a leader faces if his or her nation suffers 10,000 casualties and five natural disasters. Ten thousand is a high casualty figure that occurs in about only 1 per cent of cases, even less in democracies (0.21 per cent).

Fig. 2

Leader survival

The most obvious difference between the two panels of Figure 2 is that large coalition leaders face a much higher risk of deposition than autocrats. A comparison of the solid and dashed lines shows that the occurrence of five disasters increases the risk for autocrats by about 20 per cent and decreases a democratic leader's deposition risk by about 7 per cent. Disasters help democratic leaders stay in office, but only if they prevent people from dying. Democratic leaders are highly susceptible to casualties. Figure 2 demonstrates that the estimated hazard for leader removal nearly doubles if 10,000 people die in a democracy. In contrast, fatalities hardly matter in autocracies: the dash-dotted line reflecting high casualties is virtually indistinguishable from the zero casualty disasters case shown by the dashed line. Although the effects are only plotted for Model 9, the other models in Table 4 show similar substantive effects.

The occurrence of disasters imperils autocrats and helps democratic leaders stay in office. Democratic leaders are highly sensitive to disaster-related fatalities. Each of the models in Table 4 supports this conclusion. We offer two forms of hazard analysis due to concerns about the proportionality assumption. The Cox proportional hazard model, which is the work horse of survival analysis in the social sciences, assumes some common underlying hazard h ₀(t). The exogenous variables modify the hazard, so at time t leaders face the hazard h(t) = h ₀(t)e ^Xβ, where Xβ reflects the standard set of covariates and coefficients. Unfortunately, selectorate theory suggests how the underlying hazard varies over time depends on institutions. In particular, small coalition leaders face a high initial risk that declines over time, while large coalition leaders face a more constant threat to their tenure. Hence theory suggests that the proportionality assumption of the Cox model is violated; this conclusion is supported by statistical tests. A standard test of the proportionality assumption is to generate residuals and correlate them with the logarithm of time.Footnote ⁵⁴ These tests find significant correlations in our data between the residuals associated with covariates and time; the proportionality assumption is violated. What is more, the pattern observed in these tests is consistent with that predicted by selectorate theory. For instance, the residuals associated with the deaths variable are positively correlated with time, while the residuals associated with the interaction of deaths and W are negatively correlated with time. Further, if the analyses are performed on each size of institution separately, then non-proportionality ceases to be a problem.

The non-proportional hazard model is a standard fix when the proportionality assumption is invalid. This approach interacts variables that fail the proportionality test with the logarithm of time and re-estimates the Cox model with these interaction variables added. Unfortunately, with the inclusion of many time interactions, convergence becomes an issue. Some models will converge if the number of interactions is restricted. Further, although Licht proposes useful graphical methods, examining the substantive impact of variables in non-proportional models is difficult.Footnote ⁵⁵ Therefore we instead used a parametric approach that allows the hazard rate to vary differently according to institutions, as it is theoretically expected to do. In particular we follow the approach of Bueno de Mesquita et al. and Bueno de Mesquita and Smith, and model the hazard rate as a Weibull model with the ancillary parameter, which controls how the hazard varies over time, modelled as a function of W.Footnote ⁵⁶

The Weibull model assumes that the hazard a leader faces at time t is h(t) = $$\[--&#x003E;&#x003C;$&#x003E;\lambda&#x003C;$&#x003E;&#x003C;!--$$($$\[--&#x003E;&#x003C;$&#x003E;\lambda&#x003C;$&#x003E;&#x003C;!--$$t)^p−1, where $$\[--&#x003E;&#x003C;$&#x003E;\lambda&#x003C;$&#x003E;&#x003C;!--$$ = exp(Xβ). The shape parameter p affects how this hazard changes over time. Selectorate theory suggests that p is smaller in small coalition systems than in large ones. Models 11 and 12 estimate the shape parameter ln(p) as a function of W. For a large coalition system in which W = 1, the shape parameter p is indistinguishable from 1, suggesting that the risk of leader removal is relatively constant over time. In contrast, the risk of removal for a small coalition leader presents negative duration dependence, which indicates that the rate at which these leaders are deposed decreases over time.

Central to our analysis, irrespective of whether we look at Cox models, non-proportional models (discussed, but not shown here) or parametric models, the results with respect to disasters are similar. Small coalition leaders are sensitive to the occurrence of disasters, but their survival is unaffected by disaster-related fatalities. The opposite is true in large coalitions: leader survival is highly sensitive to casualties, but the occurrence of disasters weakly enhances leader survival.

The analyses suggest powerful incentives for leaders. Depending on the institutional setting, leaders should undertake very different levels of disaster preparedness and remediation when disasters strike. If people die in disasters then democratic leaders are likely to lose their jobs. It is therefore small wonder that they experience relatively few casualties. The tenure of autocrats is less endangered by casualties. Given fewer incentives to protect the people, it is perhaps not surprising that they do a worse job.