1. See Olson, Mancur, The Logic of Collective Action: Public Goods and the Theory of Groups (Cambridge, Mass.: Harvard University Press, 1971)Google Scholar.

2. See the following works by Kindleberger, Charles P.: The World in Depression, 1929–1939 (Berkeley: University of California Press, 1973)Google Scholar; and “Dominance and Leadership in the International Economy: Exploitation, Public Goods, and Free Riders,” International Studies Quarterly 25 (06 1981), pp. 242–54CrossRefGoogle Scholar.

3. In his original study on this topic, Kindleberger argued that a hegemon provides a source of countercyclical liquidity and a market for distressed goods, helps stabilize currencies, serves as a lender of last resort, and ensures an open international trading system. In a subsequent study, he indicated that hegemons also manage foreign exchange rates and coordinate domestic monetary policies. See ibid.

4. See Gilpin, Robert, U.S. Power and the Multinational Corporation: The Political Economy of Foreign Direct Investment (New York: Basic Books, 1975)CrossRefGoogle Scholar; Gilpin, Robert, War and Change in World Politics (New York: Cambridge University Press, 1981)CrossRefGoogle Scholar; Gilpin, Robert, The Political Economy of International Relations (Princeton, N. J.: Princeton University Press, 1987)CrossRefGoogle Scholar; Krasner, Stephen D., “State Power and the Structure of International Trade,” World Politics 28 (04 1976), pp. 317–47CrossRefGoogle Scholar; and Lake, David A., Power, Protection, and Free Trade: International Sources of U.S. Commercial Strategy, 1887–1939 (Ithaca, N. Y.: Cornell University Press, 1988)Google Scholar.

5. Hegemonic stability theorists often posit that hegemony is a necessary, though not a sufficient, condition for the development of a liberal international economic order. For example, Gilpin argues that in addition to hegemony, a “liberal ideology [and] common interests [among the states in the system] must exist for the emergence and expansion of the liberal market system.” See Gilpin, , The Political Economy of International Relations, p. 73; and Gilpin, War and Change in World Politics, chap. 3Google Scholar.

6. See Olson, The Logic of Collective Action.

7. See McKeown, Timothy J., “Hegemonic Stability Theory and 19th-century Tariff Levels in Europe,” International Organization 37 (Winter 1983), pp. 73–91CrossRefGoogle Scholar; Keohane, Robert O., After Hegemony: Discord and Collaboration in the World Political Economy (Princeton, N. J.: Princeton University Press, 1984)Google Scholar; and Snidal, Duncan, “The Limits of Hegemonic Stability Theory,” International Organization 39 (Autumn 1985), pp. 579–614CrossRefGoogle Scholar.

8. See Conybeare, John A. C., “Public Goods, Prisoners Dilemmas and the International Political Economy,” International Studies Quarterly 28 (03 1984), pp. 5–22CrossRefGoogle Scholar; Conybeare, John A. C., Trade Wars: The Theory and Practice of International Commercial Rivalry (New York: Columbia University Press, 1987)Google Scholar; Russett, Bruce, “The Mysterious Case of Vanishing Hegemony; or, Is Mark Twain Really Dead?” International Organization 39 (Spring 1985), pp. 205–31CrossRefGoogle Scholar, and Snidal, “The Limits of Hegemonic Stability Theory.”

9. See Conybeare, “Public Goods, Prisoners' Dilemmas and the International Political Economy”;and Conybeare, Trade Wars.

10. See Gowa, Joanne, “Rational Hegemons, Excludable Goods, and Small Groups: An Epitaph for Hegemonic Stability Theory?” World Politics 41 (04 1989), p. 322CrossRefGoogle Scholar. In addition, Spiro argues that these critiques need not undermine hegemonic stability theory, since rather than expecting a relationship between hegemony and economic outcomes, we should expect variations in the nature of power that is exercised during different phases of hegemony. See Spiro, David E., “American Foreign Policy and International Finance,” in Art, Robert and Brown, Seyom, eds., American Foreign Policy After the Cold War (New York: Macmillan, forthcoming)Google Scholar.

11. Conybeare, John A. C., “Tariff Protection in Developed and Developing Countries: A Cross-Sectional and Longitudinal Analysis,” International Organization 37 (Summer 1983), pp. 441–67CrossRefGoogle Scholar.

12. McKeown, Timothy J., “A Liberal Trade Order? The Long-Run Pattern of Imports to the Advanced Capitalist States,” International Studies Quarterly 35 (06 1991), pp. 151–72CrossRefGoogle Scholar.

13. See McKeown, Hegemonic Stability Theory and 19th-century Tariff Levels in Europe; Stein, Arthur A., “The Hegemons Dilemma: Great Britain, the United States, and the International Economic Order,” International Organization 38 (Spring 1984), pp. 355–86CrossRefGoogle Scholar; Gallarotti, Giulio M., “Toward a Business Cycle Model of Tariffs,” International Organization 39 (Winter 1985), pp. 155–87CrossRefGoogle Scholar; and Strange, Susan, “The Persistent Myth of Lost Hegemony,” International Organization 41 (Autumn 1987), pp. 551–74CrossRefGoogle Scholar.

14. See Keohane, Robert O., “The Theory of Hegemonic Stability and Changes in International Economic Regimes, 1967–1977, ” in Holsti, Ole R., Siverson, Randolph M., and George, Alexander L., eds., Change in the International System (Boulder, Colo.: Westview Press, 1980), pp. 131–62Google Scholar. Gilpin also notes the inability of hegemonic stability theory “to demonstrate a close association between power and outcome.” And Lake argues that because hegemonic stability theory “lacks a conception of process, or an explanation of how the constraints or interests derived from the international economic structure are transformed into decisions or political strategies within particular countries the causal link between the system-level international economic structure and national-level policy is open to question.” See Gilpin, , The Political Economy Of International Relations, p. 91Google Scholar; and Lake, David A., “International Economic Structure and American Foreign Economic Policy,” World Politics 35 (07 1983), pp. 539–40CrossRefGoogle Scholar. See also Nye, Joseph S., Bound to Lead: The Changing Nature of American Power (New York: Basic Books, 1990)Google Scholar.

15. See Russett, “The Mysterious Case of Vanishing Hegemony.” See also McKeown, “Hegemonic Stability Theory and 19th-century Tariff Levels in Europe”; Keohane, After Hegemony; Nye, Bound to Lead; Strange, “The Persistent Myth of Lost Hegemony”; and Strange, Susan, States and Markets (New York: Basil Blackwell, 1988)Google Scholar.

16. See Russett, “The Mysterious Case of Vanishing Hegemony”; and Nye, Bound to Lead.

17. See, for example, Gilpin, U.S. Power and the Multinational Corporation; Gilpin, War and Change in World Politics; Gilpin, The Political Economy of International Relations; Russett, “The Mysterious Case of Vanishing Hegemony”; Wallerstein, Immanuel, “Three Instances of Hegemony in the History of the Capitalist World-Economy,” International Journal of Comparative Sociology. vol. 24, no. 1–2, 1983, pp. 100–108CrossRefGoogle Scholar; and Kennedy, Paul M., The Rise and Fall of the Great Powers: Economic Change and Military Conflict from 1500 to 2000 (New York: Random House, 1987)Google Scholar.

18. See, for example, Krasner, “State Power and the Structure of International Trade”;Keohane, After Hegemony; and Lake, Power, Protection, and Free Trade. In addition, some scholars (particularly those who study war, rather than the international political economy) place less emphasis on economic power and define hegemony as a preponderance of political-military power. See Doran, Charles F. and Parsons, Wes, “War and the Cycle of Relative Power,” American Political Science Review 74 (12 1980), pp. 947–65CrossRefGoogle Scholar; Levy, Jack S., “The Polarity of the System and International Stability: An Empirical Analysis,” in Sabrosky, Alan Ned, ed., Polarity and War (Boulder, Colo.: Westview Press, 1985), pp. 41–66Google Scholar; Modelski, George, “The Long Cycle of Global Politics and the Nation-State,” Comparative Studies in Society and History 20 (04 1978), pp. 214–35CrossRefGoogle Scholar; Modelski, George and Thompson, William R., Sea Power in Global Politics, 1494–1983 (Seattle: University of Washington Press, 1987)Google Scholar; Organski, A. F. K., World Politics (New York: Knopf, 1958)Google Scholar; and Organski, A. F. K. and Kugler, Jacek, The War Ledger (Chicago: University of Chicago Press, 1980)Google Scholar. Still others differentiate between economic and political-military hegemony. See, for example, Goldstein, Joshua S., Long Cycles (New Haven, Conn.: Yale University Press, 1988)Google Scholar. Hence, the types of power that are emphasized in the definition and operationalization of hegemony appear to be determined, in large measure, by the issue-area that is being studied. Further, some scholars of the international political economy argue that dimensions of hegemony other than political and economic power must also be considered. For example, Russett and Nye highlight the importance of cultural aspects of hegemony, and Ikenberry and Kupchan argue that hegemons exercise control by socializing elites in secondary states. See Russett, “The Mysterious Case of Vanishing Hegemony”; Nye, Bound to Lead; and Ikenberry, G. John and Kupchan, Charles A., “Socialization and Hegemonic Power,” International Organization 44 (Summer 1990), pp. 283–316CrossRefGoogle Scholar. Despite their potential importance, these dimensions of hegemony are not considered in the present analysis because of the difficulty of operationalizing and measuring them.

19. For a more complete discussion of the importance of specifying the scope and domain of power in analyses of international relations, see Baldwin, David A., “Power Analysis and World Politics: New Trends Versus old Tendencies,” World Politics 31 (01 1979), pp. 161–94CrossRefGoogle Scholar.

20. See Haggard, Stephan and Simmons, Beth A., “Theories of International Regimes,” International Organization 41 (Summer 1987), p. 503CrossRefGoogle Scholar. See also Keohane, After Hegemony; Stein, “The Hegemon's Dilemma”; and Nye, Bound to Lead.

21. See McKeown, “Hegemonic Stability Theory and 19th-century Tariff Levels in Europe”; Russett, , “The Mysterious Case of Vanishing Hegemony”; and Frey, Frederick W., “The Distribution of Power in Political Systems,” paper presented at the annual meeting of the American Political Science Association, Washington, D. C., 1986Google Scholar.

22. See Lake, Power, Protection, and Free Trade.

23. See Conybeare, “Tariff Protection in Developed and Developing Countries”; and McKeown, “A Liberal Trade Order?”.

24. See Mansfield, Edward D., “International Trade and the Onset of War,” paper presented at the annual meeting of the American Political Science Association, Atlanta, Ga., 1989Google Scholar. The data are found in Gilpin's War and Change in World Politics and The Political Economy of International Relations and in Wallerstein's “Three Instances of Hegemony in the History of the Capitalist World-Economy”.

25. The index of concentration used in my study is based on the work of Ray and Singer. See Ray, James Lee and Singer, J. David, “Measuring the Concentration of Power in the International System,” Sociological Methods and Research 1 (05 1973), pp. 403–37CrossRefGoogle Scholar.

26. Hence, CON measures the “standard deviation of the percentage shares [divided by] the maximum possible standard deviation in a system of size N.” See Ray and Singer, ibid., p. 422.

27. See Mansfield, Edward D., “The Concentration of Capabilities and the Onset of War,” Journal of Conflict Resolution 36 (03 1992), pp. 3–24CrossRefGoogle Scholar.

28. Of course, this assumes that V > 0.

29. See Russett, Bruce M. and Sullivan, John D., “Collective Goods and International Organization,” International Organization 25 (Autumn 1971), pp. 845–65CrossRefGoogle Scholar; Snidal, Duncan, “Coordination Versus Prisoners' Dilemma: Implications for International Cooperation and Regimes,” American Political Science Review 79 (12 1985), pp. 923–2CrossRefGoogle Scholar; and Snidal, “The Limits of Hegemonic Stability Theory”.

30. See, for example, Russett and Sullivan, “Collective Goods and International Organization”.

31. One reason for examining the interactive effects of these variables via concentration (rather than via some other variable that is a function of both N and V) is that although concentration has received little attention in studies of the international political economy, many analyses of war have used concentration to measure the distribution of power. See Singer, J. David, Bremer, Stuart, and Stuckey, John, “Capability Distribution, Uncertainty, and Major Power Wars, 1820–1965,” in Russett, Bruce M., ed., Peace, War, and Numbers (Beverly Hills, Calif.: Sage, 1972), pp. 19–48Google Scholar; de Mesquita, Bruce Bueno, “Risk, Power Distributions, and the Likelihood of War,” International Studies Quarterly 25 (12 1981), pp. 541–68CrossRefGoogle Scholar; Thompson, William R., “Cycles, Capabilities, and War: An Ecumenical View,” in Thompson, William R., ed., Contending Approaches to World System Analysis (Beverly Hills, Calif.: Sage, 1983), pp. 141–63Google Scholar; de Mesquita, Bruce Bueno and Lalman, David, “Empirical Support for Systemic and Dyadic Explanations of International Conflict,”World Politics 41 (10 1988), pp. 1–20CrossRefGoogle Scholar; and Mansfield, “The Concentration of Capabilities and the Onset of War.” To my knowledge, the only study that analyzes the relationship between concentration and trade was conducted by McKeown. However, his analysis differs from the present study in a number of important ways. First, McKeown uses a different set of capabilities and major powers than I do to measure concentration. Second, his model is specified differently than mine. He examines the effects of the following on the ratio of imports to gross national product for industrialized capitalist countries: (1) the concentration of capabilities; (2) the percentage of global imports that the largest importer accounts for (TCON1); (3) the percentage of international imports that Great Britain, the United States, France, (West) Germany, and Japan account for (TCON5); (4) the ratio of TCON1 to TCON5; (5) the ratios of the nominal inome of Great Britain and the United States, respectively, to that of the other leading states in the system; (6) time; (7) the growth of nominal income; and (8) a lagged dependent variable. See McKeown, “A Liberal Trade Order?”.

32. See Waterson, Michael, Economic Theory of the Industry (Cambridge: Cambridge University Press, 1984), pp. 166–67Google Scholar. See also Scherer, F. M., Industrial Market Structure and Economic Performance, 2d ed. (Chicago: Rand McNally, 1979), pp. 56–59Google Scholar.

33. Conybeare, , Trade Wars, p. 287, fn. 4Google Scholar.

34. See Ray, and Singer, , “Measuring the Concentration of Power in the International System,” p. 430Google Scholar. For the original derivation of the Hirschman-Herfindahl index (HH), see Albert O. Hirschman, National Power and the Structure of Foreign Trade (1945; reprint, Berkeley: University of California Press,1980), pp. xviii-xx, 87–88, and 157–62). The equation for this index is as follows:

35. See Olson, The Logic of Collective Action.

36. In particular, Lake focuses on the United States, the United Kingdom, Germany, and France. Japan is also considered, beginning in 1950. See Lake, Power, Protection, and Free Trade, p. 33. For a critique of hegemonic stability theory that also centers on the effects of inequality, see Russett, “The Mysterious Case of Vanishing Hegemony”.

37. Conybeare, , Trade Wars, p. 26Google Scholar.

38. For a fuller discussion of this issue, see ibid.; Ethier, Wilfred, Modern International Economics (New York: Norton, 1983)Google Scholar; and Gowa, Joanne, “Bipolarity, Multipolarity, and Free Trade,” American Political Science Review 83 (12 1989), pp. 1245–56CrossRefGoogle Scholar.

39. See Conybeare, “Public Goods, Prisoners' Dilemmas and the International Political Economy”; and Conybeare, Trade Wars. This, of course, assumes that a state's political power is roughly proportional to its market power—that is, to its ability to influence its terms of trade. The extent to which this is the case is an empirical question beyond the scope of this article. However, it is an assumption that is made often and one that seems reasonable for the purposes of a first cut a the problem.

40. See Keohane, After Hegemony; Axelrod, Robert and Keohane, Robert O., “Achieving Cooperation Under Anarchy: Strategies and Institutions,” World Politics 38 (10 1985), pp. 226–54CrossRefGoogle Scholar; Hardin, Russell, Collective Action (Baltimore, Md.: Johns Hopkins University Press, 1982)Google Scholar; Lipson, Charles, “International Cooperation in Economic and Security Affairs,” World Politics 37 (10 1984), pp. 1–23CrossRefGoogle Scholar; Oye, Kenneth A., “Explaining Cooperation Under Anarchy: Hypotheses and Strategies,” World Politics 38 (10 1985), pp. 1–24CrossRefGoogle Scholar; and Schelling, Thomas C., Micromotives and Macrobehavior (New York: Norton, 1978), pp. 211–43Google Scholar.

41. See the following works of Waltz, Kenneth N.: “The Myth of National Interdependence,” in Kindleberger, Charles P., ed., The International Corporation (Cambridge, Mass.: MIT Press, 1970), pp. 205–23Google Scholar; and Theory of International Politics (New York: Random House, 1979)Google Scholar.

42. Of course, this assumes that larger states will not band together to deter each other from imposing optimal tariffs. Under these circumstances, the level of protectionism may remain relatively low.

43. See Gowa, “Rational Hegemons, Excludable Goods, and Small Groups”; and Gowa, “Bipolarity, Multipolarity, and Free Trade”.

44. See Gowa, , “Rational Hegemons, Excludable Goods, and Small Groups,” p. 311Google Scholar, fn. 12. See also Conybeare, “Public Goods, Prisoners' Dilemmas and the International Political Economy”; and Conybeare, Trade Wars.

45. See Hirschman, National Power and the Structure of Foreign Trade.

46. See Conybeare, “Public Goods, Prisoners' Dilemmas and the International Political Economy”; and McKeown, “Hegemonic Stability Theory and 19th-century Tariff Levels in Europe”.

47. Of course, I am only considering the range of variation of concentration found in the data. For example, if the world consisted entirely of two countries, one with few inhabitants, few resources, and little capital, and the other with the remainder of the world's population, resources, and capital, one would expect practically all trade to be intranational and the level of international commerce to be relatively small, even though the level of concentration might be quite high.

48. For discussions of the impact of war on trade, see Kindleberger, Charles P., Foreign Trade and the National Economy (New Haven, Conn.: Yale University Press, 1966)Google Scholar; Leamer, Edward E. and Stern, Robert M., Quantitative International Economics (Boston: Allyn & Bacon, 1970), p. 15Google Scholar; Krasner, “State Power and the Structure of International Trade”; Stein, “The Hegemon's Dilemma”; and Strange, States and Markets. Although I am unaware of any empirical research on the effect of war on trade at the systemic level, Brian Pollins found that among dyads of nations during the period after World War II, higher levels of conflict led to lower levels of trade. However, because wars constitute only a small subset of the conflict-events data that Pollins uses and because results at the dyadic level may diverge from those at the systemic level, it is worthwhile to examine this relationship further. See the following works of Pollins, Brian M.: “Conflict, Cooperation, and Commerce: The Effect of International Political Interactions on Bilateral Trade Flows,” American Journal of Political Science 33 (08 1989), pp. 737–61CrossRefGoogle Scholar; and “Does Trade Still Follow the Flag?” American Political Science Review 83 (06 1989), pp. 465–80CrossRefGoogle Scholar.

49. See Strange, , States and Markets, p. 167Google Scholar. See also Stein, “The Hegemon's Dilemma”.

50. See Cowhey, Peter F. and Long, Edward, “Testing Theories of Regime Change: Hegemonic Decline or Surplus Capacity,” International Organization 37 (Spring 1983), pp. 157–88CrossRefGoogle Scholar; Gowa, Joanne, “Hegemons, IOs, and Markets: The Case of the Substitution Account,” International Organization 38 (Autumn 1984), pp. 661–83CrossRefGoogle Scholar; Stein, “The Hegemon's Dilemma”; Gallarotti, “Toward a Business Cycle Model of Tariffs”; Cassing, James, McKeown, Timothy J., and Ochs, Jack, “The Political Economy of the Tariff Cycle,” American Political Science Review 80 (09 1986), pp. 843–62CrossRefGoogle Scholar; Strange, “The Persistent Myth of Lost Hegemony”; and McKeown, “A Liberal Trade Order?” A number of hegemonic stability theorists have also concluded that more attention needs to be paid to the economic determinants of trade. See Krasner, “State Power and the Structure of International Trade”; and Gilpin, , The Political Economy of International Relations, p. 91Google Scholar.

51. See Kindleberger, Foreign Trade and the National Economy.

52. See ibid.

53. It should be noted, however, that to the extent that V and N predict the level of global protectionism and that this variable, in turn, predicts the level of global trade, the level of global protectionism is endogenized. Under these circumstances, the lack of data on this variable does not pose a problem.

54. The data on global income are expressed in real terms and are adapted from Maddison's, AngusPhases of Capitalist Development (New York: Oxford University Press, 1982)Google Scholar. See my footnote 65, below, for a fuller explanation.

55. See Krasner, “State Power and the Structure of International Trade”; Gallarotti, “Toward a Business Cycle Model of Tariffs”; Cassing, McKeown, and Ochs, “The Political Economy of the Tariff Cycle”; and McKeown, “A Liberal Trade Order?”.

56. On this point, see Kindleberger, , Foreign Trade and the National Economy, p. 89Google Scholar. Of course, as aggregate gross domestic product increases, the supply curves for imports may shift and this may be of consequence, too.

57. See ibid.; Kuczynski, Thomas, “Have There Been Differences Between the Growth Rates in Different Periods of the Development of the Capitalist World Economy Since 1850?” in Clubb, J. M and Scheuch, E. K., eds., Historical Social Research (Stuttgart: Klett-Cotta, 1980), pp. 300–316Google Scholar; Maddison, Phases of Capitalist Development; and Deardorff, Alan V. and Stern, Robert M., “Current Issues in Trade Policy: An Overview,” in Stern, Robert M., ed., U.S. Trade Policies in a Changing World Economy (Cambridge, Mass.: MIT Press, 1987), pp. 15–68Google Scholar.

^58. For a discussion of the increase in global income over time, see Maddison, Phases of Capitalist Development. I chose not to use both time and global income as independent variables, since they are highly collinear (r ² = .82).

59. Bhagwati, Jagdish, Protectionism (Cambridge, Mass.: MIT Press, 1988), pp. 5–6Google Scholar.

60. Figures provided by Kuczynski are used for this purpose. See Kuczynski, , “Have There Been Differences Between the Growth Rates in Different Periods of the Development of the Capitalist World Economy Since 1850?” p. 312Google Scholar. Since for the world as a whole exports must equal imports, this variable will provide an estimate of aggregate international commerce. It should be pointed out that hegemonic stability theorists do not agree as to whether the focus of this theory should be the explanation of trade (and other) outcomes in the international political economy or policy instruments and outcomes (such as tariffs, quotas, and subsidies). On this point, see McKeown, “A Liberal Trade Order?”; and David A. Lake, “The Theory of Hegemonic Stability: An Interim Report,” paper presented at the Fifteenth World Congress of the International Political Science Association, Buenos Aires, 1991. I will restrict my attention to trade outcomes and, in particular, to the level of international trade, since there is little data on tariff levels and other policy instruments for much of the period analyzed in my study and since many noted experts agree with Hirschman's assertion that “international trade [is] the most important constituent of international economic relations.” See Hirschman, , National Power and the Structure of Foreign Trade, p. xviGoogle Scholar. It is clear, however, that trade flows and trade policy need not move in tandem. Consequently, the results of my study may not apply uniformly to all variants of hegemonic stability theory.

61. The effects of hegemony and concentration are lagged because, as Hart points out, “the core propositions in…[hegomonic stability theory] state that a change in the distribution of power at time t causes a change in international outcomes at time t + 1.” See Hart, Jeffrey A., “Polarity, Hegemony and the Distribution of Power,” paper presented at the annual meeting of the American Political Science Association, Washington, D. C., 1986, p. 15Google Scholar.

62. To illustrate this procedure, consider the data for 1900. In this case, Hegemony, CON, CON ², N, and V are measured in 1900; and delta CON and MOVE are measured from 1895 to 1900. Trade is measured in 1901, 1903, and 1905 (one-year, three-year, and five-year lags); Warfare is measured in the same years as Trade; and GDP is measured in 1900 (when Trade is lagged by one year), 1902 (when Trade is lagged by three years), and 1904 (when Trade is lagged by five years).

63. Gilpin classifies the periods from 1815 to 1914 (Great Britain) and from 1945 to 1980 (the United States) as hegemonic. Gilpin does not actually date the end of U.S. hegemony, but this is not important for present purposes, since my study does not cover the period after 1965 and it is not until around 1980 that the ending date becomes an issue for Gilpin. Wallerstein classifies the periods from 1625 to 1672 (United Provinces of the Netherlands), from 1815 to 1873 (Great Britain), and from 1945 to 1967 (the United States) as hegemonic. Although this is only a sample of scholars who have conducted research on the effects of hegemony, it should provide some idea as to whether different definitions of hegemony produce different empirical results. See Gilpin, War and Change in World Politics; Gilpin, The Political Economy of International Relations; and Wallerstein, “Three Instances of Hegemony in the History of the Capitalist World-Economy”.

64. See Levy, Jack S., War in the Modern Great Power System, 1495–1975 (Lexington: University Press of Kentucky, 1983)Google Scholar.

65. See Maddison, , Phases of Capitalist Development, pp. 86 and 170Google Scholar. Maddison provides data on the annual change in the aggregate level of gross domestic product for sixteen leading countries from 1871 to 1981. These data are used to construct an index of the level of GDP by setting the level of GDP in 1870 equal to 100. The level of GDP is computed for each subsequent year t by multiplying the value of the index in the preceding year t - 1 by the change in GDP from t - 1 to t. Maddison also provides data on the annual change in gross domestic product for some of the sixteen countries from 1850 to 1869. I determined the (unweighted) average annual rate of change for those countries for which data are available and used the procedure described above to compute the level of GDP from 1850 to 1869. It should be noted that if the rates of change in GDP among these sixteen countries differ markedly from those of the remaining states in the system, this index may not reflect global income. However, I am unaware of any more complete data on global income than those developed by Maddison.

66. Each of these components was weighted equally in arriving at values for concentration. For the iron and steel production component, iron was used until 1895; thereafter, steel was used. The index of Ray and Singer is described in their article “Measuring the Concentration of Power in the International System.” Singer, Bremer, and Stuckey list the following nations as major powers: Austria-Hungary (1816–1918); Prussia/Germany (1816–1870, 1871–1918, and 1925–1945); Russia/Soviet Union (1816–1917 and 1922-present); France (1816–1940 and 1945-present); England (1816–present); Italy (1860–1943); Japan (1895–1945); the United States (1898–present); and China (1949–present). See Singer, Bremer, and Stuckey, “Capability Distribution, Uncertainty, and Major Power Wars, 1820–1965”; Singer, J. David and Small, Melvin, The Wages of War, 1816–1965: A Statistical Handbook (New York: Wiley, 1972)Google Scholar; and Small, Melvin and Singer, J. David, Resort to Arms: International and Civil Wars, 1816–1980 (Beverly Hills, Calif.: Sage, 1982)Google Scholar.

67. See Singer, Bremer, and Stuckey, “Capability Distribution, Uncertainty, and Major Power Wars, 1820–1965.” In their analysis and in the present study, five-year periods were used in all cases except the following: 1910–1912, 1913–1919, 1935–1937, 1938–1945, and 1946–1949. These exceptions were made to avoid distorting the values of the indices by measuring the major powers' capabilities during World Wars I and II.

68. See March, James G., “The Power of Power,” in Easton, David, ed., Varieties of Political Theory (Englewood Cliffs, N. J.: Prentice-Hall, 1966), pp. 39–70Google Scholar. See also Dahl, Robert A., Modem Political Analysis, 3d ed. (Englewood Cliffs, N. J.: Prentice-Hall, 1976)Google Scholar; Frey, Frederick W., “Comment: On Issues and Nonissues in the Study of Power,” American Political Science Review 65 (12 1971), pp. 1081–1104CrossRefGoogle Scholar; Frey, “The Distribution of Power in Political Systems”; Baldwin, David A., “Interdependence and Power: A Conceptual Analysis,” International Organization 34 (Autumn 1980), pp. 471–506CrossRefGoogle Scholar; Baldwin, “Power Analysis and World Politics”; and Keohane, After Hegemony. It should be noted that there are also potential drawbacks associated with using energy consumption and iron and steel production as indicators of economic strength. On these drawbacks, see Organski and Kugler, The War Ledger; Moul, William B., “Measuring the ‘Balance of Power’: A Look at Some Numbers,” Review of International Studies 15 (04 1989), pp. 101–21CrossRefGoogle Scholar; and Oneal, John R., “Measuring the Material Base of the Contemporary East-West Balance of Power,” International Interactions, vol. 15, no. 2, 1989, pp. 177–96CrossRefGoogle Scholar.

69. In any regression analysis, two problems that might arise are autocorrelation of the residuals and heteroskedasticity. The Durbin-Watson statistics (shown in Table 1) indicate that there is no clear evidence that the disturbances are characterized by a first-order autoregressive [AR(1)] process. Rao and Griliches argue that for small samples, methods that correct for first-order autocorrelation will provide better estimates than will ordinary least squares when the absolute value of rho (the estimate of the first-order correlation among the residuals) is greater than or equal to 0.3. See Rao, Potluri and Griliches, Zvi, “Small-Sample Properties of Several Two-Stage Regression Methods in the Context of Auto-Correlated Errors,” Journal of the American Statistical Association 64 (03 1969), pp. 253–72CrossRefGoogle Scholar. The only instance in which the absolute value of rho is greater than or equal to 0.3 is when Gilpin's data on hegemony and a one-year lag are used. To correct for first-order autocorrelation in this case, generalized least squares estimates were generated. For a description of this procedure, see Hibbs, Douglas A., “Problems of Statistical Estimation and Causal Inference in Time-Series Regression Models,” in Costner, Herbert L., ed., Sociological Methodology, 1973–1974 (San Francisco: Jossey-Bass, 1974), pp. 252–308Google Scholar; Gallant, Ronald and Goebel, J. Jeffery, “Nonlinear Regression with Autocorrelated Errors,” Journal of the American Statistical Association 71 (12 1976), pp. 961–67CrossRefGoogle Scholar; Hanushek, Eric A. and Jackson, John E., Statistical Methods for Social Scientists (New York: Academic Press, 1977), pp. 141–78CrossRefGoogle Scholar; and Harvey, A. C., The Econometric Analysis of Time Series (Oxford: Halsted Press, 1981), pp. 189–220Google Scholar. While these results do not differ markedly from those in Table 1, the t-statistics of each coefficient are larger for the generalized least squares estimates than for the ordinary least squares estimates. Of particular interest is the increase in the value of the t-statistic of Hegemony from 1.56 (p = .14) to 1.91 (p = .08). To test for heteroskedasticity, the squares of the residuals were regressed on each of the independent variables and their squares, and an F-test of the regression was conducted. In no case was there any evidence of heteroskedasticity. For a description of this test, see White, Halbert, “A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity,” Econometrica 48 (05 1980), pp. 817–38CrossRefGoogle Scholar; Maddala, G. S., Introduction to Econometrics (New York: Macmillan, 1988), pp. 162–63Google Scholar; and Kelejian, Harry H. and Oates, Wallace E., Introduction to Econometrics: Principles and Applications, 3d ed. (New York: Harper & Row, 1989), pp. 240–42Google Scholar. It should also be pointed out that there is little evidence of multicollinearity among the independent variables in equation 3, since the estimated coefficients are generally statistically significant and tend to remain stable when variables are omitted from the model.

70. When the model is corrected for first-order autocorrelation, the regression coefficient of Hegemony is also statistically significant (at the .10 level) using Gilpin's data and a one-year lag. See footnote 69, above.

71. The values of Trade in Table 2 were estimated using Gilpin's data and a three-year lag because this is the only specification of equation 3 in which all of the regression coefficients are statistically significant (see Table 1). The values of N and V in Table 2 correspond roughly to the range of values that they take on during the period covered in this study.

72. After wars are concluded, it may take time for nations to reallocate resources from sectors of the economy that are vital for fighting a war to commercial sectors, and trade with former adversaries may not be quickly reestablished. As a result, the relationship between trade and the termination of war may be inverse. However, if nations rely on trade to help repair and revitalize their war-torn economies, the relationship may be direct.

73. The value of this variable Warfare_o, is determined by the number of wars between major powers ending in the five years prior to the year in which Trade is measured.

74. Economists often use the deviation from the secular trend in gross domestic product as a measure of short-term fluctuations in the business cycle. See, for example, Lucas, Robert, “Some International Evidence on Output-Inflation Tradeoffs,” American Economic Review 63 (06 1973), pp. 326–34Google Scholar; Lucas, Robert, Studies in Business Cycle Theory (Cambridge, Mass.: MIT Press, 1981)Google Scholar; and Zarnowitz, Victor, “Recent Work on Business Cycles in Historical Perspective: A Review of Theories and Evidence,” Journal of Economic Literature 23 (06 1985), pp. 523–80Google Scholar. A one-year lag is used to avoid problems of simultaneity between GDP and Trade.

75. See, for example, Snyder, Glenn H. and Diesing, Paul, Conflict Among Nations: Bargaining, Decision Making, and System Structure in International Crises (Princeton, N. J.: Princeton University Press, 1977)Google Scholar; and Waltz, Theory of International Politics.

76. See Waltz, “The Myth of National Interdependence”; and Waltz, Theory of International Politics.

77. For a discussion of the relationship between polarity and concentration, see Mansfield, Edward D., “Measuring the International Distribution of Power,” paper presented at the Fifteenth World Congress of the International Political Science Association, Buenos Aires, 1991Google Scholar.

78. See McKeown, , “A Liberal Trade Order?” p. 163Google Scholar.

79. This test (rather than, for example, an analysis-of-variance test) is appropriate because the number of observations after World War II (4) does not exceed k + 1(10), where k is the number of independent variables in the model. See Maddala, , Introduction to Econometrics, pp. 134–36Google Scholar.

80. A number of points should be made concerning predictive tests of this sort. First, because the number of observations after World War II is less than k + 1, it may be more appropriate to think of these tests as tests of unbiasedness in prediction (in other words, tests of whether or not the prediction error has a mean equal to 0), rather than as tests of stability. Second, predictive tests of stability assume that the variance-of-error term for one period is equal to that for the other period. Finally, although these tests indicate that the model is stable over time, this does not deny the fact that the effects of some of the individual coefficients may have changed over time. For a fuller explanation of these points, see Maddala, , Introduction to Econometrics, p. 136Google Scholar.

81. See Gowa, “Bipolarity, Multipolarity, and Free Trade”.

82. See, for example, Waltz, Theory of International Politics; and Gilpin, The Political Economy of International Relations.

83. See Snidal, Duncan, “Relative Gains and the Pattern of International Cooperation,” American Political Science Review 85 (09 1991), pp. 701–26CrossRefGoogle Scholar.

84. Conybeare notes that dominant states often did not impose optimal tariffs during the nineteenth and twentieth centuries, but he argues that this era is exceptional in this regard. See Conybeare, , Trade Wars, pp. 271–72Google Scholar.

85. See Krasner, “State Power and the Structure of International Trade.” According to Krasner, the opportunity costs are so large because each state derives benefits from an open system and smaller powers have difficulty existing under conditions of autarky.

86. Ibid, pp. 321–22.

87. Gilpin, , The Political Economy of International Relations, p. 57Google Scholar.

88. Stein, , “ The Hegemon's Dilemma,” p. 385Google Scholar.

89. It is clear, however, that this model of international trade suffers from a number of limitations. First, using material capabilities to measure power is admittedly crude, and the causal linkages between the concentration of capabilities and international trade are not clearly demonstrated. Second, no distinction is made between exports of manufactured goods and exports of agricultural goods. And, third, the model does not account for the effects of domestic factors on international trade. Although it is beyond the scope of this article to address these issues, it would be useful to consider them in future research on this topic.

90. On this point, see Hart, “Polarity, Hegemony and the Distribution of Power”.

91. For analyses that do take the influence of international politics into account, see Roemer, John E., “The Effect of Sphere of Influence and Economic Distance on the Commodity Composition of Trade in Manufactures,” Review of Economics and Statistics 59 (08 1977), pp. 318–27CrossRefGoogle Scholar; and Green, Robert T. and Lutz, James M., The United States and World Trade (New York: Praeger, 1978)Google Scholar. I am grateful to an anonymous reviewer for bringing these studies to my attention. For further discussions of the need to consider the influence of international politics on trade, see Cohen, Benjamin J., “The Political Economy of International Trade,” International Organization 44 (Spring 1990), pp. 261–81CrossRefGoogle Scholar; and Odell, John S., “Understanding International Trade Policies: An Emerging Synthesis,” World Politics 43 (10 1990), pp. 139–67CrossRefGoogle Scholar.