Opposites Attract? Opportunities and Challenges for Integrating Large-N QCA and Econometric Analysis

AbstractContrasting insights that can be gained from large-N QCA and econometric analysis, we outline two novel ways to integrate both modes of inquiry. The first introduces QCA solutions into a regression model, while the second draws on recent work in lattice theory to integrate a QCA approach with a regression framework. These approaches allow researchers to test QCA solutions for robustness, address concerns regarding possible omitted variables, establish effect sizes, and test whether causal conditions are complements or substitutes, suggesting that an important way forward for set-theoretic analysis lies in an increased dialogue that explores complementarities with existing econometric approaches. (ProQuest: . denotes formula omitted.)IntroductionIn its original statement by Charles Ragin (1987), Qualitative Comparative Analysis (QCA) was conceived as a methodology for small-N, comparative work in the case-oriented tradition; a conception that still resonates with much of the current work using QCA (Rihoux and Ragin 2009). However, researchers have also applied QCA to examine large-N phenomena (e.g., Fiss 2011; Greckhamer, Misangyi, Elms, and Lacey 2008; Ragin and Fiss 2008; Vis 2012). 1 These large-N applications have prompted Greckhamer, Misangyi, and Fiss (forth-coming) to suggest that currently there are in fact "two QCAs" that differ in their focus on small- and large-W phenomena as well as in some of their assumptions, objectives, and analyses processes.Several issues are raised by applying QCA to a larger number of cases. In particular, researchers applying this approach find themselves largely on the same research terrain as traditional large-W researchers using econometric tools usually based on the standard linear model. We believe that this has proven to be both an opportunity and a challenge. On the positive side, the application of QCA to large-W situations offers a considerable opportunity for both new empirical insights and new theory building. For instance, prior works that focus on hypothesis testing in particular have tended to develop theories based on correlational statements. As Ragin (2000, 2008) has argued, such thinking does not necessarily correspond to the nature of causal relations present in social research. Accordingly, the introduction of QCA to a whole new series of phenomena carries a significant upside. However, this upside does not come without challenges. Chief among these is that in large-W QCA, it is difficult to maintain the kind of intimate familiarity with the cases that small-W QCA is usually based on. As a result, measurement errors in coding of cases are more likely. Contradictory observations in large-W QCA might then at times be accepted as measurement error, whereas in small-W QCA, they will frequently trigger a re-examination of the cases selected and whether all relevant causal conditions have been included. Due to this, establishing the robustness of QCA results is a more important concern in large-W applications than it is in small-W ones. In this article, we argue that there are two aspects in particular that need to be addressed for QCA to achieve its full potential as a method covering both small-W and large-W situations.The first issue relates to distinguishing the unique contribution of QCA relative to existing econometric tools when both could be used in large-W situations. To help realize QCA's potential as a tool for large-W analysis, we briefly contrast large-W QCA with standard econometric approaches. This discussion is intended to lay the groundwork for the second issue, which focuses on potential synergies and ways to integrate the insights from QCA with other econometric tools. Specifically, we suggest that integrating QCA findings into a regression framework or a lattice-theoretic analysis that draws on recent work in lattice theory (Milgrom and Roberts 1990, 1995; Mohnen and Roller 2005) to mimic a QCA approach within a regression framework potentially allows for added insights regarding result robustness, effect sizes, complementarity and substitutability relationships between causal conditions, and the addition of causal conditions that otherwise would make a QCA too unwieldy. …