In This Article Expand or collapse the "in this article" section The Empirical Testing of Formal Models

  • Introduction
  • Journals

International Relations The Empirical Testing of Formal Models
Catherine C. Langlois, Jean-Pierre P. Langlois
  • LAST REVIEWED: 27 February 2019
  • LAST MODIFIED: 25 February 2016
  • DOI: 10.1093/obo/9780199743292-0166


The empirical testing of formal models is a sufficiently wide-ranging subject that even a bibliographical article needs to limit the scope of its coverage. A model will be considered formal if it is laid out in mathematical terms. Such models in political science are often game theoretic. But they can also be based on systems of differential equations or develop a decision theoretic framework. By empirical testing this article refers mostly to the use of large N secondary data to test the assumptions, predictions, or implied processes highlighted by the model. Exception is made to this interpretation when authors develop a series of illustrative case studies to test a formal model, or in cases where formal models are developed for normative and prescriptive purposes. The empirical referent in these latter cases might be the design of a treaty or an international organization and the articles may not include a large N analysis of the referents although the empirical intent of the analysis is clear. The literature on experimental methods is not reviewed here. This article further focuses on attempts to develop theory and empirical testing that help to understand state interaction, political or institutional behavior as it relates to international affairs, or relationships between international parties generally speaking. In such research, the formal theory proposes a rigorous description of an interaction or decision process and the empirical section seeks to provide evidence that the theory offers a valid way of understanding the process or interaction A distinction is made between three main strands in the literature: (1) the identification of requirements for the meaningful empirical testing of a formal model: Is the formal model a full description of the data generating process itself, or is it only a partial descriptor? How is the randomness inherent in any data generation process captured by the formal model? The relationship between the formal and the empirical model, if incorrectly specified, can compromise the relevance of the findings; (2) formal models of conflict and cooperation as support for new hypotheses about relationships in the data. While there are examples of research in which the formal conflict or cooperation equations define the equation to be estimated, it is more likely that the formal models lead to predictions and associations that can be tested in an empirical model that includes additional independent variables. The value of the formal model lies in its ability to predict unexpected relationships that are subsequently revealed in empirical tests that also account for a known set of interactions and dependencies; (3) formal models that seek to establish normative principles and that may or may not use large N empirical testing to assess whether there is empirical evidence that theoretical norms are indeed applied. Most of this literature addresses issues of rational design of cooperative agreements. These categories are further subdivided according to the focus of the formal model.


Journals that publish complex formal models in international relations and the testing of these models include the American Political Science Review, American Journal of Political Science, International Studies Quarterly, Journal of Peace Research, Journal of Politics, Conflict Management and Peace Science, International Interactions, and the Journal of Conflict Resolution.

  • American Journal of Political Science.

    Flagship journal of the Midwest Political Science Association, this journal publishes in all areas of political science and international relations.

  • American Political Science Review.

    This journal is considered to be the leading journal in political science. It publishes in all areas of political science and international relations.

  • Conflict Management and Peace Science.

    Affiliated with the Peace Science Society this journal publishes articles on conflict and cooperation.

  • International Interactions.

    This is an interdisciplinary journal affiliated with the International Studies Association focused on complex international interactions.

  • International Studies Quarterly.

    This is the leading journal affiliated with the International Studies Association and publishes a broad range international relations articles, from the formal to the empirical.

  • Journal of Conflict Resolution.

    Affiliated with the Peace Science Society, this journal focuses on articles related to inter- and intra-state conflict as well as issues of war and peace more generally.

  • Journal of Peace Research.

    A journal of the Peace Research Institute, Oslo, this journal publishes interdisciplinary work on peace and conflict.

  • Journal of Politics.

    Affiliated with the Southern Political Science Association this journal publishes articles of general interest in political science and international relations.

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