Keeping both corruption and the shadow economy in check: the role of decentralization

Abstract

This paper puts forward a framework for evaluating the effects of governmental decentralization on the shadow economy and corruption. The theoretical analysis demonstrates that decentralization exerts both a direct and an indirect impact on the shadow economy and corruption. First, decentralization helps to mitigate government-induced distortions, thus limiting the extent of corruption and the informal sector in a direct way. Second, in more decentralized systems, individuals have the option to avoid corruption by moving to other jurisdictions, rather than going underground. This limits the impact of corruption on the shadow economy and implies that decentralization is also beneficial in an indirect way. As a result, our analysis documents a positive relationship between corruption and the shadow economy; however, this link proves to be lower in decentralized countries. To test these predictions, we developed an empirical analysis based on a cross-country database of 145 countries that includes different indexes of decentralization, corruption and shadow economy. The empirical evidence is consistent with the theory.

Appendices

Appendix A

Proof of Lemma 2

From Lemma 1, it follows that politician’s monetary rent R is zero at t=0 and t=1 since x=1 in this case. R=0 also when θ=0 as there is no corruption and rents for the politician. This implies that the policy (t _p ,θ _p ) that maximizes monetary rents involves an intermediate level of the tax rate and a positive value of θ. The first-order conditions defining (t _p ,θ _p ) are the following:

$$\begin{aligned} & \frac{\partial R}{\partial\theta} = \beta aq(1 - t) (\omega t)^{(1 - \alpha) / \alpha} q \biggl[ (1 - x) + \frac{(1 - \alpha)}{\alpha\omega} \omega_{\theta} (1 - x) - \frac{\partial x}{\partial\theta} \biggr] = 0, \end{aligned}$$

(30)

$$\begin{aligned} & \frac{\partial R}{\partial t} = \beta aq\theta(\omega t)^{(1 - \alpha ) / \alpha} \biggl[ - (1 - x) + \frac{1 - \alpha}{\alpha t}(1 - t) (1 - x) - (1 - t)\frac{\partial x}{\partial t} \biggr] = 0. \end{aligned}$$

(31)

Substituting (11) and (12) into respectively (30) and (31), we obtain

$$\begin{aligned} \frac{\partial R}{\partial\theta} & = \beta aq(1 - t) (\omega t)^{(1 - \alpha ) / \alpha} q \\ &\quad {}\times\biggl[ (1 - x) + \frac{(1 - \alpha)}{\alpha} \frac{\omega_{\theta}}{\omega} (1 - x)\theta + \frac{\omega_{\theta}}{ \omega} \frac{x\theta}{\alpha} - \frac{xaq\theta}{(1 - \alpha)(1 - aq\theta)} \biggr] = 0, \end{aligned}$$

(32)

$$\begin{aligned} \frac{\partial R}{\partial t} & = \beta aq\theta(\omega t)^{(1 - \alpha ) / \alpha} \\ &\quad {}\times\biggl[ - (1 - x) + \frac{1 - \alpha}{\alpha t}(1 - t) (1 - x) - \frac{x}{1 - \alpha} + (1 - t) \frac{x}{\alpha t} \biggr] = 0. \end{aligned}$$

(33)

First, note that the sign of both derivatives is determined by the components within the square brackets. Rearranging terms in the square bracket of (33), we obtain the tax rate solving this equation to be t=1−α. From the square bracket of (32), it follows that there is a unique level of θ, which we call θ _p , solving the equation

$$ (1 - x) + \frac{(1 - \alpha)}{\alpha} \frac{\omega_{\theta}}{\omega} (1 - x)\theta+ \frac{\omega_{\theta}}{\omega} \frac{x\theta}{\alpha} - \frac{xaq\theta}{(1 - \alpha)(1 - aq\theta)} = 0. $$

(34)

In fact, the first component is positive while the other three are negative since ω _θ <0. Moreover, the first component is decreasing in θ as a higher level of θ increases the labor x employed in the shadow economy (see Lemma 1), while the other three components are increasing (in absolute value) in θ. This can be shown by considering the absolute value of these three components, and we can define

$$Z \equiv- \frac{1 - \alpha- \alpha x}{\alpha} \frac{\omega_{\theta}}{ \omega} \theta+ \frac{xaq\theta}{(1 - \alpha)(1 - aq\theta)}. $$

Then, we have that

$$\begin{aligned} \frac{\partial Z}{\partial\theta} & = - \frac{1 - \alpha+ \alpha x}{\alpha} \frac{\omega_{\theta}}{\omega} - \frac{\omega_{\theta}}{\omega} \theta \frac{\partial x}{\partial\theta} - \frac{1 - \alpha+ \alpha x}{\alpha} \theta \frac{\partial(\omega_{\theta} /\omega)}{\partial\theta} \\ &\quad {} + \frac{aq\theta}{(1 - \alpha)(1 - aq\theta)}\frac{\partial x}{\partial \theta} + \frac{xaq}{(1 - \alpha)} \frac{1}{(1 - aq\theta)^{2}} > 0, \end{aligned}$$

since ω _θ <0, ∂x/∂θ>0 and

$$\frac{\partial(\omega_{\theta} /\omega)}{\partial\theta} = \frac{\omega_{\theta\theta} \omega- (\omega_{\theta} )^{2}}{\omega ^{2}} < 0 $$

from the assumption that function ω(θ) is “not too concave.” Finally, notice that θ _p is not necessarily lower than 1 as it is possible that the square bracket of (32) is positive for all θ∈[0,1]. □

Proof of Lemma 3

From Lemma 2, it is straightforward that both politicians tax at the rate t ₁=t ₂=1−α as this maximizes their rent R as well as the net income y _i of the individuals. Taking into account (11) and (12), the reaction functions of the two politicians with respect to θ are the following:

$$\begin{aligned} \frac{\partial R_{1}}{\partial\theta_{1}} & = \beta aq(1 - t_{1}) (\omega_{1}t_{1})^{(1 - \alpha) / \alpha} qn_{1} \\ &\quad {}\times \biggl[ (1 - x_{1}) + \frac{(1 - \alpha)}{\alpha} \frac{(\partial\omega_{1} / \partial \theta_{1})}{\omega_{1}}(1 - x_{1})\theta_{1} + \frac{(\partial\omega_{1} / \partial\theta_{1})}{\omega_{1}} \frac{x_{1}\theta_{1}}{\alpha} \\ &\quad {} - \frac{x_{1}aq\theta_{1}}{(1 - \alpha)(1 - aq\theta_{1})} + (1 - x_{1}) \theta_{1}\frac{(\partial n_{1} / \partial\theta_{1})}{n_{1}} \biggr] = 0 \end{aligned}$$

(35)

$$\begin{aligned} \frac{\partial R_{2}}{\partial\theta_{2}}& = \beta aq(1 - t_{2}) (\omega_{2}t_{2})^{(1 - \alpha) / \alpha} qn_{2} \\ &\quad {}\times \biggl[ (1 - x_{2}) + \frac{(1 - \alpha)}{\alpha} \frac{(\partial\omega_{2} / \partial \theta_{2})}{\omega_{2}}(1 - x_{2})\theta_{2} + \frac{(\partial\omega_{2} / \partial\theta_{2})}{\omega_{2}} \frac{x_{2}\theta_{2}}{\alpha} \\ &\quad {} - \frac{x_{2}aq\theta_{2}}{(1 - \alpha)(1 - aq\theta_{2})} + (1 - x_{2}) \theta_{2}\frac{(\partial n_{2} / \partial\theta_{2})}{n_{2}} \biggr] = 0 \end{aligned}$$

(36)

where ∂n ₁/∂θ ₁=∂h(⋅)/∂θ ₁<0 and ∂n ₂/∂θ ₂=−∂h(⋅)/∂θ ₂<0. Since the terms outside the square bracket are positive, the Nash equilibrium is the solution of the following system of equations:

$$\begin{aligned} & (1 - x_{1}) + \frac{(1 - \alpha)}{\alpha} \frac{(\partial\omega_{1} / \partial\theta_{1})}{\omega_{1}}(1 - x_{1})\theta_{1} + \frac{(\partial \omega_{1} / \partial \theta_{1})}{\omega_{1}}\frac{x_{1}\theta_{1}}{\alpha} - \frac{x_{1}aq\theta_{1}}{(1 - \alpha)(1 - aq\theta_{1})} \\ &\quad = - \frac{(1 - x_{1})\theta_{1}}{n_{1}}\frac{\partial n_{1}}{\partial \theta_{1}} \end{aligned}$$

(37)

$$\begin{aligned} & (1 - x_{2}) + \frac{(1 - \alpha)}{\alpha} \frac{(\partial\omega_{2} / \partial\theta_{2})}{\omega_{2}}(1 - x_{2})\theta_{2} + \frac{(\partial \omega_{2} / \partial \theta_{2})}{\omega_{2}}\frac{x_{2}\theta_{2}}{\alpha} - \frac{x_{2}aq\theta_{2}}{(1 - \alpha)(1 - aq\theta_{2})} \\ &\quad = - \frac{(1 - x_{2})\theta_{2}}{n_{2}}\frac{\partial n_{2}}{\partial\theta_{2}}. \end{aligned}$$

(38)

Since the equilibrium is symmetric, θ ₁=θ ₂=θ _r where θ _r is the solution to the following equation:

$$\begin{aligned} & (1 - x) + \frac{(1 - \alpha)}{\alpha} \frac{(\partial\omega/ \partial \theta)}{\omega} (1 - x)\theta+ \frac{(\partial\omega/ \partial \theta )}{\omega} \frac{x\theta}{\alpha} - \frac{xaq\theta}{(1 - \alpha)(1 - aq\theta)} \\ &\quad = - \frac{(1 - x)\theta}{n} \frac{\partial n}{\partial \theta}. \end{aligned}$$

(39)

From the comparison of (39) and (34) defining θ _p , it follows that θ _r <θ _p since the left-hand side of both expressions are the same while the right-hand side of (39) is positive (as ∂n/∂θ=∂h(⋅)/∂θ<0). □

Proof of Proposition 4

Let us consider an exogenous increase (due to an increase in θ or in the fraction of product a in the formal sector that can be extorted by a bureaucrat) in the level of corruption B in a centralized state equal to dB. This leads to an increase in the labor employed in the shadow economy equal to

$$\Delta \mathit{SE}_{C} = \frac{\partial x(B)}{\partial B}\,dB. $$

Now, let us consider a federal state with two equally populated jurisdictions, so that the population size in each of them is 1/2, and assume that the increase in corruption is not uniformly distributed in all jurisdictions. In particular, let us consider the extreme case where the increase in corruption is concentrated in jurisdiction 2 and it is equal to 2 dB, so that also the total increase in corruption in the federal state is equal to dB. As the individuals with lower migration costs find it optimal to move from jurisdiction 2 to jurisdiction 1, this increase in corruption implies an increase in the labor employed in the shadow economy in the federal state equal to

$$\Delta SE_{F} = \biggl[ \biggl( \frac{1}{2} - \frac{\partial h( \cdot )}{\partial B} \biggr)\frac{\partial x(B)}{\partial B} \biggr]2\,dB = \biggl[ \biggl( 1 - 2 \frac{\partial h( \cdot)}{\partial B} \biggr)\frac{\partial x(B)}{\partial B} \biggr]\,dB, $$

where ∂h(⋅)/∂B>0 represents the size of agents moving from jurisdiction 2 to jurisdiction 1. It is immediate that the same increase in corruption dB increases the shadow economy in a centralized state more than the increase in the federal state, and this difference is equal to

$$\Delta SE_{C} - \Delta SE_{F} = 2\frac{\partial h( \cdot)}{\partial B} \frac{\partial x(B)}{\partial B}\,dB > 0. $$

 □

Appendix B

2.1 B.1 Database (1)

Symbol	Description	Source	Obs	Min	Max
Av.CPI	Transparency International’s Corruption Perceptions Index (CPI) ranks countries based on how corrupt their public sector is perceived to be. Average (1999–2005)	http://archive.transparency.org/policy_research/surveys_indices/cpi	145	1.2	9.8
Av.WGI	Control of Corruption: Reflects perceptions of the extent to which public power is exercised for private gain. Average (1998–2005, not available data for 1999),	Worldwide Governance Indicators. World Bank. (www.govindicators.org)	145	−1.5	2.46
Av.Bribe1	Percentage of firms expected to make informal payments to public officials to “get things done” with regard to customs, taxes, licenses, regulations, services, and the like. Average (1999–2007)	World Development Indicators. [IC.FRM.CORR.ZS] based on Enterprise Surveys—World Bank.	88	4.4	98.3
Av.ICRG	Political risk points by component “F-Corruption” (Scores 2005 + Scores 2011)/2.	International Country Risk Guide. The PRS Group, Inc.	127	0.8	6.0
Av.CorrGIFT	Percent of firms expected to give gifts to public officials “to get things done”. Average (2005–2010)	Enterprise Surveys; World Bank. http://www.enterprisesurveys.org	108	0.0	85.1
Av.CorrTAX	Percent of firms expected to give gifts in meetings with tax officials. Average (2005–2010)		108	0.0	66.7
Av.CorrGOV	Percent of firms expected to give gifts to secure government contract. Average (2005–2010)		107	0.0	97.7
Av.CorrLIC	Percent of firms expected to give gifts to get an operating license. Average (2005–2010)		107	0.0	16.4
Av.CorrIMP	Percent of firms expected to give gifts to get an import license. Average (2005–2010)		107	0.0	88.2
Av.CorrCONS	Percent of firms expected to give gifts to get a construction permit. Average (2005–2010)		108	0.0	61.1
Av.Corr.ELEC	Percent of firms expected to give gifts to get an electrical connection. Average (2005–2010)		107	0.0	91.6
Av.CorrWAT	Percent of firms expected to give gifts to get a water connection. Average (2005–2010)		106	0.0	71.1
Av.CorrPAST	Percent of firms experiencing at least one bribe payment request. Average (2005–2010)		103	0.0	70.9
Av.CorrREL	Percent of firms identifying corruption as a major constraint. Average (2005–2010)		108	0.0	65.2
Av.CorrJUS	Percent of firms identifying the courts system as a major constraint. Average (2005–2010)		108	0.0	68.9
INF_comp	Percent of firms competing against unregistered or informal firms. Average (2005–2010)		108	0.0	89.8
INF_rel	Percent of firms identifying practices of competitors in the informal sector as a major constraint. Average (2005–2010)		108	0.0	72.4
Shadow	Shadow Economy as percentage of official GDP. Average (1999–2007)	Buehn and Schneider (2012a), Table 3	145	8.54	66.1
Exp_Dec	100∗{1-[Total Expenditure, Noncash (Cen. Govt.)/Total Expenditure, Noncash (Gen. Govt.)]}. Average (1999–2007)	Government Finance Statistics. IMF	45	12.5	129.5
Rev_Dec	100∗{1-[Revenue, Noncash (Cen. Govt.)/Revenue, Noncash (Gen. Govt.)]}. Average (1999–2007)	Government Finance Statistics. IMF	48	12.4	130.8
D1_Fed	Classified as a federation by Elazar (1995) and updated by Treisman (2007) by adding Ethiopia, Serbia-Montenegro, Bosnia-Herzegovina, which became federal after Elazar’ article. (Federal =1.)	Treisman (2006). Available from: www.sscnet.ucla.edu/polisci/faculty/treisman/Papers/what_have_we_learned_data.xls [Fedelaz]	141	0	1
D2_Fed	Persson and Tabellini (2003). (Federal =1.)	Available from: http://didattica.unibocconi.it/mypage/index.php?IdUte=48805&idr=4273, [Federal]	81	0	1
D3_Fed	Dummy variable =1 if (a) constitution reserves decision making on at least one topic exclusively to subnational legislatures and/or (b) constitution assigns to subnational legislatures exclusive right to legislate on issues that it does not specifically assign to one level of government.	Treisman (2008) [Auton.]	68	0	1
DT_Fed	Dummy variable: Decentralized =1. (See paragraph 4.1 for details.)	Own estimation based on GFS (IMF) and Treisman (2007, 2008) Persson and Tabellini (2003)	140	0	1

2.2 B.2 Database (2)

Symbol	Description	Source	Obs	Min	Max
BritCol	Former British colony	Treisman (2006). Available from: www.sscnet.ucla.edu/polisci/faculty/treisman/Papers/what_have_we_learned_data.xls. We correct four digit errors in this file.	134	0	1
FrenCol	Former French colony		134	0	1
SpanPorC	Former Spanish or Portuguese colony		134	0	1
OtherCol	Former colony of state other than Britain, France, Spain, or Portugal,		134	0	1
NonCol	Never a colony		134	0	1
LegBritish	legal origin: British	GDN Growth Database, Available from: www.sscnet.ucla.edu/polisci/faculty/treisman/Papers/what_have_we_learned_data.xls	126	0	1
LegFren	legal origin: French		126	0	1
LegSoc	legal origin: Socialist		126	0	1
LegGerm	legal origin: German		126	0	1
LegScand	legal origin: Scandinavian		126	0	1
LGDPcap	Logarithm of GDP per capita (constant 2000 US$). Average (1999–2007)	World Development Indicators Log[NY.GDP.PCAP.KD]	143	4.5	10.8
FDI	Average from Foreign direct investment, net inflows (% of GDP). Average (1999–2007)	World Development Indicators. [BX.KLT.DINV.WD.GD.ZS]	143	−6.5	388.4
t_open	(Exports of goods and services (current LCU)+Imports of goods and services (current LCU)/(Gross national expenditure (current LCU). Average (1999–2007)	World Development Indicators. 100∗[(NE.EXP.GNFS.CN+NE.IMP.GNFS.CN)/NE.DAB.TOTL.CN]	136	0.6	514.8
School	School enrollment, secondary (% gross). Average (1999–2007)	World Development Indicators. [SE.SEC.ENRR]	135	8.4	152.6
Gov_size	General government final consumption expenditure (current LCU)/ Final consumption expenditure (current LCU). Average (1999–2007)	World Development Indicators 100∗[NE.CON.GOVT.CN /NE.CON.TOTL.CN]	116	5.4	53.0
Self	Self-employed, total (% of total employed). Average (1999–2007)	World Development Indicators [SL.EMP.SELF.ZS]	121	0.9	94.7
T_rev	Tax revenue (% of GDP). Average (1999–2007)	World Development Indicators. [GC.TAX.TOTL.GD.ZS]	117	0.2	45.2
Urban	Urban population (% of total). Average (1999–2007)	World Development Indicators. [SP.URB.TOTL.IN.ZS]	142	9.0	100
Wom_gov	Women in government at ministerial level (as % of total) 2001	Treisman (2006). Available from: www.sscnet.ucla.edu/polisci/faculty/treisman/Papers/what_have_we_learned_data.xls. [womgov01]. Original Source: UNDP, Human Development Report, 2004	96	0	47.4
Lab_part	Labor participation rate, total (% of total population ages 15+). Average (1999–2007)	World Development Indicators. [SL.TLF.CACT.ZS]	142	40.4	89.2