1

University of Salerno

CELPE

Interdepartmental Centre for Research in Labour Economics and Economic Policy

Roberto DELL’ANNO CELPE, University of Salerno

Department of Economics and Statistics, University of Salerno

Analyzing the determinants of the Shadow Economy with a “separate approach”. An application of the relationship between Inequality and the

Shadow Economy

Corresponding Authors rdellanno@unisa.it

Quaderno di Ricerca

4/2015

2

ABSTRACT

This paper suggests a “separate” approach to analyze the determinants of the shadow

economy (SE). It is applied to investigate the relationship between inequality and the SE

on a cross-section of 118 countries. We disentangle the effect of inequality on the SE ratio

by estimating both direct and indirect effects on both the numerator and denominator of

the ratio separately. We find that an increase in inequality increases the SE ratio. This

positive correlation is primarily due to a reduction in the official GDP rather than an

increase in the SE.

Keywords: Shadow Economy; Inequality; Separate approach; Unobserved Economy.

3

1. Introduction

The shadow economy (SE) is a subject of considerable interest, and the literature on the

analysis of its determinants is particularly extensive (see Friedman et al., 2000; Schneider

and Enste 2000; Schneider 2011 for an overview). This paper aims at contributing to this

issue by proposing an alternative approach to estimate the influence of a potential

determinant on the SE ratio. The basic intuition of this research is to demonstrate that

estimating the influence of an explanatory variable on a dependent variable measured as a

ratio (hereinafter, “ratio approach”) may be not conclusive because it blurs the impact of

the explanatory variable on the denominator (e.g., official economy) with the impact that it

has on the numerator (e.g., SE). Accordingly, we propose calculating the overall effect,

estimating both direct and indirect impacts on both the official and on the unobserved

Gross Domestic Product (GDP) separately (hereinafter “separate approach”). An empirical

application of this approach is conducted to explore the relationship between income

inequality and the SE.

The paper consists of two parts. In the first “methodological” part, we address the issue of

the different approaches to define (and measure) the SE and introduce the “separate

approach”. The second part of the paper applies the proposed methodological hints to

investigate the relationship between the income distribution and the SE. Over the past two

decades, several research works empirically supported the hypothesis that income

inequality and the SE are positively correlated (e.g., Rosser et al. 2000, 2003; Ahmed et

al. 2007; Chong and Gradstein, 2007). We verify that this result is empirically validated

both by utilizing the “ratio approach” and by applying the “separate approach”.

In sum, the paper contributes to the existing literature in several ways. Following the order

in which they are presented in the article, we attempt to reconcile the definitions of the SE

utilized in economic research with the Non-Observed Economy (NOE) concept adopted by

national statistical institutes; because the “ratio approach” may cause misinterpretation of

the actual influence of an explanatory variable on a ratio variable, we propose estimating

both the direct and indirect effects of the explanatory variable on the numerator (i.e., SE)

and denominator (i.e., official GDP) disjointedly; we provide a method to calculate the

effect of a determinant on the SE ratio by controlling for the double counting of a part of

the SE in the SE ratio; and concerning the relationship between inequality and the SE, we

find that the overall impact of inequality on the SE ratio is positive and higher than the

effect estimated by the “ratio approach”.

4

The paper is organized as follows. Section 2 addresses the definition of the SE and

introduces the “separate approach”. Section 3 provides theoretical background on the

interactions among inequality, official GDP and the SE. Section 4 describes the database,

econometric models and hypotheses and reports the empirical outcomes. Section 5

concludes.

2. Defining and analyzing the Shadow Economy in empirical research

2.1 Defining the Shadow Economy

We discuss two general approaches to define and measure the SE. On the one hand, the

national accounting system (SNA) employs the label NOE to refer to “all productive

activities that may not be captured in the basic data sources used for national accounts

compilation” (UNECE 2008, p. 2). Following the Eurostat’s (2005) “Tabular approach to

exhaustiveness”, the SNA classifies seven sources of non-exhaustiveness for GDP

estimates: (N1) Producers deliberately not registered to avoid tax and social security

obligations; (N2) Producers deliberately not registered as a legal entity or as an

entrepreneur because they are involved in illegal activities; (N3) Producers not required to

register because they have no market output; (N4) Legal persons or (N5) registered

entrepreneurs not surveyed due to a variety of reasons; (N6) Producers deliberately

misreporting to evade taxes or social security contributions; and (N7) Other statistical

deficiencies. For analytical purposes, OECD (2014) proposes a simplification of this

classification in four types of NOE adjustments. It defines N1+N6 as Underground

production, N2 as Illegal production, N3+N4+N5 as Informal sector production (including

those undertaken by households for their own final use) and N7 as Statistical deficiency.

The second approach to define the SE is prevalent in economic research. Here, the

adjectives informal, shadow, hidden, second, black, unrecorded, unofficial, and

unobserved, etc., are often utilized synonymously with terms such as economy, sector,

market, and GDP. However, these labels refer to distinct phenomena and should be used

appropriately (Bagachwa and Naho, 1995; Feige 1990, Feige and Urban 2008) to avoid

misunderstandings. In this literature, a plurality of macro-econometric methods to estimate

the SE is proposed. Among these methods, the Multiple Causes Multiple Indicators

(MIMIC) approach and the currency demand approach are becoming dominant.

Attempting to systematize the common definitions in this area of research, we identify two

recent studies as benchmarks for the two most common sources of macro-econometric

5

estimates of the SE, i.e., Buehn and Schneider (2012) for the MIMIC method and Alm and

Embaye (2013) for the currency demand approach. The two studies adopt two different

mainstream definitions of the SE. They differ in dealing with illegal activities in the SE.

Specifically, Buehn and Schneider (2012, p. 141) define the SE as including all market-

based legal production of goods and services that are deliberately concealed from public

authorities to avoid payment of taxes or social security contributions, to avoid having to

meet certain legal labor market standards, and to avoid complying with certain

administrative procedures or statistical questionnaires. Following Smith (1984), Alm and

Embaye (2013, p. 512) employ a somewhat broader definition of the SE that includes “all

market-based goods and services (legal or illegal) that escape inclusion in official

accounts”. In other words, while Buehn and Schneider (2012) include “all market-based

legal production”, Alm and Embaye also consider market-based illegal production.

Aiming to find a trait d’union between the most used labels in economic research (i.e., SE)

and in national accounting system (i.e., NOE), we distinguish four types of GDP

aggregates: recorded observed economy (GdpRO); recorded non-observed economy

(GdpRNOE) and unrecorded non-observed economy (GdpUNOE). Given the foregoing

definitions, we can label the total economic activity as GdpT = GdpRO + GdpNOE and the

official (published) GDP as Gdpoff = GdpRO + GdpRNOE, where the total NOE is given by

GdpNOE = GdpRNOE + GdpUNOE.

Combining this classification with the seven sources of non-exhaustiveness for GDP

estimates proposed by the Eurostat’s (2005) Tabular approach to exhaustiveness, we

obtain a precise definition of the estimates of the SE ratio calculated by Alm and Embaye

(2013) utilizing a modified Currency demand approach ( Macro

CurrSE ) and Buehn and Schneider

(2012) utilizing MIMIC modeling ( Macro

MIMICSE ).

A preliminary explanation is required here. Following Alm and Embaye’s definition literally,

we should include in the numerator only the GDP that “escapes inclusion in the official

accounts”, i.e. GdpUNOE(N1+N6). However, the currency demand approach estimate a linear

transformation of this value. In the last stage of the currency demand approach, the

amount of the unobserved GDP is obtained by multiplying the stock of currency used to

escape taxes and administrative burdens (C*) by the velocity of money (V). Considering

that the velocity of money is the ratio between the nominal (official) GDP and money

supply, what a researcher obtains by multiplying C* by V is inevitably an estimate of the

6

unobserved GDP that includes an additional share of the NOE in the same proportion –

that we denote by b – in which the recorded NOE is included in the official GDP

(hereinafter “currency demand bias”). Accordingly, we include (1+b) in the numerator of

Macro

CurrSE .

N1+N2+N61

UNOE

Macro

Curr RNOE TotalRO

b GdpSE

Gdp Gdp

(1)

Where b is the proportion of RNOEGdp on offGdp ( RNOE offGdp bGdp ).

With reference to the MIMIC estimates of the SE ratio, the numerator of Macro

MimicSE follows (1)

because of the calibration of the MIMIC model to the currency demand method.1

N1+N61

UNOE

Macro

Mimic RNOE TotalRO

b GdpSE

Gdp Gdp

(2)

This issue might be easily solved if the estimates of the imputed NOE were officially

published and homogeneously estimated at the national level. However, this is not the

normal case because national statistical offices do not regularly divulge the size of NOE

adjustments in the official statistics. Moreover, for the countries where these data are

available, these adjustments should be cautiously employed for cross-countries

comparisons because of the differences in methodologies and practices followed by

offices in estimating the NOE (UNECE 2008; OECD 2014).

In general, assuming no measurement errors, the differences between the macro-

econometric and statistical national accounting methods may be explained both by

divergences in the coverage of the NOE types and by the factor (1+b). For instance, the

discrepancy between Alm and Embaye’s (2013) estimates and the size of adjustments in

national accounting ( SNASE ) should be equal to the imputed unobserved GDP yield by

unregistered producers because they have no market output (N4+N5), statistical

discrepancies (N7) and unrecorded NOE for underground and illegal production divided by

the official economy multiplied by the factor (1+b) (i.e.,

N1+N2+N61

UNOEMacro SNA off

currSE SE b Gdp Gdp ). Again, the discrepancy between the SE ratio

obtained by Buehn and Schneider’s (2012) MIMIC specification and those obtained by the

currency demand should be equal to the proportion of unobserved economy due to illegal

1 Buehn and Schneider (2012) used as the base value Schneider’s (2007) estimate of the SE obtained by currency demand approach in 2000 to calibrate MIMIC estimates.

7

activities (N2). However, given that the estimates obtained by currency approach calibrate

the Buehn and Schneider’s (2012) MIMIC model, we cannot extrapolate N2 by comparing

these two sources of data. Hence, in the following, we will assume that the difference

between Macro

MIMICSE and Macro

CurrSE only depends on measurement errors. Concerning the

consequence of this assumption, OECD (2014) states that N1+N6 adjustments for NOE

activities almost always represent the most significant part of the adjustments for non-

exhaustiveness, reaching as much as 80% of all adjustments in some countries; therefore,

we could suppose that our simplification does not significantly affect the results. In sum,

the MIMIC and currency demand estimates of the SE approximately measure the following

ratio:

1UNOE

Macro

RO RNOE

GdpSE b

Gdp Gdp

(3)

However, grounding economic implications from this ratio is challenging. On the one hand,

given that 1NOE UNOE RNOE UNOEGdp b Gdp Gdp bGdp and assuming, realistically, that

off UNOEGdp Gdp , the numerator of the MacroSE includes a lower NOEGdp than the actual

one. On the other hand, the denominator includes a part of the numerator, i.e. RNOEGdp . As

a consequence an unambiguous definition of the SE ratio for economic analysis may be

the ratio between unobserved and observed economy. It takes into account both macro-

econometric estimate of the SE ratio and proportion of NOE-adjustments in official GDP.

Specifically, given that 1

1UNOE off MacroGdp Gdp SE b

, we obtain a ratio where the

numerator is the SE (or unobserved economy) and the denominator is the observed

economy:

*

2

1

1

MacroUNOE RNOE

RO

SE b bGdp GdpSE

Gdp b

(4)

In conclusion, by combining macro-econometric and SNA’s definitions, the SE includes all

market-based goods and services (legal or illegal) that are not observed in the basic data

sources utilized for national accounts compilation.

2.2 A Separate approach to analyze the determinants of the Shadow economy

Problems in employing ratio variables have been described in the statistical literature for

over a century (e.g., Pearson, 1897; Yule, 1910), and scholars continue to warn against

8

this problematic practice (e.g., Kuh and Meyer, 1995). However, little attention has been

paid to the use of ratio variables in the literature on the SE, where they remain popular.

In general, we argue that estimating one regression for the numerator and another one for

the denominator is a more appropriate method than the standard practice to regress the

set of the potential determinants on the SE ratio. The separate approach avoids the risk of

misinterpretation of empirical results that may occur if in addition to the effect of the

determinant on the numerator (Hp.1: 0N X ), this factor also affects the denominator

of the ratio (Hp.2: 0D X ). Furthermore, if a statistically significant relationship

between numerator and denominator exists (Hp.3: 0N D ), computing the indirect

effects in both the terms of the ratio is recommended. The rationale is that by using a

separate approach, we can calculate an overall effect by combining the direct and indirect

effects of X on both terms of the ratio. Applying this approach to the SE ratio, and given

that the marginal effect of X on GDPNOE is unrelated to the statistical office’s ability to

impute it in official GDP ( UNOE RNOEGdp X Gdp X ), then, we obtain the overall or total

effect of X on MacroSE

(5)

3. What does the literature say about the relationships among inequality, the

shadow economy and the official economy?

In this second part of the article, we apply the separate approach to investigate the

relationship between inequality and the SE. First, we theoretically support the hypotheses

that should suggest the use of this method rather than the standard “ratio approach”. In

particular, Sections 3.1 and 3.2 provide economic arguments and empirical evidence for

the existence of statistically significant relationships between inequality and the SE (Hp. 1:

0N X ) and inequality and the official GDP (Hp. 2: 0D X ). Section 3.3 surveys the

theoretical background supporting the inclusion of indirect effects in the analysis (Hp 3:

0N D ).

1 12

1 2 1

1 1

Direct Effect Indirect Effect

UNOE UNOE off

off

Macro

off off UNOE

UNOE

Direct Effect

Gdp Gdp Gdpb b

X XGdpdSE

dXGdp Gdp Gdp

X XGdp

1 2 1

1 2 1

1

Indirect Effect

b

9

3.1 The relationship between income inequality and the shadow economy (Hp.1)

Extensive research has been devoted to the study of the determinants of the SE, but

explicit analyses of the link between the SE and income inequality are relatively scarce.

The first published papers dealing empirically with the relationship between these two

phenomena are those by Rosser et al. (2000, 2003). They found a positive correlation

between inequality and the size of the SE as a percentage of official GDP within

economies with low institutional infrastructure (i.e., Transition countries). This is because

the SE reduces the amount of tax revenues, thereby reducing the effectiveness of a

government’s redistributive policies. Notwithstanding, Rosser et al. (2000) conclude that

the direction of causation in this relationship remains untested and unknown. Chong and

Gradstein (2007) also find a robust positive relationship between income inequality and the

SE. They argue that when inequality increases, the rich invest in rent seeking more and

the poor invest less. Chong and Gradstein (2007) show that the SE ratio is larger with

relation to weaker institutions, and the larger the income inequality. Likewise, utilizing a

general equilibrium model in which public policy is based on the median voter, Hatipoglu

and Ozbek (2011) provide theoretical support to the empirical evidence that the existence

of a large SE coincides with less redistribution. Again, Ahmed et al. (2007) and Dell’Anno

(2008) showed a positive relationship between income inequality and the size of the SE

ratio in a global dataset and in Latin American countries, respectively. However, part of the

literature notes that the sign of the relationship between the SE and inequality is hard to

predict by macro-econometric analyses. For instance, Valentini (2009) notes two crucial

aspects that have been scarcely considered in the literature. First, because income

inequality is measured using “declared” incomes, the bias of the indexes of inequality may

make these measures unreliable for comparisons among countries with different sizes of

the SE. Second, he argues that there are no reasons to suppose that a growth in

unobserved income is uniform along income distribution. In particular, the sign of this

correlation depends on the predominant nature of the shadow income. Accordingly, if the

unobserved income is higher (lower) for the poorer then for the richer, we could have a

positive (negative) relationship between the size of SE and income inequality, or vice

versa. Eilat and Zinnes (2002) argue that the SE can affect income distribution through

several channels, some increasing inequality and some decreasing it. Concerning the

negative correlation between the SE and income inequality, Eilat and Zinnes (2002) state

that if shadow activities are associated with anti-competitive conduct, it may transfer

10

economic surplus from consumers to equity owners, increasing inequality. In contrast, if

shadow activities provide employment to those with lower income, a “tax-free” SE may

have a positive effect on income distribution. Consistent with this, the authors find

evidence of a non-statistically significant relationship between the size of the SE and the

Gini coefficient in Transition countries.

In conclusion, the prevailing view is that an economically significant relationship between

the SE and income inequality exists, although it may be concealed in the empirical

analysis. However, when a statistically significant correlation is estimated, it is positive.

3.2 The relationship between income inequality and official GDP (Hp. 2)

The relationship between inequality and the level of economic development has interested

social scientists for many years, and it has been explored in many theoretical and

empirical studies.

Various theoretical explanations have been suggested that explain how inequality could

affect economic development. Following Amendola and Dell’Anno (2015), this literature

can be classified into two main strands: (1) political economy explanations and (2) purely

economic explanations. A first group of political economy models argues that (1.a) a more

unequal income distribution motivates more social demand for redistribution throughout

the political process (e.g., Persson and Tabellini, 1994). Typically, transfer payments and

associated taxation will distort economic decisions, and through this channel, inequality

reduces growth. A second group of political economy models (1.b) assumes that a greater

degree of inequality causes “political instability” (e.g., Alesina and Perotti, 1996) and

motivates the poor to engage in crime and disruptive activities (Bourguignon, 1999).

Through these dimensions of socio-political unrest, more inequality tends to reduce

economic growth.

With reference to “purely economic” explanations, a first group of models (2.a) assumes

that due to the presence of imperfect capital markets, a more unequal distribution of

assets means that an increased number of individuals do not have access to credit and,

thus, cannot make productive investments. Through this channel, inequality would reduce

economic growth (e.g., Galor and Zeira, 1993). A second group of models (2.b) assumes

that income inequality noticeably reduces the future growth rate because of the positive

effect of inequality on the overall rate of fertility (e.g., Becker et al., 1990). Thus, a

worsening in inequality jointly generates a rise in the fertility rate and a drop in the rate of

11

investment in human capital, and this reduces the future growth rate of GDP. A third

approach of “purely economic” models (2.c) claims that a more unequal distribution of

incomes results in smaller domestic markets (Murphy et al., 1989). The size of home

demand is, thus, too small to generate markets large enough to fully develop local

industries or to attract foreign direct investment. Following this approach, inequality

reduces the growth rate as a consequence of a lower exploitation of economies of scale

and of incentives to foreign direct investment.

Accordingly, although several surveys show the findings of this strand of empirical

research are mixed, the predominant view is that a statistically significant relationship

between the official economy and income inequality exists. In particular, a higher inequality

level is associated with lower economic development.

3.3 The relationship between official GDP and the shadow economy (Hp. 3)

The analysis of the relationship between official production and the SE is one of the most

relevant and challenging issue in this literature. Schneider and Enste (2000) state that the

effect of the SE on economic growth remains considerably ambiguous, theoretically and

empirically. The correlation between shadow and official may be both negative (dual

hypothesis) and positive (structural hypothesis). According to the dual view shadow

activities, creating unfair competition, interfere negatively with market allocation (Tokman,

1978). Then, the misallocation slows down economic growth. Loayza (1996) found

empirical evidence of negative correlation between the SE and the growth rate of the

official GDP per capita for 14 Latin American countries. The inverse relationship between

the SE and economic growth is theoretically supported by the author’s hypothesis on the

shadow economy’s congestion effect. Similarly, Eilat and Zinnes (2002) estimate an

inverse relationship between the SE and official economy in Transition countries. The

“structuralists” consider the shadow and official economy as intrinsically linked. According

to this approach, shadow activities are inclined to meet the interests of increasing the

competitiveness of regular productive units, providing cheap goods and services (Moser,

1978). Consequently, a growing official economy boosts the SE. The economic

explanation is that the value-added created in the SE is spent (also) in the official

economy. At the same time, more official production increases the demand for goods and

services produced by unobserved activities. Various studies have supported the

hypothesis of the beneficial effect of the SE on economic development. For instance,

12

Adam and Ginsburg (1985) estimate a positive relationship between the growth of the SE

and the official economy under the assumption of the low probability of enforcement.

Bhattacharyya (1999) presents clear evidence in the case of the United Kingdom (from

1960 to 1984) that the SE has a positive effect on several components of GDP (e.g.,

consumer expenditures, services, etc.). For Eilat and Zinnes (2002), the most obvious

benefit of a SE is that it helps maintain economic activity when rent seeking and corruption

raise the cost of official production. Because some of the income earned in the

unobserved economy eventually is spent in the official economy, shadow activity may

even have a positive effect on official growth and on tax revenues. Further empirical

evidence of a positive correlation between the SE and official economy is also found by

Tedds (2005) and Bovi and Dell’Anno (2010). An interesting result to rationalize these

contradictory findings is reported by Schneider (2005). He estimates that while unofficial

activities boost economic growth for developed economies, they reduce the growth rate of

the official GDP for developing countries. As a result, the sample composition of the

empirical analysis may indirectly determine the sign of correlation between the official and

unobserved economies.

Conclusively, this survey has shown that although predicting the sign remains challenging,

abundant evidence corroborates the hypothesis of a statistically significant relationship

between the official economy and SE. For that reason, indirect effects should be included

to compute the total effect of inequality on the SE ratio in the separate approach.

Last but not least, we note that a positive correlation between the official GDP and SE

should be expected because of SNA rules that prescribe to include the unobserved

economy in official statistics, i.e., Gdpoff = GdpRO + GdpRNOE.

As this section has shown, the main findings of the economic research concerning Hp.1,

Hp.2 and Hp.3 support, in theory, the application of the proposed “separate approach” with

indirect effects to analyze the relationship between the SE and inequality. The next section

aims to verify whether these results are also empirically validated in our dataset.

13

4. Empirical Analysis

4.1 Data and econometric approach

We conduct cross-sectional regressions of a set of potential determinants of the official

and SE for 118 countries, calculating the average values over the period 1999 to 2007.2

The baseline regression to analyze the effect of inequality on the SE ratio follows Chong

and Gradstein (2007):

i i iSE Ineq X 0 1 with i= 1,…, 118 (6)

where SE is the ratio between NOE and the official GDP in the ratio approach (

NOE off

i iGdp Gdp ) or the level of unobserved GDP per capita in the separate approach (

NOE

iGdp ).

As a robustness check, we employ different model specifications and alternative indicators

of the SE, inequality and institutional quality.

Measurement errors, sample bias and endogeneity are the most relevant concerns for the

empirical literature on this topic. In the following, we explain how we address these issues.

As concerns the measurement issues - probably the most puzzling topic regarding the

study of the SE - we utilize different sources of estimates of both SE and inequality

indexes. In particular, the regressions include as dependent variable the estimates of the

SE obtained by the MIMIC approach ( NOE off

Mimic PPPGdp Gdp - Buehn and Schneider, 2012) and

Alm and Embaye’s (2013) estimates based on the currency demand approach (

NOE off

Curr constGdp Gdp ). With reference to the proxies of income distribution (Ineq), we utilize the

Gini index (Gini), the income share ratios of the top to the bottom, both quintiles (T20/B20)

2 We also conduct a panel estimation analysis by utilizing both Least Squares Dummy Variable (LSDV) and pooled-OLS estimators. This analysis corroborates the results obtained by cross-sectional models. However, we consider cross-sectional analysis more reliable than the results based on panel analysis because of a lack of data. In particular, the massive presence of missing values in the indexes of inequalities (62 percent of observations are missed) precludes the possibility of specifying LSDV regressions appropriately or to control for endogeneity by a generalized method of moments estimator because these estimators are not suitable for such a small sample size and without a dynamic model specification. As a result, from a theoretical point of view, the use of a cross-sectional analysis based on nine-year averages is a better strategy than a static panel specification to consider both contemporaneous (i.e., direct) and lagged (i.e., indirect) effects of inequality on the SE. Moreover, by utilizing annual averages, we also expect to minimize measurement errors.

14

and deciles (T10/B10) of the population.3 Table 1 summarizes the correlations among the

key variables of this study.

Table 1. Correlation matrix

NOE

Mimic

off

PPP

Gdp

Gdp NOE

MimicGdp off

PPPGdp

NOE

Curr

Off

const

Gdp

Gdp NOE

CurrGdp off

constGdp

Gini Index

Quintile Ratio

Decile Ratio

NOE

Mimic

off

PPP

Gdp

Gdp

1

(118)

NOE

MimicGdp -0.318 1

(0.00;118) (118)

off

PPPGdp -0.603 0.843 1

(0.00;118) (0.00;118) (118) NOE

Curr

Off

const

Gdp

Gdp

0.547 -0.538 -0.653 1

(0.00;85) (0.00;85) (0.00;85) (85)

NOE

CurrGdp -0.556 0.671 0.888 -0.466 1

(0.00;85) (0.00;85) (0.00;85) (0.00;85) (85)

off

constGdp -0.606 0.735 0.970 -0.623 0.914 1

(0.00;118) (0.00;118) (0.00;118) (0.00;85) (0.00;85) (118)

Gini Index 0.336 -0.219 -0.332 0.290 ‒0.212 ‒0.302 1

(0.00;115) (0.02;115) (0.00;115) (0.01;83) (0.05;83) (0.00;115) (115)

Quintile ratio

0.355 -0.064 -0.199 0.205 ‒0.115 ‒0.188 0.892 1

(0.00;114) (0.50;114) (0.03;114) (0.06;82) (0.31;82) (0.05;114) (0.00;114) (114)

Decile ratio

0.350 0.001 0.139 0.154 ‒0.076 ‒0.137 0.776 0.957 1

(0.00;114) (0.99;114) (0.14;114) (0.17;82) (0.50;82) (0.15;114) (0.00;114) (0.00;114) (114)

Note: in parenthesis p-value of H0: rxy=0 and number of observations.

To address the sample bias issue,4 we collected the largest cross-sectional dataset

utilized in this area of research, i.e., 118 and 88 countries by employing estimates based

on the MIMIC and currency demand approaches, respectively.

The third relevant issue for this strand of empirical literature is endogeneity. Considering

that a set of instrumental variables with a suitable coverage of the countries of our sample

is not available for potential endogenous variables, we apply two alternative strategies.

First, we use the observation of potential endogenous control variables in the year before

the period used to estimate the country averages (i.e., 1999-2007). That means utilizing

the values observed in 1998, and if this observation was missed, we employ the first

available observation in the sample period. Second, we replace potential endogenous

control variables with a set of dummies on legal origins of the countries. These variables

3 Overall, by using the income earned by the top 10 percent of households and dividing that by the income earned by the poorest 10 percent of households (decile ratio), we obtain similar results to those shown with quartile ratio (T20/B20). For the sake of brevity, we do not show these results, but they are available upon request. 4 It is reasonable to assume that missing data are more numerous among developing countries. These countries have also a larger SE and more unequal income distribution than developed economies. In this sense, this is a potential source of sample bias in this literature.

15

identify the origin of the Company Law or Commercial Code in each country and are

extracted from Global Development Network Growth Database. They are British legal

origin (LegBrit), French legal origin (LegFren), Socialist legal origin (LegSoc), German

legal origin (LegGer), and Scandinavian legal origin (LegScan). The last one is excluded

as a base category.

Following a consolidated literature, a vector of control variables (X) is included in the

regressions to reduce potential omitted-variables bias. These are5 (logarithm of) official

GDP per capita (Gdpoff), an index of rule of law (Rol), urban population as a percentage of

total population (Urb), proportion of a country's population that is employed (EmplR), share

of taxes on income, profits and capital gains as a percentage of official GDP (TaxI), and a

proxy of tax complexity - hours to prepare and pay taxes - (TaxC);6 to account for the labor

market determinants of the SE, we also include the “vulnerable” employment as a

percentage of total employment (VunE). The definitions and sources of variables are

provided in the appendix.

Conclusively, we carry out a set of tests for residual normality and heteroskedasticity. With

reference to the heteroskedasticity tests, we apply Breusch-Pagan (1979), Godfrey (1978)

and Harvey (1976) tests. For the regressions where at least one of the two

heteroskedasticity tests suggests rejecting the null hypothesis of no heteroskedasticity at

the five percent significant level, White's (1980) estimator is applied to provide consistent

estimates of the coefficient covariances.

4.2 Model specifications and hypotheses

The econometric analysis consists of four steps. The first step of our analysis replicates

the results of the earlier literature. It aims to also validate the outcome of a positive

5 We do not include other potential causes of the SE, such as the growth rate of GDP,

unemployment rate, total tax burden, inflation rate, and regulation burden, because these variables

have been included by both Buehn and Schneider (2012) and Alm and Embaye (2013) in the

equation to estimate the SE. The only exception to this choice is the urbanization rate that is used by

Alm and Embaye (2013) among the controls to estimate the SE ratio. We consider this variable in

the vector of control variables: (1) to avoid the omission of a relevant variable - according to

Kuznets (1955), urbanization followed by industrialization is an important factor in the shift of

inequality; therefore, we include this variable in both regressions of official and unobserved GDP.

However, qualitative results do not change by removing the urbanization rate by regressions with

Alm and Embaye’s estimates; (2) to keep the same model specification among regressions using

both MIMIC and currency estimates of the SE ratio. 6 For the relevance of this variable in the SE, see Schneider and Neck (1993) and Thiessen (2010).

16

correlation between the SE ratio and inequality in our sample. The benchmark

specification regression is

Macro off

i i iSE Ineq Log Gdp X 0 1 2 with i= 1,…, 118 (7)

and the associated hypothesis is as follows:

Hypothesis 1a (Ratio approach) – direct effect on the SE ratio

Ceteris paribus, an increase in income inequality directly increases the SE ratio:

1 0MacroSE Ineq .

Specifically, a one-unit increase in the inequality index increases the SE ratio by 1

percentage points.

In the second step, we estimate two regressions where the dependent variables are the

numerator (GdpUNOE) and the denominator (Gdpoff) of the SE ratio:

0 1 21UNOE off

i i i iLog Gdp Log b Ineq Log Gdp X with i= 1,…, 118 (8)

0 2 1 21off UNOE

i i i iLog Gdp Log b Ineq Log Gdp X with i= 1,…, 118 (9)

where UNOEGdp denotes both the level of unobserved GDP in purchasing power parity per

capita UNOE

MimicGdp when the estimates of the SE are extracted by Buehn and Schneider

(2012) and the level of unobserved GDP in constant 2000 US dollars per capita NOE

CurrGdp

if the source of the SE is Alm and Embaye (2013). This difference in the way to convert the

nominal GDP in real values follows the original unit of measure of GDP employed by the

two cited studies.

As a result of log-transformation and given the small values of the estimated coefficients,

1 and 1 give us an approximation of the change in the SE for a one-unit increase in the

inequality index. The interpretation of the coefficients 2 and 2 is given as an

approximation of the expected percentage change in dependent variable when the official

or unobserved (unrecorded) GDP increases by 1% (i.e., elasticity). In appendix 2, we

report OLS estimates for regression 9 (Tables A.2 and A.3), 10 (Tables A4 and A.5) and

11 (Tables A6. and A7).

In this second step, we check whether the three hypotheses discussed in section 3 are

empirically validated. The validation of these hypotheses should guide the researcher on

applying the separate approach with indirect effects.

17

Hypothesis 1b (Separate approach) – Marginal effect on unobserved unrecorded

GDP

Ceteris paribus, an increase in income inequality (marginally) increases the unobserved

GDP per capita: 1 0UNOE IneqGdp .

Hypothesis 2 (Separate approach) – Marginal effect on official GDP

Ceteris paribus, an increase in income inequality (marginally) decreases official GDP per

capita: 1 0off IneqGdp .

Hypothesis 3(a) – (Test to include Indirect effects) Marginal effect of official on

GdpUNOE

Ceteris paribus, an increase in official GDP (marginally) increases unobserved GDP:

2 0UNOE offGdp Gdp .

Hypothesis 3(b) – Marginal effect of unobserved on official GDP

Ceteris paribus, an increase in GdpUNOE (marginally) increases official GDP:

2 0off UNOEGdp Gdp .

If the hypotheses 3(a) and 3(b) are verified, we calculate, in the third step, the direct and

indirect effects of income inequality on the numerator and denominator of the SEMacro ratio

adjusted for currency demand bias, i.e. multiplying by 1

1 b

. In particular, we substitute

(9) in (8) to obtain the overall effect of inequality on SE, i.e., 1 2 1 2 21NOE

i iGdp Ineq

, and (8) in (9) to get the total effect of inequality on official GDP, i.e.,

1 2 1 2 21off

i iGdp Ineq . As a result, from the ratio of the previous total effects, we

obtain a coefficient that can be compared in a straightforward manner with the (Log-linear

specification) of regression (7) ( 1 - i.e., ratio approach):

1 2 1 1 2 1

UNOE off

i i iGdp Gdp Ineq . Finally, because 2 2 .0001 , then 2 21 is

negligible; therefore, the estimated marginal effects give us an approximation of the direct

effects.

Hypothesis 4 – Direct effect on unobserved unrecorded GDP

Ceteris paribus, an increase in income inequality (directly) increases the unobserved

unrecorded GDP per capita: 1 12 21 0UNOE IneG p qd .

18

Hypothesis 5 – Direct effect on official GDP

Ceteris paribus, an increase in income inequality (directly) decreases official GDP per

capita: 21 121 0off IneqGdp .

Hypothesis 6 – Indirect effect on unobserved unrecorded GDP

Ceteris paribus, an increase in the inequality index indirectly decreases unobserved

unrecorded GDP: 2 2 22 2 21 0UNOE off off IneqGdp Gdp Gdp .

Hypothesis 7 – Indirect effect on official GDP

Ceteris paribus, an increase in the inequality index indirectly increases official GDP:

1 2 2 2 1 21 0off UNOE UNOE IneqGdp Gdp Gdp .

Concerning the signs of the total effects of the inequality on the numerator and

denominator of the SE ratio, they are predicted by the knowledge on the relative size of

the coefficients estimated by the separate regressions. In particular, given that 1 2 1

and 1 2 1 , the direct effects determine the signs of the total effects.

Hypothesis 8 – Total effect on unobserved unrecorded GDP

Ceteris paribus, an increase in the inequality index increases unobserved unrecorded

GDP: 1 1 122 12 21 0UNOE

iid dIneqGdp .

Hypothesis 9 – Total effect on official GDP

Ceteris paribus, an increase in the inequality index decreases official GDP:

1 1 2 22 1 1 21 0o f

i i

fd dp nGd I eq .

Conclusively, in the fourth step, we derive direct, indirect and total effects of inequality on

the SE ratio (i.e., Hp. 10, Hp. 11 and Hp. 12) by considering the variation of both the

numerator (i.e., Hp. 1b; Hp. 3 and Hp. 8) and the denominator (i.e., Hp. 2; Hp. 6 and Hp.

9).

Concerning the issue of the currency demand bias in the SEMacro ratio, we consider two

scenarios i.e., with and without adjustments for currency demand bias. Accordingly, we

modify the sample composition to estimate the averages of official and unobserved GDP

by computing, under the hypothesis of adjustments, the averages only for the countries

with available data on NOE adjustments in the official GDP. In particular, we denote by the

subscript “A” the averages of the GDP calculated over all the 118 countries of the sample,

while we indicate by the superscript “B” the average values of the GDP calculated over the

19

29 countries with available data on adjustments for NOE activities ( b ) (UNECE, 2008).

Precisely, these benchmark values are: $2262NOE

Mimic

A

Gdp ; $3659NOE

Mimic

B

Gdp ;

$1174NOE

Cur

A

rGdp ; $1467NOE

Cur

B

rGdp ;

$8742off

P

A

P PGdp ; $12920offB

PPPGdp ; $5116off

con

A

sGdp ; $6608off

con

B

sGdp ;

25.88%Macro A

MimicSE ;

10.2832 1

Macro B

MimicSE b

;

22.95%Macro A

CurrSE ;

1

0.2219 1Macro B

CurrSE b

and 16.16%b .

Hypothesis 10 – Direct effect on the SE ratio

Ceteris paribus, an increase in the inequality index directly increases the SE ratio.

The rationale for this expectation is that the inequality, on the one hand, directly increases

the SE (Hp. 1b) and on the other hand, it decreases official GDP (Hp. 2). In quantitative

terms, a one-unit increase in the inequality index directly increases the SE ratio by

1 1

1

11

Macro ADir SE

percentage points or if the value of b is available, the change in the SE

ratio adjusted for the currency demand bias is given by

1 11

11 1

Macro B

Dir

adj

SE

b

percentage

points.

Hypothesis 11 – Indirect effect on the SE ratio

Ceteris paribus, an increase in the inequality index indirectly decreases the SE ratio.

Specifically, a one-unit increase in the inequality index indirectly increases the SE ratio by

2 1 1 2

1

1 21

Macro AInd SE

percentage points, or if the value of b is available, the change in the

SE ratio adjusted for the currency demand bias is given by

2 1 1 21

1 21 1

Macro B

Ind

adj

SE

b

percentage points.

Given that hypotheses 10 and 11, we can hypothesize the following:

Hypothesis 12 – Total effect on the SE ratio

Ceteris paribus, an increase in the inequality index increases the SE ratio.

Explicitly, a one-unit increase in the inequality index changes the SE ratio by

1 2 1 2

1

1 2 1

1 1

1

Macro ATot SE

percentage points, or if data on b is available, the change in the

20

SE ratio adjusted for the currency demand bias is given by

1 2 1

1

1 1

11

1 1

Macro B

Tot

adj

SE

b

percentage points.

Conclusively, combining Hp.1a with Hp. 12, we estimate the bias in the marginal effect of

inequality on the SE ratio estimated by the ratio approach. In Table 2, we label this

outcome as follows:

Result: The difference between marginal effect estimated by the ratio approach and total

effect obtained by the separate approach

4.3 Empirical Outcomes

Table 2 sums up the outcomes of the previous hypotheses. We report findings based on

two indexes of inequality, i.e., Gini index and quintile ratio; two sources of the SE

estimates obtained by macro-econometric methods, i.e., MIMIC and currency demand

approach.

Estimated outcomes give robust evidence that hypotheses 1-12 are empirically validated

regardless of whether the coefficients are estimated by the MIMIC model or the currency

demand approach as well as whether indexes of inequality are used.

First, by applying the ratio approach, we validate the standard result that an increase in

inequality increases the SE ratio. Looking at the results based on the MIMIC estimates of

the SE, a one-unit increase in the Gini index increases the SE ratio by 0.87 percent (0.37

percentage points).

Second, by replicating the analysis through the separate approach, we find that a one-unit

increase in the Gini index directly increases the unobserved GDP per capita by 0.67

percent ($ 15 in PPP - Hp. 1b) and (directly) decreases the official GDP by 5.20 percent ($

455 in PPP - Hp. 2). The inclusion of indirect effects is justified by a significant positive

elasticity between the official and unobserved GDP; specifically, we estimate that a one

percent increase in the official (unobserved) GDP increases unobserved (official) GDP by

0.86 (0.90) percent. Indirect effects partially offset direct effects (Hp. 6 and 7) and the total

effect of a one-unit increase in the Gini index increases the numerator by 0.62 percent (

$14UNOEGdp - Hp. 8) and decreases the denominator by 5.2 percent ( $ 453offGdp

).

21

Table 2. Summary of Empirical outcomes

Hypotheses

Estimated coefficients (model)

Gini Quartile ratio Average MIMIC Currency Average MIMIC Currency Average Average

H1a: MacroSE

Ineq

1 0

0.37

{0.87%}a

(1-6)a

0.21

{0.57%}a

(I-VI)a

0.29

{0.72%}a

0.60

{1.62%}a

(1-6)b

0.24

{0.80%}a

(I-IV)b

0.42

{1.21%}a

0.35

{0.96%}a

Marginal (Direct) Effects

H1b(H4): 1 0

UNOEGdp

Ineq

0.67% (1-6)c

1.25% (I-VI)c

0.96% 1.50% (1-6)d

0.50% (I-VI)d

1.00% 0.98%

H2(H5): 1 0

offGdp

Ineq

-5.20%

(1-6)e -1.10% (I-VI)e

-3.15% -2.00% (1-6)f

-1.20% (I-VI)f

-1.60% -2.38%

H3a: 2 0

UNOE

off

Gdp

Gdp

0.86% (1-6)c

0.84% (I-VI)c

0.85% 0.88% (1-6)d

0.88% (I-VI)d

0.88% 0.88%

H3b: 2 0

off

UNOE

Gdp

Gdp

0.90%

(1-6)e 1.11% (I-VI)e

1.01% 0.92% (1-6)f

1.14% (I-VI)f

1.03% 1.60%

Indirect Effects

H6: Ind. Eff. on the 0UNOEGdp -0.04% -0.01% -0.03% -0.02% -0.01% -0.01% -0.02%

H7: Ind. Eff. on the 0offGdp 0.01% 0.01% 0.01% 0.01% 0.01% 0.01% 0.01%

Total effects

H8: Tot. Eff. on the 0UNOEGdp 0.62% 1.24% 0.93% 1.48% 0.49% 0.99% 0.96%

H9: b

Tot. Eff. on the 0offGdp -5.19% -1.09% -3.14% -1.99% -1.19% -1.59% -2.37%

Direct, Indirect and Total Effects on the SE ratio (percentage points)

H10:

;Dir Dir 1 1 0 b

1.60 [1.51]

0.55 [0.45]

1.07 [0.98]

0.92 [0.87]

0.39 [0.33]

0.66 [0.60]

0.87 [0.79]

H11: ;Indir Indir 1 1 0 b -0.01

[-0.01] -0.01

[-0.00] -0.01

[-0.01] -0.01

[-0.01] -0.00

[-0.00] -0.01

[-0.01] -0.01

[-0.01]

H12: ;Tot Tot 1 1 0 b

1.59

[1.50] {6.13%}

0.54 [0.45]

{2.35%}

1.06 [0.97]

{4.24%}

0.92 [0.86]

{3.54%}

0.39 [0.33]

{1.70%}

0.65 [0.59]

{2.62%}

0.86 [0.78]

{3.43%}

Bias of the estimated effect by ratio approach (percentage points)

Result: 1 1 0Tot

-1.22

[-1.13] -0.33

[-0.24] -0.77

[-0.68] -0.32

[-0.26] -0.15

[-0.09] -0.23

[-0.17] -0.50

[-0.43]

Notes: In curly brackets, we report the expected percentage change in SE ratio for a unit increase in Inequality. a It is obtained by Log-linear specifications of the eq. (8). Details on these regressions are available upon request. . b In square bracket, we report the adjusted effects for the currency demand bias.

Third, the direct and total effect of a change in the inequality index on the SE ratio is higher

than the estimated effect obtained by the ratio approach. In quantitative terms, we find that

the marginal effect estimated by the ratio approach is significantly biased downward

respect to the total effect estimated by the separate approach. In detail, a one-unit

increase in the Gini index increases the SE ratio by 1.50 percentage points (6.1 percent),

applying the separate approach, instead of 0.37 percentage points (0.87 percent) following

the ratio approach.

22

From a methodological perspective, we realize that the separate approach, in addition to

an unbiased estimate of the effect of a determinant on SE ratio, may be helpful in terms of

the analysis of policy implications. It is due to the fact that its property to provide a

disentangled view of the effects and mechanisms of transmission between the potential

determinant and the SE. A normative analysis of the implications of this proposition is

beyond the scope of this paper but as an illustrative example, we simulate the effects of a

public policy that generates, ceteris paribus, an increase of one-unit in the Gini index. We

consider three economies, among the countries for which the shares of NOE adjustments

in official statistics are available from (UNECE 2008, Tab. 1), as indicative of low (Sweden,

MacroSE 18.8%), medium (Italy, MacroSE 27%) and high (Mexico, MacroSE 44.5%), levels of the

SE. Table 3 reports the estimated monetary effects.

Table 3. Simulated effects of a one-unit change in the Gini index (Sweden, Italy and

Mexico)

MIMIC Approach Currency Demand Approach

Var. Baseline (PPP $)

Direct Effect

Indirect Effect

Total Effect

Baseline (Const. $)

Direct Effect

Indirect Effect

Total Effect

Sw

ed

en

b

=0

.013

;Gin

i=2

6.8

GdpUNOE

$ 5,705 $ 38.0 $ -2.5 $ 35.5 $ 3,646 $ 46.5 $ -0.3 $ 46.2

Gdpoff

$ 30,813 $ -1,602 $ 1.9 $ -1,600 $ 29,050 $ -319.6 $ 4.0 $ -315.5

GdpRNOE

$ 401 378 Macro

adjSE 18.5% 19.7% 18.5% 19.7% 12.5% 12.85% 12.55% 12.84%

MacroSE 18.8% 12.7%

, ,

1

Dir Ind Tot 1.15% -0.01% 1.14% 0.30% 0.00% 0.30%

Italy

b=

0.1

67; G

ini=

36

.6 GdpUNOE

$ 6,539 $ 43.6 $ -2.9 $ 40.7 $ 3,525 $ 51.5 $ -0.4 $ 51.1

Gdpoff $ 28,241 $ -1,469 $ 1.7 $ -1,467 $ 19,449 $ -213.9 $ 2.7 $ -211.2

GdpRNOE $ 4,716 $ 3,248

Macro

adjSE 23.2% 24.6% 23.1% 24.6% 18.1% 18.55% 18.12% 18.55%

MacroSE 27.0% 21.2%

, ,

1

Dir Ind Tot 1.43% -0.01% 1.42% 0.43% 0.00% 0.43%

Me

xic

o

b=

0.1

21; G

ini=

49

.4

GdpUNOE $ 4,555 $ 30.4 $ -2.0 $ 28.3 $ 1,698 $ 23.8 $ -0.2 $ 23.6

Gdpoff $ 11,486 $ -597 $ 0.7 $ -597 $ 5,975 $ -65.7 $ 0.8 $ -64.9

GdpRNOE $ 1,390 723 Macro

adjSE 39.7% 42.1% 39.6% 42.1% 28.4% 29.09% 28.41% 29.08%

MacroSE 44.5% 31.9%

, ,

1

Dir Ind Tot 2.45% -0.02% 2.43% 0.68% -0.01% 0.67%

The simulated output shows that a rise of income inequality increases the SE ratio mainly

because it reduces the denominator. As result, we could evaluate this policy as worsening

23

in terms of welfare principally for losses in the official economy rather than for a boost in

the SE. Conclusively, this simulation emphasizes also that in terms of policy analysis, the

separate approach provides greater and useful information about the effects of a

determinant on the SE than those obtainable estimating the marginal effect by the ratio

approach.

5 Conclusions

The paper has two main aims: to propose some methodological insights on empirical

research on the SE, and by using a separate approach, estimate the relationship between

income distribution and the SE.

From a methodological perspective, we demonstrate that analyzing the effect of a

determinant utilizing the SE ratio as a dependent variable may be misleading. That is, we

suggest disentangling the effects of inequality on the SE ratio by estimating both the direct

and indirect effects on the numerator and denominator separately. Furthermore, we

propose (i) a definition of the SE consistent with both macro-econometric and SNA

approaches and (ii) a method to correct the bias of the estimated effect of any potential

determinant of the unobserved economy due to the currency demand bias in the

estimation of the numerator of the SE ratio.

In the second part of the paper, we apply the proposed separate approach. The

econometric analysis is conducted through a worldwide cross-section. We address the

common weaknesses in this strand of the literature (i.e., sample bias, measurement errors

in both the estimates of the SE and inequality indexes, and endogeneity issue by (i)

collecting the widest cross-countries analysis in this field of the literature; (ii) utilizing

annual averages based on nine-year averages to minimize measurement errors; (iii)

testing robustness of outcomes with alternative indexes of both the SE and inequality; and

(iv) controlling the estimates by ancillary regressions based only on exogenous

explanatory variables. Despite this, our findings should be treated with some caution

because of the intrinsic measurement issues in the SE estimates and the potential reverse

causation between income inequality and official and/or unobserved GDP. Concerning the

latter, the major problem is simply that of obtaining a suitable set of instrumental variables

or obtaining panel data with an adequate sample size for a worldwide analysis is currently

unavailable. Accordingly, further investigations on the consequences of endogeneity are

required before empirical results can be conclusively validated.

24

From a positive viewpoint, the actual overall effect of inequality on the SE is

underestimated by the ratio approach. Specifically, we find that the higher is the equality of

income, the lower is the SE, both in the absolute level and in terms of the ratio. In

particular, depending on the SE proxy, a one-unit increase in the inequality index

increases the SE ratio by 2.4 percent (currency demand approach) and 6.1 percent

(MIMIC approach). For instance, an increase in income inequality measured by the Gini

coefficient from German levels (30.9) to US levels (40.8) is expected to increase the

relative size of the German SE by between 23.5 percent (Currency demand – from 12.7 to

15.6 percent) and 60.7 percent (MIMIC – from 16 to 25.7 percent).

In conclusion, we believe that the use of the proposed separate approach is helpful in

empirical research on the determinant of the SE.

References

Adam, M., & Ginsburgh, V. (1985). The Effects of Irregular Markets on Macroeconomic

Policy: Some Estimates for Belgium. European Economic Review, 29(1), 15-33.

Ahmed, E., Rosser, J. B. Jr., & Rosser M. V. (2007). Income inequality, corruption, and the

Non-Observed Economy: a global perspective. (Ed. by Salzano M. and Colander

D.) Complexity Hints for Economic Policy. Book Series New Economic Windows,

Springer Milan.

Alesina, A., & Perotti, R. (1996). Income distribution, political instability, and investment.

European Economic Review, 40, 1203-1228.

Alm, J., & Embaye, A. (2013). Using Dynamic Panel Methods to Estimate Shadow

Economies Around the World, 1990-2006. Public Finance Review, 41(5), 510-543.

Amendola, A., & Dell’Anno, R. (2015). Social Exclusion and economic growth: an empirical

investigation in European economies. Review of Income and Wealth. 61(2), 274-

301.

Bagachwa, M. S. D., & Naho, A. (1995). Estimating the second economy in Tanzania.

World Development, 23(8), 1387-1399.

Becker, G. S., Murphy, K. M., & Tamura, R. (1990). Human capital, Fertility and Economic

Growth. Journal of Political Economy, 98, 12-37.

Bhattacharyya, D. K. (1999). On the Economic Rationale of Estimating the Hidden

Economy. Economic Journal, 109(456), 348-359.

25

Bourguignon, F. (1999). Crime, violence and inequitable development, in B. Pleskovic and

J.E. Stiglitz, ed., Annual World Bank Conference on Development Economics, 199-

220, Washington, DC: The World Bank.

Bovi, M., & Dell’Anno, R., (2010). The Changing Nature of the OECD Shadow Economy.

Journal of Evolutionary Economics, 20(1), 19-48.

Breusch, T.S., & Pagan, A.R. (1979). A Simple Test for Heteroscedasticity and Random

Coefficient Variation. Econometrica, 47, 1287–1294

Buehn, A., & Schneider, F. (2012). Shadow economies around the world: novel insights,

accepted knowledge, and new estimates. International Tax and Public Finance,

19(1), 139–171.

Chong, A., & Gradstein, M. (2007). Inequality and informality. Journal of Public Economics

91, 159–179.

Dell’Anno, R. (2008). What is the relationship between Unofficial and Official Economy?

An analysis in Latin American Countries. European Journal of Economics, Finance

and Administrative, 12, 185-203.

Eilat, Y., & Zinnes, C., (2002). The Shadow Economy in Transition Countries: Friend or

Foe? A Policy Perspective. World Development, 30(7), 1233-1254.

Eurostat (2005). Eurostat’s Tabular Approach to Exhaustiveness Guidelines, 5th meeting of

the GNI committee, 5-6 July 2005. Eurostat/C1/GNIC/050 EN.

Feige, E. (1990). Defining and Estimating Underground and Informal Economies: The New

Institutional Economics Approach. World Development, 18(7), 989-1002.

Feige, E. L., & Urban, I., (2008). Measuring underground (unobserved, non-observed,

unrecorded) economies in transition countries: Can we trust GDP?. Journal of

Comparative Economics 36(2), 287-306.

Friedman, E., Johnson, S., Kaufmann, D., & Zoido-Lobaton, P. (2000). Dodging the

Grabbing Hand: The Determinants of Unofficial Activity in 69 Countries. Journal of

Public Economics, 76, 459-494.

Galor, O., & Zeira, J. (1993). Income distribution and macroeconomics. Review of

Economic Studies, 60, 35-52.

Godfrey, L. G. (1978). Testing for Multiplicative Heteroscedasticity. Journal of

Econometrics, 8, 227–236.

Harvey, A. C. (1976). Estimating Regression Models with Multiplicative Heteroscedasticity,

Econometrica, 44, 461–465.

26

Hatipoglu O., & Ozbek, G. (2011). On the political economy of the informal sector and

income redistribution, European Journal of Law and Economics, 32, 69-87.

Kuh, E., & Meyer, J. R. (1995). Correlation and regression estimates when the data are

ratios. Econometrica, 23, 400-416.

Kuznets, S. (1955). Economic Growth and Income Inequality. American Economic Review,

45, 1-28

Loayza, N., & Rigolini, I. (2011). Informal Employment: Safety Net or Growth Engine?.

World Development, 39(9), 1503-1515.

Moser, C. N. (1978). Informal sector or petty commodity production: Dualism or

independence in urban development, World Development, 6, 1041-1064.

Murphy, K. M., Shleifer, A., & Vishny, R. (1989). Income Distribution, Market Size and

Industrialization. Quarterly Journal of Economics, 104, 537-564.

OECD - Organisation for Economic Co-operation and Development (2014), Statistics Brief,

June No. 18, OECD Statistics Directorate,

(http://www.oecd.org/std/thestatisticsbrief.htm).

Pearson, K. (1897). On a form of spurious correlation which may arise when indices are

used in the measurement of organs. Proceedings of the Royal Society of London,

60, 489-498.

Persson, T., & Tabellini, G. (1994). Is inequality harmful for growth?. American Economic

Review, 84, 600-621.

Rosser, J. B. Jr., Rosser, M. V., & Ahmed, E. (2000). Income Inequality and the Informal

Economy in Transition Economies. Journal of Comparative Economics, 28, 156–

171.

Rosser, J. B. Jr., Rosser, M. V., & Ahmed, E. (2003). Multiple unofficial economy equilibria

and income distribution dynamics in systemic transition. Journal of Post Keynesian

Economics 25, 425-47.

Schneider, F., & Neck R. (1993). The Development of the Shadow Economy under

Changing Tax Systems and Structures, Finanzarchiv, 50(3), 344–369.

Schneider, F. (2005). Shadow economies around the world: what do we really know?.

European Journal of Political Economy, 21, 598-642.

Schneider, F. (2007). Shadow economies and corruption all over the world: new estimates

for 145 countries. Economics E-Journal, 2007–9, July.

27

Schneider, F. (eds.), (2011). Handbook on the Shadow Economy. Cheltenham (UK),

Edward Elgar Publishing Company.

Schneider, F., & Enste, D. H., (2000). Shadow Economies: Size, Causes and

Consequences. Journal of Economic Literature, 38, 73-110.

Smith, J. D. (1984). Market Motives in the Informal Economy. In: Gaertner, N., & Wenig,

W., (eds). The Economics of the Shadow Economy, edited by, 166–77. Heidelberg,

Germany: Springer.

Tedds, L. M. (2005). The Underground Economy in Canada. In: Bajada, C., & Schneider,

F. (eds.) Size, Causes and Consequences of the Underground Economy. Ashgate

Publishing: UK.

Thiessen, U. (2010). The Shadow Economy in International Comparison: Options for

Economic Policy Derived from an OECD Panel Analysis. International Economic

Journal, 24(4), 481-509.

Tokman, V. E. (1978). An exploration into the nature of the informal-formal sector

relationship. World Development, 6 (9/10), 1065-1075.

UNECE - United Nations Economic Commission for Europe (2008), Non-Observed

Economy in National Accounts – Survey of Country Practices (2008), United

Nations Publication, ISSN: 0069-

8458.www.unece.org/fileadmin/DAM/stats/publications/NOE2008.pdf

Valentini, E. (2009). Underground economy, evasion and inequality. International

Economic Journal, 23(2), 281-290.

White, H. (1980). A Heteroskedasticity-Consistent Covariance Matrix and a Direct Test for

Heteroskedasticity, Econometrica, 48, 817–838.

Yule, G.Y. (1910). On the interpretation of correlation between indices or ratios. Journal of

the Royal Statistical Society, 73, 644-647.

28

Appendix 1 - Table A.1 - Data sources Var. Definition Data Source [code] Mean Max Min Obs

NOE

MimicGdp (Total) NOE per capita, PPP (constant 2005 international $). It is calculated by dividing Buehn and Schneider (2012) estimates by 100 and multiplying for official GDP per capita, PPP constant 2005 international $.

Buehn and Schneider (2012) – Table 3 * 0.01

*[NY.GDP.PCAP.PP.KD] 2262 12675 131.7 118

off

PPPGdp Official GDP per capita, PPP (constant 2005 international $) WDI – World Bank

[NY.GDP.PCAP.PP.KD] 8742 65224 283.5 118

NOE

CurrGdp (Total) NOE per capita (in constant 2000 US dollars). It is calculated by dividing Alm and Embaye’s (2013) estimates by 100 and multiplying for official GDP per capita, in constant 2000 US dollars.

Alm and Embaye (2013) * 0.01 * [NY.GDP.PCAP.KD]

1174 10997 40.9 85

off

constGdp Official GDP per capita (in constant 2000 US dollars). WDI 2008– World Bank

[NY.GDP.PCAP.KD] 5116 48818 86.0 118

Gini

Gini index measures the extent to which the distribution of income (or, in some cases, consumption expenditure) among individuals or households within an economy deviates from a perfectly equal distribution. Gini index of 0 represents perfect equality, while an index of 100 implies perfect inequality.

WDI – World Bank [SI.POV.GINI]

40.7 64.3 21.1 115

T20/B20 Income share held by highest 20%/ Income share held by lowest 20% WDI – World Bank

[SI.DST.05TH.20/SI.DST.FRST.20] 9.51 39.1 3.07 114

T10/ B10 Income share held by highest 10%/ Income share held by lowest 10% WDI – World Bank

[SI.DST.10TH.10/SI.DST.FRST.10] 19.47 143 4.25 114

Rol

Rule of Law: Estimate. It captures perceptions of the extent to which agents have confidence in and abide by the rules of society, and in particular the quality of contract enforcement, property rights, the police, and the courts, as well as the likelihood of crime and violence. Higher index means better institutional quality.

WGI – World Bank http://info.worldbank.org/governa

nce/wgi/index.aspx#home -0.21 1.94 -1.69 118

Urb Urban population (% of total). Urban population refers to people living in urban areas as defined by national statistical offices.

WDI - World Bank [SP.URB.TOTL.IN.ZS]

51.26 97.3 8.93 118

EmpR Employment to population ratio, 15+, total (%). It is the proportion of a country's population that is employed . Ages 15 and older are generally considered the working-age population.

WDI - World Bank [SL.EMP.TOTL.SP.ZS]

58.91 85.7 33.6 117

TaxI Taxes on income, profits, and capital gains are levied on the actual or presumptive net income of individuals, on the profits of corporations and enterprises, and on capital gains, whether realized or not, on land, securities, and other assets. (current LCU) divided to GDP (current LCU)

WDI- World Bank [100*GC.TAX.YPKG.CN]/

NY.GDP.MKTP.CN 4.40 20.5 0.00 118

TaxC

Time to prepare and pay taxes (hours). Time to prepare and pay taxes is the time, in hours per year, it takes to prepare, file, and pay (or withhold) three major types of taxes: the corporate income tax, the value added or sales tax, and labor taxes, including payroll taxes and social security contributions.

WDI - World Bank [IC.TAX.DURS]

384.1 2600 0.00 118

VulE Vulnerable employment is unpaid family workers and own-account workers as a percentage of total employment.

WDI - World Bank [SL.EMP.VULN.ZS]

45.61 94.6 0.40 96

LegBrit legal origin: British GDN Growth Database. Available from:

www.sscnet.ucla.edu/polisci /faculty/treisman/Papers/what_ha

ve_we_learned_data.xls

0.194 1 0 103

LegFren legal origin: French 0.524 1 0 103

LegSoc legal origin: Socialist 0.223 1 0 103

LegGer legal origin: German 0.049 1 0 103

LegScan legal origin: Scandinavian 0.010 1 0 104

29

For regressions that include the estimates of the SE calculated by the MIMIC (Currency

ratio) approach, the countries in the sample are 118 (88 – the excluded countries are

underlined): Albania, Angola, Argentina, Armenia, Austria, Azerbaijan, Bangladesh,

Belarus, Belgium, Benin, Bhutan, Bolivia, Bosnia and Herzegovina, Brazil, Bulgaria,

Burkina Faso, Burundi, Cambodia, Cameroon, Canada, Cape Verde, Central African

Republic, Chad, Chile, China, Colombia, Comoros, Congo Dem. Rep., Congo Rep., Costa

Rica, Cote d'Ivoire, Croatia, Dominican Republic, Ecuador, Egypt Arab Rep., El Salvador,

Estonia, Ethiopia, Finland, Gabon, Gambia, Georgia, Germany, Ghana, Greece,

Guatemala, Guinea, Guinea-Bissau, Haiti, Honduras, Hungary, India, Indonesia, Iran,

Ireland, Israel, Italy, Jamaica, Kazakhstan, Kenya, Kyrgyz Rep., Lao PDR, Latvia, Lesotho,

Liberia, Lithuania, Luxembourg, Macedonia, Madagascar, Malawi, Malaysia, Maldives,

Mali, Mauritania, Mexico, Moldova, Mongolia, Morocco, Mozambique, Nepal, Nicaragua,

Niger, Nigeria, Norway, Pakistan, Panama, Paraguay, Peru, Philippines, Poland, Qatar,

Romania, Russian Federation, Rwanda, Senegal, Sierra Leone, Slovenia, South Africa,

Spain, Sri Lanka, Swaziland, Sweden, Switzerland, Syrian Arab Republic, Tajikistan,

Tanzania, Thailand, Togo, Tunisia, Turkey, Uganda, Ukraine, United States, Uruguay,

Venezuela, Vietnam, Yemen, Zambia.

Values of variables are calculated as the average of available observations over the period

1999-2007 with exclusion of the averages based on the estimates of the SE calculated by

currency demand approach. Given that Alm and Embaye (2013) report the estimates of

the SE up to the 2006, for official and unobserved GDP based on the currency approach

the averages are based on eight annual observations.

30

Appendix 2 – Estimated Coefficients

The following tables report estimated models with two different measures of the SE (i.e.

MIMIC and Currency demand) and income inequality (i.e. Gini, T20/B20).

Table A2. Dependent variable: unobserved unrecorded GDP as percentage of official GDP

MIMIC Approach Currency Ratio Approach 1a 2a 3a 4a 5a 6a Ia IIa IIIa IVa Va VIa Gini 0.31

** 0.34

* 0.34

** -- -- -- 0.19

** 0.30

*** 0.20

** -- -- --

Gini98 -- -- 0.36***

0.42***

0.42***

-- -- 0.14 0.23** 0.17

*

Log(Gdpoff

)a -3.68

** -3.39

-3.69

*** -- -- -- -3.09

*** -4.60

*** -3.92

*** -- -- --

Log(Gdpoff

)98 -- -- -- -3.38** -3.73 -3.60

*** -- -- -- -2.75

*** -3.57

*** -3.83

***

Rol -1.05

-- -- -- -- -- -1.42

-- -- -- -- --

Rol98 -- -- -- -1.61

-1.19 -- -- -- -- -2.06**

-2.16*

--

Urb -- 0.14 -- -- -- -- -- 0.08 -- -- -- --

Urb98 -- -- -- -- 0.12 -- -- -- -- -- 0.07* --

EmplR -- 0.04 -- -- -- -- -- -0.09 -- -- -- --

EmplR98 -- -- -- -- 0.11 -- -- -- -- -- -0.04 --

TaxI -- -0.81** -- -- -- -- -- 0.08 -- -- -- --

TaxI98 -- -- -- -- -0.83***

-- -- -- -- -- 0.35 --

VunE -- 0.06

-- -- -- -- -- -0.01

-- -- -- --

VunE98 -- -- -- -- -0.01

-- -- -- -- -- -0.01

--

TaxC -- 0.001 -- -- -- -- -- -0.00 -- -- -- --

LegBrit -- -- 1.03 -- -- 2.59 -- -- 12.95***

-- -- 13.09***

LegFren -- -- -2.05 -- -- -0.91 -- -- 10.33***

-- -- 10.32***

LegSoc -- -- -3.02

-- -- -1.88 -- -- 10.52***

-- -- 10.01***

LegGer -- -- -4.98* -- -- -3.12 -- -- 12.57

*** -- -- 12.36

***

Constant 43.23***

41.35*

54.25***

48.10***

40.59*

48.70***

47.05***

55.48***

41.66***

46.01***

46.35***

41.72***

Obs. 115 93 100 115 84 100 83 70 73 83 64 73

R2-adjust. 0.264 0.294 0.247 0.302 0.435 0.277 0.428 0.488 0.441 0.410 0.462 0.410

Het. Test1 b 0.169 0.067 0.815 0.168 0.038 0.761 0.919 0.422 0.728 0. 880 0.149 0.832

Het. Test2 c 0.424 0.012 0.000 0.811 0.132 0.000 0.717 0.275 0.000 0.995 0.119 0.000

Norm.Testd 0.040 0.439 0.037 0.158 0.055 0.279 0.483 0.734 0.375 0.672 0.487 0.616

Notes: ***

Denotes significant at 1% level; **Denotes significant at 5% level;

*Denotes significant at 10% level.

The numbers in parenthesis are the t-ratios. The p-value of F-test is equal to 0.000 for all the regressions.

aFor the SE estimates based on the MIMIC approach Gdp

off is the GDP per capita at PPP; for the SE

estimates based on the currency demand approach, Gdpoff

is GDP per capita at constant US dollars; bBreusch-Pagan (1979) and Godfrey (1978) Lagrange multiplier test where the null hypothesis is of no

heteroskedasticity. We report the p-value of F-statistic. cHarvey (1976) Test where the null hypothesis is of

no heteroskedasticity; the p-values of F-statistic are reported. dJarque-Bera Test, (p-value) the reported p-

value is the probability that a Jarque-Bera statistic exceeds (in absolute value) the observed value under the

null hypothesis. Therefore, a small probability value leads to rejection of the null hypothesis of a normal

distribution.

31

Table A.3. Dependent variables: unobserved unrecorded GDP as percentage of official GDP MIMIC Approach Currency Ratio Approach 1b 2b 3b 4b 5b 6b Ib IIb IIIb IVb Vb VIb T20/B20 0.59

** 0.64

*** 0.68

*** -- -- -- 0.27

** 0.30

** 0.27

** -- -- --

T20/B20_98 -- -- -- 0.52***

0.50***

0.65***

-- -- -- 0.18* 0.18

* 0.22

*

Log(Gdpoff

)a

-3.92

*** -3.44

-4.04***

-- -- -- -3.23***

-5.05***

-4.16***

-- -- --

Log(Gdpoff

)98 -- -- -- -3.76***

-4.34** -4.16

*** -- -- -- -2.81

*** -3.57

*** -3.92

***

Rol -1.15

-- -- -- -- -- -1.59

-- -- -- -- --

Rol98 -- -- -- -1.80**

-2.16** -- -- -- -- -2.22

** -2.81

** --

Urb -- 0.13 -- -- -- -- -- 0.12* -- -- -- --

Urb98 -- -- -- -- 0.13 -- -- -- -- -- 0.08 --

EmplR -- 0.03 -- -- -- -- -- -0.08 -- -- -- --

EmplR98 -- -- -- -- 0.15 -- -- -- -- -- -0.02 --

TaxI -- -0.84** -- -- -- -- -- -0.002 -- -- -- --

TaxI98 -- -- -- -- -0.62* -- -- -- -- -- 0.38 --

VunE -- 0.07

-- -- -- -- -- -0.001

-- -- -- --

VunE98 -- -- -- -- -0.02

-- -- -- -- -- -0.004

--

TaxC -- -0.001 -- -- -- -- -- -0.001 -- -- -- --

LegBrit -- -- 0.80 -- -- 2.65 -- -- 12.60***

-- -- 12.80***

LegFren -- -- -3.27** -- -- -2.13 -- -- 9.76

*** -- -- 9.69

***

LegSoc -- -- -3.60

-- -- -2.48 -- -- 9.03***

-- -- 9.46***

LegGer -- -- -5.24** -- -- -3.56 -- -- 11.96

*** -- -- 11.70

***

Constant 62.48***

51.04**

65.40***

60.67***

53.99***

64.47***

52.91***

66.81***

49.54***

50.31***

51.17***

48.19***

Obs. 114 92 99 115 84 100 82 69 72 83 64 73

R2-adjust. 0.281 0.339 0.323 0.356 0.453 0.323 0.449 0.472 0.477 0.438 0.584 0.417

Het. Test1 b 0.447 0.178 0.723 0.433 0.090 0.740 0.949 0.404 0.773 0.127 0.127 0.925

Het. Test2 c 0.618 0.149 0.000 0.685 0.532 0.000 0.977 0.274 0.000 0.068 0.068 0.000

Norm.Testd 0.187 0.597 0.118 0.256 0.723 0.367 0.676 0.965 0.430 0.887 0.392 0.886

See notes of Table A.2.

Table A.4. Dependent variable: Logarithm of unobserved unrecorded GDP per capita MIMIC Approach Currency Ratio Approach 1c 2c 3c 4c 5c 6c Ic IIc IIIc IVc Vc VIc Gini 0.01

** 0.01

*** 0.01

** -- -- -- 0.007

** 0.011

*** 0.007

* -- -- --

Gini98 -- -- -- 0.006 0.009** 0.007 -- -- -- 0.001 0.005

* -0.00

Log(Gdpoff

)a 0.88

*** 0.85

*** 0.87

*** -- -- -- 0.88

*** 0.81

*** 0.85

*** -- -- --

Log(Gdpoff

)98 -- -- -- 0.87***

0.82***

0.87***

-- -- -- 0.86***

0.78***

0.85***

Rol -0.07

-- -- -- -- -- -0.03

-- -- -- -- --

Rol98 -- -- -- -0.05

-0.07 -- -- -- -- 0.00

-0.03 --

Urb -- 0.00 -- -- -- -- -- 0.002 -- -- -- --

Urb98 -- -- -- -- 0.00 -- -- -- -- -- 0.003 --

EmplR -- -0.001 -- -- -- -- -- -0.003 -- -- -- --

EmplR98 -- -- -- -- 0.00 -- -- -- -- -- -0.002 --

TaxI -- -0.02** -- -- -- -- -- -0.002 -- -- -- --

TaxI98 -- -- -- -- -0.03** -- -- -- -- -- 0.004 --

VunE -- 0.00

-- -- -- -- -- -0.002

-- -- -- --

VunE98 -- -- -- -- -0.004 -- -- -- -- -- -0.005**

--

TaxC -- 0.00 -- -- -- -- -- 0.00 -- -- -- --

LegBrit -- -- 0.08 -- -- 0.10 -- -- 0.40***

-- -- 0.38***

LegFren -- -- -0.06 -- -- -0.04 -- -- 0.33***

-- -- 0.33***

LegSoc -- -- -0.10

-- -- -0.02

-- -- 0.34***

-- -- 0.37***

LegGer -- -- -0.15 -- -- -0.12 -- -- 0.37***

-- -- 0.34**

Constant -0.50 -0.44

-0.42

-0.45

-0.36

-0.15

-0.58***

-0.12

-0.76***

-0.08

0.53

-0.32

Obs. 115 93 100 115 84 100 83 70 73 83 64 73

R2-adjust. 0.904 0.941 0.929 0.885 0.909 0.893 0.965 0.975 0.964 0.959 0.972 0.958

Het. Test1b 0.038 0.121 0.211 0.056 0.039 0.086 0.339 0.003 0.839 0. 300 0.000 0.301

Het. Test2c 0.622 0.404 0.000 0.407 0.348 0.000 0.607 0.710 0.000 0.041 0.082 0.000

Norm.Testd 0.055 0.000 0.006 0.333 0.000 0.305 0.000 0.815 0.000 0.142 0.979 0.085

See notes of Table A.2.

32

Table A.5. Dependent variable: Logarithm of unobserved unrecorded GDP per capita MIMIC Approach Currency Ratio Approach 1d 2d 3d 4d 5d 6d Id IId IIId IVd Vd VId T20/B20 0.02

*** 0.02

*** 0.02

*** -- -- -- 0.01

** 0.01

** 0.01

** -- -- --

T20/B20_98 -- -- -- 0.01** 0.01

** 0.01

*** -- -- -- 0.00 0.00 0.00

Log(Gdpoff

)a 0.87

*** 0.84

*** 0.86

*** -- -- -- 0.87

*** 0.80

*** 0.85

*** -- -- --

Log(Gdpoff

)98 -- -- -- 0.86***

0.81***

0.86***

-- -- -- 0.86***

0.77***

0.85***

Rol -0.08*

-- -- -- -- -- -0.04 -- -- -- -- --

Rol98 -- -- -- -0.05

-0.09 -- -- -- -- 0.00

-0.04

--

Urb -- 0.00 -- -- -- -- -- 0.004* -- -- -- --

Urb98 -- -- -- -- 0.00 -- -- -- -- -- 0.00 --

EmplR -- -0.00 -- -- -- -- -- -0.01 -- -- -- --

EmplR98 -- -- -- -- 0.00 -- -- -- -- -- -0.00 --

TaxI -- -0.02** -- -- -- -- -- -0.00 -- -- -- --

TaxI98 -- -- -- -- -0.02* -- -- -- -- -- 0.00 --

VunE -- 0.00

-- -- -- -- -- -0.00

-- -- -- --

VunE98 -- -- -- -- -0.00 -- -- -- -- -- -0.004**

--

TaxC -- 0.00 -- -- -- -- -- 0.00 -- -- -- --

LegBrit -- -- 0.07 -- -- 0.12 -- -- 0.39 -- -- 0.39***

LegFren -- -- -0.10 -- -- -0.05 -- -- -0.31 -- -- 0.33***

LegSoc -- -- -0.13

-- -- -0.01 -- -- 0.29

-- -- 0.39***

LegGer -- -- -0.16 -- -- -0.11 -- -- 0.35 -- -- 0.36**

Constant -0.21

-0.01

-0.04

0.04

0.64

0.06 -0.35**

0.25

-0.48**

-0.07

0.63

-0.37***

Obs. 114 92 99 115 84 100 82 69 72 83 64 73

R2-adjust. 0.909 0.911 0.916 0.890 0.910 0.890 0.967 0.967 0.966 0.959 0.972 0.958

Het. Test1b 0.068 0.147 0.158 0.137 0.211 0.102 0.230 0.013 0.898 0. 132 0.000 0.238

Het. Test2c 0.268 0.331 0.000 0.801 0.509 0.029 0.937 0.704 0.198 0.305 0.053 0.006

Norm.Testd 0.083 0.000 0.024 0.001 0.004 0.447 0.002 0.466 0.000 0.000 0.962 0.099

See notes of Table A.2.

Tables A.6. Dependent variable: Logarithm of official GDP per capita Official GDP per capita, PPP Official GDP per capita, constant US $ 1e 2e 3e 4e 5e 6e Ie IIe IIIe IVe Ve VIe

Gini -0.01** -0.01

** -0.01** -- -- -- -0.01

** -0.01

*** -0.01

* -- -- --

Gini98 -- -- -- -0.02***

-0.02***

-0.02***

-- -- -- -0.01***

-0.01* -0.02

**

Log(GdpUNOE

)e 0.99

*** 0.63

*** 0.88***

-- -- -- 1.08***

1.02*** 1.19

*** -- -- --

Log(GdpNOE

)98 -- -- -- 0.98***

0.78***

-- -- -- -- 1.05***

1.12***

--

Rol 0.17** 0.11

** 0.12**

-- -- -- 0.09** 0.08 0.05

-- -- --

Rol98 -- -- -- 0.22***

0.20** -- -- -- -- 0.14

** 0.09

*** --

Urb -- 0.01** 0.01

*** -- -- -- -- 0.00 -0.01

* -- -- --

Urb98 -- -- -- -- 0.01**

0.04***

-- -- -- -- -0.00

0.06***

EmplR -- 0.00 -0.00 -- -- -- -- 0.01 0.00 -- -- --

EmplR28 -- -- -- -- -0.00 -- -- -- -- -- -0.00 --

TaxI -- 0.02** -- -- -- -- -- 0.01 -- -- -- --

VunE -- -0.01***

-- -- -- -- -- -0.00 -- -- -- -- TaxC -- -0.00 -- -- -- -- -- -0.00 -- -- -- -- LegBrit -- -- 0.22 -- 0.29

*** 0.84

*** -- -- -0.41 -- -0.43

** 1.09

LegFren -- -- 0.31 -- 0.33***

0.84***

-- -- -0.35 -- -0.43** 1.09

LegSoc -- -- 0.31 -- 0.28***

0.82***

-- -- -0.37 -- -0.33** 1.02

LegGer -- -- 0.43 -- 0.52***

0.80 -- -- -0.35 -- -0.33* 1.15

Constant 1.58***

4.25***

1.85***

2.11***

2.91***

6.26***

0.97***

1.18*** 0.78

*** 1.54

*** 1.42

*** 4.32

***

Obs. 115 93 100 114 99 100 83 70 73 78 67 100

R2-adjust. 0.916 0.947 0.921 0.895 0.900 0.675 0.983 0.976 0.965 0.968 0.966 0.680

Het. Test1b 0.015 0.121 0.474 0.036 0.039 0.313 0.155 0.031 0.962 0.038 0.033 0.194

Het. Test2c 0.278 0.160 0.587 0.031 0.447 0.725 0.115 0.488 0.590 0.052 0.647 0.673

Norm.Testd 0.009 0.123 0.000 0.000 0.000 0.226 0.000 0.431 0.000 0.236 0.000 0.746

See notes of Table A.2. e

For the regressions 1e-6e GdpUNOE

denotes unobserved unrecorded GDP based on the MIMIC approach; For the regressions Ie-VIe , Gdp

UNOE denotes unobserved unrecorded

GDP based on the currency demand approach.

33

Tables A.7. Dependent variable: Logarithm of official GDP per capita

Official GDP per capita, PPP Official GDP per capita, constant US $ 1f 2f 3f 4f 5f 6f If IIf IIIf IVf Vf VIf

T20/B20 -0.02***

-0.02***

-0.02***

-- -- -- -0.01** -0.01

** -- -- -- --

T20/B20_98 -- -- -- -0.02***

-0.02***

-0.02* -- -- -0.01

*** -0.01

*** -0.01

** -0.017

*

Log(GdpUNOE

)f 1.01

*** 0.64

*** 0.90***

-- -- -- 1.09***

1.02*** -- -- -- --

Log(GdpUNOE

)98 -- -- -- 0.99***

0.80***

-- -- -- 1.06***

1.06***

1.21***

--

Rol 0.18** 0.13

** 0.12**

-- -- -- 0.09** 0.10

** -- -- -- --

Rol98 -- -- -- 0.24***

0.22** -- -- -- 0.16

*** 0.16

*** 0.10

** --

Urb -- 0.01** 0.01

*** -- -- -- -- 0.00 -- -- -- --

Urb98 -- -- -- -- 0.01** 0.05

*** -- -- -- -- -0.00

0.06

***

EmplR -- 0.00 -0.00 -- -- -- -- 0.01 -- -- -- --

EmplR28 -- -- -- -- -0.00 -- -- -- -- -- 0.00 --

TaxI -- 0.02** -- -- -- -- -- 0.01 -- -- -- --

VunE -- -0.01***

-- -- -- -- -- -0.00 -- -- -- -- TaxC -- -0.00 -- -- -- -- -- -0.00 -- -- -- -- LegBrit -- -- 0.24 -- 0.34

** 0.99 -- -- -- -- -0.39 1.22

***

LegFren -- -- 0.35 -- 0.41***

0.98 -- -- -- -- -0.38 1.22***

LegSoc -- -- 0.34 -- 0.35***

1.01 -- -- -- -- -0.28 1.18***

LegGer -- -- 0.47 -- 0.61** 1.03 -- -- -- -- -0.025 1.33

**

Constant 1.24***

3.88***

1.35** 1.49

*** 2.20

** 5.17

*** 0.74

*** 0.92

*** 1.16***

1.16***

1.07** 3.41

***

Obs. 114 92 99 114 99 100 82 69 78 78 67 100

R2-adjust. 0.918 0.947 0.925 0.893 0.901 0.665 0.968 0.976 0.977 0.977 0.966 0.670

Het. Test1b 0.039 0.215 0.576 0.025 0.015 0.353 0.160 0.129 0.011 0.011 0.117 0.238

Het. Test2c 0.323 0.060 0.558 0.158 0.000 0.319 0.082 0.001 0.098 0.098 0.905 0.000

Norm.Testd 0.015 0.106 0.000 0.000 0.000 0.351 0.000 0.176 0.000 0.000 0.000 0.597

See notes of Table A.2 and A.6. f For the regressions 1f-6f Gdp

UNOE denotes unobserved unrecorded

GDP based on the MIMIC approach; For the regressions If-VIf , GdpUNOE

denotes unobserved unrecorded GDP based on the currency demand approach.