The Impact of Unemployment Rate on the Size of Romanian Shadow Economy

Abstract

This article estimates the size of the Romanian shadow economy (SE) using the currency demand approach, in order to evaluate if there is any relationship between the SE and unemployment rate (UR). Using Granger causality tests and error correction models, we examine the impact of both registered and International Labour Office unemployment rates (ILO_UR) on the Romanian SE covering the period between 2000Q1 and 2010Q2. We find that the Romanian SE as a percentage of official gross domestic product (GDP) is decreasing over the analyzed period, from 36.5 percent at the end of 2000 to 31.5 of real GDP at the middle of 2010. Our empirical results also support a unidirectional Granger causality that runs from the URs to the SE. The generalized impulse response functions indicate the existence of a short-run negative relationship between URs and the Romanian SE. The empirical results also indicate that there is a positive long-run relationship between both URs and SE, with a 1 percent increase in URs leading to an increase in the SE of 0.36 percent due to the registered unemployment rate and an increase of 2.27 percent due to the ILO_UR.

Keywords

shadow economy currency demand approach unemployment rate Granger causality vector error correction models generalized impulse response functions Romania

The shadow economy (SE) is a controversial topic that has aroused the interest of the specialists at least since the 1960s. Going under various names, the SE exists to some extent in all countries, regardless of their level of development. It is difficult to define the SE, given the diversity of activities that it unites. One commonly used working definition is all currently unregistered economic activities that contribute to the officially calculated (or observed) gross national product (Feige 1989, 1994; Schneider 1994, 2003, 2005; Schneider and Buehn 2007; Schneider, Buehn, and Montenegro 2010). Smith (1994) defines it as “market-based production of goods and services, whether legal or illegal that escapes detection in the official estimates of GDP.” There are of course other possible definitions, including those of the System of National Accounts and the European System of National Accounts. This article addresses the concept of SE as defined by Schneider (2006) and Schneider, Buehn, and Montenegro (2010).

The concept of SE is a generic notion including all market-based legal production of goods and services that are deliberately concealed from public authorities for the following reasons: to avoid payment of income, value added, or other taxes; to avoid payment of social security contributions; to avoid having to meet certain legal labor market standards, such as minimum wages, maximum working hours, or safety standards; or to avoid complying with certain administrative procedures, such as completing statistical questionnaires or other administrative forms. Hence, we do not deal with typical crime activities, which are all illegal actions that fit the characteristics of classical crimes like burglary, robbery, and drug dealing; we also exclude the informal household economy, which consists of all household services and production.

As emphasized by Schneider and Enste (2000, 2002), there is no single best way to estimate the size of SE. Each approach has its strengths and weaknesses, and none is close to being perfect. Because of their strengths and weaknesses, it makes sense to apply many of them, because they may complement each other and produce similar results.

Methodologies of calculating the SE may be classified into three categories: direct, indirect, and model based. The indirect methods are divided in turn into three subcategories: approaches based on national accounts (e.g., the discrepancy between income and expenditure, the discrepancy between official and actual employment); monetary approaches; and physical input methods. With reference to the “indirect” monetary approach, the currency demand approach based on Cagan’s (1958) currency demand model is often applied. This method requires econometric estimation of the currency demand models twice, once with a tax variable and once without it because tax burden is assumed to be the major reason for holding cash. The difference is used as an estimate of the size of the SE. Regardless of the specific method, any resulting estimates are necessarily subject to much imprecision.

The main empirical results regarding the Romanian SE are presented in table 1. These estimates reveal a wide range of sizes. For example, Schneider and Enste (1998) estimate that the average size of SE is 26 percent of official gross domestic product (GDP) for the period 1990/1993 and 28.3 percent in 1994/1995. In other studies that use two different estimation methods of the size of SE, the currency demand approach and the DYMIMIC model, Schneider (1998, 2002a, 2002b, 2005, 2006), Schneider and Buehn (2007), and Schneider and Klinglmair (2004) find an increasing trend, registering 27.3 percent of official GDP in 1990/1993, 33.4 percent in 2000/2001, and 37.4 percent in 2002/2003. More recently, there seems to be a slight declining trend, from 36.2 percent of official GDP in 2003/2004 to 35.4 percent in 2004/2005. Others often find different estimates when different methods are used. The size of the SE ranges between about 20 percent of GDP using the energy consumption method (Schneider and Enste 2000), and is more than 45 percent using the monetary approach (French, Balaita, and Ticsa 1999). Using the national accounts methodology reported by the National Institute for Statistics, the SE has increased from about 5 percent in 1992, to 18 percent in 1997, and to between 20 to 21 percent in 2000/2001. Albu (2007a, 2007b) uses two Romanian household surveys (September 1996 and in July 2003) and concludes that income from the SE amounts about one-fourth of the total household income (23.6 percent in 1996 and 22.7 percent in 2003). Also, Albu (2008) uses the data from these surveys in order to estimate the theoretical limit for the size of SE on the basis of limited available macroeconomic data. He finds that the estimated lower and upper bound of the SE is 28.6 to 35.9 percent of official GDP in 1990, 23.5 to 28.7 percent in 1995, 23.2 to 28.3 percent in 2002, 22.7 to 27.5 percent in 2003, 22.5 to 27.3 percent in 2004, and 22.5 to 27.8 percent in 2005.

Table 1.

Size of Romanian Shadow Economy (percentage of official GDP).

Authors	Approach	Period	Size of shadow economy (percentage of official GDP)
Albu (2008), Albu and Nicolae(2003), Albu, Iorgulescu, and Stanica (2010), and Albu, Ghizdeanu, and Stanica (2011)	Income discrepancy	1995– 2007	18.2% (1995), 21.7% (2000), 14.6% (2007)
National Institute of Statistics	Labor input	1998–2009	23.5% (1998), 16.6% (2005), 19.8% (2009)
Johnson, Kaufmann, and Shleifer (1997); Johnson, Kaufmann, and Zoido-Lobatón (1998)	Electricity	1990–1995	18% (1989/1990), 26% (1990/1993), 28.3% (1994/1995)
Lackó(1999)	Electricity	1990–1995	20.9% (1989/1990), 29% (1990/1993), 31.3% (1994/1995).
Schneider et al. (1998, 2000, 2002, 2002a, 2002b, 2004, 2005, 2006, 2007, 2009)	DYMIMIC and currency demand	1990–2005	26.2% (1990/1991), 30.6% (1994/1995), 36.1% (2001/2002), 35.4% (2004/2005)
Schneider, Buehn, and Montenegro (2010)	MIMIC	1999–2006	34.8% (1999), 35.4% (2002), 36.2% (2005), 36.7% (2006).

Note. GDP = gross domestic product.

In this article, we estimate the size of the Romanian SE using the currency demand approach for quarterly data covering the period 2000Q1–2010Q2. Importantly, we investigate the relationship between the size of the SE and the unemployment rate (UR) in the case of Romania using Granger causality analysis. Our article is the first attempt to estimate for Romania the size of the SE using quarterly data, and it is the first that treats the potential relationship between unemployment and hidden economy.

We find that the Romanian SE as a percentage of official GDP is decreasing over the analyzed period, from 36.5 percent at the end of 2000 to 31.5 of real GDP at the middle of 2010. Our empirical results also support a unidirectional Granger causality that runs from the URs to the SE. The generalized impulse response functions (GIRFs) indicate the existence of a short-run negative relationship between URs and the Romanian SE. The empirical results also indicate that there is a positive long-run relationship between both URs and the SE, with a 1 percent increase in URs leading to an increase in the SE of 0.36 percent from the registered unemployment rate (R_UR) and to an increase of 2.27 percent from the International Labour Office (ILO) measure.

In the next section, we first estimate the size of the SE. We then examine the impact of unemployment on its size. In the final section, we present our conclusions.

Estimating the Size of the Romanian SE

The Currency Demand Approach

The currency demand approach is one of the most commonly used. It has been applied to many Organisation for Economic Co-operation and Development countries.¹ The currency demand approach was first used by Cagan (1958), who calculated a correlation between the currency demand and tax “pressure” (as one cause of the SE) for the United States over the period 1919–1955. Twenty years later, Gutmann (1977) used the same approach.

Following Cagan (1958), a typical currency demand function can be written as

C_{0} = A \cdot (1 + Θ)^{α} \cdot Y_{0}^{β} \cdot exp (- γ i),

where $C_{0}$ represents the observed cash, $Θ$ represents the variable that gives incentives to make hidden transactions (e.g., government consumption normalized by GDP, tax rates [direct and indirect taxes], tax revenues to GDP), $Y_{0}$ represents the registered GDP but can also be used GDP per capita, consumption per capita, $i$ represents the interest rate, and ( $α, β, γ, A$ ) represents the parameters. Estimating equation (1) generates a predicted value $\hat{C}$ . Setting the incentive variable $Θ$ equal to zero, we obtain $\tilde{C}$ . The difference between $\hat{C}$ and $\tilde{C}$ is the amount of extra currency (EC) that represents the amount of illegal money used to finance the SE. Assuming that the velocity of money is the same in both official and shadow sectors, we can obtain an estimate of the size of SE multiplying illegal money ( $E C = \hat{C} - \tilde{C}$ ) by the velocity of money $(v = \frac{Y}{C})$ .

There are various objections to this method. One is that not all transactions in the SE are paid in cash. Also, most studies consider only one particular factor, the tax burden, as a cause of the SE, even though others are possible (e.g., the impact of regulation, taxpayers’ attitudes toward the state, “tax morality”). A further weakness of this approach, at least when applied to the United States, is discussed by Garcia (1978), Park (1979), and Feige (1996), who point out that increases in currency demand deposits are due largely to a slowdown in demand deposits rather than to an increase in currency caused by activities in the SE. Feige (1986, 1997) also criticizes Tanzi (1983) on the grounds that the US dollar is used as an international currency. Further, most studies assume the same velocity of money in both types of economies. As Hill and Kabir (1996) for Canada and Klovland (1984) for the Scandinavian countries argue, there is already considerable uncertainty about the velocity of money in the official economy; the velocity of money in the hidden sector is even more difficult to estimate. Indeed, Ahumada, Alvaredo, and Canavese (2007) show that the currency approach, together with the assumption of equal income velocity of money in both the reported and the hidden transaction, is only correct if the income elasticity is 1, and they propose an alternative way of correcting the estimates. Finally, the assumption of no SE in a base year is open to criticism. Even so, we apply this approach in our estimation.

Data and Method

Data

The time span covered by our data is from 2000Q1 to 2010Q2, so the number of observations is forty-two. Apart from the real interest rates and the real currency outside banks, the data are seasonally adjusted by means of the tramo seats method. All series are expressed in logarithmic form to reduce the problem of heteroscedasticity. The main sources used to collect the data are Eurostat, National Bank of Romania, and National Institute of Statistics. A description of the variables and their sources is given in table 2. As suggested by Guissarri (1987), Spiro (1996), Schneider and Enste (2000), and Öğünç and Yilmaz (2000), we deflate our series using the national GDP deflator.²

Table 2.

Data Description and Sources.

Variables	Description	Sources
C	Natural logarithm of real currency holdings measured as nominal currency in circulation normalized by GDP deflator (2000 = 100). 2000Q1–2010Q2 in national currency (millions RON). The values of currency, all notes and coins outside the banking system are those at the end of the quarter	The series of nominal currency is available in National Bank of Romania Monthly Bulletins 2000–2010. The series of GDP deflator (2000 = 100) is available in Eurostat, Quarterly National Accounts database
$\frac{C}{M_{2}}$	Natural logarithm of the ratio of currency holdings to money supply. 2000Q1–2010Q2	The series are available in National Bank of Romania Monthly Bulletins 2000–2010
$M_{1}$	Natural logarithm of monetary aggregate $M_{1}$ 2000Q1–2010Q2 in national currency (millions RON)	The definition of monetary aggregate according to the methodology of European Central Bank beginning with 2007 produces some changes in monetary aggregate $M,$ which includes from 2007 in addition to the structure employed until December 2006, the demand deposits of household savings expressed in RON and sight foreign currency deposits of residents previously included in quasi-money, being considered as having the same degree of liquidity as the demand deposits of economic agents. The series has been recalculated for the period 2000–2006 using data from National Bank of Romania, Monthly Bulletins 2000–2010
Y	Natural logarithm of real GDP (2000 = 100). 2000Q1–2010Q3 in national currency (millions RON)	The series is available in Eurostat, Quarterly National Accounts database
$Y_{p c}$	Natural logarithm of real GDP per capita. 2000Q1–20102 in national currency (millions RON)	All per capita values are calculated using population data for persons aged fifteen and older, from Eurostat, Quarterly Labor Force Survey database, and Quarterly National Accounts database
$? >$ ${Y_{d}}^{'}$	Natural logarithm of real disposable income (GDP at current prices − taxes) normalized by GDP deflator. 2000Q1–2010Q2 in national currency (millions RON)	The series is computed based on official data from Eurostat Quarterly Government Finance Statistics and Quarterly National Accounts databases
${Y_{d}}^{''}$	Natural logarithm of real disposable income (GDP at current prices − taxes + social benefits) normalized by GDP deflator. 2000Q1–2010Q2 in national currency (millions RON)	The series is computed based on official data from Eurostat Quarterly Government Finance Statistics and Quarterly National Accounts databases
$T a x$	Natural logarithm of 1 + total of tax revenues (taxes on production and imports, current taxes on income, wealth, social contributions) over GDP. 2000Q1–2010Q2 in percentage	The series is available in Eurostat, Quarterly Government Finance Statistics database
$R r_{12}$	Natural logarithm of twelve-month Real Romanian interbank offered rate (ROBOR). 2000Q1–2010Q2 in percentage	The series is calculated using nominal interest rate from Eurostat, Quarterly Interest Rates database, and National Bank of Romania. The series of inflation rate is calculated as a geometric mean of the chain-based monthly indices of consumer prices, from which the comparison base equaling 100 is subtracted. The source of the data was the National Statistics Institute TEMPO database
$R r_{3}$	Natural logarithm of three-month Real ROBOR. 2000Q1–2010Q2 in percentage	The series is calculated using nominal interest rate and average inflation rate from Eurostat, Quarterly Interest Rates database, National Bank of Romania, respectively, National Statistics Institute TEMPO database
$W S$	Natural logarithm of the ratio of gross wages and salaries in GDP. 2000Q1–2010Q2 in percentage	The series is computed based on official data from National Bank of Romania, Monthly Bulletins 2000–2010, National Institute of Statistics, TEMPO database
$G o v$	Natural logarithm of the ratio of final government consumption expenditure in GDP. 2000Q1–2010Q2 in percentage	The series is available in Eurostat, Quarterly Government Finance Statistics database
$E$	Natural logarithm of the ratio of private consumption expenditure in GDP. 2000Q1–2010Q2 in percentage	Private consumption expenditure includes the consumption expenditure of households and nonprofit institutions serving households. The series is available in Eurostat, Quarterly National Accounts database
R_UR	Registered unemployment rate. 2000Q1–2010Q2 in percentage	The series is available in Monthly Bulletins 2000–2010, National Bank of Romania
ILO_UR	ILO unemployment rate. 2000Q1–2010Q2 in percentage	The series is available on Tempo database, National Institute of Statistics

Note: GDP = gross domestic product.

Models

We estimate several models based on the Cagan (1958) currency demand function³:

M 1 : C_{t} = α_{0} + α_{1} \cdot Y_{t} + α_{2} \cdot T a x_{t} + α_{3} \cdot R_{r 12 t} + α_{4} \cdot W S_{t} + ε_{1 t},

M 2 : C_{t} = α_{0} + α_{1} \cdot Y_{t} + α_{2} \cdot T a x_{t} + α_{3} \cdot R_{r 3 t} + α_{4} \cdot W S_{t} + ε_{2 t}

M 3 : C_{t} = β_{0} + β_{1} \cdot Y_{t} + β_{2} \cdot T a x_{t} + β_{3} \cdot R_{r 12 t} + β_{4} \cdot G o v_{t} + ε_{3 t},

M 4 : C_{t} = θ_{0} + θ_{1} \cdot Y_{d t}^{''} + θ_{2} \cdot T a x_{t} + θ_{3} \cdot R_{r 12 t} + θ_{4} \cdot E_{t} + ε_{4 t},

M 5 : C_{t} = ϑ_{0} + ϑ_{1} \cdot Y_{d t}^{'} + ϑ_{2} \cdot T a x_{t} + ϑ_{3} \cdot R_{r 12 t} + ε_{5 t,}

M 6 : {(C / M_{2})}_{t} = γ_{0} + γ_{1} \cdot T a x_{t} + γ_{2} \cdot W S_{t} + γ_{3} \cdot R_{r 12 t} + γ_{4} \cdot Y_{p c t} + ε_{6 t},

where

C is the natural logarithm of currency in circulation outside the banks (at the end of the period in millions Romanian Leu [RON]) normalized by the GDP deflator;

${(C / M_{2})}_{t}$ is the natural logarithm of currency outside the banks and M2 (broad money);

$Y$ is the natural logarithm of real GDP in millions RON, base year (2000 = 100);

$Y_{p c}$ is the natural logarithm of real GDP per capita;

$Y_{d}^{^{'}}$ is the natural logarithm of real disposable income (GDP at current prices − taxes) normalized by GDP deflator;

$Y_{d}^{^{''}}$ is the natural logarithm of real disposable income (GDP at current prices − taxes + social benefits) normalized by GDP deflator;

$T a x$ is the natural logarithm of total tax revenues normalized by GDP;

$R r_{12}$ is the natural logarithm of 12-month real Romanian interbank offered rate (ROBOR);

$R r_{3}$ is the natural logarithm of three-month real ROBOR;

$W S$ is the natural logarithm of the ratio of gross wages and salaries in national income;

$G o v$ is the natural logarithm of the ratio of final government consumption expenditure in GDP;

$E$ is the natural logarithm of the ratio of private consumption expenditure in GDP;

$ε_{i}, i = 1, \dots, 6$ are the error terms.

Regarding the sign of the variables in the models, we expect a positive impact on currency demand for income, taxes, wages, government consumption and private consumption, and a negative effect from interest rates.

Unit Root Tests

As a preliminary step, we perform tests of stationarity (or tests for the presence of unit roots) for each series. We also employ augmented Dickey–Fuller (ADF) and Phillips–Perron (PP) tests in order to identify each variable’s integration level (Dickey and Fuller 1981).

Co-integration and Johansen Tests

After the order of integration is determined, co-integration between the series can be tested to identify any long-run relationship. We use the Johansen trace test for the co-integration tests. Cheung and Lai (1993) mention that the trace test is more robust than the maximum Eigenvalue test for co-integration. The Johansen trace test attempts to determine the number of co-integrating vectors among variables. There should be at least one co-integrating vector for possible co-integration. This procedure can be expressed in the following vector autoregression (VAR) model (Katircioglu 2007):

X_{t} = Π_{1} X_{t - 1} + \dots + Π_{K} X_{t - K} + μ + e_{t} t = 1, \dots, T

where X_t , X_t ₋₁, …, X_t _−K are vectors of current and lagged values of P variables that are I(1) in the model; Π₁, . . . , Π _K are matrices of coefficients with (PXP) dimensions; μ is an intercept vector; and e_t is a vector of random errors. The number of lagged values is determined in such a way that error terms are not significantly autocorrelated. The rank of Π is the number of co-integrating relationship(s) (i.e., r) that is determined by testing whether its Eigenvalues (λ _i ) are statistically different from zero. Johansen and Juselius (1990) propose using the Eigenvalues of Π ordered from the largest to the smallest for computation of trace statistics.⁴ The trace statistic (λ _trace ) is computed by the formula⁵:

λ_{t r a c e} = - T \sum ln (1 - λ_{i}), i = r + 1, \dots, n - 1,

with hypotheses

\begin{aligned} H_{0} : r = 0 H_{1} : r \geq 1 \\ H_{0} : r \leq {1 H}_{1} : r \geq 2 \\ H_{0} : r \leq 2 H_{1} : r \geq 3 . \end{aligned}

VAR Model with an Error Correction Mechanism

Given the nonstationarity of our series and the presence of a common stochastic trend, traditional estimation methods are ruled out, and we must then estimate a VAR model in which we include a mechanism of error correction model (ECM). The ECM has co-integration relations built into the specification, so that it restricts the long-run behavior of the endogenous variables to converge to their co-integrating relationships while allowing for short-run adjustment dynamics. The co-integration term is known as the correction term since the deviation from long-run equilibrium is corrected gradually through a series of partial short-run adjustments.

The ECM estimated can be defined as (Ito 2008)

Δ Y_{t} = δ + Γ_{1} \cdot Δ Y_{t - 1} + \dots + Γ_{t - p - 1} Δ Y_{t - p + 1} + Π \cdot Y_{t - 1} + ε_{t},

where $Δ$ is the difference operator; Y is a vector formed by the n variables used in our currency demand (C, Y, TAX, R, and WAGES); $Γ$ denotes an $(n Ã— n)$ matrix of coefficients and contains information regarding the short-run relationships among the variables; $Π$ is an $(n Ã— n)$ coefficient matrix decomposed as $Π = γ \cdot β^{'}$ , where $γ$ represents the adjustment coefficients and $β$ is the co-integrating vectors; $ε$ corresponds to residuals; and $δ$ is a constant term that can be separated in two parts, a trend term and the intercept in the co-integrating relation.

Granger Causality Test

If the variables are I(1) and cointegrated, then the Granger (1981) causality test will be run under vector error correction model (VECM; t-ratio of ECM and F-test should be statistically significant):

Δ Y_{t} = C_{0} + \sum_{i = 1}^{k} β_{i} Y_{t - i} + \sum_{i = 1}^{k} α_{i} X_{t - i} + p_{i} E C T_{t - 1} + u_{t},

Δ X_{t} = C_{0} + \sum_{i = 1}^{k} γ_{i} X_{t - i} + \sum_{i = 1}^{k} ζ_{i} Y_{t - i} + η_{i} E C T_{t - 1} + ε_{t},

where $Y, X$ are the variables; $p_{i}$ is the adjustment coefficient; and $E C T_{t - 1}$ expresses the error correction term (ECT). In equation (11), $X$ Granger causes $Y$ if $α_{i}, p_{i}$ are significantly different from zero. In equation (12), $Y$ Granger causes $X$ if $ζ_{i}, η_{i}$ are significantly different from zero. An F-test alone is not enough to have causation; the t-ratio for the ECM term should also be negative and statistically significant together with an F-value to have causation in the models.

Empirical Results

Estimating the Currency Demand Approach

Before proceeding with the estimation, each series is individually examined under the null hypothesis of a unit root against the alternative of stationarity using ADF and PP tests. The results indicate that each of the series is nonstationary when the variables are defined in levels, but first differencing the series removes the nonstationary components in all cases.

Because the series is integrated of the same order I(1), we investigate if there is a long-run relationship between variables, using the Johansen co-integration approach. The results of the co-integration test suggest at least one co-integrating vector exists for each model considered.⁶ Given the nonstationarity of our series, we estimate a VAR model in which we include a mechanism from the ECM. The results of the VECMs are presented in table 3.

Table 3.

Empirical Results for Vector Error Correction Model.

Model		$M_{1}$	$M_{2}$	$M_{3}$	$M_{4}$	$M_{5}$	$M_{6}$
Trace statistic	5 percent level	4	3	1	3	3	4
Trace statistic	1 percent level	2	2	0	2	1	2
Maximum Eigenvalue statistic	5 percent level	1	1	0	1	0	1
Maximum Eigenvalue statistic	1 percent level	0	0	0	1	0	1
$C_{t - 1}$		1.00	1.00	1.00	1.00	1.00
${(\frac{C}{M_{2}})}_{t - 1}$							1.00
$Y_{t - 1}$		1.802* (0.131)	1.878* (0.125)	1.910* (0.317)
$Y p c_{t - 1}$							4.686* (0.669)
$Y_{d t - 1}^{^{'}}$						1.975* (0.330)
$Y_{d t - 1}^{^{''}}$					1.981* (0.137)
$T A X_{t - 1}$		4.426* (1.240)	3.926* (1.239)	1.699 (3.189)	14.362* (1.427)	7.471* (3.495)	−14.453* (5.842)
$R r_{12 t - 1}$		−0.154* (0.028)		−0.100 (0.07)	−0.097* (0.025)	−0.106 (0.075)	1.293* (0.165)
$R r_{3 t - 1}$			−0.138* (0.027)
$W S_{t - 1}$		1.857* (0.228)	1.704* (0.219)				−1.087 (1.066)
$G o v_{t - 1}$				−1.007* (0.259)
$E_{t - 1}$					−1.680* (0.385)
Cons.		−16.401* (1.174)	−16.625* (1.186)	−8.438* (3.640)	−7.912* (2.777)	−12.777* (3.571)	31.741* (4.575)

$E C T_{t - 1}$		−1.222* (0.200)	−1.222* (0.205)	−0.315* (0.102)	−0.589* (0.180)	−0.453* (0.113)	0.049* (0.010)
${\overset{ˉ}{R}}^{2}$		0.47	0.46	0.12	0.16	0.23	0.39
SE		0.06	0.06	0.08	0.08	0.07	0.02
Log likelihood		56.43	56.04	46.06	46.95	48.22	107.44
F-statistic		8.06*	7.78*	2.05	2.45	3.94*	5.94*
Autocorrelation LM test		32.78 [0.13]	30.85 [0.19]	55.54 [0.00]	35.91 [0.07]	29.93 [0.02]	32.24 [0.15]
Normality test		13.97 [0.17]	16.44 [0.08]	11.57 [0.31]	8.33 [0.59]	6.86 [0.55]	10.76 [0.37]
White test		171.15 [0.67]	178.40 [0.51]	187.67 [0.33]	188.41 [0.31]	84.49 [0.86]	200.84 [0.14]
AIC		−2.52	−2.50	−2.00	−2.04	−2.16	−5.07
SBC		−2.26	−2.24	−1.75	−1.79	−1.94	−4.81

Notes. AIC = Akaike information criterion; SBC = Schwarz’s Bayesian criterion. All series used in the models are I(1). The numbers of lags in the models are determined using Schwarz’s information criterion SBC and Hannan–Quinn criterion. All models are estimated with one co-integrating equation. ${\overset{ˉ}{R}}^{2}$ is the coefficient of multiple determinations adjusted for the degrees of freedom (df). LM test is the Lagrange multiplier test of residual serial correlation at lag order 8 following χ² distribution with n df, The normality test is based on a test of skewness and kurtosis of residuals, following χ² distribution with n df. The White test is a heteroscedasticity test, following χ² distribution. Standard errors are in parentheses. SE is the standard error of the equation. [ ] denote the probability levels. The boldface values represent the coefficients for the best model M1.

*indicates significance at the 5 percent level.

As expected, in model $M_{1}$ , the coefficients for output, tax burden, and wages have a positive long-run effect, while interest rate takes the pressure off currency demand. All coefficients are strongly significant and assign a relevant weight to GDP with a coefficient of 1.80 and to taxes with a coefficient of 4.42. This latter result implies that an increase in the tax rate is likely to motivate individuals to participate in the underground economy in an attempt to increase their income. The coefficient on interest rates is negative as expected, reflecting the increasing opportunity cost in holding currency balances when interest rates are rising.

As for other models, model $M_{2}$ represents a good alternative to model $M_{1}$ , in which we introduce the real interest rate for three months. The performance of models $M_{3}$ and $M_{5}$ is weaker compared to model $M_{1}$ , and the variable interest rate is not significant. Furthermore, the ratio of private consumption expenditure (E) in model $M_{4}$ has a negative effect on currency holdings, which is contrary with the economic theory. In model $M_{3}$ , we have the same situation for the ratio of government consumption expenditure (Gov), and the interest rate is not statistically significant. Model $M_{6}$ represents an approximation of the Tanzi (1983) original specification, but the negative signs of tax rates and wage rates are troubling.

The diagnostic analysis of VECMs reveals that there is no existence of residual autocorrelation since all p values are larger than the .05 level of significance. The normality of residuals is verified for all the models with the exception of model $M_{2}$ . The residual heteroscedasticity is verified for all the VECMs.

Regarding the percentage of the total variation of the dependent variable, this is considered high enough (47 percent) only for the first model. Although the ECT has a negative sign and is statistically significant in terms of t-tests for all models, the models M ₃ and M₄ do not work properly because there is co-integration between variables.

In all, model $M_{1}$ is considered the best model. An increase of 1 percent of real GDP would imply an estimated increase of almost 1.80 percent in currency demand in the long run. Furthermore, the estimated coefficient of real GDP indicates an elastic effect on the currency demand. The tax level and wage ratio depict positive and elastic effects on the Romanian currency demand. The interest rate has a negative and inelastic effect on the currency demand (0.15 percent), reflecting the increasing opportunity cost in holding currency balances when interest rates are rising.

The significance of the ECT shows causality in at least one direction. The lagged error term ( $E C_{t - 1}$ ) is negative and highly significant. The ECT for model $M_{1}$ indicates a high rate of convergence to equilibrium, which implies that deviation from the long-term equilibrium is corrected by 122 percent over each quarter. The coefficient of the ECT is significant at the 1 percent level, and is greater than unity, implying a high speed of adjustment toward equilibrium.

Obtaining the Size of Romanian SE

After estimating the VECM and obtaining the coefficients for the long-run relationship of model $M_{1}$ , we proceed to estimate the size of SE.⁷ In order to obtain an estimate of the size of the SE, we compute $\tilde{C}$ using all the coefficients in equation (13; Bajada 1999). Then, we set the tax variable equal to zero and reestimate the equation, keeping all the other coefficients unchanged to obtain $\hat{C}$ :

{\hat{C}}_{t} = - 16.40 + 1.80 \cdot Y_{t} + 4.42 \cdot T a x_{t} - 0.15 \cdot R_{t} + 1.85 \cdot W S_{t} .

The difference between these two variables (or $\hat{C}$ and $\tilde{C}$ ) gives the amount of EC or illegal money in the economy. Following Tanzi (1983), we assume equal velocity in both the formal and the informal economies, and estimate the velocity as

\frac{Y}{M_{1} - E C} = v .

Equation (14) yields the velocity of money in the Romanian economy, where Y is the GDP, $M_{1}$ corresponds to total currency and deposits in circulation, and EC is extra currency or illegal currency. The difference between $M_{1}$ and EC can be interpreted as the amount of legal money used in economy.

Once we estimate the velocity from equation (15), the dimension of SE using the currency demand approach can be obtained multiplying EC by the velocity of money:

E C * v = Y_{s h a d o w} .

The main idea behind the model is that a rise in the underground economy will cause an increase in demand for money.

We can then infer the size of the shadow sector in formal GDP terms. From the table of normalized co-integrating coefficients, the coefficient of GDP (Y) in the model is different from 1. Following Ahumada, Alvaredo, and Canavese (2007), we correct our estimates using their suggested method, or⁸

\frac{Y_{s h a d o w}}{Y_{o f f i c i a l}} = {(\frac{C_{s h a d o w}}{C_{o f f i c i a l}})}^{\frac{1}{β}} = {(\frac{{\hat{Y}}_{s h a d o w}}{{\hat{Y}}_{o f f i c i a l}})}^{\frac{1}{β}} .

where Y is the GDP, C is the currency, and $β$ is the income elasticity. The correction basically deflates the wrong ratio $(\frac{{\hat{Y}}_{s h a d o w}}{{\hat{Y}}_{o f f i c i a l}})$ that we obtained using inappropriately the assumption $β = 1$ . Equation (16) corrects the estimation when $β = 1$ .

The empirical results of currency demand approach based on VECMs (figure 1) emphasize that there is a general downward trend in the size of the SE as a percentage of official GDP for the period 2000–2010. Thus, the size of the SE as a percentage of official GDP measures approximately 36.6 percent in 2000Q1 and follows a downward trend after registering the value of 31.0 percent by 2008. For the past few quarters, there is a slightly upward trend in the size of the SE. These results are consistent with Schneider and Buehn (2007); Albu (2007a, 2007b); Albu, Iorgulescu, and Stanica (2010); and Albu, Ghizdeanu, and Stanica (2011).

UR and the SE: A Granger Causality Analysis

In this section, we investigate the magnitude by which unemployment effects might alter the estimated magnitude of the SE. The main reason for individuals to engage in SE activities is to avoid the higher costs exacted by taxes and government regulation. In their discussion of the growth of the SE, Dell’Anno and Solomon (2007) suggested two important factors: a reduction in official working hours and the influence of the UR. Enste (2003) pointed out that reducing the number of working hours to a level below workers’ preferences raises the quantity of hours worked in the SE. Early retirement also increases the number of hours worked in the SE.

An increase in the UR reduces the proportion of workers employed in the formal sector; consequently, labor participation rates in the informal sector increase. According to Giles and Tedds (2002), two opposing forces determine the relationship between unemployment and the SE. On one hand, an increase in the UR may involve a decrease in the SE because it is positively related to the growth rate of GDP and eventually negatively correlated with unemployment via Okun’s Law. On the other hand, an increase in unemployment leads to an increase in people working in the SE because they have more time for such activities.

Dell’Anno and Solomon (2007) found a positive relationship in the short run between the UR and the US SE for the period 1970–2004. Using structural vector autoregressive analysis, they investigated the response of the SE to an aggregate supply shock that affected unemployment. Their empirical results showed that in the short run, a positive aggregate supply shock causes the SE to rise by about 8 percent above the baseline. Tanzi (1999) also considered the relationship between unemployment and the SE. The greater the number of unemployed, the more the individuals will seek a job in the informal economy; however, it is likely that opportunities to work in the informal economy should be limited when unemployment is high. See also Buehn and Schneider (2008).

Regarding the Romanian unemployment data, there are two measures available for unemployed persons: registered unemployed and ILO unemployed. There are differences between the estimates. Not all the registered employed persons from the employment agencies meet the conditions of ILO, and also not all ILO unemployed persons meet the legal requirements of the employment agencies.

According to the ILO criteria, ILO unemployed are persons aged fifty-seven to seventy-four years who, during the reference period, simultaneously meet the following conditions: they have no job and are not carrying out any activity in order to get income; they are looking for a job, undertaking certain actions during the last four weeks (registering at employment agencies, or private agencies for placement, attempts for starting an activity on own account, publishing notices, asking for a job among friends, relatives, mates, trade unions), and they are available to start work within the next two weeks, if they immediately find a job. According to the Law 76/2002, the registered unemployed are persons simultaneously fulfilling the following conditions: they are looking for a job from sixteen years of age at least to pension age; their health and physical and psychical capacities make them able to work; they have no job, they have no income, or from legal activities, they get an income lower than the national gross minimum salary, guaranteed for payment, in force; they are available to start work in the next period if they find a job; and they are registered at the National Agency for Employment (NAE) or at another supplier of employment services that is legally functioning.

These are clearly different measures of the URs. The first is the ILO unemployment rate (ILO_UR), published quarterly by the National Institute of Statistics and is based on Labor Force Survey. The second is the R_UR, calculated by NAE and based on statements of people who pass by employment agencies and said that they are unemployed. The fact that the ILO_UR is higher than the recorded one shows that some of those who declare themselves unemployed at the AMIGO surveys do not sign up at the employment agencies as persons seeking employment. The majority of registered unemployed are in the category of people with lower education and lower qualifications in need of support from unemployment insurance or from legislation on the minimum wage.

Regardless of the specific unemployment measure, it is obvious that the existing institutional framework has an influence on market behavior of individuals and businesses. It is therefore quite possible that at certain times the evolution of undeclared work in the SE will be directly related to the various changes/developments in the institutional framework regarding the unemployment phenomenon.

Figure 2 shows the evolution of the SE versus URs, and indicates a positive relationship between variables. There is a correlation coefficient between these variables of 0.22 for the ILO_UR, and 0.67 for the R_UR. Our aim now is to investigate the nature of the relationship between unemployment rates and the size of the Romanian SE and to identify the direction of causality between them using Granger causality analysis, GIRF and variance decomposition analysis.

Method and Data

Our data cover the period 2000Q1–2010Q2, giving forty-two observations. The variables used are the size of the Romanian SE expressed as a percentage of official GDP (SE) as obtained earlier by the currency demand approach; the ILO_UR; and the R_UR. The URs were seasonally adjusted by means of tramo seats method. The main source of the data for URs is the National Institute of Statistics (Tempo database) and the Monthly Bulletins, and National Bank of Romania.

The principal methods employed to analyze the time-series behavior of the data involve multivariate co-integration analysis together with Granger causality tests and two short-run analyses including impulse response function and variance decomposition from a VECM, as discussed earlier.

Empirical Results

In order to identify the level of integration of the two series, we first apply ADF and PP unit root tests, revealing that the variables are nonstationary at their levels but stationary at their first differences, being integrated of order one, I(1). Because both series are integrated of the same order, we apply the Johansen and Juselius co-integration approach to investigate whether there is a long-run relationship between SE and UR. The results of the co-integration tests are based on trace statistics, and maximum Eigenvalues point out the existence of a unique co-integrating relationship (e.g., a long-run relationship) between variables. Because a long-run equilibrium relationship is found between URs and the size of the SE, a VECM is constructed to determine the direction of causality.

These results are in Table 4. The long-run coefficients are positive and strongly significant, indicating that a 1 percent increase in ILO_UR generates an estimated increase of almost 2.22 percent in the size of the SE in the long run, while a 1 percent increase in R_UR increases by 0.28 percent the size of the SE.

Table 4.

Vector Error Correction Estimates.

Model		ILO_UR and SE	R_UR and SE
Trace statistic	5 percent level	1	1
Trace statistic	1 percent level	1	0
Maximum Eigenvalue statistic	5 percent level	1	1
Maximum Eigenvalue statistic	1 percent level	1	1
Long-run results
$S E_{t - 1}$		1.00	1.00
$I L O_U R_{t - 1}$		2.225* (0.396)
$R_U R_{t - 1}$			0.281* (0.084)
Cons.		16.126* (2.902)	30.89* (0.563)
Short-run results
$E C T_{t - 1}$		−0.438* (0.088)	−0.58* (0.137)
$Δ S E_{t - 1}$		−0.892* (0.153)	−0.339** (0.142)
$Δ S E_{t - 2}$		−1.115* (0.211)	−0.317** (0.152)
$Δ S E_{t - 3}$		−0.905* (0.225)	−0.298*** (0.168)
$Δ S E_{t - 4}$		−1.000* (0.226)	−0.379** (0.163)
$Δ S E_{t - 5}$		−0.746* (0.216)	−0.245*** (0.142)
$Δ S E_{t - 6}$		−0.461** (0.170)
$Δ R_U R_{t - 1}$			−0.396* (0.135)
$Δ R_U R_{t - 2}$			−0.168 (0.146)
$Δ R_U R_{t - 3}$			−0.258*** (0.134)
$Δ R_U R_{t - 4}$			−0.513* (0.135)
$Δ R_U R_{t - 5}$			0.008 (0.161)
$Δ I L O_U R_{t - 1}$		−0.839* (0.204)
$Δ I L O_U R_{t - 2}$		−0.750* (0.222)
$Δ I L O_U R_{t - 3}$		−0.705* (0.199)
$Δ I L O_U R_{t - 4}$		−0.836* (0.207)
$Δ I L O_U R_{t - 5}$		−0.455** (0.195)
$Δ I L O_U R_{t - 6}$		−0.200 (0.189)
${\overset{ˉ}{R}}^{2}$		0.63	0.60
SE		0.53	0.56
Log likelihood		−19.80	−23.77
F-statistic		5.86**	6.43**
Short-run diagnostic test statistics
Autocorrelation LM test		6.48 [0.17]	5.17 [0.27]
Normality test		6.95 [0.13]	15.43 [0.03]
White test		83.62 [0.31]	56.84 [0.78]
AIC		1.87	1.93
SBC		2.45	2.41

Notes. AIC = Akaike information criterion; ILO_UR = ILO unemployment rate; R_UR = registered unemployment rate; SBC = Schwarz’s Bayesian criterion; SE = shadow economy. All series used in the models are I(1). The number of lags in the models are determined using Schwarz’s information criterion SBC and Hannan–Quinn criterion. All models are estimated with one co-integrating equation. ${\overset{ˉ}{R}}^{2}$ is the coefficient of multiple determinations adjusted for the degrees of freedom (df). LM test is the Lagrange multiplier test of residual serial correlation at lag order 8 following χ² distribution with n df. The Normality test is based on a test of skewness and kurtosis of residuals, following χ² distribution with n df. The White test is a heteroscedasticity test, following χ² distribution. Standard errors are in parentheses. SE is the standard error of the equation. [ ] denote the probability levels.

*, **, and *** indicate significance at the 1 percent, 5 percent, and 10 percent levels.

The short-run coefficients are negative and strongly significant, revealing that lagged URs (registered and ILO) have a strong effect on the size of the SE in the short run. All lagged changes in SE and URs are statistically significant, further justifying the choice of optimal lag.

The ECT for the ILO_UR is −0.438 (0.088), indicating a high rate of convergence to equilibrium and implying that deviation from the long-term equilibrium is corrected by 43.8 percent over each quarter. The ECT for the R_UR, or −0.58 (0.13), suggests that the deviation from long-run equilibrium is corrected by 58 percent each quarter.

The results of VECMs indicate that the ILO_UR explains about 63 percent of the variation in SE, while the R_UR explains about 60 percent of the SE variation. The F-statistic supports both models.

Table 5 reports the F-statistics and t-statistics for the ECT defined for the null hypothesis of no causality. We conclude that we have unidirectional Granger causality that runs from R_UR to SE and from ILO_UR to SE; the t-ratio of ECT and the F-statistic are statistically significant at 1 percent and 5 percent levels, and the ECT is negative.

Table 5.

Granger Causality Test Results.

Null hypothesis	Lag level	5		6		Results
Null hypothesis	Lag level	F-statistics	$t_{E C T_{t - 1}}$	F-statistics	$t_{E C T_{t - 1}}$	Results
(1) SE and R_UR
R_UR does not Granger cause SE		6.43**	−0.58*			$R_U R \Rightarrow S E$
SE does not Granger cause R_UR		0.63	−0.42***			$R_U R \Rightarrow S E$
(2) SE and ILO_UR
ILO_UR does not Granger cause SE				5.86**	−0.438*	$I L O_U R \Rightarrow S E$
SE does not Granger cause ILO_UR				1.018	−0.011	$I L O_U R \Rightarrow S E$

Notes. ILO_UR = ILO unemployment rate; R_UR = registered unemployment rate; SE = shadow economy. Given the small size of our series, we use the lag length selected according to the Akaike criterion (six lags for ILO_UR and five lags for R_UR) running the tests. Using the results of Pantula’s principle, we select model 2 with intercept (no trend) in the co-integrating equation and no intercept in vector autoregression model as the optimal model for the deterministic components in the system for both models. The boldface values represent the values of F-test and t-test for both potential causal relationships.

* and ** denote significance for 5 percent and 1 percent levels, respectively.

The significance of the ECT shows causality in at least one direction. The lagged error term ( $E C_{t - 1}$ ) is negative and highly significant. The ECT for the R_UR for the optimal lag length (five lags) is −0.58, meaning that the SE converges to its long-run level from the contribution of the R_UR at a 58 percent speed of adjustment. The value of this coefficient for the ILO_UR for the optimal lag length (six lags) is −0.438, indicating a high rate of convergence to equilibrium and revealing that the SE converges to its long-run level by a 43.8 percent contribution of ILO_UR.

These empirical results show that in the short run, both the ILO_UR and the R_UR have a negative and statistically significant effect on the SE while in the long run both URs have a positive effect on the SE.

As argued by Buehn and Schneider (2008), the negative short-run relationship of unemployment with the SE can be explained by the fact that the income effect exceeds the substitution effect. Income losses due to unemployment reduce demand in both the shadow and the official economies. National economy shocks that affect the formal sector create a growth in unemployment that manifests itself in a similar way in the informal sector. Thus, it is possible that the opportunities to work in the SE are limited when the unemployment level is excessively high, so that fewer businesses offer jobs whether they are official or underground (Tanzi 1999). On the other hand, a substitution of official demand for goods and services for unofficial demand takes place as unemployed workers turn to the SE, where cheaper goods and services make it easier to countervail utility losses. This behavior may stimulate additional demand in the SE. So an increase of the unemployment in the formal sector in the long run causes an increase in people working in the SE, leading to an expansion of the informal sector.

In order to quantify the effects of a shock in UR in the size of the SE, we apply the GIRFs proposed by Pesaran and Shin (1998). Figure 3 shows the impulse responses and the accumulated responses of the co-integrated VAR model with six lags (ILO_UR) and five lags (R_UR), and the one restricted co-integrating vector. We conduct estimations of the GIRFs twelve periods ahead.

The graphics present the responses of the SE to shocks in unemployment. The results suggest that the SE decreases in the second quarter following the initial positive shock and increases after the first two quarters from the initial shock, due to a positive shock in both the registered and the ILO_UR. Also in the fifth quarter from the initial shock, the SE sharply declines from the positive shock.

Additionally, the accumulated response for up to the twelfth quarter is estimated to be 0.35 percent due to the R_UR and 2.27 percent due to the ILO_UR. The results support the fact that a 1 percent increase in URs increases the SE by 0.35 percent (registered unemployment) and by 2.27 percent (ILO unemployment).

Conclusion

In this article, we used the currency demand approach in order to obtain a measure of the Romanian SE. We found that the Romanian SE as a percentage of official GDP fell from 36.5 percentage of GDP at the end of 2000 to 31.5 percent at the middle of 2010. Using Granger causality tests under ECMs, we also examined the impact of both registered and ILO_URs on the Romanian SE. The empirical results support a unidirectional Granger causality that runs from both URs to the SE, revealing the existence of a negative short-run relationship and of a positive long-run relationship between both the URs and the size of the SE. The short-term effect of UR shocks on the size of Romanian SE was quantified using GIRFs, suggesting that a 1 percent increase in the R_UR leads to an increase in the SE over the twelve quarters of 0.35 percent, while an increase in the ILO_UR leads to an increase in the SE of about 2.27 percent over a period of twelve quarters.

Even so, estimating the size of the SE remains a controversial topic. Our results should be interpreted with due reserve, given the limitations of the estimation methods.

Footnotes

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

Notes

References

Ahumada

Alvaredo

Canavese

. 2007. “The Monetary Method and the Size of the Shadow Economy: A Critical Assessment.” Review of Income and Wealth 53:363–71.

Albu

L. L

. 2007a. “A Model to Estimate Informal Economy at Regional Level: Theoretical and Empirical Investigation.” International Conference on Regional and Urban Modeling, Free University of Brussels, Brussels, Belgium, June 1–2.

Albu

L. L

. 2007b. “Estimating the Size of Underground Economy in Romania.” Working Papers No. 070601, Institute for Economic Forecasting, Bucharest, Romania.

Albu

L. L

. 2008. “A Model to Estimate Spatial Distribution of Informal Economy.” Journal for Economic Forecasting 5:111–24.

Albu

L. L.

Ghizdeanu

Stanica

. 2011. “Spatial Distribution of the Informal Economy. A Theoretical and Empirical Investigation.” Scienze Regionali 1:63–80.

Albu

L. L.

Iorgulescu

Stanica

. 2010. “Estimating Hidden Economy and Hidden Migration: The Case of Romania.” Journal for Economic Forecasting 7:46–56.

Albu

L. L.

Nicolae

. 2003. “Use of Households’ Survey Data to Estimate the Size of the Informal Economy in Romania.” MPRA Paper No. 14286, University Library of Munich, Germany.

Bajada

1999. “Estimates of the Underground Economy in Australia.” The Economic Record 75:369–84.

Brambila

M. J.

Cazzavillan

. 2009. “The Dynamics of Parallel Economies. Measuring the Informal Sector in Mexico.” Research in Economics 63:189–99.

10.

Buehn

Schneider

. 2008. “MIMIC Models, Cointegration and Error Correction: An Application to the French Shadow Economy.” IZA Discussion Paper No. 3306, Institute for the Study of Labor (IZA), Bonn, Germany.

11.

Cagan

1958. “The Demand for Currency Relative to the Total Money Supply.” Journal of Political Economy 66:302–28.

12.

Cheung

Y-W

Lai

. 1993. “A fractional cointegration analysis of purchasing power parity.” Journal of Business & Economic Statistics 11: 103–112.

13.

Dell’Anno

Solomon

O. H.

. 2007. “Shadow Economy and Unemployment Rate in USA: Is there a Structural Relationship? An Empirical Analysis.” Applied Economics 19:2537–55.

14.

Dickey

D. A.

Fuller

W. A.

. 1981. “Likelihood Ratio Statistics for Autoregressive Time Series with a Unit Root.” Econometrica 49:1057–72.

15.

Enste

D. H

. 2003. “Shadow Economy and Institutional Change in Transition Countries.” In The Informal Economy in the EU Accession Countries: Size, Scope, Trends and Challenges to the Process of EU Enlargement, edited by Belev

, 81–113. Sofia, Bulgaria: Centre for the Study of Democracy.

16.

Feige

E. L

. 1986. “A Re-examination of the ‘Underground Economy’ in the United States.” IMF Staff Papers 33:768–81.

17.

Feige

E. L

. 1989. The Underground Economies, Tax Evasion and Information Distortion. Cambridge: Cambridge University Press.

18.

Feige

E. L

. 1994. “The Underground Economy and the Currency Enigma.” Supplement to Public Finance/Finances Publiques 49:119–36.

19.

Feige

E. L

. 1996. “Overseas Holdings of U.S. Currency and the Underground Economy.” In Exploring the Underground Economy, edited by Susan

Pozo

, 5–62. Kalamazoo, MI: WE Upjohn Institute for Employment Research.

20.

Feige

E. L

. 1997. “Revised Estimates of the Underground Economy: Implications of US Currency Held Abroad.” MPRA Paper No. 13805, University Library of Munich, Germany.

21.

French

Balaita

Ticsa

. 1999. Estimating the Size and Policy Implications of the Underground Economy in Romania. Bucharest, Romania: US Department of the Treasury, Office of Technical Assistance.

22.

Garcia

1978. “The Currency Ratio and the Subterranean Economy.” Financial Analysts Journal 69:64–66.

23.

Giles

D. E. A

. 1999. “Modeling the Hidden Economy in the Tax-gap in New Zealand.” Working Paper No. 99-05, Department of Economics, University of Victoria, British Columbia, Canada.

24.

Giles

D. E. A.

Tedds

L. M.

. 2002. “Taxes and the Canadian Underground Economy.” Canadian Tax Paper No. 106, Canadian Tax Foundation, Toronto, Ontario, Canada.

25.

Granger

1981. “Some Properties of Time Series Data and Their Use in Econometric Model Specification.” Journal of Econometrics 16:121–30.

26.

Guissarri

1987. “La Demanda de Circulante y la Informalidad en Argentina.” Cuadernos de Economia 72:197–224.

27.

Gutmann

1977. “Subterranean Economy.” Financial Analysts Journal 33:26–27.

28.

Hill

Kabir

. 1996. Tax Rates, the Tax Mix, and the Growth of the Underground Economy in Canada: What Can We Infer? Canadian Tax Journal/Revue Fiscale Canadienne 44:1552–83.

29.

Ito

2008. “Oil Process and Russian Economy: A VEC Model Approach.” International Research Journal of Finance and Economics 17:1450–2887.

30.

Johansen

Juselius

. 1990. “Maximum Likelihood Estimation and Inference on Co-integration with Applications to Money Demand.” Oxford Bulletin of Economics and Statistics 52:169–210.

31.

Johnson

Kaufmann

Shleifer

. 1997. “The Unofficial Economy in Transition.” Brookings Papers on Economic Activity 2:159–221.

32.

Johnson

Kaufmann

Zoido-Lobatón

. 1998. “Regulatory Discretion and the Unofficial Economy.” The American Economic Review 88:387–92.

33.

Katircioglu

S. T

. 2007. “Financial Development, Trade and Growth Triangle: The case of India.” International Journal of Social Economics 34:586–98.

34.

Klovland

1984. “Tax Evasion and the Demand for Currency in Norway and Sweden: Is there a Hidden Relationship?” Scandinavian Journal of Economics 86:423–39.

35.

Lackó

. 1999. “Hidden Economy an Unknown Quantity? Comparative Analyses of Hidden Economies in Transition Countries in 1989-95.” Working Paper No. 9905, Department of Economics, University of Linz, Austria.

36.

Öğünç

Yılmaz

. 2000. “Estimating Underground Economy in Turkey.” Discussion Paper No.15, Central Bank of the Republic Turkey, Ankara.

37.

Osterwald-Lenum

. 1992. “A Note with Quantiles of the Asymptotic Distribution of the Maximum Likelihood Cointegration Rank Test Statistics.” Oxford Bulletin of Economics and Statistics 54:461–72.

38.

Park

1979. Reconciliation between Personal Income and Taxable Income. Washington, DC: Bureau of Economic Analysis.

39.

Pesaran

H. M.

Shin

. 1998. “Generalized Impulse Response Analysis in Linear Multivariate Models.” Economic Letters 58:17–29.

40.

Schneider

1986. “Estimating the Size of the Danish Shadow Economy Using the Currency Demand Approach: An Attempt.” The Scandinavian Journal of Economics 88:643–68.

41.

Schneider

1994. “Measuring the Size and Development of the Shadow Economy: Can the Causes Be Found and the Obstacles Be Overcome?” In Essays on Economic Psychology, edited by Brandstaetter

Güth

, 193–212. Berlin, Germany: Springer.

42.

Schneider

2000. “Illegal Activities, But Still Value Added Ones (?): Size, Causes, and Measurement Of The Shadow Economies All Over the World.” CESifo Working Paper No. 305.

43.

Schneider

2002a. The Size of Development of the Shadow Economies and Shadow Economy Labor Force of 22 Transition and 21 OECD Countries: What Do We Really Know? Zagreb, Croatia: Institute of Public Finance.

44.

Schneider

2002b. Size and Measurement of the Informal Economy in 110 Countries around the World, Rapid Response Unit. Washington, DC: The World Bank.

45.

Schneider

2003. “The Development of the Shadow Economies and Shadow Labour Force of 21 OECD and 22 Transition Countries.” CESifo DICE Report 1:17–23.

46.

Schneider

2005. “Shadow Economies of 145 Countries All Over the World: What Do We Really Know?” CREMA Working Paper Series No. 2005-13, Center for Research in Economics, Management and the Arts (CREMA), Zürich, Switzerland.

47.

Schneider

2006. “Shadow Economies and Corruption All Over the World: What Do We Really Know?” Economics Working Paper No. 2006-17, Department of Economics, Johannes Kepler University of Linz, Austria.

48.

Schneider

Buehn

. 2007. “Shadow Economies and Corruption all Over the World: Revised Estimates for 120 Countries.” Economics—The Open-Access, Open-Assessment E-Journal 1:1–53.

49.

Schneider

Buehn

Montenegro

. 2010. “Shadow Economies All Over the World: New Estimates for 162 Countries from 1999 to 2007.” Working Paper No. 322, Department of Economics, University of Chile, Santiago, Chile.

50.

Schneider

Enste

. 1998. Increasing Shadow Economies All Over the World—Fiction or Reality? A Survey of the Global Evidence of their Size and of their Impact from 1970 to 1995. Bonn, Germany: The Institute for the Study of Labor (IZA).

51.

Schneider

Enste

. 2000. “Shadow Economies: Size, Causes and Consequences.” Journal of Economic Literature 38:73–110.

52.

Schneider

Enste

. 2002. The Shadow Economy: Theoretical Approaches, Empirical Studies, and Political Implications. Cambridge, UK: Cambridge University Press.

53.

Schneider

Hametner

. 2007. “The Shadow Economy in Colombia: Size and Effects on Economic Growth.” Economics Working Paper No. 2007-03, Department of Economics, Johannes Kepler University of Linz, Austria.

54.

Schneider

Klinglmair

. 2004. “Shadow Economies around the World: What Do We Know?” IZA Discussion Paper No. 1043, Institute for the Study of Labor, Bonn, Germany.

55.

Smith

1994. “Assessing the Size of the Underground Economy: The Canadian Statistical Perspectives.” Canadian Economic Observer 3:16–33.

56.

Spiro

1996. “Monetary Estimates of the Underground Economy: A Critical Evaluation.” The Canadian Journal of Economics/Revue Canadienne d’Economique 29:S171–75.

57.

Tanzi

1983. “The Underground Economy in the United States: Annual Estimates, 1930-1980.” IMF Staff Papers 30:283–305.

58.

Tanzi

1999. “Uses and Abuses of Estimates of the Underground Economy.” Economic Journal 109:338–47.