1. Introduction

Corruption and its effects on institutional change, income and economic performance continue to be debated in political science, public management and economics. According to ^{Quesada et al. (2013)}, corruption is a complex phenomenon with both a political and an administrative dimension. Political corruption refers to collusion between the political class and spheres of power to obtain benefits in the absence of institutional controls and reliable accountability mechanisms. Administrative corruption refers to fraudulent acts committed by public officials who use their technical-professional spheres to violate regulations or favor individuals.

The discussion on corrupt practices in the developing world is far from over. Some argue that corruption mainly occurs in the civil service and that a high level of transparency can be achieved through administrative measures. Others argue that corruption is a political problem rooted in culture, which can lead to political failure due to cronyistic tendencies in all societies (^{Fukuyama, 2014}).

Much academic work has focused on determining whether corruption can boost or limit economic growth, especially in developing economies. One hypothesis of economic literature is that corruption can severely limit economic performance in contexts with strong institutions and efficient bureaucracies. However, in contexts where institutions do not function adequately and bureaucratic inefficiencies occur, corruption can spur economic performance in the short term, especially in the developing world, by acting as a "greaser" of the economy. It is clear that corruption can also arise from actions between private parties interacting in markets and organizations; however, this phenomenon requires the participation of the public sector to become entrenched in the institutional fabric of a country.

The relationship between corruption, growth and institutions is not limited to the idea that the presence of functional institutions leads to more or less corruption and, therefore, to better or worse economic performance. It is important to consider how the effect of corruption relates to institutional change. When studying the effects of corruption from an economic and institutional point of view, sometimes too much attention is paid to formal rules for containing corrupt actions and neglects the fact that institutions in the developing world (especially in Latin America) still have limitations when it comes to combatting corruption as an institutionalized practice.

This paper seeks to empirically study the relationship between corruption and economic growth, considering that the evolution of institutional arrangements can influence economic performance. The hypothesis is that strengthening formal arrangements can improve economic performance by providing clear rules. However, in weak institutional contexts, corrupt practices may persist and limit progress.¹ In other words, the idea is to empirically validate that, in Latin American countries with a colonial past and low institutional development, there is a sacrifice rate between control of corruption and per capita income. This rate would depend on the strength of the institutional framework and its recent evolution, measured using indexes that capture the countries' institutional capacities.

This six-part paper discusses corruption and Latin American institutions in the 20th century, from the formation and nature of the region's democracies to the present day. Relevant literature on the relationship between corruption and economic performance was also consulted to analyze how malicious acts affect economies in the long run. Sections four and five detail the empirical strategy and discuss the model's results. The last part presents conclusions and perspectives for Latin America today.

4. Empirical strategy and model approach: some clarifications

This study reviews the impact of institutions on economic performance, with a particular focus on the regions of Latin America, the Caribbean and South America. Unlike previous research, corruption is modeled in quadratic terms, suggesting an effect of diminishing returns in developing economies. Two strategies are employed: the first considers multiple variables related to state capacity to assess the non-linear impact of corruption, and the second is based on the theoretical model of ^{Acemoglu et al. (2011)} and ^{De Vaal and Ebben (2011)}, but with adaptations of the work of ^{Levitsky and Murillo (2012)} and ^{O'Donnell (1994}, ¹⁹⁹⁷ and ²⁰⁰⁴⁾ regarding the model of constant substitution in institutional terms, which occurs in the delegative democracies studied by the latter. This mixed approach permits the capture of the non-linear effect of corruption while controlling factors such as government effectiveness and population growth, validating bidirectionality between institutions and economic growth through the use of autoregressive data panel vector techniques where bidirectionality is supported by evidence from Granger causality tests (^{Qamruzzaman, 2017}; ^{Saadaoui and Chtourou, 2022}).

The study uses the ^{World Bank's Governance Indicators database (s. f. a)} and that of ^{Kaufmann et al. (2010)}, covering 26 Latin American countries from 2002-2021 and considers heterogeneity through dummy variables referring to colonial origin. The selected strategy and basis provide complete and relatively uniform data, facilitating an empirically corroborative analysis. Variables include GDP per capita (slope variable) and population size as a control variable. Table 1 summarizes the modeled variables.

Based on a linear model with distributed panel lags:

Where i expresses the number of individuals and t represents the time periods. Y_it refers to the variable of interest in the study, γ refers to the vector of coefficients of interest, α_i represents the unobservable heterogeneity, C_i,t-k refers to the vector of variables of interest k is the optimal number of lags³ and _t refers to the vector of k institutional independent variables, β to the vector of k coefficients and ν_it to idiosyncratic error.

For this study, the resulting reduced form is:

Where Ln(PIB)_it refers to the natural logarithm of GDP per capita PPP in dollars, CO is the corruption perception index of the ^{World Bank (s. f. b)}, CO² refers to the returns to scale (or quadratic) of corruption.

LE refers to freedom of expression, capacity for political articulation and association (voice and accountability), EP to political stability, EG to government effectiveness, CR to regulatory quality, IL to the rule of law, P to population, δOC to a vector of dummy variables reflecting the colonial origin or countries and ε_it to compound error εit=αi+vit. For the estimation of the model, variance estimates such as ^{Beck and Katz (1995)} and ^{Driscoll and Kraay (1998)} were used, which correct the model for the presence of heteroscedasticity, autocorrelation⁴ and contemporaneous correlation, given the diagnoses carried out on the models.

Where * represents the number of k equations of the autoregressive panel, ∆Yit*=Y1it,Y2it,…Ykit the set of vectors of k equations of the system variables (and the t - k vector refers to said regressed variable in k periods), ∆Xit*β=X1'itβ,X2'itβ,…,Xkit'β is the independent variable vector within each of the reduced-form equations of the system, and eit*=e1it,e2it,…,ekit is the vector with the error terms of the equation system. To deal with the bias of dynamic panels, generalized methods of moments (GMM) estimation is used, using lags of the dependent variables as instruments. First differences were used to remove specific panel effects.

5. Analysis of results

Descriptive statistics

Table 2 shows the paired correlation between the variables in the model. All state capacity measures, from corruption control (CO) to regulatory quality (CR), show a solid positive relationship with the dependent variable. Only the variable of the logarithm of the total population (Ln(P)) shows a weaker but negative relationship. In turn, this shows a negative but less intense relationship with the governance indicators, except for regulatory quality, for which no strong or statistically significant association exists.

Table 2 Correlation matrix 

	Ln(PIB)	CO	EG	LI	IP	Ln(P)	EP	CR
Ln(PIB	1.0	0.645***	0.748***	0.717***	0.73***	0.133**	0.575***	0.613***
CO	0.645***	1.0	0.867***	0.899***	0.892***	-0.372***	0.776***	0.72***
EG	0.748***	0.867***	1.0	0.872***	0.874***	-0.289***	0.707***	0.78***
LI	0.717***	0.899***	0.872***	1.0	0.891***	-0.383***	0.825***	0.715***
IP	0.73***	0.892***	0.874***	0.891***	1.0	-0.354***	0.784***	0.799***
Ln(P)	-0.133**	-0.372***	-0.289***	-0.383***	-0.354***	1.0	0.563***	-0.0718
EP	0.575***	0.776***	0.707***	0.825***	0.784***	-0.563***	1.0	0.536***
CR	0.613***	0.72***	0.78***	0.715***	0.799***	-0.0718	0.536***	1.0

Notes: * p < 0.05; ** p < 0.01; *** p < 0.001.

Source: compiled by the authors.

Figure 1 shows a box plot of GDP per capita by region and colonial origin of the countries. Although there are differences in the average level between countries of Spanish colonial origin in the regions of South America (SA) and Latin America and the Caribbean (LA&C), we can see that, in the lower limit of the first quartile, there are more countries in LA&C with less than US$10,000 per capita than in SA. On the other hand, the Latin American countries of English colonial origin are diverse in terms of income levels (in other words, there is a significant level of variability in their per capita income levels). They show more substantial growth in the region in terms of the median, while countries of Dutch origin in South America show average levels of per capita income and with much less variation than countries of Spanish colonial origin in SA.

Source: Compiled by the authors using data from the ^{World Bank (s.f.a} and ^s.f.b).

Figure 1 Economic growth by region and colonial origin, 2002-2019 

Figure 2 shows the total population broken down by colonial origin and region. Countries of Spanish colonial origin in South America have an average population of 10 million, although the third quartile range extends to 50 million in 2011-2019, with Colombia, Argentina and Peru having the highest. In the case of countries of Spanish origin, the range from the first to the third quartile is much lower than in South America, but atypical data exists, exceeding 120 million inhabitants by 2019 (in the case of Mexico). This indicates that heterogeneity among countries in terms of total population is extremely high.

Source: Compiled by the authors using data from the ^{World Bank (s.f.a} and ^s.f.b).

Figure 2 Box plot, population per million inhabitants by region and colonial origin 

Institutional indicators

Figure 3 shows several significant trends linking institutional variables with per capita income. In general, all the variables studied show a positive correlation with per capita income, although they vary in strength and regional adjustment.

Source: Compiled by the authors using data from the ^{World Bank (s.f.a} and ^s.f.b).

Figure 3 Scatter plot of per capita income and institutional indicators, 2002-2021 

For example, government effectiveness has a relatively high adjustment in LA&C with an R² of 0.4842, compared to an R² of 0.4235 in South America. Political stability also demonstrates regional differences: a one-point increase in the scale is associated with an increase in per capita income of US$181.05 in South America and US$291.16 in LA&C, although with a lower R²in the latter region. Judicial effectiveness (the rule of law) demonstrates significant variability between the two regions; a one-point increase in the index is associated with an increase of US$335 in LA&C, compared to US$178.69 in South America.

Finally, although participatory institutions generally better predict per capita income in the US$10 to US$20,000 range in Latin America, the correlation is more robust in certain ranges of the institutional participation scale.

Results of the regression models

Table 3 presents the results of the proposed estimations, with several approximation methods, ranging from fixed effects with robust standard errors with the presence of autocorrelation and heteroscedasticity to methods corrected by contemporaneous correlation (estimations by ^{Driscoll and Kraay (1998)} and PCSE panel models by ^{Beck and Katz (1995)}). Some significant lags are shown in the corruption control index, but generally, all show expected signs in all specifications. Regulatory quality is a statistically significant variable with expected signs in almost all specifications, in the same way as government effectiveness. In contrast, voice and accountability show no significance except in one of the proposed regressions (corrected standard error panel with no fixed effects (5)), while the rule of law shows importance in almost all model iterations depicted in Table 3.

The robust Hausman and Mundlak tests show that there is a systematic difference between the fixed and random effects coefficients. Although they are based on different estimates, it should be noted that the model that best minimizes the mean square error is the fixed effects model with a corrected standard error panel because it corrects autocorrelation by applying the Prais-Winsten transformation to the estimation in question. Post-estimation tests indicate that the model has corrected the contemporaneous correlation by applying the Pesaran CD statistic.⁷

Based on the fact that model (6) is the one that minimizes the variance, it was decided to test the coefficients to observe the quadratic relationship described in this paper. Since the model chooses to observe the cumulative temporal effect, the following equation is used to test the hypothesis that the relationship between growth and corruption is:

Where COγ_tp is the cumulative non-linear effect of corruption on economic growth. The hypothesis test shows that there is a quadratic relationship in the coefficients. From an average of 32.10 points on the corruption control scale, we begin to observe decreasing returns to scale of corruption control.

Figure 4 shows the results of the model in a scatter plot concerning the corruption control index according to colonial origin. The countries in the sample of Spanish colonial origin follow the expected trend, as do those of English origin, although with increased dispersion. In turn, the results of the model are observed according to regions, with both regions (South America and LA&C) following the sacrifice rate.

Source: Compiled by the authors using the results of the fixed effects model with corrected standard error panels. The dotted lines are the confidence intervals and the non-dotted line is the point estimate of the quadratic relationship hypothesis test.

Figure 4 Model Predictions and Corruption Control Index by Colonial Origin and Region, 2002-2021 

Verification of Robustness

The empirical strategy of the previous section may suffer from a problem referred to in the empirical strategy section, which is the endogenous and bidirectional relationship between growth and institutions, especially between growth and corruption. ^{North (1990)} discusses that, even in contexts of low economic regulation, corruption can affect the allocation of resources (financial, factor inputs, including human capital), which may be reflected in future growth. In the previous strategy, variables reflecting state capacity dimensions were included in an attempt to obtain the best possible estimate with a one-equation model.

To verify consistency, a scenario was proposed in which the relationship between state capacity, growth, and corruption is non-linear and endogenous. For this purpose, a panel data autoregressive vector model was specified. Likewise, as in the previous section, there is a quadratic relationship between corruption and growth, in addition to the fact that the Granger test shows a bidirectional relationship between growth and corruption.⁸

Hansen's test of over-identified restrictions indicates that the instruments used (four lags of the endogenous variables) permit the solution of endogeneity and the problems associated with the dynamic panel bias evidenced by ^{Nickell (1981)}. The tests to determine the optimal number of lags for the Autoregressive Vector showed that one lag is the optimal level to specify the model based on information criteria, thus incorporating institutional path dependence into the data-generating process.

Hypothesis tests of the CO_i,t-1 and CO²_i,t-1 coefficients show a quadratic relationship between growth and output. From 47.12 points out of 100 on the growth scale [39.26-54.97] per capita, income growth starts to decline.

Figure 6 shows that, despite the heterogeneity by region and colonial origin (insofar as there are specificities in the economic development paths of each country), the "sacrifice rate" is more evident in countries with a Spanish colonial past and those in the Latin America and Caribbean region.

Source: Compiled by the authors with data from the ^{World Bank (s. f. a.} and ^{s. f. b)}.

Figure 5 Panel VAR model predictions of economic growth and corruption control index by region and colonial origin, 2002-2021 

6. Discussion of results

This paper aimed to estimate whether there is a sacrifice rate or a trade-off between growth and corruption, especially in the context of countries with institutional drift, volatile institutions, and institutionalization of distrust due to the lack of accountability mechanisms in various dimensions (vertical and horizontal societal). The research is consistent with the work of ^{Aparicio et al. (2016)}, ^{Méon and Weill (2010)}, ^{Albrecht and De la Torre (2021)}, as well as an empirical corroboration of the theoretical model of ^{De Vaal and Ebben (2011)} and that of ^{Acemoglu et al. (2011)}, concerning countries with low economic development and institutional design problems, which hinder economic performance in the presence of weak institutions or, in O'Donnell's terms, institutionalized malicious practices.

According to the results of this study, this phenomenon is because, in countries with lower GDP per capita, the income elasticity concerning control of corruption is higher before reaching a score of 32 points out of 100, a stage from which diminishing returns begin to be observed. In other words, the 32 points of the corruption control indicator are the breakpoint where the so-called "sacrifice rate" occurs. When correcting for possible endogeneity and dynamic panel bias, the sacrifice rate is 47 points out of 100. This indicator illustrates that although the gains in transparency and mitigation of political and administrative corruption generate initial dynamics of economic growth in the short term by freeing the economy from certain rules (both formal and informal) that hinder business activity, in the long run, these improvements in transparency are not sustained because they are dependent on the institutional framework where corruption tends to be entrenched and manifests itself in the mature stages of the process.

With regard to the political and institutional issue, there is a certain consensus in economic, political and public management literature that institutional conditions (understood as norms, practices, values and cultures) can hinder or accelerate GDP growth processes and, consequently, economic development. However, in many cases, these dynamics have been studied linearly from a strictly economistic approach, leaving aside the institutional dynamics that can modify countries' per capita GDP growth trajectory. This is a particular issue for Latin American countries, many of which, throughout the 19th century, exhibited economic indicators similar or superior to their peers in the developed world, especially Europe and Asia. According to the results of this research, a worthy explanation is the weakness of institutions, which in the long run ends up institutionalizing practices that may permit short-term economic growth but limit the strengthening of democracies and formal rules that characterize developed economies that maintain a long-term development path.

This is consistent with the idea of ^{Levitsky and Murillo (2012)} that institutions in Latin America cannot enforce design standards due to their volatility over time. This indicates that even improvements in accountability and institutions, as shown by ^{O'Donnell (1994}, ¹⁹⁹⁷ and ²⁰⁰⁴⁾, may not be sufficient for several reasons: horizontal accountability (which are usually the counterweights, separation and autonomy of the branches of government) can be highly reactive to cases of corruption so that, without improvements to the institutional framework in other dimensions such as regulatory quality, accountability and political participation, legal security and government effectiveness, a correct transition to institutionalized democracies is not possible.

7. Conclusions and final considerations

This paper evaluates whether there is a sacrifice rate in improvements in state transparency to fight corruption (in other words, improvements in horizontal accountability) and economic growth, as measured by the countries' per capita income over the period 2002-2021. Despite the heterogeneity between nations and the limitations of a one-equation model, a trade-off between growth and corruption is observed, even when adjusting for indicators that capture State Capacity. This adds an empirical contribution to the discussions on the institutional history of the region of Latin America and provides indirect evidence regarding the constant institutional replacement model as a possible explanation for the region's unique economic and social development situation.

This means that unless institutional volatility is reduced, in other words, institutional mimicry is eliminated. Reforms are adopted on a state level, which are based on informal discourse and social norms; formal improvements to increase the transparency of public administration will only result in limited economic growth in countries like these, with a colonial past and an institutional drift that is generally extractivist and not very inclusive (except some countries).

However, the empirical contribution is not without limitations. The ^{World Bank's governance indicators (s. f. b)} measure people's perceptions of the dimensions of governance and governability, which these indicators attempt to assess. Thus, the result ends up being consistent with other research that uses institutional indicators with similar consistency. The research opens up the possibility of investigating the specific mechanisms that facilitate this phenomenon.