Adolph Heinrich Gotthelf Wagner divulged his theory on increasing state expenditures and explained why (Wagner, 1883). Based on this theory, the doctrine established "Wagner's Law," which instituted a causality between two indicators: per capita income and public expenditure; that is, as a country increases its per capita income, the public sector increases in proportion and equivalent relevance (Bird, 1971).

Growth in government participation is driven in three ways: industrialization, income growth, and economic development. With industrialization and modernization, society must replace services provided by the public sector with private services. The complex social changes need gradual protection and systematization of the public situation. With a greater division of labor due to industrialization and urbanization, it must be necessary to increase spending to ensure the effective performance of the economy. Thus, to manage natural monopolies to increase economic efficiency, the government must change its system to the detriment of economic progress (Vieira, 2014).

After Wagner's works were translated into English and published in 1958, WL became much discussed in academia and tested by many researchers, such as Musgrave (1970), Bird (1971), Mann (1980), Henrekson (1993), Tobin (2005), Narayan et al. (2008), Jaen-Garcia (2011), Verma and Arora (2010), Bojanic (2013), Bayrakdar et al. (2015); Prado e Silva (2018); Nusair and Olson (2021); and Inchauspe, MacDonald and Kobir (2022).

Wagner, in the synthesis of his theory, was not so clear in forming a thesis and did not describe it mathematically. However, the authors tested the WL through different mathematical methods (Verma & Arora, 2010).

Since 1960, at least six WL interpretations have been empirically tested. However, no defined version states which one is the most appropriate. In this sense, as shown in Table 1, Afzal and Abbas (2010) summarize the most used WL test methods in research.

Table 1
Six Versions of Wagner's Law

Source: Afzal and Abbas (2010), adapted by the authors.

Each coefficient indicates a variable considered to test the validity of the WL, where: G = Total government expenditure; Y = Gross Domestic Product (GDP); GC = Government Consumption; and P = Population (Afzal & Abbas, 2010).

The elasticity between total government spending and GDP was used to formulate Peacock and Wiseman's (1961) version. For Gupta (1967), the growth of real per capita government spending (G/P) depends on the growth of real GDP per capita (Y/P).

In the version tested by Goffman (1968), called the final version, total government expenditure was measured as a function of real per capita GDP growth, with population growth being irrelevant information for the theory. Similarly, Pryor's (1969) version used government consumption (GC) as a variable instead of total government expenditure.

In the models mentioned above, the WL is valid when the coefficient of elasticity is greater than one. Therefore, all expressions specified the WL in absolute terms (Verma & Arora, 2010).

In theory, Wagner supported the idea of relative growth. However, for Timm (1961), the WL must be interpreted to predict an increase in the relative participation of the public sector and the growth of per capita income. For Henrekson (1993), relative growth was based on the growing participation of the population and spending to the detriment of real per capita income.

In Musgrave's (1970) version, he formulated the mathematical expression considering the ratio between public spending in the sense and nominal GDP (G/Y) as a function of real GDP per capita (Y/P). In this case, the WL is valid if the elasticity is greater than or equal to one (Henrekson, 1993). Examples of authors who used this theory are Ram (1987), Khan (1990), Murthy (1993), and Hsieh and Lai (1994).

Mann (1980) modified the mathematical expression of Peacock and Wiseman (1961) and used real GDP as an independent variable, with WL valid when elasticity was greater than zero.

According to Vieira (2014), the easiest way to interpret and empirically test the WL is by relating GDP per capita to government expenditure. For this, several studies used time series for this purpose. However, in general, the studies presented a diversity in their results, prevailing the validity of the WL. This can be inferred from the main contributions of empirical research summarized in Table 2.

Table 2
Results of Wagner Hypothesis

Source: own elaboration.

If the WL predicts the evolution of public spending on a scale greater than national income, the State goes into debt by borrowing to support fiscal deficits (Buchanan & Wagner, 1977).

Regarding the collection and allocation process, part of the literature identifies that the government's methodology is "spend and collect" (Von Furstenberg et al., 1986; Hakkio & Rush, 1991; Chang, 2002; Gamboa & Silva, 2004; Silva et al., 2010). Others identify the result of "raising and spending" (Baffes & Shah, 1994; Payne, 1998; Cheng, 1999; Chang, 2002; Afonso & Rault, 2009; Schettini, 2012; Linhares et al., 2012).

Another line of literature argues that fiscal policy is based on "fiscal synchronism" (Darrat, 1998; Cheng, 1999; Chang & Ho, 2002; Chang & Chiang, 2009; Linhares et al., 2012; Gadelha, 2011; Machado & Gentleman, 2020). Other empirical studies reached the result of "tax illusion" (Gemmell et al., 1999; Sausgruber & Tyran, 2005; Chetty et al., 2009; Dell'anno & Mourão, 2012; Silva & Siqueira, 2014; Prado & Silva, 2018).

Recent literature reinforces the perception that the current discussion orbits around the validity of Wagner's Law in contrast to the Keynesian hypothesis, such as Günay and Aygün (2022), Sek, Sim, Chea and Hoe (2022) and Sagndic, Unsaç and Tuncer (2020). In addition, the study by Cedillo and Herrera (2021) stands out, which focused their contributions on 16 Latin American countries between 1990 and 2017. The results support WL in the long term, highlighting the need for the State to direct public spending to meet social demands and, in this way, boost the economy. In the same line of confronting the WL with the Keynesian hypothesis, in the sense that, respectively, public spending varies endogenously and exogenously as a function of economic growth, Chu and Lin (2021) show that the two points of view coincide as consumption private and public spending become substitutable.

The validity of the WL demonstrates its current scientific importance in local terms, such as the studies of Bendahmane and Chenini (2021), who tested the six versions for Algeria; Nirola and Sahu (2020), who explained the reality of India; and Ghazy, Ghoneim and Paparas (2021) who demonstrated it in Egypt.

From the above, it was clear that the topic is still current and that a relevant gap to be filled is to verify whether public spending is unbalanced, that is, whether it is growing more sharply and generating indebtedness.

The FRL established norms for fiscal control, with the main objective of controlling indebtedness and curbing the State's public deficits.

For the period studied, the debt limits are stipulated in Federal Senate Resolutions nº 40 and nº 43, both from 2001, and have as a parameter the Net Consolidated Debt (NCD), which represents the amount of the consolidated public debt minus the amounts cash, financial investments, and other financial resources (Brasil, 2001). Such limitations and others provided for in the FRL may favor fiscal balance (Macedo & Corbari, 2009; Linhares, Penna, & Borges, 2013). Furthermore, a virtuous cycle is generated when the funded resource is allocated to capital expenditures (Simonassi, Gondim Filho, & Arraes, 2022). However, the expenditure profile can also influence, for example, when personnel expenses are high. In this case, the budget is committed to paying salaries, which may lead to a decrease in the budget result and increasing indebtedness (Cassimiro, Nascimento, & Viotto, 2021).

Therefore, monitoring the DCL and its fiscal limit – which are available respectively in the financial statements and in the fiscal statements of public entities – are relevant aspects for controlling public finances. In addition, it is useful to observe their evolution to characterize eventual budgetary imbalances.

As already highlighted, for Wagner, the increase in public spending drives a series of side effects that affect the performance of a given country's economy, a condition that favors an increase in GDP (Vieira, 2014).

In economic development, total public spending tends to increase concerning national income, the justification given by the fact that the increase in public spending is a natural consequence of the growth of economic activity, a circumstance that underlies the WL (Bender Filho, 2019).

According to Marques Júnior, Oliveira and Jacinto (2006), exogenous factors, such as population growth and technological advances, limit economic growth, as government spending and taxation variations have temporary effects. Thus, in the short term, the fall in public spending reduces GDP, but in the long term, if the government spends less, the balance of wealth generated will be greater, and, as a result, GDP will increase.

Several studies analyze the relationship between public spending and economic development, identifying aspects that can influence it. Bogoni, Nelson, and Beuren (2011) highlighted that spending on health, sanitation, education, culture, housing, social assistance, and social security is essential to economic growth. On the other hand, Silva and Scatolin (2012) indicate that public spending on infrastructure positively implies economic growth. Silva and Triches (2014) conclude that the high productivity of the main public expenditures increases the final economic product. Finally, Leite Filho and Fialho (2015) point out that the quality of public management positively influences economic development.

On the other hand, Sousa, Rosa and Ribeiro (2020) identified that health and sanitation, urban planning, and housing and education expenses do not affect economic growth, which differs from the results obtained in the studies presented in the previous paragraph. This same study indicates that the increase in total current expenditure is related to the reduction in GDP. Therefore, a possible explanation for this difference in results may be the expenditure profile of the municipalities studied, which is less focused on infrastructure expenditures which, as already highlighted (Silva & Scatolin, 2012), positively influence economic growth.

From these studies, it is observed that there is a direct relationship between the concepts discussed in this subsection and that it is possible to have economic development and growth in public spending, maintaining the government's fiscal balance. However, without expanding indebtedness, the imbalance scenario would no longer be favorable to economic growth.

Given the above, the following research hypothesis is formulated: in Brazilian states, the WL is valid with high frequency, and there is no fiscal balance of government management, favoring the growth of indebtedness.

During the analyzed period, the WL was valid 67 times. Twenty years of 27 states were analyzed, resulting in a sample space of 540 observations. However, considering that the variation calculation requires one observation per state and some GDP and population data are unavailable, the final sample analyzed consisted of 512 observations.

From these findings, observing which Brazilian states the WL was valid is opportune. Table 3 shows the summary of the frequency of times the WL was valid, as well as the percentage of this frequency concerning the sample of each state and the years in which the validity of the WL was observed.

Table 3: Frequency of validity of Wagner's Law by state

Table 3
Frequency of validity of Wagner's Law by state

Source: Own elaboration.

Of all the federation states, only in Alagoas was the WL not valid in any verified years. On the contrary, the highest frequency was in Amapá, where the WL was valid in 6 of the 20 years studied. However, even in this case, the WL was not valid for most of the period examined. Regarding the period, according to Table 4, it is possible to identify that in 2008 and 2016, the WL was valid more frequently.

Table 4
Frequency of validity of Wagner's Law per year

Source: Own elaboration.

Interestingly, the years 2008 and 2016 were marked by the outbreak of the global financial crisis that started in American banks and the deepening of the Brazilian economic crisis, marked by the recession that year. This situation, combined with the fiscal crisis in the Brazilian states, which was already more pronounced, can be considered a favorable scenario for the associated expansion of the studied variables.

Figure 1: Evolution of G/Y and Y/P by Brazilian region.

Source: prepared by the authors.

Figure 1 shows the evolution of the G/Y ratio concerning GDP per capita in December 2021. State data were aggregated by region according to the average to facilitate interpretation. Therefore, for the WL to be valid, the G/Y ratio should, at least, follow the Y/P ratio, thus demonstrating a directly proportional relationship. However, it is observed, for all regions, that this did not occur, reinforcing the results obtained by calculating the elasticities.

In general, the trend of the G/Y ratio is slightly decreasing to constant, indicating that public spending does not show strong fluctuations around GDP. On the other hand, the evolution of per capita GDP has an increasing trajectory over time, with a certain stagnation from 2012 onwards. Before that, attention was drawn to the reduction in per capita GDP, observed mainly in the Southeast in 2014, due to the Brazilian economic crisis. The Midwest region, in turn, stabilized its growth curve during the crisis but did not show signs of recession, a behavior that can be explained by the strong dependence of the region's GDP on agribusiness.

In search of more evidence confirming the validity or otherwise of the WL for the Brazilian states in the sample period, Table 5 brings the Pearson correlation index between the G/Y and Y/P variables. Following the logic of elasticity, from the perspective of an index that represents all the years studied, for the WL to be valid, there must be a high positive correlation between G/Y and Y/P, indicating variations in G/Y following the same proportion as variations in Y/P.

Table 5
Pearson correlation index by state between GY and YP

Source: prepared by the authors.

The results, however, point to the rejection of the hypothesis that the WL is valid for the Brazilian states. It is noted that, in 13 states, the correlations were negative, with emphasis on Ceará (-0.8189), Santa Catarina (-0.7478), and Tocantins (-0.7417). By this analysis, only Rio Grande do Sul and Pernambuco would have some success in validating the WL, but it is still questionable since they reached positive but moderate correlations of 0.5821 and 0.5019, respectively.

Therefore, even with low frequency, there were situations in which the WL was valid, giving rise to a joint assessment of its indebtedness, the subject of the following topic, which can denote whether the expansion of public spending was balanced.

From the findings in Table 6, the behavior of the indebtedness of the States is shown, which, on average, presented an increase between 2002 and 2021 of 13.67%, with emphasis on Maranhão (+1450%), Acre (+51 .72%), Rio de Janeiro (+50.85%), Amapá (-162.40%), Mato Grosso (-129.72%) and Roraima (-121.03%). In the analyzed period, the fiscal limit established in the Resolution of the Federal Senate, of twice the RCL, was exceeded 49 times, with emphasis on Rio Grande do Sul, which historically always exceeded this limit, Rio de Janeiro, which exceeded it eight times and Alagoas which exceeded six times.

Table 6: Debt variation between 2002 and 2021 and the years in which the states exceeded the tax limit

Table 6
Debt variation between 2002 and 2021 and the years in which the states exceeded the tax limit

Source: prepared by the authors.

Table 7 compares the state's public debt growth and fiscal limit, the years in which the WL was valid, and there was an increase in indebtedness.

Table 7
Wagner's Law validity and indebtedness

Source: prepared by the authors. Note: Tax limit met if DCL/RCL≤2.00.

From Table 7, it is concluded that, in 23 (34.33%) of the 67 times in which the WL was valid, there was an increase in the indebtedness of the studied federation unit. Thus, "fiscal synchronism" was not observed in these cases, in which the tendency would be the "spend and collect" methodology.

It is worth mentioning the high growth of the debt in Amapá, whose balance in 2018 was BRL 60,719,662.15, and in the following year, it increased to BRL 1,933,086,021.15, as shown in the SICONFI database. Consulting the Tax Management Report for this state, the increase occurred in Remains Payable Processed.

Also noteworthy are the Federal District and Rio Grande do Sul, which, on three occasions, showed an imbalance in public spending. In the case of Rio Grande do Sul, the evolution was not as expressive as in the Federal District; however, its fiscal debt limit was not met. Therefore, this scenario, in which there is an economic expansion, and public spending grows unbalanced, with indebtedness, is not favorable and may compromise the sustainability of the actions developed by this government, as advocated by Bogoni et al. (2011), Silva and Santolin (2012), Silva and Triches (2014) and Leite Filho and Fialho (2015)).

Through the descriptive analysis of the data, a low frequency of validity of the WL was identified in the Brazilian states, which led to reject the hypothesis of this research. In 34% of the cases in which it was valid, the indebtedness grew, showing an imbalance in public spending with an increase in indebtedness. In this situation, the tendency is to execute public expenditures to collect resources later to pay the future debts caused by this behavior. Furthermore, it was found that, of the 49 times in which the indebtedness limit was exceeded in the states, only on 3 of these occasions was the WL valid, allowing us to deduce that there was no relationship between these variables, that is, in the period studied, other aspects acted as drivers of non-compliance with the fiscal limit.

The regression results show that, except WL, all model variables influence DCL variations.

Table 8
Result of the regression analysis

The lack of significance of the WL is consistent with the result of Prado and Silva (2018), who carried out tests for Brazil without stratifying by state, identifying that the WL was null and contradicted the results of Silva and Siqueira (2014), Vieira (2014), Bendahmane and Chenini (2021) and Possa (2021) who, with the same object of study, but in a longer and different time interval, identified the validity of the WL for Brazil. This result indicates a tendency away from the "collect and spend" methodology (Afonso & Rault, 2009; Payne, 1998; Baffes & Shah,1994; Chang, 2002).

Findings like those found in this research were also identified in other countries, such as Yalçin (1987), Demirbas (1999), and Alleyne (1999). On the other hand, the results contradict those of Ganti and Kolluri (1979), Mann (1980), Legrenzi and Milas (2002), Bojanic (2013), Bayrakdar et al. (2015), Nirola and Sahu (2020), Nusair and Olson (2021), Ghazy, Ghoneim and Paparas (2021), who concluded that WL is valid in countries other than Brazil.

Bearing in mind that the time interval studied in the present research refers to a period after the FRL, the fiscal balance sought with the dictates of this rule (such as the golden rule and the restrictions for contracting credit operations by anticipated budget revenue - ARO) may be influencing this result, as identified by Macedo and Corbari (2009) and Linhares et al. (2013).

This scenario may also have been influenced by contracting debt, whose profile is the linkage of the funded resource, as advocated by Simonassi et al. (2022), and by the profile of expenditures with more limited expenses in the budget Casimiro et al. (2021).