The Effects of Public Investment on Sustainable Economic Growth: Empirical Evidence from Emerging Countries in Central and Eastern Europe

Abstract

The relationship between sustainable growth and public investment, considered one of the key factors, is a topic of interest in the context of globally adopted sustainable development strategies and current budgetary constraints, especially in the case of tight budgets in developing countries, which constrain public investment more than current expenditure, for political or other reasons. Although there are endogenous growth patterns that incorporate public spending as a factor that promotes growth, the findings in the empirical literature provide contradictory results. The study is an empirical investigation into the effects of public investment on sustainable economic growth in emerging EU and Central European countries. For the period 1995–2019, the research shows that, in most of the countries included in the sample, the long-term impact of a public capital shock on GDP is estimated to be negative. The analysis of the effect of public investment on sustainable economic growth was performed by applying the VAR model and impulse response functions, the results being confirmed by estimating the accumulated multiplier to obtain the GDP response to a shock equal to a standard deviation of public capital.

1. Introduction

Major contributions to the study of the modern public economy and public finances show that the important divergence between the public and private economies is determined by how they create surplus value and use it in the interest of society [1]. In this sense, the primary goal must be the accumulation and concentration of public capital, and the development potential of the community increases as revenues can be converted into sustainable public investment goods and high-quality organic capital, the effect of declining public spending on economic competitiveness and capital accumulation being highlighted [2].

Economic theory suggests that the allocation of public funds for investment in developing economies focuses on large infrastructure gaps, where demand for public services (including education, healthcare, and infrastructure) is growing but requires a combination of revenue and careful prioritization of expenditure.

The economic and social impact of public investment depends critically on its effectiveness, so governments and local authorities must be rigorous in their decisions on public investment and in directing public funds to those public investments that really meet the related development requirements regarding the needs of society, especially in the context of the existence of limited resources against the background of unlimited needs [3].

The concept of sustainable development emerged in response to the development paradigm, which, against the background of the globalization process, the effects of intensifying industry, and widening social gaps, left a negative impact on the environment and quality of life, threatening the long-term existence of resources for mankind’s survival. Recognition of issues of global interest has been achieved through the political adherence of the UN and EU Member States to the 2030 Agenda and the 17 Sustainable Development Goals in 2015. Sustainable economic growth is a component part of sustainable development, being one of the major goals of sustainable development.

Sustainable growth and public investment, as determining factors, are a topic of interest in the context of globally adopted sustainable development strategies and current budgetary constraints (long-term sustainability of public finances and short-term stabilization of economic activity) [4], especially in the case of tight budgets in developing countries, which constrain public investment more than current expenditure, for political or other reasons.

The paper brings added value to the empirical literature by investigating the effect of public investment on sustainable economic growth in 11 developing countries, EU members in Central and Eastern Europe.

The proposed scientific approach is different from other studies by addressing the effect of public investment on economic growth in post-communist developing countries in the current context of sustainability.

The global economic and financial crisis has led to a sharp decline in public investment in the EU, a trend that has continued following efforts to stimulate investment in infrastructure through EU support measures. After settling at around 3% of the GDP in the year 2000, reaching a maximum of 3.82% in 2009, public investment across the European Union has declined since 2011, to a minimum level of 2.8% in 2016 and 2017. The average public investment (% of GDP) in CEE countries is higher than the EU average, ranging in the period 2006–2020 from a minimum level of 3.37% of the GDP in 2016 to a maximum of 5.13% of the GDP in 2015. This is due to the cohesion funds allocated by the EU for public investment, the EEC countries being the main beneficiaries (see Figure 1, in accordance with the recorded data on [5]).

The paper is structured as follows: the next section includes a review of the literature in relation to the study, Section 3 presents the research methodology, Section 4 highlights the empirical results obtained, Section 5 is allocated to discussion, while Section 6 provides the final conclusions.

2. Literature Review

Based on the general perception of public investment as a catalyst for economic growth, it is not surprising that there is a vast body of literature that has tried to assess its macroeconomic effects. Despite numerous studies, there is still significant uncertainty about the extent of the effect of public investment on output, especially in developing economies.

According to neoclassical economic models, as the rate of economic growth is determined exogenously, government investment has no positive impact on economic growth. In most empirical studies, the estimated equations are derived from neoclassical economic theory.

The empirical relationship between investment and growth has as its starting point in the applied economics literature the works of Aschauer, who identified a strong positive relationship between public capital and GDP growth in developed economies. Until his studies, the public capital stock component was practically ignored in productivity growth analyses [6,7,8].

Growth models follow the model developed by Solow [9], which explains long-term economic growth through key elements, such as capital or labor accumulation, population growth, and productivity, and it is known as the neoclassical growth model or the exogenous growth model. The model that follows is that of endogenous growth, in which investments are treated as a significant factor, proposed in Ref. [10]. In addition, other widely applied and inspirational models in experimental research are identified, such as the one developed in Refs. [7,11].

Therefore, there are many studies with different approaches in the scientific literature that investigate the empirical relationship between public investment and economic growth after Aschauer, a considerable portion of which follow his contributions.

From the perspective of the applied methodology, there are two different approaches in the literature, among which the analysis of the contribution of public capital to economic growth by using the production functions is more noticeable [11,12,13,14,15,16]. Following an extensive study, Romp and Haan argue that the stock of public capital can enter the production function in two ways: directly, as a separate factor of production, or it can influence the multifactor productivity [17].

A second approach seeks to provide a broader picture by focusing on the feedback effects of public capital or higher investment on the economy with the most common used methods: the autoregressive vector and structural macroeconomic models.

The studies address the effect of public investment using the VAR model, considering mainly public investment and less public capital stock given the more limited availability of public capital stock data and the fact that the effects of the impact depend critically on modelling public capital as a stock or as a flow [17,18,19,20].

Another difference of approach encountered in empirical studies refers to the way of defining the public capital used as an indicator expressed in monetary or physical values. A common approach used to approximate public investment is gross fixed capital formation. Public capital stock series are usually constructed as a sum of previous investments, based on government investment flow data, adjusted for a depreciation rate [21,22,23]. However, for many developing countries, researchers face the issue of long-term data availability, which means that the stock of public capital cannot be built [24]. Reservations in using this method also result from measuring investments. Therefore, various studies use government investment or some physical measure of infrastructure instead of government capital stock.

The use of monetary values as a measure of public investment involves several difficulties [25], mainly related to the ability to validly describe public capital, such as the unclear distinction between public investment in non-military equipment and structures and other government expenditures in terms of their effect on the productive capacity of the economy.

The complexity of measuring public investment has led the OECD, in its recent effort to analyze the link between public investment and growth, to rely on stock indicators rather than on measures of the financial value of public investment or the net worth of its capital stock [26].

The empirical results of Ref. [27] indicate that the effect of public capital stock on productivity is more important in determining productivity than the flow of public spending.

According to Ref. [27], the effect of an increase in public investment on economic growth is likely to depend on the relative marginal productivity of private capital relative to public capital. In the neoclassical context, an advance in public investment, to the detriment of private investment, will increase or decrease the rate of economic growth depending on whether the marginal product of public capital exceeds or is exceeded by the marginal product of private capital [28].

Productivity growth in the United States has slowed since the early 1970s due to a lack of investment in public infrastructure and has drawn attention to the importance of public capital for infrastructure by incorporating public investment into conventional production, pointing out that a 1% increase in public capital would increase the total factor productivity by 0.39% [6].

Subsequently, many authors have estimated regressions in which the dependent variable is the output and the independent variables are public capital, private capital, labor, and a constant for the level of technology [29,30]. As an approach, some studies assess the impact by identifying the relationship between public and private investment, seeking to determine to what extent they are complementary or substitutable, and to assess the effect of crowding-in (stimulation, agglomeration) or crowding-out (exclusion) on private capital in order to analyze their roles in the process of economic growth. The crowding-in effect of public investment on private investment is “defined to occur when increased public investment is associated with increased private investment” [31], crowding-out describing the opposite [32,33].

According to Ref. [34], which investigates the nonlinear causal relationship between public and private investment and gross domestic product in the US and China, there is a feedback loop between public and private investment through economic growth, indicating that public and private investment should stimulate each other directly or indirectly.

The effect of crowding-out on private capital may be due to the way public investments are financed, determined by budgetary constraints, by raising taxes or by borrowing with interest rate implications that create an adverse environment for the private sector. Moreover, the production of goods or services directly competitive with private sector products causes a crowding-out effect.

However, this approach of the issue leads to contradictory results. Thus, some authors consider public capital as a complementary factor of production that increases the marginal productivity of private capital [35,36], while others identify a substitutable effect on private investment [37] or contradictory results [38].

Other studies show substantial differences in the impact of private and public investment on economic growth, with private investment having a much greater impact than public investment, with possible complementarities, especially in the case of public investment in infrastructure leading to increased private equity [39].

Bom and Ligthart [40] show that a permanent increase in public investment amplifies long-term well-being if the elasticity of public capital production exceeds the public investment–GDP ratio, which is, on average, 3% in OECD countries, while Arslanalp et al. [15] show, for OECD countries, a positive elasticity of output in relation to public capital, which depends on the level of income of countries (OECD versus non-OECD) and the initial level of public capital. The elasticity is somewhat stronger for OECD countries, possibly suggesting the importance of institutional factors.

Afonso and Aubyn [41] use the VAR and the impulse response function to investigate the effects of public and private investment on economic growth in a sample of OECD countries. Although the results show a positive growth effect in most countries, in some countries, public investment has led to the depletion of private investment.

Using a similar methodology, Masten and Grdovic Gnip [42] conduct research for countries in Southeast Europe and show significant multiplier effects of public investment on growth. The results of the study argue that the main way in which public investment generates such multiplier effects seems to be to stimulate private investment.

De Jong et al. [23], through an empirical analysis, provides evidence of a general positive impact of increasing the stock of public capital on production and indicates the complementarity between public and private capital.

Moreover, the effect of public investment on production is identified by analysing the production multipliers of fiscal policy. Following a meta-analysis on public capital productivity, it suggests caution in supporting fiscal expansion as the overall long-term macroeconomic impact—the multiplier effect—of public investment depends on many factors, including the efficiency of public investment, the way in which expenditure increases are financed, the ratio between public debt and GDP, and its corresponding distortive effects [43,44].

A beneficial multiplier effect on production in general can also be attributed to the realization of public investment by contracting public procurement in the private sector.

Unlike the fiscal multiplier, some authors pursue the welfare multiplier [40,45], which, based on dynamic models of general equilibrium, reached similar conclusions, according to which the public investment welfare multiplier is sensitive to the elasticity of public infrastructure production, being negative when public spending has a low utility compared to the private utility and practically zero when the elasticity of the production of the public infrastructure is 3%.

The stimulating role of public investment is treated with interest by influential international organizations and policy makers. For example, in its annual Going for Growth reports, the OECD reiterates the importance of public investment for economic growth.

An empirical study undertaken for the OECD shows that public investment has a positive effect on long-term growth and labor productivity. Public investment can also increase the speed of convergence of developing countries. Public investment is more beneficial in some areas than in others [46].

The economic literature includes many studies investigating the effect of public investment on economic growth, but most of them are addressed to developed countries (USA, China, Japan, etc.) or to different groups of countries (OECD, EU, etc.), while fewer target developing or underdeveloped states.

A smaller number of studies on countries in Southeastern Europe reveal significant multiplier effects of public investment on GDP and show that there is no crowding-out effect of public investment on private investment [42,47]. Thus, there is a lack of research in terms of analysing the topic of interest in the former socialist states of Central and Eastern Europe.

The review of the literature reveals that public investment has a positive influence on economic growth and should be combined with private investment given that public investment could more often exclude private investment in developed economies, while, in developing economies, investment is more complementary to private investment and has a stimulating effect.

Although there are endogenous growth patterns that incorporate public spending as a factor that promotes growth, the findings in the empirical literature provide contradictory results. Moreover, by reviewing empirical studies, there has been a shortage in the literature regarding the investigation of nonlinear causal relationships between public and private investment and economic growth in emerging countries, empirical evidence on the macroeconomic effects of public investment in Central and Eastern European countries being almost non-existent. There is a focus on developed countries and a smaller number of scientific works addressing individual or hypothetical economies.

This sample is considered representative given the similarities in this group of countries (political regime—formerly communist countries, institutional reforms, etc.) to obtain relevant results to support the findings. At the same time, the potential for public investment for development in these countries is higher compared to developed countries.

In this regard, the research investigates the relationship between public investment and the rate of economic growth in developing countries. A transitional but persistent increase in public investment could lead to a substantial and long-term positive domestic macroeconomic impact, as well as to the effect of considerable cross-border spreading effects. While the empirical literature on the effect of public investment on GDP usually finds a positive effect, estimates vary considerably depending on period, country, capital measurement, and estimation method. Similarly, the productivity of public investment may vary over time and may decrease. Any increase in public investment must be assessed in light of productivity, its financing, and the relative costs and benefits of financing options.

The study was based on the premise that public investment plays a key role in achieving sustainable economic growth. To confirm the research hypothesis, the following hypotheses were formulated, which provide the directions for the approach in conducting the study:

H1. 

Public investment plays a key role in achieving sustainable economic growth.

H2. 

There is a strong positive correlation between public investment and private investment (crowding-in or crowding-out effect).

In this context, the following stages were considered:

-

identifying the statistical link between private investment and the business cycle;

-

analysis of the possibility for public investment to mitigate the impact of private investment fluctuations on the economy;

-

estimating the impact of the public capital multiplier.

3. Research Methodology

To achieve the objectives, macro-econometric modelling was used as a research method, suitable for highlighting the empirical behaviour of some macroeconomic phenomena by empirically identifying the relationships between macroeconomic variables specific to the analyzed economic phenomenon.

The impact of public investment on GDP was determined by first examining the statistical link between private investment and the business cycle, and then examining whether public investment can mitigate the impact of private investment fluctuations on the economy.

According to Keynesian doctrine, investment is considered the engine of economic growth through its multiplier effect. Keynes proposed this theory of the investment multiplier by analysing its role in a government-free and closed economy (without imports and without exports).

Y = Consumption + I

(1)

∆Y = ∆Consumption + ∆I

(2)

Since Keynes considered consumption to be a function of income, it turns out that the change in consumption is equal to the change in income multiplied by the marginal propensity to consume.

PMC = ∆Consumption/∆Y

(3)

∆Y = (MPC × ∆Y) + ∆I

(4)

∆Y/∆I = 1/(1 − MPC)

(5)

k = 1/(1 − MPC)

(6)

where: Y is the national income, I is the private investment, k is the investment multiplier, and PMC is the marginal propensity to consume.

In this context, the relationship between investment and an unconventional form of output gap (GDP deviation), determined by the Hodrick–Prescott filter, was tested to demonstrate the link between real private investment and the business cycle (deviations from GDP trend real) using a sample of data from 1996Q1–2021Q2 taken from the Eurostat database. To determine causality, correlations with lags and leads were used.

Another econometric method used is the Probit regression, applied for two samples: 1997Q2–2021Q1 and 1997Q2–2019Q4, to find out if fluctuations in private investment can cause recessions. Then, correlations with lags and leads were applied, as well as Granger causality, to analyze the statistical relationship between public investment and private investment (annual data 1995–2019).

Finally, the impact of the public capital multiplier was estimated using the autoregressive vector (VAR) method and impulse response functions using a Cholesky-type order.

3.1. Testing Methodological Framework

EViews version 7.2 soft (from IHS Markit, Irvine, CA, USA) was used to test the study’s hypotheses. The Hodrick–Prescott trend was introduced in 1997 [48] to estimate business cycles, so it is a suitable tool, being one of the most-used statistical filtering techniques in practice.

The HP trend is estimated by applying a minimization function to Equation (1):

$$\mathrm{Min}({{\displaystyle \sum }}_{i=1}^n{\left(\mathrm{Yt}-\mathrm{Ti}\right)}^2+\mathsf{\lambda }{{\displaystyle \sum }}_{i=2}^{n-1}[\left(\mathrm{Ti}+1-\mathrm{Ti}\right)-\left(\mathrm{Ti}-\mathrm{Ti}-1\right){]}^2)$$

(7)

where: Yt—the dependent variable expressed in natural logarithm, and Ti represents the trend, thus the cycle or the deviation from the trend = Yt − Ti, commonly called the component of the business cycle.

The lambda parameter (λ) is a penalizing element for accelerating the trend in relation to the business cycle [49]. Hodrick and Prescott [48] consider that a cyclical component of 5% is moderately high, as well as the 8th part of the 1% change in the quarterly growth rate [Hodrick–Prescott]. Thus, if the cyclic component and the second trend difference are distributed identically and independently normally, then λ is the ratio between the standard deviation of the cycle and the standard deviation of the acceleration of the trend. The authors considered optimal √λ = 5/(1/8) = 40, λ = 1600, these values being considered in the research.

Correlations with lags and leads were also used to analyze the link between business cycles (deviations from the HP trend of real GDP) and deviations from the trend of real private investment.

$$R=\frac{{{\displaystyle \sum }}_{i=1}^{n-k}\left(Xi-Xm\right)\left(Yi-Ym\right)}{\sqrt{{{\displaystyle \sum }}_{i=1}^n{(Xi-Xm)}^2{{\displaystyle \sum }}_{i=1}^n{\left(Yi-Ym\right)}^2}}$$

(8)

where: $Xm \mathrm{is}$ average of $X$, $Ym$ is average of $Y$.

The Probit method involves using a dummy variable, which takes the values 0 and 1 as dependent variable. The value 1 assumes the existence of the recession at time t + 1. A value of 0 indicates no recession. The Probit equation is calculated using Equations (9) and (10) [50]. The recession involves two consecutive quarters of economic downturn (quarter to quarter).

$${\mathrm{Recession}}_{\mathrm{t}+1}=F(\mathsf{\alpha }+\mathsf{\beta }\times (\log \left({\mathrm{Investment}}_{\mathrm{t}}\right)-\log \left({\mathrm{Investment}}_{\mathrm{t}-4}\right)\left)\right)$$

(9)

$$F\left(z\right)={{\displaystyle \int }}_{-\infty }^{z}1/\sqrt{2\pi } \exp \left(-x2/2\right)dx$$

(10)

Granger causality does not involve determining the causality between two or more variables in the conventional sense of the word, as demonstrated by Ref. [51], but whether using one variable can improve the prognosis of another variable. Granger causality tests have the following form [52]:

$$Yt=\alpha +{{\displaystyle \sum }}_{j=1}^{m}aj\left(Yt-j\right)+{{\displaystyle \sum }}_{j=1}^{m}bj \left(Xt-j\right)+{\epsilon }_t$$

(11)

$$Xt=\theta +{{\displaystyle \sum }}_{j=1}^{m}cj\left(Xt-j\right)+{{\displaystyle \sum }}_{j=1}^{m}dj\left(Yt-j\right)+{\eta }_t$$

(12)

The $F$ statistics reported are Wald statistics for the null hypothesis:

$$b_1=b_2=b_3=\cdots =b_j=0$$

(13)

$$d_1=d_2=d_3=\cdots =d_j=0$$

(14)

Two regressions are performed on the Granger test. In the first regression, the null hypothesis is that $X$ is not a Granger cause of $Y$, and, in the second regression, $Y$ is not a Granger cause of $X$. For the first null hypothesis, $Y$ is regressed using only the variables from its past. This is a restricted regression, from which we obtain the sum of the square residues of the restricted equation, denoted SSRr. Subsequently, also for the first null hypothesis, a second regression is run containing the past values of $Y$ and $X$, from which the sum of the square residues of the unrestricted equation, SSRu, is obtained, this being an unrestricted regression. By obtaining these 2 components, the $F$ test can be performed [53]:

$$F=\frac{\left[SSRr-SSRu\right]}{m}/\frac{\left[SSRu\right]}{\left[T-\left(2\ast m+1\right)\right]}$$

(15)

where $T$—the number of observations, $m$—the number of lags.

The introduction of VAR in econometric analysis was carried out by Christopher Sims (1980). The VAR model contains “n” equations and “n” variables. Each equation contains the past values of the dependent variable, as well as the past values for the other n − 1 variables [54]. This is the reduced form of VAR.

Autoregressive vectors are very often used for predictions because they are simple models that study the dynamics of the analyzed variables. VAR is often used to estimate tax multipliers. Recursive VAR and structural VAR models are mainly used to estimate capital and tax multipliers. The recursive form was used for this study.

The recursive form of VAR constructs the residues in each equation so that they are uncorrelated with the residues in the previous equations by entering the contemporary values as regressors for some existing variables.

X_t = a₁₁ + a₁₂X_t−1 + a₁₃Y_t + a₁₄Y_t−1 + ε_xt

(16)

Y_t = a₂₁ + a₂₂Y_t−1 + a₂₃X_t + a₂₄X_t−1 + ε_zt,

(17)

where: X_t, Y_t—variables studied, ε_xt and ε_zt are uncorrelated white noises (errors are completely random).

The application of the recursive VAR in the research is based on the methodology proposed by Kamps [21]. The variables were ordered as follows: real public capital, real private capital, total hours worked, and real GDP. The variable public real capital will have contemporary effects on the other variables, real private capital will have contemporary effects on hours worked and real GDP, and hours worked will simultaneously influence real GDP. The variables were logarithmic, with the first difference operator being applied. However, the first stage is the estimation of public capital and private capital.

For the estimation of the initial capital, the simplified method of the permanent inventory was used with a similar OECD methodology [55], according to which the initial capital is determined by the following equation:

W_t = (I_t−1 + (1 − φ)I_t−2 + (1 − φ)²I_t−3 + …) = I_t−1[1 + (1 − φ)(1 + λ) + (1 − φ)²(1 + λ)² + …) = I_t−1(1 + λ)/(φ + λ) = It/(φ + λ)

(18)

where W_t = capital at time t, the initial moment from which investment data are given, It—investments, φ—depreciation rate (assumed to be constant), λ—investment growth rate, obtained by regressing investments according to a time trend.

However, unlike the OECD methodology, the initial capital was calculated using the initial value determined by the regression that estimates the growth rate to avoid extreme values. Depreciation rates depend on the income group of the sample countries based on the World Bank’s classification [56] and the IMF recommended rates in 2019 [57], presented in

Table 1. Country classifications by income.

Country	Income Group
Bulgaria	Upper middle income
Czech Republic	High income
Estonia	High income
Croatia	High income
Hungary	High income
Lithuania	High income
Latvia	High income
Poland	High income
Romania	Upper middle income
Slovak Republic	High income
Slovenia	High income

and

Table 2. Depreciation rates.

Public Capital	Depreciation Rate (%)
Low-income states	2.5
Middle-income states	3.52
High income states	4.55
Privat Capital	Depreciation rate (%)
Low-income states	4.25
Middle-income states	5.4
High income states	7

.

3.2. Description of the Database

The data used to conduct the econometric survey are collected from the official EU statistical database, Eurostat, and refer to the economies of the sampled states.

The study was based on GDP, which, although not an indicator designed to measure economic and social well-being, remains the official indicator used to monitor sustainable economic growth.

The variables used to conduct the study are:

-

Real gross domestic product (at market prices, chain linked volumes (2015), million Euro) [58]; a quarterly frequency was used as it is the most logical given the need to observe changes in GDP over time;

-

Gross fixed capital formation (chain linked volumes (2015), million Euro; quarterly frequency) [59];

-

Average number of regular weekly working hours in the main job, by sex, professional status, full-time/part-time, and occupation (employed persons, age from 15 to 64 years, hour) [60];

-

Real public capital and real private capital data are constructed by applying a perpetual inventory method.

All variables used for the analysis were expressed in logarithms.

4. Results

The results of the research show that public investment has a positive short-term impact on economic growth in developing countries and stimulates private investment, with a statistically strong link between public investment and private investment. In the case of Romania, the connection between real investments and real GDP can be observed as presented in Figure 2 and Figure 3. However, to determine the exact relationship between these two variables, correlations with lags and leads were used.

As can be seen in Figure 4, the strongest correlation is registered at the first lag, so the gross real fixed capital formation determines the real GDP in the case of Romania. The correlation is strong and positive, with the result that real private investment determines real GDP, a situation that is also found in the case of Lithuania and Slovakia. Only in the case of Bulgaria are the results unclear. Most correlations are negative and insignificant.

In the case of Croatia (Figure 5), the strongest correlation is recorded between the values without lags and the leads of the two studied variables. The correlation is positive and strong (0.6422). The second-highest correlation is recorded at the first lag (0.5017), but the values of the following correlations with leads are higher than the correlations with lags, indicating that GDP influences private investment.

Similar results are available for the Czech Republic, Estonia, Hungary, Latvia, Poland, and Slovenia. That is, periods of economic growth are followed by increased investment. The correlations with lags, as regards Estonia, have a high value (although lower than the correlations with leads), suggesting a spiral effect. Thus, periods of significant economic growth lead to an increase in private investment, which, in turn, produces major economic growth.

The results show that, in most cases, GDP determines investment, contrary to the literature. However, the relatively small sample size combined with the COVID-19 pandemic could be the cause of these results. Thus, private investment has subsequently declined due to declining economic activity due to restrictions imposed to control the spread of the virus.

Testing this theory with Probit regressions on two samples shows that, in most cases, the decrease in real private investment causes recessions, and reducing the sample to avoid the inclusion of the pandemic period improves the results and shows stronger statistical links (for example, the case of Romania—

Table 3. Probit, Romania, 1997Q2-2021Q1.

Dependent Variable: RECESSION(1)
Method: ML-Binary Probit (Newton–Raphson/Marquardt Steps)
Date: 29 December 2021 Time: 15:26
Sample (Adjusted): 1997Q2 2021Q1
Included Observations: 96 after Adjustments
Convergence Achieved after 5 Iterations
Coefficient Covariance Computed Using Observed Hessian
Variable	Coefficient	Std. Error	z-Statistic	Prob.
D4_Investment	−5.610561	1.716525	−3.268557	0.0011
C	−0.912263	0.177385	−5.142827	0.0000
McFadden R-squared	0.232463	Mean dependent var		0.156250
SSD dependent var	0.364998	SSE of regression		0.309223
Akaike info criterion	0.706966	Sum squared resid		8.988176
Schwarz criterion	0.760390	Log likelihood		−31.93436
Hannan–Quinn criter.	0.728561	Deviance		63.86873
Restr. deviance	83.21258	Restr. Log likelihood		−41.60629
LR statistic	19.34386	Avg. log. likelihood		−0.332650
Prob (LR statistic)	0.000011
Obs with Dep = 0	81	Total obs		96
Obs with Dep = 1	15

and

Table 4. Probit, Romania, 1997Q2-2019Q4.

Dependent Variable: RECESSION(1)
Method: ML-Binary Probit (Newton–Raphson/Marquardt Steps)
Date: 29 December 2021 Time: 15:26
Sample (Adjusted): 1997Q2 2019Q4
Included Observations: 91 after Adjustments
Convergence Achieved after 6 Iterations
Coefficient Covariance Computed Using Observed Hessian
Variable	Coefficient	Std. Error	z-Statistic	Prob.
D4_Investment	−0.943983	0.185773	−5.081388	0.0000
C	−6.147621	1.878791	−3.272115	0.0011
McFadden R-squared	0.267682	Mean dependent var		0.153846
SSD dependent var	0.362800	SSE of regression		0.299490
Akaike info criterion	0.672758	Sum squared resid		7.982800
Schwarz criterion	0.727942	Log likelihood		−28.61050
Hannan–Quinn criter.	0.695021	Deviance		57.22099
Restr. deviance	78.13679	Restr. Log likelihood		−39.06839
LR statistic	20.91580	Avg. log. likelihood		−0.314401
Prob (LR statistic)	0.000005
Obs with Dep = 0	77	Total obs		91
Obs with Dep = 1	14

). Only in the case of Poland does the decrease in investment not lead to recessions as the probability associated with the independent variable coefficient is higher than the chosen relevance level of 0.05 because, in Poland, there was only one recession before COVID-19, with different causes (

Table 5. Probit, Poland, 1997Q1–2021Q1.

Dependent Variable: RECESSION_POLAND(1)
Method: ML-Binary Probit (Newton–Raphson/Marquardt Steps)
Date: 31 December 2021 Time: 13:54
Sample (Adjusted): 1997Q1 2021Q1
Included Observations: 97 after Adjustments
Convergence Achieved after 7 Iterations
Coefficient Covariance Computed Using Observed Hessian
Variable	Coefficient	Std. Error	z-Statistic	Prob.
C	−1.660636	0.237238	−6.999860	0.0000
D4_POLONIA_INV	−4.129290	3.148919	−1.311336	0.1897
McFadden R-squared	0.055768	Mean dependent var		0.041237
SSD dependent var	0.199871	SSE of regression		0.200106
Akaike info criterion	0.365781	Sum squared resid		3.804031
Schwarz criterion	0.418868	Log likelihood		−15.74038
Hannan–Quinn criter.	0.387247	Deviance		31.48076
Restr. deviance	33.34007	Restr. Log likelihood		−16.67003
LR statistic	1.859310	Avg. log. likelihood		−0.162272
Prob (LR statistic)	0.172704
Obs with Dep = 0	93	Total obs		97
Obs with Dep = 1	4

and

Table 6. Probit, Polonia, 1997Q1–2019Q3.

Dependent Variable: RECESSION_POLAND(1)
Method: ML-Binary Probit (Newton–Raphson/Marquardt Steps)
Date: 31 December 2021 Time: 13:54
Sample (Adjusted): 1997Q1 2019Q3
Included Observations: 91 after Adjustments
Convergence Achieved after 7 Iterations
Coefficient Covariance Computed Using Observed Hessian
Variable	Coefficient	Std. Error	z-Statistic	Prob.
C	−1.930476	0.306594	−6.296518	0.0000
D4_POLONIA_INV	−2.843878	4.128670	−0.688812	0.4909
McFadden R-squared	0.025754	Mean dependent var		0.021978
SSD dependent var	0.147424	SSE of regression		0.148288
Akaike info criterion	0.249796	Sum squared resid		1.957053
Schwarz criterion	0.304979	Log likelihood		−9.365703
Hannan–Quinn criter.	0.272059	Deviance		18.73141
Restr. deviance	19.22657	Restr. Log likelihood		−9.613284
LR statistic	0.495162	Avg. log. likelihood		−0.102920
Prob (LR statistic)	0.481634
Obs with Dep = 0	89	Total obs		91
Obs with Dep = 1	2

).

Fiscal incentives can, in theory, counterbalance fluctuations in private investment to temper economic cycles. From an accounting point of view, a government deficit implies a cumulative surplus of companies and households (income minus expenses). However, it is not only the size of the deficit that matters but also the structure of public spending. Studies show that the public investment multiplier is the largest tax multiplier [54] Moreover, the fiscal multipliers are higher in countries with strong public investment management [55].

The second hypothesis of the research, which refers to the impact of public investment on private investment, is validated. The case of Romania is exemplified, where the strongest impact is contemporary. By analysing the correlations with lags and leads in Romania, public investments determine private investments; the correlation at the first lag is 0.3981 (Figure 6). In most cases, there is a strong correlation between public and private investment.

For the Czech Republic, Granger causation was performed to verify that, in the short-term, there is a statistical relationship between these two variables. The results show that there is no statistical link for these time series in the case of the Czech Republic (

Table 7. Granger causality—real private and public investments, Czech Republic.

Pairwise Granger Causality Tests
Date: 2 January 2022 Time: 19:05
Sample: 1995 2019
Lags: 2
Null Hypothesis:	Obs	F-Statistic	Prob.
DL_PUBLIC_INV_CZ does not Granger Cause DL_PRIVATE_INV_CZ DL_PRIVATE_INV_CZ does not Granger Cause DL_PUBLIC_INV_CZ	22	0.09625 0.84362	0.9087 0.4474

).

Because causality cannot be determined, it can be bidirectional, which can mean that private investment increases the level of public resources and, implicitly, increases the level of public investment, or that public investment decisions are determined to some extent by public investment and new infrastructure projects, or that public investment can have a rapid impact on consumption and implicitly on investment.

For the second scenario, where public investment determines private investment and affects only the current level of private investment, public investment can be used to reduce the output gap, i.e., to bring GDP to the level of potential GDP.

A recursive VAR model was used to analyze the effect of public investment on GDP, and, using impulse response functions, the impact of real public capital on real GDP was estimated. The impulse response function estimates the effect of a shock in one of the innovations on current and future values of the endogenous variables (

Table 8. Private capital growth rate in Romania.

Dependent Variable: L_PRIVATE_INVESTMENT
Method: Least Squares
Date: 13 November 2021 Time: 19:31
Sample: 1995 2019
Included Observations: 25
Variable	Coefficient	Std. Error	t-Statistic	Prob.
C	9.540681	0.081885	116.5126	0.0000
@TREND	0.055420	0.005849	9.475127	0.0000
R-squared	0.796060	Mean dependent var		10.20572
Adjusted R-squared	0.787193	SD dependent var		0.457148
SE of regression	0.210887	Akaike info criterion		−0.198369
Sum squared resid	1.022887	Schwarz criterion		−0.100859
Log likelihood	4.479616	Hannan–Quinn criter.		−0.171324
F-statistic	89.77803	Durbin–Watson stat		0.446135
Prob (F-statistic)	0.000000

,

Table 9. Public capital growth rate in Romania.

Dependent Variable: L_PUBLIC_INVESTMENT
Method: Least Squares
Date: 13 November 2021 Time: 19:38
Sample: 1995 2019
Included observations: 25
Variable	Coefficient	Std. Error	t-Statistic	Prob.
C	7.868426	0.153781	51.16631	0.0000
@TREND	0.049717	0.010984	4.526123	0.0002
R-squared	0.471092	Mean dependent var		8.465026
Adjusted R-squared	0.448096	SD dependent var		0.533108
SE of regression	0.396048	Akaike info criterion		1.062054
Sum squared resid	3.607634	Schwarz criterion		1.159564
Log likelihood	−11.27567	Hannan–Quinn criter.		1.089099
F-statistic	20.48579	Durbin–Watson stat		0.571870
Prob(F-statistic)	0.000152

and

Table 10. VAR Romania.

Vector Autoregressions Estimates
Date: 21 November 2021 Time: 14:03
Sample (Adjusted): 2000 2020
Included Observations: 21 after Adjustments
Standard Errors in ( ) & t-Statistics in []
	DL_PUBLIC	DL_PRIVAT	DL_HOURS	DL_GDP
DL_PUBLIC_CAPITAL(-1)	0.516006 (0.34066) [1.51471]	0.426459 (0.23748) [1.79580]	0.167221 (0.11532) [1.45006]	0.810452 (0.59114) [1.37100]
DL_PUBLIC_CAPITAL(-2)	−0.518615 (0.33107) [−1.56650]	−0.432465 (0.23079) [−1.87388]	−0.151487 (0.11207) [−1.35171]	−0.334249 (0.57449) [−0.58182]
DL_PRIVAT_CAPITAL(-1)	0.440382 (0.46412) [0.94886]	0.489976 (0.32353) [1.51445]	−0.116966 (0.15711) [−0.74449]	−1.626517 (0.80536) [−2.01961]
DL_PRIVAT_CAPITAL(-2)	0.689089 (0.51140) [1.34746]	0.401027 (0.35649) [1.12492]	0.027220 (0.17312) [0.15723]	0.213343 (0.88741) [0.24041]
DL_HOURS(-1)	0.926069 (0.77083) [1.20140]	0.534705 (0.53734) [0.99509]	−0.186044 (0.26094) [0.71299]	−0.810062 (1.33759) [−0.60561]
DL_HOURS(-2)	0.324784 (0.71131) [0.45660]	−0.224068 (0.49585) [-0.45189]	−0.448606 (0.24079) [−1.86307]	0.620907 (1.23430) [0.50304]
DL_GDP(-1)	0.370482 (0.20737) [1.78658]	0.442688 (0.14456) [3.06237]	-0.014564 (0.07020) [−0.20747]	0.031538 (0.35984) [0.08764]
DL_GDP(-2)	−0.125640 (0.17529) [−0.71675]	−0.078020 (0.12220) [−0.63849]	−0.005564 (0.05934) [−0.09377]	0.349650 (0.30418) [1.14949]
C	−0.019517 (0.02019) [−0.96652]	−0.007219 (0.01408) [-0.51281]	0.003013 (0.00684) [0.44073]	0.076615 (0.03504) [2.18646]
R-squared	0.742210	0.832922	0.363103	0.491030
Adj. R-squared	0.570351	0.721537	−0.061495	0.151716
Sum sq. resids	0.005535	0.002690	0.000634	0.016666
SE equation	0.021476	0.014971	0.007270	0.037267
F-statistic	4.318697	7.477859	0.855169	1.447128
Log likelihood	56.73518	64.31259	79.48209	45.16083
Akaike AIC	−4.546208	−5.267866	−6.712580	−3.443889
Schwarz SC	−4.098555	−4.820213	−6.264927	−2.996236
Mean dependent	0.050462	0.054912	−0.001065	0.035242
SD dependent	0.032764	0.028371	0.007056	0.040463
Determinant resid covariance (dof adj.)		2.72 × 10−15
Determinant resid covariance		2.90 × 10−16
Log likelihood		256.4769
Akaike information criterion		−20.99780
Schwarz criterion		−19.20719
Number of coefficients		36

).

To verify the validity of the results, the accumulated multiplier was estimated to obtain the GDP response to a shock equal to a standard deviation of public capital, presented for each country in

Table 11. Public capital multipliers.

State/Accumulated Multiplier	1st Year	2nd Year	3rd Year	4th Year	5th Year
Romania	0.0380664	0.047615263	−0.006085254	−0.032724352	−0.046915966
Bulgaria	−0.023112	−0.038777479	−0.030410276	−0.029553438	−0.026234125
Croatia	0.0011291	−0.010315389	−0.020573621	−0.016055987	−0.012892889
Czech Republic	0.0152438	0.027139093	0.033495207	0.039055488	0.032291796
Estonia	−0.035922	−0.09073286	−0.121129138	−0.098857134	−0.07208992
Hungary	0.0330821	0.052849388	0.090801964	0.110667662	0.110677508
Latvia	0.0324911	−0.005031514	−0.049024468	−0.078168318	−0.099551196
Lithuania	0.0269878	−0.068627399	−0.096489559	−0.09350067	−0.088594793
Poland	0.0531882	0.050200813	0.006161929	−0.016346494	−0.002735239
Slovakia	−0.014631	−0.035158233	−0.066331813	−0.066830568	−0.062988801
Slovenia	−0.014685	−0.042014749	−0.056372144	−0.04791697	−0.040937891

Source: calculations made by the authors through EViews 7.2 soft (IHS Markit, USA).

.

According to Figure 7, the VAR model is stable (stationary) because the roots are located inside the circle. As a result, the impulse response functions can be continued. Table 11 represents the capital multipliers, expressing the GDP response in relation to the public capital stock response and scaled by the public capital–GDP ratio.

Figure 8, Figure 9, Figure 10, Figure 11, Figure 12, Figure 13, Figure 14, Figure 15, Figure 16, Figure 17 and Figure 18 show the effect of public investment on GDP using impulse response functions. The black line reflects the evolution of the public capital multiplier and the yellow dotted line represents Standard Deviation ± 2 SE. The cumulative fiscal (public capital) multiplier in Romania is positive in the short-term (Figure 8), but it becomes negative in the medium-term, reaching −0.0469 in the fifth year (Table 11), most likely due to the crowding-out effect (increase in interest rates due to fiscal expansion).

In Bulgaria, Estonia, Slovakia, and Slovenia, the public capital multiplier is negative for the whole period (Figure 9, Figure 10, Figure 11 and Figure 12). In the Czech Republic, however, the multiplier is positive (Figure 13). At the end of the analyzed period, the multiplier is equal to 0.032 (Table 11), i.e., the increase by EUR 1 of the real public capital leads to the increase by EUR 0.032 of the real GDP. The multiplier in Croatia is positive, almost zero at first and later becoming negative (Figure 14). At the end, the multiplier reaches a value almost equal to −0.01 (Table 11).

On the other hand, in Hungary, the multiplier is positive at any time (Figure 15) and reaches a value approximately equal to 0.11 in the last two years (Table 11). In the evaluated sample, the largest public capital multipliers are registered in Hungary.

In Latvia and Lithuania, the multiplier is positive to zero at first, then becomes negative throughout the period (Figure 16 and Figure 17). Unlike Hungary, we find the smallest multipliers in Latvia. They reach a value of almost −0.1 in the last year (Table 11).

Poland’s public capital multiplier is positive in the short-term and almost zero in the medium-term (Figure 18).

5. Discussion

Comparing the multipliers in the chosen sample with the multipliers for developed European countries, it can be observed that the cumulative effect is positive to the end only in developed countries, except for Spain and Denmark [23]. The debt level in Spain is very high, almost 100%, which could greatly reduce the impact of the multiplier and amplify the crowding out effect. The research shows that only in the Czech Republic and Hungary do they have a positive impact in both the short- and medium-term, and both are rather developed countries.

An empirical exercise covering 72 developed and emerging economies recently conducted by the IMF highlights how the fiscal multiplier depends on macroeconomic uncertainty [61]. Thus, an unforeseen positive shock on public investment of 1% of the GDP increases the level of production by 0.25–0.5% in the first year, which, after two years, is higher in periods of greater uncertainty [62].

The importance of the private sector in financing sustainable investment is reiterated by the UN in the Financing Report on Sustainable Development 2021 [63]. Consequently, for a long-term recovery, it is necessary to prioritize public investment in those sectors capable of stimulating sustainable economic growth and attracting private investment (e.g., renewable energy, telecommunications)—a crowding-in effect.

These findings reinforce the results of the research undertaken, namely the positive impact of short-term public investment on economic growth in developing countries and their crowding-in effect.

6. Conclusions

The study is an empirical investigation of the effects of public investment on sustainable economic growth. Although most previous studies have found that public capital increases productivity, it is observed that, by researching developing countries, in most of the sampled countries, the long-term impact of a public capital shock on GDP is estimated to be negative.

As a first step, it has been shown that real private investment determines economic cycles. Following the application of the Hodrick–Prescott filter and the correlations with lags and leads, there is a strong statistical relationship between real private investment and GDP: the decline in private investment produces recessions. The results were confirmed by applying the Probit regression after removing the data from the pandemic period.

Starting from the fact that fluctuations in private investments can be counterbalanced by public investments to temper the economic cycles, the impact of public investments on private investments was analyzed. Private investment drives the business cycle, suggesting that significant declines in real private investment could drive the economy into a recession. The effect of real public investment on real private investment is short-term, which means that they can be an effective tool for reducing the output gap.

Therefore, the interpretation of the study results reveals a strong correlation between public and private investment, with an influence that can be bidirectional, thus validating the second hypothesis of the research (H2).

The analysis of the effect of public investment on sustainable economic growth was performed by applying the VAR model and impulse response functions, the results being confirmed by estimating the accumulated multiplier to obtain the GDP response to a shock equal to a standard deviation of public capital.

Although, in general, the public capital multiplier in the sample is positive at the beginning, in most cases, it becomes negative in the medium-term. Of the sample countries, only the Czech Republic and Hungary have a positive multiplier at any time, both in the short- and medium-term. Thus, it can be concluded that, in general, in developed countries, public investment has a strong and positive effect, validating the first hypothesis of research (H1).

The limitations of the research are determined by the applied methodology. Thus, in an econometric model, certain coordinates of the analyzed economic phenomena that are considered important are highlighted, while the relations between them are rendered in a stylized form. Therefore, there may be a residual area of data that can be quantified as a proportion but that remains beyond knowledge. The study also targets developing countries, but the sample is limited to the central and eastern areas of the European Union.

Extending research to more developing countries would help to generalize the results. Moreover, carrying out the study with an alternative indicator of GDP, which would take into account externalities, such as environmental sustainability and overall quality of life, would add value to the research. However, it is necessary to identify the indicator that creates a statistical link with public investment.

Lack of corruption and government credibility are important factors in the public capital multiplier, along with the level of debt. Consequently, for a long-term recovery, it is necessary to prioritize public investment in those sectors capable of stimulating sustainable economic growth and attracting private investment (e.g., renewable energy, telecommunications)—a crowding-in effect. Institutional quality is a key element on which depends to what extent public investment leads to economic growth, as has been observed especially in developing countries. We considered that any increase in public investment must be assessed by government decision-makers in light of criteria of efficiency, financing, and associated costs, but especially economic and social benefits for society.