1 Introduction

In this article we analyze the strength of the relationship between shadow economy and corruption, because they both impose negative externalities on societies as a whole and on individuals. Being the ‘antipode’ to the formal economy (Edelbacher et al. 2016, p. 1), shadow economy encompasses all legal business activities that are conducted outside the reach of government authorities (AT Kearney and Schneider 2013, p. 2). Following the fact that many economic agents constantly breach tax laws that are set out to regulate the formal economy, state budgets are deprived of significant amounts of tax money that could otherwise be invested to increase public goods quality and improve living standards. Not to mention that employees are deprived of social security benefits when economic agents activate within the shadow economy. Therefore, shadow economy may not only impact economies around the world by hampering economic growth, but it may also negatively affect individuals’ economic wellbeing. According to conventional wisdom, corruption is defined as the breaching of laws and ethical standards by misusing authority for personal benefit. The extent of public corruption is given by the gap between the ‘number of decisions made by public persons and the extent to which decisions are made dishonestly’ (Neild 2002, p. 6). Most research articles mention public corruption, but the phenomenon may also characterize interactions between private entities (Heffernan and Kleinig 2004, pp. 2–4; Hodgson and Jiang 2007). For the purpose of our paper, we take into consideration only public corruption acts. Corruption harms economies and individuals on multiple levels and entails long-term consequences, among which: it may undermine public authorities’ ability to promote ‘inclusive economic growth’ (International Monetary Fund 2016); it alters political agendas for private benefit (both corporate and individual), may skew voting on important society matters and may undermine competition within the economic environment (Emerson 2006; Ades and Di Tella 1999); it corrodes citizens’ trust in public authorities and the policies they implement (Pellegata and Memoli 2016).

Despite the commotion they often stir in the media and among the general public, shadow economy activities and corruption deeds are far from being infrequent acts, restricted to a particular geographic area. As phenomena, shadow economy and corruption have always been a constant presence within human societies worldwide under various forms (Harris 2003; OECD 2013; Pellegrini 2011; Williams and Schneider 2016). Yet, the complexity of these phenomena makes it difficult to be captured by standard definitions and, therefore, accurately determined. The difficulty of such measurements emerges primarily from the fact that shadow economy and corruption are not directly observable. People engaging in shadow economy activities or trying to achieve personal benefits through corruption go to great lengths in order to avoid detection. Consequently, it is difficult for authorities to identify the traces of such behaviors.

Nevertheless, during the last two decades, shadow economy and corruption have been intensively debated and studied. Empirical research has focused on assessing their extent and the factors driving them (Bardhan 1997; Buehn and Farzanegan 2013; Dreher et al. 2007; Jain 2001; Mauro 1998; Rose-Ackerman and Palifka 2016; Schneider and Enste 2000, 2013; Singh et al. 2012; Torgler and Schneider 2009). Several of these studies have been centered on the relationship between shadow economy and corruption (Buehn and Schneider 2012; Choi and Thum 2005; Dreher et al. 2009).

The existing literature suggests that the link between shadow economy and corruption is rather ambiguous, as they are two unobservable variables reported to be either substitutes or complements. Moreover, empirical studies investigating the extent to which shadow economy is linked to corruption are quite scarce, although such research reveals interesting outcomes. The aim of our study is to decrease the ambiguity concerning their relationship and to fill in the gap by showing that the impact of shadow economy on corruption becomes more salient through the right leverage. Our empirical investigation tackling this topic seems timely especially when taking into account that, at international level, political agendas have incorporated the need to mitigate these phenomena through global initiatives such as the OECD Action Plan on Base Erosion and Profit Shifting, the G20 Anticorruption Working Group or the United Nations Convention against Corruption (United Nations 2015).

By means of moderation analysis conducted on a worldwide sample of 193 countries and territories, we show that shadow economy and corruption are complements and that the impact of shadow economy on the extent of corruption is significant when moderators like judicial independence, reliability of police services, human development level and business freedom are taken into consideration. Specifically, when countries have independent judiciaries, are able to enforce law efficiently, record considerable progress in human development or regulate the business environment, a small shadow economy is associated with a low corruption level.

The choice of the moderating variables stems from the fact that institutions (be they judicial, related to public safety, or market regulating ones) are often reported to sharpen or dampen the corruption phenomenon (Alt and Dreyer Lassen 2003; Graeff and Mehlkop 2003; Goel and Nelson 2005; Rose-Ackerman and Lagunes 2015). In addition, we investigated the proposed relationship between shadow economy and corruption by considering relevant controls suggested in the literature such as: freedom of the press (Ambrey et al. 2016; Chowdhury 2004); political stability (Shleifer and Vishny 1993); openness of the economy (Ades and Di Tella 1999; Bonaglia et al. 2001; Brunetti and Weder 2003; Gurgur and Shah 2005).

We conduct the moderation analysis following the methodological approach proposed by Hayes (2013). As method for estimating confidence intervals, we chose the bias-corrected and accelerated (BCa) bootstrapping.

The structure of the paper is as follows. The second part presents relevant advances into the shadow economy and corruption literature, with particular emphasis on their relationship. The third part introduces the chosen moderating variables and the research hypotheses. The fourth part comprises the description of the sample, variables of interest, theoretical considerations regarding moderation analysis and the proposed models. The fifth part reports the results following a moderation analysis conducted on the worldwide country sample. The sixth part discusses the results and highlights concluding remarks.

2 Literature Review

Although shadow economy and corruption are often studied independently of each other with the purpose of identifying efficient methods to lessen their extent, we considered both variables in our empirical study. Starting from the existing literature, it can be stated that research investigating shadow economy and corruption is still in a preliminary stage. Shadow economy and corruption are two intricate phenomena, which makes it difficult to apply standards when it comes to defining or measuring them (Sauka et al. 2016, p. 1).

Nevertheless, the corruption phenomenon (although multifaceted) is more likely to be captured by comparable definitions across the social sciences field. Pellegrini (2011, pp. 14–17) offers an overview of such definitions, which includes the legalistic perspective, the approach of international organizations and the classic view. According to him, Williams (1999) introduced the earliest characterization of the phenomenon via the legalistic perspective and defined corruption as disreguarding the legal framework of public duties in order to secure personal benefits. The international approach on corruption is voiced by the prominent NGO Transparency International, which defines it as ‘the abuse of entrusted power for private gain’. The classic view on corruption is presented by Nye (1967, p. 419), who considered it a ‘behavior which deviates from the formal duties of a public role because of private-regarding (personal, close family, private clique) pecuniary or status gains; or violates rules against the exercise of certain types of private regarding influence’.

According to Shleifer and Vishny (1993, p. 599), corruption represents a ‘sale by government officials of government property for personal gain’. Moreover, Philp (2016, p. 45) also identifies a consensus in defining corruption embodied by the following statement: ‘A public official (A), acting for personal gain, violates the norms of public office and harms the interests of the public (B) to benefit a third party (C) who rewards A for access to goods or services which C would not otherwise obtain’. According to Philp’s definition, activities labeled as standard corruption cases generally involve the existence of a ‘triadic relationship’ between the public official, the citizenry and the beneficiary. In special circumstances (i.e., kleptocracies), the relationship becomes dyadic, as the public official and the beneficiary are identical.

If in the case of corruption one might find a similar pattern of definition, there is an extensive range of shadow economy definitions depending on the type of economic activities considered or the purpose of the research. Furthermore, the proliferation of various definitions throughout the tax literature comes from the fact that shadow economy is described via a plethora of terms like ‘grey’, ‘hidden’, ‘informal’, ‘invisible’, ‘irregular’, ‘marginal’, ‘moonlight’, ‘non-observed’, ‘parallel’, ‘social’, ‘subterranean’, ‘underground’, ‘unofficial’, ‘unrecorded’, ‘unregulated’ etc. (Henry and Sills 2006, p. 263; Frey and Schneider 2001; OECD 2002; Schneider and Williams 2013). Portes and Castells (1989, p. 12) consider that shadow economy encompasses activities that lack social and legal regulations, otherwise enacted by state authorities in the case of compliant economic agents. For Mirus and Smith (1997, p. 5), shadow economy includes monetary and non-monetary transactions generated by both legal activities (e.g., unreported self-employment income, fringe benefits, employee discounts, barter of legal goods and services, do-it-yourself work, neighbor help) and illegal activities (e.g., gambling, fraud, trading stolen goods, smuggling). According to international organizations like the OECD, although underground economic activities may be ‘quite legal’, they are kept hidden from the scrutinizing eyes of public authorities with the purpose of avoiding: (1) taxation of income, consumption, wealth, payroll; (2) compliance with legal standards related to minimum wages, working time, work safety, health; (3) compliance with administrative requirements (e.g., compiling detailed financial statements, bureaucratic procedures, tax authorities surveys). In the view of Schneider and Williams (2013, p. 25), the economic phenomenon characterizes ‘all market-based production of legal goods and services’ hidden from authorities’ monitoring for the abovementioned reasons. For Smith (1997, p. 15), shadow economy refers to ‘market and non-market-based production of goods and services, whether legal or illegal, that escapes detection or is intentionally excluded from the official estimates of GDP’.

As mentioned in the introduction, for the purpose of this paper we used the shadow economy definition provided by AT Kearney and Schneider (2013, p. 2). In the case of corruption, we considered the definition employed by Neild (2002).

Theoretical considerations in the literature categorize the relationship between the two variables as dual or ambiguous, because they are reported to be either complements or substitutes. The former term designates the situation in which there is a positive relationship between the variables, while the latter term indicates a negative relationship. The stream of literature stressing that corruption and shadow economy are complements is quite extensive (e.g., Buehn and Schneider 2012; Goel and Saunoris 2014; Hindriks et al. 1999; Johnson et al. 1999; Uslaner 2008; Wiseman 2016). For instance, using data from 145 countries, Dell’Anno and Teobaldelli (2015) report a strong positive relationship between the two in the case of centralized economies. According to their results, a higher level of decentralization lessens the effect corruption has on the extent of the shadow economy. Friedman et al. (2000) examine data from 169 countries and conclude that higher shadow economy levels are determined by corruption, red tape and a feeble legal system. Katsios (2006) shows that taxpayers’ choice of engaging in shadow economy activities is motivated by their lack of financial resources or willingness to make use of bribery techniques, in addition to lack of connections with bureaucrats.

Although the body of literature indicating that corruption and shadow economy are substitutes is less expansive than the aforementioned one, it still conveys interesting findings. For example, starting from a database of 18 OECD countries, Dreher et al. (2011) model shadow economy and corruption as latent variables and show that the former variable is linked to lower corruption levels. Moreover, their study concludes that institutional quality negatively impacts on both latent variables. Virta (2010) reports that geographical location significantly impacts on the relationship between corruption and shadow economy. As a result, countries located at the tropics register a negative link between the two variables. Also in the view of Rose-Ackerman (1997), corruption and shadow economy are negatively connected.

In addition, some studies report that the relationship between the two variables changes as a function of income levels. Therefore, corruption and shadow economy are substitutes when it comes to high income countries, but in low income countries they are complements (e.g., Dreher and Schneider 2010; Gërxhani 2004; Schneider 2008; Schneider and Buehn 2009).

3 Importance of the Present Study and Research Hypotheses

Despite the fact that numerous studies investigate how corruption influences the size of the shadow economy, the complexity of these two phenomena—which stems (among others) from the variety of existing definitions and approaches in measuring them—leaves room for additional investigations running from shadow economy towards corruption. We believe that shifting the research focus in the proposed direction may elicit valuable information on how to decrease the two phenomena by leveraging the efficiency of public institutions. Therefore, the insights from our study may assist public authorities in their quest to improve compliance with tax laws and ethical standards of civil servants.

The rationale for considering such an investigation is that taxpayers may perpetuate bribery and other forms of corruption to prevent authorities’ questioning and detection of underground economic activities (e.g., Çule and Fulton 2009; Wickberg 2013). According to Buehn and Schneider (2009), financing corruption translates into paying a ‘tax’ to noncompliant civil servants in order to avoid detection, official taxation or prosecution. By reducing the size of underground transactions, economic agents will not be incentivized to use bribes and therefore corruption may decrease along the way.

As Dreher and Schneider (2010, p. 216) point out, the literature investigating the impact of shadow economy on corruption is not sufficiently developed and, with few exceptions (e.g., Buehn and Schneider 2012; Choi and Thum 2005; Dreher et al. 2009; Schneider and Buehn 2009), empirical evidence on the matter are ‘virtually non-existent’. Moreover, there is a need for large sample investigations, especially under the form of empirical studies.

Our study aims to fill this gap by investigating the strength of the relationship between shadow economy and corruption when considering the interplay between shadow economy and several moderating variables. Various studies in the literature reported that improved and efficient institutions seem to favor the decrease of corruption. More precisely, attempts to mitigate the extent of corruption may prove successful in the presence of an independent judicial system, reliable police services, a highly developed citizenry and efficiently regulated business environments. Consequently, we will test four research hypotheses including the aforementioned moderating variables, which are described in the following paragraphs. Moreover, the models constructed to test the strength of the relationship shadow economy-corruption will include control variables suggested by the literature. Altogether, we expect the moderation effects to hold in the presence of the selected controls.

3.1 Judicial Independence

An impartial and equidistant judiciary represents the core of a solid rule of law, which guarantees the evolution of modern societies and positively influences a country’s economic growth (de la Croix and Delavallade 2011; Feld and Voigt 2003; Hayo and Voigt 2007; Voigt et al. 2015). More specific, foreign investors are drawn to countries with strong judicial systems because property rights are more likely to be protected and they may face lower market risks (Staats and Biglaiser 2011; Voigt and Gutmann 2013). In the same vein, authorities manage to establish and enhance the respect for the rule of law if the judicial system is free from any third-party influences, especially in the situation of increased competition between rival parties (Hanssen 2004). When government institutions safeguarding the rule of law are stronger, noncompliance levels in terms of revenue disclosure and conformity with ethical standards may decrease (Friedman et al. 2000; Ekici and Onsel 2013; Iwasaki and Suzuki 2012; Herzfeld and Weiss 2003; Schneider and Enste 2002). Therefore, the following hypothesis will be tested:

H1

The connection between shadow economy and corruption becomes significant under higher judicial independence.

3.2 Reliability of Police Services

Compliance with the letter and the spirit of the law is a fundamental prerequisite of well-functioning modern societies (Likhovski 2007). Authorities may foster such compliance when efficiently communicating about their capacity of enforcing laws and applying appropriate sanctions required legal frameworks (Braithwaite 2007; Ericson and Haggerty 2001; Gobena and van Dijke 2017; Murphy 2003, 2005, 2015; Verboon and van Dijke 2011). Evidence in this sense comes from tax behavior research, where it is reported that compliance levels increase if authorities are perceived as able to deter and sanction noncompliant citizens (Bergman 2003; Kirchler et al. 2008). When authorities are highly reliable in securing order and monitoring citizens, fewer economic agents may be willing to engage in corruption acts (Olken 2007). In such situations, a reduction in the size of the shadow economy may be mirrored by a reduction of the extent of corruption. This leads to our second hypothesis:

H2

The connection between shadow economy and corruption becomes significant under increased reliability of police services.

3.3 Human Development

Human development takes into consideration the physiological and safety needs, which represent the basis of the human needs pyramid (Alderfer 1969; Maslow 1943, 1970; Petrakis 2014). As a rule, needs motivate human behavior and prompt behavioral changes (Baxter and Moosa 1996; Kastanakis and Balabanis 2012; Rhoads 1999, p. 28; Vermeir et al. 2002). Solid education, for instance, induces compliance with norms and ethical standards (Glaeser and Mulloy 2006; Lewis 1982) because citizens understand the importance of conformity for society advancement and because they regard society behavioral standards as just (Carroll 2016). Moreover, a substantial improvement in the education system and living standards contributes to reducing the size of the shadow economy (Berrittella 2015; Dell’Anno 2010). When authorities diligently sustain human progress by efficiently investing in healthcare and education systems or by stimulating economic growth, efforts to scale down the shadow economy may bring about a decrease in the level of corruption. If authorities make scanty investments in human capabilities, any attempts of curbing underground economic activities will not hinder corruption acts. Consequently, we will test the following research hypothesis:

H3

The connection between shadow economy and corruption becomes significant under higher human development level.

3.4 Business Freedom

Worldwide markets are less prone to the spread of corruption when countries register high level of economic freedom and efficient monetary policies (Apergis et al. 2012; Carden and Verdon 2010; Goel and Nelson 2005; Kaymak and Bektas 2015). Moreover, corruption seems to diminish in the presence of economic freedom, irrespective of the political environment (Saha et al. 2009). As a fundamental ingredient of economic freedom, business freedom also has a significant influence on the extent of corruption. Namely, excessive regulation when it comes to starting and developing a business is generally a catalyst for the proliferation of underground economic activities and noncompliance (Echazu and Bose 2008; Friedman et al. 2000; Johnson et al. 1997). A case in point, in order to reduce the costs of red tape (i.e., numerous procedures for registering with tax authorities and being granted permits, licenses, external financing from banks), some economic agents choose to activate in the underground economy and succeed to avoid monitoring by bribing civil servants (Bose and Echazu 2007; Çule and Fulton 2009). Thus, informal economic agents manage to increase their revenues by appearing more competitive in the eyes of thrifty customers, but at the expense of formal economic agents that face taxation, regulatory burdens and difficulties in obtaining financing (Ahlin and Bose 2007; Berdiev and Saunoris 2016; Gokalp et al. 2017; Karlinger 2014). When the regulatory framework designed for the business environment becomes cumbersome and time-consuming, an increase in the size of the shadow economy may trigger more corruption. Conversely, when markets feature less burdensome and efficient regulations, a mitigating shadow economy may generate more compliance with ethical business standards in the formal sector and, therefore, less corruption. This leads to our fourth research hypothesis:

H4

The connection between shadow economy and corruption becomes significant under increased business freedom.

4 Methodology

The next section offers details about the analyzed sample, chosen variables and proposed regression models. It also briefly tackles moderation analysis in terms of the existing methodological approaches.

4.1 Sample Description

Our sample numbered 193 states and territories around the world pertaining to all strata of economic development, which registered values for the variables of interest included in the study (for a complete list, see “Appendix”). With one exception (i.e., shadow economy), 2012 was regarded as the benchmark year for all the other variables.

4.2 Variables of Interest and Sources

In this subsection, we specify the variables of interest used to investigate the relationship between shadow economy and corruption. All variables considered in this study were taken from validated databases, international reports and established research endeavors (e.g., Global Competiveness Report, Human Development Report, World Bank).

For the predicting variable Shadow economy (SE), we considered the 2007 country estimates from Schneider (2012), which were determined through a ‘multiple indicator multiple causes’ model. The size of the shadow economy was indicated as a proportion in the official GDP.

In the case of the outcome variable Corruption (CP), we took into account the 2012 Corruption Perceptions Index estimated by Transparency International, which ranked states and territories on a scale from 0 (‘highly corrupt’) to 100 (‘very clean’). Therefore, the lower the score, the higher the perceived corruption level in a particular state.

The chosen moderators (proxies for the quality of institutions) are described in the following paragraphs. The variable Judicial independence (JI) was retrieved from the Global Competitiveness Report 2012–2013 (World Economic Forum 2012, p. 393). Listed there as item 1.06, it ranked 144 countries and territories based on answers to the following question: ‘To what extent is the judiciary in your country independent from influences of members of government, citizens, or firms?’. The rating scale ranged from 1 (‘heavily influenced’) to 7 (‘entirely independent’).

The variable Reliability of police services (RPS) was retrieved from the Global Competitiveness Report 2012–2013 (World Economic Forum 2012, p. 404), being the item 1.17. It consisted in the question ‘To what extent can police services be relied upon to enforce law and order in your country?’ and it was assessed on a scale from 1 (‘it cannot be relied upon at all’) to 7 (‘can be completely relied upon’).

We also considered the Human Development (HD) Index retrieved from the Human Development Report 2013 (United Nations Development Programme 2013, pp. 144–147). With values from 0 (‘low human development’) to 1 (‘very high human development’), the composite index quantifies progress within three fundamental areas of human development, i.e., ‘long and healthy life, knowledge, decent standard of living’.

The variable Business freedom (BF), which captures the governments’ efficiency of regulating business environments, was retrieved from the 2013 Index of Economic Freedom (The Heritage Foundation and The World Bank, 2013, p. 480). On a scale from 0 (‘least free business environment’) to 100 (‘freest business environment’), the regulating efficiency is expressed by the ‘difficulty of starting, operating, and closing a business’. In other words, the variable assesses the bureaucratic obstacles faced by business owners while operating on a particular national market.

Regarding the choice of our control variables, we followed the results reported by the literature. The selected control variables were: (a) Political stability and absence of violence (PS), retrieved from 2012 World Governance Indicators dataset, commissioned by the World Bank Group; it ranges from approximately −2.5 (‘low political stability’) to 2.5 (‘high political stability’); (b) Openness of the economy (OE), for which we used the 2012 trade level measured by the Word Bank as percentage of the GDP; c) Freedom of the press (FP) retrieved from the 2011/2012 World Press Freedom Index, commissioned by Reporters Without Borders; it ranged from −10 (‘free press’) to 142 (‘repressed press’).

4.3 Moderations Analysis and Proposed Regression Models

Ever since benchmark studies like James and Brett (1984) or Baron and Kenny (1986) appeared in the mainstream literature, the nature and the conditions under which a relationship between a predictor and an outcome emerges have piqued the interest of social scientists (Aguinis 2004; Aguinis et al. 2005; Aneshensel 2013; Dawson and Richter 2006; MacKinnon 2011; O’Connor 2006; Shieh 2009, 2010; Wenzel 2002, 2004). Consequently, phenomena involving third-variable effects like moderation have started to be investigated intensively.

According to the literature, moderation specifies the conditions under which the predictor occasions the outcome (Frazier et al. 2004, p. 116; Hayes 2013, p. 21). The standard definition of a moderator was introduced by Baron and Kenny (1986, p. 1174). Fairchild and McQuillin (2010) stressed that the effects of the predictor variable were conditional or contingent on the values of the moderator. In addition, Kim et al. (2001, p. 64) stated that a moderator could also alter the direction of the relationship between the predictor and the outcome. For the abovementioned reasons, the moderator is often called ‘effect modifier’ (Tang et al. 2009, p. 315).

The methodological apparatus used to investigate moderation is very diverse, from multiple regression models (Aiken and West 1991; Aguinis and Pierce 1998; Hayes and Agler 2014; Kang and Waller 2005; Preacher et al. 2006), two-level regression models (Yuan et al. 2014), analysis of variance (Baron and Kenny 1986; Holmbeck 1997; Tang et al. 2009) to structural equation modeling (Jaccard and Wan 1995; Ping 1996).

From a theoretical standpoint and irrespective of the chosen method, the literature generally emphasizes four fundamental steps when running moderation analyses: (1) predictor and moderating variables are standardized before computing the interaction term, in order to reduce the multicollinearity phenomenon occurring in interactions (Aiken and West 1991; Aldwin 1994); (2) the interaction term is determined, which represents the core of testing moderation (Dawson 2014); (3) the size of the moderation effect is estimated; (4) the interaction is probed via specific tests and interpreted. A common test performed with the aim of probing interactions is the ‘pick-a-point approach’ (Rogosa 1981), also known as ‘simple slope analysis’ or ‘spotlight analysis’ (Hayes 2013, p. 235). This type of analysis ‘tests the significance of the relationship between the predictor and the outcome at specific levels of the moderator’ (Frazier et al. 2004, p. 122). Another popular test is the Johnson–Neyman technique (Johnson and Fay 1950; Johnson and Neyman 1936) or the ‘floodlight analysis’ (Spiller et al. 2013). Used exclusively for continuous moderators, this test is able to define region(s) of significance related to the moderator effect (Preacher et al. 2007).

For the purpose of this paper, we chose to investigate the relationship between shadow economy and corruption via moderation by running multiple regression models and estimating confidence intervals with bootstrapping, a technique introduced by Efron (1979). With regards to bootstrapping, we have chosen the bias-corrected and accelerated (BCa) method for its multiple theoretical and practical advantages suggested by the literature (Carpenter and Bithell 2000; DiCiccio and Romano 1995; Dowd 2005; Efron 2003; Efron and Tibshirani 1993, pp. 179–187; Rizzo 2008, p. 204; Rochowicz 2010). Namely, BCa is a substantially improved method compared to other bootstrapping methods (i.e., simple percentile; bias corrected percentile) because it automatically produces accurate and correct confidence intervals (being ‘second-order accurate’, the coverage error is smaller) and it does not require to verify the normality assumption. According to Efron and Hastie (2016, p. 193), the BCa method corrects standard intervals for non-normality, bias and acceleration of the variance.

In the following, the four moderated multiple regression models (MMR) corresponding to the previously mentioned research hypotheses (see Sect. 3) are presented. Overall, Corruption perceptions (CP) counted as criterion variable. Shadow economy (SE) was treated as predictor variable, while Judicial independence (JI), Reliability of police services (RPS), Human development (HD) and Business freedom (BF) were regarded as moderators. The following control variables were included in each model: Political stability (PS), Openness of the economy (OE) and Freedom of the press (FP):

$$CP_{i} = b_{0} + b_{1} SE_{i} + b_{2} JI_{i} + b_{3} SE_{i} JI_{i} + b_{4} PS_{i} + b_{5} OE_{i} + b_{6} FP_{i} + \varepsilon_{i}$$
(MMR1)
$$CP_{i} = b_{0} + b_{1} SE_{i} + b_{2} RPS_{i} + b_{3} SE_{i} RPS_{i} + b_{4} PS_{i} + b_{5} OE_{i} + b_{6} FP_{i} + \varepsilon_{i}$$
(MMR2)
$$CP_{i} = b_{0} + b_{1} SE_{i} + b_{2} HD_{i} + b_{3} SE_{i} HD_{i} + b_{4} PS_{i} + b_{5} OE_{i} + b_{6} FP_{i} + \varepsilon_{i}$$
(MMR3)
$$CP_{i} = b_{0} + b_{1} SE_{i} + b_{2} SE_{i} + b_{3} SE_{i} BF_{i} + b_{4} PS_{i} + b_{5} OE_{i} + b_{6} FP_{i} + \varepsilon_{i}$$
(MMR4)

where, i refers to each sampled country and εi is the error term.

5 Results

We performed the moderation analyses using IBM SPSS Statistics version 20 and the PROCESS macro developed by Hayes (2013). The choice of the statistical macro was driven by the numerous advantages it offers in running a moderation analysis. Firstly, it centers the independent variable and the moderator, thus reducing multicollinearity. Secondly, it produces the interaction term, whose coefficient indicates the presence of a moderation effect. Thirdly, it produces simple slope analysis, therefore showing the effect size with respect to each level of the moderator. Fourthly, it applies the Johnson–Neyman technique for probing interactions in the case of continuous moderators. We chose to examine moderation through regression because the predictor and the moderators were measured on a continuous scale (Frazier et al. 2004, p. 117).

5.1 Judicial Independence

Correlation analyses show a significant relationship between SE and JI, r = −.64, p < .01, between JI and CP, r = .85, p < .01, and between SE and CP, r = −.65, p < .01. In order to test the first hypothesis, we evaluated MMR1 by conducting a moderation analysis with 95% bias-corrected and accelerated (BCa) confidence interval and 5000 bootstrap resamples. A significant interaction effect was found, b = −.14, 95% CI [−.26, −.02], t = −2.30, p < .05. The control variables PS (b = 5.05, 95% CI [3.16, 6.94], t = 5.29, p < .001) and FP (b = −.09, 95% CI [−.16, −.03], t = −3.08, p < .01) had a significant influence. OE did not reach significance (b = −.003, p = .836).

The results displayed in Fig. 1 indicate that the relationship between SE and CP seems to be moderated by JI.

Fig. 1
figure 1

Statistical diagram of the moderation analysis assessing the role of Judicial independence (JI) in the relationship between Shadow economy (SE) and Corruption perceptions (CP). Note Values denote unstandardized regression coefficients. Asterisks represent significance at the 0.1% (***), 1% (**) and 5% (*) levels

Full size image

In order to probe the moderation effect by simple slopes analysis, the following can be stated: (a) when JI registered a low level, there was a non-significant negative relationship between SE and CP, b = −.08, p = 0.426; (b) when JI registered a medium level, there was a significant negative relationship between SE and CP, b = −.26, 95% CI [−.43, −.08], t = −2.84, p < .01; c) when JI registered a high level, there was a strong negative relationship between SE and CP, b = −.44, 95% CI [−.71, −.16], t = −3.13, p < .01. Based on the Johnson–Neyman technique, −.646 marks the beginning of the threshold for significance.

Graphing the link between the predictor and the outcome at different levels of the moderator is a required practice that facilitates the interpretation of moderating effects. In our case, Fig. 2 confirms the results of the simple slopes analysis by showing that the JI moderator enhanced the basic relationship between SE and CP.

Fig. 2
figure 2

Simple slope analysis for MMR1

Full size image

Therefore, our first hypothesis is confirmed. The two-way interaction showed the moderating effects of judicial independence on the relationship between shadow economy and corruption, which became strongly significant after increasing the level of the moderator. Namely, a small shadow economy was associated with a low corruption extent in countries and territories registering higher levels of judicial independence as opposed to those registering low levels of judicial independence. Control variables also exert a significant influence: corruption levels are lower in countries with a stable political system and a free media.

5.2 Reliability of Police Service

According to the analyses, SE is significantly correlated with RPS, r = −.62, p < .01, RPS with CP, r = .86, p < .01, and SE with CP, r = −.65, p < .01. In the process of testing the second hypothesis, the moderation analysis performed on MMR2 with 95% bias-corrected and accelerated (BCa) confidence interval and 5000 bootstrap resamples indicated a significant interaction effect, b = −.17, 95% CI [−.28, −.05], t = −2.89, p < .01. The control variables PS (b = 3.26, 95% CI [0.46, 6.05], t = 2.31, p < .01) and FP (b = −.12, 95% CI [−.19, −.06], t = −3.70, p < .001) had a significant influence. OE did not reach significance (b = −.003, p = .799).

Hence, it can be stated that the relationship between SE and CP appears to be moderated by RPS (see Fig. 3).

Fig. 3
figure 3

Statistical diagram of the moderation analysis assessing the role of Reliability of police services (RPS) in the relationship between Shadow economy (SE) and Corruption perceptions (CP). Note Values denote unstandardized regression coefficients. Asterisks represent significance at the 0.1% (***) and 1% (**) levels

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The simple slopes analysis denoted the subsequent: (a) when RPS was low, there was a non-significant negative relationship between SE and CP, b = −.05, p = .615; (b) when RPS was medium, there was a significant negative relationship between SE and CP, b = −.24, 95% CI [−.41, −.06], t = −2.67, p < .01; c) when RPS was high, there was a stronger negative relationship between SE and CP, b = −.43, 95% CI [−.68, −.17], t = −3.35, p < .01. The Johnson–Neyman test indicates that the threshold for significance begins at −.436.

Figure 4 displays the conditional effect of SE on CP at different levels of the moderator RPS. As one can notice, the moderator enhanced the connection, which is in line with our second hypothesis.

Fig. 4
figure 4

Simple slope analysis for MMR2

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The effect of shadow economy on corruption was significantly moderated by the reliability of police services. Namely, a low shadow economy was linked to less corruption in countries/territories reporting higher levels for the reliability of police services, but not in those perceiving unreliable police forces. In addition, control variables influenced the outcome variable: less corruption was registered for countries and territories experiencing a high political stability and a free press.

5.3 Human Development

By conducting a correlation analysis, we found a significant relationship between SE and HD, r = −.61, p < .01, between HD and CP, r = .71, p < .01, and between SE and CP, r = −.65, p < .01. In testing the third hypothesis via moderation analysis (MMR3) with 95% bias-corrected and accelerated (BCa) confidence interval and 5000 bootstrap resamples, we found a highly significant interaction effect, b = −2.11, 95% CI [−3.19, −1.04], t = −3.89, p < .001. Only the control variable PS (b = 6.16, 95% CI [3.15, 9.16], t = 4.05, p < .001) had a significant influence. FP (b = −.066, p = .056) and OE (b = −.005, p = .768) did not reach significance.

The statistical model presented in Fig. 5 shows that the relationship between SE and CP is apparently moderated by HD.

Fig. 5
figure 5

Statistical diagram of the moderation analysis assessing the role of Human development level (HD) in the relationship between Shadow economy (SE) and Corruption perceptions (CP). Note Values denote unstandardized regression coefficients. Asterisks represent significance at the 0.1% (***) and 1% (**) levels

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After examining the simple slopes, we concluded the ensuing aspects: (a) when HD reached a low level, a non-significant positive relationship was registered between SE and CP, b = .04, p = .765; (b) when HD reached a medium level, a stronger negative relationship was registered between SE and CP, b = −.34, 95% CI [−.55, −.13], t = −3.16, p < .01; (c) when HD reached a high level, an even stronger negative relationship was registered between SE and CP, b = −.72, 95% CI [−1.01, −.44], t = −5.04, p < .001. According to the Johnson–Neyman test, the threshold for significance starts at −.055.

The conclusions following simple slopes analysis are supported by Fig. 6, namely that the proposed moderator HD enhanced the relationship between SE and CP.

Fig. 6
figure 6

Simple slope analysis for MMR3

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Our third hypothesis is confirmed by the results, namely that the effect of shadow economy on corruption is contingent on human development. In countries/territories with higher levels of human development, a small size underground activity is associated with fewer corruption acts. Moreover, corruption seems to mitigate when citizens enjoy higher political stability.

5.4 Business Freedom

By conducting a correlation analysis, we found a significant relationship between SE and BF, r = −.50, p < .01, between BF and CP, r = .70, p < .01, and between SE and CP, r = −.65, p < .01. In testing the fourth hypothesis via moderation analysis (MMR4) with 95% bias-corrected and accelerated (BCa) confidence interval and 5000 bootstrap resamples, we found a significant interaction effect, b = −.01, 95% CI [−.02, −.002], t = −2.42, p < .05. The control variables PS (b = 6.57, 95% CI [3.89, 9.24], t = 4.86, p < .001) and FP (b = −.09, 95% CI [−.17, −.02], t = −2.41, p < .05) had a significant influence. OE did not reach significance (b = −.005, p = .770).

The statistical model presented in Fig. 7 indicated that the relationship between SE and CP might be moderated by BF.

Fig. 7
figure 7

Statistical diagram of the moderation analysis assessing the role of Business freedom (BF) in the relationship between Shadow economy (SE) and Corruption perceptions (CP). Note Values denote unstandardized regression coefficients. Asterisks represent significance at the 0.1% (***) and 5% (*) levels

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After examining the simple slopes, we concluded the ensuing aspects: (a) when BF reached a low level, a non-significant negative relationship was registered between SE and CP, b = −.21, p = .052; (b) when BF reached a medium level, a stronger negative relationship was registered between SE and CP, b = −.42, 95% CI [−.64, −.19], t = −3.62, p < .001; (c) when BF reached a high level, an even stronger negative relationship was registered between SE and CP, b = −.62, 95% CI [−.97, −.28], t = −3.60, p < .001. The Johnson–Neyman test shows that the threshold for significance begins at −16.39.

The conclusions following simple slopes analysis are supported by Fig. 8, namely that the proposed moderator BF enhanced the relationship between SE and CP, as predicted by our fourth hypothesis.

Fig. 8
figure 8

Simple slope analysis for MMR4

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The connection shadow economy-corruption is dependent on business freedom. Namely, in countries and territories with higher levels of business freedom, less underground economy is associated with less corruption acts, compared to countries and territories where economic agents face excessive red tape while running their businesses. Moreover, the extent of corruption is smaller when countries are politically stable and the media is not repressed.

6 Discussion and Conclusions

The literature acknowledges that the relationship between shadow economy and corruption is unsettled and often reported as dual, on the account that both phenomena are quite intricate and (therefore) difficult to be captured by standardized definitions. While the number of studies investigating how corruption impacts on shadow economy is considerable and represents the mainstream literature, there are only few studies analyzing whether there is a connection running from shadow economy towards corruption (Dreher and Schneider 2010). Our empirical investigation contributes to the existing literature by filling this gap and by indicating that the linkage between shadow economy and corruption becomes more salient through the right leverage. Approaching the proposed topic seems timely especially because nowadays regional and global political agendas have included the goal of mitigating these phenomena through various global initiatives.

Making use of a sample pool counting 193 countries and territories and corresponding data retrieved from reliable international reports, rankings and databases, the present study investigated the strength of the relationship between shadow economy and corruption via moderation analysis, with the help of the PROCESS add-on (Hayes 2013). Namely, we were interested to see whether the association between the predictor (i.e., shadow economy) and the outcome (i.e., corruption) varied as a function of a moderator (Hayes 2009, p. 415). Thus, we ran four multiple regression models using bootstrapping with 95% bias-corrected and accelerated (BCa) confidence interval and 5000 bootstrap resamples. The choice of the analysis method is straightforward, since we aimed to assess if there was such a relationship between the two phenomena and under what conditions it became perceptible.

Our main finding—confirmed by all four multiple regression models—denotes that shadow economy and corruption are complements, i.e., a decrease in the size of the underground economy is mirrored by a similar effect in the extent of corruption. Thus, we are in line with other empirical studies that have investigated the relationship running from shadow economy towards corruption like Buehn and Schneider (2009) or Schneider and Buehn (2009). The results of Schneider and Buehn (2009) slightly differ from ours, since they took into consideration the country income gap and identified a complementarity relationship for low income countries.

Although shadow economy alone does impact on corruption, we showed that when the moderators judicial independence, reliability of police services, human development and business freedom enhance the relationship, the level of corruption decreases considerably as shadow economy mitigates. Just as expected, all interplays between shadow economy and the chosen moderators proved to be significant. Moreover, the moderating effects were robust to the inclusion of control variables. In line with the existing theoretical and empirical literature (Ambrey et al. 2016; Chowdhury 2004; Shleifer and Vishny 1993), our results showed that corruption levels were lower in countries experiencing a stable political system and enjoyed the freedom of the press.

Compliance with law and ethical standards becomes a prevailing behavior among individuals when authorities are perceived as taking decisions ‘free from outside influence and consistent with the governing laws and facts of a case’ (Burbank et al. 2002, p. 4). In our case, countries and territories with an independent judiciary registered a significant direct relationship between shadow economy and corruption compared to those reporting low levels of judicial independence. A possible solution for the latter countries/territories would be to eliminate existing loopholes into the law that encourage systematic noncompliance (e.g., tax avoidance via transfer prices) and to financially incentivize the judiciary in order to curtail corruption (Skladany 2014).

One might say that compliance with directives enacted by authorities can become a second human nature in societies where property rights and individual liberty are thoroughly secured. The reverse is also true, irrespective of the period of time considered: compliance decreases sharply when authorities are perceived as inefficiently regulating justice. For a case in point, towards the end of the 19th century, the American political magazine ‘Harper’s Weakly (A Journal of Civilization)’ became well-known especially for conducting an intensive campaign against Tammany Hall, an organization which ruled New York City through a legendary corruption mechanism (Ackermann 2011; Lynch 2002). For that matter, the magazine published on September, 23, 1871 an epic cartoon entitled A Group of Vultures Waiting for the Storm to ‘Blow Over’–‘Let Us Prey’ signed by its main political cartoonist Thomas Nast, which pictured the Tammany leading figures. Via the tellingly cartoon, Nast managed to draw attention on the impact corruption had on justice, taxpayers and the city treasury.

According to our results, a small shadow economy was linked to less corruption in countries/territories where citizens perceived police forces as reliable to enforce laws and protecting social interests, but not in those perceiving unreliable police services. Policing authorities are generally considered impartial when serving ‘any government that operates under the Rule of Law’ (Villiers 2009, p. 55). In such contexts, many taxpayers may distance themselves from the underground economy and are less likely to engage in or to tolerate corruption acts. Therefore, countries and territories lacking reliable authorities should monitor the way the rule of law is being enforced and should increase financing to facilitate an efficient detection of noncompliant taxpayers and corrupt civil servants.

When authorities sedulously invest in and care for people’s development, the positive externalities yielded by improved education (Friedman 1962, p. 86), better healthcare and proper living standards accrue to societies as a whole. Therefore, under these conditions, a diminishing shadow economy may be mirrored by fewer corruption acts. In our sample, the relationship was significant when countries and territories benefited from a high level of human development. For that matter, the level of the interaction effect between shadow economy and human development was the highest, considering the other three moderators. This suggests that countries in which the shadow economy and corruption did not associate could take a step in this direction by firstly investing in the development of their citizens. As a consequence, citizens could understand the importance of complying with tax laws and would not finance corruption.

Similar to the countries and territories included in our sample, societies that secure a free business environment, where economic initiatives can develop without the hindrance of excessive bureaucracy, may register lower corruption levels and declining underground economic activities. Less red tape surrounding businesses facilitates economic transactions and taxpayers may be incentivized to stay in the formal economy and comply with the rules.

The current empirical study is subject to some limitations in the sense that the complexity of the relationship between shadow economy and corruption makes it difficult to run an exhaustive study by considering all the factors influencing this relationship. Nevertheless, the insights we bring into the conversation may assist authorities to limit noncompliance in terms of taxpaying and ethical standards of civil servants.

It goes without saying that authorities may target to unilaterally decrease the size of shadow economy or corruption irrespective of their connection, depending on their economic priorities and available resources. For a case in point, although the diminishing tax revenues and other negative externalities caused by shadow economy should not be neglected by public authorities, some governments facing low levels of underground activities may decide to focus primarily on corruption. Others, which register endemic shadow economy, may use a large part of their resources to curtail underground activities without any particular focus on corruption. Yet, our results suggest that authorities should try to adapt governmental policy goals provided they realize the implications judicial independence, reliability of police services, human development and business freedom have in eliciting the relationship shadow economy-corruption. Moreover, we believe that designing governing policies starting from this relationship could not only be beneficial in the long run, but also cost-effective.

In essence, whenever societies register notable progress in key areas like rule of law, health, education or business regulation, a constricting shadow economy may be associated with down-trending corruption. In the case of streamline public institutions, economic agents may discard practices of bribing civil servants who secure their underground activities and could return to the formal economy. Future research endeavors investigating the relationship between shadow economy and the extent of corruption may consider testing other economic, social and psychological variables as moderators and extending the analyses over different time spans. This way, additional results could call attention to the consequences of moderating phenomena and could give authorities considerable leverage in their effort of controlling informal activities and integrity breaches.