Table of contents 1 Introduction In 1987, the American social scientist Charles Ragin built the foundation for Qualitative Comparative Analysis (QCA) with his seminal book The Comparative Method. QCA is designed for the comparison of a small to intermediate number of cases. It enables systematic cross-case comparison without neglecting case complexity, allowing modest, medium-range generalization and theorizing. The aim of this working paper is to introduce QCA as a method to study policy processes. In particular, we discuss its application to the Global Comparative Study on REDD+ (GCS-REDD). 1 The objective of GCS-REDD is to provide policy makers and practitioners with relevant knowledge to ensure effective, cost-efficient and equitable reduction of carbon emissions from deforestation and forest degradation as well as co-benefits (3E+ criteria). Its analyses occur simultaneously with efforts to start and implement REDD+ and try to identify 'what works and what does not.' The paper was developed for Module 1 of GCS-REDD(see Brockhaus and Di Gregorio 2012) . This Module analyses the national processes that formulate and implement REDD+ policies and assesses whether the resulting outcomes are meeting the 3E+ criteria, in nine countries with additional studies in three other countries. Each full country study consists of five work modules: a country profile of the institutional context, a media analysis, a policy network analysis, a REDD+ policy content analysis, and a fifth flexible module that can be adapted to specific country research needs. Table of contents 1 Introduction This working paper gives a general idea of the logic of QCA and its methods and discusses benefits and limitations. It is not aimed at an in-depth methodological guide but rather as an introduction of the approach to readers not very familiar with methods of comparative politics. The references provide useful literature for further reading. It starts with a general overview of QCA, followed by a description of different variations on the original basic method. Next, it applies QCA to GCS-REDD. Limitations and benefits of the method are discussed, and conclusions are presented about its usefulness in guiding REDD+ policy design and implementation. Table of contents 1 Introduction 1 REDD+ means reducing emissions from deforestation and forest degradation, and enhancing forest carbon stocks in developing countries. QCA: An overview During the last decades, QCA has gained popularity among social scientists interested in alternative ways to analyze and compare a small or medium number of cases. It has thus far primarily been applied to political science and sociology. QCA: An overview 2 QCA is a research strategy as much as a set of concrete techniques (Rihoux 2007, 365) . It challenges several typical approaches of statistical methods, but also goes beyond the classical case-centered focus of traditional qualitative research. Thus, although called Qualitative Comparative Analysis, QCA is not a qualitative method in the sense of empirical qualitative research. Rather, it should be seen as a middle way that combines certain features of the qualitative approach (case orientation, interest in complexity) with those of quantitative research (interest in generalization). Ragin's aim was to use the strengths of case studies but overcome their limitations, to keep the identity of the case but allow for generalizations (Blatter et al. 2007, 190; Lauth et al. 2008, 118) . He therefore did not see QCA as a compromise between qualitative and quantitative approaches but rather as a "real alternative to conventional practices" that "transcends many of their respective limitations" (Ragin 2008, 6 ). Ragin used the term 'qualitative' in order to distinguish his approach from that of statistical logic. However, he never proposed restricting the analysis to qualitative research. For example, quantitative and macro-level data are widely used in QCA studies. In this respect, QCA is sometimes referred to as a macro-qualitative approach.In French, the term analyse quali-quantitative comparée is used (Blatter et al. 2007, 204) . QCA: An overview Numerous researchers have also combined QCA with other qualitative or statistical analytical tools (see for an overview Rihoux 2007, 377-379) , either to confront the different results or to combine them to gain a better understanding. For the analysis of policy networks and processes, Stevenson and Greenberg (2000) as well as Fischer (2011) combined social network analysis and QCA and could show the mutual benefit of these approaches. QCA: An overview Typical qualitative features of QCA are the case orientation, the holistic view of cases as a 2 For an overview, see Yamasaki and Rihoux (2009) . Examples of QCA applied to deforestation include Scouvart et al. (2007) , Rudel and Roper (1996) and Rudel (2005) . A list of publications using QCA can be found at http://www.compasss.org/wpseries/ allWPdate.htm and www.restore.ac.uk/qualquanres/papers/ Reading_two.shtml. combination of features and the need for detailed knowledge of cases. Its interest does not lie in the disaggregation of cases into analytically separate variables and the identification of a single cause, but in understanding and conceptualizing the relation between the different causes and how they combine in a given context. It requires the researcher to interpret the combinations and to define and redefine thresholds, which requires in-depth case knowledge and an iterative process (Blatter et al. 2007, 204; Rihoux 2007, 368; Fiss 2010) . In this respect, it is a qualitative approach. QCA: An overview The central principles and terms of QCA can be summarized as follows. QCA: An overview • QCA is designed for small to intermediate numbers of cases (around 5 to 50 or even 100) that are too small for statistical analysis but too big for qualitative case research, or the classical comparison of two to five cases with a most similar or most different case design (see Przeworski and Teune 1968; Lijphart 1971) . Although a QCA with fewer than 10 cases is difficult, some studies have used QCA for as few as five cases. Quite a few studies with large N (more than 100 or even more than 1000) have applied QCA (for examples, see Rihoux 2007, 379 ). QCA: An overview • The aim of QCA is enabling systematic crosscase comparison. At the same time, it is a case-sensitive approach.That means it takes the internal complexity of cases into account by allowing complex causations and counterfactual analysis. With this balancing of reduction and complexity, QCA allows modest, medium-range generalization and theorizing. QCA: An overview • In QCA, each case is understood as a specific combination of factors, which are called 'conditions.' Therefore, Ragin speaks not of 'cases' but of 'configurations' (Ragin 2000, 64ff) . A configuration is "a specific combination of factors (or stimuli, causal variables, ingredients, determinants, etc. -we call these conditions …) that produces a given outcome of interest" (Rihoux and Ragin 2009, xix) . QCA: An overview The main premise of QCA is that of multiple conjunctural causation, which means that (1) most often not one factor but a combination of factors will lead to the outcome; (2) different combinations of factors can produce the same outcome; and (3) one condition can have different impacts on the outcome, depending on its combination with other factors and the context (Rihoux 2007, 367) . These three principles are described in more detail below. Conjunctural causation The term 'conjunctural' refers to the assumption that it is usually a combination of factors (in QCA language called 'configuration') rather than a single factor that leads to an outcome. In this configuration, not only the presence but also the absence of a certain factor is assessed as influential for the outcome and therefore measured.This allows a better grasp of case-and context-specific constellations.While in statistical methods such as regression analysis (with the exception of multiple regressions), different variables are treated as competitive and the one with the highest significance is presented as the most probable determining factor, QCA logic assumes that different conditions are complementary and often interdependent. Even if the impact of one factor is small, this factor might be necessary to trigger another factor, thereby contributing to the overall outcome (Blatter et al. 2007, 203) . As a consequence, the identified causal relation is usually not one factor but a combination of given and absent factors. These are assessed qualitatively as necessary parts of the causal relation and not quantitatively on the extent of their contribution to the overall outcome. Multiple causation Not only can several factors in a specific configuration lead to an outcome -different configurations can lead to the same outcome. This principle of 'equifinality' is probably best described with the old saying that "many ways lead to Rome" (Blatter et al. 2007, 201) . In this way, QCA allows the identification of alternative ways to reach an outcome depending on the context. Multiple causation It is even possible that a certain factor has different causal effects depending on the specific configuration. Thus, depending on the combination with other factors, its presence can have a positive or negative effect on the outcome, or its presence and its absence may at different times be a necessary part of the configuration. With other methods, this would have led to the conclusion that the factor was irrelevant. Multiple causation Thus, multiple conjunctural causation implies that there is no permanent and uniform causality, but that causality is always specific to context and configuration (Berg-Schlosser et al. 2009, 8ff) . How the combination of factors works has to be explained by the researcher based on case knowledge. Necessary and sufficient conditions A central element of QCA is that, in identifying different combinations of factors, it allows differentiation between necessary and sufficient conditions or configurations. The presence of a sufficient condition (A) always leads to the outcome (X). Thus, whenever we observe condition A, we observe outcome X -condition A is a subset of outcome X (Figure 1 ). But according to the logic of multiple causation, outcome X could also be the result of another condition or configuration, without the presence of condition A. Necessary and sufficient conditions A necessary condition (B), in contrast, has to occur for outcome X to occur; the outcome cannot happen without the condition. The absence of condition B would lead in every case to the absence of outcome X. However, this does not imply that when there is B, there is always X, as according to the logic of conjunctural combination, B might have to be accompanied by another condition to be effective. Thus, outcome X is a subset of condition B (Figure 2 ). In other words, A always leads to X, but there can be X without A; B usually leads to X, but there can be B without X. Only if a condition is both necessary and sufficient will it always be observed in every case of the result and vice versa (Blatter et al. 2007, 199) . Necessary and sufficient conditions Certain conditions might be neither sufficient nor necessary but might nevertheless play a role in the outcome as part of a configuration. Such conditions can also be revealed with QCA. They are called INUSconditions and SUIN-conditions. An INUS-condition is an"insufficient but necessary part of a configuration which is itself unnecessary but sufficient for the result." Thus, condition A may by itself be neither sufficient nor necessary but may, as part of a combination, have a causal effect. A SUIN-condition is a sufficient but unnecessary part of a configuration that is insufficient but necessary for the outcome (Schneider and Wagemann 2012, 79) . We will explain these with concrete examples later. In real life, these conditions occur regularly. While they cannot be adequately tackled with classical comparative methods or large-N quantitative analysis (Blatter et al. 2007, 202ff) , QCA provides tools to systematically grasp this complexity. Software Several software tools have been developed for the application of QCA. Different tools are used to apply different versions of QCA; these versions are explained in detail in the next section. Software • QCA-DOS (for crisp-set QCA), developed by Charles Kriss Drass in 1992 and updated until 1998 (www.u.arizona Schneider and Wagemann (2012, 282) also give a good synopsis of the different software packages and their features. When analyzing a smaller number of cases with a crisp-set QCA, like the 12-case examples used in this paper, the software is not necessarily needed. However, for a larger number of cases and for fuzzy-set QCA, researchers should use adequate software. The method and its application During the past 30 years, QCA has been considerably refined and developed, partly in response to criticism of the original version (Ragin 1987) . Today, four main methodological variations exist within QCA. These are crisp-set QCA, fuzzy-set QCA, multi-value QCA, and two-step fuzzy-set QCA. In order to illustrate the method and its application, we used the data from Module 1 of GCS-REDD, which analyses national REDD+ processes in 12 countries (Table 1 ). All are forest-rich tropical developing or emerging countries with a political commitment to implement REDD+ but also with powerful drivers of deforestation, weak multilevel governance, low cross-sectoral horizontal coordination and lack of capacity. These aspects form the joint context of our cases. The method and its application The aim of this study was to use QCA to discover, through systematic comparison, under which conditions these countries can successfully implement REDD+, and to develop generalizations and policy recommendations for them and for countries that share their context.To accomplish this, we used an iterative process to select the most relevant factors affecting success or failure in establishing an adequate political framework for REDD+. This process, discussed in depth in Section 4, ultimately yielded six factors. 3 The examples in this chapter are based on the three institutional factors: A successful outcome is defined as the establishment of a comprehensive policy promoting transformational change in the REDD+ policy domain that is likely to lead to successful 3E-REDD+ implementation. 3 The key factors are all given three-or fourletter codes, and the outcome is represented by the code REDD. For the purpose of this exercise, a case = one country. Crisp-set QCA (csQCA) Ragin's original version of QCA (Ragin 1987 ) is today called crisp-set QCA (csQCA). 4 Its core element is the 'truth table,' a data matrix that contains all values of the causal conditions and outcomes. All conditions are assessed in strictly In total, 2 n combinations of conditions are possible, where n is the number of conditions. Thus, in our example with three causal factors or conditions, 2 3 or eight combinations are possible.The fact that all eight conditions are represented in our empirical cases is an extraordinary situation. Most often, some theoretically possible combinations are not observed in the selected cases. The non-observed configurations are called 'logical remainders.' (Strategies for dealing with these are discussed in 'Empirical diversity' in Section 5.) Crisp-set QCA (csQCA) In the final configuration, capital letters show the presence of a condition while lowercase letters indicate its absence. The formula of the configuration is achieved with the application of Boolean algebra, in which '+' means 'or' and '*' means 'and.' For example, the configuration for Cameroon would read as follows: PRES*EFF*cha, with the result redd (in other words, Outcome REDD = 0). In less abbreviated form, this could be expressed as follows: Pressure from a shortage of forest resources and presence of features of effective forest legislation, policy and governance and absence of already initiated policy change leads to absence of a comprehensive policy promoting transformational change in the REDD+ policy domain. Crisp-set QCA (csQCA) Three combinations lead to a positive outcome: PRES*eff*CHA (Indonesia) + pres*EFF*CHA (Vietnam) + PRES*EFF*CHA (Brazil). Crisp-set QCA (csQCA) These formulas can be further reduced: pres*EFF*CHA (Vietnam) and PRES*EFF*CHA (Brazil) both lead to REDD; it is obviously irrelevant if PRES is present in this specific combination or not. Crisp-set QCA (csQCA) According to Boolean logic, the combinations pres*EFF*CHA and PRES*EFF*CHA therefore can be reduced to EFF*CHA. Crisp-set QCA (csQCA) For the other combination (PRES*eff*CHA [Indonesia]), PRES stays included; in this context, we have no comparable cases that would indicate it is not necessary. Thus, QCA assesses the impact of each factor according to the case-specific circumstances. Both presence and absence are measured and included in the analysis; absence is not considered irrelevant. Crisp-set QCA (csQCA) The result of our analysis is thus REDD = EFF*CHA + PRES*eff*CHA. In other words, under the framework conditions of our cases successful pro-REDD policies are enabled by the presence of key features of effective forest legislation, policy and governance and the presence of already initiated policy change, or by pressure from a shortage of forest Fuzzy-set QCA (fsQCA) One major criticism concerning crisp-set QCA is its binary approach. It requires the assessment of factors as either true or false; there is no room for gradual assessment. Even factors such as economic development, unemployment or age have to be classified as true or false. As a reaction to this criticism, Ragin himself (2000 Ragin himself ( , 2008 developed fuzzy-set QCA. It allows the researcher to define the value of conditions not only in a dichotomous way, but also in gradual variations, and is thus closer to statistical methods.The following description of fuzzy-set QCA is based on Blatter et al. (2007, 215-226 ) and Ragin's own revised version of fuzzyset QCA (Ragin 2008 (Ragin , 2009 ). Fuzzy-set QCA (fsQCA) Fuzzy sets allow for the possibility of partial membership. Fuzzy-set theory evolved in the 1960s in the natural sciences to tackle uncertainties, where "the boundary of yes and no is ambiguous" (Pennings 2007, 347) . In social and political sciences, fuzzyset theory was used only by a small number of researchers until Ragin (2000) linked it to his QCA concept. Fuzzy-set QCA (fsQCA) The major difference between crisp-set QCA and fuzzy-set QCA is that, in addition to crisp-set QCA's false/absent or true/present, fuzzy-set QCA also makes possible partial fulfillment of conditions, with values between 0 (non-membership in the set/ completely false status) and 1 (full membership in the set/completely true status). This approach allows more differentiation and more precise description. It is up to the researcher to decide how many grades should be used and to define the threshold for each grade. The following is an example of a four-value fuzzy set: 0 = absent (no membership) 0.33 = more absent than present 0.67 = more present than absent 1 = present (full membership) Fuzzy-set QCA (fsQCA) The calibration of set membership (the definition of the thresholds between the values) is based on theoretical knowledge, expert judgment and empirical evidence. It can be based on statistical data, but in that case, the data should not be automatically computed but also assessed by the researcher. Their definition has to be transparent and well substantiated. Adequate empirical categorization and definition of thresholds are of critical importance. In principle, the researcher must re-question category boundaries and experiment with them until the analysis is finalized. As fuzzy-set QCA includes more variation among the cases, many scholars argue that more cases are required to establish significant findings (Pennings 2007, 351; Rihoux 2007, 369 ; see also Schneider and Wagemann 2007; Schneider and Wagemann 2012, 32-41) . Fuzzy-set QCA (fsQCA) Going back to our example, Table 3 shows the assessment of the three conditions as fuzzy sets, with conditions and outcome refined based on a fourvalue scale. Fuzzy-set QCA (fsQCA) As the configuration can no longer be represented by a simple formula, the values of the conditions are measured based on the extent to which they are represented in each possible configuration. The configurations can be considered as ideal types. Next, we check which of these ideal types most resembles the concrete assessment of the real cases. For this purpose, each configuration (combination of conditions) is given the value of the condition within it that has the lowest value. For each case there will be only one configuration with a value higher than 0.5, and that one is considered the best fit. Thus, unlike in crisp-set QCA, no case fully represents a configuration. In Table 4 , the best fitting configuration is printed in bold. For example, for Mozambique, the value 0.67 is given for the configuration PRES*eff*cha because, when looking at the individual conditions, PRES = 1, eff (the absence of EFF) = 1, and cha (the absence of CHA) = 0.67 Fuzzy-set QCA (fsQCA) So far, we have a description of each case but no indication of causal relations. Therefore, in a second step, we want to identify the causal relations between the configurations and the outcome. For this, the requirements differ for necessary and sufficient conditions: Fuzzy-set QCA (fsQCA) • For necessary conditions, all fuzzy-set scores for the configuration must be equal to or higher than the fuzzy-set score for the outcome. Fuzzy-set QCA (fsQCA) • For sufficient conditions, the fuzzy-set score for the outcome must be equal to or higher than all fuzzy-set scores for the configuration. Table 5 shows that in our sample there is no necessary configuration, but a sufficient one: pres*EFF*CHA. three or four valued conditions should be used (enough for differentiation, but not enough to cease being parsimonious). Yet factors can also remain dichotomous. Often, one or two multivalue conditions are employed while the others are dichotomous. Thus, as Vink and van Vliet (2007, 3) put it, it is "a kind of middle-way between the greater parsimony of crisp-set QCA and the greater empirical richness of fuzzy-set QCA. It is ´not quite crisp´ because it allows the use of intermediate values, but it is also ´not yet fuzzy´ because the outcome is always dichotomous." Fuzzy-set QCA (fsQCA) This approach allows more differentiation and more homogeneous groupings of conditions than crispset QCA, for example, when it comes to conditions such as GDP, unemployment rate or age. But more important, it allows a better grasp of multicategorical factors such as region, religion, ethnicity, drivers of deforestation, political system, or type of opposition. 5 While factors such as GDP could also be measured by fuzzy-set QCA, such multicategorical nominal conditions cannot be measured by ordinal scales. Fuzzy-set QCA (fsQCA) In our example, to illustrate the logic of the analysis in multi-value QCA, we decided to transform the 5 These could also all be grasped in crisp-set QCA, but only as individual conditions, which would increase complexity. Fuzzy-set QCA (fsQCA) To explain the logic of this process, it helps to visualize the sufficient condition (Figure 3 ). Fuzzy-set QCA (fsQCA) For a sufficient condition, all cases have to be located on the diagonal or in the upper left triangle. This means that if the condition is fully present, then the outcome is also fully present, or if the condition is present to the extent 0.33, then the outcome is also present to the extent 0.33. If cases show the outcome without the condition (cases appear in the upper left side rather than on the diagonal line), this is not problematic, because the configuration, while sufficient, might not be a necessary condition (there might be multiple causation). If, however, the condition is more strongly present than the outcome (cases appear in the lower right triangle), then the configuration is obviously not a sufficient cause for the outcome. Unlike in crisp-set QCA, we have established only one sufficient configuration (pres*EFF*CHA). Multi-value QCA (mvQCA) Multi-value QCA aims to tackle the same key limitation of crisp-set QCA as fuzzy-set QCA does: the obligation to use only dichotomous presence/ absence conditions (Cronqvist and Berg-Schlosser 2009) . With multi-value QCA, any number of values is possible, which allows inclusion of multicategorical conditions in the analysis. Ideally, conditions EFF and CHA into multi-value factors. Multi-value QCA (mvQCA) We redefined EFF into three degrees: 0 = no features of effective forest legislation, policy or governance 1 = some key features of effective forest legislation, policy and governance 2 = sufficient features of effective forest legislation, policy and governance Herewith, we have more scope of variation to assess the effectiveness of the governance framework. For condition CHA, a multi-categorical differentiation also makes sense: 0 = no previous policy change 1 = previous policy change on climate change (e.g. Nationally Appropriate Mitigation Actions) 2 = previous policy change on antideforestation 3 = previous policy change on Payment for Environmental Services 4 = previous policy change in more than one area PRES and the outcome remain dichotomous. Multi-value QCA (mvQCA) In principle, the same Boolean algebra and minimization rules are applied. Only the notation is different than in crisp-set QCA, as lowercase and capital letters can reflect only two values. In multivalue QCA, the values are indicated with subscript numbers (Table 6 ). Multi-value QCA (mvQCA) We can identify the following causal combinations for the outcome REDD 1 : REDD 1 = PRES 1 *EFF 2 *CHA 1 +PRES 1 *EFF 1 *CHA 4 +PRES 0 *EFF 2 *CHA 4 . Multi-value QCA (mvQCA) More differentiation in the conditions reduces the number of contradictory cases (cases with the same configuration but different outcomes). However, the bigger the number of possible values for a condition, the higher the number of possible configurations. Therefore, often (like in our example), no further reductions are possible and 'logical remainders' (logically possible combinations that are not observed in the cases) need to be included in the analysis to achieve parsimony (see Section 5). Two-step QCA The newest innovation in QCA is two-step fuzzyset QCA, developed by Schneider and Wagemann (2006) . 6 This method differentiates between remote and proximate conditions (factors), which are then analyzed separately in two steps. Remote conditions are distant in space and time from the outcome, are stable over time and cannot easily be changed by actors. Thus, they are what is often called context. Proximate conditions are close to the outcome in space and time, vary over time and can easily be changed (Schneider and Wagemann 2006; Mannewitz 2011) . 6 Schneider and Wagemann used the two-step approach for fuzzy-set QCA, but they viewed the dichotomous conditions of crisp-set QCA as a variant of fuzzy-set QCA. A two-step approach hence certainly can also be applied to crisp-set QCA and multivalue QCA. This is why we speak simply of two-step QCA. It often depends on the research question and framework whether a factor is considered remote or proximate (Table 7) . For example, the forest tenure system can be considered a remote condition if we are interested in how actors act within its framework. But it can be seen as a proximate condition if we look at how a legislature may change the law to ensure effective REDD+ implementation. Two-step QCA In the first step of a two-step QCA, only the remote conditions are analyzed in order to identify 'outcome-enabling conditions.' This produces one or more configurations that are identified as enabling context. In the second step, each step-1 configuration is analyzed together with the identified proximate factors. Thus, several analyses take place in parallel, but only with those cases that show the relevant (outcome-enabling) context. Those remote conditions that proved irrelevant are not considered. This approach thus allows for inferences about which factors play a role if certain context conditions exist. Figure 4 shows the process of a two-step QCA with seven conditions. Four conditions (A, B, C and D) are defined as remote and three conditions (E, F and G) as proximate. In the first step, analysis of the remote conditions (with the processes described above) leads to the identification of two outcomeenabling configurations: ABd and bC. In a second step, each of the two is separately analyzed with the three proximate conditions; this leads to the final result of four causal configurations. Two-step QCA While fuzzy-set QCA and multi-value QCA were developed to address the problem of binary coding, the aim of two-step QCA is to tackle the problem of limited empirical diversity and therewith the often big number of logical remainders. In our example we have seven factors (A-G); hence, the number of possible variations is 2 7 = 128. If we then have 30 cases which resemble 28 different observations (i.e. two configurations occur twice), the number of logical remainders is 128−28 = 100. Thus, for 100 logically possible configurations we do not know the outcome, which limits the value and validity of our result. If we apply a two-step approach with four remote and three proximate factors, the number of possible combinations is 2 4 + 2 3+2 ('3+2' refers to the three proximate factors plus the two earlier identified remote conditions). Thus, we have 16 + 32 = 48 logically possible combinations, of which 28 are observed, so that the number of logical remainders is reduced to 20. However, it is clear that the more enabling contexts are identified, the more combinations are possible, and thus there is no longer a substantial reduction of logical remainders (Mannewitz 2011) . Beside the reduction of logical remainders, an additional merit of two-step QCA is that it provides good ground for the analysis of interactions between the two factor levels and for the identification of factors that play a role in a given context. Two-step QCA For the QCA of national REDD+ policy processes, we used the two-step QCA as a crisp-set QCA, in other words using only binary codings. To this end, the three already introduced factors (PRES, EFF, CHA) were defined as remote factors and considered together with three proximate ones: All six factors are described in detail in Appendix 1. Table 8 shows the binary values for all six factors. Two-step QCA Step 1, the analysis of the remote factors, is equivalent to the analysis described in the part 'Crisp-set QCA', and yields this result: EFF*CHA + PRES*eff*CHA. The next step is to find out which proximate conditions need to be combined with these two enabling configurations of remote conditions. For this step, only those cases that show the enabling factors are included. Table 9 presents the configurations for remote condition EFF*CHA. We can thus observe that when some key elements of effective forest legislation, policy and governance, and already initiated policies, exist in combination with national ownership of REDD+ and pro-REDD+ coalitions, comprehensive policies for REDD+ can be established. We can also observe that an inclusive policy process is not necessary for the outcome in this context, because both Brazil and Vietnam have the outcome REDD = 1 although only Brazil has an inclusive process. Also, the contradictory outcomes of Brazil and Bolivia (Table 2 ) can now be explained: Bolivia has the enabling context, but it lacks the necessary proximate conditions, hence it has outcome 0. Two-step QCA The second combination of remote conditions that leads to the outcome REDD = 1 (PRES*eff*CHA) can be observed for only one country: Indonesia (Table 10 ). Two-step QCA This gives us the configuration PRESS*eff*CHA* OWN*COAL*incl for Indonesia. Hence, for Indonesia the same two present proximate conditions as for Brazil and Vietnam can be observed. These are obviously necessary for the outcome notwithstanding the context. Figure 5 shows the process of analysis. Two-step QCA In step 1 we analyzed the three remote conditions and identified two configurations as enabling the outcome REDD = 1: EFF*CHA and PRES*eff*CHA. In two parallel processes (step 2), we then analyzed each of these configurations separately with the three proximate conditions. As a result, we achieved two configurations as sufficient conditions for REDD = 1. In our study, for both remote configurations almost the same proximate configuration was sufficient. However, with this method we can also determine if, depending on remote conditions, different proximate conditions come to play a role. Table 11 summarizes the benefits and weaknesses of the different types of QCAs and shows the differences that choice of QCA leads to in the results for our example. Figure 5 . Two-step crisp-set QCA applied to GCS-REDD. Two-step QCA Step 1 Step 2 As shown above, QCA makes it possible to translate complexity in in-depth case studies into reduced and comparable formulas and to formulate inferences on enabling factors. This process can be effectively applied to REDD+, but it requires engagement by country experts and coordinators. This study used QCA both to organize data and to draw inferences from it. Using QCA to structure data One use of QCA occurs before the analysis begins: the summarization and coherence check of data. Factors affecting successful implementation of REDD+ were explored thoroughly; the list was then narrowed to a manageable number of the most important factors, and these were operationalized by assigning them indicators by which they could be assessed. Using QCA to structure data First, we used QCA in a descriptive way to summarize data acquired during 2 years of project implementation by dozens of researchers. In order to get an overview of all factors considered important in the REDD+ process, a preliminary list of potential factors was developed in a workshop with participants from several country teams. This list formed the basis for an online survey conducted among GCS-REDD researchers. It was not a representative survey, but it provided input on the factors relevant for cross-country comparison. In several subsequent steps, including a review of country-specific context studies on REDD+ produced by the country teams (see e.g. Indarto et al. 2012; Pham et al. 2012) , these factors were reduced For the comparative analysis, a second round of reduction of factors took place. Eight factors were selected for inclusion in the analysis and operationalized by indicators. The indicators were developed after the first assessments revealed discrepancies in valuation. Their aim was to ensure transparency and comparability of the assessments. The assessment was done by experts from the respective country teams of the GCS-REDD project in a joint workshop, which allowed cross-checking of results. These data provided a reliable and valid basis for starting the QCA, during which the factors were discussed further and changed again -a typical feature of QCA, sometimes referred to as "dialogue with the case" (Rihoux and De Meur 2009, 48) . Finally, six factors were chosen as key to explaining the success or failure in achieving 3E REDD+ policy outputs. Analysis was conducted using the software TOSMANA (see above). Using QCA to structure data The process took several months, but it ensured that intersubjective verifiable data were achieved that respect case specifics but at the same time reduce complexity and are comparable. QCA helped ensure that all country teams shared the same understanding and definition of factors. Putting all data in a truth table and discussing it jointly enabled everybody to get a broad overview of the project and reduced the complexity of the information derived from numerous extensive case studies. It also showed discrepancies in assessments, which could then be clarified. With the definition of indicators, the process ensured that all would have the same understanding and that assigned values would be comparable but still context-sensitive enough to capture reality. Using QCA to structure data The process is described in more detail in the text below. Generating a full list of factors Shortening the list The initial 14 factors were presented to key GCS-REDD staff members for prioritization in an online survey. Based on survey results and a further review of the literature, five conditions were removed from the list. 'Horizontal coordination' and 'capacities' were defined as joint context for all countries, as they were assessed as weak in almost all cases. Shortening the list 7 'Capacities' also overlapped with another factor, 'effectiveness.' Three factors -'international engagement,' 'federalism' and 'economic stability' -were excluded due to their relatively weak theoretical relation with REDD+ and their lack of prioritization by survey respondents. Shortening the list The 10 remaining factors were divided into two categories: remote factors (elements of the institutional context) and proximate factors (elements of the policy arena). The 12 countries analyzed all have in common several factors that are important for the success or failure of REDD+. As they do not differ among the countries, they are not included as causal factors but are the joint context which defines the general setting in which the causal conditions for REDD+ are analyzed. This joint context is that all cases are forest-rich tropical developing or emerging countries with a political commitment to REDD+ but with powerful drivers of deforestation, weak multilevel governance, low cross-sectoral horizontal coordination and inadequate capacity -all characteristics that hinder the quick implementation of a 3E REDD+. Political commitment to REDD (COM) 10. Inclusiveness of the policy process (INCL) Further shortening the list These were further reduced as follows: PRES was seen as partly overlapping with AUT (in the aspect of economic significance of forests), with AUT being more relevant. Therefore, PRES was excluded. LEG and EFF were seen as closely related as well, as many country experts commented on the lack of effectiveness and implementation of legislation. Therefore, both were combined into a new condition, 'effectiveness of forest legislation, policy and governance' (also coded EFF); four cases in which the values for the two conditions differed were reassessed. OWN was seen as being partly represented by COM and INCL and was assessed as among the least important factors in the online survey, so it was excluded. CHA was also rated low in the online survey; it was as part of a government's political commitment (COM) or even as an outcome rather than a factor. Thus, CHA was excluded as well. As a result of this process, six factors were chosen for the two-step QCA, again divided into remote and proximate conditions. Dialogue with the cases Next, a first round of QCA -a 'dialogue with the cases' -was conducted. Among the remote conditions, we saw it as necessary to include at least one environmental factor; thus, PRES was reinstated and took the place of AUT (which, as mentioned above, overlapped with PRES); this aspect is now covered from a more natural-resources-oriented perspective. Since GOV had weak values in almost all countries, we decided to consider it as a joint framework condition. Dialogue with the cases Among the proximate conditions, political commitment (COM) was assessed positive in all the study countries, so we removed it from the list and reinstated national ownership (OWN). Dialogue with the cases Already initiated policy change (CHA) was also reinstated but defined more strictly as a factor rather than an outcome. And it was redefined as a remote condition, as it is something that happens before REDD+ policies are established and thus is among the preconditions. Dialogue with the cases These exercises produced the final list of factors, providing the comparable quintessence of two years of intensive case-specific research by almost 50 experts. Using QCA to draw inferences from data QCA is useful both for structuring data and validating assessments, as described in the previous section, and for analyzing the resulting material to produce tentative answers. Using QCA to draw inferences from data One objective of GCS-REDD is to formulate recommendations for national policy makers about strategies and institutional designs for achieving efficient, effective and equitable REDD+ policy. Using QCA to draw inferences from data These recommendations can be formulated specifically for the countries studied, but in order to make more general recommendations that could apply to other countries, it is important to have a basis for making reliable generalizations. QCA allows such inferences to be made without neglecting the very different case-specific circumstances and the different paths countries may choose to realize REDD+. Using QCA to draw inferences from data Box 1 summarizes the main inferences and results we got from the QCA analysis of GSC-REDD data. Using QCA to draw inferences from data As could be shown, with this tool it was possible to identify not only the institutional conditions that need to be in place to achieve successful REDD+ policies, but also which elements of the policy process are needed and how these two levels interrelate with each other. Using QCA to draw inferences from data However, since we have only three cases (Brazil, Indonesia and Vietnam) with the outcome REDD = 1 (in other words, that have established a comprehensive policy targeting transformational change in the REDD+ policy domain), and these had different enabling remote conditions, the inferences we can draw from their comparison are limited; too many possible combinations of conditions are unobserved. Nevertheless, in particular when compared with the combinations leading to outcome REDD = 0 and linking the results to case knowledge (Korhonen-Kurki et al. 2013) , some clear inferences can be made. When more countries have established successful REDD+ policies, the new data can be fed into the QCA and we will get a more robust base for inferences. Challenges and limitations of QCA This section discusses some drawbacks to QCA and the challenges in applying it to GCS-REDD and the REDD+ process. Selection of cases and conditions The selection of cases, conditions and indicators has a strong impact on the research results, including conclusions on causal relations, and therefore must be based on careful consideration and strong arguments in order to avoid subjectivity. For this study, the cases were preselected by their inclusion in GCS-REDD, which hindered theory-based case selection, and were low in number. QCA faces the same challenge as all studies with a small number of cases: only a limited number of factors or conditions can be considered if one wants to make valid inferences. The research design involves many factors that are assumed to have an impact; these are complemented by those that evolve from empirical research. It was necessary to reduce the number of factors and to find a theoretically based common definition of cases in order to define them as a sample. The reduction of conditions took place through an extensive participatory process. Selection of cases and conditions A greater variety of cases leads to a greater number of conditions. Less variety enables only limited generalization but provides better grounds for comparison. One possible strategy is to seek cases that share features or have a similar context, so that many factors are controlled for. In the GCS-REDD context, it was important to find a clear definition of the countries included in the analysis that also makes the range of possible inferences clear. Empirical diversity Related to the classical problem of too few cases and too many variables is the challenge of limited empirical diversity. With 12 cases, GCS-REDD is at the lower limit of adequate cases for QCA. As outlined above, 2 n possible combinations of conditions need to be checked, where n = the number of conditions. Ideally, all these possible combinations would be observed and analyzed. But this is hardly ever the case, so that for some combinations of factors, the truth table will not show any cases. Some combinations are simply not possible for logical reasons -for example, a high coverage Box 1. Insights from two-step QCA for establishing REDD+ in the context of weak governance Forest governance is weak in most REDD+ countries and can be expected to undermine efforts to establish REDD+. Therefore, CIFOR's QCA study on REDD+ has aimed to identify which preconditions are necessary and/ or sufficient for REDD+ to achieve transformational change* in the context of weak governance. Using the twostep QCA, we can notice that only three of the 12 countries achieved outcome 1 (Brazil, Indonesia and Vietnam), and these are divided into two sets of enabling remote conditions ( EFF*CHA and PRES*eff*CHA). In step 2 of the analysis, OWN and COAL were observed as necessary proximate factors with both remote settings. Empirical diversity Although the number of cases in step 2 was very limited, by comparing the configurations of these successful cases with those of unsuccessful cases, it is possible to draw some clear inferences about the necessary conditions and different sets of sufficient configurations for comprehensive REDD+ policies to be formulated and implemented. Empirical diversity A crucial institutional factor is having already initiated policy changes, which is a necessary part of both sufficient configurations. Especially in a context of overall weak law enforcement and governance, existing policy change efforts can smooth the path for REDD+. For example, in Vietnam, a path change from businessas-usual approaches was initiated with the launch of pilot Payment for Environmental Services schemes in 2008. Empirical diversity Nevertheless, the present analysis shows that this factor alone is not sufficient to enable comprehensive REDD+ policies, but must be accompanied by either key elements of effective forest legislation, policy and governance (as in Brazil and Vietnam) or by high pressure from a shortage of forest resources (as in Indonesia). As the case of Peru shows, even in the presence of national ownership and transformational coalitions, REDD+ policy development will not be successful if no enabling institutional preconditions other than prior policy change are in place. Empirical diversity Among the policy arena conditions, national ownership and transformational coalitions are necessary conditions and when in combination with both outcome-enabling remote configurations they are sufficient for outcome. All the successful countries have strong national ownership of their REDD+ policy processes. All three successful cases are also characterized by the presence of transformational coalitions. The present analysis indicates that the inclusiveness of policy processes plays only a minor role. Countries that have centralized and relatively authoritarian systems (e.g. Vietnam) or that have strong national leadership over the process (e.g. Indonesia) have successfully established the necessary foundations for effective REDD+ even though the process is not inclusive. Empirical diversity To conclude, these results indicate path dependencies and institutional stickiness in all the study countries. Only countries already undertaking institutional change have been able to establish REDD+ policies in a relatively short period -but only in the presence of either high pressure from forest resource shortages or key features of effective forest legislation, policy and governance. Furthermore, where an enabling institutional setting is in place, the policy arena conditions of national ownership and transformational coalitions are crucial. When these proximate conditions did not have the enabling remote setting, they did not lead to a successful outcome. Empirical diversity * 'Transformational change' is understood here as a shift "in discourse, attitudes, power relations, and deliberate policy and protest action that leads policy formulation and implementation away from business as usual policy approaches that directly or indirectly support deforestation and forest degradation" (Brockhaus and Angelsen 2012, 16-17) . Empirical diversity of tropical rainforests in the northern hemisphere, or an authoritarian regime with a high degree of stakeholder participation. Others are historically implausible -for example, a powerful role for private forest businesses and a high degree of equitable benefit sharing with indigenous people. But even if these are excluded from the analysis, a number of combinations of conditions usually remain that are possible but do not occur in the sample ('logical remainders'). We do not know whether or not these would lead to the outcome, and this restricts the validity of our inferences. Empirical diversity The best way to reduce the number of logical remainders is to select as few conditions as possible. As a matter of fact, their number is higher in fuzzyset QCA and multi-value QCA, as conditions can have more than two values and thus more combinations are possible. Schneider and Wagemann (2006) saw it as a virtue that the researcher is forced to think about nonexistent cases, but conceded that no really convincing solution to the problem of logical remainders existed. Therefore, they developed the two-step fuzzy-set QCA approach described above. Blatter et al. (2007, 210ff) proposed several solutions to reduce the number of logical remainders, although they considered none of them really satisfying: Empirical diversity • Most parsimonious solution: For all outcomes values are chosen (with computer simulation by software) so that the most parsimonious reduced formula is obtained. Empirical diversity • Blanket assumption: All outcomes are treated as if they showed the outcome 0, and only empirically observed cases are included in the analysis. Empirical diversity • Thought experiment: The outcome is assessed based on theoretical assumptions by the researcher. Empirical diversity The problem is less relevant if we want to make only statements about the cases we observed and accept that the result will be more complex, but it is more relevant if we want to make more parsimonious and generalized statements. Empirical diversity In our study, 2 3 + 2 3+2 combinations are possible (see the discussion of two-step fuzzy-set QCA in Section 3). Of these 8 + 32 = 40 logically possible combinations, only 12 were observed. This problem was in particular relevant for the analysis of the proximate factors in the two-step QCA, as only three countries had a positive outcome and could be included in the comparison. Thus, while all eight possible combinations of the remote factors were evident, of the 32 possible combinations of the proximate conditions with the two remote conditions, only four could be observed. In principle, this was not enough to make meaningful inferences. While these two challenges in principle apply to all QCA applications, other problems occur specifically with certain types of QCA or research settings. Binary coding (csQCA) The original version of QCA (crisp-set QCA) makes it necessary to dichotomize all factors -every condition has to be assessed as either being fully present (1) or fully absent (0). This does not allow gradual assessment. Critics argue that many social and political phenomena are too complex for a binary assessment (Pennings 2007, 347 ) -such as economic development, unemployment and poverty (in the REDD+ context, this could be participation, corruption or forest degradation). On the other hand,
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