Exploring the Non-Linear Relationship between Economic Growth and Its Main Drivers over the Last Decade in EU: Evidence from a Panel Smooth Transition Regression

Abstract

Rising oil, coal, and natural gas prices linked to the conflict between Russia and Ukraine have raised concerns about global economic growth and inflationary trends (International Monetary Fund (IMF), 2023). It is therefore interesting to examine the possible impact of oil prices on the relationship between economic growth and its determinants, including inflation. This article addresses this issue, using a panel dataset of 26 EU countries over the period 2011–2023 and studying the evolution of their growth within a Panel Smooth Transition Regression (PSTR) framework. Our empirical findings show that the real oil price is a significant transition variable between two extreme regimes and, accordingly, reveal that the determinants of economic growth have a time-varying intensity; notably, domestic investment, government spending, budget deficit, energy consumption of (non)renewable energy, trade balance, population growth, monetary policy as captured by the term spread and the M2 money growth, as well as the energy-related inflation.

1. Introduction

The escalating conflict between Russia and Ukraine has triggered a surge in oil, coal, and natural gas prices, prompting concerns about their potential impact on global economic growth and inflationary trends, as highlighted by the International Monetary Fund (IMF) in 2023. In response to these heightened uncertainties, there has been a notable uptick in academic interest surrounding the causes of inflation trends observed over the past decade and their potential repercussions on economic growth. Advanced econometric models such as the Panel Smooth Transition Regression (PSTR) are employed to provide a nuanced understanding of the multifaceted relationships at play and their potential non-linear features.

More specifically, this paper explores and provides evidence of the non-linearity of the relationship between economic growth and its main determinants by identifying two different regimes linked to changes in the real price of oil within the Eurozone between 2012 and 2022.

Following Hansen’s [1] approach, incorporating the concept of smooth transitions between regimes, allowing for a more flexible representation of non-linear relationships, one uses the PSTR model to explore non-linearities in the relationship between economic growth and its determinants to identify threshold points where the relationship between these variables changes, providing a more nuanced understanding of how economic dynamics evolve under different conditions in the particular context one mentioned.

The paper builds on Ben Cheikh et al. [2] approach investigating the relationship between energy consumption, income, and environmental pollution, with a focus on the impact of CO₂ emissions, using a non-linear regime-switching model to identify endogenous turning points in the relationship between economic development and environmental quality. The analysis, applied to Middle East and North African (MENA) countries, uses a non-linear panel smooth transition regression (PSTR) model to capture heterogeneity in pollutant emissions. The findings emphasize the importance of considering non-linear relationships for a nuanced understanding of environmental sustainability, economic growth, and energy consumption.

Based on these findings, this paper examines the complex relationship between economic growth and its determinants, including the common factors that explain the business cycle as well as certain monetary factors, and, more specifically, energy-related inflation. Noteworthy contributors to this non-linearity include a country’s level of investment and energy consumption from non-renewable sources.¹ Special focus will also be paid on the real oil price as one source of non-linearity.

Our main contribution is to show how a PSTR approach can provide interesting insights into the complex interplay of economic growth and its determinants by highlighting the role of real oil prices in this non-linearity.

The results we obtain, while they need to be interpreted with caution due to the short period studied, could offer policymakers a more nuanced understanding, enabling them to develop targeted strategies for navigating the complex economic landscape, particularly in the face of geopolitical conflicts and crises.

The paper is organized as follows. The first part is devoted to a short literature review, and the second one is devoted to the presentation of the methodology. The data are described in part 3. The results are commented on in part 4. Part 5 concludes.

2. Related literature review

The inquiry into the impact of inflation on economic growth is a topic of considerable interest and discussion in the academic literature, as evidenced by works such as Gillman and Kejak [3]. While ongoing debate exists, there is a general consensus that inflation has a globally adverse effect on medium and long-term growth [4, 5, 6, 7, 8]. However, it has been proposed that the connection between economic growth and inflation is not a straightforward linear relationship; rather, it is influenced by the level of inflation. Fischer [9] introduces the idea of a threshold above and below which the growth effects of inflation differ. Specifically, he suggests a positive relationship between inflation and growth for low inflation levels but a negative or insignificant one for high levels. Additionally, in cases of negative impact, the marginal growth costs appear to vary with inflation; the effect is stronger at lower inflation rates than at higher ones [10, 11, 12].

While the non-linear nature of the inflation–growth relationship is widely acknowledged, controversies persist regarding the inflation level acting as the threshold, the sensitivity of this non-linear relationship to factors such as data frequency, analytical framework, methodology, country classification (developed/developing), and the presence of high-inflation observations.

PSTR model has found application in a diverse range of economic modeling problems. These applications encompass investigations into the connection between pollution and economic growth [13, 14], the inflation-growth relationship [15, 16, 17], the impact of oil prices on the current account of oil-exporting nations [18, 19], borrowing costs of European countries during the recent financial crisis [20, 21, 22] or the behavior of exchange rates [23], among others [2, 24, 25]. These diverse studies highlight the PSTR model’s capability to effectively capture heterogeneity in panel data.

3. Methodology: A PSTR approach

The multi-regime non-dynamic panel smooth transition regression (PSTR) model with individual (${\mu }_i$) and possible time (${\lambda }_t$) effects are specified as:

$$Y_{\mathit{it}}={\mu }_i+{\lambda }_t+{\beta }^{\left(0\right)\prime }{X}_{\mathit{it}}+{\beta }^{\left(1\right)\prime }{X}_{\mathit{it}}\ast g\left(q_{\mathit{it}};\gamma ,c\right)+u_{\mathit{it}}$$E1

for $i=1,\dots N$ (cross-section dimension) and $t=1,\dots T$ (time dimension).

$Y_{\mathit{it}}$ denotes the dependent variable, ${\mu }_i$ denotes the individual effect (which does not depend on time), and ${\lambda }_t$ denotes the time effect (which does not depend on the individuals).

$X_{\mathit{it}}$ is the K-dimensional vector of time-varying explanatory variables.

$q_{\mathit{it}}$ is the transition variable and $u_{\mathit{it}}$ the error term.

$g\left(q_{\mathit{it}};\gamma ,c\right)$ is the (scalar) transition function normalized to vary between 0 and 1.

In the simplest case, just one transition is supposed to occur between two extreme regimes ($m=1$ transition). In this case, for the first (extreme) regime, the specification of $Y$ is a linear function of $X$ with parameter ${\beta }^{\left(0\right)}$. It is observed when $g\left(q_{\mathit{it}};\gamma ,c\right)$$\to 0$, while, in the second extreme regime, observed when $g\left(q_{\mathit{it}};\gamma ,c\right)$$\to 1$, $Y$ is another linear function of $X$ with parameters ${\beta }^{\left(0\right)}+{\beta }^{\left(1\right)}$.

It is worth emphasizing that the regime, at date $t,$ is an intermediate one characterized by a linear function of $X$, with parameters ${\beta }^{\left(0\right)}+{\beta }^{\left(1\right)}g\left(q_{\mathit{it}};\gamma ,c\right)$ between ${\beta }^{\left(0\right)}$and ${\beta }^{\left(0\right)}+{\beta }^{\left(1\right)}$. Accordingly, the model has time-varying coefficients.

The transition function is generally specified as a logistic function:

$$g\left(q_{\mathit{it}};\gamma ,c\right)={\left(1+exp\left(-\gamma \prod _{j=1}^m(q_{\mathit{it}}-c_j\right)\right)}^{-1}$$E2

with $m$ denoting the number of transitions.

$\gamma$ is the slope parameter supposed to be strictly positive and $c=(c_1,c_2,\dots ,c_m)$ with $(c_1<c_2<\dots <c_m)$ is the set of the threshold parameters.

With $\mathrm{m}=1$, the simplest specification of the panel logistic smooth transition regression (PLSTR) model is obtained with the transition function specified as follows: $g\left(q_{\mathit{it}};\gamma ,c_1\right)=$$\frac{1}{1+exp\left(-\gamma \left(q_{\mathit{it}}-c_1\right)\right)}.$²

In this case, the LSTR model implies that the two extreme regimes are associated with low and high values of $g\left(q_{\mathit{it}};\gamma ,c\right)$ with a single monotonic transition of the coefficients form ${\beta }^{\left(0\right)}$ to ${\beta }^{\left(0\right)}+{\beta }^{\left(1\right)}$ as $q_{\mathit{it}}$ increases, where the change is centered around $c_1.$

When $\gamma \to +\infty$, $g\left(q_{\mathit{it}};\gamma ,c\right)$ becomes an indicator function $1_{q_{\mathit{it}}>c_1}$(equal to1 if $q_{\mathit{it}}>c_1,$ and 0 otherwise). In that case, the PSTR model is similar to the two-regime panel threshold model of Hansen [1].

A generalization of the PSTR model to allow for more than two different regimes is the additive PSTR model [26]:

$$Y_{\mathit{it}}={\mu }_i+{\lambda }_t+{\beta }^{\left(0\right)\prime }{X}_{\mathit{it}}+\ast \sum _{j=1}^r{\beta }^{\left(j\right)}\prime X_{\mathit{it}}g\left(\underset{\mathit{it}}{\overset{\left(j\right)}{q}};{\gamma }_j,c_j\right)+u_{\mathit{it}}$$E3

where the transition functions $g\left(q_{\mathit{it}}^{\left(j\right)};{\gamma }_j,c_j\right)$are defined as in (2) with $c_j=(c_{j,1},c_{j,2},\dots ,c_{j,m_j})$.

If, $\forall j=1,..,r,m_j=1$ and $q_{\mathit{it}}^{\left(j\right)}=q_{\mathit{it}}$ , the model in (3) becomes a PSTR model with $r+1$ regime. Accordingly, the additive PSTR model can be viewed as a generalization of the multiple regime panel threshold model as shown by Hansen [1].

When the largest model that can fit the data is a two-regime PSTR model (1) with $r=1$and $m=1,$as in the present study, model (3) plays a role in the evaluation of the estimated model as explained below.

Estimating the ${\beta }^{\left(0\right)},{\beta }^{\left(j\right)},{\gamma }_j,c_j,j=1,\dots ,r$parameters in the additive PSTR model is a relatively straightforward application of the fixed effects estimator and non-linear least squares (NLS).

Finally, the model is evaluated by using two misspecification tests.

• A test of parameter constancy over time with an alternative specifying that the parameters change smoothly over time;

• A test of no remaining non-linearity where the alternative is that the parameters change smoothly over time.

For both tests, an extension of the PSTR model is proposed in the form (3).^3,4

In order to investigate the potential non-linear effect exerted by the situation on the oil market on the relationship between the gross domestic product (GDP) growth and its usual determinants for the 26 countries of the Eurozone, the panel smooth transition regression methodology appears to be particularly well adapted. More precisely, the PSTR analysis of the problem, referring to specification (1), will include the following variables. For each country i and year t, the dependent variable is the GDP growth rate, ${\mathit{\text{GDPG}}}_{\mathit{it}}$ and the explanatory variables are as follows:

• Growth rate of the nominal oil price $\mathrm{\Delta }{\mathit{\text{LnOIL}}}_t$

• Year-to year inflation rate $\mathrm{\Delta }{\mathit{\text{LnCPI}}}_{\mathit{it}}$

• Initial GDP, ${\mathit{GDP}}_{i0}$

• Domestic investment growth, ${\mathit{\text{INVG}}}_{\mathit{it}}$

• Population growth, ${\mathit{\text{POPG}}}_{\mathit{it}}$

• Government expenditures growth, ${\mathit{\text{GEXPG}}}_{\mathit{it}}$

• Non-renewable energy consumption growth, ${\mathit{\text{NRECG}}}_{\mathit{it}}$

• Terms of trade growth, ${\mathit{\text{TOTG}}}_{\mathit{it}}$

• Budget deficit, ${\mathit{BD}}_{\mathit{it}}$

• Term spread variation, ${\mathit{TS}}_{\mathit{it}}$

• M2 money growth, $M2G_{\mathit{it}}$

The transition variable is the real oil price, in logarithm, ${\mathit{\text{LnROIL}}}_t$, whose dynamics can be considered stationary (see Figure 1a of Appendix).

As usual, the oil price and the related inflation rate are considered as exogenous variables, as well as the initial GDP and the population growth given the short period (only 13 years). In addition, the budget deficit dynamics display sufficient inertia to be assumed as an exogenous variable. Likewise, the monetary policy as captured by M2 money growth is expected to have somewhat delayed effects on economic growth. However, potential endogeneity issues can be expected for the inflation rate, domestic investment growth, government expenditures growth, terms of trade growth as well as term spread which are, therefore, introduced with one lag.

Finally, the model which will be estimated becomes:

$$\begin{array}{ll}{\mathit{\text{GDPG}}}_{\mathit{it}}=& {\mu }_i+({\beta }_1^{\left(0\right)}\mathrm{\Delta }{\mathit{\text{LnOIL}}}_t+{\beta }_2^{\left(0\right)}\mathrm{\Delta }{\mathit{\text{LnCPI}}}_{i,t-1}+{\beta }_3^{\left(0\right)}{\mathit{GDP}}_{i,0}+{\beta }_4^{\left(0\right)}{\mathit{\text{INVG}}}_{i,t-1}+{\beta }_5^{\left(0\right)}{\mathit{\text{GEXPG}}}_{i,t-1}+\\ & +{\beta }_6^{\left(0\right)}{\mathit{\text{POPG}}}_{i,t}+{\beta }_7^{\left(0\right)}{\mathit{\text{NRECG}}}_{i,t-1}+{\beta }_8^{\left(0\right)}{\mathit{\text{TOTG}}}_{i,t-1}+{\beta }_9^{\left(0\right)}{\mathit{BD}}_{i,t}+{\beta }_{10}^{\left(0\right)}{\mathit{TS}}_{i,t-1}+{\beta }_{11}^{\left(0\right)}M2G_{i,t})\\ & +\left[\right({\beta }_1^{\left(1\right)}\mathrm{\Delta }{\mathit{\text{LnOIL}}}_t+{\beta }_2^{\left(1\right)}\mathrm{\Delta }{\mathit{\text{LnCPI}}}_{i,t-1}+{\beta }_3^{\left(1\right)}{\mathit{GDP}}_{i,0}+{\beta }_4^{\left(1\right)}{\mathit{\text{INVG}}}_{i,t-1}+{\beta }_5^{\left(1\right)}{\mathit{\text{GEXPG}}}_{i,t-1}\\ & +{\beta }_6^{\left(1\right)}{\mathit{\text{POPG}}}_{i,t}++{\beta }_7^{\left(1\right)}N{\mathit{\text{RECG}}}_{i,t-1}+{\beta }_8^{\left(1\right)}{\mathit{\text{TOTG}}}_{i,t-1}+{\beta }_9^{\left(1\right)}{\mathit{BD}}_{i,t}+{\beta }_{10}^{\left(1\right)}{\mathit{TS}}_{i,t-1}\\ & +{\beta }_{11}^{\left(1\right)}M2G_{i,t}\left)\right)g\left({\mathit{\text{LnOIL}}}_t;{\gamma }_1,c_1\right)+u_{i,t}\end{array}$$E4

4. Data and variables

Our panel data sample covers the period 2011–2023 and includes the 26 European Union (EU) countries: Austria, Belgium, Bulgaria, Croatia, Cyprus, Czech Republic, Denmark, Finland, France, Germany, Greece, Hungary, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Poland, Portugal, Romania, Slovakia, Slovenia, Spain, and Sweden. We collect the data at a yearly frequency from Eurostat, European Central Bank, and World Development Indicators Databases. We aim to tackle the non-linear contribution of the determinants of economic growth (particularly inflation) depending on the conditions in the oil market; accordingly, we choose the real oil price (in logarithm) as the transition (threshold) variable. We retain a set of explanatory variables inspired by the empirical literature, including Barro [5], Sala-i-Martin [27], Ozturk [28], López-Villavicencio and Mignon [17], and Eggoh and Khan [24].

Our monetary and financial variables vector comprises the term spread and the money growth. We compute yearly averages using monthly data on government bond yields coming from the European Central Bank (ECB). Term spreads are the difference between each country’s 10-year bond rates and the 3-month Euribor rate. This spread is commonly used to study yield curves (e.g., [29]). A 10-year-3-month term spread approaching zero suggests a “flattening” yield curve. In addition, a negative value of the spread, which is observed for inverted yield curves, is generally considered a sign of recession. Annual M2 money growth (as a broader measure of the money supply in an economy) accounts for inflation rate changes and their implications on economic growth.

The data related to the macroeconomic variables comes from Eurostat and refers to inflation, terms of trade, budget balance (deficit or surplus), and primary energy consumption. We use the harmonized Consumer Price Index (CPI) to measure inflation. The export-import price index ratio is taken to determine the terms of trade. Current prices divided by chain-linked quantities using 2015 as the reference year provided. This variable quantifies the percentage change over 5 years (year Y to year Y–5) and reflects how much an economy can import per unit of export products and services, suggesting its trade competitiveness. The government budget balance, whether deficit or surplus, is taken as a percentage of GDP and serves as an indicator of fiscal policy. In addition, the World Development Indicators database provides data on annual economic growth, energy consumption, domestic investment, government consumption expenditures, and population growth. We use growth rate of real GDP per capita (at constant 2015 US prices) as a dependent variable. Among the explanatory variables vector, we also consider the initial level of GDP per capita measured by the natural logarithm of the value of GDP per capita every 5 years. This variable captures Solow’s [30] convergence process in which countries with a lower initial capital stock per capita (or production per capita) expand faster. According to the literature, the coefficient of this variable should be negative. In line with neoclassical growth theory, our PSTR models contain both population growth and domestic investments (via the annual growth of gross fixed capital formation). The first variable is expected to negatively impact GDP growth, while increased investment rates should have a favorable impact on the evolution of economic activity. The government spending growth rate (the general government’s final consumption expenditure growth) is expected to be positively or negatively linked to economic growth. Alesina et al. [31], for example, show that fiscal corrections relying mostly on spending cuts that are concentrated on government wages and transfers tend to be expansionary, whereas those relying mainly on tax increases are contractionary.

In addition to these traditional variables influencing economic growth, we also consider the non-renewable energy consumption growth (in kg of oil equivalent per capita). Indeed, fossil fuels account for a large part of the energy mix, at least, 74.2%, observed in 2023. Recent growth models (e.g., Stern [32], Soytas and Sary [33]) emphasize the role of energy in economic growth, whereas neoclassical growth models (e.g., Solow [30]) focus solely on exogenous technological changes. These theoretical findings inspired empirical research (e.g., Kraft and Kraft [34], Ozturk [28], Apergis and Payne [35]) on causality between these variables to guide environmentally friendly energy strategies. Energy consumption is expected to stimulate economic growth, as proposed by the “growth hypothesis” in the related literature. Its validation means that energy is essential to economic growth; hence, strong energy policies are needed to boost growth or constrain energy consumption to decelerate growth.

As indicated before, we aim to determine the extent to which fluctuations in oil energy prices contribute to non-linearities in the relationship between economic growth and its determinants. To this end, we consider the natural logarithm of the real oil energy price from the World Bank Commodity Price Data. It refers to the average annual organization of the petroleum exporting countries (OPEC) crude real oil price: the crude oil, the average spot price of Brent, Dubai, and West Texas Intermediate, equally weighed/$ per bbl. This variable, ${\mathit{\text{LnROILP}}}_t$, whose dynamics can be considered as stationary over the period of study, is the threshold variable in our PSTR models.

As indicated before, for each country i and year t, the dependent variable is the GDP growth rate, ${\mathit{\text{GDPG}}}_{\mathit{it}}$ and the explanatory variables are:

• Growth rate of the nominal oil price $\mathrm{\Delta }{\mathit{\text{LnOIL}}}_t$

• Year-to year inflation rate $\mathrm{\Delta }{\mathit{\text{LnCPI}}}_{\mathit{it}}$

• Initial GDP, ${\mathit{GDP}}_{i0}$

• Domestic investment growth, ${\mathit{\text{InvG}}}_{\mathit{it}}$

• Population growth, ${\mathit{\text{POPG}}}_{\mathit{it}}$

• Government expenditures growth, ${\mathit{\text{GEXPG}}}_{\mathit{it}}$

• Non-renewable energy consumption growth, ${\mathit{\text{NRECG}}}_{\mathit{it}}$

• Terms of trade growth, ${\mathit{\text{TOTG}}}_{\mathit{it}}$

• Budget deficit, ${\mathit{BD}}_{\mathit{it}}$

• Term spread variation, ${\mathit{TS}}_{\mathit{it}}$

• M2 money growth, $M2W_{\mathit{it}}$

Table 1 of Appendix shows us the matrix correlation between the explanatory variables. Since there is no substantial correlation between these variables (except for the link between initial GDP and population growth), they can be included in the model simultaneously.

Furthermore, Tables 2 and 3 of the Appendix provide definitions and main descriptive statistics of variables in our growth regression analysis. Regarding our variable of interest, Table 3 indicates that the lower real oil price was 41.14 $/barrel while the highest level corresponds to 95.29 $/barrel. OPEC’s nominal oil price averaged 68.44 $/barrel. In the EU economies, between 2011 and 2022, inflation averaged 2.13% per year, while real GDP growth averaged 2.9%, respectively. In addition, Figures 2–4 display the trends of inflation, real GDP growth, and real oil prices (see Appendix) among EU countries. Figure 2 shows the scatter plot for the whole sample on the link between economic growth and inflation. Globally, there is a positive relationship between inflation and growth. This relationship seems to break down, however, midway between 4 and 8% inflation; above that threshold, there is a negative relationship between these two variables. However, the inverted U-shaped relationship between inflation and economic growth (observed in EU economies) has been documented in the recent empirical literature (see, e.g., [17]). The next Figure 5 illustrate these patterns by country.

To avoid spurious results, tests for cross-sectional independence in the errors and variable stationarity checks were performed. Table 4 in the appendix significantly rejects the null hypothesis of no cross-sectional dependency at the 1% level of significance for all variables, indicating reliable interdependencies between the countries. Considering the cross-dependence results, the Pesaran [2007] CIPS panel unit root findings show that the most part of our variables are stationary in level (except for the logarithm of budget deficit and the terms of trade). Some variables, such as oil prices do not have enough observations (11 in total) to test for stationarity, but, as previously indicated, the dynamics of the oil price can be considered graphically as stationary. Considering these findings, we may confidently move forward with the PSTR estimations regarding the relationship between economic growth and its determinants.

5. Results and discussion

Before estimating Eq. (4), we checked for linearity (homogeneity) in the relationship between GDP growth and inflation, conditioned by the oil price transition variable. Thus, testing whether the model has nonlinearity features is a necessary step before performing PSTR model estimation.

The results are detailed in Table 5 of the Appendix. For the test of linearity, we check whether the order m is one or not. We find that null hypothesis of linearity is rejected at the 1% significance level meaning that there exists a non-linear relationship between inflation and growth when the real oil price is considered as a transition variable. According to the two statistics (LR and LMF statistics), 2 regimes are fund (i.e., there is evidence on the existence of one threshold in the model). Additionally, the logistic specification is preferred over the exponential one since the logistic model had lower LM and LMF p-values.

Table 6 provides real oil price thresholds for the EU-26 countries as a whole. The real oil price threshold for the EU countries is 4.03. Since our data on real oil price are in natural logarithm, to compute the corresponding threshold value in dollar, we applied an exponential function to the constant value (4.03). This transformation informs us that the threshold for real oil price is 56 $ for the EU-26 countries.

In both regimes, the effect of oil-related inflation has a negative and statistically significant influence on economic growth at a 5% level of significance. It dominates the effect of consumption-based inflation whose effect is found non-significant in both regimes.

As expected, initial GDP has a positive impact on GDP growth, whatever the regime, but population growth has no significant impact.

Delayed investment growth has a positive and significant impact in the second regime; not surprisingly, this determinant of GDP growth plays no significant role in the critical and highly uncertain periods that primarily determine the first regime. Similarly, the lagged budget deficit has a positive impact on GDP growth in the second regime but not in the first. The same applies to terms trade’s delayed growth, whose positive impact is only significant in the second regime.

Interestingly, the growth rate of non-renewable energy appears as a positive determinant of GDP growth for both regimes, meaning that the “growth hypothesis” is validated; the non-renewable energy being a key ingredient for the economic growth in the EU countries.

The growth rate of money supply (M2) should have a positive effect on GDP growth over the decade 2011–2023, due to the quantitative easing decided by the ECB to deal with the consequences of the sovereign debt crisis, as well as the Covid crisis. However, overall, the relationship between M2 and the growth rate is negative during the studied period.

Of course, the central bank’s balance sheet is clearly related to phases of sustained growth and structural change, but it above all reflects the only ability of central banks to react very quickly to critical shocks by implementing stabilizing measures. Although the two waves of support programs implemented by the ECB (the public sector purchase programs-PSPP) following the sovereign debt crisis and pandemic emergency purchase programs (PEPP), following the pandemic, resulted in a sharp acceleration in the growth of the money supply, they were implemented in response to major recessions, which have a negative impact on this relationship over a relatively short and specific period.

The results must therefore be qualified with regard to the link between growth and money supply, even if this control variable remains significant at the scale of the regime. Delayed effects on the role of the money supply in stimulating growth may need to be investigated further over a longer period.

Finally, the lagged term spread has a negative and positive impact respectively in the first and second regimes. However, once again, the role of the term spread as an early indicator of recessions is difficult to highlight in the period studied, where we observe only one recession during the period covered by the study.

6. Conclusion

The real oil price is found a significant transition variable between two regimes of relations between growth and macroeconomic variables, distinctively affecting their intensity. While the oil price maintains a negative relationship with the annual GDP growth rate, erasing the expected impact of inflation; this relationship is non-linear and depends on a minimum oil price threshold, affected mainly by supply/demand imbalances in the oil market through an exogenous geopolitical context.

However, as we have pointed out, the period studied is short, quite heavily impacted by very critical periods, namely the sovereign debt crisis and the Covid event. What is more, the annual frequency is too low to really assess the impact of the financial variables traditionally introduced to explain economic growth. Consequently, these results cannot provide a solid basis for extrapolating what may happen in the future, by comparing the oil price to a reference value.

All in all, we consider that the results obtained are encouraging to develop a more in-depth analysis, notably by using a higher frequency database, over a longer period, distinguishing sub-panels of countries, in order to obtain a finer and more robust analysis of the non-linear relationship between economic growth and its determinants, as a function of oil market conditions.

Appendix

	GCEXG	INFLH	INVG	LBD	LGDP0	ROILP	M2G	NECG	POPG	TOTG	TS	DLNOILP
GCEXG	1.00
INFLH	−0.02	1.00
INVG	0.21	−0.03	1.00
LBD	0.10	−0.18	0.11	1.00
LGDP0	0.06	−0.10	0.05	0.27	1.00
ROILP	−0.21	0.58	−0.21	−0.15	−0.03	1.00
M2G	0.10	−0.07	0.04	−0.01	−0.22	−0.47	1.00
NECG	−0.10	−0.30	−0.11	0.16	−0.18	−0.09	−0.03	1.00
POPG	0.19	−0.04	0.11	0.29	0.64	−0.03	−0.15	−0.26	1.00
TOTG	0.04	−0.27	0.03	0.27	−0.21	−0.46	0.37	0.14	−0.15	1.00
TS	−0.40	0.13	−0.22	−0.28	−0.40	0.33	−0.03	−0.08	−0.24	0.03	1.00
DLNOILP1	0.09	0.16	−0.13	0.11	0.04	0.37	−0.24	0.33	−0.07	−0.16	−0.13	1.00

Table 1.

Correlation matrix for explanatory variables: 2012–2022.

Note: INFL—inflation; LROIL—real oil price(ln); DLNOIL—nominal oil price inflation, LGDP0—initial GDP (ln); INVG—domestic investment; POPG—population growth; GEXG—gov. spending growth rate; NECG—energy consumption growth; TOTG—terms of trade growth rate; LBD—budget deficit (ln); M2G—M2 growth rate; and TS—term spread.

Variable	Explanation, computation	Data sources
GDPG	The annual growth rate of GDP per capita based on constant local currency	World Bank
InvG	The Gross fixed capital formation (annual % growth)	World Bank
TOTG	The terms of trade growth is computed based on the export-import price index. Current prices divided by chain-linked quantities using 2015 as the reference year provide these. This variable quantifies the percentage change over five years (year Y to year Y–5) and reflects how much an economy can import per unit of export products and services, suggesting its trade competitiveness.	Eurostat
INFHC	Annual increase in harmonized Consumer Price Index (CPI), 2015=100	World Bank
POPG	Population growth (derived from total population, annual)	World Bank
LGDPio	The logarithm of the value of GDP per capita every five years	World Bank
GEXG	Gov. spending growth rate based on the general government final consumption expenditure (annual % growth)	World Bank
LBD	The logarithm of the budget balance (LBD): Net lending (+) /net borrowing (−) as percentage of GDP	Eurostat, World Bank
OILP	The average annual OPEC crude oil price. It refers to the crude oil, average spot price of Brent, Dubai and West Texas Intermediate, equally weighed/ $ per bbb.	World Bank Commodity Price Data
NECG	The non-renewable energy consumption growth. It is computed based on the energy use (tonnes of oil equivalent per capita, TOE) - It refers to use of primary energy before transformation to other end-use fuels, which is equal to indigenous production plus imports and stock changes, minus exports.	Eurostat, World Bank
M2G	The M2 money growth rate	ECB
TS	The term spread computed as the difference between each country’s 10-year gov. bond rates and the 3-month Euribor rate. This spread is commonly used to study yield curves.	ECB

Table 2.

Data description and sources (summary).

Note: GDPG—the growth rate of GDP per capita; GEXG—domestic investment growth; INFL—inflation; LOIL—nominal oil price(ln); LGDP_io—initial GDP (ln); InvG—domestic investment; POPG—population growth; NECG—energy consumption growth; TOTG—terms of trade growth rate; BD—budget deficit (ln); M2G—M2 growth rate.

	GCEXG	INFH	INVG	LBD	LGDPI0	ROILP	M2G	NECG	POPG	TOTG	TS	DLNOILP1
Mean	1.63	1.47	3.03	−1.12	10.1	68.4	5.65	−0.94	0.22	0.84	2.33	−0.01
Median	1.35	1.30	2.64	−1.53	10.1	63.1	5.20	−0.54	0.23	0.90	1.56	−0.01
Maximum	14.9	5.80	101.	2.12	11.6	95.3	21.1	12.7	3.93	12.8	22.2	0.52
Minimum	−7.47	−1.60	−40.4	−3.38	8.81	42.1	−9.37	−19.3	−6.19	−11.3	−0.09	−0.64
Std. Dev.	2.94	1.40	11.4	1.31	0.65	19.1	3.61	5.11	0.97	3.47	2.36	0.32
Skewness	0.79	0.32	3.12	0.62	0.08	0.21	0.20	−0.53	−0.75	−0.06	3.29	−0.31
Kurtosis	6.13	2.78	25.8	2.30	2.35	1.52	6.12	3.83	11.4	3.48	22.3	2.53
Observations	286	286	286	286	286	286	286	286	286	286	286	286

Table 3.

Main descriptive statistics.

Note: authors computation.

Variable	Pesaran CD – Stats (probability)	Pesaran CIPS – t-Stat (model with constant)	Pesaran CIPS – t-Stat (model with constant and trend)
GDPG	44.58 (0.000)	−2.290^**	−2.719
InvG	16.592 (0.000)	−3.514^***	−2.874^*
TOTG	22.328 (0.000)	−1.964	−1.742
INFHC	56.776 (0.000)	−2.300^**	−2.655
POPG	3.106 (0.0019)	−2.416^**	−2.611
Ln GDPio	55.020 (0.000)	—	—
GEXG	15.603 (0.000)	−3.356^***	−3.834^***
Ln BD	37.091 (0.000)	−1.928	−3.594^***
Ln OILP	59.791 (0.000)	—	—
NECG	32.890 (0.000)	−4.090^***	−6.312^***
M2 G	41.361 (0.000)	−3.621^***	−5.320^***
TS	45.397 (0.000)	−3.016^***	—

Table 4.

Cross-section dependence test (Pesaran – CD) and related panel unit root test (Pesaran CIPS) results: 2012-2022.

Note: (i) ^{***, **, *} significant at 1% level, 5% level, and 10% level, respectively; (ii) ln BD is weakly stationary as well as TOTG (around 12%).

Model	Hypotheses	Test	Stat	(p-value)
PSTR UE	H0 : m= 0 vs H1 : m=1	LM	101.604^***	(0.000)
		LMF	12.473^***	(0.000)
	H0 : m= 1 vs H1 : m=2	LM	18.788	(0.065)
		LMF	1.451	(0.152)

Table 5.

LM and LMF tests of linearity (p-values).

Notes: (i) ^***,**,* - significant at 1% level, 5% level and 10% level, respectively; (ii) LM and LMF tests are the Lagrange Multiplier and Fischer tests for linearity; (iii) H0: linear model; H1: PSTR model; iv) m=1 and m=2 are the logistic and the exponential transition functions, respectively; v) ^*** - indicates the strongest rejection of the linearity.

Panel models	PSTR UE_26
	Regime 1		Regime 2
	Coef.	t-Stat	Coef.	t-Stat
Transition parameters
Speed of transition – γ1	13.9944
Threshold parameter – c1	4.0305		56.28
Expanatory variables
Dlog Nominal Oil price	−0.8034	−0.4899	−4.2965	−0.2413
Inflation(−1)	−0.1145	−0.356	−0.3214	−0.8241
GDP initial	5.7499^*	1.7673	−0.0122	−0.1341
Domestic Investment growth (−1)	−0.0007	−0.0187	0.0744^*(1)	−1.4607
Pop. Growth	−0.8447	−0.7964	−1.3829	−1.2651
Gov. spending growth(−1)	−0.1057	0.2799	−0.8283^*	1.6617
Non-renew. Cons. Growth	0.1915	−0.1241	1.6120	−0.9788
Terms of trade growth(−1)	−0.1986	−1.4467	0.2378^*	1.6416
Budget deficit t−1	0.4248^*	1.7860	−0.3009	−1.0284
Term spread (−1)	−6.8085^***	−4.6942	7.7431^***	4.6546
M2 growth	−0.3680	0.0357	−2.2983	0.2131
No. Obs	286x13		286x13
No. Countries	26		26
RSS	1017.382		1017.382
AIC criterion	1.528		1.528
BIC criterion	1.835		1.835
Nb. parametters	24		24
Opti no. transit. fc.	1		1

Table 6.

PSTR estimates with the OPEC nominal oil price as the threshold variable: 2012–2022.

Note: i) ^***,**,* - significant at 1% level, 5% level and 10% level, respectively; ii) the threshold 1.46 indicates a coefficient which is significant at 7% risk level for a unilateral test (a positive effect of investment growth on GDP growth is expected).

Figure 1.

(a) The evolution of the real OPEC oil price: 2012–2022; (b) BRENT crude oil price. Note: Authors computation.

Figure 2.

The scatterplot on the link between inflation and GDP growth. Note: Authors computation.

Figure 3.

GDP growth rates by EU member state: 2012-2022. Note: Authors computation.

Figure 4.

The evolution of inflation in the EU countries: 2012–2022. Note: Authors computation.

Figure 5.

The evolution of M2 growth in the EU countries: 2012–2022. Note: Authors computation.