Public and private investments at the subnational level: the Brazilian experience in a Keynesian perspective

ABSTRACT

This article evaluates the relationship between public and private investments at the subnational level. The previous literature on this topic has little emphasized the analysis of regional dynamics, since the IBGE does not provide detailed historical series of Gross Fixed Capital Formation (GFCF) at the local level. To help fill this gap, such relationships are revisited for Brazil, with the use of panel data from a Generalized Method of Moments (GMM) Model. We built different proxies to capture the private and public dimensions of investments for the 27 Federation Units. The results obtained converge with international and national evidence of the predominance of positive effects of public investments over private ones, which reinforces the perspective suggested in the Keynesian and structuralist literatures.

JEL Classification: E22; E32.

KEYWORDS:
Public investments; private investments; crowding-in effect; states and federal district

INTRODUCTION

In the twenty-first century, especially after the outbreak and unfolding of the global financial crisis (2007-2009) and the COVID-19 pandemic, greater state activism has been accompanied by a renewed interest in the study of fiscal policy (Rowthorn, 2020; Setterfield, 2019; Stockhammer et al., 2019). New methodologies and databases were used to identify the multiplier effects of discretionary spending – government purchases, transfers and investments – and tax reduction, the relationship between public and private investments, the healthy limits for public indebtedness, among other topics. This “renaissance”, to use Ramey’s expression (2019, 2021), emphasizes the relationships between public and private investments, with a predominance in the verification of positive long-term effects of government spending on infrastructure (Abiad et al., 2016; Deleidi, 2020; Matvejevs and Tkacevs, 2023).

It is in this context that the present work is inserted. We seek to contribute with more evidence on the regional dimension of these relationships, since the previous empirical literature, with few exceptions, as in the case of Sanches and Rocha (2010), emphasizes the national aggregates (Bredow et al., 2022; Fraga and Lara, 2023; Reis, 2008; Reis et al., 2019; Rocha and Teixeira, 1996; Sanches and Rocha, 2010). In part, this is due to the absence of detailed historical series of Gross Fixed Capital Formation (GFCF) at the subnational level, with the disaggregation between its main components, such as construction or machinery and equipment. To help fill this gap, such relationships are revisited using panel data from a Generalized Moment Method (GMM) Model. We built different proxies to capture the private and public dimensions of investments for the twenty-seven Federation Units. We do exercises to test the hypothesis that private investment responds positively to public investments. The results obtained for the period 2003-2020 converge with international and national evidence of the predominance of positive effects of public investments over private ones.

In addition to this brief Introduction, the work is organized into four more sections: it begins with a brief review of the theoretical and empirical literature underlying the proposed objectives (Section 2); in the following, there is a description of the recent evolution of investments in Brazil (Section 3). Section 4 presents the methodology, the data used, the results of the estimates and their discussion. The final considerations follow (Section 5), which summarize the contributions of the work and explore its normative implications.

PUBLIC AND PRIVATE INVESTMENTS: THEORETICAL AND EMPIRICAL LITERATURE

There is no consensus in the theoretical literature on the relationship between public and private investment. From the conventional perspective, Barro (1974) uses an overlapping generation model to suggest a negative effect of public spending on private investment. This result would derive from the way in which the increase in public spending would reduce the real money supply, by increasing prices, raising the interest rate and, consequently, reducing private spending and investment (crowding-out effect). From the perspective of the Keynesian and structuralist traditions, public investments would act on the gross capital formation of the private sector through two channels: (1) the increase in productivity in the economy, which exerts downward pressures on the supply price of capital goods, via cost reductions; and (2) the increase in aggregate demand, driven by these public expenditures, which would increase the expectations of returns from private investments and their demand price (Bresser-Pereira, 2022; Jespersen and Finn, 2019; Lavoie, 2022; Kalecki [1954], 2003; Keynes [1936], 2007; Sawyer, 2019; Taylor, 2004;)¹.

One of the most cited pieces of evidence of the positive relationship between public and private investment is that of Aschauer (1989), who draws attention to the need to distinguish between productive public spending, such as infrastructure, which usually has positive effects on investment; a relationship he observed for the United States. In the wake of that work, Bajo-Rubio and Sosvilla-Rivero (1993) and Argimón et al. (1997) present evidence of crowding-in for OECD countries. Although this conclusion of complementarity between public and private investment was supported by Greene and Villanueva (1991) and Blejer and Khan (1984), Aschauer’s results were criticized by Evans and Karras (1994), among others.

Erden and Holcombe (2005) compare the interaction of public and private investment in developed and developing economies and conclude that, although public investment is complementary to private investment in developing countries, the effect is the opposite in developed countries. The difference in results is attributed to the distinct structural characteristics between the two types of economies: while public investment can provide the necessary infrastructure in developing countries and thus boost private investment, in developed economies the public sector is already large and can compete with the private sector. Eden (2006), using panel data from 19 developing countries, in the period between 1980 and 1997, identifies that public investment is complementary to private investment.

In a heterogeneous regression panel for Latin-American economies, Fraga (2019) found a positive impact of government investments in infrastructure on private capital formation. In addition, the physical deterioration of the infrastructure stock decreases the elasticity of private investment relative to its determinants, resulting in a lower sensitivity of private investment to positive shocks. More recently, Fraga and Lara (2023) and Javid (2019) have found evidence that public investment, especially in infrastructure, can have a positive impact on private investment and economic growth. Javid (2019), in a study for Pakistan, estimates the long-term relationship of the two variables of interest using fully modified ordinary least squares (FMOLS) to solve the problem of reverse causality. Its main conclusion is that both public and private investments in infrastructure have positive, albeit different, effects on economic growth.

For the case of India, Mitra (2006) estimates a structural VAR model (using data from 1969 to 2005) in three variables (public investment, private investment, and production) and argues that public investment “excludes” private investment. Bahal et al. (2018) find evidence of crowding-in effect in that same country from 1980 onwards, which was largely explained by the reform policies introduced since the early 1990s. Bahal et al. (2018) show that institutional factors would explain the signal of the relationship between public and private investments in the Indian economy.

Eberts (1987) discussed the influence of public spending on private investment, particularly in the context of local politics, finding a crowding-in effect. The studies by Fujii et al. (2013) and Pereira (2003) presented more nuanced conclusions, with the former suggesting that public investment can have varying effects on different economic sectors, and the latter highlighting the potential of public investment to change the composition of private sector performance. In this line of regional studies, Martínez (2006) shows a positive effect of public investment on private investment for the case of the Spanish regions during the period 1965-1997, using the panel data methodology. The results indicate a positive effect of productive and social public investment (especially in education) on private investment. Mazzucato (2014) brings evidence of this relationship in the manufacturing industry.

Izquierdo et al. (2019) identify that the multiplier effects of public investments are greater in economies that start from a smaller capital stock. This was found in 31 European countries, whose quarterly data covered the period 1987-2014. It was also verified: (i) the presence of the crowding-in effect; and (ii) that the multiplier of public investments after two years reached 0.8, three times higher than the multiplier of current public sector expenditures. In the case of the USA, data from the States between 1987 and 2016 were analyzed, producing convergent results: multiplier of 0.98 and relevance of the initial capital stock. Once again, in the case of Argentina, with analysis of the data from the provinces, the basic relationships were maintained, with a multiplier of public investments higher than 1.6 and sensitivity to variations in the initial level of the capital stock.

Matvejevs and Tkacevs (2023) organized a panel with annual data from 34 OECD countries (1995-2019), identifying the crowding-in effect on private investments with a long-term multiplier of 2.0, that is: for every dollar of new public investments, private sector investments would increase by two dollars. Kamiguchi and Tamai (2023) simulate the effects of public investments in a model that uses parameters derived from OECD economies. They conclude that an increase of one percentage point in the public debt/GDP ratio increases the rate of economic growth by 35 percentage points. A positive result also occurs in the growth rate of private capital and public capital. The assumption for such a result is that, at the beginning of the period, when there is a shock in the debt financing variable, the growth rate is higher than the interest rate.

In the case of Brazil, Jacinto and Ribeiro (1998) found evidence of complementarity in the long term after testing the relationship between public and private investments with annual data between 1973 and 1989. The dependent variable is private investment, explained by public investments, and use of the following controls: installed capacity, credit and inflation rate. The regression was estimated by Ordinary Least Squares, in the first difference due to the presence of stationarity. In the short term, a crowding-out effect was found. This is the same result found by Cruz and Teixeira (1999), through the use of similar variables in an autoregressive econometric model of distributed lags, for the years 1947 and 1990.

Ferreira and Malliagros (1998) show that a 1% increase in infrastructure capital produces productivity increases between 0.48% and 0.49%. In addition, they conclude that the drop in factor productivity, observed since the 1980s, would be explained by the reduction in investments in infrastructure that occurred in the same period. Ribeiro and Teixeira (2001) show evidence of a negative relationship between public and private investment in the short run, positive effects of aggregate demand on investment, a positive influence of credit availability, and an adverse impact of economic instability on private sector investment in Brazil.

In a more disaggregated and sectoral analysis, Luporini and Alves (2010) study the relationship between private investments in machinery and equipment and public investments in Brazil. The econometric model was used for panel data with fixed estimators. In addition to the investment variables, on an annual basis (1996-2005), the following series were used: industrial production; utilization of installed capacity; interest rate; BNDES credit disbursements; inflation rate; debt service/Gross Domestic Product (GDP); and real exchange rate. Among the conclusions, it is pointed out that the 10% increase in public investments generates a 3.3% increase in private investments in machinery and equipment.

With annual data, between 1950 and 2006, and with a perspective focused on the importance of public investments in economic development, in a Keynesian and structuralist approach, Reis (2008) presents data on total investments broken down by institutional sectors and, based on descriptive statistics, analyzes two distinct political regimes for public investments: first between 1950 and 1979, characterized by developmentalism; the second between 1980 and 2006, the neoliberal period. The main conclusion is that the reduction of public GFCF during the second regime, in comparative terms with the first, is among the causes for the low economic growth of the country since the 1980s. In the first regime, a high correlation was observed between public and private investments, although in the 1970s this correlation occurred with a lag, indicating that public investments acted as sustainers of the cycle that then generated impetus for private investment.

Sanches and Rocha (2010) tested the complementarity between public and private investments at the state level, between the years 1991 and 2004, with annual data. The scarcity of data at the subnational level was circumvented through the construction of indicators that sought to estimate state investments based on the GFCF of civil construction, without considering investments in machinery and equipment. The estimated elasticities ranged from (0.917) to (1.0). Thus, increases of 1% in public investment would lead to variations between +0.92% and +1.0% in private investment.

Reis et al. (2019) performed a theoretical analysis of the overall investment dynamics and an econometric analysis applying a vector error correction (VEC) model. The trajectory of the Brazilian economy and the empirical results reveal the presence of crowding-in between public and private investments. For the authors, crowding-in was justified by the effects on demand through the Keynesian multiplier and through the expansion of the internal market (particularly provided by infrastructure) and by the effects on the supply of private capital through the reduction of production costs, the increase in productivity and through structural changes facilitated by public policies. Complementarity is confirmed both with regard to investments by the public administration and by state-owned enterprises (or those controlled) by the federal government.

Bredow et al. (2022) analyze the dynamic effects generated by public investments on private investments in machinery and equipment in Brazil, between the years 1996 and 2018. Using an econometric model of Autoregressive Vectors (VAR) that allows treating public investments as exogenous to the system, they show that the increase in public investments boosted private investments during the analyzed period. Fraga and Lara (2023), applying the Bayesian Model Averaging and Weighted-Average Least-Squares approach in a flexible investment accelerator model and using Kalman filtering techniques, identify that public investment in infrastructure stimulates private investment. On the other hand, they also indicate that private investment is limited by the availability of bank credit. In addition, they show that infrastructure stock and public investment are two of the main determinants of private investment elasticities.

SLOWDOWN IN GROWTH AND COLLAPSE IN INVESTMENTS IN BRAZIL

After four decades of semi-stagnation, the challenge for the Brazilian economy to regain the ability to sustain a long cycle of income expansion and, at the same time, face social and environmental liabilities that have been neglected for many generations is no small challenge. Since the beginning of the 1980s, the country’s per capita income has grown below the global average by about 1 p.p. per year. When compared to upper-middle-income countries, the stratum where the country is located, this difference is -2.5 p.p. per year² (Dathein and Fonseca, 2024; Gamacho and Rocha, 2022; Marquetti et al., 2023; Nassif et al., 2020).

This reality has not changed in the 2000s, despite the multiplication of government programs aimed at investments in infrastructure and the strengthening of the manufacturing industry. Between 2003 and 2016, the period of greatest state activism, the country’s per capita income varied, on average, +1.5% p.a. (-0.3 p.p. below the global average of 1.8% p.a.). From 2017 to 2022, this performance worsened, with the Brazilian per capita income varying +0.8% p.a. compared to +1.6% p.a. in the world. In the last two years, the government elected in 2022 has launched new programs such as the “New PAC” and the “New Industry Brazil”, which signal the resumption of the public sector’s effort to induce more robust trajectories of investment and production by the private sector.

According to official estimates, BNDES, the central instrument of those policies, which currently generates disbursements of just over 1% of GDP (or less than half of the average of the last 30 years of 2.3% of GDP), should inject credit in the order of 2% of GDP by 2026³. This amount would remain below the historical average and the values observed during the “Investment Support Program” (PSI – “Programa de Sustentação dos Investimentos”), created in 2009, after the global financial crisis, and which guaranteed disbursements above 4% of GDP. The PSI and the industrial policies of the 2000s, with more resources and meritorious objectives, have not been able to reverse deindustrialization and the anemia of the country’s gross capital formation. The New Growth Acceleration Plan (“PAC”) has changed little, so far, the picture of very low investment by the Union, which is at the historical low around 0.3% of GDP or 0.9% of GDP, when federal state-owned companies are computed (see Table 1). The Federation Units (FU) invested, on average, 0.6% of GDP in the 2010s, and 0.8% of GDP in the early 2020s, well below the historical average.

Table 1
Gross Fixed Capital Formation Rate, by private and public sectors, Brazil, 1947-2022 (% of GDP)

	1940s	1950s	1960s	1970s	1980s	1990s	2000s	2010s	2020s	1947-2022
Gross Fixed Capital Formation – total	13.4	15.5	16.4	21.9	21.9	18.8	18.2	17.7	18.9	18.4
Private Sector	9.4	11.3	10.1	14.1	15.9	15.0	15.0	14.7	16.6	13.6
Public Sector	3.9	4.2	6.3	7.8	6.0	3.8	3.2	3.0	2.3	4.8
Central Government	2.2	1.8	1.8	1.4	0.9	0.5	0.4	0.5	0.3	1.1
States	1.2	1.3	1.7	1.3	1.1	1.0	0.7	0.6	0.8	1.1
Municipalities	0.2	0.3	0.7	0.8	0.8	0.9	0.8	0.7	0.7	0.7
SOE	0.4	0.8	2.0	4.3	3.2	1.4	1.2	1.3	0.6	1.9

Table 2 presents the average share of GFCF investment from each sector (private and public) in total investment, as well as the specific shares of governments at the subnational level. The last column presents the long-term average, which refers to the period 1947-2022. It is observed that, between the 1960s and 1980s, the increase in the level of investments was due to the performance of the public sector, directly or through state-owned companies. In turn, from the 1990s onwards, the loss of state capacity to invest generated reverse effects.

Table 2
Composition of Gross Fixed Capital Formation in the private and public sectors, Brazil, 1947-2022 (%)

	1940s	1950s	1960s	1970s	1980s	1990s	2000s	2010s	2020s
Gross Fixed Capital Formation – total	100.0%	100.0%	100.0%	100.0%	100.0%	100.0%	100.0%	100.0%	100.0%
Private Sector	70.6%	73.0%	61.8%	64.3%	72.7%	79.8%	82.5%	82.8%	87.9%
Public Sector	29.4%	27.0%	38.2%	35.7%	27.3%	20.2%	17.5%	17.2%	12.1%
Central Government	16.1%	11.7%	11.1%	6.5%	4.0%	2.9%	2.4%	2.7%	1.3%
States	8.8%	8.5%	10.6%	5.8%	5.1%	5.2%	4.1%	3.5%	4.0%
Municipalities	1.6%	1.8%	4.2%	3.7%	3.8%	5.0%	4.4%	3.8%	3.6%
SOE	2.9%	5.0%	12.2%	19.7%	14.4%	7.2%	6.7%	7.1%	3.1%

The drop in the investment/GDP ratio of the public sector needs to be qualified. During this period, there was a process of transfer of ownership from the public sector to the private sector in activities typically responsible for large amounts of investment in fixed assets. Beginning in the 1990s, state-owned enterprises (SOE) in sectors such as steel, chemical/petrochemical, energy, telecommunications, rail transport, and mining, to name a few, were privatized. Thus, the drop in investment by state-owned companies from 3% to 4% of GDP in the 1970s and 1980s to somewhere between 1% and 2% of GDP in the 2000s reflects, in part, the effects of privatizations.

In parallel, local governments underwent several structural adjustments from monetary stabilization (Real Plan – 1994). The prolonged coexistence with indexation mechanisms, the strategic use of payment deferral in the context of high inflation, the indebtedness of the federative units to the capital market, the equity imbalances of state-owned companies, among other aspects, generated distortions that were the object of the structural policies of the period. In 1997, the federal government assumed the debts of the state governments and the Federal District through the Restructuring and Fiscal Adjustment Program (PAF). Targets were established for various indicators of the fiscal situation, such as primary result, financial debt and personnel expenses. The sale or federalization of public assets, particularly state banks, was part of the federal government’s strategy. One of the main results of the restructuring of state debts was to generate restrictions on the investment capacities of the federated entities (see Table 1).

In 2016, the deterioration of public accounts led to the introduction of Complementary Law No. 156, of December 28, 2016, which provided a new round of structuring of fiscal parameters in line with the determinations of the Fiscal Responsibility Law (LRF – “Lei de Responsabilidade Fiscal”). The 2017 Fiscal Recovery Regime (RRF – “Regime de Recuperação Fiscal”) offered the possibility of easing fiscal rules, granting credit operations, and suspending debt payments, provided that the FU adopted institutional reforms (spending caps, pension reform, etc.) with the aim of restoring fiscal balance.

As a result of these adjustments, there was a significant decline in the capacity of governments to make investments (gross fixed capital formation – GFCF) and, in some cases, restrictions were increased in the supply of services such as education, health and security, areas that are intensive in the use of human resources and in expenses with costs (school materials, medicines, various inputs, etc.). Between 2016 and 2022, the average amount of GFCF in the Federation Units was 0.8% of Brazil’s GDP, below the historical average – 1947-2022 (1.1%); and well below the peaks in the 1960s and 1970s (2% of GDP) (Table 1). Such relative decline affects the federative units, which are responsible for the provision of public goods that are fundamental to citizenship, notably health, education, security and transport infrastructure, to name a few.

PUBLIC AND PRIVATE INVESTMENTS IN BRAZIL: AN EMPIRICAL ANALYSIS

Except for the work of Sanches and Rocha (2010), the national literature places little emphasis on the analysis of local or state dynamics. In part, this is due to the absence of detailed historical series of GFCF at the subnational level, with the disaggregation between its main components, such as construction or machinery and equipment. To help fill this space, such relationships are revisited for Brazil, with the use of panel data from a Generalized Method of Moments (GMM) Model.

This research is based on data on public investments from the 27 Federation Units (FU) and private investments in machinery and equipment (Gross Fixed Capital Formation – Machinery and Equipment – GFCF-ME), between 2003 and 2020, a period in which there was information for all variables of interest and control at the time of the study. The working hypothesis is that public investments have a positive effect on the induction of private investments in FU.

The IBGE does not provide historical series of “GFCF-ME” for the FU. As a result, we established two proxies of this variable.

1. GDP – Gross Fixed Capital Formation – machinery and equipment (R$ 2010 – millions) 1995-2022. The original IBGE series of GFCF – machinery and equipment for Brazil was taken. To arrive at the value of each FU, in each year, the national value was multiplied by the participation of the FUs in the total disbursements of the BNDES system.

2. GFCF – Non-Financial Companies – is based on the total value for Brazil 2000-2020, according to IBGE data – Special Tables. To estimate the value of each FU, the participation in BNDES disbursements was used. The values were transformed into R$ of 2010 from the implicit deflator of the IBGE GDP.

Likewise, there are no long-term historical series on the public investments of the FUs in the IBGE and other official sources. To get around this limitation, we have developed the following measures:

• InvPub1 – is the investment by the FUs, according to data from the Treasury – SIAFI at 2010 prices, deflated by the implicit GDP deflator of the IBGE. This is the main measure available, as it is the official accounting record of these expenses.

• InvPub2 – the aggregate data of investments is taken, according to the IBRE database, with subsequent weighting by the participation of each FU in the apparent consumption of cement. Values at 2010 prices updated by the implicit GDP deflator of the IBGE, from 2003 to 2020.

The control variables used were: (i) CDI, monthly rate deflated by the IPCA and annualized; this variable is expected to have a negative effect on private investment; (ii) VIX, a volatility index, made available by the CBOE, which captures the influence of global credit cycles and risk perceptions; the lower the VIX, the greater the propensity to take risks (and vice versa). A negative relationship between the VIX and private investments in machinery and equipment is also expected; (iii) the balance of credit operations (in R$ million, at 2022 prices) from BNDES (in R$ million, at 2022 prices); (iv) the total amount of credit in the National Financial System (R$ million at 2022 prices, deflated by the IPCA); and (v) the GDP (in R$ million, at 2010 prices), made available by the IBGE, would have a positive influence on the GFCF-ME. Some models use alternative proxies to evaluate the behavior of demand, such as the final consumption of electricity (in MWh) from EPE – Empresa de Pesquisa Energética (Energy Research Company); and the terms of trade (ToT), available in the IMF database. The Appendix presents the descriptive statistics.

Considering the dynamic character and potential endogeneity of economic growth regressions, it is proposed to estimate dynamic panel data models with GMM estimators (Hsiao, 2014; Wooldridge, 2015), with the following general specification:

$\begin{array}{l}FCF=GFC{F}_{it-1}{\beta }_1+I_{it}{\beta }_2+r_{it}{\beta }_3+Y_{it}{\beta }_4+E{E}_{it}{\beta }_5+\\ +TO{T}_{it}{\beta }_6+TO{T}_{it}{\beta }_7+C{r}_{it}{\beta }_8+C{T}_{it}{\beta }_9+u_i+{ϵ}_{it}\end{array}$

Where: GFCF_it is the explanatory variable of the model is the gross fixed capital formation; GFCF_it−1 is the gross fixed capital formation lagged in a period, which captures the effects of possible omitted variables; I_it is the investment in Brazilian states; r_it is the CDI interest rate; Y_it is the GDP of the Brazilian states; EE is the final consumption of electricity by state; ToT_it represents the terms of trade; VIX is the volatility index; Cr is the BNDES’ credit; and, finally, CT is NFS’ total credit. ε is an unobservable variable that represents the individual heterogeneity of the FU, and may include geographic position, demographic factors, among others that may be correlated with the gross fixed capital formation of these states. The term represents the error vector. The results are robust in the different specifications, which suggests the stability of the conclusions⁴.

Table 3 explores the relationship between the consolidated public investment of the Brazilian states and the private investment, represented by the GFCF in machinery and equipment (GFCF-ME), over the period from 2013 to 2020. Here, the variable of interest is the investment of the states and the Federal District effectively made and recorded in their official balance sheets (“liquidated investment”).

Table 3
GFCF-ME and Public Investment by FU, 2013-2020

	GMM-System 1	GMM-System 2	GMM-System 3
GFCF-ME (-1)	0.5012*** (0.16)	0.3607** (0.16)	0.5105*** (0.16)
InvPub1	1.5742* (0.91)	1.8866*** (0.59)	1.5153* (0.84)
CDI	-28988.4628*** (10372.15)	-34383.7683*** (12257.97)	-40194.5890*** (10851.40)
VIX	-181.4365** (75.28)	-165.3996** (62.21)	-161.5697** (74.65)
BNDES Credit	-0.0020 (0.00)
Energy		0.0001 (0.00)
Credit		-0.0015 (0.00)	-0.0014 (0.00)
TI			15.4830 (48.66)
Constant	7104.2407*** (2319.62)	9790.7757* (5692.42)	11935.1183** (5012.04)
Observations	189	189	189
Instruments	13	12	13
Arellano-Bond test for AR(2) in first difference (p-value)	0.3170	0.3107	0.3153
Hansen test	0.3650	0.2113	0.3315

The coefficients for the variable GFCF-ME, which is lagged in the three specifications (GMM-System 1; GMM-System 2; GMM-System 3), indicate significant positive associations with private investment. This suggests that the increase in private investment in the previous period is related to an increase in private investment in the current period. The variable of investment of the States (InvPub 1) also shows a positive and significant relationship with private investment, with positive coefficients and higher than the unit in all specifications, with coefficients ranging between 1.51 and 1.88. Thus, for each additional R$ 1.00 of investment by the States, private investment would increase between R$ 1.51 and R$ 1.88. This result is supported by the international literature. For example, Eden and Kraay (2014), in a study that considered a sample of 39 low-income countries, found a “crowding-in” effect of an additional US$ 2.00 of private investment and US$ 1.50 of production for an extra US$ 1.00 investment from the government. On the other hand, Bahal et al. (2015), using quarterly data 1996Q2-2015Q1 for India, find a multiplier of 0.30, 1.24, and 1.07 after 4, 8 and 12 quarters, respectively, for each additional rupee of public investment.

The CDI interest rate and the financial market volatility index (VIX) showed negative and significant associations, indicating that an increase in these variables is related to a reduction in private investment. This result coincides with the evidence presented by Fraga and Lara (2023). The other controls were not statistically significant. The additional statistical tests show that the model is robust, with low autocorrelation in the differences and validity in the instruments used.

Table 4 replicates the initial model (Table 3) with the public investment in a shorter time horizon (2013-2020) and logarithmic transformation of the variables, which allows normalizing the distribution of data, contributing to a more robust analysis of the established relationships. In the three specifications, it is verified that the estimated coefficient for InvPub1 was positive and significant, so that, for each 1% (10%) increase in public investments, an expansion in private spending on machinery and equipment is expected between 0.3% (3%) and 0.4 (4%). Lagged private investment, interest rate (CDI) and risk perception (VIX) showed statistical significance and signs in line with what the literature recommends.

Table 4
GFCF-ME and Public Investments (on a logarithmic scale) by FU, 2013-2020

	GMM-System 1	GMM-System 2	GMM-System 3
GFCF-ME (-1)	0.7795***	0.7745***	0.6826***
	(0.16)	(0.21)	(0.14)
InvPub 1	0.2912*	0.2973*	0.3954**
	(0.16)	(0.15)	(0.16)
CDI	-0.1998**	-0.2102***	-0.1763**
	(0.08)	(0.06)	(0.07)
VIX	-1.0802**	-1.0178***	-0.9092**
	(0.41)	(0.28)	(0.35)
BNDES Credit	-0.0159
	(0.19)
Energy		-0.1760	0.0401
		(0.24)	(0.15)
Credit		-0.2832	0.1579
		(0.80)	(0.82)
Constant	2.0828 (2.26)	8.8401 (13.74)	-1.5248 (12.73)
Observation	162	162	162
Instruments	14	12	21
Arellano-Bond test for AR(2) in first difference (p-value)	0.6557	0.6693	0.6784
Hansen test	0.4120	0.6716	0.4586

To test the robustness of the previous results, the same exercise was carried out with a broader period (2003-2020) and variables with logarithmic transformation (Table 5). To this end, instead of working with the liquidated public investment (recorded in the balance sheets of the governments of the states and the Federal District), the InvPub2 (weighted by cement consumption) was considered, both for expenditures on machinery and equipment (table 8) and for the gross fixed capital formation of non-financial companies.

Table 5
GFCF-ME and Estimated Public Investments (on a logarithmic scale), 2003-2020

	GMM-System 1	GMM-System 2	GMM-System 3	GMM-System 4
GFCF-ME (-1)	0.3581***	0.4603***	0.4438***	0.5812***
	(0.12)	(0.10)	(0.12)	(0.14)
InvPub2	0.3094*	0.3683*	0.3351**	0.3945***
	(0.16)	(0.18)	(0.16)	(0.13)
CDI	-0.0741	-0.0688	-0.0972	0.0322
	(0.05)	(0.06)	(0.08)	(0.07)
GDP	2.4970***		-0.6805
	(0.78)		(0.72)
Energy	-2.0482***	0.0520		-0.2990
	(0.64)	(0.21)		(0.23)
Credit	-0.0907	-0.2985
	(0.28)	(0.30)
VIX		0.3618***
		(0.11)
Constant	9.4085*	4.4454	9.5655	5.7906*
	(4.94)	(5.92)	(7.03)	(3.01)
Observations	432	432	432	432
Instruments	25	27	23	14
Arellano-Bond test for AR(2) in first difference (p-value)	0.2948	0.2691	0.3201	0.2327
Hansen test	0.2102	0.1803	0.1347	0.1780

With this new design, the estimated models also generated statistically significant parameters for our variable of interest, oscillating 0.3 and 0.4. That is to say, increases of 1% (10%) in public investments would be associated with increases between 0.3% (3%) and 0.4% (4%) of private investments, controlling for other variables. The control variables varied in each specification: in the first, the GDP had the expected sign and was statistically significant; energy had the opposite sign; in the second variant, only the VIX was significant, but with the opposite sign; and in the following specifications, no control variable presented statistically significant results. The lagging private investment was significant in the four specifications.

Table 6 introduces the GFCF-NFC (gross capital formation of non-financial corporations), associating it with the expanded series of public investments. Once again, our variable of interest showed positive and significant coefficients, close to 0.3. Private investments, interest rates and credit also showed results with the expected signs and statistical significance.

Table 6
GFCF-NFC (non-financial corporations) and Estimated Public Investments, 2003-2020

	GMM-System 1	GMM-System 2
GFCF-NFC (-1)	0.4164***	0.4063***
	(0.08)	(0.07)
InvPub2	0.2904*	0.2785*
	(0.17)	(0.14)
CDI	-0.1084*	-0.0996*
	(0.05)	(0.05)
GDP	0.5298
	(0.69)
Energy	-0.3260	0.2419
	(0.64)	(0.16)
Credit	0.5679**	0.6004**
	(0.28)	(0.25)
VIX		0.0984
		(0.09)
Constant	-6.4189	-10.1635**
	(5.70)	(4.62)
Observations	432	432
Instruments	31	32
Arellano-Bond test for AR(2) in first difference (p-value)	0.2685	0.2480
Hansen test	0.4381	0.6858

Luporini and Alves (2010) found that a 10% increase in public investment increases private investment in machinery and equipment by 3.3% in the period 1996-2005. Similar parameters are found in Conte-Filho (2013), where for every 10% increase in investments in the transport and electricity sectors, private investments would increase by 3.5% and 1.8%, respectively. From a theoretical and normative point of view, the perspective of the Keynesian and structuralist literature is corroborated, which suggests that the public sector has an essential role in sustaining private investments and, therefore, with the search for full employment (Bresser-Pereira, 2022; Jespersen and Finn, 2019; Lavoie, 2022; Sawyer, 2019; Taylor, 2004).

FINAL CONSIDERATIONS

This article revisited the theme of the relationship between public and private investments in Brazil in the 2000s. We sought to contribute to the previous literature based on the analysis in a subnational cut, which considered the 27 Federation Units. In view of the absence of historical series of GFCF data made available by the IBGE for this level of aggregation, different proxies to capture the private and public dimensions of investments. The variables used were broader than those of similar studies, particularly that of Sanches and Rocha (2010). This possible contribution is the main highlight of the work and also a possible limitation, as the results presented are contingent on the methodological strategies employed.

All variants of the main model generated consistent results in terms of a positive and statistically significant relationship between the variables of interest, public and private investments. In terms of elasticities, the estimated coefficients ranged between 0.28 (~0.3) and 0.39 (~0.4), indicating that a 10% increase in public investments in the states and the Federal District can increase private investments between 3% and 4%, which converges with estimates that used similar methodologies. Future studies may benefit from the availability by the IBGE of more accurate estimates for private and public GFCF indicators with disaggregation at the subnational level.

The evidence obtained points to the importance of subnational governments resuming more robust levels of investments. In recent decades, particularly after the inflationary stabilization derived from the Real Plan, successive fiscal adjustments and new institutional frameworks have prioritized the generation of primary surpluses, without discriminating the nature of final spending, whether current or capital. Recent literature points to the existence of positive relationships between public and private investments, especially in infrastructure (Abiad et al., 2016; Deleidi, 2020; Matvejevs and Tkacevs, 2023; Ramey, 2019, 2021). As suggested by works that are inspired by structuralist and Keynesian traditions (Bresser-Pereira, 2022; Jespersen and Finn, 2019; Lavoie, 2022; Sawyer, 2019; Taylor, 2004), derived increase in income and productivity growth rates should be considered when designing a new generation of public policies.

Currently (2010s), Brazil’s GFCF is 7 p.p. of GDP lower than the world average, as well as below the regional standard (-1.4 p.p. of GDP) and that observed in upper-middle-income countries (-15.0 p.p.). In terms of per capita, Brazilian investments (US$ 1.5 thousand/year/inhabitant, at constant 2015 prices) are equivalent to half of the global average (US$ 3 thousand/year/inhabitant)⁵. While in the global economy as a whole, 1/4 of investments originate in the public sector, in Brazil this share is only 12% (see Table 2). There is, therefore, an important gap to be reduced, which will require a joint effort by companies and governments at its three levels.

An important alternative to create fiscal space in FUs is to reorganize the stock of their liabilities with the Union. A new legislative measure in this direction was approved by Congress and sanctioned by the Presidency of the Republic, in the so-called Program for the Full Payment of State Debts (Propag), which creates various incentives (reduction of interest, extension of payment terms, possibility of transferring state assets from the states to the Union as a form of debt reduction, creation of an equalization fund for less indebted states) and has as a counterpart the requirement of public investments in social areas, infrastructure and climate resilience. It is still too early to assess whether this new program will be able to achieve the intended effects. However, this agenda is in line with the prescriptions of multilateral bodies such as the OECD (OECD, 2019, 2023), United Nations (2023), IEA (2024), part of the private sector (JP Morgan, 2024; WEF, 2024) and independent research (Abiad et al., 2016; Deleidi, 2020; Matvejevs and Tkacevs, 2023).

Data availability statement:

The research data is only available upon request.

• 1
  Reis et al. suggest that, in the Brazilian case, public investment affects private decisions throughout the following channels: “The two mechanisms on the supply side state that public investment has the power to reduce the production costs of private investment and stimulate the productive capacity of industries based on the purchasing policies of government-owned enterprises. The mechanisms on the demand side, in turn, have as their premise the incentive of private investment, first, via the multiplier effect and, second, via the physical expansion and integration of the domestic market, particularly through infrastructure” (2019, p.836).
• 2
  Estimates based on World Bank data: “GDP per capita growth (annual %)” series. See: https://data.worldbank.org.
• 3
  BNDES Open Data Portal. See: https://dadosabertos.bndes.gov.br/.
• 4
  To evaluate the validity of the instruments used, the results of the Hansen test and RA test(2) are presented, which play a crucial role in verifying the robustness of the models. The Hansen test evaluates the joint validity of the instruments, while the RA test(2) examines the autocorrelation of the residuals, contributing to the reliability of the results. These procedures aim to ensure the solidity of the results presented, grounding the analysis for a more accurate and reliable interpretation of the relationships investigated.
• 5
  Own estimates with data from the World Bank (World Bank, 2024).

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Appendix 1
Variables Used and Data Sources

Expected signal	Definition of Variables
	GFCF-ME: GDP – gross fixed capital formation – machinery and equipment (2010 prices) – R$ 2010 (millions) – 1995-2022. The original IBGE series of GFCF – machinery and equipment for Brazil was taken. The values of each state were estimated using as proxy the participation of the FUs in the total disbursements of the BNDES system (https://www.bndes.gov.br/wps/portal/site/home/transparencia/estatisticas-desempenho/desembolsos).
	GFCF-NFC: Non-Financial Companies = R$ million (2010 prices) part of the total value for Brazil 2000-2020, according to IBGE data – Special Tables. To estimate the value of each state, the participation in BNDES disbursements was used. Deflated by the implicit GDP deflator of the IBGE (https://www.ibge.gov.br/estatisticas/economicas/contas-nacionais/9300-contas-nacionais-trimestrais.html?=&t=resultados).
+	INVPUB 1: Investment according to data from the Treasury – SIAFI – 2013-2022 (https://www.tesourotransparente.gov.br/visualizacao/fichas-dos-estados-informacoes-fiscais). At 2010 prices, deflated by the implicit GDP deflator of the IBGE.
+	INVPUB 2: The aggregate data for the country comes from the base estimated by IBRE - https://observatorio-politica-fiscal.ibre.fgv.br/series-historicas/investimentos-publicos/investimentos-publicos-1947-2023. To estimate the value of each state, the apparent consumption of cement (% of each state in the national total in each year) was used. Values at 2010 prices updated by the implicit GDP deflator of the IBGE. NOTE: The total values settled and estimated by IBRE are very close, with an average difference of less than 5%. However, there are important differences between the settled and the estimated for each state.
–	CDI: Monthly rate deflated by the IPCA and annualized (% p.a.), 1995-2022. Subsequently, the monthly average was taken to calculate the annual data.
+	Control 2: GDP – R$ million at 2010 prices. IBGE Series (IPEADATA), 1995-2020.
+	Energy: Final consumption of electricity by State. MWh. NOTE: The base does not provide the year 1997, which was estimated as the simple average of the two years before and after (1995, 1996, 1998, 1999).
Indeterminate a priori	TI: Terms of Exchange (% p.a. and index number, 1995 = 100) for Latin America and the Caribbean, 1995-2022. International Monetary Fund, World Economic Outlook Database, October 2023.

Appendix 2
Descriptive Statistics

	Average	SD	Medium	Maximum	Minimum	Kurtosis	Asymmetry	N
GFCF-ME	8,313	13,801	3,148	90,895	0.23	11.97	3.23	756
GFCF-NFC	12,994	25,982	3,218	311,137	2.99	36.67	4.81	567
INVPUB1	2,824	4,179	1,498	42,917	106.88	34.44	4.79	270
INVPUB2	1,840	3,425	741	45,581	7.46	56.99	6.01	540
CDI	0.08	0.07	0.07	0.27	-0.05	1.13	0.95	28
GDP	111,422	191,230	49,581	1145,524	3,113	14.63	3.70	702
Energy Consumption	14275,318	23014,705	6128,962	138280,630	182,274	13,36	3,46	756
TT	1.38	4.14	2.50	7.35	-8.81	-0.29	-0.71	28
VIX	20,20	6,10	18,73	32,70	11,09	-0,87	0,39	28
BNDES Credit	626,863	205,194	603,121	958,914	328,830	-1.27	0.23	16
Credit	2924,525	1555,490	2915,518	5361,248	1170,884	-1.76	0.11	28

• Editor responsible for the evaluation process:
  Luiz Carlos Bresser-Pereira

Publication Dates

• Publication in this collection
  10 July 2026
• Date of issue
  2026

History

• Received
  24 Feb 2025
• Accepted
  03 Sept 2025