quaderno di ricerca 4/2015
TRANSCRIPT
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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 [email protected]
Quaderno di Ricerca
4/2015
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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.
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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”.
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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
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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
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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.
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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
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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
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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
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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
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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,
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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.
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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.
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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.
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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.