Integrating national accounting and macroeconomic approaches to estimate the underground, informal, and illegal economy in European countries

Abstract

This article proposes a hybrid national accounts (NA)-macroeconometric approach to fill the gap between the demand for reliable and internationally comparable estimates and the sparse availability of official statistics based on the NA approach. The proposed method combines data from Eurostat’s Tabular approach for the exhaustiveness of NA with estimates based on theoretical hypotheses on the drivers of non-observed production. We estimate underground, informal, and illegal economies for 22 European countries over the period 2000–2020.

1 Introduction

Good quality of national accounts is unanimously considered essential for economic policymaking and economic research (OECD, 2002), and to achieve this purpose, in the last two decades, the analysis of the hidden side of the official economy has grown rapidly.¹ However, if the importance of measuring the size of the shadow, underground, informal, non-observed economy (NOE)² is not in dispute, how these estimates have to be calculated is a controversial issue.³

OECD (2002) distinguishes two main approaches to estimating the NOE: the macroeconometric (or macroeconomic or macro) methods and the national accounting (NA) approach. The macro methods are essentially indirect approaches because they measure the traces that informality leaves in official data. They generally specify econometric models where discrepancies in observed variables are assumed a proxy for the hidden economy.⁴ Although the reliability of macro estimates is often questioned for the arbitrariness of the underlying assumptions,⁵ these estimates are largely applied in the economic literature because of the lack of suitable alternatives. In particular, regarding the most reliable alternative to estimating the hidden economy, i.e., the NA approach, several reasons limit its use in the economic literature. For instance, (a) the NA classification of the NOE is not consistent with the usual positive and normative aims of economic research; (b) the National Institutes of Statistics (NIS) are not fully transparent on how these estimates are calculated, and they do not make available disaggregated data to the scientific community; and (c) NOE estimates are not published regularly, and from an international perspective, with the exclusion of a subset of European countries, the NIS apply different methods and with different degrees of coverage for the different typologies of unrecorded production (informal, statistical, illegal, underground, etc.). This is due to the common practice of not publishing disaggregated estimates of NOE and do not make available to NIS outsiders.⁶ As a consequence of all these factors, NA estimates are usually not a practicable option for applied economists.

Finally, an additional issue slows the progress of knowledge in this field of research: macroeconomic and NA approaches are often considered rivals rather than complementary methods. As Dell’Anno (2022) notes, this has caused a debate between factions of scholars. On the one hand, the “hardliners” consider estimates of the shadow economy based on macroeconomic approaches as the results of misleading exercises of limited value in terms of reliability and accuracy.⁷ On the other hand, the “indulgents” consider it worthwhile to apply macro methods because they are, in relative terms, the only source of data functional for economic research.

In this scenario, this study addresses this issue by taking advantage of a recent novelty in terms of the availability and transparency of the NA approach for European countries. Since 2022, it has been possible to download the Gross National Income (GNI) Inventory for several European countries by CIRCABC.⁸ Specifically, for the first time, European NIS have provided numerical information on the GDP/GNI compilation process within a common and comparable framework (i.e., they make available Process Tables (PT) of Eurostat’s Tabular Approach to Exhaustiveness (TAE). This greater transparency of NA estimates has allowed us to contribute to this literature. First, we propose a hybrid NA-Macroeconometric (hereinafter only “hybrid”) approach to estimate the underground, informal, illegal and shadow economy in 22 European countries for the period 2000–2020. Second, by starting from NA estimates and definitions, we obtain estimates that are consistent with both international statistical standards and the aims of economic analyses. Third, we show that macro and NA approaches can be utilized as complementary tools to enhance knowledge in this field of research. Fourth, comparing NA estimates at the European level, we find evidence that in some countries, the NA estimates may be downward biased. Accordingly, we hypothesize some possible causes of this underestimation of the NOE.

The remainder of this article proceeds as follows. Section 2 outlines the perimeter of this research in terms of institutional reasons behind the recent greater transparency of the NA approach and the definitions of the underground, informal and illegal economy. Section 3 describes the dataset and the hybrid approach. Section 4 provides the empirical findings. The paper ends with some general conclusions on the reliability and limitations of the proposed approach. Six online appendices support the results of the article.

2 Eurostat’s tabular approach to exhaustiveness

2.1 The origins of TAE and the new deal toward the transparency of the NA approach

Blades and Roberts (2002, pp. 2–3) indicate three main reasons driving the efforts of national accountants to address the measurement of the NOE in the nineties: (1) “the increasing use of national accounts statistics as the basis for levying contributions and distributing subsidies in the EU has required that all Member States adopt common and demanding standards to ensure the exhaustiveness […]; (2) the collapse of central planning in the former Soviet block […]; (3) the increasing role of new “global players”—China, India and Brazil among others—has highlighted the need for better statistics to measure their economic weight in the World. These countries face particular difficulties in accurately measuring the levels of GDP both because of the drastic changes in their industrial structures that are now occurring and because of the growth of informal and underground activities in rapidly expanding urban areas.” Indeed, while up to the 1990s, informal production was generally considered a relevant matter only for developing countries, when the former socialist countries implemented the System of National Accounts (SNA),⁹ the measurement of their (large) parallel economies became an important issue for the international institutions dealing with the SNA and, definitely, one of the priorities for the European Statistical Office (Eurostat).¹⁰ Accordingly, the aspiration to include the unobserved economy in official statistics has led the European Commission (EU Decision of 22 February 1994 n. 168) to compel each European NIS to “cover not only production, primary income and expenditure which are directly observed in statistical surveys or administrative files, but include production, primary income and expenditure which are not directly observed.” (art. 2). In 1996, Eurostat started to work intensively with the European Union Candidate Countries (i.e., former European socialist economies) on the improvement of consistency, reliability, and exhaustiveness of their NA to ensure strict comparability of coverage of the NA among EU member states (Eurostat, 2021a). Between 1998 and 2003, these projects with the EU Candidate Countries led Eurostat and OECD experts to develop the TAE. This process has been built up in different phases. The first phase (1998–2000) was developed by the first pilot project “Exhaustiveness of National Accounts” and suggested the use of a framework very similar to that used by the Italian Institute of Statistics (ISTAT), from which it was originally derived and known as T1-T8.¹¹ The second pilot project was conducted in 2002–2003 and modified the boundaries between the different types of non-exhaustiveness adjustments (this is how NIS labels the different types of NOE within the GDP/GNI compilation process). Specifically, this second phase of the project changed the TAE framework, replacing the T1-T8 framework with an N1-N7 categorization (N-types). According to UNECE (2008), “The main difference between the two classifications is that while the T1-T8 framework relates the non-exhaustiveness types to the NOE problem areas, the N1-N7 framework is based on subdividing the producers according to their potential for non-exhaustiveness”. Further projects were carried out at the European level in the subsequent years but without significant change from the N1-N7 framework, so that, this version became the general framework for presenting the NIS’s work on exhaustiveness. Although, since 2016, the TAE has been applied by all member states, the official documents and supporting materials¹² have been accessible only to the members of the NIS and international groups of NA experts (i.e., the Gross National Income Expert Group—GNIG). The exclusion of the scientific community from the assessment of the NA approach partially changed only recently. Indeed, thanks to the Commission Implementing Regulation (EU) 2020/1546 of 23 October 2020, it is now possible to have partial access to international comparable documentation on exhaustiveness adjustments required to ensure the exhaustiveness of GDP/GNI estimates.¹³ EU regulation has also compelled the NIS to provide detailed arrangements of the inventory of the sources and methods used to produce GNI and—fundamental for this research—to dedicate one of the ten chapters of the GNI inventory (the 7th) to describe which and how the adjustments for exhaustiveness are implemented in each EU member state. Moreover, this regulation has also fixed a deadline (31 December 2021) to transmit materials on TAE to Eurostat.¹⁴ This recent availability of details on the NA estimates of the NOE is also explained by two main legislative sources: Regulation (EU) No 2019/516 of the European Parliament and of the Council of 19 March 2019 on the harmonization of GNI at market prices (also known as GNI Regulation) and the European legislation on open data (Directive 2019/1024 of the European Parliament and of the Council of 20 June 2019).

The GNI Regulation (art. 3) stipulates that Member States provide Eurostat with an inventory of the sources and methods used to produce GNI aggregates and their components (i.e., the GNI Inventories). These inventories include so-called “process tables” giving numerical information on the results of all consecutive stages of the GNI compilation process, from the statistical sources, through various adjustments, to the final national accounts data. The inventories are the basis for Eurostat's assessment of the quality of GNI data in terms of comparability, reliability, and exhaustiveness.

The second EU Directive (Directive 2019/1024 on open data) encourages public sector bodies in EU countries to make as much information available for reuse as possible. Thanks to these legislative measures, GNI Inventories are now freely accessible on CIRCABC.¹⁵ Although complete accessibility of the TAE, at the moment, is far from being achieved,¹⁶ the documents downloadable from CIRCABC can be considered the most significant step toward the transparency of the NA approach in recent decades.

2.2 Definition of the unobserved economy and Eurostat’s TAE

At the state of the art, we do not have a well-established definition for the unrecorded/informal economy that meets both statistical standards, i.e., consistency, measurability, harmonization, and economic requirements, i.e., outline a meaningful concept suitable for economic analyses. As emerges from the literature,¹⁷ differences among definitions are motivated by divergences in national accounters’ aims and economists’ purposes. For instance, the universally accepted definition of NOE applied in the NA context—NOE includes “all productive activities that may not be captured in the basic data sources used for national accounts compilation” (UNECE, 2003: 2)—has encountered limited success in the economic literature due to the limited relevance of the concept of the exhaustiveness of GDP for economic research. In the same way, the most commonly used definition in the economic literature, i.e., the shadow economy,¹⁸ while outlines a concept that is consistent with positive and normative analyses, is unsuitable for NA’s aims to include all unobserved economies (e.g., illegal economy, unintentionally concealed production).

According to OECD (2002), the “statistical” concept of NOE can be splitted into five "problem areas": underground production, informal production, illegal production, household production for own final use, and production missed due to deficiency in data collection programme.

Among these problem areas, the first three better fit with economic analysis, indeed, underground production includes production activities that are legal but deliberately concealed from public authorities to avoid paying taxes or social security contributions, meeting statutory standards, or complying with official procedures and regulations. Informal production includes legal production activities that are characterized by a low level of organization, with little or no division between labor and capital as a factor of production, and it does not rely on official agreements. It is broadly characterized as consisting of units engaged in small-scale production of goods and services with the primary objective of generating employment and incomes for the persons concerned. The third is the illegal economy, which accounts for productive activities that are forbidden by law or that become illegal when carried out by unauthorized persons.

In this paper, following Gyomai and van de Ven (2014), we aggregate the seven (N1-N7) adjustments for the exhaustiveness of NA proposed by Eurostat’s TAE¹⁹ in the above three categories of economic-based definitions of unobserved production. Specifically, the underground economy is equal to the sum of exhaustiveness adjustments accounting for N1 and N6; the informal economy is given by N3 + N4 + N5; and the illegal economy corresponds to N2. Accordingly, to estimate the total amount of NOE, we should also include the last type of adjustment (N7) that addresses “statistical deficiency”.

2.3 Eurostat’s TAE and its main shortcomings

Eurostat developed the TAE as a systematic method for identifying potential sources of non-exhaustiveness in the GDP/GNI. Figure 1 summarizes the seven types of adjustments for exhaustiveness as calculated by the TAE.

Fig. 1

Eurostat’s Tabular Approach to Exhaustiveness (TAE)—Eurostat (2021a)

Regarding the left side of Fig. 1, we have to include, within the NOE, the value added created by a producer that is not covered by statistical surveys or by an administrative source because it fails to register because it is involved in underground activity (N1)²⁰ or illegal activities (N2)²¹ or it does not need to register (N3)²² or it is a legal person (N4) or registered entrepreneurship (N5), but it is not surveyed due to a deficiency in the register-updating procedures. Regarding the right-hand side of Fig. 1, we have to adjust NA by accounting for the value added generated by producers that are in scope and are covered by a statistical survey or by administrative data collection. In this case, although the producer is surveyed, the resulting data may not be adequate because the producer intentionally misreports (N6)²³ or there are statistical deficiencies in the data (N7).²⁴

The estimates of each N-type can be calculated according to the three GDP methods, i.e., the output (or production), expenditure, and income approach. As Eurostat (2021a, p. 7) argues, the TAE’s classification of the types of non-exhaustiveness is based on producers’ characteristics and the data sources used for the output approach (i.e., surveys or administrative collections from enterprises). This implies a preference for the output approach, rather than the income or expenditure methods, to estimate the N1-N7 adjustments. From a comparative perspective of the compiling approach, note that while the output approach is normally²⁵ independent of the expenditure approach, the income approach is not independent and is completely integrated within the production approach. Because of these different degrees of dependency, in the following, we normally use the estimates of N1-N7 adjustments based only on the output approach. However, if the estimates based on this approach are missed or lower than those based on the expenditure or income method, then we use the values based on these two approaches. Due to heterogeneity in TAE across countries, we provide full details on this procedure in Sect. 3.1 and Appendix B.

2.4 Data collection and potential shortcomings of the NA approach based on Eurostat’s TAE

Two main aspects catch the reader’s eye in the literature on estimation methods of the NOE/shadow economy: (a) the divergence in the growing size of research production between publications dealing with macroeconomic estimates and the limited extent of empirical analyses using the NA approach; (b) the differences in the estimated values (i.e., the size of the shadow economy based on macro methods are generally higher than those based on the NA approach).²⁶ We deal with these two issues in the following sub-sections.

2.4.1 Challenges in gathering estimates of the NOE using the NA approach

While scientific articles on the macro methods have increased in the last twenty years, scientific publications dealing with the NA approach are practically absent in academic journals. To find some examinations of the NA approach, we can only consult documents, technical reports, and minutes of NA meetings, where the authors are officers of national and international institutions that apply the method (e.g., OECD, 2002; UNECE, 2003, 2008; Gyomai et al., 2012; Gyomai and van de Ven, 2014; ISTAT, 2021; Eurostat, 2005, 2014, 2020, 2021a, 2022). The main reason for this gap in the extent of research production should be sought in the difficulty for outsiders of NIS to access data and details on how NIS estimates each type of non-observed productive activity. With special reference to the European focus of this research, although several European NIS have recently published disaggregated data on the TAE in an open-access database (i.e., CIRCABC), several obstacles to data collection for the scientific community remain. Fernandes (2022, p. 30) noted that TAE estimates “are not provided as a regular series, or as part of Eurostat’s database, but rather split into multiple files uploaded to a platform used mainly for file exchange among the GNIG and other stakeholders”. In line with Fernandes’ experience, the collection of NA estimates for this research has implied to browse numerous GNI inventories, PT, and meeting minutes, with frameworks that are not perfectly comparable across countries and verification cycles. Specifically, the CIRCABC platform has a hierarchy of folders that compels scholars to move among dozens of folders, on different levels that are defined in terms of the “type” of NA documents, the “verification cycles”, and the countries.²⁷

The collection of data becomes even more challenging if the PT are not available. This occurs for the largest part of the European countries and all the NA estimates were published before the second verification cycle (2020–2024). In these cases, a scholar has to download the GNI inventory (generally it is about 400 pages) to look for the estimates of non-exhaustiveness adjustments in the text. Sometimes these figures are reported in Chapter 7, so that the scholar can extract them manually, in other cases, only partial information on N1-N7 adjustments is available.²⁸ Again, in other cases, the scholar may have a sense of frustration because adjustments are explained in the text of the GNI inventory but they are not reported.²⁹ To enhance the difficulty of this compilation, it is notable that each verification cycle spans only one year, and this timeframe varies across different countries. This collection process is more demanding for the first verification cycle (2016–2019), because PT are missed, and for the NA estimates before the first verification cycle, because scholars have to look for data within the minutes of the Meeting group included in other folders of the CIRCABC platform or by searching among external documents published by NIS (e.g. ISTAT, 2021) or by International Organization (e.g. Gyomai et al., 2012; UNECE, 2008, etc.).

In conclusion, although the CIRCABC platform (second verification cycle) includes 31 folders (one for each European country), 9 are empty and among the 22 remaining countries-folders, only for 14 countries NIS provide comparable PT, and among these, some large European economies, such as Germany or Spain, are missed. These PTs, even when available, refer to only one year for each verification cycle (2016–2019 and/or 2020–2024). Moreover, within this subsample of 14 countries with comparable PTs, significant heterogeneities in terms of GDP estimation methods emerge. For instance, Finland and Norway do not estimate the informal economy, and Italy, Finland, and Norway report N1-N7 adjustments only based on the output approach.

2.4.2 Potential sources of downward bias in the National Accounts estimates based on Eurostat’s TAE

The aim of this section is not to establish the existence of a downward bias in the NA estimates because these estimates are lower than those derived from macroeconomic approaches³⁰ but to underscore which could be the potential factors contributing to what appears as a common perception for scholars in this strand of economic literature: NA approach generates strikingly low estimations of underground, informal, and illegal economies in certain countries. Accordingly, this analysis is based on speculative³¹ hypotheses on the reasons for these potential underestimations (the so-called "unmeasured economy" in NA terminology). In particular, we hypothesize at least six possible sources for a potential downward bias in the NA estimates based on Eurostat’s TAE³²:

• (1) With reference to the underestimation of the underground economy, we can observe that N6 adjustments are usually limited to the recording of output and intermediate consumption in the business accounts of small and medium companies and the self-employed, while large companies are often not targeted by these adjustments.

• (2) Regarding the informal economy (i.e., N3 “Producers not required to register”, N4 “Legal persons not surveyed” and N5 “Registered entrepreneurs not surveyed”), rapid technological advancements and evolving business models lead to underestimating the unobserved production in services characterized by the digital economy, e-commerce, and, more generally, the value added generated by the economics of knowledge, gig economy, and sharing economy.

• (3) A further source of downward bias that may affect estimates of both the underground and informal economy depends on the key hypothesis behind the method to adjust the most important source of NOE: hidden employment, i.e., the labor input method. This method is based on the assumption that data collected by household or labor force surveys are not significantly biased. If this assumption holds, then it is possible to estimate the size of irregular employment by comparing the number of employed persons according to the household (e.g., Survey on Statistics on Income and Living Conditions—SILC) and/or labor force survey (LFS) with the number of employed persons reported in enterprise statistics, which cover only persons formally employed. However, at least three main sources of bias may affect these estimates: differences across countries in terms of social capital, differences in the scope of the two information sources (demand and supply side of the labor market), and differences between labor regulations and definitions of employment status in the labor survey.

  According to the former, differences in social stigma and tax morale may affect households’ and workers’ attitudes toward concealing their informal jobs in LFS/SILC. Regarding the second source of downward bias, the labor input method is complicated by differences in the scope of the two information sources. For instance, the LFS is generally conducted to be representative of the supply side of the labor market and is usually exclusively for private households. In this sense, it hardly covers the working population living in collective households (e.g., hospitals, residential homes, prisons, military barracks, religious institutions), workers who have no established address (e.g., undocumented immigrants), or persons working abroad for national employers. On the other side of the labor market, employment statistics based on the records of enterprises aim to be primarily representative of a sample of employers. A third potential source of bias concerns possible differences between the definition of unemployment status used in administrative contexts (i.e., national regulations) and LFS (usually ILO definition).³³

• (4) An additional source of underestimation may depend on the so-called “materiality threshold” applied by the NIS. It consists of a pragmatic rule where based on a cost–benefit principle, NIS “should avoid committing disproportionate resources to calculate insignificant items” (Eurostat, 2014, p. 2). The GNIG approved a threshold of 0.1% of GNI to be used to this end (Eurostat, 2021b). This means that, for instance, an N adjustment omitted by a NIS of a large European economy, such as France or Italy, is larger than the total NOE estimated by a small economy (e.g., Cyprus, Estonia, Iceland) and larger than the estimated NOE for a country with slight unobserved production (e.g., Luxembourg, Finland).³⁴ An additional, and more relevant, source of downward bias due to the materiality threshold depends on its nonlinear effect on NOE. Indeed, given that the probability that an N-adjustment is under the threshold is higher for countries with lower levels of non-observed production, the effect of this omission is inversely proportional to the level of N adjustments. In other words, it amplifies the differences between countries with high and low levels of underground, informal, and illegal economies.

• (5) Several NIS, especially for small countries, have neither the statistical sources nor resources to produce a new estimate of each N-type of non-observed economy every year. In most cases, they use the estimates for a reference year and project the values of N adjustments over time.³⁵ This is a strong assumption, especially if these projections are estimated for more than a few years or if business cycle fluctuations are substantial.

• (6) The lack of cross-country comparability and reliability of the estimates based on the NA approach becomes even more relevant for the N2-adjustment (illegal economy). Indeed these estimates are largely based on data sources collected externally from NIS. In particular, the comparability and consistency of data on drug trafficking are often unsatisfactory because they are frequently based on administrative data collected by different public institutions (e.g. Police and Fiscal Police departments, Domestic Affair, Justice or Health Ministries, etc.) that have, as their primary aim, to fight against drug trafficking and consumption, rather than the measurement of their extension.³⁶ A lack of cross-country comparability of N2-adjustment is even greater when NIS deal with the estimation of value added generated by prostitution. Here, there are two main issues to take into account: (a) the heterogeneous (legal or illegal) nature of this activity and the absence of a common framework for data collection across European countries. About the first issue, prostitution has a different impact within the TAE because, while in some countries value added generated by prostitution is included in the (observed) GDP as it is a legal or regulated productive activity,³⁷ for countries that only partially regulate or consider this activity as illegal, it is indirectly measured and included in N2-adjustment.³⁸ The secondary factor contributing to the lack of cross-comparison of data on prostitution depends on the statistical quality of the survey used to collect data. Frequently, data are collected by surveys administered by non-profit entities, prostitutes' associations, or academic research initiatives. Such data collection methodologies may exhibit deficiencies in terms of accuracy, comprehensiveness, and national representativeness when compared to the established standards of other NIS data.

In conclusion, although accessibility of NA estimates through the CIRCABC platform can be considered the most significant step for better transparency and availability of NOE estimates, there is a long road ahead to consider the NA approach to be fully reliable and satisfactory for economic analysis. Until then, the macroeconomic or hybrid methods can still play a significant role in economic research on the different aggregates of non-observed economies.

3 The hybrid method for estimating underground, informal and illegal economies

The basic intuition of the hybrid method is to combine data from the NA approach with causal analysis based on economic literature. In other words, we replace missing NA estimates by using predicted values based on econometric regressions that differ in terms of potential drivers for underground, informal, and illegal economies.

Bearing in mind that a reciprocal accusation between scholars applying the macro method and the NA approach is the lack of transparency and clarity in exposition, in the following sections, we describe, step by step, how the hybrid method estimates the underground, informal, and illegal economies as a share of official GDP. Specifically, the proposed approach involves four steps.

The first consists of collecting as many of the NA estimates for European countries as possible by preserving the intertemporal and cross-country comparability and reliability of the NA estimates. Accordingly, we only include statistics from documents authored by NA institutions (NIS or international groups of European NA experts such as OECD and UNECE). The second step consists of increasing the sample size by projecting the NA estimates over a short time. These projections are possible by exploiting the detailed information on the distribution across sectors, types of expenditure, or income of the N1-N7 adjustments within the national economy available from the TAE of the second verification cycle 2020–2024 (Eurostat, 2022). Once the dependent variable has been built, in the third stage, we select the drivers of the underground, informal, and illegal economies and predict the values of these three macro aggregates as a percentage of official GDP. The final step generates the actual values of underground, informal, and illegal (and shadow) economies by calibrating predicted values with the most recent available NA estimates as extracted by TAE.

3.1 Step 1: Collecting N1-N7 adjustments for exhaustiveness from NA documents

We collect data from four types of sources to include as many comparable estimates of N-adjustments as possible. Sorting the sources of NA estimates in descending order of accuracy and comparability, the most reliable consists of NA estimates extracted by PT of GNI Inventories associated with the verification cycle 2020–2024 as extracted by the CIRCABC platform (Eurostat, 2022).³⁹

The TAE provides up to three different estimates for each N adjustment according to the three methods for compiling GDP/GNI (i.e., output/production, expenditure, and income approaches). As a general rule, we use the estimates based on the production method because it is both the main approach in NA, and the adjustments made by this approach are often mirrored in the expenditure and income approaches.⁴⁰ However, by accounting for measurement errors and potential downward bias in NA estimates, if available, we select the compiling method that provides the highest estimate of underground, informal, and illegal productions) at the country level.

The second group of estimates of N1-N7 is still extracted by Eurostat (2022), but they come from NIS, which does not provide exhaustive numerical information on the TAE (i.e., PT are not uploaded on the CIRCABC platform). This occurs for seven countries of the verification cycle 2020–2024 (i.e., Austria, Denmark, Greece, Iceland, Luxembourg, Portugal, and Slovenia) and for all the countries included in the verification cycle 2016–2019. For these countries, data on N1-N7 are extracted from the text of the GNI Inventory (usually from Chapter 7).

The third source of NA estimates is UNECE (2008). It includes estimates for four countries (i.e., Croatia, Hungary, Estonia, and Poland) with reference to one year over the period 2000–2002. The fourth source is Gyomai et al. (2012), who report NA estimates collected by a report, also known as the “OECD Survey”, which includes the estimates of N adjustments for 11 countries in our sample and only one year over the period 2007–2009. Finally, we extract NA estimates for the Czech Republic (years 2000 and 2002) by Eurostat (2005) and, only concerning the illegal economy (N2) in Italy, we collect data for the period 2016–2019 by ISTAT (2021).⁴¹ Details on the dataset and selection of the compiling method of N-adjustments are provided in Appendix B.

3.2 Step 2: Projections of NA estimates based on TAE

To increase the estimates based on NA estimates, we exploit the accurate picture of the structure and distribution of NOE over 14 European economies as emerge from PT that are available for one year (t^*) over the verification cycle 2020–2024. Although full details on how these projections are calculated are provided in Appendix C, here we provide indications of the intuition behind the replacement procedure for these missing values. In sum, it consists of four phases. In the first step, we reclassify the TAE to obtain a simplified matrix of NA according to each compilation method (output, expenditure, and income). This simplification is aimed at obtaining a matrix where the totals per row correspond to data that are publicly available in the Eurostat database for the period t = 2000,…, 2021. The second step consists of calculating, at time t^*, the contribution of each N-adjustment to the official value added of that sector. In the third step, we project the proportion of N-adjustments (second step) at time t^* − 1 and t^* + 1⁴² by multiplying the totals of the row of the reclassified TAE (see Table C.1 in Appendix C) for the variables available from the Eurostat database at the country level. The fourth step adjusts the predicted ratios between N-adjustments and official GDP to take into account minor differences between NA statistics provided in the PT and those available in the Eurostat database.

The economic hypothesis behind these projections is that, for the estimates based on the output approach, the proportion of each adjustment for exhaustiveness in each NACE sector does not change between the reference period (i.e. the benchmark, t^*) and the closest years. If this hypothesis holds, then the missing values at time t^* − 1 and t^* + 1 can be calculated by multiplying these proportions by the official statistics at time t^* − 1 and t^* + 1 extracted by the Eurostat database.⁴³ The same procedure is applied to N-adjustments calculated by the expenditure and income approaches.⁴⁴

This is done as conjectural validation of the soundness of the hypothesis of invariance of proportionality of the type of adjustment for exhaustiveness to the size of industry, consumption, or nature of income within the national economy. Although an empirical test of this hypothesis is unfeasible due to the lack of NA estimates for consecutive periods, examining the unbalanced panel collected in step 1 (Sect. 3.1) reveals a low variability of N1-N7 estimates over time at the country level.⁴⁵

In conclusion, by replacing missing values with these projected values (Proj-TAE), the estimates of each N-adjustment increase by 28 observations: two values (t^* − 1 and t^* + 1) for each of the 14 countries with available TAE.

3.3 Step 3: Econometric specification of the underground, informal, and illegal economies

In this step, we aim to estimate the marginal effects of potential causes of underground, informal, and illegal economies using the unbalanced panel dataset of 22 European countries collected through the previous two steps.

The multifaceted nature of the NOE makes the identification of potential factors that affect its size problematic. Therefore, to have a consistent specification of the causal model, we consider a tripartition in the underground, informal, and illegal economies. Following the ample economic literature on drivers of informality (e.g., Andrews et al., 2011; Schneider and Enste, 2013; Goel and Nelson, 2016; Pham, 2017; Dell’Anno 2022; Zhanabekov, 2022), we consider three separate regressions that include the potentially relevant drivers of these aggregations of NA estimates of N-adjustments for exhaustiveness as a percentage of official GDP. A detailed treatment of the variable selection is beyond the scope of this paper; therefore, we summarize by Eq. (1) the general specification of the econometric model, where for each type of aggregate N-adjustment (i.e., underground, informal, or illegal economy), there are six vectors of potentially relevant explanatory variables:

$${{}_{N}NOE}_{it}={Sect}_{it}{\beta }^{S}+{EcDev}_{it}{\beta }^{ED}+{PubF}_{it}{\beta }^{PF}+{LabM}_{it}{\beta }^{LM}+{Ist}_{it}{\beta }^{Is}+{Ineq}_{it}{\beta }^{In}+{c}_{i}+{y}_{t}+{\varepsilon }_{it}$$

(1)

where if $N=N1+N6$ then we analyze the underground economy; if $N=N3+N4+N5$ then we estimate the informal economy, and if $N=N2$ the dependent variable is the illegal economy; $i=1,\dots ,22$; $t=2000,\dots ,2020$; and ${c}_{i}$ and ${y}_{t}$ are country and time fixed-effects, respectively.

From a causal inference perspective, we apply a fixed-effects (within) estimator to address the omitted variables problem by removing unobserved time-invariant and country-specific effects.⁴⁶ The first vector of explanatory variables includes the potential determinants of the $NOE$ that account for the productive structure of the national economy $\left({Sect}_{it}\right)$. Specifically, there is evidence that industries that supply the largest part of their productions to households, which involve small-scale productive units, and that employ a low-qualified workforce have a higher risk of generating an informal or underground production. Accordingly, we include the relative size of the sectors where these characteristics prevail (i.e., the ratio between the gross value added of industry and the total gross value added of the economy (${{\text{GVA}}}_{{\text{it}}}^{{\text{Nace}}}={{\text{GVA}}}_{{\text{it}}}^{{\text{Nace}}}/{{\text{GVA}}}_{{\text{it}}}^{{\text{Tot}}}$). In particular, for the underground economy, we include the relative size of the construction industry (${{\text{GVA}}}_{{\text{it}}}^{{\text{F}}}$); retail trade, the maintenance and repair of motor vehicles (${{\text{GVA}}}_{{\text{it}}}^{{\text{G}}}$); hotels and restaurants (${{\text{GVA}}}_{{\text{it}}}^{{\text{I}}}$); professional activities (${{\text{GVA}}}_{{\text{it}}}^{{\text{M}}}$); Arts, entertainment and recreation and activities of households as employers (${{\text{GVA}}}_{{\text{it}}}^{{\text{RT}}}$). For the informal economy, we consider the same sectors as for the underground economy with the exclusion of “professional activities (M)” that are replaced by the relative size of sector S (i.e., "other service activities",${{\text{GVA}}}_{{\text{it}}}^{{\text{S}}}$).

The other vectors of explanatory variables are partially common to the two regressions for the informal and underground economies. They include proxies for the country’s economic development (${EcDev}_{it}$); characteristics of the tax system and public expenditure $\left({PubF}_{it}\right)$; labor market $\left({LabM}_{it}\right)$; institutional variables $\left({Ist}_{it}\right)$; and indicators of income distribution and poverty $\left({Ineq}_{it}\right)$. We include controls for simultaneous responses to idiosyncratic shocks such as time effects (${t}_{t}$) and country effects (${c}_{i})$.

Regarding the illegal economy, due to the peculiarities of these activities (namely, the NA estimates generally include prostitution services, drug trafficking, and smuggling of products), we use a slightly different specification. In particular, we do not include the controls for the productive structure of the economy and tax system as potential determinants of this source of unobserved economy. In contrast, we include a set of proxies for the incidence of people usually involved in the abovementioned illegal production activities. Specifically, we consider the ratio between public expenditure for social protection benefits and official GDP (${SocBen\_rGDP}_{it}$), the incidence of migrant people in the total population (${Migr\_net\_r}_{it}$), the share of the population below the poverty line (${Pov\_gap}_{it}$) and the level of income inequality (${Gini}_{it}$). To account for gender differences in these criminal activities, we include male unemployment as a percentage of the male labor force (${Unem\_m}_{it}$); to account for the perceived effectiveness of law enforcement, we include an index of (perceived) corruption (${Corrup}_{it}$).

Table 1 reports the specific variables included in the control vectors for each regression.⁴⁷ Appendix D provides further details on these explanatory variables.

Table 1 Econometric specifications

An additional issue for making inferences on the marginal effects of the drivers of unobserved economy regards how to address the presence of missing values in dependent variables (${{}_{N}NOE}_{it}$). Indeed, it is realistic to assume that the missing data are not random but negatively correlated with the NIS’s ability to estimate the NOE framework. Specifically, the higher the NIS’s proficiency in estimating the N1-N7 adjustments, the better the availability and reliability of NA estimates are. As noted by Heckman (1979), the presence of selection bias can be viewed as an omitted variable problem in the selected sample and lead to inconsistent estimation of marginal effects (Wooldridge, 2010). However, for this empirical application to NOE estimation, the overall effect between “more bias”—due to the self-exclusion of countries with NIS that have inadequate proficiency to estimate NOE—and “less bias”—due to the exclusion of those estimates with more measurement errors—is uncertain. In our view, if we restrain the relevance of estimated marginal effects on the underground, informal, and illegal economies to the countries included in the sample, then the hypothesis that the missing values are not random may be beneficial in terms of the overall reliability of the estimates (${{}_{N}\widehat{NOE}}_{it}$). In contrast, if we are mainly interested in causal inference, then we have to recognize that it may be risky to extrapolate general conclusions on the marginal effects of the determinants of NOE for those countries that are out of the sample ($\widehat{\beta }$).⁴⁸

Table 2 reports the best panel model specifications for each NOE type.⁴⁹ As the main aim of the hybrid approach is to predict the different types of NOEs, we select the model specifications that maximize the goodness of fit. Specifically, we apply four main selection criteria: adjusted R²; Akaike’s Bayesian information criterion (AIC); parsimony of specification as driven by statistical significance; and economic interpretation of coefficients.

As a robustness check, we report estimates based on three datasets: (a) only NA estimates; (b) NA estimates and projections based on step 2 (see Sect. 3.2); (c) NA estimates and weighted projections, i.e. we apply a Weighted Least Squares (WLS) estimator to control for the different reliability between (endogenous) projections of NA estimates based on PT and (exogenous) NA estimates of N-adjustments.⁵⁰ The estimated coefficients based on WLS and LS with fixed effects are reported in Table 2 and predicted values of NOE aggregates are shown in Figs. 2, 3, and 4. In general, results are sufficiently robust to different hypotheses and have satisfactory goodness of fit.

Table 2 Fixed effects estimates

Considering that providing normative implications from this analysis is beyond the scope of this paper, we merely report the main results:

• (1) The statistical aggregate of NOE cannot be used for the economic analysis of informality, underground, or shadow economy. Indeed, there is clear evidence that underground, informal, and illegal economies have significantly different drivers; therefore, combining them all can lead to biased inference and misleading normative implications.

• (2) For all three types of NOE aggregates, we find that the intraclass correlation is high (Rho > 0.98). This can be interpreted as a signal that the dependent variables are significantly explained by unobserved heterogeneity across countries (i.e., residuals within countries). By speculating on these sources of heterogeneity controlled by country-fixed effects in the models, we guess that levels of tax morale, tax enforcement, and proficiency of NIS to estimate NOE may be the most relevant. Again, taking into account that the appropriate model specifications include also time-fixed effects, we can infer that all three NOE aggregates are affected by external common temporal trends and shocks across all countries (e.g. European policy changes, global financial crisis, growth of digital transactions, different degrees of implementation and measurement errors in the adoption of the Eurostat’s N1-N7 framework over time).

• (3) In general, the econometric specifications show considerable differences in terms of goodness-of-fit performance. Although the F-tests provide evidence that all the coefficients in each model are jointly different than zero, the vector of explanatory variables for the underground economy has better predictive performance than those for the informal and illegal economies (e.g. R²-within statistics for model (b: NA + Proj.) are equal to 0.88, 0.72, and 0.62, respectively).

• (4) Regarding the underground economy, while the overall tax burden and the structure of the tax system have no significant marginal effects on underground production, we find that the higher social benefits per capita (${\beta }^{SocBen\_pc}>0$), the larger the ratio between underground production and GDP. The underground economy exhibits procyclical behavior over the business cycle (${\beta }^{Gdp\_pcap\_g}>0$); an increase in the rate of self-employment as a percentage of the labor force (${\beta }^{Self\_empl}>0$) and a decrease in employment in agriculture (${\beta }^{Agr\_empl}<0$), are correlated to a larger underground economy. Regarding the ratios between the gross value added of industries where the underground economy is expected to be larger and the total gross value added of the economy, we find that the lower the official value added in “Retail trade, the maintenance and repair of motor vehicles” (${\beta }^{{GVA}_{it}^{G}}<0$) and “Arts, entertainment and recreation and activities of households as employers” (${\beta }^{{GVA}_{it}^{RT}}<0$), the larger the underground economy.

• (5) Concerning the informal economy, the most important drivers are related to the characteristics of employment. Specifically, the higher the employment in agriculture as a percentage of total employment (${\beta }^{Agr\_empl}$>0) and the lower the male contributing family workers and own-account workers as a percentage of total male employment (i.e. vulnerable male employment, ${\beta }^{Vuln\_empl\_m}$<0), the larger the informal production as a percentage of GDP. Likewise, a decrease in income inequality (${\beta }^{Gini}<0$) and an expansion of public policies and regulations that promote private sector development (i.e. Regulatory Quality, ${\beta }^{Regul}$>0) increase the size of the informal economy.

• (6) Concerning the illegal economy, the incidence of migrant people in the total population (${\beta }^{Migr\_net\_r}>0$), the employment in agriculture as a percentage of total employment (${\beta }^{Agr\_empl}$<0), and the perceptions of the extent to which public power is exercised for private gain $({\beta }^{Corrup}$<0) are significantly correlated to the illegal production. About the relative size of migrant people, we interpret this result as proof of the hypothesis that an increase of people with a higher risk of being involved in illegal productive activities is positively correlated to the types of illegal activities estimated by the NA approach (i.e. prostitution, drug trafficking, smuggling). Regarding the index of “Control of Corruption”, taking into account that low values of the “Control of Corruption” index indicate high levels of perceived corruption, we interpret this variable as a general proxy of the (lack of) law enforcement.

3.4 Step 4: Calibration of predicted values

The last step consists of calibrating the predicted values estimated by marginal effects obtained from regression 1 and fixing an intercept to obtain the values of predicted underground, informal, and illegal economies equal to the most recent estimates based on the NA approach (generally, Eurostat, 2022, 2nd Verification cycle 2020–2024). Specifically, in the first stage, we predict the uncalibrated (${{}_{N}{}^{u}\widehat{NOE}}_{it}$) based on estimated coefficients (from Table 2); in the second stage, we estimate the intercepts $({}^{N}{\widehat{\beta }}_{i}^{c}$) that equalize the predicted values (${{}_{N}{}^{u}\widehat{NOE}}_{i{t}^{*}}$) to the exogenous NA estimates ${({}_{N}NOE}_{i{t}^{*}})$ in reference period t* for each i-th country (i.e., ${}^{N}{\widehat{\beta }}_{i}^{c}={{}_{N}NOE}_{i{t}^{*}}-{{}_{N}{}^{u}\widehat{NOE}}_{i{t}^{*}}$). Accordingly, “final estimates” are calculated by ${{}_{N}\widehat{NOE}}_{it}={}^{N}{\widehat{\beta }}_{i}^{c}+{{}_{N}{}^{u}\widehat{NOE}}_{it}$.

As the next section will show, the proposed calibration approach may generate negative estimates of informal and illegal economies for countries where the NA exogenous estimates of these aggregates are very low (i.e. lower than 0.5% of official GDP). A method to deal with this issue of unrealistic negative predictions may be to include an additional calibration step that is applied only to the countries where at least a negative predicted value emerges, i.e. $Min\left({{}_{N}\widehat{NOE}}_{it}\right)<0$. For these countries, we could add a constant that is equal to the absolute value of the minimum of the time series of the estimated NOE subcomponent, i.e. ${}_{neg}{}^{N}{\widehat{\beta }}_{i}^{c}=\left|Min\left({{}_{N}\widehat{NOE}}_{it}\right)\right|.$ Accordingly, “final adjusted estimates” in these countries are equal to: ${{}_{N}{}^{adj}\widehat{NOE}}_{it}={}^{N}{\widehat{\beta }}_{i}^{c}+{}_{neg}{}^{N}{\widehat{\beta }}_{i}^{c}+{{}_{N}{}^{u}\widehat{NOE}}_{it}$.

Given that the primary aim of this article is to propose a hybrid method that extends the NA estimate of the NOE by using the macro-econometric methods, rather than estimating the most reasonable estimates of the NOE by correcting the potential underestimation of the NA estimates, then we don’t apply this “adjusted” calibration approach in the following section.⁵¹

4 Estimates of underground, informal, and illegal economies based on the hybrid approach

4.1 Estimates of the hybrid approach and calibrating values

This section presents both the estimates of the underground, informal, and illegal productions as estimated by the hybrid approach and it compares them with existing NA estimates aggregated according to the same definitional framework.

Figures 2, 3, and 4 show predicted values (${{}_{N}\widehat{NOE}}_{it}$) at the country level. To highlight the negative predicted values, we report a red horizontal line at the value of 0% on the y-axis. We draw a horizontal (dotted) line to highlight the reference year used for calibration (t^*) and the confidence intervals at 95% based on model (b) (i.e. including both NA estimates and unweighted projections).⁵² Appendix E reports annual estimates based on the hybrid method and NA approach.

Fig. 2

Underground economy as a percentage of official GDP

Fig. 3

Informal economy as a percentage of official GDP

Fig. 4

Illegal economy as a percentage of official GDP

From this analysis, three main findings emerge: (1) estimates based on the hybrid approach are consistent with the estimates based on the NA approach by construction; (2) there are only slight differences among estimates based on different treatments of projections based on TAE⁵³ and (3) Scandinavian countries, Portugal, Iceland, the Netherlands, Luxembourg, and other countries have some unrealistically negative values of informality and/or the illegal economy. We interpret this result as a consequence of the extremely low NA estimates of the informal economy and illegal economy used to calibrate the model. For instance, for nine of the 22 countries of our sample, the NA estimates of the informal economy used for calibration are lower than 0.5% (e.g. in Greece and Luxembourg NIS estimate that informality is zero). For the illegal economy, where we find at least a negative value in 18 of 22 countries, the NA estimates used for calibration are higher than 0.5% only in 8 of 22 countries (i.e. Croatia, Denmark, Greece, Hungary, Italy, Netherlands, Poland, and Slovakia) and, for Norway and Luxemburg the estimated values of illegal production is about zero, i.e. 0.00% and 0.01%, respectively.

In conclusion, the negative values of the estimates of the informal and illegal economies estimated by the hybrid approach depend on exogenous NA sources used for calibration; consequently, they can be interpreted as a signal of potential downward bias in NA estimates for some countries. The reasons for these underestimations are discussed in Sect. 2.4. A potential solution to deal with this issue in the hybrid method consists of applying the “adjusted” calibration approach as proposed in Sect. 3.4.

4.2 Comparison of hybrid, macro, and na estimates of the shadow economy

This section offers a comparative analysis of the estimates obtained by the hybrid approach with those calculated by the macroeconometric and the NA approaches. Specifically, the first three blocks of Table 3 (“Underground”, “Informal” and “Illegal”) compare the hybrid to the NA approach (i.e., Eurostat, 2022 and Gyomai et al., 2012), the last block reports the estimates of the shadow economy based on five estimation approaches. We introduce the macroeconomic aggregate of the shadow economy because macro approaches often do not distinguish between underground and informal production therefore using this “economic” concept of the non-observed economy makes possible a comparison among similar aggregates. Following Medina and Schneider’s (2021, p. 11) definition of the shadow economy,⁵⁴ the shadow economy estimates based on the hybrid approach are calculated as the sum of underground and informal economies. The first column (“Hybrid”) of the shadow economy block of Table 3 reports these values. The second column of this block reports Schneider’s (2022) and, only for Iceland, Schneider and Medina’s (2021) estimates based on the MIMIC approach (“MIMIC”). The third column reports the Dynamic General Equilibrium model-based estimates of informal output as estimated by Elgin et al. (2021), i.e. “DGE”. The column “CDA” reports the estimates based on the Currency Demand Approach as estimated by Dybka et al. (2019). The last column reports the estimates based on the NA approach (“Eurostat”) where the shadow economy is calculated by adding N1, N3, N4, N5, and N6 adjustments for exhaustiveness as extracted by Eurostat (2022).

Table 3 Comparison of estimates based on different approaches (averages on 4 years)

For the sake of space, Table 3 shows the averages calculated over 4 years, with the exclusion of the last two years, where the averages over 2020 and 2021 are reported. Appendix F shows graphical comparisons of the shadow economy as a percentage of official GDP by including also Dybka et al.’s (2019) MIMIC estimates. A discussion of the comparison of the shadow economy estimates across methods is outside the scope of this paper, however, the main message that emerges from this analysis is that, with few exceptions,⁵⁵ macro approaches estimates are higher than the hybrid and NA estimates. This result mainly depends on the different exogenous sources used to calibrate the different methods (e.g. for hybrid estimates, we use the last available values obtained by the NA approach, while for macro methods, authors use other macro sources or their own estimates).

5 Conclusions

This paper addresses the divisive topic of estimating the unobserved, underground, informal, illegal, and shadow economies. As Dell’Anno (2023) notes, the two main difficulties in this field are that, differently from other topics of applied economics, there is not an “acid test”, where the “predicted” values are compared to the “observed” ones. This leaves an aura of uncertainty on the predictive performance of the estimation approaches. The second question essentially depends on the skepticism from some researchers in the economic literature (e.g., Slemrod and Weber 2012; Breusch, 2016; Feige, 2016; Kirchgässner, 2017) and some institutions (e.g., OECD, 2002; ISWGNA, 20062002) on the values of macroeconometric methods to estimate NOE.

This paper addresses the first issue by changing perspective. Let us assume that the NA approach provides the most reliable estimates of the unobserved economy; then, the objective is to overcome the two main limitations of this approach: the lack of available estimates to utilize in econometric analysis and the use of a statistical concept (i.e., the NOE) that is not suitable for economic analysis. Accordingly, we propose a hybrid national accounts-macroeconometric approach intended to overcome these problems in four steps. First, starting from the N1-N7 framework proposed by the Eurostat TAE, these adjustments are rearranged for the exhaustiveness of GDP/GNI estimates into three economically relevant aggregates (underground, informal, and illegal economies). Second, it collects all the available comparable data at the European level using the previous classification. Third, it replaces the missing values with predicted values, where the predictions are made using separate fixed effects regressions created from the nonmissing data part of the dataset, and where each model specification includes the main potential determinants of underground, informal, and illegal production as emerge from the economic literature. Fourth, by assuming that the comparability and precision of NA estimates remain a work in progress, it calibrates the predicted values to obtain estimates based on the hybrid approach equal to the last available estimates of N1-N7 based on the NA approach (i.e., Eurostat, 2022).⁵⁶ Accordingly, this paper aims to contribute to this literature in several ways.

From a methodological viewpoint, it proposes an estimation strategy that combines economic literature with the NA approach. The proposed hybrid method expands our knowledge of the dynamics and sizes of the different types of NOEs by providing estimates of underground, informal, and illegal economies, which, unlike NA estimates, are available for a long period (20 years). Specifically, our estimates cover 22 European countries and are consistent with both the standards of European NA (i.e., ESA2010) and the requisites for applied economic research (e.g., definitions of macroeconomic aggregates consistent with causal inference).

From a more general perspective, we also provide factual evidence that the open-access principle recently applied for the NA estimates is an effective strategy to enhance scientific research. Specifically, we imagine that the hybrid approach may also be applied to a worldwide context as soon as the SNA implements a common framework, such as Eurostat’s TAE, and makes available to the scientific community disaggregated data on the GDP compilation process, e.g., GDP/GNI inventory and PT. However, although Eurostat’s decision to make these statistics available in an open-access repository is an important step towards full transparency of the NA approach to estimate NOE, this process is still incomplete. At this moment (February 2024), scholars don’t have access to other worthwhile data calculated by NIS, such as the complete time series of N1-N7 adjustments applied to estimate official GDP/GNI over the last ten years, or at least since 2016, and the disaggregation at regional level (e.g. at NUTS 1 level) of each N-type of adjustments for exhaustiveness.

In conclusion, a clear answer on how much we can trust the estimates based on the hybrid model is not easily obtained. As Schneider (1997) stated, each approach has its strengths and weaknesses and can provide specific insights and results. However, by assuming that the NA approach provides the most reliable source of the non-observed economy, the estimates presented here can be considered the best available option to handle estimates of comparable aggregates at the European level.

In response to the mutual skepticism between supporters of the macroeconomic and the NA approaches, I attempt to include both sides of the debate. As an economist who has extensively applied different macroeconomic methods, I am aware of the lack of empirical and theoretical evidence on the causal relationships between macroeconomic variables and the different types of the NOE as well as the dependence of these methods of external estimates to calibrate the estimates of these methods. On the other hand, as a user of the NA estimates, remain concerned about the heterogeneous degree of implementation of the TAE framework across European NIS and the potential downward bias that seems to emerge for some countries. The idea behind the proposed hybrid method is guided by the awareness that two methods may work better than one alone.

As a final point, I believe that much should still be done to declare that the reliability and comparability of the NA estimates of the NOE made useless alternative approaches to the estimation of the underground, informal, and illegal economies. In contrast, all research efforts aimed at augmenting our knowledge of estimating informality and NOE are welcome to fill the gap between scholars’ demand for quantitative knowledge on informality and the scarce availability of NA estimates. In line with this perspective, a useful instrument to increase the quality of research in this strand of literature is to make easily available all data on Eurostat’s TAE through a data warehouse. Indeed, the current platform, CIRCABC, is a collaborative workspace to share digital documents among work groups sponsored by the European Union institutions but it is not suitable as a digital platform to download and collect data for longitudinal and comparative analyses.