Download Shadow Economy in Mediterranean Countries

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.
†
Dipartimento di Scienze Economiche e Statistiche, Università degli Studi di Salerno, Via Ponte Don Melillo, 84084
Fisciano (Sa) – Italy; e-mail: [email protected]

Departamento de Economía Aplicada VI Facultad de Ciencias Económicas y Empresariales, Universidad
Complutense de Madrid – Spain; e-mail: [email protected]
♦
Departamento de Economía Aplicada I Facultad de Ciencias Económicas y Empresariales, Universidad
Complutense de Madrid – Spain; e-mail: [email protected]
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 country1, 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.
1
See Schneider (1997) or Tedds (1998).
-2-
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
matrix2 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 economics4.
In this paper, one special case of SEM is applied, the Multiple Indicators and Multiple
Causes model5. 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 field6.
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 x1   2 x2  ....   q xq  
(1)
Hence an alternative name for this field is "analysis of covariance structures".
Bollen K.A. (1989), pp. v.
4 Just to cite the most comprehensive discussions of its applications: for the sociology: Bielby and Hauser (1977), for
the psychology: Bentler (1986), for the economics: Goldberg (1972), Aigner et al. (1984) and for an overview about
SEM: Hayduk (1987), Bollen (1989), Hoyle (1995), Maruyama (1997), Byrne (1998).
5It is a member of the LISREL “Linear Interdependent Structural Relationships” family of models (see Jöreskog and
Sörbom, 1993) An analytical derivation of MIMIC method is exposed in appendix B.
6 Following Frey and Weck-Hanneman’s, other economists have used this approach for their statistical analysis of
the “unofficial” economy: Aigner, Schneider and Ghosh (1988), Helberger and Knepel (1988), Loayza (1996), Pozo
(1996), Giles (1995, 1998, 1999a 1999b), Tedds (1998), Eilat and Zinnes (2000)6, Salisu (2000)6, Cassar (2001),
Prokhorov (2001), Giles and Tedds (2002), Chatterjee, Chaudhuri and Schneider (2003), Dell’Anno (2003),
Dell’Anno, Schneider (2003), Alañón y Gómez-Antonio(2003).
2
3
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The latent variable (η) determines, linearly, subject to a disturbances ε1, ε2,
… ,
εp, a set of
observable endogenous indicators y1, y2, … , yp :
y1  1   1 , y2  2   2 ,
.... , y p  p   p .
(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:
   x  
(3)
y    
(4)
by assuming E    0 and defining E  2    2 and E    2 , where  is diagonal
(pxp)
matrix with  , displayed on its diagonal7. The model can be solved for the reduced form as
function of observable variables:
y    x       x  v
(5)
the reduced form coefficient matrix and disturbance vector are respectively:
   , and v     .
In the standard MIMIC model the measurement errors are assumed to be independent of each other, but this
restriction could be relaxed. (see Stapleton D.C. 1978, pp. 53). The assumption on independence between structural
disturbance ζ, and measurement errors ε is central to the reliability of estimates. Unluckily, the SEM packages, do not
perform this kind of test. Hayduk (1987) explains it“…is purely a matter of arbitrary convention”7 and is possible through
a model re-parameterisation to test this assumption. An attempt to tests the hypothesis of independence between
structural and measurement errors, is supplied in Dell’Anno (2003). In our analysis, greater number of models
estimated, the covariance among the indicators is often not statistically different from zero. Yet, in the models where
this assumption is relaxed the changes in the estimates of structural coefficients are slightness, therefore the standard
restriction is hold in order to have more degrees of freedom.
7
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Therefore, the covariance matrix (model-implied) is obtained:
ˆ  E(vv)   2    2 .
(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 matrix8.
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  (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 years9, 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
parameters10. We have that ˆq   q* 11 , where ˆq indicate the estimated coefficients, and  q*
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
Bollen K.A. (1989), pp. 93. More clearly, the number of observed variances and covariances must be equal to or
greater than the number of parameters to be estimated (including variance of latent factor, variances of disturbances,
covariances among observed variables, etc.).
9 See Dell’Anno (2003) for more details.
10 The size of variability and the relative estimates (but not t-value) of the determinants of hidden economy are
proportional to the λ that have been fixed exogenously.
8
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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.
11
Duncan O. D. (1975), pp. 149, cited in Giles D.E.A., Tedds L.M. (2002), pp. 103.
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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 economy12, 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 job14. 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.
Giles D.E.A., Tedds L.M. (2002), pp. 127.
Tanzi V. (1999), pp. 341.
14 Tanzi V. (1999), pp. 343.
15 Tanzi V. (1999), pp. 343
12
13
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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.
a) Real Gross Domestic Product (variable of scale)
As have been mentioned previously in the MIMIC approach we need to fix a scale
variable to estimate the rest of the parameters as a function of this scale variable. The value of fix
parameter is arbitrary, but using a positive (or negative) unit value is easier to find out the relative
magnitude of the other indicator variables16. The choice of the ‘sign’ of coefficient of scale (λ11) is
based on theoretical and empirical arguments. In the literature there is no agreement about the
effects of the shadow economy on economic growth. On the one hand Adam, Ginsburgh (1985),
Tedds (1998), Giles (199b), Giles, Tedds (2002), Chatterjee, Chaudhuri, Schneider (2003) and
Alañón y Gómez-Antonio (2003), estimate a positive relationship between official and unofficial
economy. And on the other hand Frey and Weck-Hannemann (1984), Loayza (1996), Kaufmann
and Kaliberda (1996), Eilat and Zinnes (2000), Dell’Anno (2003), Dell’Anno, Schneider (2003)
16
“For instance if the estimate of one of the other elements of λ is 3, then the corresponding indicator variable is 3
times as important as the variable that is the basis for normalization.” Giles D.E.A., Tedds L.M. (2002), pp. 109.
-8-
find an inverse relationship between these variables. In this work the second hypothesis is held,
meaning that there is a flow of resources from legal to underground economy. That means that
many activities goes underground when we are in the recession part of the cycle.
b) Participation Ratio of the Labour Force
Some authors have estimated the size of the Hidden Economy from changes in the
labour force participation rate. A decline in this rate over time or a low rate relative to those in
comparable economies may reflect a movement of the workforce from the measured economy
into hidden activities. The labour force participation rate is calculated as the ratio between labour
force total (LF) / the total working age (15-64 years old), and the expected sign for this variables
is theoretically ambiguous. The literature does not agree on whether or not changes in this rate
reflect changes in the hidden economy. There is, however, a tendency to conclude that people do
not withdraw from the measured labour market in order to participate in the hidden economy.
There is evidence that much unrecorded economy activity is undertaken by members of the
measured workforce.
Following Schneider and Bajada (2003), it is possible that the participation rate as well as
the number of hours worked may be unaffected by shadow economy activity if such activities are
undertaken after hours or on weekends when individuals are not working in the legitimate
economy.
However, we include this variable as indicator in order determine empirically if there is a
flow of resources between official and underground economy. If we find a positive sign it means
that official workers are not incorporating to shadow economy in recession cycles and a negative
sign would mean that there is a flow of worker from official to shadow economy.
Therefore, the participation ratio is considered a weak indicator for the Shadow
Economy. Anyway, in the cases where this indicator is excluded by the estimation method
(MIMIC 5-1-2, 4-1-2, 3-1-2, etc.) the estimated coefficients are very similar (to the MIMIC 5-1-3,
4-1-3, 3-1-3, etc.).
c) Currency in circulation outside of banks
This indicator is the basis of the monetary approach to estimate the size of shadow
economy activities. Its use is based on the assumption that irregular transactions are only paid by
cash instead of by check or credit card in order to circumvent the auditing controls. Hence, if this
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assumption is accepted, it is possible to estimate the hidden economy by comparing the actual
demand for cash with the demand that could be expected if there were no shadow economy, and
the expected sign is positive.
In the estimated models the ratio between the time series (seasonally adjusted) of the
aggregate M1 and M3 is utilized.
4.
Model Identification and estimates of the Shadow Economy
The identification procedure starts from the most general specification (MIMIC 6-1-2)
and continues leaving out the variables which have not structural parameters statistically
significant17 (Graph 1).
Graph 1: MIMIC 6-1-3
X1
+γ11
X2
Real GDP pro-capita
+γ21
Y1
-1
X3
+γ31

Shadow Econ.
X4
X5
+γ41
λ12
Partecipatio Ratio of
Labour Force
Y2
+γ51
λ13
Currency ratio
Y3
+γ61
X6
A relevant point, often undervalued in the previous analyses of shadow economy with
SEM, is the detection of multivariate normality. This assumption is central to preserve the
17
The SEM permits to consider and estimate the correlations between the X-variables. In my analysis as expected is
statistically different from zero the correlation between tax burden and government consumption.
- 10 -
statistical properties of estimators, as well as the “chi-square” tests used to evaluate the fit of
models with the dataset. This choice is based on: the statistical significativity of parameters, the
parsimony of specification, the p-value of “chi-square” and the Root Mean Square Error of
Approximation (RMSEA) test. The models are not multinormally distributed, therefore regarding
the selection of the kind of estimators, it is risky (but inevitable) to apply the Maximum
Likelihood Estimator. When the variables are not (multivariately) normally distributed, then it is
possible for maximum likelihood estimators, to produce biased standard errors and an illbehaved “chi-square” test of overall model fit. To determine whether multivariate nonnormality
is present, Mardia’s test (1970)18 is used. It is important to highlight that, the maximum likelihood
estimations, are quite robust to several types of violations of multivariate normality19.
Given an unacceptable level of non normality, we have some possible corrections.
Among these, Bollen (1989) suggests to employ another estimator that, in spite of the
nonnormality, keeps the asymptotic efficiency, for instance the Generalized (or Weighted) least
squares estimator. This strategy is not available in our analysis because the GLS requires a very
large sample. For the analysis of the Mediterranean Shadow economy a different strategy
proposed by Bollen is followed, consisting in transforming the time series in order to solve both
the non-stationarity and non-multi-normality altogether.
Table 1, 2(a), 2(b) and 2(c), reports the estimates of several specifications for the French,
Spanish and Greek informal economy are presented. First, in table 1, a general model which
includes 4 cause variables (Tax burden, Unemployment, Self employment and Employment of
government) and 3 indicator variables (Real GDP, Currency and the Participation ratio of labor
force) is estimated for every country. For the French case all the causal variables included are
significant but public employment ratio, indicating that this variable is not capturing the grade of
regulation in the economy. The sign of the unemployment rate is positive, indicating that there is
a flow of resources from official to shadow economy in recession cycles. When the fiscal burden
is decompose20 only the direct fiscal burden is significant, in table 2(a) it can be seen how the
influence of tax burden in French shadow economy is due to direct taxation, since nor social
security contributions neither indirect taxes coefficients are significant. The indicator of labor
force participation became also significant and positive, indicating that there is not a flow of
This test is performed by PRELIS 2.53. It is a computer software that accompanies LISREL 8.53 and performs
normality diagnostics. It provides measures of univariate and multivariate skewness and kurtosis. In addition, a test
“chi-square” can be used to check whether there is statistically significant difference from multivariate normality.
19 Jaccard J., Wan C.K. (1996), pp. 75.
20 From all the presented models, the selected one appears always at the end raw of each table, that is F8 for France,
S11 for Spain and G10 for Greece.
18
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resources between official economy and hidden economy. The self employment variable is always
significant in all the models and with a positive sign acting a one of the main causes of shadow
economy in this country.
For the Spanish case the results in table 1 all the variables have the expected sign by the
theory and the unemployment causal variable present a positive sign according with the negative
one obtained by the indicator labor participation rate. That means that in Spain many workers
from the official economy go underground when they are laid off. As can be seen in table 2(b)
direct taxation is not an important cause of hidden economy in Spain, whereas social security
contributions and indirect taxation coefficients are significant. The rest of causes of hidden
economy in Spain are the employment of the government, with a positive sign meaning that this
causal variable is acting as a good proxy of the grade of regulation in the economy. A surprising
thing in this model is the non significance of self employed variable in explaining the shadow
economy because it is thought that for the Spanish Economy most of the underground activities
are developed by this collective.
Unlike French and Spanish cases fiscal burden, as a whole, is not significant for the
Greek case (table 1). Anyway when this variable is decomposed into direct taxation, indirect
taxation and social security contributions only the latter are significant in most of models. The
best Greek model in terms of fit is g10, where only social security contributions, unemployment
rate and self employed causal variables are significant. These results could reflect that Greek
regulations and tax burden are weaker than in the Spanish an the French cases, since neither
direct an indirect taxation nor employment of the government are relevant causes of shadow
economy. However these results, though statistically significant, should be interpreted carefully.
It is due to the unexpected negative sign of currency in circulation indicator variable. According
to our theoretical assumptions most of hidden economy actors prefer paying in cash better than
using credit cards of other means of payment which are more transparent to fiscal authorities.
Therefore shadow economy and currency in circulation should be positively correlated.
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Table 1: Output LISREL - Coefficients and Tests – FRANCE-SPAIN-GREECE
Particip. Currency
RMSEA
Tax
Employ
Self
Chi-square
Multi
Models1
Unemploy.
ratio L.F.
(pDf5
Burden
Governm.
employment
(p-value)2
Normal
value)3
0,44*
0,53
1,16*
2,74*
-2,59
17,60
42,14
0,16
F1: MIMIC 4-1-3
0,000
(2,48)
(0,41)
(3,73)
(5,21)
(-1,10)
1,42
(0,00012) (0,0011)
0,52*
2,07*
1,03*
0,15
-33,18*
-8,96
13,11
0,0
S1: MIMIC 4-1-3
0,000
(3,17)
(4,26)
(6,99)
(0,65)
(-5,00)
(0,68)
(0,52)
(0,69)
-0,09
-2,68*
0,86*
0,83*
66,41* -40,92*
43,89
0,17
G1: MIMIC 4-1-3
0,000
(-1,15)
(-2,84)
(2,73)
(2,65)
(3,19)
(-2,29)
(0,00)
(,00063)
Models1
Direct
Tax
0,89*
(3,05)
0,88*
F3:MIMIC 5-1-3
(3,19)
0,75*
F4:MIMIC 4-1-3
(2,80)
0,80*
F5:MIMIC 5-1-2
(2,81)
0,79*
F6:MIMIC 4-1-2
(2,82)
0,63*
F7:MIMIC 3-1-2
(2,34)
0,80*
F8:MIMIC 3-1-3
(2,98)
F2:MIMIC 6-1-3
Table 2 (a): Output LISREL - Coefficients and Tests - FRANCE
Partp.
Social Sec.Indirect Employ. Unempl. Self
Chi-square
Ratio
Currency
Contr.
Tax
Govern. rate
Employ.
(p-value)2
L.F.
0,54
-0,05
-1,58
1,30*
2,49*
2,86
4,26
44,47
(1,62)
(-0,14)
(-1,25)
(4,35)
(4,89)
(1,04)
(0,64)
(0,007)
0,53
-1,52
1,28*
2,52*
2,74
3,17
43,49
-(1,62)
(-1,20)
(4,28)
(4,93)
(0,98)
(0,53)
(0,001)
-1,25
1,40*
2,45*
2,96
4,04
43,33
--(-0,99)
(4,71)
(4,75)
(1,04)
(0,60)
(0,000)
0,53
0,16
1,30*
2,67*
22,56
10,67*
--(1,58)
(0,12)
(4,24)
(5,15)
(1,72)
(0,638)
0,54
1,31*
2,64*
22,58
4,93*
---(1,64)
(4,62)
(5,37)
(1,71)
(0,840)
1,47*
2,54*
22,27
4,68*
----(5,35)
(5,11)
(1,64)
(0,456)
0,91
1,31*
2,73*
0,50
16,76*
---(1,90)
(4,89)
(5,61)
(0,22)
(0,053)
For notes 1,2,3,4,5 see table 2 (c)
RMSEA Multi
(p
Normal Df5
value)3 .4
0,107
0,000 24
(0,040)
0,129
0,000 19
(0,009)
0,173
0,000 13
(0,000)
0,000*
0,000 13
(0,780)
0,000*
0,000 9
(0,910)
0,000*
0,000 5
(0,560)
0,105*
0,000 9
(0,120)
Table 2 (b): Output LISREL - Coefficients and Tests - SPAIN
Models1
Direct
Tax
Social Sec.Indirect
Contr.
Tax
S2:MIMIC 6-1-3
-0,54
(-1,63)
0,77*
(2,18)
0,93*
(3,22)
0,90*
(3,17)
0,72*
(2,01)
0,62
(1,64)
S3:MIMIC 5-1-3 -S4:MIMIC 4-1-3 -S5:MIMIC 6-1-2
-0,56
(-1,66)
S6:MIMIC 5-1-2 -S7:MIMIC 4-1-2
-0,50
(-1,44)
S8:MIMIC 4-1-2 -S9:MIMIC 5-1-2 -S10:
MIMIC 5-1-2
S11:
MIMIC 4-1-2
0,08
(0,31)
--
-0,62
(1,60)
0,93*
(3,20)
0,89*
(3,03)
0,90*
(2,97)
For notes 1,2,3,4,5 see table 1 (c)
0,64
(1,78)
0,59*
(2,03)
0,61*
(2,12)
0,59
(1,61)
0,57
(1,43)
0,64
(1,75)
-0,60*
(2,02)
0,62*
(2,11)
0,62*
(1,99)
Particip.
RMSEA Multi
Employ. Unempl. Self
Chi-square
ratio L.F. Currency
(pNormal Df5
Govern. rate
Employ.
(p-value)2
3
value) .4
1,47*
1,08*
0,48
0,12
-1,33*
58,80
0,136
0,000 24
(2,75)
(7,97)
(1,76)
(1,24)
(-4,33)
(0,000)
(0,002)
1,99*
0,98*
0,18
-34,14* -1.00
14,66*
0,000*
0,000 20
(4,27)
(6,84)
(0,84)
(-5,02)
(-0,08)
(0,795)
(0,91)
1,96*
0,97*
-35,05* -1,23
11,48*
0,000*
-0,001 14
(4,21)
(6,70)
(-5,01)
(-0,09)
(0,648)
(0,79)
1,28*
1,03*
0,49
-6,79*
12,86*
0,000*
-0,000 17
(2,37)
(7,61)
(1,76)
(-4,55)
(0,746)
(0,870)
1,43*
1,09*
0,54
--8,60
3,14*
0,000*
0,000 14
(2,41)
(7,02)
(1,79)
(-0,67)
(0,999)
(1,00)
1,28*
1,03*
-6,07*
10,99*
0,053*
--0,000 10
(2,31)
(7,36)
(-4,47)
(0,276)
(0,420)
1,52*
1,08*
0,60*
-9,39
1,60*
0,000*
-0,000 9
(2,52)
(6,92)
(1,97)
(-0,73)
(O,997)
(1,000)
1,99*
0,98*
0,18
-34,13*
4,95*
0,000
-0,000 14
(4,24)
(6,80)
(0,83)
(4,97)
(0,987)
(0,990)
1,95*
0,98*
-34,92*
2,40*
0,000*
--0,000 14
(4,18)
(6,67)
(-4,96)
(1,000)
(1,000)
1,95*
0,97*
-35,05*
3,68*
0,000*
--0,001 10
(3,99)
(6,57)
(-5,27)
(0,961)
(0,980)
Table 2 (c): Output LISREL - Coefficients and Tests - GREECE
Models
1
G2:MIMIC 6-1-3
Direct
Tax
Social Sec.Indirect
Contr.
Tax
0,14
(1,18)
0,59
(1,96)
0,67*
(2,12)
G3:MIMIC 5-1-3 -G4:MIMIC 4-1-3 --
--
0,08
(0,55)
1,04*
G6:MIMIC 6-1-2
(2,04)
0,79*
(2,11)
3,83*
(3,48)
3.94*
(3,59)
3,72*
(3,39)
3,97*
(3,65)
4,01*
(3,69)
G5:MIMIC 5-1-3
G7:MIMIC 5-1-2 -0,99
(1,96)
0,93
G9:MIMIC 4-1-2
(1,84)
G10:
-MIMIC 3-1-2
G8:MIMIC 5-1-2
-0,39*
(-2,57)
-0,38*
(-2,56)
-0,39*
(-2,50)
-0,30
(0,71)
0,21
(0,51)
----
Partecip.
RMSEA Multi
Employ. Unempl. Self
Chi-square
ratio L.F. Currency
(pNormal Df5
Govern. Rate
Employ.
(p-value)2
3
value) .4
-2,65*
0,81*
0,97*
67,56*
-42,10* 55,88
0,114
0,000 28
(-2,94)
(2,78)
(2,88)
(3,24)
(-2,30)
(0,001)
(0,013)
-2,77*
0,81*
0,95*
65,79*
-42,29* 47,56
0,135
0,000 20
(-3,00)
(2,80)
(2,91)
(2,30)
(-2,31)
(0,000)
(0,005)
-2,56*
0,87*
0,89*
68,54*
-39,90* 27,78
0,114*
0,000 14
(-2,87)
(2,80)
(2,78)
(3,19)
(-2,28)
(0,015)
(0,053)
-2,99*
0,82*
0,98*
60,86*
-39,23* 53,30
0,148
0,000 20
(-3,06)
(2,76)
(2,89)
(3,43)
(-2,30)
(0,000)
(0,001)
1,82
2,51*
1,50*
-20,34* 16,74*
0,000*
-0,000 20
(1,07)
(3,68)
(2,13)
(-2,38)
(0,670)
(0,830)
1,55
2,55*
1,38*
-26,67* 11,24*
0,000*
-0,000 14
(0,91)
(3,73)
(2,02)
(-2,98)
(0,667)
(0,810)
1,98
2,67*
1,64*
-21,04* 15,06*
0,007*
-0,000 15
(1,16)
(3,99)
(2,36)
(-2,45)
(0,447)
(0,63)
2,19*
1,32*
-20,49* 14,70*
0,091*
--0,000 9
(4,03)
(2,03)
(-2,35)
(0,995)
(0,190)
2,24*
1,21
-25,70* 4,49*
0,000*
--0,000 5
(4,08)
(1,91)
(-2,82)
(0,482)
(0,590)
Notes:
t-statistic are given in parentheses.
* Means |t-statistic|>1,96.
1 The Estimation procedure presents for some MIMIC specifications of the French and Spanish shadow economy convergence problems. For Lisrel users, the matrix PSI is not
positive definite. Anyway, in the case in which exists the inverse of matrix PSI (e.g. MIMIC 5-1-2, etc.) the estimates of the coefficients are very alike to the others models.
2 If the structural equation model is correct and the population parameters are known, then the matrix S (sample covariance matrix) will equal to Σ(θ) (model-implied covariance
matrix) therefore the perfect fitting correspond to p-value=0,000. This test has a statistical validity if there are large sample and multinormal distributions.
3 p-value for Test of Close Fit (RMSEA < 0,05)
4 Is reported the output of PRELIS 2.53: Test of Multivariate Normality for Continuous Variables, p-value of skewness and kurtosis (Mardia, 1970). D’agostino (1986, pp. 391)
recommends N > 100 for this test. In our case the sample is approximately eighty for this, the results should be interpreted cautiously.
5 The degrees of freedom are determined by 0,5(p+q)(p+q+1)-t, where “p” is the number of indicators, “q” the number of causes and “t” is the number of free parameters.
5
Results
Once the models have been selected and identified, an index of shadow economy can be
constructed. The index of shadow economy is estimated by equation (5), the structural
coefficients are multiplied for the “filtered” data for stationary 21, therefore the latent variable is
estimated in the same transformation of independent variables (first difference):
ˆ  ˆ11 X 1  ˆ12 X 2  ˆ13 X 3  ˆ14 X 4  ˆ15 X 5  ˆ16 X 6
(5)
Graphs 2, 3 and 4 show the evolution of shadow economy indexes for France, Spain and
Greece respectively. Whereas in the French case Shadow economy index follows a decreasing
path, the Spanish and Greece ones are rising. This difference may be due to the level of
development of these economies, since richer economies may have less incentives or chances to
go underground than the less developed ones. Allthough we have focused on fiscal burden as
one of the main causes of shadow economy, economic agents in a less developed country with
non progressive taxes and soft regulations could also have stronger incentives to join
underground such as low incomes and not enough provision of public goods and services.
Sectoral composition of labour force also helps to explain differences in shadow
economy behaviour according to the level of economic development, since agriculture and
related sectors employ a high share of non declared workers. Whereas the participation of labour
force in agriculture in the french and in the spanish cases is low, in Greece it still accounts for a
half.
As it is shown in table 3, the differences in gross domestic product per head betwen
France, decreasing shadow economy path, and Greece and Spain, rising shadow economy paths,
are very significant over the period of time analysed. However this hypothesis is only tentative
since further research is nedded to test it.
It also can be noted that the evolution of shadow economy is more volatile and abrupter
in Greece than in Spain or in France. One possible reason which could explain part of this
volatile behaviour is the low level of political stability of Greece over the period, above all, if it is
compared to France. This hypothesis needs to be tested by futher research again.
Graph 2 Shadow Economy Index: France
21
Cointegration analysis is carried out in appendix C
- 18 -
- 19 -
Graph 4 Shadow Economy Index: Greece
2002s1
2000s1
1998s1
1996s1
1994s1
1992s1
1990s1
1988s1
1986s1
1984s1
1982s1
1980s1
1978s1
1976s1
1974s1
1972s1
1970s1
1968s1
index Shadow Economy
Graph 3 Shadow Economy Index: Spain
2002s1
2000s1
1998s1
1996s1
1994s1
1992s1
1990s1
1988s1
1986s1
1984s1
1982s1
1980s1
1978s1
1976s1
1974s1
1972s1
1970s1
1968s1
index Shadow Economy
2002s1
2000s1
1998s1
1996s1
1994s1
1992s1
1990s1
1988s1
1986s1
1984s1
1982s1
1980s1
1978s1
1976s1
1974s1
1972s1
1970s1
1968s1
index Shadow Economy
Table 3 Gross domestic product per head at current
market prices and pps; relative level EU-15=100.
France
Spain
Greece
1967-76
108
75
65
1977-86
109
73
67
1987-91
107
75
59
1992-96
105
79
64
2002
103
84
67
Source: EC Economic Data pocket book, (7-8, 2003)
European Communities 2003, Luxembourg
Successively, the index may be converted in a “level” time series. In order to obtain the actual
values of the underground economy in term of official GDP, a priori known value is required. As
discussed at the end of section 2 we think more reasonable showing only the evolution of
shadow economy indexes, since graphs of shadow economy as a percentage of GDP may be
misleading
6
Conclusions
In this paper we have estimate MIMIC models to explain shadow economy evolution in
France, Spain and Greece, using cointegration techniques to control for stationarity problems
The main conclusion that can be drawn are the following:
1) Unemployment appears as one of the main causes for the existence of shadow economy.
This indicator presents a positive sign in all the models and for all the countries. This aspect is
very important if we have into account that these workers suppose a double cost for the state.
- 20 -
In one hand they receive monetary perceptions from state and in the other hand the state is
losing the taxes they should be paying for their incomes.
2) There is a positive relationship between size economy and the self employment indicator. It
reflects that this collective is one of the main contributors to the existence of shadow
economy irrespective of GDP per head of the economy.
3) Social contributions are a significant cause of shadow economy for the three countries. So,
job market regulations becomes a common cause of shadow economy in Spain, Greece an
France.
4) In Spain indirect taxes are the main fiscal determinants for the appearance of shadow
economy, by contrast in France direct taxes are the main contributors to the existence of
shadow economy and we find no evidence in Greece. So we can conclude that the more
developed the fiscal system is and the bigger is the growth in a country it seems that agents
perceive clearer the taxes paid and try to evade in different kind of taxes.
5) The level of development of a country, measured in terms of gross domestic per head, and
of political stability seems plausible explanations of shadow economy. Low incomes per head,
and non enough provision of public good and services (education, health, security, etc) may
foster the need of additional and non declared sources of income.
6) Greek results, although statistically significant, should be interpreted with caution, due to
unexpected sign of currency indicator variable.
- 21 -
References
Adam Markus, Ginsburgh C. Victor (1985). The Effects of Irregular Markets on Macroeconomic
Policy: Some Estimates for Belgium. European Economic Review, 29/1, pp. 15-33.
Alañón, A., y Gómez-Antonio, M., (2003) Estimación Del Tamaño De La Economía Sumergida
En España: Un Modelo Estructural De Variables Latentes. MIMEO
Aigner Dennis J., Schneider Friedrich, Ghosh Damayanti (1988). Me and my shadow: estimating
the size of the U.S. hidden economy from time series data. Dynamic Econometric modelling.
Proceedings of the Third International Symposium in Economic Theory and Econometrics. Edited by
Barnett W. Berndt E. White H. Cambridge University Press, pp. 297- 334.
Allingham M., Sandmo A., (1972). Income Tax Evasion: A Theoretical Analysis, Journal of Public
Economics, 1, pp. 323-338.
Bentler P. M. (1986). Structural Equation Modelling and Psycometrika: An historical perspective
on growth and achievements. Psycometrika, 51, pp. 35-51.
Bielby W.T., Hauser M. (1977). Structural equation models. Annual Review of Sociology, 3, pp. 137161.
Bollen K. A. (1989). Structural equations with latent variables. New York: John Wiley & Sons.
Boomsma A. (1982). The robustness of LISREL against small sample sizes in factor analysis
models. In K. J. Jöreskog and H. Wold (Eds.), Systems under indirect observation: Causality,
structure, prediction (Part 1).Amsterdam: North-Holland.
Bordignon Massimo, Zanardi Alberto (1997). Tax Evasion in Italy. Giornale degli Economisti e
Annali di Economia Volume 56, N. 3-4, pp. 169-210.
Byrne Barbara M. (1998). Structural equation modelling with LISREL, PRELIS, and SIMPLIS
Mahwah, N.J.: Lawrence Erlbaum Associates. Multivariate applications book series
Cassar Alan. (2001). An index of the underground economy in Malta. Bank of Valletta Review, No.
23, Spring, pp. 44-62.
Chatterjee S., Chaudhuri K., Schneider F., (2003). The Size and Development of the Indian
Shadow Economy and a Comparison with other 18 asian countries: An Empirical
Investigation. Presented at European Public Choice Society, Annual meeting 2003 in Aarhus
(DK) (mimeo).
Cooley W. W. (1978). Explanatory observational studies. Educational Researcher, pp. 9-15.
- 22 -
Cowell F. A. (1990). Cheating the government: The economics of Evasion MIT Press,
Cambridge, MA.
D’Agostino R. B. (1986). Tests for the normal distribution. In R.B. D’agostino and M.A.
Stephens, eds. Goodness-of-Fit Techniques. New York: Marcel Dekker, pp. 367-419.
Dell’Anno, R., (2003) Estimating the Shadow Economy in Italy: a Structural Equation
Approach», University of Aarhus, Department of Economics, DK. Working paper 20037.
Dell’AnnoR., Schneider F. (2003). The Shadow Economy of Italy and other OECD Countries:
What do we know?. Mimeo.
Duncan Otis D. (1975). Introduction to structural Equation Models. New York: Academic Press.
Eilat Y., Zinnes C. (2000). The Evolution of the Shadow Economy in Transition Countries:
Consequences for Economic Growth and Donor Assistance. CAER II Discussion Paper
No. 83. Harvard Institute for International Development.
Feige Edgard L. (1989). The Underground economies, Tax evasion and information distortion.
Cambridge University Press. Cambridge.
Frey Bruno, Weck-Hanneman Hannelore (1984). The Hidden Economy as an “Unobservable”
variable. European Economic Review, Vol. 26, No. 1, pp. 33-53.
Giles David E.A. (1995). Measuring the size of the hidden economy and the tax gap in New
Zealand: an econometric analysis. Working Paper No. 5a, Working Paper on Monitoring the
Health of the Tax System, Inland Revenue Department,Wellington.
Giles David E.A. (1997). The hidden Economy and the tax gap in New Zealand: a latent variable
analysis. Discussion Paper 97-8, Department of Economics, University of Victoria, Canada.
Giles David E.A. (1998). The Underground Economy: Minimizing the Size of Government.
Working Paper, Department of Economics, University of Victoria, Canada.
Giles David E.A. (1999a). Measuring the hidden Economy: Implications for Econometric
Modeling”. The Economic Journal, Vol. 109, No 46, pp.370-380.
Giles David E.A. (1999b). Modeling the hidden Economy in the Tax-gap in New Zeland.
Working Paper, Department of Economics, University of Victoria, Canada.
Giles David E.A., Tedds Lindsay M. (2002). Taxes and the Canadian Underground Economy.
Canadian Tax paper n.106. Canadian Tax Foundation. Toronto.
- 23 -
Goldberger A. S. (1972). Structural Equation Methods in the Social Sciences. Econometrica, Vol.40,
pp. 979-1001.
Hayduk L. A. (1987). Structural equation modelling with LISREL. Essential and advances. The
Johns Hopkins University Press. London.
Helberger C., Knepel H. (1988). How big is the Shadow Economy? A Re-Analysis of the
Unobserved-Variable Approach of B.S. Frey and H. Weck-Hannemann. European
Economic Review, 32 pp.965-976.
Hoyle R. H. (ed.) (1995). Structural Equation Modeling: Concepts, Issues, and Applications.
Thousand Oaks, CA: Sage.
Jaccard James, Wan Choi K. (1996). Lisrel approach to interaction effects in multiple regression.
Series: Quantitative Applications in the Social Science. Sage University paper. SAGE publications.
Johnson S., Kaufmann D., Shleifer A. (1997). The Unofficial Economy in Transition. Brooking
Papers of Economic Activity, 0:2, pp. 159-221.
Johnson S., Kaufmann D., Zoido-Lobatón P. (1998). Regulatory Discretion and the Unofficial
Economy. American Economic Review, 88:2, pp. 387-92.
Jöreskog K., Goldberger A. S. (1975). Estimation of a model with multiple indicators and
multiple causes of a single latent variable, Journal of the American Statistical Association, 70,
pp. 631-639.
Jöreskog K., Sörbom D. (1993). LISREL 8, User’s Reference Guide. Chicago: Scientific Software
International.
Kaufmann Daniel, Kaliberda Aleksander (1996). Integrating the Unofficial Economy into the
Dynamics of Post-Socialist Economies: A Framework of Analysis and Evidence, in
Economic Transition in the Newly Independent States, B. Kaminski editor, Armonk, New York:
M.E. Sharpe Press.
Lippert Owen, Walker Michael (eds.) (1997). The Underground Economy: Global Evidences of
its Size and Impact. Vancouver, B.C., The Frazer Institute.
Loayza Norman V. (1996). The Economics of the Informal Sector: A Simple Model and Some
Empirical Evidence from Latin America. Carnegie-Rochester Conference Series on Public Policy
45, pp. 129-162.
Mardia K. V. (1970). Measures of multivariate skewness and kurtosis with applications.
Biometrika, 57, pp. 519-530.
- 24 -
Maruyama Geoffrey M. (1997). Basic of Structural Equation Modeling, SAGE Publications.
Pedersen Soren (1998). The Shadow Economy in Western Europe, Measurement and Results for
selected Countries. The Rockwool Foundation Research Unit. Copenhagen.
Pozo Susan (ed.) (1996). Exploring the Underground Economy. Studies of Illegal and
Unreported Activity. Michigan, W.E. Upjohn, Institute for Employment Research.
Prokhorov Artem (2001). The Russian Underground Economy as a “Hidden” Variable.
Presented at Midwest Slavic Conference, Cleveland, Ohio, March 29-31.
Schneider F. (1994a). Measuring the Size and Development of the Shadow Economy. Can the
Causes be Found and the Obstacles be Overcome?. In Brandstaetter, Hermann, and
Guth, Werner (eds.), Essays on Economic Psychology, Berlin, Heidelberg, Springer
Publishing Company, pp. 193-212.
Schneider F. (1994b). Can the Shadow Economy be reduced Through Major Tax Reforms? An
Empirical Investigation for Austria. Supplement to Public Finance / Finances Publiques, 49,
pp. 137-152.
Schneider F. (1997). The shadow economies of Western Europe. Economic Affairs, 17:3 pp.42-48,
September.
Schneider F. (1998). Further empirical results of the size of the shadow economy of 17 OECDcountries over time, Paper presented at the 54. Congress of the IIPF Cordowa,
Argentina and discussion paper, Department of Economics, University of Linz, Linz,
Austria.
Schneider F. and Bajada (2003). The size and Development of the Shadows economies and
Shadow economy labor force of 18 Asian and 21 OCDE Countries: First results for the
90s. Invited Paper
prepared for the Asia Pacific Finance Association (APFA)
Conference 2001 “Rebuilding Our Financial Architecture”, Bangkok, Thailand, July
22-25.
Schneider, F., Eneste D. (2000). Shadow Economies Around the world: Size, Causes, and
Consequences, IMF Working Paper n.26.
Tanzi Vito (1999). Uses and Abuses of Estimates of the Underground Economy.” The Economic
Journal, 109 (June), pp. 338-347.
Tedds Lindsay (1998). Measuring the size of the hidden Economy in Canada. MA extended essay,
University of Victoria, Department of Economics.
- 25 -
Thomas Jim (1992). Informal economic activity. LSE, Handbooks in Economics, London, Harvester
Wheatsheaf.
Thomas Jim (1999). Quantifying the black economy: 'measurement without theory’ yet again? The
Economic journal, 109 (June), pp. 381-389.
Stapleton David C. (1978). Analyzing political participation data with a MIMIC Model. Sociological
Methodology Vol. 15. pp. 52-74.
Zellner A. (1970). Estimation of regression relationships containing unobservable variables,
International Economic Review, 11, pp. 441-454.
Appendix A – Sources of Data –
Appendix B – Analysis of Normality –
Appendix C – Analysis of Non-Stationarity –
- 26 -
Appendix A - Sources of data –
Var. CAUSES
X1
X2
X3
X4
X5
X6
Sources
OECD
–
Outlook.
Social Security Contributions received OECD
by Government /GDP
Outlook.
OECD
Total Indirect Tax/GDP
Outlook.
OECD
Self Employment/Labour Force
Outlook.
OECD
Unemployment rate
Outlook.
Government Employment /Labour OECD
Force
Outlook.
Total Direct Tax/GDP
Economic
Economic
Economic
Economic
Economic
Economic
Transf.
Used1
Annotations
Δ(X1)
-
Δ(X2)
Social security contributions /GDP
Δ(X3)
-
Δ(X4)
-
Δ(X5)
-
ΔLN(X6) -
INDICATORS
Y1
Y2
Y3
Real Gross Domestic Product pro- OECD
capita
Outlook.
OECD
Participation ratio of Labour Force
Outlook
Currency ratio (M1/M3)
OECD
Outlook
-
Economic
-
Economic
–
Notes: (p-value are calculated on transformed data).
1
“Δ” means first difference, “LN” means natural logarithm.
Economic
ΔLN(Y1)
[GDP market price value /deflator of GDP]/ Population in
working age (15¬64 years old)
ΔΔ(Y2)
The frequency is modified from monthly to half-annual. There
are missing values from 1965 to 1980 and from 1998 to 2003.
For Greece the missing values are from 1965 to 1980 and from
to 2000 to 2003.
Money supply M1 -SA/Money supply M3 -SA
Appendix B -Analysis of Normality -
The following tables present the tests of Normality (Univariate) of the most general model estimated:
the MIMIC 6-1-3. For the tests of multivariate normality distribution, the results are reported in tables
2(a), 2(b) and 2(c). The sample size is about 79.
Causes
Δ[Direct Tax/GDP]
Δ[Indirect Tax/GDP]
Δ[Social S. Contr./GDP]
Δ[Empl.Gov./Lab. For. ]
Δ[Unemployment rate]
Δ[Self Empl./Lab. For. ]
Indicators
Δ LN[Real GDP pro capita]
Δ Δ [Curr. ratio (M1/M3)]a
Δ[Part. ratio Lab. Force]
France
0,000
0,000
0,000
0,548
0,860
0,000
Spain
0,000
0,146
0,001
0,126
0,145
0,001
Greece
0,185
0,052
0,080
0,000
0,000
0,000
0,000
0,067
0,029
0,484
0,763
0,233
0,112
0,038b
0,000
Notes:
a
p-value of the Jarque-Bera Test. This test is used instead of Skewness
and Kurtosis test because PRELIS does not perform normality test for
the sample size smaller then 51 observtions. To obtain J-B test has been
used Eviews 4.1.
b
The trasformation is the first difference.
- 28 -
Appendix C - Analysis of Non-Stationarity –
In this appendix, the tests to detect the order of integration in the time series are shown. Pioneer to
tackle the problem of non-stationary in the MIMIC models has been Giles (1995). To find out the unit
roots, the Augmented Dickey-Fuller (ADF) Test and the Philliphs-Perron (PP) Test are used, to choose
a number of lags sufficient to remove serial correlation in the residuals, are applied the the Schwarz
information criterion.
In the following tables the p-value of over mentioned tests are reported, the null hypothesis is the
presence of unit root, therefore a value larger than 0,05 means non-stationary time series.
The plot graphs relate to raw data, the econometric software Eviews 4.1 is used in order to carry out
this analysis. As Giles and Tedds (2002) point out the more appropriate way “…to consider the nonstationary is consider the possibility of cointegration. Unfortunately, there is no established literature to
serve as a guide to this procedure in the context of the MIMIC model”.
France –
Variable
Include in
equat.
Causes
Direct Tax/GDP
Empl.Gov./Lab. For.
Indirect Tax/GDP
Self Empl./Lab. For.
Unemployment rate
Social S. Contr./GDP
- 29 -
T&C
T&C
C
T&C
T&C
T&C
Level
First difference
Second difference
ADF
P.P.
ADF
P.P.
ADF
P.P.
0,957
0,999
0,008
0,817
0,969
0,983
0,579
0,999
0,099
0,889
0,980
0,994
0,018
0,000
0,029
0,000
0,001
0,000
0,000
0,009
0,000
0,000
0,011
0,001
0,016
0,001
0,000
0,000
0,000
0,000
0,000
0,000
0,000
0,000
0,000
0,000
Include
in equat.
Variable
Indicators
Real GDP pro capita
Curr. ratio (M1/M3)
Part. ratio Lab. Force
T&C
T&C
T&C
Level
First difference
Second difference
First differ. LogN
ADF
P.P.
ADF
P.P.
ADF
P.P.
ADF
P.P.
0,529
0,031
0,422
0,485
0,986
0,970
0,000
0,104
0,000
0,000
0,221
0,000
0,000
0,000
0,000
0,000
0,000
0,000
0,000
0,084
--
0,000
0,1961
--
– Spain –
Variable
Include
in equat.
Causes
Direct Tax/GDP
Empl.Gov./Lab. For.
Indirect Tax/GDP
Self Empl./Lab. For.
Unemployment rate
Social S. Contr./GDP
- 30 -
T&C
T&C
T&C
T&C
T&C
T&C
Level
First difference
Second difference
ADF
P.P.
ADF
P.P.
ADF
P.P.
0,919
0,989
0,736
0,780
0,642
0,378
0,935
0,969
0,857
0,780
0,897
0,690
0,019
0,000
0,000
0,000
0,084
0,026
0,000
0,000
0,000
0,000
0,069
0,005
0,000
0,000
0,000
0,000
0,000
0,000
0,000
0,000
0,000
0,000
0,000
0,000
Variable
Include
in equat.
Indicators
Real GDP pro capita
Curr. ratio (M1/M3)
Part. ratio Lab. Force
- 31 -
T&C
C
T&C
Level
First difference
Second difference
First differ. LogN
ADF
P.P.
ADF
P.P.
ADF
P.P.
ADF
P.P.
0,677
0,106
1,000
0,823
0,256
1,000
0,042
0,120
0,002
0,042
0,298
0,002
0,000
0,000
0,000
0,000
0,000
0,000
0,054
---
0,051
--
Greece
Include
in equat.
Variabile
Causes
Direct Tax/GDP
Empl.Gov./Lab. For.
Indirect Tax/GDP
Self Empl./Lab. For.
Unemployment rate
Social S. Contr./GDP
Variabile
Include
in equat.
Indicators
Real GDP pro capita
Curr. ratio (M1/M3)
Part. ratio Lab. Force
- 32 -
T&C
T&C
C
T&C
T&C
T&C
T&C
T&C
T&C
Level
First difference
Second difference
ADF
P.P.
ADF
P.P.
ADF
P.P.
0,004
0,927
0,066
0,001
0,146
0,075
0,605
0,895
0,552
0,311
0,422
0,155
0,258
0,001
0,031
0,005
0,056
0,002
0,000
0,061
0,033
0,000
0,146
0,099
0,545
0,000
0,000
0,000
0,000
0,002
0,000
0,000
0,000
0,000
0,000
0,000
Level
First difference
Second difference
First differ. LogN
ADF
P.P.
ADF
P.P.
ADF
P.P.
ADF
P.P.
0,130
0,129
0,572
0,683
0,003
0,228
0,378
0,054
0,001
0,035
0,003
0,002
0,000
0,000
0,000
0,000
0,000
0,000
0,457
---
0,047
---