Shadow Economies Around the World: What Did We Learn Over the Last 20 Years?
  • 1 https://isni.org/isni/0000000404811396, International Monetary Fund

Contributor Notes

Author’s E-Mail Address: lmedina@imf.org, friedrich.schneider@jku.at

We undertake an extended discussion of the latest developments about the existing and new estimation methods of the shadow economy. New results on the shadow economy for 158 countries all over the world are presented over 1991 to 2015. Strengths and weaknesses of these methods are assessed and a critical comparison and evaluation of the methods is carried out. The average size of the shadow economy of the 158 countries over 1991 to 2015 is 31.9 percent. The largest ones are Zimbabwe with 60.6 percent, and Bolivia with 62.3 percent of GDP. The lowest ones are Austria with 8.9 percent, and Switzerland with 7.2 percent. The new methods, especially the new macro method, Currency Demand Approach (CDA) and Multiple Indicators Multiple Causes (MIMIC) in a structured hybrid-model based estimation procedure, are promising approaches from an econometric standpoint, alongside some new micro estimates. These estimations come quite close to others used by statistical offices or based on surveys.

Abstract

We undertake an extended discussion of the latest developments about the existing and new estimation methods of the shadow economy. New results on the shadow economy for 158 countries all over the world are presented over 1991 to 2015. Strengths and weaknesses of these methods are assessed and a critical comparison and evaluation of the methods is carried out. The average size of the shadow economy of the 158 countries over 1991 to 2015 is 31.9 percent. The largest ones are Zimbabwe with 60.6 percent, and Bolivia with 62.3 percent of GDP. The lowest ones are Austria with 8.9 percent, and Switzerland with 7.2 percent. The new methods, especially the new macro method, Currency Demand Approach (CDA) and Multiple Indicators Multiple Causes (MIMIC) in a structured hybrid-model based estimation procedure, are promising approaches from an econometric standpoint, alongside some new micro estimates. These estimations come quite close to others used by statistical offices or based on surveys.

1. Introduction

The shadow economy is, by nature, difficult to measure, as agents engaged in shadow economy activities try to remain undetected. The request for information about the extent of the shadow economy and its developments over time is motivated by its political and economic relevance. Moreover, total economic activity, including official and unofficial production of goods and services is essential in the design of economic policies that respond to fluctuations and economic development over time and across space. Furthermore, the size of the shadow economy is a core input to estimate the extent of tax evasion and thus for decisions on its adequate control.

The shadow economy is known by different names, such as the hidden economy, gray economy, black economy or lack economy, cash economy or informal economy. All these synonyms refer to some type of shadow economy activities. We use the following definition: The shadow economy includes all economic activities which are hidden from official authorities for monetary, regulatory, and institutional reasons. Monetary reasons include avoiding paying taxes and all social security contributions, regulatory reasons include avoiding governmental bureaucracy or the burden of regulatory framework, while institutional reasons include corruption law, the quality of political institutions and weak rule of law. For our study, the shadow economy reflects mostly legal economic and productive activities that, if recorded, would contribute to national GDP, therefore the definition of the shadow economy in our study tries to avoid illegal or criminal activities, do-it-yourself, or other household activities.2

Empirical research into the size and development of the global shadow economy has grown rapidly (Feld and Schneider 2010, Gerxhani 2003, Schneider 2011, 2015, 2017, Schneider and Williams 2013, Williams and Schneider 2016, and Hassan and Schneider 2016). The main goal of this paper is to analyze the growth of knowledge about the shadow economy in a review covering the past 20 years, concentrating mainly on knowledge about established or new estimation methods; definition or categorization of the shadow economy and new measures of indicator variables such as the light intensity approach, as well as to present estimates of the size of the shadow economy for 158 countries over 25 years. The concrete goals are as follows:

  • (1) To extensively evaluate and discuss the latest developments regarding estimation methods, such as the national accounts approach and new micro and macro methods, and the crucial evolution of the macro methodologies (Currency Demand Approach (CDA) or Multiple Indicators Multiple Causes (MIMIC)) tackling the problem of double counting.

  • (2) To present shadow economy estimates for 158 countries all over the world for the period 1991 to 2015 while addressing early criticism. In particular: (a) When using the MIMIC approach it is often a problem that GDP per capita or growth rate of GDP or first differences in GDP are used as cause as well as indicator variables. We try to avoid this problem by using a light intensity approach instead of GDP as an indicator variable. We also run a variety of robustness tests to further assess the validity of our results; and (b) There has been a long and controversial discussion on how to calibrate the relative MIMIC estimates of the shadow economy (compare Hashimzade and Heady (2016), Feige (2016a), Schneider (2016) and Breusch (2016)). In this paper, we additionally use a fully independent method, the Predictive Mean Matching Method (PMM) by Rubin (1987), which overcomes these problems. To our knowledge this is one of the first attempts to include both the light intensity approach as an indicator variable within MIMIC and to use a full alternative methodology, as PMM3.

  • (3) To compare the results of the different estimation methods, showing the strengths and weaknesses of these methods, and critically compare and evaluate them.

Our paper is organized as follows: In section 2 some theoretical considerations are drawn and the most important cause variables are discussed. Section 3 discusses methods available to estimate the shadow economy and presents new estimation results. It also discusses the econometric results of the MIMIC estimations and critically evaluates them. Moreover, it addresses the macro methods’ shortcomings, as well as it introduces the use of night lights as a proxy for the size of an economy and discusses additional robustness tests. Section 3 presents results on the size of the shadow economy of the 158 countries. In section 4 a comparison of the MIMIC results with micro survey results and National Discrepancy Method results is undertaken. Section 5 summarizes and concludes.

2. Theoretical Considerations

Individuals are rational calculators who weigh up costs and benefits when considering breaking the law. Their decision to partially or completely participate in the shadow economy is a choice overshadowed by uncertainty, as it involves a trade-off between gains, if their activities are not discovered, and losses, if they are discovered and penalized. Shadow economic activities SE thus negatively depend on the probability of detection p and potential fines f, and positively on the opportunity costs of remaining formal, denoted as B. The opportunity costs are positively determined by the burden of taxation T and high labor costs W – individual income generated in the shadow economy is usually categorized as labor income rather than capital income – due to labor market regulations. Hence, the higher the tax burden and labor costs, the more incentives individuals have to avoid these costs by working in the shadow economy. The probability of detection p itself depends on enforcement actions A taken by the tax authority and on facilitating activities F accomplished by individuals to reduce the detection of shadow economic activities. This discussion suggests the following structural equation:

SE=SE[p¯(A+,F¯);f¯;B+(T+,W+)]

Hence, shadow economic activities may be defined as those economic activities and income earned that circumvent government regulation, taxation or observation. More narrowly, the shadow economy includes monetary and non-monetary transactions of a legal nature; hence all productive economic activities that would generally be taxable were they reported to the state (tax) authorities. Such activities are deliberately concealed from public authorities to avoid payment of income, value added or other taxes and social security contributions, or to avoid compliance with certain legal labor market standards such as minimum wages, maximum working hours, or safety standards and administrative procedures. The shadow economy thus focuses on productive economic activities that would normally be included in national accounts, but which remain underground due to tax or regulatory burdens.4 Although such legal activities would contribute to a country’s value added, they are not captured in national accounts because they are produced in illicit ways. Informal household economic activities such as do-it-yourself activities and neighborly help are typically excluded from the analysis of the shadow economy.5 What are the most important determinants influencing the shadow economy?

A. Causes and Signs/Indicators of Informality

The size of the shadow economy depends on various elements. The literature highlights specific causes and indicators of the shadow economy6. In Table 1 the main causes and indicators determining the shadow economy are presented.

Table 1.

The main causes/indicators determining the shadow economy

article image
article image
article image
Source: Schneider (2017).

3. Estimation Methods and MIMIC Estimation Results

A. Measuring the Shadow Economy7

This subsection describes the methodologies used to measure the shadow economy, highlighting their advantages and drawbacks.8 These approaches can be divided into direct or indirect (including the model-based):

Direct approaches

In this sub-section, four direct and micro methods of measuring the shadow economy9 are briefly presented10 and critically evaluated.

  • (i) Measurement by the System of National Accounts Statistics – Discrepancy method;

  • (ii) Survey technique approach;

  • (iii) The use of surveys of company managers; and

  • (iv) The estimation of the consumption-income-gap of households.

(i) System of National Accounts Statistics – Discrepancy method

This method is described in detail in the paper by Gyomai and van de Ven (2014). The authors start with a classification for measuring the non-observed economy as follows (Gyomai and van de Ven, p. 1):

  • (i) Underground hidden production: Activities that are legal and create a value added, but are deliberately concealed from public authorities.

  • (ii) Illegal production: Productive activities that generate goods and services forbidden by law or which are unlawful when carried out by unauthorized procedures.

  • (iii) Informal sector production: Productive activities conducted by incorporated enterprises in the household sector or other units that are registered and/or less than specified size in terms of employment and have some market production.

  • (iv) Production of households for own (final) use: Productive activities that result in goods or services consumed or capitalized by the households that produced them.

  • (v) Statistical “underground”: All productive activities that should be accounted for in basic data collection programs, but are missed due to deficiencies in the statistical system.

Goymai and van de Ven (2014) provide a precise definition in order to reach the goal of exhaustive estimates, as follows:

(1) Hidden activities (System of National Accounts):

SNA 2008, § 6.40: Certain activities may clearly fall in the production boundary of the SNA and also be quite legal, but are deliberately concealed from public authorities for the following kinds of reasons:

  • (i) to avoid the payment of income tax, value added or other payments;

  • (ii) to avoid the payment of social security contributions;

  • (iii) to avoid having to meet certain legal standards such as minimum wages, maximum hours, safety or health standards, etc.;

  • (iv) to avoid complying with certain administrative procedures, such as completing statistical questionnaires or other administrative forms.

(2) Illegal activities:

SNA 2008, § 6.43: There are two kinds of illegal production:

  • (i) The production of goods or services whose sale, distribution or possession is forbidden by law;

  • (ii) Production activities that are usually legal but become illegal when carried out by unauthorized producers; for example, unlicensed medical practitioners.

In SNA 2008, § 6.45 it is written that both kinds of illegal production are included within the production boundary of the SNA provided they are genuine production processes whose outputs consist of goods or services for which there is an effective market demand.

With this classification, the authors provide a comprehensive and useful categorization of the various shadow economy/underground activities. This estimation method is applied by National Statistical Offices and is explained in detail in the Handbook for Measuring the Non-Observed Economy, OECD (2010). The authors argue that non-observed economy estimates take place at various stages of the integrated production process of national accounts:

First, data sources with identifying biases on reporting on scope are corrected via imputations.

Second, upper-bounded estimates are used to access the maximum possible amount of non-observed economy (NOE) activity for a given industrial activity or product group based on a wide array of available data.

Third, special purpose surveys are carried out for areas where regular surveys provide little guidance and small scale models are built to indirectly estimate areas where direct observation and measurement is not feasible.

In Figure 3.1 the classification of the NOE in order to reach estimates with the National Accounts Method (NAM) is shown.

Figure 3.1:
Figure 3.1:

Classification of NOE (Non-Observed Economy)

Citation: IMF Working Papers 2018, 017; 10.5089/9781484338636.001.A001

Source: Van de Ven (2017), PowerPoint Presentation, OECD Paris, p. 8.

We clearly see that this is a careful procedure which considers all possible situations to achieve an exhaustive estimation. The concept of the national accounts method (NAM) to capture all non-observed economic activities is the following:

It includes the following non-observed economy categories:

  • Economic underground: N1+N6

  • Informal (and own account production): N3+N4+N5

  • Statistical underground: N7

  • Illegal: N2

Much work has been done on the first three categories, less so on illegal activities. However, there is increased interest in illegal activities in the European Union nowadays, since its inclusion has become mandatory with the introduction of ESA 2010.

In general, discrepancy analysis is performed at a disaggregated level and the nature of adjustment has the effect that various NOE categories can be at least partly identified. The methodological descriptions provided by countries reveal that country practices in many areas of adjusting for NOE are often quite similar.

Still, substantial differences show up between various OECD countries. Table 2 presents NOE adjustments by informality type for 16 developed OECD countries over the years 2011 to 2012. It shows that the total non-observed economy varies considerably among countries11. Also the adjustments in the different categories are quite considerable. Using this method, some countries such as Italy have relatively large shadow economies with 17.5 percent, followed by the Slovak Republic with 15.6 percent and Poland with 15.4 percent of official GDP. The smallest one here is Norway with 1 percent.

Table 2.

NOE adjustments by informality type – percent of GDP (share of adjustment type within total NOE); 2011–2012

article image
Source: Gyomai and van de Ven (2014, p. 6).

(ii) Micro approach: Representative surveys

Representative surveys12 are often used to get some micro knowledge about the size of the shadow economy and shadow labor markets. This method is based on representative surveys designed to investigate public perceptions of the shadow economy, actual participation in shadow economy activities and opinions about shadow practices. As an example we present some results of such surveys which were designed by the Lithuanian Free Market Institute and its partner organizations for Belarus, Estonia, Latvia, Lithuania, Poland and Sweden. The surveys took place between May 22 and June 15, 2015. The target audience included local residents aged 18–75. The total sample size comprised 6,000 respondents across the six countries. For our purpose the most important results of the surveys are presented in Tables 3 and 413. Table 3 contains undeclared working hours as a proportion of normal working hours from the year 2015. Undeclared hours, as a share of normal working hours based on a weekly calculation, vary between 4.2 percent in Sweden and 20.7 percent in Poland which is quite a huge variation. This is not unexpected, because the shadow economy in Sweden is much smaller than the one in Poland. If one considers the average weekly undeclared hours worked by respondents with shadow experience, the range is much narrower. The work ranges between 25.5 hours in Poland and 16.8 hours in Lithuania. Table 4 shows the extent of aggregated shadow wages as a proportion of GDP. Obviously Sweden has by far the lowest with 1.7 percent of GDP as shadow employment, Belarus the largest with 32.8 percent, followed by Poland with 24 percent. We also notice quite considerable variance here.

Table 3.

Undeclared working hours as a proportion of normal working hours; year 2015

article image
Note: Figures for the experience of friends or relatives in the shadow labor market and average weekly undeclared hours are taken from the survey, while normal average weekly working hours come from the Eurostat Database for the year 2014. In the absence of such data for Belarus, it was estimated as an average of normal working hours for Central and Eastern European countries that belong to the European Union.Source: Zukauskas and Schneider (2016, p. 128).
Table 4.

Extent of aggregated shadow wages as a proportion of GDP; year 2015

article image
Note. Undeclared hours worked per year are calculated as shadow frequency/100 x average weekly undeclared hours worked by persons who carried out shadow activities x 52 x total population aged 18–74. Figures for shadow frequency, average undeclared weekly hours, and average undeclared hourly wage are taken from the survey, while the population aged 18–74 and GDP at current prices are taken from the Eurostat Database for the year 2014.Source: Zukauskas and Schneider, 2016.

(iii) Micro approach: Measuring the shadow economy using surveys of company managers

Putnins and Sauka (2015) and in a similar way Reilly and Krstic (2017) use surveys of company managers to measure the size of the shadow economy. They combine misreported business income and misreported wages as a percentage of GDP. The method produces detailed information on the structure of the shadow economy, especially in the service and manufacturing sectors. It is based on the premise that company managers are most likely to know how much business, income and wages go unreported due to their unique position in dealing with both types of income. They use a range of survey-designed features to maximize the truthfulness of responses. Their method combines estimations of misreported business income, unregistered or hidden employees and unreported wages in order to calculate a total estimate of the size of the shadow economy as a percentage of GDP. In their opinion their approach differs from most other studies of the shadow economy, which largely focus either on macroeconomic indicators or on surveys about households. Putnins and Sauka have developed first results for Estonia, Latvia and Lithuania. Results are shown in Table 5. For all countries, there is a decline over the period 2009 to 2015 and the largest shadow economy is Latvia with 27.8 percent average over 2009 to 2015, followed by Estonia with 17.4 percent and Lithuania with 16.4 percent.

Table 5.

A comparison of the size of the shadow economy (in percent of GDP) in the Baltic countries 2009 – 2015 by Putnins and Sauka with Schneider

article image
Source: Putnins and Sauka (2015, Table 1, p. 12).

Indirect approaches

Indirect approaches, alternatively called “indicator” approaches, are mostly macroeconomic in nature. These are in part based on: the discrepancy between national expenditure and income statistics; the discrepancy between the official and actual labor force; the “electricity consumption” approach of Kauffman and Kaliberda (1996); the “monetary transaction” approach of Feige (1979); and the “currency demand” approach of Cagan (1958) and Tanzi (1983) among others.

  • (i) Discrepancy between national expenditure and income statistics: If those working in the shadow economy were able to hide their incomes for tax purposes but not their expenditure, then the difference between national income and national expenditure estimates could be used to approximate the size of the shadow economy. This approach assumes that all components on the expenditure side are measured without error and constructed so that they are statistically independent from income factors.14

  • (ii) Discrepancy between official and actual labor force: If the total labor force participation is assumed to be constant, a decline in official labor force participation can be interpreted as an increase in the importance of the shadow economy. Fluctuation in the participation rate might have many other explanations, such as the position in the business cycle, difficulty in finding a job and education and retirement decisions, but these estimates represent weak indicators of the size of the shadow economy.15

  • (iii) Electricity approach: Kaufmann and Kaliberda (1996) endorse the idea that electricity consumption is the single best physical indicator of overall (official and unofficial) economic activity. Using findings that indicate that electricity-overall GDP elasticity is close to one, these authors suggest using the difference between growth of electricity consumption and growth of official GDP as a proxy for the growth of the shadow economy. This method is simple and appealing, but has many drawbacks, including: (i) not all shadow economy activities require a considerable amount of electricity (e.g. personal services) or they may use other energy sources (such as coal, gas, etc.), hence only part of the shadow economy growth is captured; and (ii) electricity-overall GDP elasticity might significantly vary across countries and over time.16

  • (iv) Transaction approach: Using Fischer’s quantity equation, Money*Velocity = Prices*Transactions, and assuming that there is a constant relationship between the money flows related to transactions and the total (official and unofficial) value added, i.e. Prices*Transactions = k (official GDP + shadow economy), it is reasonable to derive the following equation Money*Velocity = k (official GDP + shadow economy). The stock of money and official GDP estimates are known, and money velocity can be estimated. Thus, if the size of the shadow economy as a proportion of the official economy is known for a benchmark year, then the shadow economy can be calculated for the rest of the sample. Although theoretically attractive, this method has several weaknesses, for instance: (i) the assumption that k would be constant over time seems quite arbitrary; and (ii) other factors like the development of checks and credit cards could also affect the desired amount of cash holdings and thus velocity.17

  • (v) Currency demand approach (CDA): Assuming that informal transactions take the form of cash payments, in order not to leave an observable trace for the authorities, an increase in the size of the shadow economy will, consequently, increase demand for currency. To isolate this “excess” demand for currency, Tanzi (1980) suggests using a time series approach in which currency demand is a function of conventional factors, such as the evolution of income, payment practices and interest rates, and factors causing people to work in the shadow economy, like the direct and indirect tax burden, government regulation and the complexity of the tax system. However, there are several problems associated with this method and its assumptions: (i) this procedure may underestimate the size of the shadow economy because not all transactions take place using cash as means of exchange; (ii) increases in currency demand deposits may occur because of a slowdown in demand deposits rather than an increase in currency used in informal activities; (iii) it seems arbitrary to assume equal velocity of money in both types of economies; and (iv) the assumption of no shadow economy in a base year is arguable.18

  • (vi) Multiple Indicators, Multiple Causes (MIMIC) approach: This method explicitly considers several causes, as well as the multiple effects, of the shadow economy. The methodology makes use of associations between the observable causes and the effects of an unobserved variable, in this case the shadow economy, to estimate the variable itself (Loayza, 1996).19 This methodology is described in detail in subchapter 3.1.3.

The model or macro MIMIC approach

The MIMIC model is a special type of structural equation modeling (SEM) that is widely applied in psychometrics and social science research and is based on the statistical theory of unobserved variables developed in the 1970s by Zellner (1970) and Joreskog and Goldberger (1975). The MIMIC model is a theory-based approach to confirm the influence of a set of exogenous causal variables on the latent variable (shadow economy), and also the effect of the shadow economy on macroeconomic indicator variables. At first, it is important to establish a theoretical model explaining the relationship between the exogenous variables and the latent variable. Therefore, the MIMIC model is considered to be a confirmatory rather than an explanatory method. The hypothesized path of the relationships between the observed variables and the latent shadow economy based on our theoretical considerations is depicted in Figure 3.1. The pioneers to apply the MIMIC model to measure the size of the shadow economy in 17 OECD countries were Frey et al. (1984). Following them, various scholars such as Schneider et al. (2010), Hassan et al. (2016), and Buehn et al. (2009) applied the MIMIC model to measure the size of the shadow economy. Formally, the MIMIC model has two parts: the structural model and the measurement model.

In the following, we briefly explain the MIMIC estimation procedure (compare also Figure 3.2):

  • (1) Modeling the shadow economy as an unobservable (latent) variable;

  • (2) Description of the relationships between the latent variable and its causes in a structural model: η = Γx + ξ; and

  • (3) The link between the latent variable and its indicators is represented in the measurement model: y = Λyη + ε.

Figure 3.2:
Figure 3.2:

MIMIC estimation procedure

Citation: IMF Working Papers 2018, 017; 10.5089/9781484338636.001.A001

Source: Schneider, Buehn and Montenegro (2010).

where

η: latent variable (shadow economy);

X: (q×1) vector of causes in the structural model;

Y: (p×1) vector of indicators in the measurement model;

Γ: (1×q) coefficient matrix of the causes in the structural equation;

Λy: (p×1) coefficient matrix in the measurement model;

ζ: error term in the structural model and ε is a (p×1) vector of measurement error in y. The specification of the structural equation is:

[shadoweconomy]=[γ1,γ2,γ3,γ4,γ5,γ6,γ7,γ8]x[Shareofdirecttaxation][Shareofindirecttaxation][Shareofsocialsecurityburden][Burdenofstateregulation]+[ζ][Qualityofstateinstitutions][Taxmorale][Unemploymentquota][GDPpercapita]

The specification of the measurement equation is:

|EmploymentQuotaChangeoflocalcurrencyAverageworkingtime|=|λ1λ2λ3|x|ShadowEconomy|+|ɛ1ɛ2ɛ3|

where γi and λi are coefficients to be estimated.

How do we proceed to get the absolute figures? We use the following steps:

  1. The first step is that the shadow economy remains an unobserved phenomenon (latent variable) which is estimated using causes of illicit behavior, e.g. tax burden and regulation intensity, and indicators reflecting illicit activities, e.g. currency demand and official work time. This procedure “produces” only relative estimates of the size of the shadow economy.

  2. In the second step the currency demand method is used to calibrate the relative estimates into absolute ones by using absolute values of the currency demand method as starting values for the shadow economy.

    The benchmarking procedure used to derive “real world” figures of shadow economic activities has been criticized (Breusch, 2005a, 2005b). As the latent variable and its unit of measurement are not observed, SEMs only provide a set of estimated coefficients from which one can calculate an index that shows the dynamics of the unobservable variable. Application of the so-called calibration or benchmarking procedure, regardless which one is used, requires experimentation, and a comparison of the calibrated values in a wide academic debate. Unfortunately, at this stage of research it is not clear which benchmarking method is the best or most reliable.20

    The economic literature using SEMs is well aware of these limitations. It acknowledges that it is not an easy task to apply this methodology to an economic dataset, but also argues that this does not mean one should abandon the SEM approach. On the contrary, following an interdisciplinary approach to economics, SEMs are valuable tools for economic analysis, particularly when studying the shadow economy. Moreover, the objections mentioned should be considered incentives for further research in this field rather than a reason to abandon the method.

Identification problem with MIMIC estimates

We have already discussed that the MIMIC approach estimations “produce” only relative weights. Hence, we need another approach to normalize these estimates and their validity depends on the reliability of this second approach. Hence it is very difficult to draw statistically confirmed conclusions about the causal relations in the real world and not only in the estimated model from these estimates.

Why is this so? As Kirchgaessner (2016, page 103) correctly argues… “A necessary condition for testing whether a variable x has a causal impact on a variable y, is that the two variables are measured independently. The MIMIC Model approach assumes, that causal relations exists and , therefore, estimates are linear combination of these (supposedly) causal variables, that more or less fits several indicator variables. This linear combination is assumed to be a representation of the unknown variable shadow economy.”

We should be aware that this calculation of the shadow economy is not an empirical test either of the actual existence of this calculated shadow economy or that the used causal or explanatory variables have a statically significant impact on the “true” shadow economy. Kirchgaessner (2016, page 103) argues further, that ...” significant test statistics in the structural model only show, that the used explanatory (or causal) variables contribute significantly to the variance of the constructed variable, shadow economy. We have to assume, that this construction represents the shadow economy to make statements about possible causal relations.” Hence these causal variables cannot be used again in subsequent studies to indent iffy policy variables that might reduce or increase the shadow economy. If this is done, a statistically significant relation must trivially result argue Feld and Schneider 2016, page 115).

To overcome this problem Kirchgaessner (2016, p. 103) suggests, to use other macro approaches like the electricity one, which measures the size of the shadow economy independently from the causes used in the MIMIC model. Then one can check whether a tax increase leads to a rise in the shadow economy. To conclude: we have to very careful when using shadow economy figures in order to test the impact of a tax reduction on the shadow economy. This is only possible if the shadow economy series is derived from an approach, where the tax variable has not been used for the construction of the shadow economy.

A new macro method of currency demand and MIMIC models: structured, hybrid-model based estimation approach

Dybka, Kowalczuk, Olesinksi, Rozkrut and Torój (2017) developed a novel hybrid procedure that addresses previous critique of the currency demand approach (CDA) and MIMIC models by Feige and Breusch, and particularly the misspecification issues in the CDA equations and the “vague” transformation of latent variable obtained via the MIMIC model into interpretable levels and paths of the shadow economy.21

This proposal is based on a new identification scheme for the MIMIC model, referred to as “reverse standardization”. It supplies the MIMIC model with panel-structured information on the latent variable’s mean and variance obtained from the CDA estimates, treating this information as given in the restricted full-information maximum likelihood function. This approach does not require choosing an externally estimated reference point for benchmarking or adopting other ad hoc identifying assumptions (like unity restriction on a selected parameter in the measurement equation).

Furthermore, the proposed estimation procedure directly addresses the numerical problem of negative variances in the MIMIC estimation that was largely disregarded in the previous, off-the-shelf software. The non-negativity restriction on variances within the MIMIC framework can materially affect the significance, specification decisions and measurement results. Paying due respect to the (intuitive) constraint on the non-negativity of variances may in fact lead to a surprising result of flattening the trajectory of the shadow economy.

Also, the ANOVA decomposition of SE estimated by means of our hybrid strategy confirms the findings from the previous literature by showing that as much as 97.2–98.2 percent of the SE variance in the panel is due to the CDA component (between cross-sections), while only the small remaining fraction is due to MIMIC’s fine-tuning job. The latter finding may lead to a legitimate question on the actual contribution of MIMIC models to shadow economy measurement.

Firstly, the authors estimate and extend a panel version of the CDA-equation using both frequent and neglected variables (describing the development of an electronic payment system) and abandon the controversial assumption that the share of the shadow economy in the total economy is zero.

Secondly, the authors estimate a MIMIC model by maximizing a (full-information) likelihood function reformulated in two ways: (i) instead of anchoring the index of an arbitrary time period and using arbitrary normalizations or other discretionary corrections, they use the means and variance estimated in the CDA model; (ii) they constrain the parameter vector to explicitly assume away the negative variances of structural errors and measurement errors. Their hybrid model proposes a solution to the long-standing problem of identification in the MIMIC model which, in a number of ways, outperforms previous approaches to just-identification. Their approach clearly implies a scale and unit of measurement, avoids obscure ad hoc corrections and paves the way to the construction of a sensible confidence interval. This new method is a promising approach to overcome the usual critiques of the CDA and MIMIC model.

In Table 6 a comparison of the shadow economy estimates by statistical offices provided by Gyomai and van de Ven (2014) and Dybka et al. (2017) with MIMIC estimates in this paper is undertaken. We show here the MIMC macro and the MIMIC adjusted figures. If we compare the results of Dybka et al. (2017), we see that within the three methods the size of the shadow economy varies considerably, but is on average much lower than the MIMIC macro and MIMIC adjusted ones. If one considers the MIMIC adjusted values, they come close to the values of Dybka et al. (2017) for Bulgaria and Switzerland. Comparing the values of Dybka et al. (2017) with the statistical offices, they are in a similar range for Bulgaria, Israel, Mongolia, Sweden, UK and Croatia if we take the FGLS44-AR variant. In the case of Croatia, Dybka et al. (2017) obtain considerably higher values than those provided by the statistical offices. In the case of Moldova it is the opposite; the statistical office has with 23.7 percent a considerably higher value of the size of the shadow economy than Dybka et al. (2017). To summarize, this new estimation method is promising and most of the values are considerably lower than those obtained using the traditional macro methods of the CDA and/or MIMIC.

Table 6.

Comparison of the shadow economy estimates of statistical offices and from the currency demand models of Dybka et al. (2017)

article image
Source: Goymai and van de Ven (2014) for the data of statistical offices; Dybka et al. (2017, p.22, Table 7) for FGLS, FGLS44 and FGLS44-AR; and our own estimations (macro and adjusted).

The problem of “double counting”

One big problem with macro approaches such as the MIMIC or CDA is that they use causal factors like tax burden, unemployment, self-employment and regulation, which are also responsible for people undertaking do-it-yourself activities or asking friends and neighbors to do things. Hence, do-it-yourself activities, neighbors’ or friends help and legally bought material for shadow economy activities are included in these macro approaches. This means that in these macro approaches (including the electricity approach, too) a “total” shadow economy is estimated which includes do-it-yourself activities, neighbors’ help, legally bought material and smuggling.

In Table 7 a decomposition of the shadow economy activities for the countries Estonia and Germany is undertaken. Table 7 starts with line (1) of the macro MIMIC estimates of 24.94 percent in Estonia as an average value for 2009 to 2015 and 9.37 percent for Germany for an average over 2009 to 2015. Legally bought material for shadow economy or do-it-yourself activities and friends’ help are deducted. Then illegal activities such as smuggling are deducted. Furthermore, do-it-yourself activities and neighbors’ help are deducted. Due to these factors from lines (2) to (4) one gets a corrected shadow economy which is roughly two thirds of the macro size of the shadow economy. It is 65 percent for Estonia and 64.2 percent for Germany. In the following, this correction factor is used to calculate an adjusted size of the shadow economy using the MIMIC method. The results for 31 European countries for 2017 are presented in Figure 3.3. The shadow economy appears considerably smaller and this might be a more realistic value of the actual size of the shadow economy using a macro method.

Table 7.

Decomposition of shadow economy activities in Estonia and Germany

article image
Source: Own calculations based on the work of Enste and Schneider (2006) and Buehn and Schneider (2013), p.12.
Figure 3.3:
Figure 3.3:

Size of the shadow economy of 31 European countries in 2017 – macro and adjusted MIMIC estimates

Citation: IMF Working Papers 2018, 017; 10.5089/9781484338636.001.A001

Source: Own calculations.

B. MIMIC Estimation Results

In tables 8, 9, and 10, which include six specifications per table, the MIMIC estimation results over the period 1991–2015 for 158 countries (maximum sample) are presented.22 Table 8 contains the estimation results for all countries. All cause variables (trade openness, unemployment, size of government, fiscal freedom, rule of law, control of corruption, government stability), have the theoretically expected signs, and most of them are highly statistically significant. The indicator variables also have the theoretical expected signs and are highly statistically significant. The test statistics are satisfactory.

Table 8.

MIMIC Model Estimation Results: 1991-2015, All Countries

article image
Source: Own calculations.Note: *** p<0.01, ** p<0.05, * p<0.1

Table 9 contains the estimation results for 105 developing countries (maximum sample). Here the cause variable rule of law is not statistically significant in specification 1, nor is control of corruption in specification 2. These variables are significant and show the expected sign in the other specifications. The indicator variable labor force is again highly statistically significant.

Table 9.

MIMIC Model Estimation Results: 1991-2015, Developing Countries

article image
Source: Own calculations.Note: *** p<0.01, ** p<0.05, * p<0.1

Finally, results for 26 advanced countries are presented in Table 10. Here trade openness is not statistically significant in all specifications, but in all other specifications most cause variables have the expected sign and are statistically significant, except government stability and size of government.23 The indicator variables are all statistically significant and have the expected signs.

Table 10.

MIMIC Model Estimation Results: 1991-2015, Advanced Countries

article image
Source: Own calculations.Note: *** p<0.01, ** p<0.05, * p<0.1

C. Addressing Potential shortcomings

Night Lights Intensity Approach

Even though the standard MIMIC model of Schneider (2010) and others has been widely used in the literature for many years, it has also been the subject of criticism. Mainly on: (i) the use of GDP (GDP per capita and growth of GDP per capita) as cause and indicator variables, (ii) the fact that the methodology relies on another independent study to calibrate from standardized values to estimate the size of shadow economy in percent of GDP, and (iii) the estimated coefficients are sensitive to alternative specifications, the country sample and time span chosen. Points (ii) and (iii) will not be discussed in our paper; as they are extensively discussed in Schneider (2016).24

We address the main criticism of (i) as follows:

Instead of using GDP per capita and growth of GDP per capita as cause and indicator variables, we use the night lights approach by Henderson, Storeygard, and Weil (2012) to independently capture economic activity. In their paper, they use data on light intensity from outer space as a proxy for the “true” economic growth achieved by countries.25 They also use the estimated elasticity of light intensity with respect to economic growth to produce new estimates of national output for countries deemed to have low statistical capacity. Therefore, by using the night lights approach we address MIMIC criticisms related to the endogeneity of GDP in a novel way, which is totally independent from problematic GDP measures traditionally used (See Medina et al (2017)).

Estimation Results using the Night Lights Intensity Approach

In tables 11, 12, and 13, which include five alternative specifications per table, the MIMIC estimation results are shown for the period 1991–2015 for different country samples depending on data availability. Table 11 contains the estimation results for all countries, and uses light intensity as an indicator variable. All cause variables (trade openness, unemployment, size of government, fiscal freedom, rule of law, control of corruption, government stability), have the theoretically expected signs, and most of them are highly statistically significant, except control of corruption. The indicator variables also have the theoretical expected signs and are highly statistically significant. The test statistics are satisfactory.

Table 11.

MIMIC Model Estimation Results (night lights instead of GDP): All Countries

article image
Source: Own calculations.Note: *** p<0.01, ** p<0.05, * p<0.1

Table 12 contains the estimation results for 103 developing countries. Here the cause variable unemployment is not statistically significant; nor are rule of law and control of corruption. The indicator variable labor force is again highly statistically significant.

Table 12.

MIMIC Model Estimation Results (night lights instead of GDP): Developing Countries

article image
Source: Own calculations.Note: *** p<0.01, ** p<0.05, * p<0.1

The results for 24 advanced countries are presented in Table 13. Here trade openness is not statistically significant in all specifications, but in all other specifications most cause variables are statistically significant, except government stability. The indicator variables are all statistically significant and have the expected signs.

Table 13.

MIMIC Model Estimation Results (night lights instead of GDP): Advanced Countries

article image
Source: Own calculations.Note: *** p<0.01, ** p<0.05, * p<0.1

An alternative procedure: Predictive Mean Matching

Predictive Mean Matching (PMM), (Rubin, 1987) treats the empirical challenge in the estimation of the size of the shadow economy as a missing data problem: for a number of countries, we have survey-based estimates of the size of the shadow economy,26 but for other countries this is missing.

Missing data can result from three types of mechanisms: missing completely at random (MCAR), missing at random (MAR) or missing not at random (MNAR), (Little and Rubin, 1987). The PMM analysis assumes that for the shadow economy, the mechanism is MAR. This means that the probability that an observation is missing can depend on observed co-variates of non-missing units and missing units, but it cannot depend on missing data on the size of the shadow economy. In other words, we assume that the probability that a country is missing data on its shadow economy can depend on characteristics relevant for the shadow economy, but the size of the shadow economy itself should not be a factor. This assumption can be challenged because one can argue that a large shadow economy would be difficult to measure, resulting in missing data. Furthermore, a large shadow economy can be associated with institutional weaknesses that would also make it less likely to be measured due to capacity constraints. However, when we look at the survey data available, we see that there are data available for large informal economies as well, such as Niger and Burundi. Therefore, at least in practice, the MAR assumption is somewhat validated, but would have to be checked through sensitivity analyses that would operate under MNAR.

The objective is to match the countries where data exist to the those where data are missing using characteristics that would be relevant to the size of the shadow economy.

One of the challenges inherent in the empirical problem of estimating the size of the shadow economy is that, for many countries, it is hard to estimate due to institutional capacity constraints. The shadow economy is complex, encompassing many related factors that in any estimation procedure may produce problems of endogeneity and other empirical challenges. A principal constraint in this exercise is that those countries for which some estimation of the shadow economy is available are not very similar to countries where this is missing.

Predictive Mean Matching (PMM) circumvents this challenge somewhat by producing multiple datasets using a Bayesian setup. Therefore, where we lack the data for similar countries, the method is able to compensate by taking advantage of the inherent uncertainty associated with a missing data problem.

The other advantage of the PMM method is that in its actual estimation step, it is non-parametric. It does not suffer from any of the problems associated with a regular regression method in which dissimilar countries would be estimated using the same co-variates, and assuming linear extrapolations across co-variate distributions that may be different and far apart from each other. The principle of similarity in PMM avoids this fundamental problem: it matches countries lacking data to countries that have data, based on their similarity. But how is this similarity itself estimated? This is the crux of the methodology. Similar to PMM, Propensity Score Matching (PSM) is also a promising candidate. However, the constraint with PSM in this case is that not enough similar observations are matched to be able to then run separate regressions or even make non-parametric estimates for each group due to the number of estimations required.

The similarity principle for PMM is established using a linear regression. Here, we estimate the following simple OLS model:

Yit=α+βge0*GE0+βrq*RQ+βc*C+βrol¯*β*ROL+βbf*BF+βse*SE+βHDI*HDI+βE*E

Where Y is the size of the shadow economy as a percentage of GDP, GE is a government effectiveness index, RQ is a regulatory quality index, C is a corruption index, ROL is a rule of law index, BF is a business freedom index, SE is self-employment levels, HDI is the Human Development Index, and E is an education variable.

The distinctive feature of the PMM is that this regression is not actually used for the estimation of the size of the shadow economy, but rather as a matching tool. For this we have the following seven stages that are computed using the SAS Proc MI procedure27:

  • (1) A random draw is made from the posterior predictive distribution of the estimated co-variate coefficient matrix β.−, resulting in a new co-variate coefficient matrix β*¯.

  • (2) Using β*¯., we predict Y* for all countries.

  • (3) The algorithm then identifies countries where we had actual Yi and whose predicted Y*, are closest to the predicted Y* of the countries missing the data. Hence we have matches between Y*iobs and Y*imiss: predicted values for the outcome variable originally missing and originally having an estimate of the size of the shadow economy.

  • (4) Each country with missing data is assigned to a group that has similar countries with data from the previous procedure.

  • (5) In each group, the MI algorithm randomly selects a match to the countries originally missing the outcome, and assigns the observed outcome from the match to be the estimated outcome variable for the country missing the outcome.

  • (6) Steps 1–5 are repeated five times, generating five distinct datasets with imputed values of the shadow economy, mimicking the inherent variability due to the uncertainty associated with the missing data mechanism.

  • (7) To produce a final estimate, we take the average of the five datasets for the size of the shadow economy.28

The results are consistent with the rankings produced by the MIMIC method (see Table 14), with Spearman’s rank correlation at 61 percent and significant at one percent statistical significance. Furthermore, when the MIMIC and PMM samples are divided into three subgroups of countries, specifically “lower than 20 percent of GDP,” “between 20 and 40 percent of GDP,” and “higher than 40 percent of GDP,” most countries coincide between samples (over 60 percent).

Table 14.

Size of the shadow economy using the Predictive Mean Matching Method

article image
article image

Average over 1991-2015

Average over 1991-2015; results from this paper’s MIMIC estimations.

Source: Own calculations.

Additional Robustness Test: Excluding GDP and GDP per capita from the regressions

This section further tests the robustness of the results by fully removing the effects of GDP, by dropping both GDP per capita as cause and growth of GDP per capita as indicator.

MIMIC estimation results for the period 1991–2015 for different country samples depending on data availability are presented in tables 15, 16, and 17; they include six alternative specifications per table. These results are consistent with those in the previous sections.

Table 15.

MIMIC Model Estimation Results (Excluding GDP and GDP per capita), All Countries

article image
Source: Own calculations.Note: *** p<0.01, ** p<0.05, * p<0.1
Table 16.

MIMIC Model Estimation Results: (Excluding GDP and GDP per capita), Developing Countries

article image
Source: Own calculations.Note: *** p<0.01, ** p<0.05, * p<0.1
Table 17.

MIMIC Model Estimation Results: (Excluding GDP and GDP per capita), Advanced Countries

article image
Source: Own calculations.Note: *** p<0.01, ** p<0.05, * p<0.1

D. Results on the Size of the Shadow Economy of 158 Countries using the MIMIC Approach

In Table 18 the most important results for the 158 countries, listed in alphabetical order, are shown29. The mean value of the size of the shadow economy of the 158 countries is 31.9. The median is 32.3, indicating that both values are quite close to each other, so there is not a strong deviation. The three largest shadow economies are Zimbabwe with 60.6, Bolivia with 62.3 and Georgia with 64.9. The three smallest shadow economies are Austria with 8.9, the United States with 8.3 and Switzerland with 7.2. The average shadow economy comes close to Equatorial Guinea with 31.8 percent and Suriname with 32.2 percent of official GDP.

Table 18.

Summary statistics of the shadow economy of 158 countries over the period 1991 to 2015

article image
article image
article image
article image
article image
Source: Own calculations.