Mitigating natural disasters through collective action: the effectiveness of tsunami early warnings.

1. Introduction

While not the most prevalent of all the natural disasters plaguing humankind, tsunamis have proven more devastating in their potential than any of the others. Tsunamis occur for a variety of reasons, including landslides and submarine volcanic and seismic activity, though by far the most common cause is the latter. This type of tsunami may be generated any time tectonic plates scrub together beneath a body of water severely enough to cause one plate to drive beneath another, a process known as subduction. When this occurs, the seabed buckles, thrusting a column of water upward. Once the column reaches the surface, this mass of water or set of waves races at speeds sometimes in excess of 700 km/h, potentially devastating any adjacent land areas.

[FIGURE 1 OMITTED]

Because Earth's surface is made up of constantly shifting tectonic plates, an earthquake-generated tsunami may occur almost anywhere there is a large mass of water. While potentially striking all of the world's oceans and seas, tsunamis are most common in the Pacific basin; although, the rapid development of coastal areas of the past decades has increased the devastating potential of tsunamis, these great waves and humankind share a long history. Our earliest evidence of a tsunami shows that one occurred in the Aegean Sea in 1480 BC from the volcanic explosion on the island of Santorini, which effectively wiped out the thriving Minoan civilization on the island of Crete. More recently, since 1966 alone, there have been 202 tsunamis worldwide (see Figure 1, which identifies the primary area, known as the tsunami's run-up, where each of these events had its greatest impact). The worst of these was caused by the megathrust earthquake that struck the Indian Ocean on December 26, 2004, the epicenter of which was only about 30 km from the shores of the densely populated Indonesian island of Sumatra. The subduction of the oceanic India-Australia tectonic plate beneath the Burma subplate of the continental Eurasia plate caused the seabed to suddenly and violently rise by some 10 m, generating the series of waves that claimed the lives of about 150,000 individuals in Indonesia alone and as many as 290,000 individuals in total.

Given the widespread nature and destructive potential of tsunamis, it is surprising that much of the world lacks even the most rudimentary of tsunami warning systems, especially because such systems are not particularly expensive to establish and have been in place in the Pacific for more than 50 years, (1) Of the many potential explanations for the lack of global coverage, two are interrelated and most closely tied to the present study and deal with the collective good nature of warning systems and their effectiveness. One might reasonably question whether the limited coverage is due to the common collective-good problem of free-riding. That is, in the absence of the international cooperation necessary to minimize or eliminate the incentive for countries to take advantage of warnings issued by others without having to bear the costs of creating and operating warning systems such free-riding would seem predictable. (2) The early history of the warnings systems in the Pacific may point to the free-rider problem in that prior to 1965 most countries in that area could benefit from Pacific-wide warnings issued by the national tsunami warning centers operated until that time by the United States, Japan, and the Soviet Union. Unfortunately, data on warnings issued prior to the mid-1960s are not available, thus we can only offer this as a possible explanation for the limited international cooperation in the Pacific basin prior to that time. At a minimum, however, only three of the wealthiest countries in the region operated warning systems in the early period, which is consistent with the existence of a free-rider problem. Since 1965, however, the free-rider issue in the Pacific has become a moot point: These national systems became international in nature through the creation of the United Nations Educational, Scientific and Cultural Organization's (UNESCO's) 26-member International Coordinating Group for the tsunami warning systems covering the entire Pacific basin, as is discussed later.

Contrary to the situation for countries within the Pacific basin prior to 1965, international free-riding by countries outside that basin on the Pacific systems' warnings has never been much of a possibility. The reason for this is simply that the Pacific's various warning systems, prior to 2006, lacked the technology and equipment necessary to accurately sense the formation of tsunamis outside the Pacific basin. Of course, while countries outside the Pacific could not free-ride on the Pacific systems' warnings, the possibility of free-riding may help explain why warning systems have not come into being outside the Pacific basin. To the extent that this problem exists, international coordination of the type put in place in the Pacific by UNESCO in the mid-1960s would likely prove effective. We return to this point in the paper's conclusion.

A second potential explanation for the poor coverage outside the Pacific basin may simply be that these warning systems are of limited effectiveness. This question is the focus of the current paper. Specifically, the purpose of this paper is to assess the effectiveness of tsunami early warning systems in terms of lives saved. To do so, we analyze 146 of the 202 tsunamis occurring worldwide between 1966 and the end of 2004. Controlling for the dynamics of the tsunami and socioeconomic factors of the affected areas, as well as other relevant factors, we find that when tsunamis are accompanied by warnings, there is a statistically significant reduction in deaths. In the following section, we offer an overview of prior research with respect to the mitigation of natural hazards and give a brief history of the warning systems in the Pacific, along with a description of how these systems operate. We then describe the data, empirical methods, and results for our primary models. Next, to provide some idea of the stability of the results of the primary models, we offer results from a number of alternatives to those models, followed by a summary conclusion.

2. Natural Hazard Mitigation and the Tsunami Early Warning System

Tsunamis are one example of a lengthy list of natural hazards confronting humankind. A nonexhaustive list would include earthquakes, floods, tornadoes, avalanches, landslides, mudslides, and hurricanes. The potentially disastrous effect of each is subject, to one degree or another, to human mitigation. A growing body of literature addresses the effectiveness of mitigation efforts. For example, Simmons and Sutter (2005) identify a significant decline in fatalities from major tornadoes in the United States during the last century, controlling for factors like increasing population densities and income levels. More broadly, Sudo, Kameda, and Ogawa (2000) consider the Japanese government's aggressive attempts to mitigate various natural hazards since the 1940s through such programs as early warning systems. They note that while natural hazards of all types claimed an annual average of 1941 lives in the 1950s, that number fell to just 200 in the 1980s, a downward trend that has continued, with the exception of the massive Kobe earthquake in 1995. Good general surveys of the recent progress made with respect to early warning systems can be found in Mileti (1999) and Sorensen (2000). (3) However, a rigorous analysis of the effectiveness of tsunami warnings has never been presented.

Before we offer our analysis, insight can be had by considering the evolution of the existing tsunami warning system in the Pacific. One of the most destructive tsunamis of the past century resulted from a great earthquake centered near Unimak Island in Alaska's Prince William Sound on April 1, 1946. (4) This event lead to the deaths of 165 people from Alaska to Hawaii and marked a tipping point with respect to the commitment of the United States to develop a warning system for tsunamis in the Pacific. As is often the case, particularly severe examples of recurring disasters can galvanize policy makers to undertake mitigating actions, such as creating early warning systems to reduce the damage done by similar future events. The first steps in this direction were taken in 1947 and 1948 by scientists working within various federal agencies, most notably the U.S. Coast and Geodetic Survey, with the establishment of the Pacific Tsunami Warning Center (PTWC) headquartered in Honolulu. The system was composed of two parts: a set of three seismological observatories and nine coastal tide stations distributed throughout the Pacific. The PTWC was charged with providing early warnings of tsunamis that might affect Hawaii or any of the islands making up the U.S. Trust Territories of the Pacific. By 1953, this charge was extended to include the provision of early warnings to the west coast of the continental United States.

A second tsunami warning center, the West Coast/Alaska Tsunami Warning Center based in Palmer, Alaska, was soon added to complete U.S. coverage of the Pacific. Other countries--most notably Japan, the Soviet Union, and Chile--quickly developed their own national warning centers. Following the great earthquake of March 28, 1964, centered in the Gulf of Alaska, which killed 120 individuals, what had been examples of national collective action became international in nature when, in 1965, the existing national warning centers were brought together to form an international warning center, the Tsunami Warning System in the Pacific (TWSP), hosted by the United States at its PTWC in Honolulu. At the same time, the International Tsunami Information Center was established by the UNESCO Intergovernmental Oceanographic Commission to monitor the effectiveness of the TWSP and to facilitate technology transfer to countries establishing national warning systems. At the outset, 23 nations joined in this effort; currently, 26 are members.

Since the establishment of the United States' first warning system in the 1940s, significant progress has been made in the ability to sense seismic activities and detect the generation of tsunamis. Even so, the basic way in which the current international system and the various regional systems operate is not very different from the earlier systems. The first step in the process toward the issuance of a tsunami warning is the detection of a submarine earthquake.

While the early system in the United States relied on just three seismic sensors, the current international system has more than 100 continuously monitored sensors spread throughout the Pacific. Once a major earthquake is detected (typically a quake with a magnitude above 6.5 on the Richter scale, though this threshold varies by location) near or under a significant body of water, the warning center turns to its coastal tide gauges to ascertain whether a tsunami has been generated. If it has, the center issues a warning for the areas that are expected to be affected.

There is currently a two-pronged but highly coordinated approach to tsunami warnings. When a tsunami is detected that has the potential to affect a large part of the Pacific basin, the TWSP issues a Pacific-wide warning. When a tsunami is detected that is either likely to have only a localized impact or is generated very close to a shoreline that has a regional center, a local warning can be expected. In either case, the warning is distributed to local officials in the areas expected to be affected. At that point, the effectiveness of the warning is determined by the ability of the local officials to transmit the warning to their populations, the education of the local populations with respect to interpreting and properly responding to warnings, the existence of the infrastructures necessary to provide the local populations with ways to quickly move inland, and finally the existence of search and rescue and health care facilities necessary to care for those affected. That is, warnings are likely to achieve their maximum effectiveness only when local populations are well-versed about tsunami warnings, have the ability to react to them, and have reasonable access to care after a tsunami strikes.

At the same time, warning centers must be somewhat cautious in issuing warnings. False positives that are issued too frequently can leave a local population tone-deaf to warnings, putting them at increased risk when a severe event actually strikes. Such was the case recently on the U.S. Oregon coast when a tsunami warning was issued in error. According to the mayor of Waldport, Scott Beckstead, "A big fear that I have is that pretty soon, people are going to hear a siren or a warning and think that it's just crying wolf, and not take steps to evacuate when, in fact, a real event has occurred." Warning centers must also take into account the significant economic costs associated with false positives. According to the National Oceanographic and Atmospheric Association, a needless evacuation of Hawaii would cost approximately $68 million in lost productivity alone (Jean 2005). Thus, while warning systems clearly offer hope of saving lives and protecting property, the professionalism and training of staffs must match the technology of the equipment for the system to make its maximum contribution to well-being.

3. Data, Empirical Methods, and Primary Results

The unit of observation in our sample is a tsunami caused by a submarine earthquake occurring anywhere in the world between 1966 and the end of 2004 for which complete data exist. We selected 1966 as the sample's starting point because several important variables for the multivariate analysis are either unavailable or unreliable prior to the mid-1960s. (5) As noted previously, there were 202 tsunamis worldwide during the 1966-2004 period. We are able to subject 146 of these to empirical analysis, lacking necessary data on the remaining 56. For a majority of those 56, we lack information relating to socioeconomic conditions of the affected area or data on the tsunami itself. (6)

The key variable in our analysis is the issuance of an early warning of tsunami (WARNING). One might think that because early warning systems have been in operation since the late 1940s, a complete, easily accessible catalog of warnings would be readily available. This is not the case. After an exhaustive search, we were able to positively identify the warning status of only 166 of the 202 tsunamis occurring between 1966 and 2004. (7) Information on warning status was taken from UNESCO's International Tsunami Information Center's periodical Newsletter, which dates back to the late 1960s and contains case studies of a few tsunamis (produced by the International Tsunami Information Center), warning information available from the regional centers operating in the Soviet Union/Russia and Japan, various press accounts of specific events, and direct contact with the International Tsunami Information Center. (8) Of the 146 tsunamis in our final sample, about 21% were accompanied by a warning (WARNING) from one of the various agencies, 31 to be exact, as noted in Table 1, which provides descriptive data on each of the variables used in the primary analysis that follows.

The dependent variable in each of our models is the number of deaths (DEATHS) associated with a given tsunami. The descriptive statistics for this variable show a mean of 1864 killed for the average tsunami, with a rather broad range of 0 to 150,000. This variable is taken from the National Geophysical Data Center's (NGDC) Significant Earthquake Database and the Historical Tsunami Database for the Pacific, which is maintained by the Novosibirsk Tsunami Laboratory. A better intuitive feel for the distribution of deaths in the sample can be had by considering Table 2, which categorizes the 146 tsunamis in the sample based on the associated number of deaths. As is common with count data relating to natural hazards, we have a fairly large number of tsunamis (51) that lead to no deaths at all. However, the sample offers a good deal of variation, with the category of 1-50 deaths being most common (57), and 10 tsunamis that caused more than 1000 deaths.

Case studies of tsunamis have focused on the dynamics and location of tsunamis and their underlying earthquakes as the primary determinants of the destructiveness of a given event. In general, a tsunami's destructiveness is an increasing function of the severity of the underlying earthquake and a decreasing function of the depth beneath the water's surface where the quake has its epicenter and the distance of that epicenter to the affected region. A worst-case scenario of the way these three variables come together was witnessed with the Indian Ocean tsunami of December 26, 2004. The underlying quake in this case was the fourth largest, by magnitude, to strike in 100 years (the largest in 40 years), with an epicenter estimated to be no more than 33 km beneath the surface of the ocean, and only about 30 km from the densely populated northern Indonesian island of Sumatra. The resulting tsunami, coming ashore in just 30 min with a height of 20 m, proved terribly devastating. The three key variables--magnitude, depth, and distance--of a tsunami-generating earthquake, taken together with local conditions such as the slope of the seabed, determine the maximum height of an incoming set of tsunami waves. This maximum wave height at landfall yields a tsunami's Imamura-Iida scale (IIDA) value, as defined below, which is used to estimate potential destructiveness. The scale is based on the work of Iida (1958) and Iida, Cox, and Pararas-Carayannis (1967). While perhaps not as well-known as magnitude and intensity scales developed for other natural hazards such as the Richter scale (earthquakes), Volcanic Explosivity Index, the Safir-Simpson index (hurricanes), and the Fujita scale (tornadoes), the IIDA scale, while not without some detractors (which is addressed below), is the most commonly used measure of tsunami magnitude.

IIDA categorizes tsunamis on a continuous scale running from -6 to 10. Larger values indicate a tsunami of greater magnitude. We expect IIDA to be positively associated with the deaths caused by a tsunami. In our sample, IIDA runs from -4.64 to 5, with a mean value of 0.06. This variable is taken from the NGDC Significant Earthquake Database. To see the simple relationship between IIDA and DEATHS, consider Table 3, which categorizes the tsunamis in our sample by their IIDA values along with the mean, standard deviation, and range of deaths for each group. As is apparent, when incoming waves of a tsunami are small in height (negative IIDA values indicate waves of less than a meter), relatively few deaths result--a weighted average of about 136 lives are lost. By comparison, when IIDA is nonnegative in value, the weighted average number of deaths increases to more than 2650.

While a tsunami's magnitude is critical in determining the number of lives lost, equally important are factors such as the slope of the seabed and shape of the shoreline in the affected area, as well as a number of local socioeconomic conditions. Perhaps most important among the latter of these are the number of people at risk and their income levels. The first of these is proxied by the population density (POP DENSITY) of the affected region, which ranges in our sample from a low of 30 persons to just over 5200/[km.sup.2]. Overall population density of the province or state is a proxy for those at risk from a tsunami in that, typically, only those in low-lying coastal areas are truly at risk. However, data on the proportion of a population living in these areas are not available. (9) We expect that POP DENSITY will be positively associated with tsunami deaths.

As has been pointed out recently by Anbarci, Escaleras, and Register (2005) and Kahn (2005), the level of development within an area bears a strong and consistent relationship to the level of destruction caused by natural disasters. This might come about for a variety of reasons, including the establishment of high-level building codes and zoning, better developed health care and emergency facilities, and more fully established civil defense mechanisms. To control for the level of development, we take from the World Bank's Worm Development Indicators per capita GDP, in constant 2000 U.S. dollars (GDP PER CAPITA). The mean value of GDP PER CAPITA in our sample is about $7700, with a range of $120 to just over $38,000, and we expect that this variable will exert negative pressure on the number of tsunami fatalities. Finally, to control for the possibility that local institutions play a role in determining the death toll of a tsunami, we include the democracy index (DEMOCRACY) provided by Polity IV. This scale, which runs from 0 to 10, ranks countries annually as to the general openness of their public institutions, with lower values indicating lesser degrees of openness. We include this variable as a proxy for what might be thought of as good government, and we expect that it will exert a negative influence on the number of deaths due to a given tsunami. In our sample, DEMOCRACY has a mean of 5.6, and individual observations cover the entire potential range. (10)

While the socioeconomic variables listed should control for most region-specific factors, it is possible that other local factors remain at work. To capture them, we create, without expectation as to their effect, a set of four continent binary variables for ASIA, EUROPE, AFRICA, and AMERICA. Of the 146 tsunamis in our sample, nearly 66% struck Asia (96 tsunamis), about 4% occurred in Europe (six tsunamis), about 2% in Africa (three tsunamis), and the remaining 28% in the Americas (41 tsunamis). Finally, we take into account whether there has been a significant change over time in the estimated relations by including a time trend variable in the analysis (TIME). The expectation for this variable is unclear. On the one hand, given recent technological improvements in the detection of tsunami formation and in communications, one might expect to find falling death tolls from tsunamis over time. On the other hand, the recent rapid development and growing popularity of coastal regions in every corner of the world have put increasing populations at risk of tsunamis, which may well lead to a positive coefficient on this variable. Between 1990 and 1995 alone, the population of the world living within 100 km of a coastline increased by 10%, providing homes to about 40% of the world's population on this 20% share of the world's total land area. And this migration to the seas is, if anything, intensifying (see Burke et al. 2001, p. 3).

Prior to turning to the multivariate analysis, insight into the effectiveness of early warnings can be had by considering the mean differences between deaths and the magnitude of tsunamis for those events where a warning is issued and those without such a warning, as presented in Table 4. (11) As expected, the mean level of magnitude, IIDA, is greater for those events that are accompanied by warnings. More importantly, while those events with warnings tend to be more severe, they also result in far fewer deaths. In each case, the difference is both statistically significant and of great practical importance. Specifically, those events for which there is no warning on average result in about 2300 more deaths than when a warning is issued. Given that the Indian Ocean tsunami of December 2004 was not accompanied by a warning, it is reasonable to question whether this outcome is driven by that extreme case. To determine this, the analysis of Table 4 was replicated without this observation. Interestingly, while the mean difference is much smaller, those events for which there is no warning are still found to result in a statistically significant greater number of deaths than when a warning is issued, even when the Indian Ocean tsunami of December 2004 is omitted. Of course, univariate results of this nature are only suggestive of the effectiveness of early warnings. To more rigorously test these relations, we estimate the following model:

[DEATHS.sub.it] = [[alpha].sub.0] + [[alpha].sub.1] [WARNING.sub.it] + [[alpha].sub.2][IIDA.sub.it] + [[alpha].sub.3]POP [DENSITY.sub.it] + [[alpha].sub.4]GDP PER [CAPITA.sub.it] + [[alpha].sub.6][DEMOCRACY.sub.it] + [[alpha].sub.7][ASIA.sub.it] + [[alpha].sub.8][EUROPE.sub.it] + [[alpha].sub.9][AFRICA.sub.it] + [[alpha].sub.10[]TIME.sub.t] + [[epsilon].sub.it], (1)

where DEATHS is a count of the deaths due to tsunami, i, in year t; WARNING is a binary variable with a value of unity when a warning is issued and 0 otherwise; IIDA is a measure of a tsunami's magnitude; POP DENSITY is the population density of the area affected; GDP PER CAPITA is the per capita GDP of the country affected; DEMOCRACY is the degree of governmental openness; ASIA, EUROPE, and AFRICA are binaries for those continents referenced against the Americas; TIME is a trend variable; and e is a random error representing unobserved heterogeneity that is assumed to be uncorrelated with the explanatory variables. (12)

The dependent variable in the model is the number of deaths due to a tsunami. Generally, Poisson estimation is appropriate when using nonnegative count data as the dependent variable. Poisson is best suited, however, for counts with relatively narrow ranges because it assumes equality between the conditional mean and variance of the dependent variable. When this assumption does not hold, estimated standard errors are typically greatly reduced, leading to correspondingly large, unrealistic t-ratios. The data in the present case are at least indicative of overdispersion of this type, so we make use of a negative binomial estimation strategy, which avoids the Poisson's mean-variance equality assumption by adding a parameter (identified as in Tables 5 and 6) that adjusts for unobserved heterogeneity between observations. Further, consistent with negative binomial estimations, all variables, except dummies, are entered in natural logs. (13) It should also be noted that all of the estimations reported below employ standard errors that are fully robust with respect to arbitrary heteroskedasticity (Wooldridge 2002).

Given that we have no theoretical model directing the inclusion of variables, we start with a simple model showing the basic relationship between DEATHS and WARNING status. Following this, we sequentially add the socioeconomic variables, followed by the continent binary variables and the time trend, both to show the degree of consistency of the key relationships and to provide insight into the goodness of fit of the models. Prior to discussing the individual results presented in Table 5, three elements of goodness of fit should be noted. First, in each case a test of the significance of the parameter [alpha] entered to control for unobserved heterogeneity between observations shows that, well beyond the 0.05 level, the likelihood of this data arising from a Poisson process is virtually nil, arguing strongly in favor of the negative binomial specification. Further, the log-likelihood values across the models show an increasing pattern as variables are added, indicating that each addition of new control variables increases explanatory power. Finally, in each case the models give likelihood ratios that are highly significant, beyond the 0.05 level, indicating that the independent variables taken as a group are quite significant in explaining the death toll of a given tsunami. (14)

The key result in Table 5 is the finding of a significant, negative coefficient on the WARNING status variable, across specifications. In the full model of column 4, the WARNING status result indicates that--holding constant the magnitude of the tsunami, socioeconomic conditions, degree of governmental openness, continent-specific effects, and time--when tsunamis strike, the issuance of an early warning significantly reduces the number of lives lost. In each case, the outcome for the WARNING status variable is significant well beyond the 0.05 level. To put the effect of the issuance of a warning into perspective, we calculated the difference in the prediction function when WARNING has a value of 0 versus a value of 1, holding all other independent variables at their means. This calculation indicates that the issuance of a warning, that is, the discrete change in WARNING from 0 to 1, decreases the expected number of deaths by 286. By extension, given the sample's mean number of deaths of 1864, this calculation suggests that the issuance of a warning can be expected to lead to a reduction in deaths of roughly 15.3% in a typical tsunami. We take this to be not just a statistically significant outcome but one of significant practical importance.

Given its extreme death toll, we would be remiss if we did not address the great Indian Ocean tsunami of December 26, 2004. To do so, we replicate the method employed previously, but given the focus on a specific event, we make use of the actual values of the independent variables, other than WARNING. That is, we calculate the difference in the prediction function when WARNING is, alternately, 0 and 1, with the remaining independent variables set to their actual values for this event. This calculation indicates that had a warning system been in place in the Indian Ocean on December 26, 2004, roughly 13,940 lives would have been spared. To provide a sense of the economic importance of this, note that a fully functional, modern early warning system capable of serving the entire Indian Ocean is expected to cost approximately $200 million to establish, with an additional $25 million per year in operating and upkeep costs (Jean 2005). Such a system, which would serve roughly 30 countries surrounding the Indian Ocean basin and have a nearly endless effective life with proper upkeep, would seem effective not only in the number of lives saved but also in costs.

Whether the focus is on the overall sample or the great Indian Ocean tsunami, some might question why the estimated reduction in deaths is not even greater. Several related points should be made here. First, as discussed previously, the issuance of a warning is made after receiving evidence of a significant submarine quake and resulting rise in sea level at a tide station. In many of these cases, because of seabed slopes, shoreline shapes, and the like, the correctly identified tsunami proves to be only a minimal threat once it arrives onshore. In a case like this, the estimated effect of a "correct" warning is minimal and reduces the calculated mean effectiveness of a warning system. In later paragraphs, we look into this matter by considering the relative effectiveness of warnings of tsunamis of differing magnitudes. Further, to have maximum effectiveness, those potentially affected must have a high level of understanding with respect to interpreting and properly responding to warnings, infrastructures must exist to provide the local populations with a way to quickly move inland, and search and rescue and health care facilities must be in place to care for those affected. As these elements of tsunami preparation improve over time, one can expect the increased effectiveness of early warning systems. In some cases, however, tsunamis are generated by earthquakes striking so close to shorelines that there is not enough time to issue an effective warning. Such was likely the case with the great Indian Ocean tsunami, which reached Sumatra in about 30 min. Of course, even this factor is subject to human intervention through improvements in the technology necessary to sense the formation of a tsunami and in the methods of communicating warnings.

Turning to the remaining variables in the model, we generally find equally predictable outcomes. As expected, the severity of a tsunami, as given by the IIDA index, is positively and significantly related to its resulting death toll. Similarly well-behaved are the socioeconomic control variables for the affected region's population density (POP DENSITY) and the average income of its inhabitants (GDP PER CAPITA). While the first of these outcomes tells us little that would not be expected--deaths due to tsunamis are greater when they strike locations with relatively high population densities--the result for average income is of particular interest. As Kahn (2005) found for a variety of nontsunami natural disasters and as Anbarci, Escaleras, and Register (2005) report specifically for earthquakes, we find that deaths due to tsunamis are significantly lower in areas with relatively high levels of per capita GDP. There are many reasons why higher income levels provide protection for areas affected by natural disasters generally and tsunamis in particular, and these reasons likely vary by location, but a defensible list would include (i) more tsunami and other natural disaster sensitivity in building codes and zoning practices, (ii) better and more broadly available health care for those adversely affected by a given event, (iii) more rapid and sophisticated search and rescue systems, (iv) more extensive public education about natural hazards and warning systems, (v) more fully developed civil defense mechanisms, and (vi) better communications networks to warn of impending hazards for those events, such as tsunamis and hurricanes, for which warning systems exist. Regardless of the exact nature of the benefit from greater incomes, however, the result for per capita GDP is consistent with the prior research noted previously in suggesting that natural disasters in general and tsunamis in particular are subject to human mitigation. (15)

The only socioeconomic variable that fails to reach significance is DEMOCRACY, the measure of the degree of openness in public institutions. We included this as a control for what might generally be considered good government. In each case the coefficient, while insignificant, does have the expected negative sign. The lack of significance of DEMOCRACY may reflect either the unimportance of openness in public institutions in determining the death toll of tsunamis or the well-known relationship between per capita income and the openness of institutions, which would be expected to lead to inflated standard errors for one or both of these variables.

The binary variables reflecting the continent where the tsunami comes ashore suggest that, relative to the Americas, deaths can be expected to be lower for any given tsunami when the affected area is in ASIA, EUROPE, or AFRICA. The first of these results most likely reflects the well-established civil defense programs in effect, primarily in Japan, as well as that country's high level of public awareness of and education about tsunamis, at least as compared with the Americas. The results for EUROPE and AFRICA are less clear, though the former may reflect the broad availability of advanced health care in Europe, relative to the Americas, especially relative to those events that take place in South America. A further possible explanation for both the results for EUROPE and AFRICA is that, given the very few numbers of tsunamis striking these two continents (six and three, respectively) during the survey period, what we are really capturing are localized special characteristics, rather than true continent effects. As an example, it may be that the few tsunamis that have affected Europe and Africa struck in areas where the slope of the seabed near the point of impact is much different from the typical location of impact in the Americas. Equally plausible, at least for those events occurring in Africa, is the relatively less-developed coastlines that exist in that continent, relative to the Americas. Finally, in the full model, we find the TIME variable significant and positive, most likely reflecting the growth in development and increasing population that coastal areas worldwide have experienced in the last few decades, which has put ever larger proportions of local populations at risk.

4. Auxiliary Regressions

In this section we summarize the results of a number of alternative estimations of the full model just presented as a means of testing the sensitivity of that model's negative and significant result for the WARNING status variable. These models involve several sample restrictions, alternative variable definitions for tsunami magnitude, consideration of potentially differential effects of relatively severe versus minor tsunamis, and the use of a variable for the lead time of a warning, ELAPSED TIME (for those events where such data exists) in lieu of the WARNING variable itself. These results are presented in Table 6, which omits coefficient estimates and standard errors for all but the WARNING and warning-related variable, ELAPSED TIME. The reason for this is twofold: The purpose of these regressions is to provide a sense of the stability of the WARNING result reported previously, and, further, the results for the remaining independent variables are very consistent with those reported for the full model. Because the nonwarning related variables add little and given the very strong fit statistics offered by each of these models, we limit our discussion here to the results for the WARNING and warning-related variable ELAPSED TIME. (16)

Row 1 of Table 6 gives the coefficient estimate and standard error of the WARNING variable taken from the full model of Table 5 to ease the comparison with the alternative models in Table 6. In row 2, we question whether the results of the full model are due to outliers. While the negative binomial estimating procedure is designed to take into account overdispersion, it is still reasonable to consider whether the results for the full sample are driven by one or a few outlying tsunamis that resulted in extreme loss of life, given that the range of deaths is from 0 to 150,000, with relatively few at the high end. To test this, we restrict the sample by omitting the six events with death tolls of 7500 or more and estimate the full model. When we restrict the sample in this way, the ratio of the standard deviation of DEATHS to that variable's mean falls from the full sample's seven to a bit more than four, thus substantially reducing any potentially misleading effects of outliers.

In the following three rows of Table 6, we estimate variants of the full model based on the tsunami's location and magnitude. In the first of these, we restrict the sample to those tsunamis occurring in the Pacific because no warning systems existed outside the Pacific basin during the sample period. When the sample is limited to the Pacific basin, we have 110 tsunamis to analyze, the results of which are presented in row 3 of Table 6. In row 4 we report results relying on the 126 tsunamis that had underlying earthquakes with magnitudes above the thresholds (greater than 6.5 on the Richter scale) typically necessary to prompt warning centers to do the follow-up that might lead to a warning. We then tie these two auxiliary regressions together by estimating the full model for the 101 tsunamis that both occurred in the Pacific and had underlying earthquakes with magnitudes greater than 6.5, as presented in row 5 of Table 6.

In row 6, we acknowledge that there is some debate in the scientific literature as to the best method of estimating the magnitude of a tsunami. (17) As an alternative way of controlling for a tsunami's magnitude, we estimate the full model using, in lieu of IIDA, three variables associated with the underlying earthquake: (i) the quake's magnitude on the Richter scale, (ii) the depth of the quake's epicenter beneath the water's surface, and (iii) the distance from the epicenter to the affected region. (18)

Further, we consider the likelihood that if early warnings are effective, that effectiveness is likely to reach its peak with relatively severe events. We test this proposition by dividing the sample into two parts: (i) as reported in row 7, those relatively weak tsunamis--46--with IIDA values less than 0 (tsunamis with IIDA values of this magnitude lead to very modest destruction) and (ii) in row 8, the 100 relatively more severe tsunamis with IIDA values of 0 and above.

Finally, it should be noted that all warnings are not the same. To some extent, the comparison between the outcomes of the 31 tsunamis in the original 146 tsunami sample with accompanying warnings and their nonwarned counterparts biases the results against the effectiveness of warning systems. The reason for this is that early warnings do not all come with the same degree of prewarning. An extended elapsed time between a warning and a tsunami's landfalling run-up is likely to lead to a much smaller death toll than a similar-sized tsunami with a warning that has only a few minutes of lead time prior to landfall. Thus, while we identified a roughly 286 fatality reduction between tsunamis with and without warnings, such analysis essentially assumes that the elapsed time between warning and run-up is constant. This is, of course, not true. All things the same, relatively more elapsed time between the issuance of a warning and a run-up should be associated with greater estimated effectiveness than would be true for a limited-time warning. We can offer only modest evidence on this point. Data on the time elapsing between warning and run-up are available only for 15 of the 31 tsunamis in the overall sample, all from the mid-1990s to the present. With the caveat that this is clearly very little data with which to draw conclusions, we ran the full model from Table 5 for the 115 tsunamis that had no warning plus the 15 that did, as presented in row 9 of Table 6. That is, we omitted the 16 tsunamis that had warnings but for which we had no elapsed time between the warning and the tsunami's run-up. In this model, the elapsed time (ELAPSED TIME) between the warning and the run-up, in minutes, is introduced in lieu of the warning variable. Those tsunamis without warnings were simply coded as having zero elapsed times. (19)

As a group, the regressions reported in Table 6 offer strong support for the full model results discussed previously. Most importantly, it is immediately apparent that the result on the key WARNING status variable reported in the full model of Table 5 is quite insensitive to model specification. That is, the coefficient on WARNING is both negative and significant in each alternative model, with the exception of the model in row 7, which we address in the next paragraph. Whether we consider the entire sample, limit the sample to those events with fewer than 7500 deaths, limit the sample based on its location or the magnitude of its underlying earthquake, make use of alternate indicators of the magnitude of the tsunami, (20) or focus strictly on the most severe events, the conclusion is the same: We find a consistently negative and statistically significant relation between the issuance of an early warning and a tsunami's death toll. Perhaps of equal importance, the model reported in row 9, which includes ELAPSED TIME in lieu of the WARNING status variable, points to the importance of timely warnings. The mean lead time of the 15 warned tsunamis in this subsample was about 45 min, with a standard deviation of roughly 15 min. Given the negative and significant coefficient on ELAPSED TIME, we calculated the difference in the prediction function's value, assuming all other variables are held at their means, and found that an increase in the typical 45 minutes of lead time to about an hour is associated with a reduction in deaths of a bit more than 13%.

The only case in which the WARNING status variable is insignificant in these alternative regressions is when the sample is limited to those 46 observations with IIDA values less than 0, as presented in row 7. In reality, this is as expected. Dividing the sample into the relatively severe (row 8) and the relatively minor tsunamis of row 7 allows for a test of the proposition that warnings have greater estimated effectiveness when the accompanying event actually puts a great many lives at risk because of its ferocity (conversely, warnings of extremely minor tsunamis, while accurate, likely save few lives because few were actually at risk). To put this into perspective, when we calculate the difference in the prediction function's value when WARNING is 1 rather than 0 and hold all other variables at their means, we find for the relatively severe events in row 8 an expected reduction in lives lost of 715. The mean number of lives lost in these 100 relatively severe events is 2651; consequently, for relatively severe events, the issuance of a warning reduces deaths by about 27%, nearly double the 15.3% reduction for the overall sample. Thus, the effectiveness of early warnings calculated for the entire sample is clearly a minimum estimate; effectiveness will increase when technological and communications abilities allow for better targeting of warnings for those tsunamis capable of significant loss of life.

When coupled, these final two stability checks relatively greater effectiveness of warnings for more powerful tsunamis and for tsunami warnings with greater lead times--indicate that as technology improves we can expect to find enhanced effectiveness for tsunami early warning systems. Regardless, the results of all of the estimations point to a very consistent outcome: Early warnings greatly mitigate the deadly effects of tsunamis.

5. Conclusion

Tsunamis have plagued humankind for as long as written records exist. Their devastating potential was made clear to all in December 2004 when an estimated 290,000 lives were lost, primarily in Indonesia, as a massive tsunami rolled through that region. While tsunamis are most common in the "Ring of Fire" of the Pacific basin, any site near a large body of water may be subject to their wrath. Since the mid-1940s, attempts have been made to mitigate the effects of tsunamis through the creation of early warning systems. The first of these was established by the U.S. government and initially covered most of the northern Pacific region. Since that time, the U.S. system in the Pacific has been expanded and refined, and other countries, most notably Japan, the Soviet Union/Russia, and Chile, have developed and deployed their own warning systems. By the mid-1960s, an international warning system was opened, serving the entire Pacific basin.

This is the first attempt to estimate the effectiveness of these systems. To do so, we analyze, by way of a negative binomial regression strategy, 146 tsunamis caused by submarine earthquakes occurring worldwide between 1966 and 2004. We find that controlling for other factors likely to influence a tsunami's destructiveness, early warnings of tsunamis very significantly and consistently serve to reduce the death toll wrought by these great waves. Of the other factors included in the model, the most consistently significant are those associated with a tsunami's magnitude and local socioeconomic conditions. While the former is common sense, in the latter case, the most important specific factors are per capita GDP, which likely serves to protect local populations through means such as better-developed building codes and hazard-sensitive zoning, and a local area's population density. Also consistently significant is a variable for time that indicates, controlling for all else in the model, that death tolls have been rising due to tsunamis, likely pointing to the increased development and population of coastal areas worldwide. Further, it is important to note that these results seem quite insensitive to the precise specification of the model and to the control variables included. Finally, given recent and ongoing technology-driven improvements in tsunami detection and warning, future studies will likely find even stronger results for tsunami mitigation. (21)

It seems clear that expanding tsunami warning systems to parts of the world that are not now served should lead to a great reduction in the number of lives lost. As a collective good, much of which is international in nature, the incentive to free-ride may well have, to date, blunted the development of warning systems outside the Pacific. If so, the coordinated actions now being undertaken by UNESCO's Intergovernmental Oceanographic Commission and the governments of the countries affected by the Indian Ocean tsunami of December 26, 2004, should serve to curb free-riding and its ill-effects at least in that tsunami-prone area. Specifically, these groups have committed to the development of a coordinated warning system much like that in the Pacific capable of providing coverage for the entire Indian Ocean. Similar coordinated commitments have been made for other regions such as the Caribbean, Gulf of Mexico, and the entire Atlantic basin. With these new systems coming on line, and with further technological advances improving the performance of all systems, we should see an even greater degree of mitigation of the effects of tsunamis through early warnings than reported here. Thus, while tsunami early warning systems may be an example where coordinated actions of international agencies and individual countries are required to minimize the free-rider problem, it appears that just such action is being taken on a number of fronts and should prove quite effective, given the results reported here.

We thank Vadym Volosovych and Shu Lin for their comments, Paula Dunbar of NOAA/NESDIS National Geophysical Data Center for her assistance with data collection, Brian Anyzeski for his assistance with geographic elements of this study, and seminar participants at Florida Atlantic University and the 2006 Southern Economic Association meetings for their suggestions. Special thanks are in order for Dr. George Pararas-Carayannis, director of UNESCO's International Tsunami Information Center from 1974 to 1992, without whose assistance this project could not have been completed. We also thank John Pepper, coeditor, and two anonymous referees of this journal for their many useful comments. Finally, we thank Eileen Smith and Eileen Schneider for their editorial assistance. Remaining errors are our own.

Received: April 2006; Accepted: April 2007.

References

Anbarci, N., M. Escaleras, and C. A. Register. 2005. Earthquake fatalities: The interaction of nature and political economy. Journal of Public Economics 89:1907-33.

Burke, L., Y. Kura, K. Kassem, C. Revenga, M. Spalding, and D. McAllister. 2001. Pilot analysis of global ecosystems: Coastal ecosystems. Washington, DC: World Resources Institute.

Card, Steve, and Terry Dillman. 2005. "False Tsunami Warning Had Communities Scrambling." News Times, 21 October. Accessed 15 September, 2006. Available at http://newportnewstimes.com/articles/2005/1021/news.

Cohen, J. E. 1995. How many people can the Earth support? New York: W. W. Norton.

Gonzalez, F. I., H. M. Milburn, E. N. Bernard, and J. C. Newman. 1998. Deep-ocean assessment and reporting of tsunamis (DART): A brief overview and status report. Proceedings of the International Workshop on Tsunami Disaster Mitigation, 19 January 1998, Tokyo, Japan.

Iida, K. 1958. Magnitude and energy of earthquakes accompanied by tsunami and tsunamic energy. Journal of Earth Science 6:101-12.

Iida, K., D. Cox, and G. Pararas-Carayannis. 1967. Preliminary catalog of tsunamis in the Pacific Ocean. Report No. 5. Hawaiian Institute of Geophysics, University of Hawaii.

Jean, G. 2005. Indian Ocean Tsunami Warning System to Become Operational in 2007. National Defense. Accessed 5 January, 2006. Available at http://www.nationaldefensemagazine.org/issues/2005/nov/indian_ocean.htm.

Kahn, M. E. 2005. The death toll from natural disasters: The role of income, geography, and institutions. Review of Economics and Statistics 87:271-84.

Long, J. S. 1997. Regression models for categorical and limited dependent variables. Thousand Oaks, CA: Sage Publications.

Milburn, H. B., A. I. Nakamura, and F. I. Gonzalez. 1996. Real-time tsunami reporting from the deep ocean. Proceedings oh/ the Oceans 96 MTS/IEEE Conference, September 23, 1996, Fort Lauderdale, Florida.

Mileti, D. 1999. Decisions by design. Washington, DC: Joseph Henry Press.

Papadopoulos, G. A., and F. Imamura. 2001. A proposal for a new tsunami intensity scale. ITS 2001 Proceedings, Session 5, Number 5-1.

Pararas-Carayannis, G. 1986. The Pacific tsunami warning system. Earthquakes and Volcanoes 18:122-30.

Reymond, D., and E. A. Okal. 2000. Preliminary determination of focal mechanisms from inversion of spectral amplitudes of mantle wave. Physics of the Earth and Planetary Interiors 121:249-71.

Rogers, A. 1985. Regional population projection models, Series No. 4, Scientific Geography. Beverly Hills, CA: Sage.

Sandler, T. 2002. Financing international public goods. In International public goods: Incentives, measurement, and financing, edited by M. Ferroni and A. Mody, Washington, DC: World Bank.

Sandler, T. 2005. Collective versus unilateral responses to terrorism. Public Choice 124:75-93.

Sigman, H. 2002. International spillovers and water quality in rivers: Do countries free ride? American Economic Review 92:1152-9.

Simmons, K., and D. Sutter. 2005. Protection from nature's fury: Analysis of fatalities and injuries from F5 tornadoes. Natural Hazards Review 6:82-7.

Sorensen, J. 2000. Hazard warning systems: Review of 20 years of progress. Natural Hazards Review 1:119-25.

Sudo, K., H. Kameda, and Y. Ogawa. 2000. Recent history of Japan's disaster mitigation and the impact of IDNDR. Natural Hazards Review 1:10-7.

Wooldridge, J. 2002. Econometrics of cross section and panel data. Cambridge, MA: MIT Press.

Monica P. Escaleras * and Charles A. Register ([dagger])

* Florida Atlantic University, Department of Economics, 777 Glades Road, Boca Raton, FL 33431, USA; E-mail [e-mail]; corresponding author.

([dagger]) Florida Atlantic University, Department of Economics, 777 Glades Road, Boca Raton, FL 33431, USA; E-mail [e-mail].

(1) According to Dr. Laura S. L. Kong, director of the International Tsunami Information Center, a fully functioning system could be put in place in the Indian Ocean for about $200 million (Jean 2005).

(2) A good discussion of international public goods and their financing can be found in Sandier (2002); examples of such goods and the associated free-rider problem can be found in Sigman (2002) and Sandler (2005).

(3) A great deal of information on mitigation efforts and their effectiveness can be found at the University of Colorado's Natural Hazard's Center at http://www.colorado.edu/hazards/.

(4) This section draws heavily on Pararas-Carayannis (1986).

(5) As indicated above, warning systems have typically been established in response to a specific major tsunami, potentially leading to a problem of endogeneity for empirical modeling. Given that all existing systems were established prior to the period we are analyzing; however, for our modeling, both the systems and their warnings can be assumed to be exogenous.

(6) For 26 of these 56 events, necessary data are unavailable for the tsunami itself, such as the location of the run-ups, the number of waves that came ashore, and/or the number of deaths associated with the waves. We also omitted 18 tsunamis striking the Soviet Union in the early part of our sample period because we lacked reliable per capita income data. For the remaining 12 events, the democracy variable was missing.

(7) The lack of a single, complete source for tsunami warnings was confirmed by Dr. George Pararas-Carayannis.

(8) Warning status information can be found at the following Web sites: the International Tsunami Information Center at http://www.tsunamiwave.info, the Yuzhno-Sakhalin Tsunami Warning Center at http://www.science.sakhalin.ru/ tsunami/, and the Japan Meteorological Agency at http://www.jma.go.jp. Our contact with the International Tsunami Information Center was facilitated through numerous discussions and correspondences with Dr. George Pararas-Carayannis, who served as the director of that center from 1974 to 1992. Dr. Pararas-Carayannis both provided direct information on warnings for a number of specific tsunamis in our sample and confirmed the accuracy of the warning data that we collected from other sources. He also provided a great deal of information about and analysis of various natural hazards, along with a brief biographical sketch of his career at the Tsunami Page, a Web site that he maintains, available at http://www.drgeorgepc.com.

(9) Population and land area data come from several sources: (1) The World Gazetteer, http://www.world-gazeneer.com; (2) GeoHive, http://www.xist.org; and (3) Population Statistics by Jan Lahmeger, http://www.library.unn.nl. To provide annual data on populations, we made projections following the procedures outlined in Rogers (1985). Further, as noted by Cohen (1995), for predictions over only a few years, as made here, the specific type of function used has relatively little influence on the quality of the predictions.

(l0) Available at http://www.bsos.umd.edu/cidcm/polity/index.html.

(11) Differences in means tests rely on methods that take into account unequal variances based on preliminary differences in variances tests.

(12) Long (1997) provides a good discussion of the negative binomial regression.

(13) The value of 5 has been added to the IIDA scale and 1 to the DEMOCRACY scale to allow for the taking of logs.

(14) All models presented throughout the remainder of the paper rely on fully robust standard errors and yield strong measures of goodness of fit.

(15) Some degree of colinearity exists between per capita GDP and the establishment of warning systems. Two points are important here. First, should there be significant colinearity, the result would be inflated standard errors for the variables involved. Because each is consistently significant, as a practical matter, any existing colinearity is apparently not sufficient to cause estimation problems. Second, given a simple correlation between WARNING and GDP PER CAPITA of less than 0.25, the extent of colinearity is likely not particularly great.

(16) Full results for each of these models are available on request from the authors.

(17) A discussion of this debate can be found in Papadopoulos and Imamura (2001).

(18) The distance variable was created by first identifying the latitude and longitude of the affected region using the Getty Thesaurus of Geographic Names, available at http://www.getty.edu. These coordinates were then compared with the latitude and longitude of the epicenter of the quake, given by the NGDC Significant Earthquake Database. Calculation of the distance between these two points makes extensive use of the ESRI ArcView Geographic Information System.

(19) Given the need to use logs in the negative binomial model, an arbitrarily small value for elapsed time (0.000001 min) was given to tsunamis for which there were no warnings.

(20) The three variables used in lieu of the IIDA index work well. Specifically, the underlying quake's magnitude is positively and significantly associated with deaths while the quake's depth and distance to population centers are each negatively associated with deaths, though only the latter is statistically significant.

(21) Examples include improvements in sensing of earthquakes capable of producing tsunamis through the Tsunami Risk through Seismic Moment with Real Time System (see Reymond and Okal 2000) and more sensitive detection of changes in water pressure through Deep-Ocean Assessment and Reporting of Tsunamis gauges (see Milburn, Nakamura, and Gonzalez 1996 and Gonzalez et al. 1998).

Table 1. Descriptive Statistics

Variable           Mean         SD       Minimum      Maximum

DEATHS           1864.37    13,211.76        0       150,000
WARNING             0.21         0.41        0             1
IIDA                0.06         1.89       -4.64          5
POP DENSITY       193.58       690.47       30          5223.67
GDP PER CAPITA   7726.87    10,831.67      120.00     38,222.02
DEMOCRACY           5.65         4.32        0            10
ASIA                0.66         0.47        0             1
EUROPE              0.04         0.19        0             1
AFRICA              0.02         0.14        0             1
AMERICA             0.28         0.45        0             1

Table 2. Distribution of Tsunamis by Deaths

Deaths                     Number of Tsunamis

0                                  51
1-50                               57
51-100                             10
101-500                            17
501-1000                            1
1001-5000                           3
5000 and above                      7

Table 3. Relation between IIDA, Deaths, and Number of Tsunamis

                                             Deaths
                   Number of
IIDA               Tsunamis      Mean         SD         Range

[greater than or      13       11,808.46   41,525.46   0-150,000
  equal to] 2.5
0-2.49                87        1,298.73    6,169.49   0-50,000
<0 - -2.50            31          196.10      986.49   0-5502
< - 0                 15           12.40       21.33   0-62

Table 4. Relation between Deaths, Warning, and IIDA

           WARNING = 1   WARNING = 1   WARNING = 0   WARNING = 0
Variable      Mean           SD           Mean           SD

DEATHS        32.52         54.25        2353.92     14,847.77
IIDA           0.67          1.61          -0.10          1.93

                   Difference
Variable             t-test

DEATHS             2321.41 * (1.69)
IIDA                 -0.77 ** (2.26)

t-statistics for differences in means are in parentheses.
** and * denote significance at 5 and 10%, respectively.

Table 5. Correlates of Deaths from Tsunamis

Variable                          (1)                  (2)

Intercept                    7.76 ** (0.585)      2.60 ** (1.006)
WARNING                     -4.28 ** (0.656)     -3.75 ** (0.669)
IIDA                                              2.90 ** (0.628)
POP DENSITY
GDP PER CAPITA
DEMOCRACY
ASIA
EUROPE
AFRICA
TIME
LR Chi-square ([alpha])        18,000 **            15,000 **
Log-likelihood              -662.49              -653.52
LR Chi-square                 42.66 **             49.84 **
Number of observations            146                  146

Variable                          (3)                  (4)

Intercept                    3.79 ** (1.852)      4.29 ** (1.810)
WARNING                     -2.15 ** (0.641)     -2.24 ** (0.665)
IIDA                         2.33 ** (0.477)      2.18 ** (0.535)
POP DENSITY                  1.09 ** (0.193)      1.11 ** (0.230)
GDP PER CAPITA              -0.54 ** (0.195)     -0.65 ** (0.238)
DEMOCRACY                   -0.59    (0.405)     -0.24
ASIA                                             -3.05 ** (0.893)
EUROPE                                           -3.58 ** (1.402)
AFRICA                                           -3.99 ** (1.501)
TIME                                              0.07 ** (0.023)
LR Chi-square ([alpha])        13,000 **            11,000 **
Log-likelihood              -637.09              -629.30
LR Chi-square                 96.19 **            130.99 **
Number of observations            146                  146

Robust standard errors in parentheses.
** Denotes significance at 5%.

Table 6. Sensitivity of Warning Coefficient to Alternative
Specifications

                                Warning               Number of
Model                          Variable              Observations

(i) Full model                 -2.24 **  (0.665)         146
(ii) Deaths < 7500             -1.286 ** (0.576)         140
(iii) Pacific tsunamis         -2.08 **  (0.708)         110
(iv) Quake magnitude > 6.5     -2.16 *   (0.637)         126
(v) Pacific and quake
  magnitude > 6.5              -2.07 **  (0.694)         101
(vi) Alternate measure of
  tsunami magnitude            -1.45 **  (0.613)         146
(vii) IIDA < 0                 -2.49     (5.016)          46
(viii) IIDA [greater
  than or equal to] 0          -2.89 **  (0.710)         100
(ix) ELAPSED TIME (a)          -0.10 **  (0.047)         130

                                   LR
                               Chi-Square      Log-          LR
Model                          ([alpha])    Likelihood   Chi-Square

(i) Full model                 11,000 **      -629.30     130.99 **
(ii) Deaths < 7500               5200 **      -528.93      40.05 **
(iii) Pacific tsunamis           3100 **      -428.13      71.04 **
(iv) Quake magnitude > 6.5     11,000 **      -559.77     157.53 **
(v) Pacific and quake
  magnitude > 6.5                3100 **      -399.84      72.78 **
(vi) Alternate measure of
  tsunami magnitude              4800 **      -617.49     174.64 **
(vii) IIDA < 0                   6969 **      -120.92      18.38 **
(viii) IIDA [greater
  than or equal to] 0          11,000 **      -500.25     130.11 **
(ix) ELAPSED TIME (a)           11,000**      -579.43     122.59 **

Robust standard errors in parentheses.

(a) In this model, ELAPSED TIME is used in lieu of WARNING.

** Denotes significance at 5%.