Everybody out of the Pool! Reconstructing the Democratic Peace

EVERYBODY OUT OF THE POOL! RECONSTRUCTING THE DEMOCRATIC PEACE

CSSS WORKING PAPER 55

MICHAEL D. WARD, RANDOLPH M. SIVERSON, AND XUN CAO

Abstract. Research in international politics may have produced misleading results because (1) typical data contain dependencies that have been ignored, (2) popula- tions are treated as samples, with unwarranted reliance on misleading significance tests, and (3) scant attention is devoted to how well the model can predict the events of interest. Using the democratic peace research program as an example, we show that the three elements of the Kantian model-mutual democracy, high trade and common membership in IGOs–have at best weak effects on dampening the occurrence of militarized international disputes within dyads. Neither do they offer meaningful predictions about which dyads will be involved in these disputes. A model incorporating several types of dependencies among countries yields results with high levels of predictive accuracy and provides new substantive insight about the prominence of dependencies in international relations.

In a recent paper, Frieden & Lake (2005) take stock of the state of research in international politics. Their overall argument is that “progress in the study of international politics– including. . . making its lessons more relevant to policy–depends on more not less, rigorous theory and, more not less, systematic empirical testing” (p. 137). While we agree with their overall sen- timents, the argument we present here is that different modes of systematic empirical research are needed to avoid problems that have had unrecognized consequences for the quality of the research results reported in the literature. In this paper we identify three major problems with prevailing practices in the empirical analysis of international politics. These are (1) the lack of independence in the cases, (2) an unwarranted reliance on tests of significance and, as a consequence (3) a neglect of how well a “tested” model predicts the outcome of interest. The combination of these problems can produce misleading results. We show in this article that because popular statistical procedures overlook the dependencies in the data, they result in an over-confidence in the Kantian hypothesis that joint democracy, mutual trade, and shared participation in the international governmental organizations each independently reduce international conflict. Authors’ Note: Version of February 3, 2006. Ward’s research was supported by a grant from the Methods, Measurement, and Statistics Program at the National Science Foundation, grant number: SES-0417559. Peter Hoff and Anton Westveld provided much guidance and helpful discussions on this topic, as well as many others. This research greatly benefitted from the scrutiny and helpful suggestions of Neal Beck, Bruce Bueno de Mesquita, James Caporaso, Jeff Gill, Jonathan Mercer, and Aseem Prakash. David Callaway and John E. Daniels of the Social Science Data Service at the Institute of Governmental Affairs at the University of California at Davis were especially helpful to us at a critical point in our quest for distributed computing resources which we found at the San Diego Supercomputer Center at the University of California at San Diego. Special thanks go to SS and SW for their forbearance and editorial guidance during their vacations, and after. And before. And, then again.

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Three Problems The first problem is that both dyadic data and international relations are known to contain dependencies that are omitted by most popular procedures for analyzing data.1 Because regression-based approaches assume that the data are exchangeable and the errors independently and identically distributed, they are unable to capture the extent to which dependent data may actually reflect the ebb and flow of international politics. International Organization published a symposium in 2001 that examined the robustness of statistical findings in many dyadic studies of international conflict. Green, Kim & Loon (2001) surveyed more than four dozen panel studies in the field of international relations that appeared in prominent scholarly journals over the period from 1996-1999. They raised the question of whether the democratic peace is a powerful explanation, or whether dyad-based fixed effects were statistically more powerful. In summarizing this debate, King (2001) noted that the thorniest problem is to unravel the dependencies in dyadic data that result in biased estimates of coefficients and covariance structures, and further suggested that “[a] logical methodological starting point for addressing the problems at hand would be based on Bayesian hierarchical, random effects, or split population models” (page 506). Below we present one such model to examine the role of dependencies in the democratic peace literature.2 What are these dependencies? Maoz (2004) has shown for example that countries which are involved in conflicts in one decade are quite prone to them in the next. He illustrates that Sweden, Switzerland, and Venezuela, for example, generally are not involved in militarized disputes and wars, while historically, Israel, Pakistan, India, Jordan, and Syria (among others) are repeatedly involved in both disputes and wars. These historical facts result in dependencies among the ebb and flow of, as well as the data we collect on, interstate disputes and wars. These dependencies are at the core of this research. They reflect the fact that it is common to observe patterns of interstate conflict having the same initiator but different targets. For example, pursuing an active foreign policy may lead a country into conflict with many different countries over time. Similarly, disputes having different initiators but the same targets are also common, as in the case of the first Gulf War where a large number of countries were engaged in conflict with Iraq. These actions are at least partially dependent upon one another and can not be treated as completely independent occurrences. Additional, there are often pairs of countries that are in repeated, or protracted, conflicts that are typically described as rivalries (Diehl, Goertz & Jones 2005). Episodic conflicts and disputes are not independent, either statistically or historically. The geopolitics of the Middle East is replete with such dyadic dependencies. Table 3, below, displays some of the most prominent dependencies in international conflict data. A second important problem we address concerns the basic inferential model that dominates popular practice in the field of international relations, as well as many other disciplines. Since most research in international relations is based on observational studies that have a large number of cases, there is an appearance of statistical significance in almost all the findings in the literature, even considering the well-known publication bias for positive and statistically significant results. Actually, the prevailing popular statistical approach reflects the ability of the tests to detect small differences–i.e., the power of the tests–as well as the number of observations more than it reveals any underlying statistical significance of hypothesized causal linkages (Savage 1957, Gill 1999). This research tradition somehow expects more from tests of significance, an expectation that probably creates more problems than it solves.

1One early eﬀort examined strategic dependencies in the context of endogenous choice calculus (Smith 1999). Another important initiative (Signorino 1999) extends the Quantile Response Equilibrium in the context of a solution to certain game-theoretic models of strategic choice. 2Clark & Regan (2003) have examined split population models, examining heterogeneity in diﬀerent samples, but not examining dependencies.

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While observational data rarely comprise a random sample, they nevertheless are frequently treated as an enormous one. Large samples have immense statistical power that large collections of observational data normally do not. The null hypothesis implicit in most of the statistical examinations of these models is that the quantities of primary interest are all equal to zero. Why this would be the case in observational data is not clear. In situations characterized by rare events with a preponderance of non-occurrences, we should not expect the pooled correlations to be identical for all groupings of observations. Zero correlation is a meaningful expectation if and only if one knows that the two groups of cases (for example: the disputes and the non-disputes) are either randomly assigned to the treatment (dispute) or randomly selected from the covering population in such a way that they are matched on the important covariates. Neither of these conditions can plausibly be argued to be the case for observational data on militarized interstate disputes, nor, for that matter, in almost any data currently being used in the study of international politics. As a result, statistical significance tests can be badly misleading in terms of producing information about the underlying data generating processes by allowing scholars to attribute statistical significance to summary characteristics known a priori to be different. Below we show that it is not necessary to embrace the sampling framework in order to extract useful information from observational data in the context of the democratic peace. Third, most studies have focused solely on statistical significance as a measure of “fit,” while at the same time avoiding evaluations of the in-sample fit of estimated model predictions with actual data. Regression diagnostics are only one heuristic, not the terminus of scientific investigation. Indeed, they can often be misleading. We show that a predictive heuristic helps to protect scholars from making statistical inferences that may be problematic. The basic idea is quite simple: a good model will not only have estimated coefficients that are informative, but it also should accurately map the covariate information into the dependent variable. That is, the model should accurately identify the observed patterns in the dependent variable. Because of the misapplication of statistical significance in observational studies, it is possible that specifications shown empirically to be “statistically significant” will be unable to identify patterns in the data correctly. We analyze the issues involved in incorporating higher-order dependencies into statistical models of dyadic data and illustrate a two-faceted solution to this shortcoming of popular approaches. Our approach not only explicitly incorporates higher-order dependencies in a hierarchical framework, but also relies on using predictions as a heuristic for model evaluation. It is simple to predict the absence of conflict between pairs of countries, whether they are democratic or not.3 This is easy because conflict itself, though enduring and ever present, is at the same time relatively rare. Over the period from 1886-1992, for example, there are approximately 150,000 dyad-years in which two specific countries could have engaged in a militarized dispute with one another, but this happened less than 1% of time. Ignoring all temporal, systemic, dyadic, or country-specific information about what may cause militarized interstate disputes, a good guess is that about 1% of the dyads may be involved in a dispute at any given point in time. So unconditional on any additional information, the best guess is that any two countries will not be engaged in a militarized interstate dispute during any year. This expectation is overwhelmingly correct, 99% of the time. Such an observation is not especially helpful from a scientific point of view. It provides no basis for either explaining or predicting which of the dyads will be involved in one of the rare events.

3Although, as Schrodt (2002) notes, actual predictions by scholars are quite rare. However, see his (forthcoming) predictive results on the Balkans and Bueno de Mesquita’s volume on Predicting Politics (2002). Siverson (2000) also discusses the value of prediction in the context of policy. Pevehouse & Goldstein (1999) is another example of predictive work in international relations. Feder (1987) wrote an early piece on forecasting in the U.S. Intelligence Community that has since been declassiﬁed. See Ward & Gleditsch (2002) as well as Beck, King & Zeng (2000) for additional studies employing in-sample and out-of-sample predictions in international relations.

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In undertaking this analysis, we aspire to add nuance to the growing literature on the democratic peace by demonstrating that jointly democratic regimes do have a lower probability of militarized dispute involvement, but that this probability is sufficiently low to be uninformative in a predictive sense. In the research area known as the democratic peace scholars have made concerted efforts to embrace these dependencies at the theoretical level, but have been less successful in leveraging them in empirical analyses. Instead, we find that the dependencies among countries are far more powerful in explaining the existence of militarized disputes among contemporary countries than the factors identified in the Kantian model.

Democratic Peace The standard model of the democratic peace examines the pacifying effects of trade, international organizations, and democracy upon the initiation and continuation of militarized interstate disputes. There is a substantial and important scholarly literature largely built upon statistical studies of observational data reporting the incidence of dyadic militarized interstate disputes and wars in various periods since 1816. This literature has recently evolved from its roots in exploring whether pairs of democratic countries have a reduced probability for war with one another (Maoz & Abdolali 1989, Small & Singer 1976) into a continued and broader examination of the covariates of militarized interstate disputes.4 Most empirical scholarly literature on this topic uses a regression perspective, identifying those variables and factors thought to be more or less important in explaining the occurrence of militarized disputes, assessing by statistical significance the power of various bivariate hypotheses concerning the democratic peace.5 This approach is, of course, wide-spread and has been adopted by numerous research programs. “The Kantian Peace” (Oneal & Russett 1999) is, in our opinion, the canonical study of the democratic peace. It uses a general linear model to estimate the occurrence of militarized interstate disputes over the period 1886-1992. Many other studies have employed these exact or similar data along with various perturbations of the specified regression equation. The basic insight of this line of research has been that democratization, international commerce, and participation in international organizations are each shown to be independently pacifying forces in world politics. Oneal & Russett (1999, page 33) summarize their work by noting that “. . . analyses for the years 1885-1992 indicate that Kant was substantially correct: democracy, economic interdependence, and involvement in international organizations reduce the incidence of militarized interstate disputes.” Similar declarations are by now legion in scholarly writing, and are also frequently found in the policy pronouncements of the governments of industrialized democracies, among others. Because the Oneal & Russett article, as well as the data and methods therein, are widely referred to, we use it as a reference point to begin our analysis. Table 1 presents Oneal & Russett’s statistical results. These results were obtained with a general estimating equation specified to take into account the time-series and cross-sectional nature of the data.6 As in many other published studies of this phenomenon, the accumulation of asterisks is substantial. Similar results are found throughout the observational, empirical literature, and serve as part of the basis for the strength standing behind the democratic peace idea. Apart from a strong demonstration of statistical significance, how well do these kinds of results capture the observed existence of the militarized interstate disputes? One way to answer this

4Summaries of the literature on the democratic peace include Chan (1997), Ray (1998), and Morrow (2002).

5Cederman (2001) and Cederman & Rao (2001) are examples of different approaches. 6Oneal & Russett made not only their database available, but also their Stata program; accordingly, we have exactly replicated their published results. We also replicated their statistical procedures using a different implementation of the GEE estimator, this one found in the statistical package R; these results are essentially identical, and slight numerical discrepancies are attributed to differences in the underlying scale parameters estimated by each of the two algorithms.

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Table 1. Models of the Kantian Peace, 1886-1992, Predicting Dyadic Involvement in Militarized Disputes, taken from Oneal & Russett (1999, page 22). Entries are rounded to three digits. Oneal & Russett use asterisks to indicate classical probability levels with ∗ ∗ ∗ flagging coefficients that have p<.001, using one-tailed tests for statistical significance. Standard errors are not shown here, but may be found in the original article.

Variable All Dyads Lower democracy -0.066*** Trade/GDP -57.865*** International organizations -0.001 Capability ratio -0.234*** Alliances -0.251 Noncontiguity -2.004*** Log distance -0.465*** Only minor powers -1.839*** Constant -1.935*** 2 χ8 1354.80 N 149,373 question is to examine the number of correct and incorrect predictions that this model produces. Put differently, we seek to move beyond the statistical significance associated with a particular model and instead to explore how well it captures the occurrence of militarized interstate disputes. Since the dependent variable is binary and the underlying model produces a probability estimate, we need to establish an appropriate probability threshold (or cut-point) above which a predicted probability will be coded as predicting the occurrence of a militarized dispute. By convention many statistical studies use 0.5 as the threshold, as this value equalizes the cost of false positives (predicting a militarized dispute in a dyad-year without such a dispute) and false negatives (failing to predict an actual militarized dispute). In the case of militarized interstate disputes, a ratio that equalizes these costs will not be sensible, since we know that 99% of the time there is no militarized interstate dispute. Indeed, as shown in the top half of Table 2, if we use this threshold, we will be unable to correctly identify any single instance of a militarized interstate dispute; the model will always predict the absence of a dispute, irrespective of the values of the independent variables. We chose a more reasonable alternative. The mean of the dependent variable is 0.009. Employing this as a cut-point, how well does the model predict to actual militarized disputes in the data?7 As shown in the bottom half of Table 2, because the cost of falsely predicting disputes is low for this threshold, over 22,000 pairs of countries are predicted to be involved in disputes. To be sure, about 80% of the MIDs are correctly identified, but at the cost of an overwhelming number of false positives: 95% of the predicted disputes are actually non-disputes. The states, dyads and years yielding the largest number of correctly predicted dispute participation are shown in Table 3. Major powers are frequent members in the set of countries that are correctly predicted to be involved in a militarized dispute. The United States is most frequently correctly identified as being in a dispute (some 151 times), followed by the Soviet Union (139), the

7 This value suggests that it is about 110 times more costly (to the decision maker using these results) to incorrectly predict a militarized dispute than it is to predict a non-dispute when there is actually a dispute. It is important to re- member that this is just an illustration. Decision theory requires that the cost assessments be obtained independently of the actual data that are analyzed. However, we ignore this important requirement for didactic purposes. We chose this small, extreme number to illustrate what assumptions are also necessary to obtain some correct predictions of militarized interstate disputes using of this model.

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Table 2. Using the basic results from the Oneal & Russett (1999) model (Table 1, column 1) replicated above it is impossible to predict accurately the occurrence and non-occurrence of dyadic, militarized interstate disputes over the period from 1886 to 1992. In both choices of cut-points, the model has great diﬃculty in distinguishing between disputes and the absence of a dispute.

Cut-point: 0.50 Non-Disputes Disputes Predicted Non-Disputes 147,989 1,415 Predicted Disputes none none Cut-point: 0.009 Predicted Non-Disputes 125,502 274 Predicted Disputes 22,487 1,141

Table 3. There is a relatively small number of countries, dyads, and years that account for all the correctly predicted militarized disputes in the Oneal & Russett model, using the mean on the dependent variable as the threshold for predicting a dispute. The number in parentheses gives the number of dyad years for which the entry is correctly predicted (out of 1,141). There are 137 countries, 5,860 dyads, and 95 years in the database.

60% in top 9 countries 15% in top 7 dyads 28% in top 8 years Soviet Union (124) Soviet Union↔Japan (35) 1938 (121) UK (120) US↔Soviet Union (26) 1913 ( 34) US (119) Soviet Union↔China (23) 1983 ( 34) China ( 68) UK↔Soviet Union (21) 1986 ( 30) France ( 64) India↔Pakistan (27) 1982 ( 28) Germany ( 50) Chile↔Argentina (24) 1984 ( 26) India ( 43) Greece↔Turkey (24) 1961 ( 25) Italy ( 38) China↔Japan (16) 1985 ( 25) Greece ( 33) 1960 ( 24)

UK (125), and China (76), and France (70). The most frequently correctly predicted dyads are also unsurprising: the Soviet Union-Japan (35 instances), the US-Soviet Union (26), India-Pakistan (27), Greece-Turkey (24), Soviet Union-China (23), and the UK-Soviet Union (21). The years immediately preceding World War I and II account for over 20% of the correct predictions. Recent predictions are also better, with an annual average of 19 disputes being correctly predicted in the post-1938 period, compared to 8 in the pre-1939 era. In short, this model is not informative beyond making a large number of false positive predictions and suggesting that major and regional powers are more likely to be involved in disputes. The results from the pooling procedure appear primarily to support an overconfidence based on statistical significance that is not borne out in the accuracy of predictions. Moreover, the countries, dyads, and years identified are not surprising and might have been identified a priori. Using the residuals from this model yields results that appear to be astonishing. The Pearson residuals were mapped into the set S{0, 1} such that large outliers were set to 1 and all others were assigned a value of 0. Table 4 illustrates the results of using these recoded Pearson residuals to identify militarized interstate disputes. The residuals actually contain all of the correct information about the existence of dyadic, militarized interstate disputes. The converse is that the originally estimated canonical model of the democratic peace contains virtually no information about the dependent

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Table 4. Using Pearson Residuals from Oneal & Russett (1999) Model replicated above it is possible to perfectly predict the occurrence and non-occurrence of dyadic, militarized interstate disputes over the period from 1886 to 1992.

Non-Disputes Disputes Predicted Non-Disputes 147,979 0 Predicted Disputes 0 1,415 variable. Better in-sample predictions are produced by the residuals than are produced by the model.8 Why? Since the model fits poorly, the residuals essentially recapture the dependent variable. As a result they provide an overwhelmingly good fit to the dependent variable. Few studies have examined the fit of the democratic peace idea, focusing instead on the statistical properties of estimated coefficients thought to represent the insights of the democratic peace. The message of the above exercise is that the in-sample, predictive power of the estimated binomial model representing the democratic peace is low, while the predictive power of the errors from that model is almost perfect. This should perhaps lead to the admonition that “more research is needed.” If so, perhaps an additional admonition is that we should try to work beyond significance testing on huge bodies of observational data and instead direct our attention to other approaches that lend themselves to dealing with the kind of data that dominates quantitative international relations scholarship.

A Bayesian, Hierarchical, Bilinear, Mixed Effects Model Modeling Dependencies. As noted above, dyadic data in international relations are replete with dependencies. For example, because states have relatively stable policies it is reasonable to expect that data emanating from a single country are likely to be correlated, as are data directed to a single country. Similarly, dyads are likely to have data correlated over time. The social relations model introduced a method to decompose variance in such data into sender and receiver effects as well as permit within-dyad correlations via the analysis of variance (ANOVA) protocol (Warner, Kenny & Stoto 1979, Wong 1982).9 The idea of further decomposing the variance in the context of dyadic data was further developed (Gill & Swartz 2001, Li & Loken 2002) to permit the statistical analysis of normally distributed dyadic data using additive effects. These ideas have been extended to a generalized linear model that incorporates third-order dependence via a bi-linear effect similar in spirit to that first introduced by Gabriel (1998). Dyadic data are almost always characterized by third-order dependencies known in the social networking literature as transitivity, balance, and clustering (Wasserman & Faust 1994). By

8 Oneal & Russett’s Table 2 suggests that the Kantian variables have substantial marginal effects on the occurrence of international disputes. It is important to recognize that difference statistics–even when calculated correctly–do not reflect the underlying base rates and as a result may be less informative than tabulations of in-sample predictions. . 1,415 When the base rate of international disputes is 0 009 (i.e., 149,373 ), a reported 36% decrease in disputes associated with increasing democracy by one standard deviation reduces the rate to 0.006. More concretely, the difference between these two effects is, of course, 0.003, which implies a decrease of about 4 disputes in the data set. When looked at in this light, the changes attributed to the variables reported do not look quite so powerful. A change in probability from 0.25 to 0.75 seems consequential, while one from 0.01 to 0.03 does not, especially if the costs of reduction are substantial. 9 In the context of transactions, the language of sender and receiver is clear. However, in the context of conflict, it is more complicated, since many disputes are protracted and while initiators of episodes can often be specified, it is over-simplistic to assign prime mover status to that country. In what follows, we use sender and receiver to represent different sides of a dyadic relationship. Every country is a potential sender and a potential receiver. This sociomatrix is square having all countries arrayed along the columns and rows. A country is the sender in a particular militarized dispute if it is among that set of countries identified to have first taken militarized action, according to the MID data.

7 Everybody Out of the Pool! February 3, 2006 way of explanation, transitive relations among three actors implies that “a friend of a friend is a friend,” for example; balance implies that if two actors behave similarly towards each other, then they will behave similarly to other actors as well; clustering implies that sets of actors can be described in which relations are positive among all actors in the set and negative with all actors not in the set. An early use of this kind of clustering in the field of international relations can be found in Bueno de Mesquita (1975). Early uses of balance and transitivity can be found in studies employing graph theory such as Harary (1959, 1969), Brams (1968), and Zinnes (1967). Using the social relations re-formulation to capture sender (initiator), receiver (target), and higher-order dependencies in the Militarized Interstate Dispute (MID) data, we explore a model analogous to the original specification of Oneal & Russett. This model is analogous, but has two distinct advantages. First, it permits the direct estimation of important dependencies in the dyadic data. Second, because the model has a hierarchical format it is unnecessary to force non-dyadic variables to have a dyadic character (or vice versa), an unfortunate practice that is widespread in the empirical literature. Each partner to any particular interaction has associated covariates at both the country and dyad level. The hierarchical specification allows relational as well as country specific linkages to be coherently included in a single model. As a result of these advantages we have been able to adopt a simple approach to measuring the three putative foundations of the democratic peace: democracy, trade, and international organizations. Dyadic variables (xi,j) capture the pillars of the democratic peace: (1) joint governance structures measured as the product of the polity score of sender and receiver, (2) the imports of the sender from the receiver, and (3) the number of international organizations in which both are members. Like most empirical studies, we also added a measure of the distance between pairs of countries; we use the distance in kilometers between the capital cities. In the dyadic context, i and j index the sending and receiving countries. For both sender and receiver, three country-level covariates (xi) capture the population, the economic size measured in terms of gross domestic product, as well as the regime type of each country.10 The model is: ′ ′ ′ ′ (1) θi,j = βdxi,j + βsxi + βrxj + ai + bj + uivj + ǫi,j, where

βdxi,j = d ∈ dyadic eﬀects: joint democracy, imports, joint IO membership, distance

βsxi = s ∈ sender eﬀects: population, GDP, democracy

βrxj = r ∈ receiver eﬀects: population, GDP, democracy

ai = random eﬀect of sender

bj = random eﬀect of receiver ′ uivj = separate latent positions for sender and receiver ǫi,j = error.

Statistical Results. We modeled the probability of a militarized dispute yi,j with a logistic link function: eθi,j P (yi,j = 1 | θi,j)= . 1+ eθi,j This setup adds covariates that are specific to senders and receivers into standard logistic setup, but also includes both sender and receiver random effects, along with an estimate of the 10 Detailed information on each of the covariates and their sources may be found in Appendix A. Open source software written for the R computer language is available to estimate general bilinear mixed effects models at the project web site.

8 Everybody Out of the Pool! February 3, 2006 unmeasured latent positions of each country in the militarized interstate dispute network. These latent positions (ui and vj) index the propensities for country pairs to have similar interaction patterns toward other countries. The latent positions of two countries will be similar if countries are responsive to one another or if they have similar response patterns involving other countries. Latent similarity captures transitivity and balance, and reveals clustering. One strong benefit of this specification is that in addition to the latent positions, four additional quantities of interest are developed. Each reflects some aspect of the higher-order dependencies. Since we model the random 2 effects as being multivariate normal, we can estimate their covariance structure: σa is the variance 2 of the sender random effects and σb the variance of the receiver random effects. Additionally, the covariance between these two components is given by σab. In a similar way, the covariance of the errors across dyads, i.e., the covariance of the errors between ǫi,j and ǫj,i, can also be parameterized 2 as ρσǫ , allowing a specific measure of reciprocity to be estimated (ρ). In this simple way, higher- order dependencies are posited in four new quantities of interest that have been previously assumed to be nonexistent or unimportant. For the first time, it is possible to estimate these quantities.11 Since it has been demonstrated that the empirical results for the democratic peace are stronger since the end of the World War II (Gowa 1999, Box-Steffensmeier, Reiter & Zorn 2003), we have focused on the last five decades, 1950-2000 and estimated this model for eleven years: {1950, 1955,..., 1995, 2000}. Table 5 provides the “big table of numbers” for the Bayesian estimation of the hierarchical, bilinear random effects model for the year 2000, as an illustration of our basic results.12 It is important to note that the 95% empirical credible limits for all the dyadic variables representing the democratic peace argument include zero. Stated differently, the three traditional explanatory variables that undergird the notion of a democratic peace do not have strong, unambiguous empirical effects in the most recent year available for analysis. In most other years however, the patterns are more supportive of the notion that higher levels of democracy tend to reduce conflict probabilities. Figure 1 presents the boxplots for the posterior distributions of the estimated coefficient for dyadic democracy in equation (1). This figure illustrates that in most years dyadic democratic exerts a modest, negative impact on the probability of a militarized interstate dispute.

Figure 1. Posterior distributions of the estimated coeﬃcients for dyadic democracy in each of eleven years are displayed as boxplots. Dyadic democracy tends to weakly dampen participation in militarized interstate disputes in most years. Dyadic Democracy

0.1

0.0

−0.1

−0.2

−0.3

−0.4 1950 1960 1970 1980 1990 2000

While the interaction of democracy levels in pairs of countries has a modest impact on reducing their conflict, the effects of trade and IGO membership are more mixed. Figure 2 illustrates this by presenting a boxplot of the yearly posterior distributions. As the figure shows, 11 Hoff (2005) provides details and full conditionals for this model. 12 Full results for each year are available on the replication archive for this project.

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Table 5. Bayesian estimates for equation (1) are the posterior means for the estimated quantities. Quantile-based, empirical credible intervals of 95% are presented. The mean posterior log likelihood is -30.139.

Posterior Distributions for Year 2000. 2.5% Mean 97.5% Constant −82.78 −55.59 −34.32

Dyadic Eﬀects: Polityi × Polityj −0.08 −0.02 0.05 Importij −0.40 −0.18 0.01 IGOij −0.22 0.02 0.26 Distanceij −8.18 −5.55 −3.94

Sender Eﬀects: Populationi −0.01 0.01 0.03 GDPi 0.00 0.01 0.01 Polityi −0.54 0.39 1.37

Receiver Eﬀects: Populationj −0.03 −0.00 0.02 GDPj 0.00 0.01 0.01 Polityj −0.65 0.35 1.30 2 Dependencies: Common Sender σa 170.4 Sender-Receiver σa,b 125.4 2 Common Receiver σb 148.0 Reciprocity ρ 0.99 0.99 1.00 2 Error Variance σǫ 270.9

co-membership in international organizations has varying impacts, occasionally actually appearing to increase the probability of a militarized dispute between two countries. The results for IGOs in Oneal and Russett are the weakest of the three Kantian variables, and are signiﬁcant in their main analysis only for politically relevant dyads. However, in a separate paper (Russett, Oneal & Davis 1998) covering the years 1950 to 1985, IGOs are closely linked to reductions in conﬂict.

Figure 2. Posterior distributions of the estimated coeﬃcients for counts of shared membership in IGOs in each of eleven years are displayed as boxplots.

IGO comemberships

1.0

0.5

0.0

−0.5

−1.0

−1.5

1950 1960 1970 1980 1990 2000

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Trade, shown in Figure 3, also shows a very weak linkage to the probability of dispute involvement. Since trade is measured in current dollars, each year has been scaled to permit display on the same scale. Imports generally exert weak downward pressure on the probability of dispute involvement, but this eﬀect is often indistinguishable from zero. In 1955 and 1975 the estimated coeﬃcients have a posterior mean that is positive.

Figure 3. Posterior distributions of the (scaled) estimated coeﬃcients for imports in each of eleven years are displayed as boxplots.

Imports

1950 1960 1970 1980 1990 2000

The results in Table 5 also demonstrate that the higher-order dependencies posited are rampant in the data. These dependencies are represented, in part, by the common sender variance, the sender-receiver covariance, and the common receiver variance. Each is large and important. Taken together, these three components exert a much stronger influence on the probability of a militarized dispute among pairs of countries than the standard covariates. Together they are substantially larger than the error variance. It is also worth noting that the dyadic reciprocity in this particular year is large, a result similar to the large autoregressive coefficients widely reported in empirical literature on the democratic peace. The size of these components serves to underscore the importance of dependencies in these dyadic data on militarized interstate disputes. These results hold in all years.13 Figure 4 illustrates the country level posterior distributions for the level of democracy of the non-initiating country in the MID. This has a slight, positive effect on the probability of involvement in militarized interstate disputes, but this effect had declined over time to become almost negligible in most recent years.14 Predicting Militarized Interstate Disputes. How well does this more elaborate model predict militarized interstate disputes? Figure 5 displays the predicted probabilities for each of the 114 dyadic MIDs in 2000. The dyads arrayed along the x-axis. The data are sorted on the size of the predicted probabilities. Black lines that overlay gray bars may be considered “correct” in-sample predictions of specific dyadic militarized interstate dispute involvement. Since the underlying model is a probability model, in some sense no predictions are “wrong” because even events with very low probabilities happen occasionally. However, most analysts use cut points to assign predictive success to such models. This graphic illustrates that choosing different cut point will affect the number of correctly identified militarized disputes. It also shows that even with very high cut 13 All the results from the generalized bilinear model in each year, as well as plots similar to the above figures may be found on the replication Web Site for this project. 14 Similar results are found for the receiver, but are not presented.

11 Everybody Out of the Pool! February 3, 2006

Figure 4. Posterior distributions of the estimated eﬀects of the country level democracy scores for noninitiators of militarized interstate disputes.

Democracy of non−initiator

−2

1950 1960 1970 1980 1990 2000

points the model’s predictions will identify a large number of MIDs. Similar predictions (not shown) using only the linear covariates and excluding the higher-order terms do not identify a single MID correctly. Thus, the higher-order dependencies enable the model to correctly classify 63 out of 114 militarized interstate disputes (52%, for a cut point of 0.0048), accompanied by only 12 false positives.

Actual MID and Predicted Probability, 2000

1.0

0.8

0.6

0.4

0.2

0.0

Figure 5. Predicting Militarized Interstate Disputes. The light gray lines represent the 114 dyadic MID involvements in the year 2000. The darker lines overlay these MIDs with the predicted probabilities. Thus, black lines on gray lines represent the set of disputes that could be correctly predicted for some cut-point.

We also provide predictions mirroring our earlier experiment with the Oneal & Russett model in Table 6, which reﬂects data for a single year. Thirty-seven disputes are correctly identiﬁed by our model using a cut-point of 0.50, with only six false positives. There is a substantial number of false negatives (77). Using the ex post ante mean to determine the prediction threshold, 63

12 Everybody Out of the Pool! February 3, 2006 correct dyadic MID involvements are predicted, with 12 false positives and 51 false negatives. It appears that model is making reasonable predictions, correctly identifying about one-half of the observed disputes, accompanied by a relatively low rate of false predictions.15 Importantly, of the 75 predicted disputes about 85% are actual disputes. Table 6. The predictions from the bilinear, mixed effects model. Thirty-seven dispute involvements are correctly identified with a 0.50 cut-point, sixty-three when the posterior mean is used. These basic patterns do reflect a model that is accurate, however, in comparison to most published studies.

Cut-point: 0.50 Non-Disputes Disputes Predicted Non-Disputes 23442 77 Predicted Disputes 6 37 Cut-point: 0.0048 Predicted Non-Disputes 23436 51 Predicted Disputes 12 63

Other years have much more modest predictive success. For example, in 1950 (shown in Table 7) only a few militarized dispute involvements are correctly predicted. However, seven disputes are correctly predicted out of a possible 36–almost 20%, accompanied by only three false positives. Even in years that are sparse in the number of MID involvements, the model still performs better than previous models. Table 8 illustrates the predictions of the model for every year using the posterior mean for each year as the cut-point. Table 7. The predictions from the bilinear, mixed eﬀects model for the year 1950. The cut point of 0.0063 is the mean frequency of militarized interstate disputes in 1950.

Cut-point: 0.50 Non-Disputes Disputes Predicted Non-Disputes 5663 33 Predicted Disputes 3 3 Cut-point: 0.0063 Predicted Non-Disputes 5661 29 Predicted Disputes 3 7

By way of summary, we observe that a bilinear, latent space approach allows more coherent heuristics about models that are based on dyadic data. In particular, we learned that it is possible to make new inferences about the democratic peace. Prime among these is that the democratic peace tripod is shakier in some years than in others, and we need to understand better this temporal fragility. It seems most solid in years in which scant conﬂict occurs, but worse in years in which 15 The Brier score is a measure of the predictive accuracy of probability models in the context of binary data, and is widely employed in weather forecasting (Brier 1950); it ranges between 0 and 1 with low scores representing better performance. Since there are so many correctly predicted non-events, the Brier score approaches zero in all models considered. The Brier score for the Oneal and Russett model discussed earlier is 0.009 for the entire period, and 0.007 for the period since 1949. The Brier scores for the current study average 0.003. A similar metric of “ﬁt” is the Proportional Reduction in Error, variously known as the PRE or λP statistic, which is an index of the association between two nominal scales. Using 0.50 as the cut-point yields a PRE in 2000 of 0.27 and 0.45 when the cut-point is set to the posterior mean of 0.0048.

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Table 8. The predictions of the basic bilinear model for each year show a modest improvement in most years over a model that always predicts zero. Predictive success is best in the most recent year.

Correctly Predicted Correctly MID False False Predicted Year Cut-point Involvements Negatives Positives Zeros MIDs Dyads Countries 1950 0.0063 7 29 3 5661 36 5700 76 1955 0.0045 1 29 0 6612 30 6642 82 1960 0.0031 0 34 0 10886 34 10920 105 1965 0.0039 6 50 4 14220 56 14280 120 1970 0.0029 12 36 2 16462 48 16512 129 1975 0.0022 0 42 0 19140 42 19182 139 1980 0.0021 0 40 4 18588 40 18632 137 1985 0.0030 2 54 2 18574 56 18632 137 1990 0.0030 2 53 1 18576 55 18632 137 1995 0.0023 6 49 6 23809 55 23870 155 2000 0.0048 63 51 12 23436 114 23562 154 there is a lot of conflict. Ideally a predictive model of conflict should be as strong when there are more conflicts as when there are fewer. We also learned that interaction dependencies abound in the existing data on the democratic peace. Under the standard approach to the democratic peace, and, we suspect, many other problems in international relations research, second- and third-order dependencies among the data overwhelm the impacts of the standard covariates thought to explain why democracies do not fight one another. This does not mean that empirical theories are incorrect, necessarily. It does mean that they are incomplete if they fail to take into account these contextual dependencies. In particular, we must recognize that countries have a character to their foreign policies that is broadly consistent, imposing a correlation in their actions toward others. Often this is the result of coordination. For example, Gerhard Schröder and Jacques Chirac held informal bilateral dinners every six weeks over the past several years, reportedly in part to coordinate their foreign policies in opposition to the United States. Similarly, some countries elicit similar responses from many others, imposing a correlation in their dyadic behavior patterns. These two new features of the social relations model are missing from most models in international relations, even those that recognize consistent patterns within dyads over time. These results also show that context is neither impossible to take into account systematically, nor solely the domain of qualitative analysis.

Conclusion Let us summarize brieﬂy the results that emerge from our analysis. Our argument has been that the empirical analysis in international relations has proceeded on the basis of (1) a false assumptions that the cases we observe in international relations data sets are independent of each other and are exchangeable, (2) tests of statistical signiﬁcance that can be misleading about the power of the theories being tested, and (3) a consequent neglect of how well a model’s results actually match up to the world it is putatively explaining. As our analysis of the widely accepted results of the democratic peace has shown, the use of pooled cross sectional time series does not obviate these problems. The use of such techniques may indeed control some sources of variation in the data, but what is missing is the recognition of the dependencies that pervade dyadic data about international relations.

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With respect to the dependencies in the data, we employed tools that embrace a standard regression framework, but that also explicitly incorporate important dependencies between and among states. It is apparent that the previously unobserved dependencies are of hugely greater importance in explaining conflict than the variables typically associated with the Democratic Peace. These dependencies between and among states show persistent large effects influencing the results we obtain. The tools we employed allowed us to make substantially improved assessments about the effects of several hypothesized relationships as well as markedly better predictions about the occurrence of militarized interstate disputes. Prediction is a useful heuristic in pointing to the practical as well as theoretical importance of empirical models. Scientists must usually choose among theories that purport to explain the same phenomena. Two of the criteria most often invoked in making such judgements is the theory’s logical rigor and the results of empirical research. A logically coherent theory that does not allow scientists to predict meaningful patterns in the data is a theory that should not generate much confidence among researchers. In that spirit, our analysis should raise some skepticism about the robustness of the Demo- cratic Peace. When dependencies are taken into account, the current results only weakly support the existence of the democratic peace, in spite of the fact that we used data from a period when the democratic peace is thought to be strongest. To be sure, shared democratic political institutions in a dyad does reduce the probability of conflict, but the overall effect is modest. The idea that shared memberships in intergovernmental institutions reduces conflict shows great variation over time, and in recent years actually appears to have a modest positive effect. Finally, support is virtually nonexistent for the idea that high levels of trade dampen conflict. Thus, two legs of the Kantian tripod, as it is termed by Russett, Oneal and Davis (1998), are broken and one is weak.

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Gill, Paramjit S. & Tim B. Swartz. 2001. “Statistical Analyses for Round Robin Interaction Data.” The Canadian Journal of Statistics. La Revue Canadienne de Statistique 29(2):321–331. Gleditsch, Kristian Skrede. 2002. “Expanded Trade and GDP Data.” Journal of Conflict Resolution 46(5):712–724. Gowa, Joanne. 1999. Ballots and Bullets: The Search for the Elusive Democratic Peace. Princeton, N.J.: Princeton University Press. Green, Donald P., Soo Yeon Kim & David H. Loon. 2001. “Dirty Pool.” International Organization 55:441–468. Harary, Frank. 1959. “Graph Theoretic Methods in the Management Sciences.” Management Science 5:387–403. Harary, Frank. 1969. Graph Theory. Reading, MA: Addison-Wesley. Hoff, Peter D. 2005. “Bilinear Mixed Effects Models for Dyadic Data.” Journal of the American Statistical Association 100:286–295. King, Gary. 2001. “Proper Nouns and Methodological Propriety: Pooling Dyads in International Relations Data.” International Organization 55:497–507. Li, Heng & Eric Loken. 2002. “A Unified Theory of Statistical Analysis and Inference for Variance Component Models For Dyadic Data.” Statistica Sinica 12(2):519–535. Maoz, Zeev. 2004. “Pacifish and Fightaholism in International Politics: A Structural History of National and Dyadic Conflict, 1816-1992.” International Studies Review 6(4):107–134. Maoz, Zeev & Nasrin Abdolali. 1989. “Regime Types and International Conflict, 1816-1976.” Journal of Conflict Resolution 33(1):3–35. Morrow, James D. 2002. International Conflict: Assessing the Democratic Peace and Offense-Defense Theory. In Political Science: The State of the Discipline, ed. Ira Katznelson & Helen V. Milner. New York: W. W. Norton & Company pp. 172–196. Oneal, John & Bruce Russett. 1999. “The Kantian Peace: The Pacific Benefits of Democracy, Interdependence, and International Organization.” World Politics 52(1):1–37. Pevehouse, Jon C. & Joshua S. Goldstein. 1999. “Serbian Compliance or Defiance in Kosovo? Statistical Analysis and Real-Time Predictions.” Journal of Conflict Resolution 43(4):538–546. Ray, James. 1998. “Does Democracy Cause Peace.” Annual Review of Political Science 1:27–46. Russett, Bruce M., John R. Oneal & David R. Davis. 1998. “The Third Leg of the Kantian Tripod for Peace: International Organizations and Militarized Disputes, 1950-1985.” International Organization pp. 441–468. Savage, I. Richard. 1957. “Nonparametric Statistics.” Journal of the American Statistical Association 52:331–344. Schrodt, Philip A. 2002. Forecasts and Contingencies: From Methodology to Policy. Annual Meetings of the American Political Science Association Boston, MA: American Political Science Association. Schrodt, Philip A. forthcoming. Forecasting Conflict in the Balkans Using Hidden Markov Models. In Programming for Peace: Computer-Aided Methods for International Conflict Resolution and Prevention, ed. Robert Trappl. Kluwer Academic Publishers. Signorino, Curtis. 1999. “Strategic Interaction and the Statistical Analysis of International Conflict.” American Political Science Review 92(2):279–298. Siverson, Randolph M. 2000. “A Glass Half-Full? No, But Perhaps a Glass Filling: The Contributions of International Politics Research to Policy.” PS: Political Science and Politics XXXIII(1):59–64. Small, Melvin & J. David Singer. 1976. “The War Proneness of Democratic Regimes.” Jerusalem Journal of Inter- national Relations 1(1):49–69. Smith, Alastair. 1999. “Testing Theories of Strategic Choice: The Example of Crisis Escalation.” American Journal of Political Science 43:1254–1283. Ward, Michael D. & Kristian Skrede Gleditsch. 2002. “Location, Location, Location: An MCMC Approach to Modeling the Spatial Context of War and Peace.” Political Analysis 10(3):244–260. Warner, R., David A. Kenny & Michael A. Stoto. 1979. “A New Round Robin Analysis of Variance for Social Interaction Data.” Journal of Personality and Social Psychology 37:1742–1757. Wasserman, Stanley & Katherine Faust. 1994. Social Network Analysis: Methods and Applications. Cambridge: Cambridge University Press. Wong, George Y. 1982. “Round Robin Analysis of Variance via Maximum Likelihood.” Journal of the American Statistical Association 77(380):714–724. Zinnes, Dina A. 1967. “An Analytical Study of the Balance of Power Theories.” Journal of Peace Research 3:270–288.

Appendix A. Data All the data employed in this study, as well as more detailed results from our empirical estimations are available on the replication archive for this project.

A.1. Country Level Data.

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A.1.1. GDP. Data on the annual Gross Domestic Product were taken from Kristian Skrede Gled- itsch’s “Expanded Trade and GDP Data, version 4.1” (2002). These data in 1999 US dollars are available at weber.ucsd.edu/∼kgledits/exptradegdp.html.

A.1.2. Democracy and Autocracy. We use the annualized polity score (called Polity2), which ranges from -10 for highly authoritarian states to +10 for highly democratic societies, to gauge the domestic institutions in each country. These data are available from http://www.cidcm.umd.edu/inscr/ polity/, with registration. Some of these data were updated with information on so-called “micro- states” from the separate database maintained at the University of California at San Diego by Kristian Skrede Gleditsch (2003) Modiﬁed Polity P4 and P4D Data, Version 1.0., available at weber.ucsd.edu/∼kgledits/Polity.html.

A.1.3. Population Data. Data on population were taken from Kristian Skrede Gleditsch’s population data archive, “Expanded Population Data,” University of Essex.

A.2. Dyadic Data.

A.2.1. Militarized Interstate Disputes. We employed the Militarized Interstate Disputes database (version 3.02) which is maintained by Faten Ghosn and D. Scott Bennett, and described in Code- book for the Dyadic Militarized Interstate Incident Data, Version 3.0, 2003. These data and the documentation are available at http://cow2.la.psu.edu/. The dependent variable in this study is the existence of a militarized dispute between any two pairs of countries in a given year, coded as a 1. Senders are those countries designated by the MID data to have ﬁrst initiated action.

A.2.2. Dyadic Democracy. The product of the polity score for any given pair of countries deﬁnes the jointly democratic characteristics of regime types in the two countries.

A.2.3. Trade. Imports were taken from Kristian Skrede Gleditsch’s “Expanded Trade and GDP Data, version 4.1” (2002). These data are available at weber.ucsd.edu/∼kgledits/exptradegdp. html. The trade data are used in billions of current year US dollars.

A.2.4. International Organizations. We used the IGO data on international governmental organizations with at least three independent states as members (Version 2.1) maintained by Jon Pevehouse and Timothy Nordstrom and described in Jon Pevehouse, Timothy Nordstrom, and Kevin Warnke, “Intergovernmental Organizations, 1815-2000: A New Correlates of War Data Set, 2003.” These data are at http://cow2.la.psu.edu/.

A.2.5. Distance. Distance was calculated using the Haversine formula with data on latitude and longitude of capital cities taken from the world.cities database maintained as part of the maps package in the R statistical programming package. These are available from cran.r-project.org. Distance was calculated in 1000s of Kilometers.

A.3. Countries Analyzed. We used all the data available to us for each year, which resulted in a superset of 165 countries over the period from 1950-2000: Afghanistan, Albania, Algeria, Angola, Argentina, Armenia, Australia, Austria, Azerbaijan, Bahrain, Belgium, Benin, Burkina Faso, (Upper Volta), Bhutan, Belarus, Bangladesh, Bolivia, Botswana, Brazil, Burundi, Bulgaria, Cambodia, Canada, Cameroon, Cote D’Ivoire, Central African Republic, Chad, Chile, China, Colombia, Comoros, Congo, Costa Rica, Croatia, Cuba, Cyprus, Czechoslovakia, Czech Republic, Denmark, Djibouti, Dominican Republic, Democratic Republic of Congo (Zaire), Democratic Re- public of Vietnam, Ecuador, Egypt, Equatorial Guinea, Eritrea, Estonia, Ethiopia, Finland, Fiji, France, Gabon, Gambia, German Democratic Republic, German Federal Republic, Ghana, Ger- many, Guinea-Bissau, Greece, Georgia, Guatemala, Guinea, Guyana, Haiti, Honduras, Hungary, India, Indonesia, Ireland, Iran, Iraq, Israel, Italy, Jamaica, Jordan, Japan, Kenya, Kuwait, Kyrgyz

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Republic, Kazakhstan, Laos, Latvia, Liberia, Lebanon, Lesotho, Libya Lithuania, Mauritania, For- mer Yugoslav Republic of Macedonia, Madagascar, Malaysia, Mauritius, Malawi, Mexico, Moldova, Mali, Mongolia, Morocco, Myanmar, Mozambique, Namibia, Nepal, New Zealand, Nicaragua, Nige- ria, Niger, Norway, Netherlands, Oman, Pakistan, Panama, Paraguay, Peru, Philippines, Papua, New Guinea, Poland, Portugal, People’s Republic of Korea, Qatar, Republic of Korea, Romania, Russia, Republic of Vietnam, Rwanda, South Africa, El Salvador, Saudi Arabia, Senegal, Serbia, Sierra Leone, Singapore, Slovakia, Slovenia, Somalia, Spain, Sri Lanka , Sudan, Swaziland, Swe- den, Switzerland, Syria, Tajikistan, Taiwan, Tanzania, Thailand, Turkmenistan, Togo, Trinidad and Tobago, Tunisia, Turkey, United Arab Emirates, Uganda, United Kingdom, Ukraine, Uruguay, United States of America, Soviet Union, Uzbekistan, Venezuela, Arab Republic of Yemen, Yemen, People’s Republic of Yugoslavia (Serbia), Zambia, & Zimbabwe.

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About the authors: Michael D. Ward: Department of Political Science, University of Washington, Seattle, Washington, USA, 98195-3530 E-mail address: [email protected]

Randolph M. Siverson: Department of Political Science, University of California, Davis, One Shields Avenue, Davis, California, USA, 95616 E-mail address: [email protected]

Xun Cao: Department of Political Science, University of Washington, Seattle, Washington, USA, 98195-3530 E-mail address: [email protected]