Does Centralized Corruption Reduce Bribes?

A Stochastic Frontier Analysis

Jiali Xing

December 30, 2018

Abstract

How industrial organization of corruption influences the amount of bribes is contro-

versial as its theoretical predictions as well as empirical results are so often inconclusive.

Moreover, underreporting in the interview data rises concerns in empirical research. In

this paper, we first test the firm level survey dataset BEEPS 1999 for underreporting in

bribes and conclude that there is no evidence of underreporting about bribes. Then we

apply the single–output Cobb–Douglas cost frontier to study bribes as a shadow cost. Af-

ter considering heteroskedasticity, spatial autocorrelation, and robustness, we find that

centralized bureaucracy does not lower corruption by reducing minimum bribes, i.e., the

bribe frontier, but does lower the bribes by reducing the bribe inefficiency. It means that

once the entrepreneurs pay bribes efficiently, a more centralized bureaucratic structure

will not help reduce their bribes anymore. In contrast with BRIBE, SIZE and spatial

lagged variable influence not only the bribe efficiency, but also the bribe frontier, sup-

porting the corruption contagion and economies of scale phenomenon.

Keywords: Centralization, Corruption, Stochastic frontier analysis, Underreporting

1

Contents

1 Introduction 3

2 Background 4

3 Hypothesis Test of Underreporting 7

4 Model Specification 8

4.1 Stochastic Frontier Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

4.2 Spatially Lagged Variable . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

4.3 Heteroskedasticity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

5 Results 14

5.1 Bureaucratic Centralization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

5.2 Other Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

5.3 Robustness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

5.4 Shortcomings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

6 Conclusion 18

A Testing for spatial autocorrelation via Moran’s I statistic 19

B Stochastic Frontier Estimation Results 20

C Other Regression Results 24

2

1 Introduction

According to the IMF (2016), public sector corruption siphons $1.5 trillion to $2 trillion an-

nually from the global economy in bribes and costs far more in stunted economic growth,

lost tax revenues and sustained poverty. Corruption is an old research topic for economists

and political scientists, and thus has extensive literature (Jain, 2001). Some studies develop

theoretical models of corruption (Echazu and Bose, 2008; Shleifer and Vishny, 1993; Waller,

Verdier, and Gardner, 2002), while others rely on empirical techniques to test aforesaid mod-

els (Diaby and Sylwester, 2014). Most of these relevant studies focus on its causes (Schulze

and Zakharov, 2018), consequences (Dreher and Gassebner, 2013), or cures. As Obydenkova

and Libman (2015) point out, Russia (and its sub-national regions) is like, from scholars’ per-

spectives, a natural laboratory for testing new theories. Therefore, we also choose to build

our empirical model on Russia (along with other transition countries).

Since some scholars (e.g. Diaby and Sylwester, 2014; Stefes, 2008) base their empiri-

cal researches on the Business Environment and Enterprise Performance Survey (BEEPS)1,

and show the concern about underreporting in the interview data, we test whether the self-

reported response bias exists in BEEPS. Furthermore, based on the rejection of our hypothe-

sis we put forward a more appropriate approach to model bribes—stochastic frontier analysis.

If bribes are considered as a shadow cost, then we can study it via cost frontier function.

Moreover, we test and take into consideration the possible heteroskedasticity and spatial au-

tocorrelation in our cost frontier model. Our results show no evidence of positive correla-

tion between the centralization of corruption and the reduce of cost frontier of bribes, but

we find that centralized corruption does influence the variances of two error components

significantly, which supports the conclusion of Diaby and Sylwester (2014) and Shleifer and

Vishny (1993) in a more theoretically reasonable and informative way. It shows that central-

ized corruption does not reduce the minimum bribes a entrepreneur needs to pay for his or

her business (it does not reduce bribe frontier), but it does help the entrepreneur reach the

minimum bribes (it reduces bribe inefficiency).

1 BEEPS is a firm-level survey (more specifically, five rounds surveys so far) about quality of thebusiness environment, based on face-to-face interviews with managers implemented by European Bankfor Reconstruction and Development (EBRD) and World Bank.

3

In the rest of our paper, we discuss the relevant literature in section 2, introduce our dataset

and test the hypothesis of underreporting in section 3, justify our model and address spatial

autocorrelation in section 4, analysis the regression result in section 5, and conclude in sec-

tion 6.

2 Background

Shleifer and Vishny (1993) examine how three different kind of regimes2 influence the level

and effects of corruption via theoretical models. By modeling bribes as an extra charge from

a monopolist in a single government good market, Shleifer and Vishny (1993) suggest a sim-

ilarity between bribes and revenue-maximizing commodity taxes. When comparing a joint

monopolist agency with independent monopolist agencies, things get worse in the latter case.

If we consider it as a special case of the tragedy of the commons stemming from negative exter-

nality, it is intuitive that when the official agencies are monopolists in single permit markets,

or when they collude in multiple permits, they can collect more revenues with a lower level

of bribes than under the independent monopoly scenario. The extreme case is that when

there is a free entry for officials to add new complementary permits exclusively, the sales of

package of government goods, as well as bribe revenues, fall to zero. Parallel with the analysis

of industrial organization, a helpful analogy of the three scenarios is tollbooths on the road.

One toll for the entire road and independent tollbooths from different towns correspond to

the joint monopoly solution and independent monopolists’ solution, respectively. The vol-

ume of traffic and aggregate toll collections fall, in fact, to zero when any party can erect its

own tollbooth on this road. Based on the analysis of industrial organization of corruption,

the authors conclude that well-organized corruption leads to fewer bribes per entrepreneur

and a better economic performance than decentralized corruption.

In this paper of Shleifer and Vishny (1993), government hierarchy structure and the principal-

agent problem are treated as exogenous. To further study the effect of different industrial

organizations of corruption while allowing an endogenous principal-agent problem, Waller,

Verdier, and Gardner (2002) give us a more complicated corruption model with a parameter

2 They have different corruption networks: well-organized corruption, no need for corruption,and decentralized corruption.

4

space divided by crucial parameters like the number of lower-level officials, their official wage,

and their probability of being monitored. In this setting, the autocrat levies taxes on the legal

sector, pays civil servants wages out of the budget, monitors bureaucrats, and receives kick-

backs from those bureaucrats detected taking bribes, while each bureaucrat chooses a bribe

to charge for issuing special permits (these permits are complements to each other). Waller,

Verdier, and Gardner (2002) divide the parameter space of the model into three mutually ex-

clusive sets. Under one set of circumstances (roughly, a government with high monopoly

power and lower public sector wages), centralization of corruption increases overall corrup-

tion, because it is simply adding an additional layer of corrupted officials at the top. This

centralized regime is corrupted at both levels of government3, where total bribes per en-

trepreneur is higher than in the decentralized corruption case, but the total amount of bribes

paid to the government is lower. Adding a layer of government to the corruption problem

leads to a worse outcome (smaller formal economy) than in the uncoordinated decentralized

equilibrium. Intuitively, when the expected cost of bureaucrats of getting fired is low and

the after-tax relative return of the legal sector as compared to the informal sector is high, the

temptation for bureaucrats to ask for an additional bribe (the amount of bribe after paying

kickback) is quite high, making it difficult for the autocrat to fight corruption at that level of

the bureaucracy. Hence, his optimal response is to choose the two-level corruption regime

and take bribes independently along with his bureaucrats. This result contradicts the claim

of Shleifer and Vishny (1993).

Echazu and Bose (2008) provide another theoretical frame with formal and informal sec-

tors. Their model portrays three corrupt bureaucratic agencies, two granting permits in the

formal sector, and a regulator who monitors the informal/shadow economy. Then they probe

four different kinds of bureaucratic organization4. They generalize the model of Shleifer and

Vishny (1993) (termed as S&V effect), and show identical results under the horizontal cen-

tralization structure. However, they indicate that vertical centralization increases bribery

3 It is also called Two-level Bribe Regime, which tends to happen when k (the measure of how manyhigh return investment projects there are in the economy) is large relative to y (the expected cost ofbureaucrats of getting fired).

4 They are: decentralized corruption (postcommunist Russia), vertically centralized corruption,when a bureaucrat granting permits in the formal sector also monitors the informal sector (environ-mental offices), horizontal centralization, with a bureaucrat in the formal sector and a separate andindependent regulator in the informal sector (Soviet Union), and totally centralized corruption.

5

and reduces welfare since increases of bribes relocate firms to the shadow economy, where

returns to corrupt activity increase.

Even more complicated, Blackburn and Forgues-Puccio (2009) develop a dynamic gen-

eral equilibrium model with endogenous growth, and predict that countries with organised

corruption networks are likely to display lower levels of bribes. These different theoreti-

cal models show the difficulties of analyzing corruption: Different regimes can be specified

by multiple parameters or different corruption structures, indicating how sensitive empirical

studies are to the specification of corruption and why empirical results are so often inconclu-

sive.

Among plenty of studies referring to these papers as their theoretical foundation and test-

ing whether these theories correspond with empirical results, there are many contradictory

results due to the ambiguous predictions made by theoretical literature. For instance, Diaby

and Sylwester (2014) and Fisman and Gatti (2002) both test whether decentralized govern-

ment structures increase corruption. Estimates of Fisman and Gatti (2002) suggest that fiscal

decentralization in government expenditure is strongly and significantly associated with lower

corruption; In contrast, Diaby and Sylwester (2014) verify the positive relationship between

decentralized bureaucracy and corruption through BEEPS data and a cross-section OLS re-

gression5. The work of Diaby and Sylwester (2014) is a straightforward empirical extension

of models of Shleifer and Vishny (1993) with several shortcomings about their regressions:

1. Dependent variable BRIBE may be exposed to response bias, since respondents do not

want to imply that they engage in corrupt activities.6

2. They fail to provide a theoretical model for their empirical analysis.

3. They do not address any concern about potential heteroskedasticity, spatial autocorre-

lation, and endogeneity.

The authors mention a few other weaknesses as well. For examples, their regression only

captures the within-country effects of bureaucratic structures on bribes. Moreover, it fails to

5 More precisely, OLS along with ordered probit models and interval regression6 Hillman (2010) discusses the effects of expressive behavior, which may be a source of survey bias.

6

distinguish whether a firm pays bribes actively or merely reacts to an official’s demands. De-

spite this shortcomings, the empirical results are significant under multiple robustness checks.

They verify the theories of Shleifer and Vishny (1993): The amount of bribes paid by firms is

lower in a centralized bureaucracy than under a decentralized one.

This paper is what inspires our research. The authors acknowledge the concern in their

paper that reporting biases might arise because of fear of retaliation from bureaucrats. Pro-

vided that it is the case, there must be a one-side bias among reported bribes in the BEEPS

data, since no firm has incentives to overreport its bribe payment. Therefore, the residuals

we get from OLS regression would have a negative skewness assuming the existence of under-

reporting, which is rejected after our hypothesis test in section 3.

Additionally, there are some other approaches of modeling corruption. Obydenkova and

Libman (2015) and Schulze and Zakharov (2018) see the Russia corruption as historical lega-

cies. To learn the impact of corruption, M. S. Gupta (1998) uses latitude, English speaking

in homes, and index of ethnolinguistics as IVs of corruption, and S. Gupta, Davoodi, and

Alonso-Terme (2002) use democracy as an IV for corruption. Kunieda, Okada, and Shibata

(2016) consider “Human Genetic Diversity” an effective instrumental variable for corruption.

We choose not to use IVs because most of the IVs for corruption are tenuous and unconvinc-

ing.

3 Hypothesis Test of Underreporting

Following Diaby and Sylwester (2014), our dataset is the 1999 Business Environment and

Enterprise Performance Survey (BEEPS) implemented by the EBRD and the World Bank.

Because it has a better design of questions than newer ones. For instance, it has question Q26b,

measuring the degree of bureaucratic centralization which is omitted afterwards. Besides, the

predefined discrete scales of bribe payments leads to a better response compared with the

continuous scale in BEEPS V. Our results about skewness test and cost frontier analysis also

hold with BEEPS V dataset, which shows the robustness of our approach. But as we seek to

7

study the relationship between BRIBE7 and bureaucratic centralization, we have to use the

BEEPS 1999 dataset.

If the managers in the survey underreport the bribes they pay, there would be a one–sided

error of the reported bribes and the residuals of OLS regression ought to be negatively skewed

(Anthopolos and C. M. Becker, 2010). Coelli (1995) noted that the presence of an inefficiency

term (here it is underreporting) would negatively skew the residuals from an OLS regression

and suggests a simple test of the third sample moment of the residuals for the skewness. The

null hypothesis of our test is: The third sample moment is less than or equal to zero (Kumb-

hakar and Lovell, 2003).

We test both the residuals of the OLS used by Diaby and Sylwester (2014) and the OLS

residuals generated by variables of our choice, and reject H0 at 0.1% significant level, which

implies a positive skewness of residuals. Figure 2 shows the OLS residuals generated by vari-

ables in our model, where the mean is to the right of the median, and it is by definition positive

skewness. Although there is no evidence of underreporting of bribes, it is hard to believe that

interviewees will overreport for whatever reason. The only possibility is that there is a model

misspecification problem: OLS is not the correct model to study BRIBE, and hence not the

correct model to test the relationship between BRIBE and bureaucratic centralization. Thus,

we come up with a new approach to model BRIBE and probe the relationship between BRIBE

and bureaucratic centralization based on the new model.

4 Model Specification

4.1 Stochastic Frontier Analysis

Scholars have been considering corruption as costs from various aspects. Johnson, Lafoun-

tain, and Yamarik (2011) find that corruption plays a significant and causal role in lower-

ing growth and investment across the state. Lio and Lee (2016) show that corruption even

costs residents’ life expectancy. Shleifer and Vishny (1993) and Waller, Verdier, and Gard-

7 BRIBE is the answer of question Q27: “On average, what percent of revenues do firms like yourstypically pay per annum in unofficial payments to public officials”, as shown in Figure 1.

8

0.0

0.1

0.2

0.3

0.4

0% Less than 1% 1 − 1.99% 2 ... 9.99% 10 ... 12% 13 ... 25% Over 25%

On average, what percent of revenues do firms like yours typically pay per annum inunofficial payments to public officials?

Den

sity

Figure 1: Dependent Variable: BRIBE

mea

n

med

ian

0.0

0.1

0.2

0.3

0.4

0.5

−2 0 2

Residuals

dens

ity

Density Plot Illustrating Skewness

Figure 2: Skewness of Residuals

ner (2002) treat corruption as a shadow cost of enterprises, which leads to our theoretical

model. Although the bribes are by nature shadow costs for enterprises, scholars have never

tried to study the “efficiency” of paying bribes via stochastic frontier analysis. Dal Bó and

Rossi (2007), Hanousek, Shamshur, and Tresl (2017), and Yan and Oum (2014) have modeled

corruption as an explanatory variable in their efficiency studies, but our approach is more

9

innovative for the purpose of studying the determinants of bribes.

According to Kumbhakar and Lovell (2003), the stochastic cost frontier can be written as:

Bi ⩾ c(yi , wi ;β)× evi (1)

Here Bi is bribes actually paid by enterprise i , while c(yi , wi ;β)×evi is the stochastic shadow

cost frontier, which contains two parts, a deterministic part c(yi , wi ;β) identical for all en-

terprises, and a enterprise–specific random part evi . If we assume that the deterministic part

takes log-linear Cobb-Douglas form, then we can rewrite the stochastic shadow cost frontier

model Equation 1 as:

lnBi =β0+βy ln yi +∑

n

βn ln wn,i + vi + ui (2)

The term yi is outputs induced from shadow cost of enterprise i , theoretically it should be

measured as the sum of economic values of government goods/services (permits, licenses,

contracts, etc.) it gets by paying bribes, vector wi is input prices faced by enterprise i : here

it should be a vector containing the unit bribes required for different purposes/government

goods. Finally, vi is the symmetric error random noise component, whereas ui is the non-

negative cost inefficiency component. Because there is no questions in the BEEPS 1999 ques-

tionnaire concerning yi and wi directly, we have to use proxies of them in our empirical model.

And after adding the variable of our interest–centralization of the bureaucracy–to Equation 2,

we have:

BRIBEi =β0+CENTβc +Total_Salesiβy + Shareiβs +XiβX + vi + ui (3)

Where CENT is the degree of centralization of the bureaucracy8, which has been thoroughly

discussed in the paper of Diaby and Sylwester (2014). Total_Sales9 is a proxy for yi , since we

can not identify the sum of government goods enterprises get by paying bribes. Share10 is a

8 It is measured by question Q26b: “If a firm pays the required additional payment to a particulargovernment official, another government official will subsequently require an additional payment forthe same service”. The value of CENT takes 1 to 6 for answers from “Always” to “Never”.

9 It is measured by question Q51a: “The estimate of your firms total sales in the last one year”.10 It is measured by question Q29: “Of the total unofficial payments that a firm like yours would

10

vector of shares of shadow payments spent on different purposes, as our proxy of unit bribes

required for different purposes/government goods. Here rises another potential problem that

wn,i in Equation 2 is the prices of government goods/services n, i.e. the unit bribe required

for permit (or contract) n, but we only have total percentages of payments spent on different

purposes. Last but not least, notice that we do not take natural logarithm of BRIBE, CENT,

Total_Sales, and all other variables except AGE11, because the data we have almost always take

integer scales. For instance, our Total_Sales takes 1 to 11 as the estimate of the firms total sales

in the last one year grows from under $250.000 to $250-$499000, · · · , to $500 million or more.

Thus, there is no need and reason to take logarithm again.

X is our control variables, comprising PREDICT, ASSURE, HONEST, LOBBY, TIME,

TAX, SUBSIDY, AGE, SIZE, sector dummy variables, and Impacts12. All of these control

variables except ASSURE and Impacts are well defined by Diaby and Sylwester (2014). PRE-

DICT and ASSURE are variables about transition costs of bribes, measuring to what extent

entrepreneurs know in advance about how much additional payments are, and to what extent

their services are delivered as agreed after paying bribes. HONEST, reflecting the bureau-

cratic competition, is controlled since Shleifer and Vishny (1993) argue that countries with

more political competition have stronger public pressure against corruption. Furthermore,

officials in these countries demand significantly lower bribes than other countries in order to

compete against their political rivals (Demsetz, 1968). Thus, HONEST actually reflects the

bureaucratic centralization in a different way compared with CENT according to Shleifer and

Vishny (1993): If CENT is the indicator of whether bureaucrats require bribes jointly or in-

dependently for their complementary government goods, then HONEST is the indicator of

whether they compete against each other in providing substitute government goods. LOBBY,

TIME, TAX, SUBSIDY, AGE, SIZE, and sector dummy variables are just characteristics of

enterprises, while Impacts is a bundle of variables measuring the extents of various forms of

corruption have had an impact on these enterprises.

make in any given year, can you please give me an estimate of what share/percentage of those paymentswould be spent on each of the following purposes”.

11 AGE = ln(2000−Q6yr).12 They are from questions Q26a, Q26c, Q26, Q31, Q32, Q24, Q48a, Q65a, Q6yr, S5ful, S3, and

Q68 respectively.

11

4.2 Spatially Lagged Variable

While in the paper of Diaby and Sylwester (2014), the influences of covariates on bribes are

treated as country–specific, S. O. Becker, Egger, and Seidel (2009) demonstrate corruption,

with few specific exceptions, is a regional phenomenon based on spatial econometrics anal-

ysis of a cross-section of 123 economies. Additionally, Goel and Saunoris (2014) also find

evidence of own contagion across nations in both corruption and shadow economy activ-

ity. About more empirical evidences of corruption contagion, also see S. O. Becker, Egger,

and Seidel (2009), Goel and Nelson (2007), and Majeed and MacDonald (2011). Therefore,

we need to be extremely cautious about the potential spatial autocorrelation problem. In or-

der to continue our stochastic frontier analysis, we will not employ the heteroskedasticity–

and spatial autocorrelation–consistent estimator of the variance–covariance matrix, i.e., the

methodology of S. O. Becker, Egger, and Seidel (2009) and Kelejian and Prucha (2007), to get

a efficient estimator. Rather, we apply a simple workaround to address spatial autocorrelation

problem while keeping focusing on our initial objective:

1. First, we get the the latitudes and longitudes of centroids of all countries13 in BEEPS

1999 dataset, and use them as the locations of enterprises.

2. Second, we calculate Moran’s I statistic via the latitude and longitude to test for global

spatial autocorrelation (Li, Calder, and Cressie, 2007; Moran, 1950). More specifi-

cally, we employ the row–standardized binary spatial weight matrix with threshold dis-

tance as 100, 600, and 1000 kilometers separately when constructing Moran’s I statistic

(Kondo, 2018). Results from STATA are listed in Appendix A, showing that there is sig-

nificant spatial interdependence in BRIBE regardless of the threshold distances, which

is not to our surprise. Notice that the approach we apply to create spatially lagged vari-

able not only captures the international corruption contagion, but also comprises the

country–specific effect by definition. After all, all enterprises in the same country has

the “same” latitude and longitude in our specification.

3. Then we add the spatially lagged dependent variable into Equation 3, as our new em-

13 It is because we do not have more accurate positions of individual enterprises.

12

pirical model:

BRIBEi =β0+CENTβc+Total_Salesiβy+Shareiβs+XiβX+W ·BRIBE+vi+ui (4)

where W is the row–standardized binary spatial weight matrix with threshold distance

as 600 kilometers. Thus, W ·BRIBE is the spatially lagged dependent variable, named

as “Spatial_Lag” in Appendix B, which addresses the spatial autocorrelation problem

(Kondo, 2017) in our model.

Model (1) in Appendix B is the estimation result of Equation 4. Along with Model (2), (3), and

(4), the always statistically significant coefficients upon Spatial_Lag verifies our conjecture of

the presence of corruption contagion.

4.3 Heteroskedasticity

There is no reason to assume our stochastic frontier Equation 4 is homoskedastic, just as the

results in Appendix B shows that there is significant heteroskedasticity in the determinants of

BRIBE. Depending on what factors the sources of noise vary with, the two–sided idiosyncratic

error vi could be heteroskedastic. Similarly, the asymmetric bribe inefficiency error term ui

may also be heteroskedastic (Anthopolos and C. M. Becker, 2010; Kumbhakar and Lovell,

2003). To this end, we allow both the error components’ variances vary with some of our

explanatory variables.

More, specifically, the Model (1) in Appendix B has no heteroskedasticity. The Model (2)

has SIZE and CENT in its σ2v and σ2

u , while the Model (3) has SIZE and spatially lagged vari-

able in its two error variance functions. The Model (3) has SIZE, CENT, and spatially lagged

variable in its heteroskedasticity. The size of firms is traditionally conceived to be associated

with potential sources of noise, as well as the sources of technical inefficiency (Anthopolos

and C. M. Becker, 2010). The reason we consider CENT in two error variance functions is

that CENT is the degree of centralization of the bureaucracy, also indicating the uncertainty

of bribe. Moreover, since CENT is the variable of our interest, it is natural to discover the pos-

sible channel CENT influencing BRIBE, in terms of both the deterministic frontier part and

the bribe inefficiency part. Besides, the variances of symmetric error component and bribe

13

inefficiency could probably vary with spatially lagged variable, as the effect of neighboring

corruption tend to be positive and statistically significant in spatial econometric studies (Goel

and Nelson, 2007).

5 Results

5.1 Bureaucratic Centralization

Appendix B presents the estimation results of our stochastic frontier analysis based on the

aforementioned approaches. Model (1) has no heteroskedasticity, while Model (2), (3), and (4)

have different random error variance function and bribe inefficiency variance function, from

where we can conclude that there is no evidence of negative correlation between the CENT

(centralization of corruption) and the cost frontier of bribes. To further study the effects of

CENT, we also incorporate many possible interactions between CENT and other character-

istics of enterprises, e.g., SIZE, AGE, and sector dummy variables. But it turns out that, just

like the coefficients upon CENT as a covariate, none of them are statistically significant. Nor

does the square of CENT have a statistically significant estimation. Hence, we do not report

them here.

In actuality, the coefficient of CENT is only significant in Model (2), where the sign is in

the opposite direction from the expectation of Shleifer and Vishny (1993). One possible rea-

son is that, theoretically, CENT is not a part of deterministic bribe frontier (see Equation 2),

and thus should not play a role in the cost frontier of paying bribe. Its economic implication

is: If we consider bribes as the shadow costs of getting government goods (e.g., licenses, per-

mits, and contracts etc.), then enterprises facing a more centralized bureaucracy do not have

systematically lower cost frontier (minimum bribes needed for their businesses) than those

facing a more decentralized bureaucratic structure. It also means that given all the other vari-

ables constant, the centralization of the bureaucracy does not reduce the minimum bribes for

a enterprise to get things done. However, the coefficients upon CENT in the idiosyncratic

random error term and bribe inefficiency error term do indicate the expected significant re-

lationship between bureaucratic centralization and fewer bribes, which means that the more

centralized bureaucracy enterprises face, the less variance of bribes they need to pay when

14

reaching the frontier, at the same time, the more likely they can “reach” the frontier, i.e.,

the fewer bribes they need to pay due to the less variance of the one–sided bribe inefficiency.

Combining it with the insignificant coefficients of CENT in the deterministic part, we can

interpret it as: centralized bureaucracy does not lower corruption by reducing the minimum

bribes (i.e., the bribe frontier), but does lower bribes by decreasing the variances of error

terms, both the two–sided error and the inefficiency error. Therefore, entrepreneurs under

decentralized bureaucracy do not necessarily need to pay more bribes—they can reach the

similar minimum bribes level as those under centralized bureaucracy14, they are just exposed

to a larger variance, i.e., a larger probability of paying bribes inefficiently. As a consequence,

once the entrepreneurs pay bribes efficiently, a more centralized bureaucratic structure will

not help reduce their bribes anymore.

5.2 Other Results

In marked contract to the coefficient of CENT, which is only significant in error terms, the

spatially lagged variable is a good example to help illustrate the meaning of coefficients of

CENT, because the spatially lagged variable is significantly positive not only in deterministic

frontier, but also in random error term and bribe inefficiency term. It verifies the expected

neighboring effect of corruption: The more bribes paid by your neighbors, the more bribes

you tend to pay (in terms of both the frontier and the efficiency), and the larger variance of

your payments. Notice that here the spatially lagged variable makes differences to both the

frontier and the error terms in a way that a less corrupted business environment (measured

in the average amount of bribes paid by their neighbors) lowers the bribe inefficiency while

it also lowers the minimum amount of bribes at the efficient scenarios. In contrast, CENT

does not influence the minimum amount of bribes at the efficient scenarios. This discovery is

also in line with Shleifer and Vishny (1993). Because theft15 sometimes helps reduce the price

of government good from p to b , the market competition between private agents prefers

14 According to the empirical results of Diaby and Sylwester (2014), entrepreneurs under decentral-ized bureaucracy usually pay more bribes, which is true but can not deepen our comprehension aboutwhy it happens.

15 Theft means that the official only takes the bribe and does not turn over the official governmentprice p to the government. With theft, the price reduces to the bribe, which may be less than theofficial government price p, but not always, as b > p is also possible.

15

bribers over legitimate agents, which drives entrepreneurs to pay bribes actively when they

perceive others are doing so. This theory explains why corruption acts contagiously and

spreads among entrepreneurs, and why in our models Spatial_Lag is always significant.

Economies of scale (measured in the SIZE variable) applies to paying bribes according

to the estimated coefficients of SIZE in both frontier part and inefficiency part. Enterprises

tend to pay fewer bribes and to pay bribes more efficiently as their sizes grow. It could be

attributed to greater resources the large companies have to protect themselves (Diaby and

Sylwester, 2014), or to the fact that larger companies might have more substitutes of bribes

to get things down, e.g., social capital, connections and “guanxi” (Dasgupta and Serageldin,

2001; Smart, 1993). As a matter of fact, we believe that here both the factors have some

power to explain the coefficients of SIZE. We discuss it further in subsection 5.4. As for

other coefficients, the statistically significant coefficients upon TIME16 might rise the concern

of reverse causation provided that some of the time senior managements spend in dealing

with government officials involves paying bribes. But removing TIME does not alter our

estimation results, so this problem does not change the essence of our analysis.

5.3 Robustness

For robustness, we test our model with different specifications and control variables, with

the results listed in Appendix C. For example, we replace Total_Sales and Spatial_Lag with

DIFF as another series of control variables, which is the answers of question Q17: “How

problematic are the following for the operation and growth of your business”. The results of

our new stochastic frontier estimations are listed in Table 2 without a spatially lagged vari-

able and Table 3 with a spatially lagged variable. As we discussed in subsection 5.1, among

all the various models, none of them has a significantly negative coefficient upon CENT in

bribe frontier part, while they all verify the significant corruption contagion (with variable

Spatial_Lag) and economies of scale phenomenon (with variable SIZE).

In addition, we replicate the same methodology on another dataset to justify our model

specifications. Our results about skewness test and cost frontier analysis also hold with BEEPS

16 The answer of question Q14: “What percentage of senior managements time per year is spent indealing with government officials about the application and interpretation of laws and regulations”.

16

V dataset, which shows the robustness of our approaches. Specifically, since BEEPS V does

not provide a proxy for bureaucratic centralization, we can not study the correlation between

them, but we do find the same skewness of bribes17 and the significant stochastic frontier

analysis results. However, as it is irrelevant to our topic of bureaucratic centralization, we

choose not to report them here.

5.4 Shortcomings

There are several shortcomings about our model specification and estimations. First of all,

Total_Sales seems to be a bad proxy of yi , as it is not significant in any of our models18. Second,

though significant, the sign of Share is not the same as our expectation drawn from the ordi-

nary cost frontier analysis, where the coefficients of prices of inputs are supposed to be posi-

tive. Moreover, corruption is multiform, charging bribes is just one kind of corruption of our

interest, while there are many other substitute ways like hiring the relatives of government

officials with higher salaries than market level. Dasgupta and Serageldin (2001) and Smart

(1993) have discussed social capital, bribes, and gifts. As a consequence, unfortunately, we are

exposed to potential omitted-variable bias in the deterministic part (bribe frontier). And for

the bribe inefficiency term, it is possible that CENT also captures the effect of CONNEC-

TION in influencing the bribe efficiency, which leads to the exaggeration of the coefficients

of CENT. It means that bureaucratic centralization may not help entrepreneurs pay bribes

more efficiently. It is the abuse of social connections (or other kinds of corruption, which are

probably tangled in CENT) that reduces bribes. Of course, it would be fascinating to include

the analysis of relationship between CENT and CONNECTION, but there is no questions

in our dataset that allow us to do so. Last but not least, as mentioned in the last paragraph in

section 2, we fail to find convincing IVs to address the endogeneity problem.

17 While in BEEPS V, the bribes are measured by question J7a: “On average, what percentage of totalannual sales, or estimated total annual value, do establishments like this one pay in informal paymentsor gifts to public officials for this purpose”.

18 Recall that as yi is outputs induced from shadow cost of enterprise i , theoretically it should bemeasured as the sum of economic values of government goods/services it gets by paying bribes ratherthan the total sales of enterprise i .

17

6 Conclusion

In this paper, we follow the research done by Diaby and Sylwester (2014) and test the cross–

country firm level survey dataset (BEEPS 1999) for underreporting in bribes as well as the

association between bureaucratic centralization and bribes with stochastic frontier analysis.

To the best of our knowledge this is the first study of underreporting of bribes in survey data,

and also the first study applying stochastic frontier analysis to model bribes.

Our hypothesis test suggests that there is no evidence of underreporting about bribes.

Rather, there is significant positive skewness of OLS residual, which inspires our investiga-

tion of its causes. Parallel with the single–output Cobb–Douglas cost frontier proposed by

Kumbhakar and Lovell (2003), we treat bribes as a shadow cost and model it with the cost fron-

tier Equation 3. After testing BRIBE for spatial autocorrelation we add the spatially lagged

variable with respect to BRIBE. By using stochastic frontier analysis, we seek to delineate the

bribes into two parts: a deterministic cost frontier part representing the minimum bribes

from other typical entrepreneurs in their line to get things done, and a bribe inefficiency part

representing the amount of bribes exceeding the efficient frontier. Our empirical results are

significant and robust, indicating that centralized bureaucracy does not lower corruption by

reducing the minimum bribes (i.e., the bribe frontier), but does lower the bribes by reducing

the bribe inefficiency. It means that once the entrepreneurs pay bribes efficiently, a more cen-

tralized bureaucratic structure will not help reduce their bribes anymore. In contrast with

BRIBE, SIZE and spatial lagged variable influence not only the bribe efficiency, but also the

bribe frontier, supporting the corruption contagion and economies of scale phenomenon.

Our work, though creative, is still exposed to traditionally conceived problems: potential

endogeneity and omitted-variable bias. Future work will attempt to find convincing IVs and

dive deeper into the effect of social capital and connections on bribes.

18

A Testing for spatial autocorrelation via Moran’s I statistic

D i s t a n c e by s i m p l i f i e d v e r s i o n of Vincenty formula ( u n i t : km)

−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−| Obs . Mean S .D. Min . Max .

−−−−−−−−−−−−−+−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−D i s t a n c e | 1274519 2 4 2 0 . 3 9 2 1 5 1 0 . 9 1 0 1 6 9 . 7 0 2 5 3 9 9 . 3 2 5

−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

Moran ’ s I S t a t i s t i c Number of Obs = 1655

−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−D i s t a n c e t h r e s h o l d ( u n i t : km ) : 100

−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−V a r i a b l e | Moran ’ s I E ( I ) SE ( I ) Z ( I ) p−v a l u e

−−−−−−−−−−−−−+−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−BRIBE | 0 . 0 8 3 8 3 −0.00060 0 . 0 0 3 7 5 2 2 . 4 9 0 5 5 0 . 0 0 0 0 0

−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−D i s t a n c e t h r e s h o l d ( u n i t : km ) : 600

−−−−−−−−−−−−−+−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−V a r i a b l e | Moran ’ s I E ( I ) SE ( I ) Z ( I ) p−v a l u e

−−−−−−−−−−−−−+−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−BRIBE | 0 . 0 6 5 0 7 −0.00060 0 . 0 0 2 3 4 2 8 . 0 6 7 2 0 0 . 0 0 0 0 0

−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−D i s t a n c e t h r e s h o l d ( u n i t : km ) : 1000

−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−V a r i a b l e | Moran ’ s I E ( I ) SE ( I ) Z ( I ) p−v a l u e

−−−−−−−−−−−−−+−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−BRIBE | 0 . 0 2 9 6 1 −0.00060 0 . 0 0 1 6 4 1 8 . 4 4 2 3 9 0 . 0 0 0 0 0

−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−Null Hypothes i s : S p a t i a l Randomization

19

B Stochastic Frontier Estimation Results

Dependent variable:

BRIBE

Model Model Model Model

(1) (2) (3) (4)

CENT −0.0151 0.0296∗∗ 0.00601 0.0140

(0.0300) (0.0108) (0.0149) (0.0197)

Total_Sales −0.0263 −0.00148 0.00248 −0.00398

(0.0221) (0.0108) (0.0112) (0.00837)

Share_CON −0.0273 −0.0325∗∗∗ −0.0221∗ −0.0171∗∗

(0.0340) (0.00939) (0.0110) (0.00660)

Share_LIC −0.0285 −0.0339∗∗∗ −0.0228∗ −0.0171∗∗

(0.0340) (0.0102) (0.0113) (0.00634)

Share_TAXES −0.0247 −0.0305∗∗∗ −0.0211∗ −0.0175∗∗

(0.0340) (0.00897) (0.0106) (0.00638)

Share_GOV −0.0224 −0.0293∗∗ −0.0204+ −0.0153∗

(0.0340) (0.00941) (0.0107) (0.00609)

Share_CUS −0.0208 −0.0277∗∗ −0.0194+ −0.0143∗

(0.0340) (0.00919) (0.0104) (0.00589)

Share_COU −0.0300 −0.0340∗∗∗ −0.0230∗ −0.0167∗∗

(0.0340) (0.00871) (0.0112) (0.00599)

Share_HEA −0.0233 −0.0317∗∗∗ −0.0201+ −0.0154∗∗

(0.0340) (0.00953) (0.0104) (0.00568)

Share_LAW −0.0249 −0.0344∗∗∗ −0.0198+ −0.0225∗∗

(0.0341) (0.00942) (0.0103) (0.00777)

Share_OTHER −0.0313 −0.0340∗∗∗ −0.0238∗ −0.0167∗∗

(0.0340) (0.00954) (0.0116) (0.00586)

PREDICT −0.0749∗∗ −0.0417∗ −0.0304+ −0.0192+

20

(0.0263) (0.0196) (0.0169) (0.0112)

ASSURE −0.0455 0.0194 −0.00515 0.00748

(0.0308) (0.0208) (0.0217) (0.00632)

HONEST 0.110∗∗∗ 0.0215 0.0123 0.0170∗

(0.0289) (0.0240) (0.0160) (0.00856)

LOBBY 0.0633 0.0764 0.0405 −0.0294

(0.0804) (0.0504) (0.0509) (0.0247)

TIME 0.128∗∗∗ 0.0800∗∗∗ 0.0523∗∗ 0.0363∗∗

(0.0275) (0.0218) (0.0199) (0.0128)

TAX 0.0415∗∗ 0.0193 0.0176+ 0.00912∗∗

(0.0156) (0.0120) (0.00914) (0.00340)

SUBSIDY 0.0754 0.251∗∗∗ 0.0815 0.172∗

(0.141) (0.0761) (0.0994) (0.0679)

SIZE −0.0620∗ −0.0190 −0.0453∗ −0.0160

(0.0310) (0.0154) (0.0215) (0.0134)

AGE 0.0576 0.0438 0.0601∗ 0.0413∗∗

(0.0573) (0.0324) (0.0286) (0.0150)

Agriculture −0.790 −0.563∗∗ −0.445∗∗ −0.328∗∗

(0.514) (0.171) (0.154) (0.102)

Mining −1.051 −0.690∗∗∗ −0.408∗ −0.309∗∗

(0.775) (0.193) (0.170) (0.0942)

Manufacture −0.775 −0.646∗∗∗ −0.465∗∗ −0.417∗∗∗

(0.507) (0.171) (0.168) (0.120)

Construction −0.653 −0.535∗∗∗ −0.362∗∗ −0.376∗∗∗

(0.509) (0.155) (0.138) (0.104)

Power 0.422 1.040∗ 0.242 0.907∗

(0.975) (0.420) (0.959) (0.401)

Trading −0.545 −0.469∗∗∗ −0.355∗ −0.341∗∗∗

(0.505) (0.137) (0.149) (0.0962)

Retail −0.540 −0.481∗∗∗ −0.333∗∗ −0.375∗∗∗

(0.507) (0.133) (0.120) (0.106)

Transport −0.822 −0.773∗∗∗ −0.534∗∗ −0.555∗∗∗

21

(0.537) (0.195) (0.196) (0.128)

Financial −1.106 −0.537∗∗∗ −0.676 −0.298

(0.692) (0.148) (0.599) (0.246)

Personal −0.293 −0.371∗ −0.213+ −0.261∗∗

(0.518) (0.152) (0.122) (0.0829)

Business −0.514 −0.422∗∗∗ −0.300∗∗ −0.291∗∗∗

(0.517) (0.112) (0.109) (0.0880)

Charity −0.350 −0.229 −0.158 −0.146

(0.646) (0.414) (0.244) (0.121)

Impact_CEN 0.0532 −0.000655 0.0290 −0.00763

(0.0450) (0.0308) (0.0314) (0.0202)

Impact_PAR 0.0992 0.0610 0.0109 0.0409∗

(0.0647) (0.0420) (0.0348) (0.0208)

Impact_PRE 0.110+ 0.0521 0.0453 0.0000669

(0.0625) (0.0343) (0.0344) (0.0394)

Impact_CRI −0.233∗∗ −0.133∗ −0.0844∗ −0.0884∗

(0.0730) (0.0552) (0.0374) (0.0401)

Impact_ARB 0.0556 0.0106 −0.0000917 0.0288

(0.0710) (0.0564) (0.0349) (0.0233)

Impact_BRI 0.0885+ 0.0684∗ 0.0379 0.0582∗∗

(0.0517) (0.0278) (0.0351) (0.0189)

Impact_PAT 0.120∗ 0.0564∗∗ 0.0289 0.0369

(0.0503) (0.0214) (0.0389) (0.0233)

Impact_CON −0.0694 −0.0422 −0.0207 −0.0206

(0.0549) (0.0272) (0.0328) (0.0404)

Spatial_Lag 0.732∗∗∗ 0.395∗∗∗ 0.194∗ 0.216∗∗

(0.132) (0.0917) (0.0835) (0.0791)

Constant 1.744 3.080∗∗ 3.331∗∗∗ 2.607∗∗∗

(3.465) (0.992) (1.003) (0.523)

lnσ2v

SIZE 2.447∗∗∗ 2.770∗∗∗ 2.684∗∗∗

(0.417) (0.299) (0.407)

22

CENT −3.812∗∗∗ −3.676∗∗∗

(0.601) (0.568)

Spatial_Lag 2.787∗∗ 0.928

(0.997) (1.114)

Constant −2.146∗∗∗ −9.664∗∗∗ −29.25∗∗∗ −14.06∗∗

(0.468) (2.705) (3.490) (4.533)

lnσ2u

SIZE −0.139∗∗∗ −0.141∗∗∗ −0.162∗∗∗

(0.0408) (0.0415) (0.0388)

CENT −0.114∗∗ −0.147∗∗

(0.0428) (0.0461)

Spatial_Lag 0.969∗∗∗ 1.149∗∗∗

(0.191) (0.193)

Constant 1.049∗∗∗ 2.188∗∗∗ −1.354∗ −1.308∗

(0.117) (0.211) (0.619) (0.608)

N 630 630 630 630

Standard errors in parentheses+ p < 0.10, ∗ p < 0.05, ∗∗ p < 0.01, ∗∗∗ p < 0.001

23

C Other Regression Results

Table 2: Stochastic frontier estimations without spatially

lagged variable

Dependent variable:

BRIBE

(1) (2) (3) (4)

Half Exponential Hetero Hetero with

Normal with SIZE SIZE, CENT

PREDICT −0.0867∗∗ −0.112∗∗∗ −0.0283 −0.0506∗∗∗

(0.0277) (0.0300) (0.0222) (0.00799)

CENT 0.00104 −0.00936 −0.000652 0.0160∗

(0.0282) (0.0304) (0.0178) (0.00639)

ASSURE −0.0159 −0.0306 −0.00886 0.0373∗∗∗

(0.0300) (0.0343) (0.0292) (0.00754)

HONEST 0.101∗∗ 0.151∗∗∗ 0.0194 0.0395∗∗∗

(0.0324) (0.0295) (0.0195) (0.0102)

LOBBY 0.214∗∗ 0.261∗∗ 0.141∗∗ 0.111∗∗∗

(0.0791) (0.0879) (0.0520) (0.0245)

TIME 0.124∗∗∗ 0.166∗∗∗ 0.0559∗ 0.0558∗∗

(0.0300) (0.0313) (0.0232) (0.0191)

TAX 0.0214 0.0237 −0.0111 0.00150

(0.0158) (0.0170) (0.00931) (0.00582)

SUBSIDY 0.115 0.178 0.116 0.284∗∗∗

(0.146) (0.153) (0.116) (0.0550)

YEAR −0.00140 −0.000549 −0.000436 −0.000834

(0.00283) (0.00289) (0.00207) (0.000683)

SIZE −0.0779∗∗ −0.0814∗∗ −0.0639∗∗ −0.0383∗∗∗

24

(0.0278) (0.0305) (0.0227) (0.00584)

Agriculture −0.286 −0.373 −0.177 −0.0838

(0.568) (0.688) (0.222) (0.0603)

Mining −0.375 −0.376 −0.264 −0.208∗

(0.660) (0.826) (0.167) (0.0839)

Manufacture −0.320 −0.401 −0.193 −0.126∗

(0.547) (0.670) (0.190) (0.0615)

Construction −0.153 −0.179 −0.0489 −0.138∗

(0.556) (0.679) (0.164) (0.0704)

Power 0.851 0.582 0.635 1.535∗∗∗

(1.008) (1.105) (1.053) (0.460)

Trading −0.216 −0.314 −0.116 −0.106

(0.551) (0.672) (0.152) (0.0761)

Retail −0.189 −0.208 −0.121 −0.148∗

(0.551) (0.675) (0.148) (0.0621)

Transport −0.325 −0.315 −0.0887 −0.135+

(0.566) (0.693) (0.199) (0.0817)

Financial −0.480 −0.835 −0.225 −0.195+

(0.690) (0.784) (0.158) (0.101)

Personal 0.258 0.274 0.0736 0.0853+

(0.554) (0.678) (0.164) (0.0515)

Business −0.250 −0.147 −0.206 −0.176∗∗∗

(0.554) (0.686) (0.146) (0.0379)

Others −0.247 −0.302 −0.0864 −0.185

(0.684) (0.821) (0.150) (0.117)

LICENSING 0.0656+ 0.0994∗ 0.0672∗ 0.0555∗∗∗

(0.0362) (0.0424) (0.0289) (0.0124)

CUSTOMS 0.0782∗ 0.0682 0.0315 0.0384∗∗∗

(0.0378) (0.0434) (0.0284) (0.0106)

LaborREGULATION −0.0208 −0.0532 0.00682 0.0413

(0.0447) (0.0479) (0.0353) (0.0252)

CURRENCY 0.0588 0.0837+ 0.0224 0.00967

25

(0.0411) (0.0459) (0.0196) (0.0112)

ENV −0.0290 −0.00735 −0.0359 −0.00676

(0.0464) (0.0489) (0.0395) (0.0133)

SAFETY 0.0182 −0.0115 0.0304 −0.0414∗

(0.0451) (0.0502) (0.0302) (0.0183)

TaxREGULATION 0.0166 −0.00363 −0.000663 0.0187∗

(0.0519) (0.0558) (0.0251) (0.00938)

HighTAX −0.0328 0.0100 −0.0271 −0.0569∗∗∗

(0.0586) (0.0632) (0.0366) (0.0140)

Share_CON −0.0351 −0.0380 −0.0361∗ −0.0205∗∗

(0.0336) (0.0408) (0.0151) (0.00730)

Share_LIC −0.0373 −0.0388 −0.0405∗ −0.0227∗∗

(0.0336) (0.0407) (0.0160) (0.00822)

Share_TAXES −0.0303 −0.0313 −0.0336∗ −0.0191∗∗

(0.0336) (0.0408) (0.0150) (0.00709)

Share_GOV −0.0300 −0.0302 −0.0356∗ −0.0188∗

(0.0336) (0.0407) (0.0152) (0.00746)

Share_CUS −0.0333 −0.0341 −0.0387∗ −0.0208∗∗

(0.0336) (0.0407) (0.0160) (0.00796)

Share_COU −0.0354 −0.0351 −0.0396∗ −0.0230∗∗

(0.0336) (0.0408) (0.0156) (0.00761)

Share_HEA −0.0286 −0.0294 −0.0362∗ −0.0193∗∗

(0.0336) (0.0407) (0.0155) (0.00651)

Share_LAW −0.0342 −0.0369 −0.0365∗ −0.0229∗∗∗

(0.0336) (0.0408) (0.0150) (0.00694)

Share_OTHER −0.0360 −0.0382 −0.0385∗ −0.0207∗∗

(0.0336) (0.0407) (0.0157) (0.00743)

Impact_CEN 0.0593 0.0530 0.00437 0.0145

(0.0452) (0.0507) (0.0357) (0.0137)

Impact_PAR 0.0250 0.0585 −0.0155 −0.000314

(0.0679) (0.0749) (0.0562) (0.0127)

Impact_PRE 0.119+ 0.0688 0.114∗ 0.0541∗∗

26

(0.0678) (0.0747) (0.0540) (0.0206)

Impact_CRI −0.106 −0.0984 −0.113+ −0.106∗∗

(0.0749) (0.0778) (0.0671) (0.0384)

Impact_ARB 0.0200 0.0309 0.0615 0.0544

(0.0724) (0.0755) (0.0562) (0.0403)

Impact_BRI 0.0902 0.125∗ −0.0165 0.0292+

(0.0549) (0.0546) (0.0496) (0.0163)

Impact_PAT 0.124∗ 0.133∗ 0.0913∗∗ 0.0605∗∗∗

(0.0496) (0.0562) (0.0348) (0.0157)

Impact_CON −0.125∗ −0.0888 −0.0391 −0.0543∗∗

(0.0549) (0.0626) (0.0319) (0.0173)

Constant 6.747 5.129 5.971 4.647∗∗∗

(6.619) (7.172) (4.627) (1.375)

lnσ2v

SIZE 2.778∗∗∗ 2.297∗∗∗

(0.301) (0.379)

CENT −3.240∗∗∗

(0.476)

Constant −2.315∗∗∗ −0.851∗∗∗ −20.35∗∗∗ −9.695∗∗∗

(0.550) (0.192) (1.946) (2.472)

lnσ2u

SIZE −0.0931∗ −0.114∗∗

(0.0425) (0.0386)

CENT −0.0975∗

(0.0422)

Constant 1.080∗∗∗ −0.322 1.596∗∗∗ 2.022∗∗∗

(0.119) (0.208) (0.164) (0.208)

N 631 631 631 631

Standard errors in parentheses+ p < 0.10, ∗ p < 0.05, ∗∗ p < 0.01, ∗∗∗ p < 0.001

27

Table 3: Stochastic frontier estimations with spatially

lagged variable

Dependent variable:

BRIBE

(1) (2) (3) (4)

Half Hetero with Hetero with Hetero with

Normal SpatLag in σv SpatLag in both SpatLag in σu

PREDICT −0.0668∗ −0.0227 −0.0223 −0.0217

(0.0269) (0.0240) (0.0250) (0.0289)

CENT 0.00969 0.0258 0.00686 0.00761

(0.0304) (0.0185) (0.0161) (0.0177)

ASSURE −0.0239 0.00658 0.000538 −0.000613

(0.0319) (0.0318) (0.0281) (0.0290)

HONEST 0.101∗∗ 0.0418+ 0.0354∗ 0.0335+

(0.0363) (0.0214) (0.0157) (0.0190)

LOBBY 0.100 0.0482 0.0341 0.0400

(0.0806) (0.0527) (0.0329) (0.0363)

TIME 0.124∗∗∗ 0.116∗∗∗ 0.0857∗∗∗ 0.0817∗∗∗

(0.0290) (0.0126) (0.0230) (0.0245)

TAX 0.0356∗ 0.0160 0.0113 0.00741

(0.0156) (0.0154) (0.0164) (0.0134)

SUBSIDY 0.110 0.230+ 0.250+ 0.195+

(0.147) (0.135) (0.128) (0.117)

YEAR −0.00366 −0.000704 −0.000720 −0.000719

(0.00282) (0.00346) (0.00232) (0.00216)

SIZE −0.0801∗∗ −0.0835∗∗ −0.0869∗∗∗ −0.0809∗∗∗

(0.0280) (0.0260) (0.0218) (0.0202)

Agriculture −0.463 −0.0468 −0.207∗ −0.0992

28

(0.570) (0.158) (0.0917) (0.144)

Mining −0.603 −0.540∗∗∗ −0.504∗∗ −0.440∗

(0.679) (0.143) (0.177) (0.186)

Manufacture −0.523 −0.341+ −0.380∗∗∗ −0.313∗

(0.544) (0.184) (0.0986) (0.125)

Construction −0.382 −0.295 −0.386∗∗ −0.261+

(0.550) (0.202) (0.130) (0.154)

Power 0.780 0.894 0.662 0.745

(0.982) (1.017) (1.046) (1.025)

Trading −0.347 −0.194 −0.291∗ −0.175

(0.545) (0.169) (0.121) (0.122)

Retail −0.265 −0.105 −0.239∗∗ −0.144

(0.545) (0.138) (0.0922) (0.124)

Transport −0.424 −0.278 −0.459∗∗ −0.255

(0.567) (0.198) (0.174) (0.197)

Financial −0.637 −0.390∗∗∗ −0.473∗ −0.368+

(0.707) (0.117) (0.190) (0.208)

Personal 0.145 0.228 0.0675 0.155

(0.548) (0.192) (0.132) (0.160)

Business −0.319 −0.189 −0.263∗∗ −0.162

(0.547) (0.159) (0.100) (0.143)

Charity −0.0955 0.431∗ 0.0135 0.149

(0.683) (0.207) (0.189) (0.235)

LICENSING 0.0303 0.0461 0.0389 0.0414

(0.0381) (0.0363) (0.0289) (0.0367)

CUSTOMS 0.118∗∗ 0.118∗∗∗ 0.0581+ 0.0810∗

(0.0403) (0.0248) (0.0346) (0.0390)

LaborREGULATION −0.00296 0.0609∗ 0.0308 0.0284

(0.0460) (0.0301) (0.0248) (0.0277)

CURRENCY −0.00571 −0.0423∗ −0.0233 −0.0268

(0.0420) (0.0182) (0.0240) (0.0293)

ENV −0.0160 0.00200 0.0161 −0.00490

29

(0.0462) (0.0247) (0.0379) (0.0270)

SAFETY 0.0219 0.0234 −0.00279 0.0210

(0.0465) (0.0494) (0.0345) (0.0316)

TaxREGULATION −0.00162 −0.0316 0.0236 0.00443

(0.0557) (0.0283) (0.0370) (0.0359)

HighTAX −0.0623 −0.0445 −0.0691+ −0.0489

(0.0570) (0.0385) (0.0387) (0.0379)

Share_CON −0.0323 −0.0467∗∗∗ −0.0297∗ −0.0335∗

(0.0316) (0.0136) (0.0140) (0.0141)

Share_LIC −0.0335 −0.0480∗∗∗ −0.0304∗ −0.0345∗

(0.0315) (0.0143) (0.0142) (0.0140)

Share_TAXES −0.0287 −0.0399∗∗ −0.0250+ −0.0282∗

(0.0316) (0.0130) (0.0136) (0.0131)

Share_GOV −0.0266 −0.0419∗∗ −0.0251+ −0.0297∗

(0.0315) (0.0145) (0.0142) (0.0138)

Share_CUS −0.0288 −0.0431∗∗ −0.0272+ −0.0319∗

(0.0315) (0.0136) (0.0145) (0.0141)

Share_COU −0.0331 −0.0470∗∗∗ −0.0310∗ −0.0348∗

(0.0316) (0.0140) (0.0141) (0.0143)

Share_HEA −0.0264 −0.0392∗∗ −0.0230+ −0.0274∗

(0.0315) (0.0142) (0.0135) (0.0136)

Share_LAW −0.0332 −0.0460∗∗∗ −0.0287∗ −0.0325∗

(0.0315) (0.0138) (0.0138) (0.0142)

Share_OTHER −0.0355 −0.0468∗∗∗ −0.0292∗ −0.0329∗

(0.0315) (0.0139) (0.0142) (0.0141)

Impact_CEN 0.0320 −0.00656 −0.0381 −0.0320

(0.0462) (0.0469) (0.0455) (0.0429)

Impact_PAR 0.0280 −0.0282 −0.0443 −0.0268

(0.0710) (0.0479) (0.0628) (0.0647)

Impact_PRE 0.166∗ 0.170∗∗ 0.171∗∗ 0.146∗

(0.0680) (0.0590) (0.0634) (0.0629)

Impact_CRI −0.192∗ −0.193∗∗ −0.101 −0.119+

30

(0.0775) (0.0606) (0.0732) (0.0691)

Impact_ARB 0.0400 −0.000280 −0.0294 −0.0165

(0.0720) (0.0520) (0.0609) (0.0537)

Impact_BRI 0.0893 0.0723 0.0396 0.0257

(0.0557) (0.0603) (0.0474) (0.0429)

Impact_PAT 0.142∗∗ 0.128∗∗ 0.0634 0.0819+

(0.0498) (0.0457) (0.0448) (0.0441)

Impact_CON −0.0989+ −0.0276 0.0148 0.0147

(0.0553) (0.0502) (0.0231) (0.0219)

Spatial_Lag 0.731∗∗∗ 0.573∗∗∗ 0.311∗∗ 0.345∗∗

(0.126) (0.0875) (0.111) (0.112)

Constant 9.063 4.775 4.531 4.771

(6.546) (7.353) (4.752) (4.405)

lnσ2v

SIZE 3.024∗∗∗ 2.745∗∗∗ 2.795∗∗∗

(0.356) (0.314) (0.310)

Spatial_Lag 2.415+ 3.265∗∗

(1.239) (1.176)

Constant −2.497∗∗∗ −30.05∗∗∗ −30.79∗∗∗ −20.59∗∗∗

(0.720) (4.312) (4.022) (2.025)

lnσ2u

SIZE −0.0682 −0.0695

(0.0468) (0.0458)

Spatial_Lag 0.809∗∗∗ 0.754∗∗∗

(0.216) (0.212)

Constant 1.040∗∗∗ 1.457∗∗∗ −1.394∗ −0.961

(0.137) (0.177) (0.695) (0.683)

N 582 582 582 582

Standard errors in parentheses+ p < 0.10, ∗ p < 0.05, ∗∗ p < 0.01, ∗∗∗ p < 0.001

31

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