Recent Experience in the Use of Surveys and other Methods Measuring and Understanding the Shadow Economy, Tax and Benefit Fraud

1
Recent Experience in the Use of Surveys and other
Methods Measuring and Understanding the Shadow
Economy, Tax and Benefit Fraud
ShadEcTaxBenefit.pptE-mail friedrich.schneider_at_j
ku.atPhone 0043-732-2468-8210Fax
0043-732-2468-8209http//www.econ.jku.at
Prof. Dr. DDr.h.c. Friedrich SchneiderDepartment
of EconomicsJohannes Kepler University of
LinzA-4040 Linz-Auhof
2

• Introduction Defining the Shadow Economy
• The Size of the Shadow Economies of OECD and EU
  countries
• 2.1 DIMIMIC Results of 21 OECD countries
• 2.2 Survey Results of 27 EU countries
• 2.3 Survey Results Germany
• 2.4 Individual Analysis of Tax and Benefit Morale
  for Austria
• Methods to Estimate the Size of the Shadow
  Economy
• 3.1 Direct Approaches
• 3.2 Indirect Approaches
• 3.3 The Latent Estimation Approach
• Concluding Remarks Problems and Open Questions
• 4.1 Surveys
• 4.2 Estimations of national account statisticans
• 4.3 Monetary and/or electricity methods
• 4.4 DYMIMIC method

3
1. The Definition of the Shadow Economy

• (1.1) The shadow economy includes all legal
  production and provision of goods and services
  that are deliberately concealed from public
  authorities for the following four reasons
• (i) To avoid payment of income, value added or
  other taxes,
• (ii) To avoid payment of social security
  contributions,
• (iii) To avoid having to meet certain legal
  standards such as minimum wages, maximum hours,
  safety standards, etc., and
• (iv) To avoid complying with certain
  administrative procedures, such as completing
  statistical questionnaires or other
  administrative forms.

4
1. The Definition of the Underground and Informal
Household Economy

• (1.2) Underground (classical crime) activities
  are all illegal actions that fit the
  characteristics of classical crime activities
  like burgarly, robbery, drug dealing, etc.
• (1.3) Informal household economy consists of
  household enterprises that are not registered
  officially under various specific forms of
  national legislation.
• (1.4) To a large extent these two sectors ((1.2)
  classical crime and (1.3) household production)
  are not included in the shadow economy activities.

5

• Figure 1.1 Legal, Shadow, Illegal and Informal
  Economy

Illegal (criminal) underground economy
Shadow economy
Informal household economy
Legal/official economy
6
2.1 The Size of the Shadow Economies Econometric
(DYMIMIC) Estimates for 21 OECD countries
Table 2.1.1 DYMIMIC Estimation of the Shadow
Economy of 21 highly developed OECD Countries,
years 1990/91 to 2004/05 PART 1
7
Notes t-statistics are given in parentheses ()
means the t-statistics is statistically
significant at the 90, 95, or 99 confidence
level. 1) Steigers Root Mean Square Error of
Approximation (RMSEA) for test of close fit
RMSEA lt 0.05 the RMSEA-value varies between 0.0
and 1.0. 2) If the structural equation model is
asymptotically correct, then the matrix S (sample
covariance matrix) will be equal to S (?) (model
implied covariance matrix). This test has a
statistical validity with a large sample (N
100) and multinomial distributions both is given
for a all three equations in tables 3.1.1-3.1.3
using a test of multi normal distributions. 3)
Test of Multivariate Normality for Continuous
Variables (TMNCV) p-values of skewness and
kurtosis. 4) Test of Adjusted Goodness of Fit
Index (AGFI), varying between 0 and 1 1
perfect fit. 5) The degrees of freedom are
determined by 0.5 (p q) (p q 1) t with p
number of indicators q number of causes t
the number for free parameters.
Table 2.1.1 DYMIMIC Estimation of the Shadow
Economy of 21 highly developed OECD Countries,
years 1990/91 to 2004/05 PART 2
8
Figure 2.1.1 Size of the Shadow Economy in 21
OECD COUNTRIES, in of GDP, 2007
Source Own calculations.
9
2.2 Survey Results 27 EU Countries

1. Eurobarometer pilot survey on undeclared work
   (UDW) in May/June 2007 done by tns Infratest
   Munich, 2007.
2. It was designed to empirically test the
   feasibility of a direct survey on undeclared work.

Source tns Infratest, Munich 2007
10
Figure 2.2.1 Demand side Total EU 27
2.2 Survey Results 27 EU Countries
"Have you in the last twelve months acquired any
goods/services of which you had a good reason to
assume that they embodied undeclared work?"
Base total population aged 15
Source tns Infratest, Munich, 2007
11
Figure 2.2.2 Demand side Demand by country
2.2 Survey Results 27 EU Countries
"Have you in the last twelve months acquired any
goods/services of which you had a good reason to
assume that they embodied undeclared work?"
EU-27
Source tns Infratest, Munich, 2007
Base total population aged 15
12
Figure 2.2.3 Supply side
2.2 Survey Results 27 EU Countries
"Did you yourself carry out any undeclared
activities in the last 12 months for which you
were paid in money or in kind? Herewith we mean
again activities which were not or not fully
reported to the tax or social security
authorities and where the person who acquired the
good or services was aware of this?"
Base total population aged 15
Source tns Infratest, Munich, 2007
13
Figure 2.2.4 Supply side Envelope wages
2.2 Survey Results 27 EU Countries
"Sometimes employers prefer to pay all our part
of the regular salary or the remuneration for
extra work or overtime hours cash-in-hand and
without declaring it to tax or social security
authorities. Did your employer pay all or part of
your income in the last 12 months in this way?"
Base DEPENDENT EMPLOYEES ONLY!
Source tns Infratest, Munich, 2007
14
Figure 2.2.5 Supply side Total supply by country
2.2 Survey Results 27 EU Countries
Source tns Infratest, Munich, 2007
Base total population aged 15
15
Figure 2.2.6 Comparison of supply and demand I
2.2 Survey Results 27 EU Countries

• Certain discrepancy is plausible (UDW supposedly
  often done for more than one client)
• Extraordinarily large differences in a country
  can e.g. indicate that
• large parts of UDW are done by suppliers with
  many clients (e.g. firms/self-employed)
• large parts of UDW done by groups of people
  hardly/not captured by the survey (e.g.
  immigrants)
• to buy UDW is much more accepted than to perform
  UDW

Source tns Infratest, Munich, 2007
Base total population aged 15
16
Overall Evaluation
2.2 Survey Results 27 EU Countries

1. First attempt to measure undeclared work (UDW)
   European wide by the method of a survey hence,
   character of a pilot study.
2. Face to face interviews and the number of cases
   per country is quite small. Consequence Results
   are tentative, especially with respect to a deep
   analyses of the structures of undeclared work.
3. This questionnaire was never tested before in
   Eastern and Southern Europe. It was tested in a
   similar form in Denmark, Sweden, Germany, and the
   U.K.

17
Table 2.3.1 Do you regularly work in the shadow
economy? (yes or no)? Germany, 2007
2.3 Survey Results Germany
(1) Do you work regularly in the shadow economy? Values in percent
No Yes No answer 77,3 20,7 (25 male, 16 female) 2
(2) Do you regularly demand shadow economy activities? Values in percent
No Yes 69,2 30,8 (35.4 male, 26.5 female)
Representative questionnaire, Germany, January 2007 Source IDW Koeln, Germany Representative questionnaire, Germany, January 2007 Source IDW Koeln, Germany
18
Table 2.3.2 Reasons, why shadow economy
activities are demanded, Germany, 2007
2.3 Survey Results Germany
Reasons why shadow economy activities are demanded Values in percent
(1) One saves money or they are much cheaper than the official ones (2) The tax and social security burden is much too high (3) Due to the high labour costs in the official economy one would not demand these activities (extreme assumption no shadow economy 22 demand in the official economy 30 do-it-themselves and 48 no demand at all!) (4) The firms offer them themselves (5) Its so easy to get quick and reliable workers 90 73 68 52 31
Representative questionnaire, Germany, January 2007, Source IDW Koeln Representative questionnaire, Germany, January 2007, Source IDW Koeln
19
Table 2.3.3 A comparison of the Size of the
German Shadow Economy using the survey and the
DYMIMIC-method, year 2006
Various kinds of shadow economy activities/values Shadow Economy in of official GDP Shadow Economy in bill. Euro share of the overall shadow economy
Shadow economy activities from labour (hours worked, survey results) Material (used) Illegal activities (goods and services) already in the official GDP included illegal activities 5.0 6.0 3.0 4.0 4.0 5.0 1.0 2.0 117 140 70 90 90 117 23 45 33 40 20 25 25 33 7 - 13
Sum (1) to (4) 13.0 17.0 300 392 85 111
Overall (total) shadow economy (estimated by the DYMIMIC and calibrated by the currency demand procedure) 15.0 340 100
Source Enste/Schneider (2006) and own calculations. Source Enste/Schneider (2006) and own calculations. Source Enste/Schneider (2006) and own calculations. Source Enste/Schneider (2006) and own calculations.
20
2.3 Survey Results Germany

• Some remarks when comparing the values from the
  survey method with the total value added in the
  shadow economy sector achieved by the DYMIMIC
  method. The rather large difference can be
  explained with the following facts
• Table 2.3.3 contains earnings and not the value
  added of the shadow economy. This means material
  is not considered.
• Demanders are overwhelmingly households, the
  whole sector of the shadow economy activities
  between firms (which are especially a problem in
  the construction and craftsmen sectors) is not
  considered.
• All foreign shadow economy activities are not
  considered.
• The amount of income earned in the shadow
  economy, the hourly wage rate and hours worked
  per year vary considerably.

21
Table 2.3.4 The Size of the Shadow Economy in
Germany According to Different Methods (in
percentage of official GDP)
Method/Source Shadow economy (in percentage of official GDP) in Shadow economy (in percentage of official GDP) in Shadow economy (in percentage of official GDP) in Shadow economy (in percentage of official GDP) in Shadow economy (in percentage of official GDP) in Shadow economy (in percentage of official GDP) in Shadow economy (in percentage of official GDP) in Shadow economy (in percentage of official GDP) in
Method/Source 1970 1975 1980 1985 1990 1995 2000 2005
Survey/IfD Allensbach, 1975 - 3.6 1) - - - - - -
Survey/IfD Allensbach, 1975 - - - - - - 4.1 2) 3.1 2)
Survey/IfD Allensbach, 1975 - - - - - - 1.3 3) 1.0 3)
Discrepancy between expenditure and income/(Lippert and Walker, 1997) 11.0 10.2 13.4 - - - - -
Discrepancy between official and actual employment/(Langfeldt, 1983) 23.0 38.5 34.0 - - - - -
Physical input method (Feld and Larsen, 2005) - - - 14.5 14.6 - - -
Transactions approach Feige (1989) 17.2 22.3 29.3 31.4 - - - -
Currency demand approach/ (Kirchgässner, 1983) (Langfeldt, 1983, 1984) Schneider and Enste (2000) 3.1 6.0 10.3 - - - - -
Currency demand approach/ (Kirchgässner, 1983) (Langfeldt, 1983, 1984) Schneider and Enste (2000) 12.1 11.8 12.6 - - - - -
Currency demand approach/ (Kirchgässner, 1983) (Langfeldt, 1983, 1984) Schneider and Enste (2000) 4.5 7.8 9.2 11.3 11.8 12.5 14.7 -
Latent ((DY)MIMIC) approach/(Frey and Weck (1983)) Pickardt and Sarda (2006) Schneider (2005, 2007) 5.8 6.1 8.2 - - - - -
Latent ((DY)MIMIC) approach/(Frey and Weck (1983)) Pickardt and Sarda (2006) Schneider (2005, 2007) - - 9.4 10.1 11.4 15.1 16.3 -
Latent ((DY)MIMIC) approach/(Frey and Weck (1983)) Pickardt and Sarda (2006) Schneider (2005, 2007) 4.2 5.8 10.8 11.2 12.2 13.9 16.0 15.4
Soft modelling/(Weck-Hannemann (1983)) - 8.3 4) - - - - - -
Feld and Larsen, 2005
Feld and Larsen, 2005
1) 1974 2) 2001 and 2004 calculated using wages
in the official economy 3) 2001 and 2004
calculated using actual black hourly wages paid.
22
2.4 Individual Analyis of Tax and Benefit Moral
for Austria

• 2.4.1 Three Research Questions
• Determinants of benefit morale?
• ? Taxpayers attitude toward claiming
  unjustified government benefits/subsidies.
• Determinants of tax morale?
• ? Taxpayers attitude toward avoiding taxes.
• Impact of Benefit - tax morale on actual
  behavior (income).

Source Martin Halla Friedrich G. Schneider
(2005).
23
2.4 Individual Analyis of Tax and Benefit Moral
for Austria

• 2.4.2 Tax Morale Literature
• Intrinsic motivation (tax morale) is therefore a
  key determinant in understanding compliance
  behavior!
• Using Canadian data Torgler (2003) shows that tax
  morale rises with financial satisfaction, age,
  patriotism, trust in government, religiosity and
  deteriorates with rising income.
• Torgler and Schneider (2004) stress the influence
  of cultural differences in explaining tax morale
  and find strong evidence for interactions between
  culture and institutions.
• Torgler and Schneider (2005) investigate tax
  morale in Austria. Societal variables (e.g.
  perceived tax evasion, patriotism, trust in legal
  system) are key determinants!

Source Martin Halla Friedrich G. Schneider
(2005).
24
2.4 Individual Analyis of Tax and Benefit Moral
for Austria

• 2.4.2 Benefit Morale
• To best knowledge of Halla and Schneider, no
  investigation of the individual taxpayers
  decision on claiming unjustified subsidies (e.g.
  by underreporting income) exists so far in the
  economic literature. Only Orviska and Hudson
  (2003) touch upon this issue.
• From a theoretical point of view a subsidy is a
  negative tax, but
• in empirical applications a distinction may be
  reasonable, since
• the size of theoretical determinants (e.g.
  probability of detection) can differ,
• Individuals may have different opportunities.
  Some may not have the opportunity to avoid taxes,
  but it may be feasible for them to claim
  unjustified subsidies,
• Individuals may have distinct basic attitudes
  towards these two issues.

Source Martin Halla Friedrich G. Schneider
(2005).
25
2.4 Individual Analyis of Tax and Benefit Moral
for Austria

• 2.4.3 Data
• Austrian data from the European Values Survey
  (1990 1999).
• Surveys contain information on basic attitudes,
  beliefs and human values covering religion,
  morality, politics, work and leisure.
• In particular respondents were asked to evaluate
  on a ten-point scale
• cheating on tax if you have the chance () can
  always be justified, never be justified, or
  something in between. ? tax morale
• claiming state benefits which you are not
  entitled to () can always be justified, never
  be justified, or something in between. ? benefit
  morale
• N 2,982 ? After cleaning data N 1,887 (N1990
  835, N1999 1,052).

Source Martin Halla Friedrich G. Schneider
(2005).
26
2.4 Individual Analyis of Tax and Benefit Moral
for Austria
2.4.3 Data and Descriptive Statistics Table
2.4.1 Descriptive Statistics
Variable Mean Std. Dev. Min Max
Tax morale 8.92 1.86 1 10
Benefit morale 9.09 1.66 1 10
Income (100 p.m.) 13.03 6.25 0 24.99
Spearmans Rho (tax morale, benefit morale) 0.43 Spearmans Rho (tax morale, benefit morale) 0.43 Spearmans Rho (tax morale, benefit morale) 0.43 Spearmans Rho (tax morale, benefit morale) 0.43 Spearmans Rho (tax morale, benefit morale) 0.43
Ten is the highest tax- benefit morale.
Income is given on a household basis (ten
ranges). To account for inflation we assign the
lower bound of each range.
Source Martin Halla Friedrich G. Schneider
(2005).
27
2.4 Individual Analyis of Tax and Benefit Moral
for Austria

• 2.4.4 Estimation of the Determinants of Tax
  Benefit Morale
• Closely related issues we apply a system of
  equations
• Tax morale a1 ß11 benefit morale ß11
  income G1 ?1 e1
• Benefit morale a2 ß21 tax morale ß22
  income G2 ?2 e2
• If stated attitudes are translated in actual
  behavior, income is endogenous too,
• because simultaneity prevails!
• Halla and Schneider instrument income with chief
  wage earners sex job rank and the
  socio-economic status of the household.

Source Martin Halla Friedrich G. Schneider
(2005).
28
2.4 Individual Analyis of Tax and Benefit Moral
for Austria
Table 2.4.2 2SLS Estimation of Tax and Benefit
Morale
Tax morale Benefit morale
Tax morale - 0.463 (0.220)
Benefit morale 0.607 (0.282) -
Income -0.024 (0.013) 0.002 (0.013)
Age -0.004 (0.005) 0.011 (0.003)
Female 0.003 (0.094) 0.122 (0.077)
Married 0.182 (0.105) -0.043 (0.109)
School leaving age -0.022 (0.013) 0.001 (0.013)
Tax morale Benefit morale
Employed -0.083 (0.130) 0.226 (0.096)
1999 0.141 (0.180) -0.480 (0.090)
Religious 0.136 (0.053) -0.006 (0.061)
Patriotic 0.157 (0.101) 0.132 (0.093)
Distrust legal system -0.137 (0.054) -
Children - 0.073 (0.032)
Volunteer - 0.136 (0.083)
Observations 1,887 1,887
Basmann Statisticb 0.237 0.584
Sargan Statisticc 0.232 0.580
a Standard errors are in parenthesis. , and indicate a statistical significance at the 10-percent-level, 5-percent level and 1-percent level. Dummies for the nine Austrian provinces are included in each regression. Base group is Vorarlberg. b P-value of Basmanns test of overidentifying restrictions of all instruments (Basmann, 1960).
c P-value of Sargans tests of overidentifying
restrictions of all instruments (Sargan, 1958). ?
A different estimation strategy applying ordered
probit estimations in both stages of the
estimation of the tax- benefit morale eqs.
Deliver qualitatively very similar results.
29
2.4 Individual Analyis of Tax and Benefit Moral
for Austria

• 2.4.5 Estimation of Impact on Actual Behavior
• Income a3 ß31 tax morale ß32 benefit
  morale G3 ?3 e3
• A neg. significant coefficient of tax morale
  indicates actual noncompliance behavior,
• A neg. significant coefficient of benefit morale
  shows actual claims of unjustified subsidies,
• because in both cases a higher net wage is
  ceteris paribus expected!
• Durbin-Wu-Hausman-Test for endogeneity of tax-
  benefit morale P-value 0.01
• ? Endogeneity prevails we instrument for tax-
  and benefit morale.
• Instruments are Confidence in the legal system,
  voluntary labor children.
• Test(s) for overidentifying restrictions confirm
  the instruments (e.g. P-value of Basmanns test
  0.62)

Source Martin Halla Friedrich G. Schneider
(2005).
30
2.4 Individual Analyis of Tax and Benefit Moral
for Austria
Table 2.4.3 2SLS Estimation on Income
Independent Variable Dependent Variable Income
Tax morale 1.610 (1.293)
Benefit morale -2.916 (1.309)
Chief wage earners job rank 0.113 (0.096)
Chief wage earner is female -3.410 (0.475)
Socioeconomic status 4.382 (0.294)
Year -0.066 (0.597)
Vienna -0.112 (0.713)
Tirol -1.827 (0.728)
Constant 12.477 (6.280)
a Standard errors are in parenthesis. , and indicate a statistical significance at the 10-percent-level, 5-percent level and 1-percent level. Dummies for the nine Austrian provinces are included in each regression. Base group is Vorarlberg. b P-value of Basmanns test of overidentifying restrictions of all instruments (Basmann, 1960). c P-value of Sargans tests of overidentifying restrictions of all instruments (Sargan, 1958). ? A different estimation strategy applying ordered probit estimations in both stages of the estimation of the tax- benefit morale eqs. Deliver qualitatively very similar results.
Observations 1,887
Basmann Statisticb 0.622
Sargan Statisticc 0.620
Source Martin Halla Friedrich G. Schneider
(2005).
31
2.4 Individual Analyis of Tax and Benefit Moral
for Austria

• 2.4.5 Results of the 2SLS Estimation on Income
• Not statistically significant impact of tax
  morale on household income!
• Statistically significant impact of benefit
  morale on household income!
• - One point higher benefit morale reduces
  household income by 292 p.m.
• Households with female chief wage earners have
  about 341 lower income p.m.
• A higher socio-economic status (self reported,
  measured on four-point scale) is associated with
  438 more income p.m.

Source Martin Halla Friedrich G. Schneider
(2005).
32
2.4 Individual Analyis of Tax and Benefit Moral
for Austria

• 2.4.6 Conclusions
• Tax morale (basic attitude towards avoiding
  taxes) and benefit morale (basic attitude towards
  claiming unjustified subsidies) have different
  determinants.
• Halla and Schneider found empirical evidence that
  tax morale and benefit morale have different
  impact on realized behavior. Only statistically
  significant effect of benefit morale on income.
• Low (high) benefit morale leads indeed (not) to
  unjustified claims on benefits and therefore to
  higher (lower) income!
• These differences can be explained by
• Different probability of detection,
• By a different penalty rate or by
• More opportunities to cheat on the state by
  unjustified subsidies in contrast to tax evasion.

Source Martin Halla Friedrich G. Schneider
(2005).
33
3) Methods to Estimate the Size of the Shadow
Economy 3.1 Direct Approaches 3.2 Indirect
Approaches 3.3 The Model/Latent Estimation
Approaches
34
3) Methods to Estimate the Size of the Shadow
Economy

• 3.1 Direct Approaches
• These micro approaches employ either well
  designed surveys and samples based on voluntary
  replies or tax auditing and other compliance
  methods.
• 3.1.1 Survey-method
• 3.1.2 Tax-auditing-method

35
3) Methods to Estimate the Size of the Shadow
Economy

• 3.2 Indirect Approaches
• These approaches, which are also called
  indicator approaches, are mostly macroeconomic
  ones and use various (mostly economic) indicators
  that contain information about the development of
  the shadow economy (over time).
• 3.2.1 The Discrepancy between National
  Expenditure and Income Statistics
• 3.2.2 The Discrepancy between the Official and
  Actual Labor Force
• 3.2.3 The Transactions Approach
• 3.2.4 The Currency Demand Approach
• 3.2.5 The Physical Input (Electricity
  Consumption) Method
• 3.3 The Model/Latent Estimation Approach

36
3.2.4 The Currency Demand Approach
3) Methods to Estimate the Size of the Shadow
Economy

• The basic regression equation for the currency
  demand, proposed by Tanzi (1983), is the
  following
• ln (C / M2)t bO b1 ln (1 TW)t b2 ln (WS /
  Y)t b3 ln Rt b4 ln (Y / N)t ut
• with b1 gt 0, b2 gt 0, b3 lt 0, b4 gt 0
• where
• ln denotes natural logarithms,
• C / M2 is the ratio of cash holdings to current
  and deposit accounts,
• TW is a weighted average tax rate (as a proxy
  changes in the size of the shadow economy),
• WS / Y is a proportion of wages and salaries in
  national income (to capture changing payment and
  money holding patterns),
• R is the interest paid on savings deposits (to
  capture the opportunity cost of holding cash),
  and
• Y / N is the per capita income.

37
The most commonly raised objections (criticism)
against the current demand approach are
3) Methods to Estimate the Size of the Shadow
Economy The Currency Demand Approach Cont.

• Not all transactions in the shadow economy are
  paid in cash. The size of the total shadow
  economy (including barter) may thus be larger.
• Most studies consider only one particular factor,
  the tax burden, as a cause of the shadow economy.
  If other factors also have an impact on the
  extent of the hidden economy, the shadow economy
  may be higher.
• Blades and Feige, criticize Tanzis studies on
  the grounds that the US dollar is used as an
  international currency, which has to be
  controlled.
• Another weak point is the assumption of the same
  velocity of money in both types of economies.
• Ahumada, Alvaredo, Canavese A. and P. Canavese
  (2004) show, that the currency approach together
  with the assumption of equal income velocity of
  money in both, the reported and the hidden
  transaction is only correct, if the income
  elasticity is 1. As this is for most countries
  not the case, the calculation has to be
  corrected.
• Finally, the assumption of no shadow economy in a
  base year is open to criticism.

38
3. Methods to Estimate the Size of the Shadow
Economy The MIMIC (Latent) Approach
3.3 Multiple Indicators, Multiple Causes (MIMIC)
approach

• The MIMIC approach explicitly considers several
  causes, as well as the multiple effects of the
  informal economy.
• The methodology makes use of the associations
  between the observeable causes and the observable
  effects of an unobserved variable, in this case
  the informal economy, to estimate the unobserved
  factor itself.
• Formally, the MIMIC model consists two parts
• The structural equation model describes the
  relationship among the latent variable
  (informal economy IE) and its causes.
• The measurement model represents the link between
  the latent variable IE and its indicators i.e.
  the latent variable (IE) is expressed in terms of
  observable variables.

39
3. Methods to Estimate the Size of the Shadow
Economy The MIMIC (Latent) Approach cont.
Multiple Indicators, Multiple Causes (MIMIC)
approach
The model for one latent variable (IE) can be
described as follows IE ? x ? (1)
Structural equation model ? ? IE e (2)
Measurement model where IE is the unobservable
scalar latent variable (the size of the informal
economy), ? (?1, ?p) is a vector of
indicators for IE, x (x1,xq) is a vector of
causes of IE, ? and ? are the (px1) and (qx1)
vectors of the parameters and e and ? are the
(px1) and scalar errors.
40
3. Methods to Estimate the Size of the Shadow
Economy The MIMIC (Latent) Approach cont.
Figure 3.1 General structure of a MIMIC Model
Indicators
Causes
?1
?1
x1t
y1t e1t
?2
?2
x2t
y2t e2t
IEt
?q


?p
xqt
ypt ept
41
3. Methods to Estimate the Size of the Shadow
Economy The MIMIC (Latent) Approach cont.
3.3 Multiple Indicators, Multiple Causes (MIMIC)
approach
Equation (1) links the informal economy with ist
indicators or symptoms, while equation (2)
associates the informal economy with ist causes.
Assuming that these errors are normally
distributed and mutually uncorrelated with var(?)
s2 ? and cov(e) Te, the model can be solved
for the reduced form as a function of observable
variables by combining equations (1) and (2) ?
p x µ (3) where p ? ? , µ ? ? e and
cov(µ) ? ? s2? Te.
42
4. Concluding Remarks

• 4. Concluding Remarks Problems and Open
  Questions
• 4.1 Surveys
• Quite often only households or only partly firms
  are considered
• Non-responses and/or incorrect responses
• Results of the financial volume of black hours
  worked and not of value added
• 4.2 Estimations of national account statisticians
  (quite often the discrepancy method)
• Combination of meso estimates/assumptions
• Calculation method often not clear
• Documentation and procedures often not public

43
4. Concluding Remarks

• 4. Concluding Remarks Problems and Open
  Questions
• 4.3 Monetary and/or electricity methods
• Some estimates are very high
• Are the assumptions plausible?
• Breakdown by sector or industry not possible!
• 4.4 DYMIMIC method
• Only relative coefficients, no absolute values.
• Estimations quite often highly sensitive with
  respect to changes in the data and
  specifications.
• Difficulty to differentiate between the selection
  of causes and indicators

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4. Concluding Remarks Problems and Open Questions

• 4.5 What did we learn?
• No ideal or dominating method all have serious
  problems and weaknesses.
• If possible use several methods.
• Much more research is needed with respect to the
  estimation methodology and empirical results for
  different countries and periods.
• Experimental methods should be used to provide a
  micro-foundation.