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Abstract

There are many different ways of analyzing panel data in QCA. In this article, I have demonstrated one of these ways, that is, how to build a panel data QCA model, following Garcia-Castro and Arino (2016). I have applied my own research data, and analyzed it through the packages, “QCA” and “Set Methods”, software R. I have particularly focused on two main steps in panel data QCA analysis, first, how to test for necessary and sufficient conditions, and second, how to interpret panel data QCA results. By demonstrating these steps, I hope to help future scholars in their own work on panel data QCA.

Keywords

Panel data QCA Software R panel data consistency scores panel data coverage scores robustness in panel data QCA model

Introduction

Qualitative Comparative Analysis (QCA) was originally developed by Ragin (1987) in his book, “The Comparative Method”, as a comparative case-oriented research method, based on combining Boolean algebra and fuzzy-set theory. The aim of QCA is to help a researcher understand the configuration or pathway through which a condition can impact an outcome, by testing for necessary and sufficient conditions (Sager and Thomann, 2017). To do this, QCA believes in causal complexity, which includes three main assumptions, conjunctural causation, equifinality, and causal asymmetry (Ragin 1987, 2000, 2008, 2014; Rihoux and Ragin, 2009; Schneider and Wagemann 2012; Ragin and Fiss, 2017; Ragin and Fiss, 2019; Sager and Thomann, 2017; Schneider and Maerz 2017; Dusa 2021; Oana, Schneider, and Thomann 2021; Mello 2021.

Though initially applied to analyze cross-sectional data, in the last few years, researchers have started to apply QCA while analyzing panel data, as well. One of the most common approaches is Garcia-Castro and Arino’s (2016) panel data QCA model. In their article, “A General Approach to Panel Data Set-Theoretic Research”, Garcia-Castro and Arino (2016), describes the theoretical and mathematical assumptions behind panel data QCA.

Despite this, there are no clear guidelines regarding how to apply Garcia-Castro and Arino’s (2016) panel data QCA model, including the testing for necessary and sufficient conditions, and interpreting the data analysis results, in a panel data QCA model. In this methodological note, I address this gap, by discussing the steps that a researcher is expected to follow, while building and analyzing a panel data QCA model. I have applied the R packages SetMethods package (Oana et al., 2021) and QCA package (Dusa, 2019) to demonstrate these steps. In the following sections, I will first briefly review the assumptions of panel data Qualitative Comparative Analysis. Second, I will discuss the different steps of a panel data QCA research process. In section III, I will apply my research data to demonstrate the testing of necessary and sufficient conditions, and how to interpret the data analysis results. In section IV, I will discuss the importance of panel data QCA as a method of data analysis. And, in section V, I will conclude my methodological report, by briefly summarizing the main steps of Garcia-Castro and Arino's (2016) panel data QCA model. Through this, I hope to guide current and future research scholars in their own work on panel data QCA.

Assumptions of QCA, including panel data QCA

There are six main assumptions of QCA. First, in QCA, independent variables are known as conditions and dependent variables are known as outcomes (Ragin, 1987: XXIII). Second, QCA emphasizes the effect of the combination of conditions, through multiplication (logical AND), instead of focusing on the average effect of each condition on an outcome (Schneider and Wagemann, 2012: 105; 70–71). Third, QCA emphasizes equifinality or multiple causation (Schneider and Wagemann, 2012: 94–95). According to this assumption, there might be many different pathways to the same outcome. Each of these pathways are joined through addition, also known as logical OR. Each pathway might also consist of INUS or SUIN conditions (Schneider and Wagemann, 2012: 70–71; 94–95).

Fourth, a QCA model analyzes causality by testing for necessary and sufficient conditions. In panel data QCA, the results from the testing of these conditions are interpreted with the help of cross-sectional consistency and coverage, and across time consistency and coverage (Garcia-Castro and Arino, 2016). The across-time consistency and coverage act as a robustness check for cross-sectional consistency and coverage, and helps a researcher understand whether the impact of conditions varies over the time-period and across cases studied (Garcia-Castro and Arino, 2016: 63). So, in a panel data QCA model, there are three main types of consistency and coverage scores (Furnari, 2018; Garcia-Castro and Arino, 2016). I have described each of these consistency and coverage scores below and summarized it in Table 1.

Table 1.

Types of panel data consistency and coverage scores.

Measures	Definition	Number of measures
Within consistency (WICONS)	Longitudinal consistency of the set-subset relation for each case in the panel over time, by holding the time as constant.	Depends on the number of cases/countries studied
Between consistency (BECONS)	Cross-sectional consistency of the set-subset relation for each year in the panel, by holding the case as constant.	Depends on the number of years studied
Pooled consistency (POCONS)	Overall consistency when the country/time is not taken into account	One
Within coverage (WICOV)	Measures the set-subset across time for each country in the panel	Depends on the number of cases/countries studied
Between coverage (BECOV)	Measures the cross-sectional coverage for each year t in the panel	Depends on the number of years studied
Pooled coverage (POCOV)	Overall coverage score, without taking the country or year into consideration	One

Fifth, QCA believes in the set-theoretic assumptions of asymmetric relations (Schneider and Wagemann, 2012: 93–94). The reasons for the occurrence of an outcome are different from the non-occurrence of an outcome (Schneider and Wagemann, 2012: 93–94). As a result, the reasons for the occurrence and the non-occurrence of an outcome should be studied separately Mello 2021, pp. 69-73; Ragin 1987, Schneider and Wagemann, 2012; pp. 93-94) (Ragin, 1987; Schneider and Wagemann, 2012: 93–94).

Finally, in a panel data QCA model, the unit of analysis is country_year.

Consistency types in a panel data QCA model

As shown in Table 1, there are three main types of consistency scores in a panel data QCA model. The within consistency (WICONS) can be defined as the longitudinal consistency of the set-subset relation, for each case in the panel over time, by holding the time as constant (Garcia-Castro and Arino, 2016). The between consistency (BECONS) can be defined as the cross-sectional consistency of the set-subset relation, for each year in the panel, by holding the case as constant (Garcia-Castro and Arino, 2016). The pooled consistency (POCONS) refers to the overall consistency, when the country or time is not taken in account (Garcia-Castro and Arino, 2016). In a panel data QCA model, the number of WICONS depends on the number of cases/countries studied, the number of BECONS depends on the number of years, and there is one single POCON value (Garcia-Castro and Arino, 2016).

To interpret the results of a panel data QCA model, a researcher needs to first determine the value of POCON (Garcia-Castro and Arino, 2016). If country and time do not play a key role in determining the set-subset relation, then the value of POCON is one (Garcia-Castro and Arino, 2016). In case the value of POCON is not equal to one, it shows that there are inconsistencies (Garcia-Castro and Arino, 2016). These inconsistencies might be due to cases (BECONS) or years (WICONS; Garcia-Castro and Arino, 2016). Hence, a researcher needs to study all the values in the model, to understand whether the model shows inconsistent BECONS or WICONS (Garcia-Castro and Arino, 2016).

A researcher can also study the BECONS distance and WICONS distance. These distances range from zero to one (Garcia-Castro and Arino, 2016). The BECONS and WICONS distance needs to be closer to zero to show that the set-subset relation is not time or case dependent (Garcia-Castro and Arino, 2016). There are four different options while analyzing the BECONS and WICONS distances (Garcia-Castro and Arino, 2016). I have tabulated these options in Table 2 (Garcia-Castro and Arino, 2016: 67).

Table 2.

Options while analyzing the BECONS and WICONS.

BECONS distance = WICONS distance = 0 (no evidence of case or year effects)

BECONS distance = WICONS distance ≠ 0 (some evidence of case or year effects)

BECONS distance > WICONS distance (year effects > cross-sectional effects)

WICONS distance > BECONS distance (cross-sectional effects > year effects)

Coverage types in a panel data QCA model

If a panel data QCA model shows time (WICONS) or case (BECONS) inconsistency, we then need to analyze whether these inconsistencies are empirically relevant. We can analyze this relevance with the help of the coverage scores (Garcia-Castro and Arino, 2016). There are three main types of coverage scores, POCOV, BECOV, and WICOV (Garcia-Castro and Arino, 2016). The POCOV indicates the overall/pooled coverage score, without taking the time or the country effects into consideration (Garcia-Castro and Arino, 2016). The BECOV (between coverage) is a measure of the cross-sectional coverage, for each year t in the panel (Garcia-Castro and Arino, 2016). The WICOV (within coverage) measures the set-subset relation across time, for each country in the panel (Garcia-Castro and Arino, 2016).

In the next section, I have first summarized the main steps in building a panel data QCA model, and in sections III and IV, I have applied my own research data, to demonstrate how researchers can test for necessary and sufficient conditions in a panel data QCA model.

Steps in building a panel data QCA model

There are five main steps in building a panel data QCA model (Rihoux and Lobe, 2009). These five steps are case-study knowledge, theory specification, set-calibration, specifying the directional expectations regarding the impact of conditions on an outcome, testing for necessary conditions, testing for sufficient conditions, and if necessary, theory-evaluation.

Amongst these five steps, the testing of necessary and sufficient conditions in Garcia-Castro and Arino’s panel data QCA model is a little bit different, as compared to cross-sectional QCA. Hence, in this research note, I have just focused on describing the steps required for testing necessary and sufficient conditions in a panel data QCA model. I have applied my own research data to demonstrate each of these steps, in sections III and IV, below.

Testing necessary conditions in a panel data QCA model

In panel data QCA, a necessary condition is a condition that must be present for the outcome to occur (Ragin, 1987: 99). A condition (X) is necessary for Y, if X is always present when Y occurs, Y does not occur in the absence of X, and X is a superset of Y (Dusa, 2019). The statement X is necessary for Y can be written as “X≤Y” (Dusa, 2019). In QCA, a condition X is necessary for Y, if its consistency value is at least equal to 0.9, along with a high coverage and a RoN score of greater than 0.5 (Oana, Schneider, and Thomann 2021, pp. 74-75) (Dusa, 2019; Schneider and Wagemann, 2012).

After measuring the consistency, a researcher can also measure the coverage value of a condition. Coverage is a measure of how trivial or relevant a condition X is for an outcome Y (Dusa, 2019: 110–118). A necessary condition should have a high coverage value, along with a higher Relevance of Necessity (RoN) score as compared to the coverage score (Dusa, 2019: 112). If a condition X is necessary for Y, then following QCA’s assumption of causal asymmetry the absence of condition X cannot lead to the presence of outcome Y. Hence, the presence and absence of a condition needs to be tested separately (Schneider and Wagemann, 2012: 155–159).

How to test for necessary conditions in a panel data QCA model?

In the next few paragraphs, I am going to apply my own research data (Bhattacharya 2020), to demonstrate the testing of necessary conditions in panel data QCA. In my research, I have analyzed how microfinance institutions lead to an increase the economic participation of women at the level of the national economy. My research shows that microfinance institutions combine with factors, like the presence of human rights treaties, high life expectancy for females, high female literacy rate, high government control of corruption, high access to basic facilities like sanitation, unemployment benefits, and becoming a member of the European Union, to increase the economic participation of women (Bhattacharya, 2020). The effect of these factors varies across the three countries and the years that I have studied, Bosnia and Herzegovina (BiH), Croatia (HRV), and Montenegro (MNE), 1999–2015, further emphasizing the importance of contextual factors.

I have tested two main hypotheses:

First, I have hypothesized that microfinance institutions, by itself, will be able to increase the economic participation of women, at the level of the national economy. So, I have tested the extent of microfinance institutions as a necessary condition. According to this hypothesis, we will not be able to increase the economic participation of women, in the context of newly independent post-conflict countries, without applying microfinance.

Second, I have hypothesized that the presence of other political, economic, and social freedoms, along with the presence of microfinance institutions, might be able to increase the economic participation of women, at the level of the national economy. In this case, the extent of microfinance institutions becomes a sufficient condition. According to this hypothesis, microfinance will be able to increase the economic participation of women, only in the presence of basic political, economic, and social freedoms, as mentioned in Sen’s Theory of Development as Freedom (2000) and found in my case studies.

My necessary condition is the presence of microfinance institutions. I have created this macro-condition, by combining three variables, through fuzzyand() My sufficient conditions are access to political freedom (measured through high political rights and civil liberty scale, Freedom House Report), economic facilities like economic growth (measured through high GDP, World Bank [2023b]), social opportunities like access to education and health care (measured through high percentage of literate females and high life expectancy at birth for females, World Bank [2023c]), transparency guarantees like high control of corruption (Control of Corruption Scale, World Bank), and access to protective security measures, measured through high government effectiveness (World Governance Indicators; World Bank 2023d, 2023e, 2023f). I have also measured whether my cases are members of the European Union, and whether they have signed the 18 international human rights laws (measured through the UN Human Rights Office of the High Commissioner), as sufficient conditions, that might impact the economic participation of women.

My dependent variable is economic participation of women. I have created this variable by combining the four main economic sectors of own-account workers (informal economy), family workers (informal economy), employees (formal economy), and employers (formal economy), as mentioned in the 2016 International Labor Organization’s Key Indicators of Labor Market report (ILO KILM, 2016). These four sectors are interconnected, and sometimes, employees tend to move from one sector to the other. Hence, I have combined these four sectors into one macro-condition. I have tabulated my conditions and outcome variables in Table 3.

Table 3.

Causal analysis model (conditions and outcome variables).

Table built based on concepts, as defined by Goertz (2006).

Concept	Dimension/characteristic	Indicator/variable	Abbreviations	Type of set	Type of calibration	Set label
Macro-condition: presence of microfinance	Number of microfinance institutions, government support for microfinance institutions, and whether microfinance institutions were created throughout the country	Presence of MFISsource: World Bank\| Databank\|MIX Market	HPM	Crisp for each condition	Crisp set	High presence of microfinance
Macro-condition: access to political freedom	Access to political and civil rights, and the extent of democracy within the country	Democracy scale, Source: Polity IV DatasetPolitical Rights & Civil Liberty ScaleSource: Freedom Rating Scale, Freedom House Reports	HPF	Fuzzy	Ragin’s indirect calibration method	High access to political freedom
Access to economic facilities	Economic growth-> increases opportunities available to individuals for production, consumption, and exchange	Gross Domestic ProductSource: World Bank	GDP	Fuzzy	Ragin’s indirect calibration method	High access to economic facilities
Macro-condition:access to socialopportunities	Access to basic education and health care which will help an individual live a better life	Percentage of literate females between the ages 15 and 24 years.Source: World BankLife expectancy at birth for females.Measured in years.Source: World Bank	HSO	Fuzzy	Ragin’s Indirect Calibration Method	High Social Freedom
Access to transparency guarantees	Society operates on the basic presumption of trust. Need for openness, guarantees of disclosure, and lucidity	Control of corruption scaleSource: World Governance Indicators\| World Bank	NCOR	Fuzzy	Ragin’s indirect calibration method	High control of corruption
Access to protective security	Effectiveness of public institutions in ensuring access to basic facilities like sanitation, health, and unemployment benefits	Government effectiveness scaleSource: World Governance Indicators\| World Bank	NEFFECT	Fuzzy	Ragin’s indirect calibration method	High government effectiveness
E.U. membership	Are the countries full members of the E.U.?	Joining the E.U.: 27 members of the E.U.Source: European Union database (Case Study Condition)	EUMB	Fuzzy	Ragin’s direct calibration method	Full members of the European Union
Signed the 18 international human rights treaties	Members of human rights treaties to eliminate all forms of racial and gender equality	Ratification of 18 international human rights treaties Source: UN Human Rights Office of the High Commissioner	INTHRT	Fuzzy	Ragin’s indirect calibration method	High presence of fundamental international human rights treaties
Macro-condition: Economic participation of women	Outcome 1: Economic contribution of women as own-account workers(Self-employed do not have any persons working for them) Outcome 2: Economic contribution of women as female family workers (Self-employed have family members working for them) Outcome 3: Economic contribution of women as female employees (Holds paid employment jobs with remuneration and contract) Outcome 4: Economic contribution of women as female employers (Self-employed, but have employees working for them with paid employment contract)	Number of women employed belonging to the age group of 15–65 years.Source: Employment by Sex and Status in Employment (KILM 3); ILO Modeled Estimates – Annual, calculated in thousands	NWE: fuzzyand(OWN, FAM, EMPE, EMPR)	Fuzzy	Ragin’s indirect calibration method	High economic participation by female own-account workers

Interpreting the results from the testing of necessary condition

My data analysis results show that microfinance, by itself, is not able to increase the economic participation of women, Table 5. Though the between-consistency scores (2008-2014) are greater than 0.9, the coverage score is less than 0.5, and the absence of microfinance still led to the presence of the outcome, for these between-consistency scores. Similarly, my other political, economic, and social conditions, like access to education, health care, economic growth, and availability of political and civil liberties, are also not able to increase the economic participation of women, independently. As seen in Table 4, the pooled consistency scores (inclN) for the presence of each of the conditions are less than 0.9. Hence, none of the conditions, including the presence of microfinance institutions, can increase the economic participation of women, by itself.

Table 4.

Testing each condition as a necessary condition.

	inclN	RoN	covN
HPM	0.601	0.276	0.307
~HPM	0.399	0.942	0.769
EUM	0.652	0.745	0.583
~EUM	0.752	0.648	0.554
HRT	0.615	0.741	0.561
~HRT	0.758	0.638	0.549
GDP	0.896	0.821	0.760
~GDP	0.472	0.588	0.364
HPF	0.416	0.573	0.322
~HPF	0.767	0.758	0.649
HSO	0.664	0.952	0.884
~HSO	0.758	0.438	0.440
NCOR	0.609	0.670	0.497
~NCOR	0.659	0.674	0.527
NEFFECT	0.671	0.683	0.540
~NEFFECT	0.628	0.673	0.509

I have applied the cluster () function from the QCA package, to achieve these results (Dusa, 2019).

If a researcher uses this cluster () function in the R software, then the result from the testing of necessary condition looks like Table 5. Researchers then need to restructure this into Table 4. This restructured table only reports the pooled consistencies and coverage scores, with the absence of conditions denoted with a tilde sign (∼). To test the Relevance of necessity, I have applied the parameters of fit, pof () command, from the QCA package (Dusa, 2019). Researchers can also apply the QCAfit () function in setMethods package (Oana and Schneider, 2018. We can visualize the results through the pimplot(), xyplot(), xy.plot(), and Venn diagrams (Oana and Schneider 2018, Dusa 2019). I have applied the xyplot () function to visualize the data analysis result from the testing of HPM as a necessary condition (Figure 1).

Table 5.

Necessary condition (presence of MFIs) and outcome (economic participation of women).

Consistencies:
Pooled:	0.601
Between 1999 (3) :	0.379
Between 2000 (3) :	0.389
Between 2001 (3) :	0.392
Between 2002 (3) :	0.394
Between 2003 (3) :	0.401
Between 2004 (3) :	0.438
Between 2005 (3) :	0.494
Between 2006 (3) :	0.527
Between 2007 (3) :	0.526
Between 2008 (2) :	1
Between 2009 (2) :	1
Between 2010 (2) :	1
Between 2011 (2) :	1
Between 2012 (2) :	1
Between 2013 (2) :	1
Between 2014 (2) :	1
Between 2015 (2) :	1
Within BiH (17) :	1
Within HRV (9) :	0
Within MNE (17) :	1
Distances:
Between to Pooled:	0.098
Within to Pooled:	0.408
Coverages:
Pooled:	0.307
Between 1999 (3) :	0.288
Between 2000 (3) :	0.292
Between 2001 (3) :	0.294
Between 2002 (3) :	0.294
Between 2003 (3) :	0.296
Between 2004 (3) :	0.297
Between 2005 (3) :	0.281
Between 2006 (3) :	0.282
Between 2007 (3) :	0.291
Between 2008 (2) :	0.35
Between 2009 (2) :	0.313
Between 2010 (2) :	0.345
Between 2011 (2) :	0.328
Between 2012 (2) :	0.339
Between 2013 (2) :	0.334
Between 2014 (2) :	0.303
Between 2015 (2) :	0.298
Within BiH (17) :	0.546
Within HRV (9) :	NaN
Within MNE (17) :	0.068

Figure 1.

High Presence of Microfinance (HPM) as necessary condition for Outcome (High Economic Participation of Women, NWE)

In a panel data QCA model, we can also understand how the impact of a condition has changed over time, by interpreting the pooled, within, and between consistency scores. If the pooled consistency is not equal to one, then the data results show time or case effects. The between consistency (BECONS), shows the effect of the condition “MFIS” on the outcome for each year, holding the cases/countries studied constant. The within consistency (WICONS), shows the effect of the condition “MFIS” on the outcome holding the years constant (shown in brackets, Table 5). The results for the presence of MFIs (Table 5), show that the pooled consistency is 0.601 (not equal to one). Hence, there are time or country effects on the set–subset relationship between the condition “MFIS” and the outcome. The between-consistency score changes drastically for the year 2008 (increase from 2007, Table 5). The distances of between and within consistency scores show that the overall within case consistency (Within to pooled, 0.408) is greater than the between case consistency (Between to pooled, 0.098), meaning that the effect of microfinance institutions on the economic participation of women, depend on the country/cases more, as compared to the years studied (Table 5).

Since HPM is not a necessary condition, we do not need to interpret the coverage and the relevance score of necessary condition. But, just to demonstrate, the overall coverage score is 0.307, as seen in Table 4 and 5. This indicates low coverage. While testing for necessary conditions, we also need to analyze the relevance of necessary (RoN) score. If the relevance of necessary condition (RoN) score is higher than the coverage score, then it shows that the variable is a relevant necessary condition. In this case, HPM is neither a necessary condition nor is it relevant for economic participation of women, at the level of the national economy, HNWE (Bhattacharya, 2020), as the RoN score is less than the coverage score (Table 4). This can be seen in Figure 1, as there are a few data points which are below the diagonal, but below the y-value of 0.5 (lower right quadrant) (Oana, Schneider, and Thomann 2019, pp.75-77).

Testing sufficient conditions in a panel data QCA model

In QCA, researchers can also analyze causality by testing for sufficient conditions. This can help a researcher understand if a combination of conditions causes an outcome. According to Ragin, a cause can be defined as sufficient if it can produce the outcome but is not the only cause to do so (Ragin, 1987: 99). As an example, X is a sufficient condition for Y, if X is present when Y occurs, X does not occur in the absence of Y, and X is a subset of Y (Dusa, 2019). In sufficiency, X can be a single condition or a combination of conditions (*) and is denoted by “X => Y”. For a sufficient condition, consistency score should be at least 0.75, along with high coverage and a PRI score of greater than 0.50, to avoid simultaneous subset relations (Oana, Schneider, and Thomann 2021, pp.93-96) (Schneider and Wagemann, 2012: 144).

There are three main steps in the testing for sufficient conditions in a panel data QCA model. The first step is to create a truth table. A truth table is the same as a data matrix but slightly different (Ragin, 1987: 87–88). In a truth table, the columns represent the variables, while each row represents the logically possible combinations for each independent variable independent variable, that leads to the presence of the outcome (Outcome, 1) (Ragin, 1987: 87-88). A truth table also shows rows with logical remainders (outcome, ?), and absence of outcome (outcome, 0) (Oana, Schneider, and Thomann 2021, p. 109) (Ragin, 1987: 87–88). (Dusa, 2019).

The second step is to simplify the results of a truth table through Boolean minimization which helps us identify redundant conjuncts and logically redundant prime implicants (Oana, Schneider, and Thomann 2021, pp. 112-114) (Ragin, 1987: 93–98). Boolean minimization helps us remove remove redundancies from the truth table. The third step is to identify and address logical remainders (with outcome, ?) (Oana, Schneider and Thomann, 2021, pp. 122-130). This step is knows as standard analysis, and it creates three types of solutions: conservative/complex, most parsimonious, and intermediate (Oana, Schneider and Thomann, 2021, pp. 122-130). The fourth step is to create enhanced standard analysis solutions by identifying and removing untenable assumptions, logical remainders which are contradictory simplifying, contradicts claims of necessity, and are implausible remainders (Oana, Schneider and Thomann, 2021, pp. 131-140). There are three different types of enhanced standard analysis solutions: enhanced conservative, enhanced parsimonious, and enhanced intermediate. In QCA, researchers are always encouraged to focus on the enhanced intermediate solution for further analysis (Dusa, 2019: 139–193; Schneider and Wagemann, 2012).

In the testing of sufficient conditions in a panel data QCA model, there is one last step, that is using the results (pathways) of the enhanced intermediate/parsimonious solution, as sufficient condition (Dusa, 2019: 139–193), to understand how the causal pathways or configurations, vary over time and across cases.

I have applied my own research data to demonstrate these steps. I have added the results from the truth table, Boolean minimization, conservative solution, parsimonious solution, intermediate solution, enhanced conservative solution, enhanced parsimonious solution, and enhanced intermediate solution, as online supplementary material.

I have tested my model for robustness, by including graphical representation of my variables (to understand change over time and across cases), a check for skewness, applying a theoretical basis to understand the directional expectation for my conditions and outcome variable, testing for necessary conditions first, then testing for sufficient conditions, using different calibration measures, and testing any change in results, and following the enhanced intermediate solution to interpret the data analysis results.

How to test for sufficient conditions in a panel data QCA model? Demonstration

To test for sufficient conditions, I have first created a Truth Table, then logically minimized it, then created the conservative, most parsimonious, intermediate, enhanced conservative, enhanced parsimonious, and enhanced intermediate solutions. As discussed above, we also need to analyze whether the impact was context dependent (countries studied, WICONS) or time dependent (years studied, BECONS). To do this, I have applied the cluster () command in the set methods QCA package (Oana and Schneider, 2018). I have then applied the smmr() function to focus on the most-typical case, as a part of my data analysis interpretation and post QCA analysis. Below, I have interpreted the results from my most typical case, Bosnia and Herzegovina, 2011.

Table 6.

Directional Expectation between Conditions and Outcome for the intermediate and enhanced intermediate solutions.

Conditions	Increases eco. participation	Decreases eco. Participation
HPM	Present (1)	Absent (0)
EUM	Present (1)	Absent (0)
HRT	Present (1)	Absent (0)
GDP	Present (1)	Absent (0)
HPF	Present (1)	Absent (0)
HSO	Present (1)	Absent (0)
NCOR	Present (1)	Absent (0)
NEFFECT	Present (1)	Absent (0)

My data analysis results from the testing of sufficient conditions, show that microfinance institutions can increase the economic participation of women, by combining with political, economic, and social resources, as mentioned in Sen's Theory of Development as Freedom. In fact, there are two different models (Model 1 and Model 2), through which microfinance institution might be able to increase the economic participation of women at the level of the national economy (Table 7).

Table 7.

Sufficient Conditions that can increase the economic contribution of women.

Path	Solutions	Consistency	PRI	Sol.Coverage	UniqueCoverage	CasesCovered
Model 1:
1	HPMEUM~HPF*~HSO	0.991	0.891	0.337	0.146	13,16; 34,36
	+
2	~HPM~EUMGDPHPFNEFFECT	1.000	1.000	0.176	0.176	2; 5; 8,11
	+
3	HPMEUMHRTGDP~HPF*NCOR	1.000	1.000	0.202	0.010	38
		Overall Solution consistency: 0.994
		Overall Solution PRI: 0.983
		Overall Solution coverage: 0.523
Model 2:
1	HPMEUM~HSO*~NCOR	0.804	0.219	0.363	0.207	13,16; 34,36
	+
2	~HPM~EUMGDPHPFNEFFECT	1.000	1.000	0.176	0.176	2; 5; 8,11
	+
3	HPMEUMHRTGDP~HPFHSONCOR	1.000	1.000	0.167	0.012	38
		Overall Solution consistency: 0.861
		Overall Solution PRI: 0.661
		Overall Solution coverage: 0.550

Model 1:

HPM*EUM*∼HPF*∼HSO + ∼HPM*∼EUM*GDP *HPF*NEFFECT + HPM*EUM*HRT*GDP*∼HPF*NCOR -> NWE

Model 2:

HPM*EUM*∼HSO*∼NCOR + ∼HPM*∼EUM*GDP*HPF*NEFFECT + HPM*EUM*HRT*GDP*∼HPF*HSO*NCOR -> NWE

My most typical was Bosnia and Herzegovina, 2011. There are two different pathways through which microfinance institutions was able to increase the economic participation of women: in Bosnia-Herzegovina, for the year 2011. Pathway 1: HPM*EUM*∼HPF*∼HSO → NWE, and Pathway 2: HPM*EUM*HSO*NCOR → NWE.

These pathways show a combination between high presence of microfinance (HPM), and becoming a potential candidate for European Union membership, that increased the economic participation of women, despite women in BiH lacking access to high social opportunities (∼HSO), high government control of corruption (∼NCOR), and/or high political freedom (∼HPF), Table 7. The final step in a QCA research process is to interpret why this case turned out to be the most typical case. To do this, researchers usually apply their case study knowledge. Researchers can also adopt process-tracing to analyze which of these two pathways increased the economic participation of women, in the most typical case, Bosnia-Herzegovina, 2011 (Goertz 2017; Oana, Schneider and Thomann, 2021). Since the purpose of this article is to demonstrate how to apply Garcia-Castro and Arino's panel data QCA model, I am just going to highlight a few reasons here.

BiH had faced a negative impact of the 2008 economic crisis, which led to huge unemployment. To address this, the World Bank and European Union had started financing new microfinance projects. This further support might have increased the presence of microfinance institutions, in turn creating new employment opportunities for women. Since BiH had already become a potential candidate of EU, it has been receiving economic and political support from EU. And one of the economic development policies that has been supported by EU is the application of microfinance institutions to increase the economic participation of women.

To visualize the data analysis results from the testing of sufficient conditions, researchers can apply the XYplot(), xy.plot(), and Venn diagrams (Oana and Schneider 2018, Dusa 2019). Another crucial factor in the testing for sufficient conditions is interpreting the unique and solution coverage scores. If a data model shows more than one pathway, then the unique coverage shows the relevance of each causal pathway, while the solution coverage shows the overall relevance of the entire model. In this case, for the pathway, HPM*EUM*∼HPF*∼HSO, the overall solution coverage is 0.337, and the unique coverage of this pathway is 0.146. I have applied the XYplot() function, to visualize Model 1, in Figure 2.

Figure 2.

Visualizing Model 1 as Sufficient Condition (Table 7)

Importance of panel data QCA as a data analysis method

In his book, “The Comparative Method”, Ragin (1987) defined Qualitative Comparative Analysis (QCA), as a comparative case-oriented research method that can be applied to study test a small to medium number of cases, to analyze whether a condition (independent variable) impacts an outcome (dependent variable), and to understand the causal pathway (how) the causal conditions impact an outcome (Ragin, 1987). Hence, in the realm of comparative research methods, panel data QCA is important because it can help us study how macro-social units have developed over time and across cases. Second, it can help us understand whether the change is due to the years (BECONS), or the countries studied (WICONS) (Verweij and Vis, 2021). Third, like cross-sectional QCA, panel data QCA can help researchers study a smaller number of cases. Fourth, a researcher can include data from various levels of analysis like micro, meso, and macro, to build a panel data QCA model.

Fifth, by combining features from both qualitative and quantitative research, panel data QCA has been able to broaden the range of data analysis approaches available to research scholars in the school of mixed methods. As an example, Garcia-Castro and Arino (2016) developed the panel data QCA model based on panel data econometrics. But, to build this model, researchers need to understand the cases studied, include variables from the case-study, calibrate variables based on the concept of relevant variation and qualitative change, and finally interpret the data analysis results based on the case study. And these are features that are usually applied in qualitative research.

But, in the last few years, scholars of QCA have pointed out a few disadvantages of this panel data QCA method. As an example, QCA usually believes in the concept of “qualitative change over time”, but, the panel data model as suggested by Garcia-Castro and Arino (2016), might not be able to capture this qualitative change over time. To address these disadvantages, researchers can apply alternatives like creating separate panel data models for equal intervals during the time studied, and applying comparative historical analysis, to understand whether condition A occurred before condition B. Researchers can also follow the guidelines of multi-method research as suggested by Goertz (2017) and Thomann (2019) and conduct a post QCA case study through process-tracing, to understand how the pathway for this impact changes over time and across cases.

Despite these disadvantages, Garcia-Castro and Arino’s (2016) panel data QCA model is an important development in the world of comparative research. This is due to its’ strengths like, focus on a small to medium number of case studies, include data from various levels of analysis, understand how the presence of conditions impacts an outcome, and how the pathway of this impact changes over time and across cases. Hence, in this research note, I have applied my own research data to highlight these advantages of panel data QCA. In the next section, I conclude my research note by briefly summarizing the main steps required to build a panel data QCA model.

Conclusion

Garcia-Castro and Arino's panel data QCA model (2016) can help us analyze how the impact of necessary and sufficient conditions, has changed over time and across cases. To do this, we include two additional columns in our data analysis, one identifying the cases (unit_id), and one identifying the years in which each case is being studied (cluster_id) (Dusa 2019, Oana, Schneider and Thomann, 2021, Bhattacharya 2020).

Second, we need to use the cluster () function, to analyze how the impact of a condition or combination of conditions has changed over time and across cases.

Moreover, while testing for sufficiency, with the cluster() function, we need to use the enhanced parsimonious or enhanced intermediate solutions, as the result or input (Dusa 2019).

Supplemental Material

sj-csv-1-mio-10.1177_20597991231179389 – Supplemental material for How to build and analyze a panel data QCA model? A methodological demonstration of Garcia-Castro and Arino’s panel data QCA model

Supplemental material, sj-csv-1-mio-10.1177_20597991231179389 for How to build and analyze a panel data QCA model? A methodological demonstration of Garcia-Castro and Arino’s panel data QCA model by Preya Bhattacharya in Methodological Innovations

Supplemental Material

sj-docx-2-mio-10.1177_20597991231179389 – Supplemental material for How to build and analyze a panel data QCA model? A methodological demonstration of Garcia-Castro and Arino’s panel data QCA model

Supplemental material, sj-docx-2-mio-10.1177_20597991231179389 for How to build and analyze a panel data QCA model? A methodological demonstration of Garcia-Castro and Arino’s panel data QCA model by Preya Bhattacharya in Methodological Innovations

Supplemental Material

sj-xlsx-3-mio-10.1177_20597991231179389 – Supplemental material for How to build and analyze a panel data QCA model? A methodological demonstration of Garcia-Castro and Arino’s panel data QCA model

Supplemental material, sj-xlsx-3-mio-10.1177_20597991231179389 for How to build and analyze a panel data QCA model? A methodological demonstration of Garcia-Castro and Arino’s panel data QCA model by Preya Bhattacharya in Methodological Innovations

Footnotes

Declaration of conflicting interests

The author declared no potential conflicts of interest with respect to the research,authorship,and/or publication of this article.

Funding

The author received no financial support for the research,authorship,and/or publication of this article.

ORCID iD

Preya Bhattacharya

Supplemental material

Supplementary material for this article is available online at Harvard Dataverse,

Author biography

Preya Bhattacharya is a postdoctoral fellow at the Sam Nunn School of International Affairs,Georgia Institute of Technology. She is currently working on her book manuscript,“An Introduction to Panel Data QCA in R”,and can be reached at pbhattac7@gatech.edu .

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