**3.2 Empirical model**

Empirical studies generally opt for the nonlinear approach to study the impact of corruption on economic growth (Méon and Sekkat [11]; [14, 16, 17]; Allan and Roland [19]; [27–29]). This is a quadratic function based on the hypothesis that the impact of corruption on growth is not always negative and that a moderate corruption level could have advantages for economic growth.

In order to verify this, a cross-sectional framework is used in which growth rate and the ICRG index are observed only once for each country. The scatter plot (**Figure 1**), using the fitted Kernel curve, illustrates and confirms the hypothesis that the relationship between corruption and economic growth (fitted values) is nonlinear.


**Table 1.** *Descriptive statistics.*

**Figure 1.**

*Growth and corruption: countries distribution.*

The curve is clearly increasing in the middle range of corruption and decreasing where corruption is least and most.

Therefore, we propose the following quadratic model. Subscripts i (i = 1,…,65) and t (t = 1987,…,2021) denote index country and time, respectively.

$$\text{Growth}\_{\text{it}} = \alpha\_{\text{i}} + \beta \text{I} \text{rf}\_{\text{it}} + \gamma \text{Trad}\_{\text{it}} + \mu \text{Fdi}\_{\text{it}} + \delta \text{Icrg}\_{\text{it}} + \lambda \text{Icrg}^2\_{\text{it}} + \varepsilon\_{\text{it}} \tag{1}$$

Past studies have used a panel of 5-year averages and the system GMM estimator because this choice reduces, in general, short run fluctuations and resolves the endogeneity due to time invariant effects; but this method will not address endogeneity due to the possible interactions between higher growth rates and greater resources to combat corruption or other time-varying effects. Levin and Satarov [30] and Paldam [31] have presented evidence for the existence of both types of endogeneities.

Recently, the empirical studies characterized by having repeated observations over time on some countries are resolved by others' models. In this study, we will follow the Beck and Katz [4] methodology, who suggested estimating linear models of timeseries cross-section (TSCS) data by ordinary least squares (OLS), and they proposed the panel-corrected standard errors (PCSE) estimator.

The results for GDP growth using the PCSE estimator are reported in **Table 2**.

It can be seen that corruption negatively affects (−1.0853466) economic growth unlike the square coefficient of corruption, which positively affects (0.1982614) economic growth. The significance of Icrg2 coefficient confirms the nonlinearity of this model and shows the presence of a threshold above which there will be a change of sign.

*The Impact of Corruption on Economic Growth: A Nonlinear Evidence DOI: http://dx.doi.org/10.5772/intechopen.108876*


#### **Table 2.**

*Panels corrected standard errors (PCSE).*

#### **3.3 Determining the threshold**

We will determine the governance level that allows for achieving maximum growth. The resulting model is:

$$\text{Growth} = 2.153 - 0.0391 \text{l} \eta \text{f} + 0.011 \text{Trad} - 1.08 \text{l} \text{crg} + 0.198 \text{l} \text{crg}^2 + 0.062 \text{Fdi} \tag{2}$$

In deriving growth through governance, we get:

$$\frac{\partial \text{Grow}}{\partial \text{lcrg}} = -1.08 + 0.396 \text{lcrg} = 0 \tag{3}$$

Relationship (3) shows that an optimum is achieved by Icrg = 1.08/0.396 = 2.73. This indicates that up to a corruption index of 2.73, the trend of the bell-shaped curve (**Figure 2**) increases showing that there is a positive relationship between corruption and economic growth.

This bell-shaped curve (**Figure 2**) is interpreted by the fact that corruption, through tax evasion, has two types of effects in economics.

First, it offers households a tax that can be consumed or invested, and therefore, it could improve growth up to a certain threshold. This optimal threshold represents the reversal point of the curve otherwise the country can be found in an underdevelopment trap like several countries that are immersed in corruption. This corruption, if significant, will reduce state resources because of productive public spending, which will lead to a loss in economic growth that sooner or later will lead to an uprising calling for establishing democratic principles and good governance.

These results indicate that low of corruption (Icrg <2) negatively affects economic growth. This result disappears in the presence of corruption (Icrg >3). However, for an average corruption of (2 ≤ Icrg ≤3), we will be at an optimum level of growth (**Figure 2**).

This result may surprise those who advocate lack corruption, but it can be explained by the fact that administrative delays resulting from absence of "bribes" paid in a corrupt economy may dampen economic growth and reduce economic development.

**Figure 2.** *Bell-shaped curve of growth through governance.*

The results obtained are derived from static panel model, which has some shortcomings. One of the reasons is not to take into account growth's lag operator. Indeed, economic growth is attributed to the results obtained a year earlier, and therefore, it is desirable to include this variable in the model. Therefore, a dynamic panel is needed.
