Functional trinity of public finance in an emerging economy

The literature on government finances has gravitated toward the following issues: (1) the impact of public budget expenditures on the degree of society’s general development, especially the productive outcome of the economy; (2) the collected taxes as the most important component of the public budget’s income; and (3) the capacity of government to obtain credit from financial markets as a complementary resource for its own expenses.

The corresponding literature is characterized by strikingly contradictory viewpoints.

Some authors have commented that government expenditure is almost neutrally related to aggregate output: besides the famous Harberger (1964, 2003) conjecture (Engen and Skinner 1996; Mark et al. 1997; Mendoza et al. 1997; Wasylenko 1997; Hines 2002; Xing 2011). Some studies have considered this impact negative: Mark et al. (1997), Beach (1998), Poulson and Kaplan (2008), McBride (2012), Pettinger (2017). The opinions positing the positive influence of government spending on economic growth predominate, and such a role is attributed to the so-called productive items of the public budget (Kneller et al. 1999); notably, Asimakopoulos et al. (2016) included them into their macroeconomic production function.

Divergent opinions have also been formulated concerning public budget taxes. Mertens and Ravn (2013) identified immediate effects on output induced by changes in average tax rates. Engen and Skinner (1996) posited, “the tax level is likely to exert a modest, but cumulatively important, influence on long-term growth rates. (p. 36).” Structurally, many studies have outlined the unequal consequences of various taxes on output. Therefore, although taxation of income and profit, payroll and labor, property, and social security contributions would cause distortions, no such effect was identified for other taxes (Kneller et al. 1999). Concerning capital taxation, the theoretical modeling indicated a complicated sinusoidal evolution, from level zero (Judd 1985; Chamley 1986) to relatively high rates (Piketty and Saez 2013). Lee and Gordon (2005) found that the corporate tax rate is negatively correlated with economic growth, but other tax variables are not significantly associated.

The variegated picture of the research conclusions on the “public budget–economic growth” tandem was described in overviews, such as Huang (2006), Kenny and Winer (2006), Afonso et al. (2008), Myles (2009), Magazzino and Forte (2010), Martinez-Vazquez et al. (2011), Magazzino (2012), McBride (2012), Nygård and Revesz (2015), Afonso and Alves (2016), Dobrescu (2016a), Winer (2016), Churchill et al. (2017), Fisman et al. (2017), and Gomez-Puig and Sosvilla-Rivero (2017).

How can such interpretative diversity be explained? The epistemological premises of various studies and the real specificities of studied experiences cannot be ignored. Working on this paper, we concluded that only these circumstances are not sufficient.

A significant cognitive impact arises from underestimating the temporal scale to which the examined problems refer. Or concerning government finance, the delimitation of three perspectives seems essential.

The first one considers the global historical trajectory of modern society, for example, the Wagnerian hypothesis (Wagner 1883). With roots in classical economics, the anticipation that economic development will be accompanied by an increasing share of government expenditure in national income has been confirmed by authorized statistical series. Inherent parallel growth of taxation—admitted still by Wagner—was comprehensively discussed by Kaldor (1962, 1963a, b). The syntagm “Wagner–Kaldor law” is justified.

Another perspective concerns the limited temporal segment, provisionally named a “given structural state–society relationship,” as a distinct component of the larger notions, such as human social environment (Barnett and Casper 2001), social capital (Field 2008), social structure in a network-based perspective (Mukherjee 2007), or a given historical context (Dobrescu 2016a). The binomial state–society is dynamic, its forms and ampleness modifying along global history and within the same social system. Such changes occur periodically, and existing intervals with sufficiently stable features include: the dominant behaviors of people as taxpayers and beneficiaries of public spending. In this paper, we shall refer exactly to these intervals.

Finally, note the short–medium horizon, and the problems of such a time span being prioritary for macroeconomic policies. Keynesian and post-Keynesian models remain relevant for such intervals.

In our opinion, if empirical research does not account for these temporal scales, its consistency is inevitably affected.

The trap of applying or checking the theorems on improper samples of observations was unavoidable. Among such temptations, especially risky would be to relate the Wagner–Kaldor law to limited historical information or, by contrast, to expostulate the Keynesian schemes to long and very long series.

Similar problems occur when PANEL analyses involve data belonging to economies in different development stages. The assertion—sometimes deduced from such studies—that data corroborate the Wagner–Kaldor law for low-income countries while rejecting it in the case of rich ones, overlooks that this law envisages the global historical trajectory of society and not its various segments.

A possible disregard of the temporal scale of analysis can also be observed in model specification. The econometrics of the Wagner–Kaldor law is again edifying and intended for a relationship on very long horizon between output and ratio of government spending to gross domestic product (GDP). In its formalization, the main difficulty stems from the non-unitary evolution of the involved variables. Although the potential output registered an obvious increasing trend, the share of government expenditure in GDP cannot extend unlimitedly. At superior development stages, despite the increasing per-capita income, the social acceptability of taxation decelerates, tending toward an asymptotical level. (Normally, it is situated under unity, which is its maximum potential limit.) This trend seems to be linked to the extending capacity of the private sector to provide some public goods and services, and enforcing democratic control on government decisions. Consequently, in modeling the size of the government in relation to economic growth long term, the threshold regression methods are more suitable (Christie 2011) as well as nonlinear functions (Kuckuck 2012; Hajamini and Falahi 2014; Aghion et al. 2016), including the logistic one (Florio and Colautti 2002; Magableh 2006). In this context, notably, is the conclusion drawn by Fölster and Henrekson (2001): The relationship between government expenditure and growth is negative in rich countries.

This research focused on government finance for a given structural state–society relationship in the frameworks of the second aforementioned delimited temporal scale. Under such conditions, the relative stability of three dominant social behaviors is assumed, namely:

All these conditions are sociological reactive processes [as characterized in Mahoney (2000)]. Any change in the institutional framework of public budget expenditures, taxation, or public debt evolution is followed—as a rule—by counter reactions (i.e., upback or pushback) on the side of domestic economic agents, foreign markets, civic organizations, mass media, political formations, and public opinion in general.

The tendency toward equilibrium of society generates some steady-state levels of leading indicators, defining quantitatively the aforementioned behaviors: the share of public budget expenditures in GDP, degree of tax acceptability, and public debt size. Obviously, these levels are specific for each given structural state–society relationship.

Admittedly, the dynamics of actual processes around the steady-state levels is submitted concomitantly—similarly to other economic dependences—to the scale efficiency and diminishing marginal returns’ theorems. The advantages of scale efficiency appear more intensive when the involved indicators are situated at the left side of the steady-state levels (low government spending, taxation, and public debt), whereas the diminishing marginal returns become prevalent at the right side of these points (higher government spending, taxation, and public debt). Sociologically, the first slope could be considered a self-reinforcing sequence, and the second a sui-generis self-undermining one. The U-shaped form of the main relationships of government finance therefore approximates the real socioeconomic life. A deeper discussion of these problems exceeds the intended framework of this paper and was evoked only as assumptions of the subsequent analyses.

In the empirical research, a database was used for an emergent medium-sized EU economy (Romania, as a case study), with series for two and half decades, namely, 1990–2016. Despite the transformations induced by the transitional processes, after the first package of reforms in 1990s, the structural state–society relationship became, to a great measure, congruent with the functional market economy’s requirements. In principle, therefore, such a database can be admitted as relevant to the paper’s goal. The specificities of an emergent economy could be a profitable challenge to a scientific plan because they extend the cognitive area of an issue developed, until now, preponderantly on advanced occidental countries.

More concretely, the involved in-paper indicators refer to the general consolidated budget (GCB), which aggregates data for the central and local public budgets, the social insurance budget, and other similar funds. The classification of GCB revenues and expenditures adopted by the 2012 version of the Romanian macromodel (Dobrescu 2013a, b, 2015b) has been used. This classification is presented in Additional file 1: Appendix A, and the corresponding statistical series are detailed in Additional file 2: Appendix B.

This paper continues with a description of the main functional relationships characterizing government finances, including the collinearity problem associated with the U-shaped form of these relationships. More specifically, the Barro–Armey–Rahn–Scully (BARS) curve, the Laffer in narrower sense (LINS) curve, the specifications for non-fiscal public budget revenues (NFBR), and the public budget balance restriction (BBR) are examined separately (like in the literature) and as an integrated model. With such an aim, we introduced a compatibility restriction derived from the unitary framework, within which these functions intimately interact under a given structural state–society relationship.

Several conclusions and further possible research opportunities complete the paper.

Econometric Eqs. (5), (7), (10), (13), (14), and (15) (supplemented by the corresponding accounting identities, some dummy variables, and the Ar terms) were integrated into a unitary model. This operation was accomplished in two steps.

First, these equations were solved as such, without any additional constraint. As a starting point, the iterative least squares were applied (Additional file 3: Appendix C-Sys2018OLS1). Since this method does not account for the possible interequation correlations, a seemingly unrelated regression (Additional file 3: Appendix C-Sys2018SUR1) was subsequently used.

The most significant results are concentrated in Table 2. The differences between the OLS and SUR estimations show that the impact of the interequation correlations cannot be ignored. Notably, the pair estimators c(1)–c(2), c(5)–c(6), and c(8)–c(9) have the expected algebraic signs in both procedures, which means that all the components of the BARS, LINS, and BBR functions display U-shaped slopes (an inverted form in the first two cases, and as such in the third one).

Although the BARS, LINS, and BBR relationships are gathered into a unique system, they are not explicitly interconnected. The second step of the present computational approach addresses this problem. The general equilibrium theory is useful in such a matter. If an integrated system has several optimizing entities, a structural compatibility is ultimately achieved among them. Why not consider the public finance blocks similarly? Since these blocks constitute a unitary system, rejecting the supposition that their dynamic trajectories are also interdependent would be difficult. More specifically, it would be implausible to assert that—for a given structural state–society relationship—the dominant social preference concerning taxation would have no link to the dominant social choice for public expenditures.

This reasoning can be extended to budget balance, significantly influenced by the optimizing behavior of the potential lenders.

Returning to the examined system, from the optimal points of Eqs. (14a)–(14c), two significant equalities result:

Based on (15a) and (15b), equilibrium formula (4) is added to the system in the following expression:

This expression could be considered a “compatibility restriction” of the public budget model. Notably, (16) is not a simply computational artifice; by contrast, it comes from consistent socioeconomic reasons. Such a condition restrains the range of “estimating ambiguity” inducible by collinearity. Certainly, this solution requires further research, which would be justified not only for this discussed application but also for other economic problems approachable in a similar manner.

Re-computing our system under the compatibility restriction, the OLS method has failed to converge even after one million iterations (Additional file 3: Appendix C-Sys2018OLS2). Instead, the SUR technique (Additional file 3: Appendix C-Sys2018SUR2) has functioned and provided the estimations presented in Table 3.

In the static framework, the BARS, LINS, and BBR curves are calculated for a given temporal interval, changing their determinants within a large economically plausible range. The other explicative variables were fixed (maintained at the basic year level). The used estimators were provided by OLS1, SUR1, and SUR2.

The BARS curve, in the form IGDPc = f(cbe), is approximated for the variation of cbe(− 1) from 0.15 to 0.65, under the constancy of IGFCFc(− 1), which is equal to 1.0626, and time factor (= 27) (Fig. 6).

The modification of the IGDPc depends on the cbe configures; therefore, there is a clear inverted U-shaped BARS curve. Related to public spending and constancy of the investment influence, the economic growth reaches the maximum (1.053378) for cbe = 0.38 in the proximity of ocbe (= 0.381631). Notably, such a level of cbe is higher than the actual one (0.338161 in 2016).

The LINS curve, as letg = f(atax), is calculated for a change of atax(− 1) from 0.2 to 0.7, and the time factor is the same (= 27) (Fig. 7).

Again, an inverted U-shaped curve is obtained, with the maximum (= 0.601526) for atax = 0.43 (oatax = 0.427548), compared with 0.3869 in 2016.

The BBR function, in the form cbb = f(pdg), is simulated for a variation of pdg(− 1) from zero (absence of the public debt) to 0.6. (the Maastricht Treaty ceiling). As in the previous exercises, the cyclical factor (sint4) is fixed (Fig. 8).

In conclusion, the static simulations confirm the presence of the BARS, LINS, and BBR curves in the statistical database.

Undoubtedly, revealing how the model reacts as an integrated dynamic system to modifications in taxation and relative public debt would be of interest. Are the BARS, LINS, and BBR functions still valid under the intertemporal effect of the involved model factors? With this aim, the system was solved for ten post-sample successive intervals, and a horizon long enough to identify the dynamic properties of the model was observed. These intervals are labeled posts_i, where i = 0 for the basic year, and 1…10 for the subsequent years. Simulations are operated using the estimators obtained from the SUR2 variant.

The main hypothesis of the inertial scenario is the constancy of atax (at basic year level 0.3869), which signifies a fixed taxation system. The other indicators evolve strictly in concordance with the model estimators. Only the accounting relationship for cbe is increased yearly by 0.035, as an equivalent of the expected supplementary in-flows of non-reimbursable financial resources and, in particular, from the European Union structural funds. Computed under these premises, the resulting indicators are presented in Table 4.

The inertial scenario is useful as a referential or experimental subject for other applications; however, as such, it does not allow the identification of U-shaped trajectories appropriate for the main functional relationships of government finance. More suited for such a purpose are the simulations involving a significant modification of the main determinants of the model.

This is why the inertial scenario was solved for atax, determined by multiplying its basic level in all following ten intervals by a coefficient ranging between 0.7 and 1.5 (pace 0.025, meaning 33 variants). The arithmetic mean of letg (noted mletg) for the entire generated in such a way series are displayed depending on the level of atax in Fig. 9.

The dynamic simulation re-confirms the LINS curve.

Increasing taxation induces a growth of government spending, respectively, of cbe. For each variant, there were computed average geometric indexes of the real GDP (noted aIGDPc), and the arithmetic mean of cbe (noted mcbe) on the entire set of ten post-sample intervals. Figure 10 plots the variation of aIGDPc depending on mcbe.

Consequently, the BARS curve is also present in the dynamic simulations.

To check the BBR curve, the simulations are operated on the level of the pdg in the basic interval as starting point of the series (noted pdg0). The resulting indicator of interest in this case is the arithmetic mean of the ratio to GDP of the public budget balance (noted mcbb). Figure 11 describes its evolution.

The dynamic simulations also attest the BBR curve.

Obviously, the present exercises cannot be considered as practical recommendations, although such suggestions emerge. Our only goal was to illustrate the behavioral characteristics of the discussed model. Its operationalization would require transformations; among them, the explicit representation of the interconnections among the BARS, LINS, and BBR curves with other macroeconomic dependencies is essential.

In line with the mainstream economic literature, this paper circumscribes government finances within the macrosocial triangle constituted by the following:

The temporal scale of analysis is particularly important in an examination of this triangle. From this viewpoint, the paper distinguishes the following main perspectives:

Each of these perspectives is characterized by specific requirements concerning the modeling work. Contradictory results provided in the empirical literature are explainable, at least partially, by the utilization of inadequate methodological instruments (theoretical hypotheses and functional specifications) on the available samples.

Our research focused on the second temporal scale, for which analysis—in mirror with the enounced functional triangle—the BARS, LINS, and BBR, curves were considered adequate. In addition to the literature that examined these relationships separately, this paper attempts to integrate them into a unitary system.

This paper assumes that under a given structural state–society relationship, the social propensity for government spending, tax acceptability, and risk aversion to public indebtedness move—more or less transparently—toward steady-state levels approximated by the optimal points of the BARS, LINS, and BBR as U-shaped (as such or inverted) curves.

In accordance with the general equilibrium paradigm, such points cannot be viewed separately because they are inherently interdependent. It seems natural to presume, for example, that the dominant social preferences concerning taxation are relatively concordant with the dominant social choices for public expenditures. Obviously, this reasoning can be extended to a balanced budget, which is significantly influenced by risk aversion to public indebtedness and optimizing behavior of potential lenders.

Consequently, the model specification was completed with an equation interlinking the optimal points of the BARS, LINS, and BBR functions, and this was admitted as a “compatibility restriction” of the system.

By using the database for an emergent medium-sized EU economy, the econometric analysis was finalized by model simulations in static and dynamic conditions. In static conditions, the resulting BARS, LINS, and BBR curves were determined for a given temporal interval, changing only their determinants of interest (with the other explicative variables remaining at their basic year level). In the second case, the entire system was solved for ten post-sample successive intervals, a horizon long enough to identify the dynamic properties (including the intertemporal effects) of all the involved indicators. Both types of simulations revealed the presence of the BARS, LINS, and BBR curves.

Certain crucial issues require, however, additional clarification. A deepened characterization of the given structural state–society relationship requires further multidisciplinary research from both the qualitative socioeconomic and quantitative statistical perspectives. A rigorous mathematical foundation of the “compatibility restriction” is also of great interest. Notably, the inclusion in the model of the possible variability of the optimal points of BARS, LINS, and BBR curves would be especially opportune under the present intensity of technological, demographic, and institutional changes.