Shadow Economy in three very different Mediterranean Countries: France, Spain and Greece. a MIMIC Approach

Roberto Dell’Anno[†], Miguel Gómez[(], Angel Alañon Pardo[♦]

February 2004

Abstract

This paper offers estimations of shadow economy in three very different Mediterranean countries: France, Spain and Greece. A multiple indicator and multiple choice model based on the latent variable structural theory has been applied using cointegration techniques to control for stationarity problems. The model includes tax burden (as a whole and decomposed in indirect taxes, direct taxes and social security contributions), regulation, unemployment rate and self-employment as causes of shadow economy and the participation ratio and currency ratio as indicator of the underground economy. Results confirm that unemployment, fiscal burden and self-employment are relevant causes of shadow economy. The level of GDP per head and political stability may also be important causes of hidden economy.

Keywords: Shadow Economy, Structural Equation Model,

JEL Classification: O17, C39, H26.

1  Introduction

The effects of the existence of shadow economy are numerous and relevant, it determines a very important loss in public revenues, misleading official indicators (growth, income distribution etc…), changes in individual incentives and factors remuneration etc. That is the reason why interest in shadow economy, both from an academic and a political point of view, has grown exponentially in OCDE countries during last decades. Whereas most researches are devoted to a pool of countries or to a single country[1], in this paper we estimate the determinants of shadow economy in three countries which share very important cultural roots, but which recent economic performance is very different: France, Spain and Greece.

The methods usually applied to estimate shadow economy can be classified into direct or indirect approaches. Direct methods are based on contacts with or observations of persons and/or firms, to gather direct information about not declared income. There are two kinds: (1) the auditing of tax returns and (2) the questionnaire surveys. Indirect methods try to determine the size of hidden economy, by measuring the “traces” it leaves in the official statistics. They are often called “indicator” approaches and use mainly macroeconomics data. This kind of methods include six categories: (1) Discrepancy between national expenditure and income statistics; (2) The discrepancy between the official and actual statistics of labour force; (3) The transaction approach; (4) The currency demand (or cash-deposit ratio) approach; (5) The physical input (e.g. electricity) method; (6) The model approach or MIMIC (Multiple Indicator and Multiple Choice) method.

In this paper the MIMIC approach is applied for estimating the evolution of shadow economy in three Mediterranean countries. The model approach is based on the statistical theory of latent variables, which considers several causes and several indicators of the hidden economy. The model approach or MIMIC approach considers the dimension of the hidden economy like a “latent variable”, therefore it applies the statistical modelling, namely Structural Equation Modelling (SEM), usually utilised by social research (psychology, sociology, marketing, etc.) to explore unobservable variables like attitudes, personality, belief, satisfying, etc.

The paper is organised as follows. In section 2 SEM is presented and MIMIC method is analysed, in section 3 the specification of the models and the structural relationships between causes and indicators are discussed, for being identified and estimated in section 4. Results are presented in section 5, and finally, the main conclusions are presented in section 6. Five statistical appendixes are supplied.

2  The Structural Equation Approach and Shadow Economy

The Structural Equation Model (SEM) are statistical relationships among latent (unobserved) and manifest (observed) variables. It implies a structure of the empirical covariance matrix[2] which, once the parameters have been estimated, can be compared to the resulting model-implied covariance matrix. If both matrices are consistent, then the structural equation model can be considered as a likely explanation for the relations among the examined variables. The structural equation models are “regression equations with less restrictive assumptions that allow measurement error in the explanatory as well as the dependent variables”[3]. So this method is theoretically superior than regression analysis as it explores all information contained in the covariance matrix and not only in the variance, and also because it allows variables to be measured with error, but compared with regression and factor analysis, SEM is a relatively unknown tool in economics[4].

In this paper, one special case of SEM is applied, the Multiple Indicators and Multiple Causes model[5]. The first to consider the size of hidden economy as an “unobservable variable” were Frey and Weck-Hanneman (1984), they introduced the MIMIC model of Zellner (1970), Goldberger (1972), Jöreskog and Goldberger (1975) and others in this field[6].

This kinds of models is composed by two sort of equations, the structural one and the measurement equations system. The equation that captures the relationships among the latent variable (η) and the causes (Xq) is named “structural model” and the equations that links indicators (Yp) with the latent variable (underground economy) is called the “measurement model”.

So the shadow economy (η) is linearly determined, subject to a disturbance ζ, by a set of observable exogenous causes x1, x2, … , xq :

(1)

The latent variable (η) determines, linearly, subject to a disturbances ε1, ε2, … , εp, a set of observable endogenous indicators y1, y2, … , yp :

(2)

The structural disturbance ζ, and measurement errors ε are all normal distributed, mutually independent and all variables are taken to have expectation zero.

Considering the vectors:

x’ = (x1, x2, … , xq) observable exogenous causes

γ’ = (γ1, γ 2,.. , γ q) structural parameters (Structural Model)

y’ = (y1, y2, … , yp) observable endogenous indicators

λ’ = (λ1, λ 2,.. , λ p) structural parameters (Measurement Model)

ε’ = (ε1, ε2,..., εp) measurement errors

υ = (υ 1, υ 2,..., υ p) standard deviations of the ε’s

The (1) and (2) are wrote as:

(3)

(4)

by assuming and defining and , where is diagonal matrix with , displayed on its diagonal[7]. The model can be solved for the reduced form as function of observable variables:

(5)

the reduced form coefficient matrix and disturbance vector are respectively:

Therefore, the covariance matrix (model-implied) is obtained:

. (6)

To facilitate the identification of SEM some conditions are available but, unfortunately, none of these are necessary and sufficient conditions (Bollen, 1989). Especially in the case of this work the following restrictions are respected:

The necessary (but not sufficient) condition, so-called t-rule, enunciates that the number of nonredundant elements in the covariance matrix of the observed variables must be greater or equal to the number of unknown parameters in the model-implied covariance matrix[8].

A sufficient (but not necessary) condition of identification, is that the number of indicators is two or greater and the number of causes is one or more, provided that is assigned a scale to h (MIMIC rule). For assigning a scale to the latent variable it is needed to fix one λ parameter to an exogenous value. Although several econometric improvements are introduced in the last years[9], in our opinion, the most important criticism to the MIMIC method is the strong dependence of the outcomes by the (exogenous) choice of the coefficient of scale (λ).

The criticism rises against the difficulty to assign a “exact” size to the values of structural parameters[10]. We have that , where indicate the estimated coefficients, and are the “not-definite-scale” coefficients.

This could be clearer by means of a comparison to the classic linear regression. In the Structural Equation Approach the estimated coefficients are not calculated in order to minimize the differences between estimated series and the observed one (as in the linear regression by the OLS), but to duplicate the implicit covariance matrix. The different estimation strategy and the necessity to choice an exogenous value (λ11) to identify the system, produce often estimated coefficients that make hard to calculate a (realistic) index of the hidden economy as ratio to the Official GDP, because numerator and denominator have different unit of measure. In our case, for instance, the causes variables are measured as ratio, while the indicators are measured as monetary quantities. In conclusion, as Giles and Tedds (2002) state: the model approach is a work in progress and supplementary improvements are “not only possible but necessary”. That is the reason why we do not estimate real values of underground economy as a percentage of GDP and we only offer an index that reports the evolution of shadow economy in the three countries. We think this is of sufficient interests as we can derive policy implications about the results of the fight against shadow economy in these countries during the period analyzed (1968-2004).

3  Theoretical background behind the choice of variables

In this section we expose the theoretical model applied to estimate underground economy taking into account that as Duncan (1975) points out: “The meaning of the latent variable depends completely on how correctly, precisely and comprehensively the causal and indicator variables correspond to the intended semantic content of the latent variable”[11], likewise Thomas (1992) we think that the choice of variables the only real limit of this approach.

As we mentioned before this kind of models are determined by several causes of the latent variable and several indicators.

3.1 Explanatory variables (Causes)

a) Tax burden

In literature the most popular determinant of tax evasion is fiscal burden. The common hypothesis is that an increase of tax burden furnishes a strong incentive to work in the unofficial market, so a positive sign for the parameter associate to this variable is expected. In all MIMIC applications this variable is included as a cause of underground economy and always a strong (direct) effect on the shadow economy, is confirmed.

In the econometric framework, tax burden is measured by means of the total share of total taxes in gross domestic product. This indicator has been also decomposed into different partial proxies like direct, indirect taxes and social contributions, as a percentage of gross domestic product, in order to test if all components of tax burden has the same effects on shadow economy. The theoretical analysis tell us that direct taxes and social contributions are more visible than indirect taxes, because indirect taxes suffers from fiscal illusion Therefore a positive sign in all the indicators of tax burden is expected but a greater one in the direct ones.

We also want to determine if the effects of each fiscal component differs or have the same importance in the three countries analysed.

b)  Employment of the Government on Labour Force

We introduce this variable in order to take into account the degree of regulation in the economy. The expected sign for this indicator is ambiguous. Some authors find a negative sign arguing that, in some sectors, the presence of the state could disincentive people to incorporate in the shadow economy. Other papers find a positive relation, arguing that we are capturing the degree of regulation in the economy, so the most regulated the economy is, firms find more incentive to develop their activities in the underground economy. Following Aigner et al. (1988), we think that a rise in the size of public sector, and/or the degree of regulation of the economic system, gives a relevant incentive to enter in the informal economy.

Therefore, an eventual positive sign of this coefficient will support the hypothesis that “more State” in the market, and subsequently an increase in regulation, gives an incentive to operate in the unofficial economy, and a negative sign will support the hypothesis that a greater presence of state in some activities disincentive people to evade taxes.

c) Unemployment rate

As Giles and Tedds (2002) state, there are two antagonistic forces which determine the relationship between unemployment rate and shadow economy. By one side an increase in unemployment could imply a decrease in the black economy as underground economy could be positively related to the growth rate of GDP and the latter is negatively correlated to unemployment. On the other side some “official” unemployed spend a part of their time working in the black economy[12], thus we may find a positive correlation.

Tanzi (1999) writes that “…the relation between the shadow economy and the unemployment rate is ambiguous”[13]. He remarks that the labor force of hidden economy is composed by very heterogeneous people: unemployed and non official labor force (retired people, illegal immigrants, minors or housewives) and, furthermore, there are people who have at the same time an official and unofficial job[14]. In this sense, the official unemployment rate is weakly correlated with the shadow economy. In the same work, Tanzi states that “...for OECD countries there seems to be a broad relation between the panel data of the size of underground economy and the official unemployment rates”[15].

Therefore, economic theory does not give a clue to determine whether the expected sign of this variable is positive or negative, it has to be solved by the empirical analysis in each country.

d)  Self-employment

The rate of self-employment as a percentage of the labor force is considered as a determinant of informal economy. According to Bordignon and Zanardi (1997) the significant diffusion of small firms and the large proportion of professionals and self-employed respect to the total workforce are important characteristics that justify higher level of the Shadow Economy. This kind or workers have more possibilities to evade as they usually have greater number of deductions in base and deductions in quote in personal income taxes. They are also very close to the customers so they can collude with them and evade in indirect taxes. Finally, these people have the possibility to employ irregular workers, because they do not have the same internal and external auditing control than bigger firms. Therefore, ceteris paribus, the higher the rate of self-employed the larger the shadow economy would be.

3.2 Indicators

As we argued in previous paragraphs the model approach is superior from a theoretical point of view than other indirect methods because it combines much more information than the others, in this case three indicators at a time are introduced instead of only one as the other indirect methods do.