Crisp and Fuzzy Set Qualitative Comparative Analysis (QCA)

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1 Crisp and Fuzzy Set Qualitative Comparative Analysis (QCA) Peer C. Fiss University of Southern California (I thank Charles Ragin for the use of his slides; modified for this workshop)

2 QCA Background QCA s home base is comparative sociology/comparative politics, where there is a strong tradition of case-oriented work alongside an extensive and growing body of quantitative cross-national research. The case-oriented tradition is much older and is populated largely by area and country experts. In contrast to the situation of qualitative researchers in most social scientific subdisciplines, these case oriented researchers have high status, primarily because their case knowledge is useful to the state (e.g., in its effort to maintain or enhance national security) and other corporate actors. Case-oriented researchers are often critical of quantitative cross-national researchers for ignoring the gap between the results of quantitative research and what is known about specific cases. They also have little interest in the abstract, high-level concepts that often characterize this type of research and the wide analytic gulf separating these concepts from case-level events and processes. QCA, plain and simple, attempts to bridge these two worlds. This attempt has spawned methodological tools which are useful for social scientists in general.

3 Charles C. Ragin Chancellor's Professor of Sociology at the University of California, Irvine Some Key QCA Works: The Comparative Method (1987) Fuzzy-Set Social Science (2000) Redesigning Social Inquiry: Fuzzy Sets and Beyond (2008)

4 Four (relatively abstract) answers to the question, What is QCA? 1. QCA bridges qualitative and quantitative analysis Most aspects of QCA require familiarity with cases, which in turn demands indepth knowledge. At the same time, QCA is capable of pinpointing decisive cross-case patterns, the usual domain of quantitative analysis. QCA s examination of cross-case patterns respects the diversity of cases and their heterogeneity with regard to their different causally relevant conditions and contexts by comparing cases as configurations.

5 Four (relatively abstract) answers to the question, What is QCA? 2. QCA provides powerful tools for the analysis of causal complexity With QCA, it is possible to study INUS conditions causal conditions that are insufficient but necessary parts of causal recipes which are themselves unnecessary but sufficient. In other words, using QCA it is possible to assess causation that is very complex, involving different combinations of causal conditions capable of generating the same outcome. This emphasis contrasts strongly with the net effects focus prevailing in conventional quantitative social science. QCA also facilitates a form of counterfactual analysis that is grounded in case-oriented research practices.

6 Four (relatively abstract) answers to the question, What is QCA? 3. QCA is ideal for small-to-intermediate-n research designs QCA can be usefully applied to research designs involving small and intermediate-size Ns (e.g., 5-50). In this range, there are often too many cases for researchers to keep all the case knowledge in their heads, but too few cases for most conventional statistical techniques. However, more recently QCA has also been applied to large-n situations marked by hundreds or thousands of cases. This kind of application requires some changes to how QCA is employed, but many of its advantages for analyzing causal complexity still remain.

7 Four (relatively abstract) answers to the question, What is QCA? 4. QCA brings set-theoretic methods to social inquiry QCA is grounded in the analysis of set relations, not correlations. Because social theory is largely verbal and verbal formulations are largely set theoretic in nature, QCA provides a closer link to theory than is possible using conventional quantitative methods. Note also that important causal relations, necessity and sufficiency, are indicated when certain set relations exist: With necessity, the outcome is a subset of the causal condition; with sufficiency, the causal condition is a subset of the outcome. With INUS conditions, cases with a specific combination of causal conditions form a subset of the cases with the outcome. Only set theoretical methods are well suited for the analysis of causal complexity.

8 An Exciting Time for Work with QCA In 2012 we celebrate 25 years of QCA A growing community and greater interest than ever before PDWs, symposia, methods retreats, etc. Greater receptiveness and publication opportunities Recent publications in top management journals, including AMJ, AMR, JBR, JIBS, Org Studies, ORM as well as a growing number and edited volumes and special issues (e.g. Rihoux & Ragin, 2009; Fiss, Cambré & Marx, 2012; Marx & Rihoux, 2012) New measures, tools, and ways of presenting results New package for R (Thiem & Dusa); STATA routine, fsqca 2.5 Consistency and coverage measures have become standard Configuration tables are becoming a standard way of presenting results (e.g. Ragin & Fiss, 2008; Crilly, 2011; Fiss 2011; Greckhamer 2011);

9 The Comparative Method

10 The Underlying Model of Social Research Ideas/Theory mostly inductive Analytic Frames retroduction Representations mostly deductive Images Evidence/Data Source: Ragin, Constructing Social Research, 1994

11 Two Main Methodological Approaches to Social Research Case-Oriented Approach Only through close examination of individual cases do we have any chance of understanding social phenomena Most phenomena have been misrepresented or incompletely represented This can be remedied only through close engagement and intensive examination. Variable-Oriented Approach Underlying truths are evident only when we look at broad patterns across many cases Individual cases can be deceptive Patterns reveal underlying structures and relationship purged of the specificity of any individual case.

12 The Methodological Divide Source: Ragin (2000:25)

13 The Case-Oriented/Variable- Oriented Dimension Single Case The Comparative QN Study of Study Method Covariation Case-Oriented Small-N Qualitative Intensive With-in Case Analysis Problem of Representation??? Variable-Oriented Large-N Quantitative Extensive Cross-Case Analysis Problem of Inference

14 The Basics of QCA

15 Sets are Central to Social Scientific Discourse Many, if not most, social scientific statements, especially empirical generalizations about cross-case patterns, involve set-theoretic relationships: A. Organizations with high levels of internal and external fit are high-performing. (Highly fit organizations are a subset of high-performing organizations) B. Professionals have advanced degrees. (Professionals are a subset of those with advanced degrees.) C. Democracy requires a state with at least medium capacity. (Democratic states are a subset of states with at least medium capacity.) D. "Elite brokerage" is central to successful democratization. (Instances of successful democratization are a subset of instances of elite brokerage.) E. No bourgeoisie, no democracy. (Barrington Moore, Jr.) An urban bourgeoisie is one of the preconditions for the development of democracy. Usually, but not always, the subset is mentioned first. Sometimes, it takes a little deciphering to figure out the set-theoretic relationship, as in E.

16 Explaining Outcomes and Set-Theoretic Reasoning 1. When explaining outcomes, the focus is on temporally bounded qualitative change. 2. Often, the explanation of the outcome is combinatorial, citing a confluence of actors, events, and structures. 3. Explaining how things happen(ed) is central to case study and comparative research: The origins of. Becoming a. The decline of. The emergence of. 4. With more than one case, there may be multiple combinations of conditions (i.e., multiple causal recipes), with different cases following different paths to the same outcome. 5. Each path can be understood as a different combination of conditions, which in turn can be formulated as an intersection of sets (a causal recipe). 6. Sufficiency is established when it can be shown that instances of the causal recipe constitute a subset of instances of the outcome.

17 Correlational Connections Correlation is central to conventional quantitative social science. The core principle is the idea of assessing the degree to which two series of values parallel each other across cases. The simplest form is the 2x2 table cross-tabulating the presence/absence of a cause against presence/absence of an outcome: Cause absent Outcome present cases in this cell (#1) contribute to error Outcome absent many cases should be in this cell (#3) Cause present many cases should be in this cell (#2) cases in this cell (#4) contribute to error Correlation is strong (and in the expected direction) when there are as many cases as possible in cells #2 and #3 (both count in favor of the causal argument, equally) and as few cases as possible in cells #1 and #4 (both count against the causal argument, equally). Correlation is completely symmetrical.

18 Correlational Versus Set-Theoretic Connections A correlational connection is a description of tendencies in the evidence: Org. Structure A Org. Structure B Firm survived 8 11 Firm failed 16 5 An explicit connection is a subset relation or near-subset relation: Org. Structure A Org. Structure B Firm survived Firm failed 6 0 In the second table all firms with structure B survived, that is, they are a subset of those that survived. The first table is stronger and more interesting from a correlational viewpoint; the second table is stronger and more interesting from the perspective of explicit connections even though the correlations are almost identical.

19 Anyone interested in demonstrating necessity and/or sufficiency must address set-theoretic relations. Necessity and sufficiency are difficult to assess using conventional quantitative methods. CAUSE IS NECESSARY BUT NOT SUFFICIENT Cause absent Cause present Outcome present 1. no cases here 2. cases here Outcome absent 3. not relevant 4. not relevant CAUSE IS SUFFICIENT BUT NOT NECESSARY Cause absent Cause present Outcome present 1. not relevant 2. cases here Outcome absent 3. not relevant 4. no cases here

20 Necessity (without Sufficiency) I. Expressed as a simple truth table: Cause Outcome II. Expressed as an inequality: (value of the outcome) (value of the cause) III. Expressed as a research strategy: Find instances of the outcome (i.e., select on the dependent variable) and assess their agreement on the causal condition (i.e., make sure that the cause does not vary substantially across instances of the outcome). This strategy is central to many forms of qualitative research.

21 Sufficiency (without Necessity) I. Expressed as a simple truth table: Cause Outcome II. Expressed as an inequality: (values of the cause) (value of the outcome) III. Expressed as a research strategy: Find instances of the causal condition (i.e., select on the independent variable) and assess their agreement on the outcome (i.e., make sure that the outcome does not vary substantially across instances of the cause).

22 Causal Complexity Causal complexity is pervasive but hard to tackle with conventional methods. For instance, a researcher studies production sites in a strikeprone industry and considers four possible causes of strikes: technology = the introduction of new technology wages = stagnant wages in times of high inflation overtime = reduction in overtime hours sourcing = outsourcing portions of production Possible findings include: is logical and (1) technology strikes + is logical or (2) technology wages strikes (3) technology + wages strikes (4) technology wages + overtime sourcing strikes In (1) technology is necessary and sufficient (2) technology is necessary but not sufficient (3) technology is sufficient but not necessary (4) technology is neither necessary nor sufficient

23 INUS Causation In situations of causal complexity, no single cause may be either necessary or sufficient, as in the logic equation: TECHNOLOGY*WAGES + OVERTIME*SOURCING STRIKES In The Comparative Method, this situation is called multiple conjunctural causation. In The Cement of the Universe, Mackie (1974) labels these causal conditions INUS causes because each one is: Insufficient (not sufficient by itself) but Necessary components of causal combinations that are Unnecessary (because of multiple paths) but Sufficient for the outcome

24 The Degree of Consistency of a Subset Relation The consistency of a crisp subset relation is straightforward. It is simply the number of cases displaying both the cause and the outcome (cell 2) divided by the number of cases displaying the causal condition (the sum of cells 2 and 4). For example, in the following table the consistency of the evidence with the argument that having org. structure B is sufficient for survival: 14/(2 + 14) = 14/16 = Org. Structure A Org. Structure B Firm survived Firm failed 11 2 Only cases in the second column are involved in the assessment of consistency of the evidence with the subset relation. The following is a Venn diagram illustrating this high but less-than-perfect degree of consistency.

25 The Degree of Consistency of a Subset Relation 13 Set of surviving firms 14 Set of firms with org. structure B 2 Consistency of subset relation = 14/(2+14) = 14/16 = 0.875

26 The Degree of Coverage of a Subset Relation Once it has been established that a subset is at least roughly consistent, it is possible to assess its degree of coverage. The calculation of coverage for crisp sets is straightforward. It is simply the number of cases with both the causal condition and the outcome (again, cell 2) divided by the number of cases with the outcome (cell 1 + cell 2). In other words, coverage answers the question: What proportion of cases with the outcome has been explained? or How common is the cause (or causal combination) among the cases with the outcome? 14/( ) = 14/27 = Org. Structure A Firm survived Firm failed 11 2 Org. Structure B Only cases in the first row are involved in the assessment of coverage. The key consideration is the proportion of the larger set covered by the interior set.

27 The Degree of Consistency of a Subset Relation 13 Set of surviving firms 14 Set of firms with org. structure B 2 Coverage of subset relation = 14/( ) = 14/27 = 0.519

28 Set Coincidence Set coincidence combines and bridges consistency and coverage. Set coincidence focuses on the degree to which two sets overlap that is, the degree to which they are one and the same set. While degree of set coincidence can be assessed using multiple sets (i.e., more than two), it is easiest to grasp the basic principles using two sets. For example, the degree to which the set of surviving firms and the set of firms with org. structure B are one and the same is indicated by the degree to which the cases than have both of these two traits embraces the set of cases that have either trait. In other words, set coincidence is the number of cases found in the intersection of two sets, expressed relative to the number of cases found in their union: (# of cases in intersection)/(# of cases in union)

29 Set A Set B Low set coincidence: set intersection is a small fraction of set union. Set A Set B High set coincidence: set intersection almost fully covers set union.

30 Crisp Set Analysis

31 Overview of the Steps in csqca Step 1: Identify relevant cases and causal conditions Step 2: Construct the data set Step 3: Test for necessary conditions Step 4: Construct the truth table and resolve contradictions Step 5: Analyze the truth table Step 6: Evaluate the Results Step 7: Return to step 3 and repeat the analysis for the negation of the outcome

32 Step 1: Identify relevant cases and causal conditions 1-1. Identify the outcome of interest and the cases that exemplify this outcome. Learn as much as you can about these positive cases Based on #1, identify negative cases those that might seem to be candidates for the outcome but nevertheless failed to display it ( negative cases). Together #1 and #2 constitute the set of cases relevant to the analysis Again based on #1, and relevant theoretical and substantive knowledge, identify the major causal conditions relevant to the outcome. Often, it is useful to think in terms of different causal recipes 1-4. Try to streamline the causal conditions as much as possible, e.g. combine two conditions into one when they seem substitutable.

33 Step 1: Examples Identify positive instances of mass protest against austerity measures mandated by the International Monetary Fund (IMF) as conditions for debt renegotiation ( conditionality ). Peru, Argentina, Tunisia,... Identify negative cases: for example, debtor countries that were also subject to IMF conditionality, but nevertheless did not experience mass protest. Mexico, Costa Rica,...

34 Step 1: Examples Cont d Identify relevant causal conditions: severity of austerity measures, degree of debt, living conditions, consumer prices, prior levels of political mobilization, government corruption, union strength, trade dependence, investment dependence, urbanization and other structural conditions relevant to protest mobilization. One recipe might be severe austerity measures combined with government corruption, rapid consumer price increases and high levels of prior political mobilization. Streamlining: Based on case knowledge, the researcher might surmise that high levels of trade dependence and high levels of investment dependence are substitutable manifestations of international economic dependence and therefore create a single condition from these two, using logical or.

35 Step 2: Construct the data set QCA data sets have the standard format: Cases define the rows, and aspects of cases define the columns. However, it is important to remember that the columns are sets and that the relevant sets must be carefully conceptualized and labeled. The cells of the data spreadsheet are filled with set membership scores. When using crisp sets, there are only two possible values: 1 (member) and 0 (nonmember).

36 Step 2: Construct the data set It is important to specify set membership criteria as carefully as possible and make sure that the membership scores that are assigned are faithful to the set label and how it is conceptualized. Very often it is useful to use to same evidence (e.g., parental income) as a basis for more than one set. For example, the set of individual with high-income parents has different membership than the set of individual with not-low income parents. The former is a subset of the latter. These multiple conceptualizations based on the same source variable (e.g., parental income) can be used in the same analysis.

37 Here s a sample data set with crisp sets : Case ID PriorMob SevereAus GovCor PriceRis Protest a b c d e f g h i j k l m n o p q r s t u v w x y z etc

38 Step 3: Test for necessary conditions The core of QCA is truth table analysis, which looks for causal combinations ( recipes ) that are sufficient for the outcome. Before conducting a truth table analysis, however, it is useful to see if any of the causal conditions might be considered necessary (but not sufficient) conditions for the outcome. If a causal condition is necessary for an outcome, then instances of the outcome constitute a subset of instances of the causal condition. With crisp sets, the simplest way to assess necessary conditions is the use QCA s crosstabs procedure and ask for row percentages. Look across the row showing the presence of the outcome; if all instances (or almost all instances) agree in displaying a particular causal condition, then that condition might be interpreted as a necessary condition.

39 Using the data set presented earlier might we find: N Row % priormob protest Total N 71 Missing 0 N Row % severeaus protest Total N 71 Missing 0 N Row % govcor protest Total N 71 Missing 0 N Row % priceris protest Total N 71 Missing 0

40 Step 3: Test for necessary conditions The key calculation is the percentage of the cases with the outcome (second row in these tables) that also display the causal condition (cell 4, in these tables). The causal condition severeaus (severe austerity) is close enough (at 93.9%) to be considered a candidate for necessity ( almost always necessary). When evaluating possible necessary conditions, I look for consistency scores of at least 90%. It is important to evaluate whether the condition makes sense as a necessary condition! Remember that a necessary condition is a superset of the outcome, while a sufficient condition (or combination of conditions) is a subset. In general, it is useful to know which conditions are necessary, because they are often eliminated from parsimonious solutions.

41 Step 4: Construct the truth table and resolve contradictions 4-1. Construct a truth table based on the causal conditions specified in step 1 or some reasonable subset of these conditions (e.g., using a recipe that seems especially promising). A truth table sorts cases by the combinations of causal conditions they exhibit. All logically possible combinations of conditions are considered, even those without empirical instances Assess the consistency of the cases in each row with respect to the outcome: Do they agree in displaying (or not displaying) the outcome? Consistency for crisp sets is the percentage of cases in each row displaying the outcome. Consistency scores of either 1 or 0 indicate perfect consistency for a given row, while a score of 0.50 indicates perfect inconsistency.

42 Step 4: Construct the truth table and resolve contradictions 4-3. Identify contradictory rows. Technically, a contradictory row is any row with a consistency score that is not equal to 1 or 0. However, it is sometimes reasonable to relax this standard, for example, if an inconsistent case in a given row can be explained by its specific circumstances Compare cases within each contradictory rows. If possible, identify decisive differences between positive and negative cases, and then revise the truth table accordingly.

43 An example, using one possible recipe as a starting point: Row# Prior Severe Gov t Rapid price Cases w/ Cases w/o Consistency mobiliz.? austerity? corrupt? rise? protest? protest 1 0 (no) 0 (no) 0 (no) 0 (no) 0 0?? 2 0 (no) 0 (no) 0 (no) 1 (yes) 0 0?? 3 0 (no) 0 (no) 1 (yes) 0 (no) (no) 0 (no) 1 (yes) 1 (yes) (no) 1 (yes) 0 (no) 0 (no) 0 0?? 6 0 (no) 1 (yes) 0 (no) 1 (yes) (no) 1 (yes) 1 (yes) 0 (no) 0 0?? 8 0 (no) 1 (yes) 1 (yes) 1 (yes) (yes) 0 (no) 0 (no) 0 (no) (yes) 0 (no) 0 (no) 1 (yes) (yes) 0 (no) 1 (yes) 0 (no) (yes) 0 (no) 1 (yes) 1 (yes) 0 0?? 13 1 (yes) 1 (yes) 0 (no) 0 (no) (yes) 1 (yes) 0 (no) 1 (yes) (yes) 1 (yes) 1 (yes) 0 (no) (yes) 1 (yes) 1 (yes) 1 (yes)

44 a) This table has five rows without cases (1, 2, 5, 7, 12). In QCA, these rows are known as remainders. Having remainders is known as limited diversity. b) There are seven noncontradictory rows, three that are uniform in not displaying the outcome (consistency = 0.0; rows 3, 9, 11) and four that are uniform in displaying the outcome (consistency = 1.0; rows 6, 8, 14, 16). c) The remaining four rows are contradictory. Three are close to 0.0 (rows 4, 10, 13), and one is close to 1.0 (row 15). d) Suppose that the three (unexpected) positive cases (one each in rows 4, 10, 13) are all cases of contagion a neighboring country with severe IMF protest spawned sympathy protest in these countries. These contradictory cases can be explained using case knowledge, showing that these instances are irrelevant to the recipe in question. Thus, these three cases can be safely set aside. e) e. Suppose the comparison of the positive and negative cases in row 15, reveals that the (unexpected) negative cases all had severely repressive regimes. This pattern suggests that having a not-severelyrepressive regime is part of the recipe and that the recipe has five key conditions, not four. The revised truth table follows.

45 Prior mobiliz.? Severe austerity? Gov t corrupt? Rapid price rise? Cases w/ protest? Cases w/o protest 0 (no) 0 (no) 1 (yes) 0 (no) 0 (no) (no) 0 (no) 1 (yes) 1 (yes) 0 (no) (no) 1 (yes) 0 (no) 1 (yes) 0 (no) (no) 1 (yes) 1 (yes) 1 (yes) 1 (yes) (yes) 0 (no) 0 (no) 0 (no) 0 (no) (yes) 0 (no) 0 (no) 1 (yes) 1 (yes) (yes) 0 (no) 1 (yes) 0 (no) 0 (no) (yes) 1 (yes) 0 (no) 0 (no) 1 (yes) (yes) 1 (yes) 0 (no) 1 (yes) 0 (no) (yes) 1 (yes) 1 (yes) 0 (no) 1 (yes) (yes) 1 (yes) 1 (yes) 0 (no) 0 (no) (yes) 1 (yes) 1 (yes) 1 (yes) 1 (yes) Not repressive? Consistency This is the revised truth table. Notice that now there are no contradictions. The three cases of contagion have been removed, and the contradictory cases in row 15 of the previous table have been resolved. The full version of this truth table would have 32 rows and 20 remainders (causal combinations lacking cases).

46 Step 5: Analyze the truth table The fsqca software can be used to analyze truth tables like the two just shown. The goal of the analysis is to specify the different combinations of conditions linked to the selected outcome The first part of the fsqca algorithm compares rows of the truth table to identify matched pairs. For example, these two rows both have the outcome, but differ by ONLY ONE causal conditions, providing an experiment-like contrast: Prior mobiliz.? Severe austerity? Gov t corrupt? Rapid price rise? Not repressive? Cases w/ protest? Cases w/o protest Consistency 1 (yes) 1 (yes) 1 (yes) 0 (no) 1 (yes) (yes) 1 (yes) 1 (yes) 1 (yes) 1 (yes)

47 Step 5: Analyze the truth table Prior mobiliz.? Severe austerity? Gov t corrupt? Rapid price rise? Not repressive? protest? Cases w/ protest Cases w/o tency Consis- 1 (yes) 1 (yes) 1 (yes) 0 (no) 1 (yes) (yes) 1 (yes) 1 (yes) 1 (yes) 1 (yes) This paired comparison indicates that if prior mobilization, severe IMF austerity, government corruption, and a nonrepressive regime coincide, it doesn t matter whether there are also rapid price increases; protest will still erupt. The term that differs is eliminated, and a single, simpler row replaces the two rows shown This process of bottom-up paired comparison continues until no further simplification is possible. Only rows with the outcome are paired; only one condition may differ in each paired comparison. The one that differs is eliminated.

48 5-3. Rows without cases ( remainders ) also may be used to aid the process of simplifying the patterns. For example, there are no instances of the second row listed below. However, based on substantive and theoretical knowledge, it is reasonable to speculate that if such cases existed, they would be positive instances of IMF protest, just like the empirical cases they are paired with: Prior Severe Gov t Rapid Not Repressive? Cases w/ Cases w/o Consis- mobiliz.? austerity? corrupt? price rise? protest? protest tency 0 (no) 1 (yes) 0 (no) 1 (yes) 0 (no) (yes) 1 (yes) 1 (yes) 1 (yes) 0 (no) 0 0?? The reasoning is as follows: (1) the remainder case resembles the empirical cases above it in every respect except one; (2) the one difference (the remainder case has government corruption) involves a condition that should only make IMF protest more likely; (3) therefore, the remainder case, if it existed, would display IMF protest, just like the empirical cases. This pairing allows the production of a logically simpler configuration, eliminating the absence of government corruption as a possible (INUS) ingredient. This example shows how fsqca incorporates a form of counterfactual analysis that parallels practices in qualitative case-oriented research.

49 5-4. The process of paired comparisons culminates in a list of causal combinations linked to the outcome. fsqca then selects the smallest number of these that will cover all the positive instances of the outcome fsqca presents three solutions to each truth table analysis: (1) a complex solution that avoids using any counterfactual cases (rows without cases remainders ); (2) a parsimonious solution, which permits the use of any remainder that will yield simpler (or fewer) recipes; and (3) an intermediate solution, which uses only the remainders that survive counterfactual analysis based on theoretical and substantive knowledge (which is input by the user). Generally, intermediate solutions are best. For the table just presented, the three solutions are: Complex: SA gc PR nr + PM SA GC NR + SA GC PR NR Parsimonious: GC NR + SA PR Intermediate: PM SA GC NR + SA PR (Multiplication indicates set intersection combined conditions; addition indicates set union alternate combinations.)

50 Because they are logical statements, these two recipes for IMF protest can be factored. For example, the intermediate solution can be factored to show that severe austerity (SA) is present in both: SA (PR + PM GC NR) The expression indicates that IMF protest erupts when severe austerity (SA) is combined with either (1) rapid price increases (PR) or (2) the combination of prior mobilization (PM), government corruption (GC), and nonrepressive regime (NR). Recall that severe austerity was close to perfection as a necessary condition in the crosstabs analysis, so its importance here is not surprising. Notice, however, that severe austerity is absent from one of the recipes in the parsimonious solution, suggesting that the parsimonious solution is probably too parsimonious.

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