# Effect of the Complexity of the Customs Tax System on the Tax Effort

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Definitions: Tax Effort, Revenue Potential, and Tax Complexity

## 3. Literature Review

- Construction of the Stochastic Tax Frontier

- I represents the number of observations;
- t is a time period;
- ${y}_{it}$ is the actual revenue collected by the Customs Administration (i) in year (t);
- ${x}_{it}$ corresponds to the set of variables that explain the potential revenue of i in year (t);
- ${\beta}_{0}$ is a constant;
- $\beta $ represents the input parameters of the production function;
- ${\nu}_{it}$ is a random error and an independent and identically distributed stochastic component with a mean of zero and a constant variance N (0, ${\sigma}_{v}^{2})i.i.d$ that represents any exogenous factor that cannot be controlled by the Customs Administration, e.g., a tax exemption that affects revenue collection. It may also refer to measurement errors. ${\nu}_{it}$ may take a positive or negative value;
- ${\mu}_{it}$ is a random stochastic component of the technical inefficiency and a non-negative term that is assumed to be independently distributed. In this context, the inefficiency represents the inability to achieve the maximum amount of revenue collection. The components ${\nu}_{it}$ and ${\mu}_{it}$ are assumed to be independent of each other and the estimators.

- Factors influencing the Tax Effort

- ${Z}_{it}$ is the set of exogenous variables that would explain the inefficiency in tax collection;
- $\delta $ is a vector of coefficients to be estimated; and
- ${W}_{it}$ is a random variable defined as a truncated normal distribution with mean of zero and a constant variance. The point of truncation is $\delta {Z}_{it}$, so that ${W}_{it}\ge -\delta {Z}_{it}$.

^{2}with a value on a scale of 0 to 1.

## 4. Methodology and Data

- Estimate the tax capacity or potential tax revenues, in which the maximum level of tax revenue considered is influenced by the socio-economic characteristics of the country; and
- Decompose the error term into two components (random noise and the tax effort), so it is possible to model the tax effort through a set of variables. For example, we can determine whether the complexity of the customs tax system has any influence on the revenue collection efficiency.

#### 4.1. Model Specification

#### 4.2. Data Description

- Ri
^{2}is the share of customs tax i in the total revenue, squared; and - n is the total number of customs taxes.

## 5. Results and Discussion

^{®}software. The software estimates the tax effort (${\mu}_{it}$) using the method suggested by Battese and Coelli (1988) (“TE1”) as well as the one suggested by Jondrow et al. (1982) (“TE2”).

## 6. Conclusions

- The countries whose customs tax system has a lower degree of complexity have a better level of collection and tax effort (Peru, Chile, and Bolivia). Therefore, the greatest possible degree of simplicity in the design of the tax system is desirable.
- Panama’s potential customs revenue collection is very close to its actual customs revenue collection, but its actual revenue collection is low compared with the other countries in the sample. Therefore, work could be carried out on aspects that help to reduce the shadow economy in order to improve tax revenues.
- An improvement in the quality and dissemination of statistical data helps to improve transparency and the possibility of questioning government decision-making, which contributes to improving the tax effort. Notably, labor efficiency levels tend to increase when there are means to audit through tangible results.
- When revenue levels from non-renewable natural resources such as minerals and oil increase, the tax effort shows a downward trend. In the case of Ecuador, a certain degree of laziness in tax control was observed during the years when the WTI crude oil price increased that did not justify the increase in the level of debt. In contrast, a greater tax effort could have been made to increase customs revenues, for example through a reduction in the complexities of the customs tax system.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Appendix A

**Table A1.**Data source for variables used to estimate the potential capacity and determinants of tax effort: stochastic frontier model.

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**Figure 1.**Periodic comparison of Ecuador’s total public debt (% GDP), WTI oil price (USD/barrel), and tax effort (%). Source: Appendix A.

**Figure 2.**Tax effort (overall country average, 2006–2017). Source: Appendix A.

**Figure 3.**Revenue collected by Ecuador’s Customs Administration (% of FOB imports) versus tax effort (%): average for the period 2006–2017.

Variable | Description |
---|---|

Stochastic Tax Frontier | |

i | Country of Customs Administration |

t | Year t (t = 2006… 2017) |

${\beta}_{0}$ | Constant |

${\beta}_{1}\dots {\beta}_{6}$ | Coefficients of elasticities measuring the percentage change in the dependent variable with respect to the unit percentage change in the independent variable |

$ln{\left(R\_pib\right)}_{it}$ | Logarithm of customs revenue as a proportion of the gross domestic product (GDP) of country i in year t |

$ln{\left(PIBpc\right)}_{it}$ | Logarithm of the gross domestic product per capita by purchasing power parity (constant 2011 international dollars) for country i in year t |

$ln{\left(PIBpc\right)}_{it}^{2}$ | Ln (PIB pc) squared |

$ln{(C\_pib)}_{it}$ | Logarithm of merchandise trade as a proportion of the GDP for country i in year t |

$ln{\left(Gini\right)}_{it}$ | Logarithm of the Gini coefficient |

$ln{\left(Edu\_pib\right)}_{it}$ | Logarithm of government expenditure on education as a percentage of the GDP for country i in year t |

$ln{(e\_sum\_pib)}_{it}$ | Logarithm of the shadow economy as a proportion of the GDP for country i in year t |

${\nu}_{it}$ | Assumed to be $N(,{\sigma}_{v}^{2})i.i.d$ error terms independent of ${\mu}_{it}$ |

${\mu}_{it}$ | The term of inefficiency for country i in year t. It is a non-negative disturbance term and is assumed to be $N\text{}(\mu ,{\sigma}_{\mu}^{2})i.i.d$. We assumed a half-normal distribution and estimated this term following the procedure suggested by Battese and Coelli (1988), which the SAS software identifies as TE1. |

The effects of inefficiency | |

${\delta}_{0}$ | Constant |

${\delta}_{1}\dots {\delta}_{6}$ | Elasticity coefficients measuring the percentage change in the dependent variable with respect to the unit percentage change in the tax effort |

${\left(IHH\right)}_{it}$ | Hirschman–Herfindah concentration index used as a proxy for the degree of complexity of the customs tax system for country i in year t |

${\left(min\_pib\right)}_{it}$ | Mineral rents as a percentage of the GDP for country i in year t |

${\left(oil\_pib\right)}_{it}$ | Oil rents as a percentage of the GDP for country i in year t |

${(stat)}_{it}$ | Statistical capacity indicator for country i in year t |

${(gp\_pib)}_{it}$ | Public expenditure as a percentage of the GDP |

$Yeardum$ | Dummy variable for the time period (1 = 2006… 12 = 2017) |

Variable | Unit/Range | Arithmetic Mean | Standard Deviation | Extreme Values | |
---|---|---|---|---|---|

Minimum | Minimum | ||||

R_PIB | % del PIB | 4.20541 | 1.21971 | 2.26546 | 6.84701 |

PIBpc | GDP (constant 2011 USD) | 12,689.10 | 5250.76 | 4778.72 | 22,331.23 |

C_PIB | % of PIB | 54.8901137 | 19.9516675 | 26.9274299 | 105.0440641 |

Gini | 0–100 | 49.0513889 | 3.4076547 | 43.2 | 56.7 |

E_sum_pib | % of PIB | 37.47328 | 15.60411 | 12.64000 | 61.77000 |

Edu_PIB | % of PIB | 3.8975423 | 0.9708080 | 2.3256992 | 6.2673162 |

IHH | 0–1 | 0.3992382 | 0.2276815 | 0.0820689 | 0.7476185 |

Min_pib | % of PIB | 4.751 | 5.919 | 0 | 20.917 |

Oil_pib | % of PIB | 3.460 | 4.700 | 0 | 18.477 |

Stat | 0–100 | 81.20371 | 9.11059 | 66.66667 | 98.88889 |

GP_PIB | % of PIB | 29.9565 | 9.5988 | 17.1190 | 54.8 |

Yeardum | annual | 6.5 | 3.4762778 | 1 | 12 |

Variable | Mean | Standard Error | Type | ||

Ln_R_PIB | 1.392752 | 0.302494 | Frontier (Prod) Half-Normal | ||

Model Fit Summary | |||||

Number of Endogenous Variables | 1 | ||||

Endogenous Variable | Ln_R_PIB | ||||

Number of Observations | 72 | ||||

Log Likelihood | 57.48817 | ||||

Maximum Absolute Gradient | 0.00549 | ||||

Number of Iterations | 32 | ||||

Optimization Method | Quasi-Newton | ||||

AIC | −96.97634 | ||||

Schwarz Criterion | −76.48635 | ||||

Sigma | 0.16979 | ||||

Lambda | 2.73209 | ||||

Parameter Estimates | |||||

Parameter | DF | Estimate | Standard Error | t Value | Approx.Pr > |t| |

Dependent variable Ln_R_PIB, assuming a half-normal distribution for μ_{it} | |||||

Intercept | 1 | 56.220266 | 8.878678 | 6.33 | <0.0001 |

Ln_PIBpp | 1 | −9.447874 | 1.861098 | −5.08 | <0.0001 |

Ln_PIBpp2 | 1 | 0.473165 | 0.100365 | 4.71 | <0.0001 |

Ln_c_pib | 1 | 0.557979 | 0.048773 | 11.44 | <0.0001 |

Ln_gini | 1 | −2.033298 | 0.175228 | −11.60 | <0.0001 |

Ln_e_sum_pib | 1 | −0.447409 | 0.042602 | −10.50 | <0.0001 |

Ln_edu_PIB | 1 | −0.394444 | 0.083245 | −4.74 | <0.0001 |

_Sigma_v | 1 | 0.058359 | 0.020406 | 2.86 | 0.0042 |

_Sigma_u | 1 | 0.159442 | 0.031864 | 5.00 | <0.0001 |

Summary Statistics of Continuous Response | |||||

Variable | Mean | Standard Error | Type | Lower Limit | Upper Limit |

TE1 | 0.883614 | 0.070368 | Truncated | 0 | 1 |

Model Fit Summary | |||||

Number of Endogenous Variables | 1 | ||||

Endogenous Variable | TE1 | ||||

Number of Observations | 72 | ||||

Log Likelihood | 118.47527 | ||||

Maximum Absolute Gradient | 0.0000243 | ||||

Number of Iterations | 14 | ||||

Optimization Method | Quasi-Newton | ||||

AIC | −220.95055 | ||||

Schwarz Criterion | −202.73722 | ||||

Parameter Estimates | |||||

Dependent variable tax effort, assuming a truncated distribution for μ_{it} | |||||

Intercept | 1 | 0.648964 | 0.119214 | 5.44 | <0.0001 |

IHH | 1 | 0.137516 | 0.073344 | 1.87 | 0.0608 |

Yeardum | 1 | −0.013865 | 0.002727 | −5.09 | <0.0001 |

Min_pib | 1 | −0.007127 | 0.00329 | −2.17 | 0.0303 |

Oil_pib | 1 | −0.012981 | 0.00216 | −6.01 | <0.0001 |

Stat | 1 | 0.003632 | 0.001333 | 2.72 | 0.0065 |

Gp_pib | 1 | 0.00203 | 0.001155 | 1.76 | 0.0789 |

_Sigma | 1 | 0.054205 | 0.005719 | 9.48 | <0.0001 |

Country | Bolivia | Chile | Colombia | Ecuador | Panama | Peru | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

Year | TE_{1} | TE_{2} | TE_{1} | TE_{2} | TE_{1} | TE_{2} | TE_{1} | TE_{2} | TE_{1} | TE_{2} | TE_{1} | TE_{2} |

2006 | 0.92229 | 0.92130 | 0.82023 | 0.81900 | 0.95765 | 0.95713 | 0.81178 | 0.81056 | 0.89813 | 0.89697 | 0.95589 | 0.95534 |

2007 | 0.92997 | 0.92906 | 0.88098 | 0.87975 | 0.95739 | 0.95686 | 0.89420 | 0.89302 | 0.93254 | 0.93166 | 0.96334 | 0.96291 |

2008 | 0.84175 | 0.84049 | 0.97212 | 0.97183 | 0.95420 | 0.95363 | 0.77177 | 0.77061 | 0.95310 | 0.95251 | 0.97104 | 0.97074 |

2009 | 0.85336 | 0.85210 | 0.93443 | 0.93358 | 0.91821 | 0.91718 | 0.90055 | 0.89940 | 0.89809 | 0.89692 | 0.93215 | 0.93127 |

2010 | 0.87608 | 0.87483 | 0.94575 | 0.94505 | 0.95857 | 0.95807 | 0.88759 | 0.88638 | 0.94393 | 0.94320 | 0.91729 | 0.91625 |

2011 | 0.77658 | 0.77541 | 0.91308 | 0.91201 | 0.86756 | 0.86631 | 0.73935 | 0.73824 | 0.91282 | 0.91175 | 0.83511 | 0.83387 |

2012 | 0.78662 | 0.78544 | 0.93900 | 0.93821 | 0.81844 | 0.81722 | 0.74912 | 0.74800 | 0.89051 | 0.88931 | 0.87856 | 0.87733 |

2013 | 0.87873 | 0.87749 | 0.94077 | 0.93999 | 0.77392 | 0.77275 | 0.79639 | 0.79520 | 0.87244 | 0.87119 | 0.93274 | 0.93187 |

2014 | 0.95511 | 0.95455 | 0.92857 | 0.92765 | 0.79335 | 0.79216 | 0.71800 | 0.71692 | 0.83401 | 0.83277 | 0.95085 | 0.95022 |

2015 | 0.97886 | 0.97868 | 0.95031 | 0.94967 | 0.81109 | 0.80987 | 0.92473 | 0.92377 | 0.89501 | 0.89383 | 0.96063 | 0.96016 |

2016 | 0.91535 | 0.91430 | 0.92759 | 0.92665 | 0.75642 | 0.75528 | 0.79470 | 0.79351 | 0.86754 | 0.86629 | 0.95085 | 0.95023 |

2017 | 0.90063 | 0.89948 | 0.91041 | 0.90931 | 0.73180 | 0.73070 | 0.75795 | 0.75681 | 0.81544 | 0.81422 | 0.93490 | 0.93405 |

Mean | 0.88461 | 0.88359 | 0.92194 | 0.92106 | 0.85822 | 0.85726 | 0.81218 | 0.81104 | 0.89280 | 0.89172 | 0.93195 | 0.93119 |

Pearson Correlation Coefficient, N = 72 | ||||||
---|---|---|---|---|---|---|

Prob > |r| Assuming H_{0}: Rho = 0 | ||||||

Ln_PIBpp | Ln_PIBpp2 | Ln_C_PIB | Ln_Gini | Ln_E_sum_pib | Ln_Edu_PIB | |

Ln_PIBpp | 1 | |||||

Ln_PIBpp2 | 0.99967 | 1 | ||||

(<0.0001) | ||||||

Ln_C_PIB | 0.11184 | 0.12283 | 1 | |||

(0.3496) | (0.304) | |||||

Ln_Gini | 0.00814 | 0.01018 | 0.07302 | 1 | ||

(0.9459) | (0.9324) | (0.5421) | ||||

Ln_E_sum_pib | −0.50701 | −0.50768 | 0.31014 | 0.16473 | 1 | |

(<0.0001) | (<0.0001) | (0.008) | (0.1667) | |||

Ln_Edu_PIB | −0.4005 | −0.38583 | 0.18416 | −0.21645 | 0.00286 | 1 |

(0.0005) | (0.0008) | (0.1215 | (0.0678) | (0.981) |

Pearson Correlation Coefficient, N = 72 | |||||
---|---|---|---|---|---|

Prob > |r| Assuming H_{0}: Rho = 0 | |||||

IHH | Min_pib | Oil_pib | Stat | Gp_pib | |

IHH | 1 | ||||

Min_pib | 0.84589 (<0.0001) | 1 | |||

Oil_pib | −0.25482 (0.0308) | −0.43442 (0.0001) | 1 | ||

Stat | 0.57777 (<0.0001) | 0.59179 (<0.0001) | −0.21168 (0.0743) | 1 | |

Gp_pib | −0.26038 (0.0272) | −0.44105 (0.0001) | 0.37837 (0.001) | −0.63918 (<0.0001) | 1 |

Variable: Resid_Ln_R_PIB (Ln_R_PIB Residual) | ||||
---|---|---|---|---|

Test | Statistical | p Value | ||

Shapiro–Wilk | W | 0.971471 | Pr < W | 0.1009 |

Kolmogorov–Smirnov | D | 0.082440 | Pr > D | >0.1500 |

Variable: Resid_TE1 (TE1 Residual) | ||||
---|---|---|---|---|

Test | Statistical | p Value | ||

Shapiro–Wilk | W | 0.973903 | Pr < W | 0.1396 |

Kolmogorov–Smirnov | D | 0.094733 | Pr > D | >0.1075 |

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**MDPI and ACS Style**

González Aguirre, J.; Del Villar, A.
Effect of the Complexity of the Customs Tax System on the Tax Effort. *Economies* **2022**, *10*, 55.
https://doi.org/10.3390/economies10030055

**AMA Style**

González Aguirre J, Del Villar A.
Effect of the Complexity of the Customs Tax System on the Tax Effort. *Economies*. 2022; 10(3):55.
https://doi.org/10.3390/economies10030055

**Chicago/Turabian Style**

González Aguirre, Jazmín, and Alberto Del Villar.
2022. "Effect of the Complexity of the Customs Tax System on the Tax Effort" *Economies* 10, no. 3: 55.
https://doi.org/10.3390/economies10030055