1 Introduction

Current scientific papers offer various approaches to definitions of food security and its pillars, as well as its quantification and insight into the current situation in the world. The first time was this term used at the World Food Conference in 1974. At that time, it was focused on price stability and food availability. Later in 1983, FAO (Food and Agriculture Organization) extended this concept by a pillar connected with physical access to food. But in general, there existed still various attitudes to food security and some of them were linked primarily to food sufficiency (Matkovski et al., 2020). The most frequently used definition of food security was formulated at the World Food Summit in 1996. It states that food security at the individual, household, state, regional and world levels is achieved when all people always have a physical and economic approach with enough safe and adequate food to satisfy their needs and different preferences for an active and healthy life. The World Food Summit 2009 introduced the food security concept based on four dimensions: stability, accessibility, access, and use and is still used by FAO. Currently can be found in the literature more than two hundred definitions of food security and its determinants (Kumar & Sharma, 2022).

1.1 Food security measuring

Food security measuring is a complex problem which should not be simplified into dichotomous variables indicating security or insecurity. Webb et al. (2006) emphasize situations when someone gets into a food insecure condition although does not experience immediate hunger, in contrast with others who could be in a desperate position. This should be considered also in the development of food security indicators, which should recognize between transitory and chronic food insecurity (Cafiero, 2013).

Various agencies use different indicators to assess food security and as highlighted by Carletto et al. (2013) there is a lack of consensus about it. Aggregation of indicators at the global level can offer just general information about the situation in the country and hide issues related to endangered segments of households and groups of individuals. In addressing food help it is therefore especially important to focus on groups and individuals in direct danger of food insecurity. Aggregated indicators at the global level play therefore key role also primary data collected from households and individuals (Poudel & Gopinath, 2021). The most frequently used measures based on primary data are the Consumption score developed by the World Food Program based on the frequency of different food groups' consumption by household, the Household dietary diversity score developed by the United States Agency for International Development based on number of unique foods consumed by household and The Coping Strategy Index which assess how household copes with food shortages. These measures suggest a strong correlation between food security and poverty, which can be also evaluated by different approaches. Sen (1976) in his classical work discussed questions related to its measuring, and emphasized the contributions of Atkinson (1970), Rowntree (1901) and Townsend (1954). The authors stressed the importance of income distribution in the population and suggested measures including the Gini coefficient to include income inequalities in the population.

On the other hand, Jacobs et al. (2004) highlight the vital role of composite indicators at the national level for the evaluation of summary performance and identification of policy priorities. The most frequently used measures used at the national level are the Global Food Security Index proposed by The Economist Intelligence Unit, the prevalence of undernourishment used by FAO, the Global Hunger Index developed by the International Food Policy Research Institute (IFPRI), the Global Poverty index developed in collaboration with Oxford University, The Hunger Reduction Commitment Index. According to many authors there exists between these measures a significant level of variability (Pangaribowo et al, 2013; Poudel & Gopinath, 2021; Pérez-Escamilla et al., 2017; Pingali, 2016).

The Global Food Security Index (GFSI) belongs among the indicators used the most often in scientific papers. However, Chen et al. (2019), Izraelov and Silber (2019), Maričič et al. (2016) and Thomas et al. (2017) critically reviewed it. Authors agree that GFSI is suitable for the evaluation of food security at the national level, however, all claim that its subjective weighting scheme is biased. Similar analysis was conducted also by Palkovič (2023), which compared performance of constructed indicator with GFSI. The result is that despite the solid methodology and reliable data GFSI focused more on food security determinants than its outcomes. A more complex study of composite indicators conducted by Nardo et al. (2005) and Saisana et al. (2005) suggests that the weighting scheme of composite indicators should be based on objective statistical methods, such as Data envelopment analysis (DEA) or Principal components analysis. The alternative can be also to use equal weights, or to derive weights based on the variability or correlation matrix of input indicators. Lovell and Pastor (1999), Kao (2010), Liu et al. (2011), and Blancas et al. (2013) used DEA technique of deriving an objective weighting scheme for composite indicators. The authors used a special type of DEA without explicit inputs or outputs. Chen et al. (2019) also used this method for a reassessment of the Global Food Security index.

1.2 Food security factors

Food security is a complex problem with multiple dimensions. According to Grote (2014), is food security or insecurity influenced by demand, supply, and market conditions. This means, that all factors affecting these variables have a direct impact on food security.

Improving food security is according to Chavas (2017) one of the most important policy goals, however, there are multiple ways to achieve it: increasing the food supply, improving food access, and increasing purchasing power of the population. Fan and Brzeska (2016) add that the essential role in achieving food security have agriculture and food production. But Matkovski et al. (2020) conclude that all these ways of food insecurity reduction could be successful only in stable environments and not in crisis conditions as was recently Covid 19 pandemic, or military conflict in Ukraine. Jambor and Babu (2016) argue that good availability of food does not always mean decent food security. Developing countries usually have poorer stability of trade, food prices and food supply indicators which influence their food security situation. For example, Papič Brankov and Milovanovič (2015) analyzed factors influencing food security in Serbia and found that the highest impact on food security had Gross domestic product and corruption. Kovljenič and Raletič-Jovanovič (2020) also conducted a similar study in Serbia and showed a significant influence on economic development, foreign trade, population growth and investments in agriculture. Matkovski et al. (2020) analyzed factors influencing food security in EU and Balkan countries. Results suggest a significant effect of the added value of agriculture on GDP, agricultural production per capita, land productivity and negative impact has agricultural export.

Many studies tried to investigate the relationship between food security and trade liberalization (e.g., Dorosh et al. 2016; Feleke et al., 2005, and Pyakuryal et al., 2010) and found, that it has either insignificant or positive effects on food security. Another research conducted by Dithmer and Abdulai (2017) continued with an investigation of trade influence further and confirmed, that trade openness and economic growth positively influenced food security. It improves especially dietary diversity and diet quality of the population. They used other food security determinants measuring the influence of country characteristics, economic and demographic development, variables measuring non-economic events and variables measuring economic policy.

Poudel and Gopinath (2021) compared the performance of multiple food security indicators. They compared also differences in results related to food security determinants. Based on their survey, they used as explanatory variables GDP and agricultural GDP, arable land, urban population, gross capital formation, trade openness, literacy, and internet access. They assessed the influence of trade openness as insignificant. In addition to traditional sources of food security, such as economic development, and focus on resources e.g., capital and urbanization, their results also highlight the key role of information access. Le and Nguyen (2018) also accentuated the value of information in food-related consumer behaviour.

Several studies investigated the effect of urbanization on food security. Farrukh et al. (2022) assumed that urbanization harms food security in their analysis conducted in Pakistan. According to Li et al. (2023), urbanization can affect food security in both positive and negative ways. It depends on the economic development of the country and the urbanization mode, which is present, but it does not endanger food security. Liu et al. (2021) agree that urbanization has positive and negative aspects and suggests using its positive effects on food security especially in rural areas. However, Malhotra (2021) discusses the limitations of conventional econometrics approaches in the evaluation of variable importance.

Climate change is another crucial problem significantly influencing various aspects of life on the planet. Many research papers investigated its relationship and impact on food security. For example, Lee et al. (2024) found a significant effect of climate change on food security in China. Authors concluded that it brings more uncertainty risks to the food security situation, however, they found heterogeneity in its impact across regions. Hadley et al. (2023) supported this result emphasizing various mechanisms through which climate change disrupts food security, such as extreme weather, increasing food prices and lower food quality. These have a significant impact on the health and nutrition of the population. Mirzabaev et al. (2023) focused especially on climate change effects on the food security of the most vulnerable segments of the population. Mekonnen et al. (2021) add that climate change awareness in the population can significantly improve the food security status of the most vulnerable people.

Presented paper develops further partial research results, which were published first in Palkovič (2023)Footnote 1 related to indicators and food security factors. However, despite the same resources and principles of applied methodology, both works used different approach to variable selection and food security pillars.

The main objective of the presented paper is to determine the main factors influencing food security in European countries. To achieve it was necessary first to produce an objective indicator for evaluating the food security level in Europe and to characterize its development over the analyzed period. Analysis assumes that the overall level of food security in Europe will be good with disparities across regions. The produced measure was used as food security output which helped to determine the main factors influencing it. This was the second objective of the presented paper. According to research papers in the theoretical part was selected a wider set of indicators considered in the modelling process. Based on its result was quantified impact of five major food security determinants. It is assumed that factors influencing European food security, in the long run, will be the same, but in the short run, there will be significant differences in how they affect food security in different countries.

The added value of the presented paper has more dimensions. First, the paper suggests a methodological framework based on data envelopment analysis for creating objective composite indicators usable for measuring and identification of food security issues in European countries. The paper also shows the development of food security and its disparities among European countries over the years. The last available year in the presented analysis is 2020 when covid nineteen pandemic spread across Europe. The paper offers deeper insight into food security conditions in European countries in this period. An important asset of the presented paper lies also in the determination of the main factors influencing the food security situation in Europe in the long run and in all individual states in the short run. Presented pooled mean group estimation can extend current knowledge in the investigated field and add a new point of view to food security analysis.

2 Material and methods

The first step in the analysis was the determination of variables which could be used to evaluate the actual food security situation in Europe and to construct a composite indicator according to the definition of food security by FAO in four pillars: availability, access, stability, and utility. The intention was to use the largest possible number of variables. All indicators should have nonzero variability in European countries and should be available at least until the year 2020. The list of all available indicators in the food security section of FAOstat met the previously mentioned requirements with only nine variables. These were supplemented by three variables from the World Bank database to ensure an equal number of indicators in every pillar. (Food production index in pillar Availability, Consumer price index and Gini index in pillar Access). A list of analyzed variables is in Table 1. All variables were available for 38 European countries in the period 2001–2020. The reason for the smaller number of selected indicators was that variables included in the FAOstat database focused more on developing countries and their values were not available for the European region or had ridiculously small variability in developed countries. Missing values were extrapolated or interpolated to maximize the number of observations available for analysis.

Table 1 List of variables used to create composite food security index. Source: FAOstat and World Bank
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Table 1 shows variables used to produce composite food security indicators with objective weights using Data envelopment analysis (DEA) with dummy input. The constructed food security indicator was related to the main factors influencing food security. Their selection respected the results of other authors and partial results in pre-analysis. The limitation was twenty observations for one country, which means that in the Pooled mean group model, it was not possible to use too many variables to ensure its robustness. Five final food security factors selected from wide range of thirty available indicators are in Table 2. Variables selection was based on results by Poudel and Gopinath (2021), Matkovski (2020), Lee et al. (2024) and Hadley et al. (2023).

Table 2 List of variables used as food security determinants. Source: World Bank
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Variables were in a standardized form, which allowed us to compare their importance according to estimated functional parameters. Using cumulative Gross capital formation instead of per capita value may be controversial. It was result of the insignificance of per capita indicators of gross capital formation in pre-analysis models. However, cumulated values also include information about the size and economic power of the country.

2.1 Estimation of composite food security indicator

To obtain a composite indicator with consistent ranking, it was necessary to normalize all input variables according to the process described by Kao (2010) and Chen et al (2019). Variables where higher values are better were normalized according to function 1. This was applied to most analyzed variables.

$$Y=\frac{y-\text{min}\left(y\right)}{\text{max}\left(y\right)-\text{min}\left(y\right)}$$
(1)

Variables, where smaller values mean better results, such as the prevalence of moderate or severe food insecurity in the total population, consumer price index, per capita food supply variability, coefficient of variation of habitual caloric consumption, Gini index and incidence of caloric losses at retail distribution level were normalized according to Eq. 2.

$$Y=\frac{\text{max}\left(y\right)-y}{\text{max}\left(y\right)-\text{min}\left(y\right)}$$
(2)

In both equations are min and max the smallest and the highest values among thirty-eight countries for each variable.

A composite indicator of food security was constructed with Data envelopment analysis (DEA). Standard DEA is a method to measure the efficiency of the transformation of inputs into outputs for every DMU. Lovell and Pastor (1999), Kao (2010), Liu et al. (2011), Blancas et al. (2013) and Chen et al. (2019) suggested that DEA can be applied also in situations without explicit inputs or outputs to generate objective weights for composite indicators. The constructed indicator will be given in contrast to the Global Food Security Index, where weights are set subjectively by the panel of experts. In the case of composite indicator would be suitable to use hierarchical DEA following the structure of individual pillars of food security as proposed by Chen et al. (2019). In this case, it was not possible due to the few available indicators in each pillar.

Let yi (i = 1, 2…M) be the indicator for each DMU j (j = 1, 2…N). As proposed by Kao (2010), input-oriented DEA can be used to generate objective weights for composite indicators for j-th DMU by assuming input equal to one (dummy input). The objective function has the form:

$$Max\theta _{j} = \sum\limits_{{i = 1}}^{M} {u_{{ij}} y_{{ij}} i = {\text{1,2}}, \ldots Mj = {\text{1,2}}, \ldots N}$$
(3)

Subject to

$$\sum\limits_{{i = 1}}^{M} {u_{{ij}} y_{{ij}} \le 1,i = {\text{1,2}}, \ldots Mj = {\text{1,2}}, \ldots N}$$
(4)

where θ is the value of the composite food security index, u is the weight for variable I and country j, and y is the value of variable i and country j.

According to Eqs. 1 and 2 will be weights generated objectively without external influence the way, it will maximize the value of the indicator for each DMU (country in this case), and constraints will ensure, that the index for all other countries will be less or equal than one (Ramathan, 2006). This formulation also means that the food security index for each country will depend on the performance of all other analyzed countries in the current year. For this reason, the calculation of the food security composite index included data for all 38 European countries available at FAOstat (Eq. 4 means 38 constraints, one for every country).

According to the assumption of a simple additive weighting scheme model also included a constraint that the sum of weights should be equal to one. This constraint represents Eq. 5.

$$\sum\limits_{{i = 1}}^{M} {u_{{ij}} = 1i = {\text{1,2}}, \ldots Mj = {\text{1,2}}, \ldots N}$$
(5)

To avoid zero weights for small indicator values in the maximization function, it was necessary to add constraints to restrict maximum and minimum value of weight. According to some authors, these values could be decided by expert opinion. The goal of this paper was to determine objective weights, so it applied the scheme suggested by Chen et al. (2019) based on average weight without subjective elements (Eqs. 6 and 7).

$$Lb=\frac{1}{\left(number \, of \, indicators \, in \, composite \, index\right)}-50\%$$
(6)
$$Ub=\frac{1}{\left(number \, of \, indicators \, in \, composite \, index\right)}+50\%$$
(7)

Constrain for the nonzero weight of indicator has form:

$$Lb\le {u}_{ij}\le Ub i=\text{1,2},\dots M j=\text{1,2},\dots N$$
(8)

where Lb is the lower bound for indicator weight, Ub is the upper bound for indicator weight and uij is the weight of variable i and country j. In the presented case with twelve indicators included in the composite index was minimum weight equal to 0.0417 and the maximum weight to 0.125. This means that the minimum weight of one food security pillar could be 0.125 and the maximum weight 0.375.

Every value of the produced composite index was the solution to the maximization problem with forty constraints. This was solved for 38 European countries for the period 2001–2020. The indicator only considered the performance in European countries, so the result of every country in the current year depends on the performance of all other European countries in the analyzed period. The indicator can take values between 0 and 1. Value closer to 1 means better food security performance. Despite using DEA, the estimated value of the indicator is not efficient, and no country reached a value equal to 1.

2.2 Influence of food security factors analysis

The standard approach to the analysis of causal relationships assumes that the composite food security indicator produced as a result of DEA analysis is a function of considered food security factors according to Eq. 1.

$${y}_{it}=f\left({x}_{1it},{x}_{2it},\dots {x}_{5it}\right) \, for i=\text{1,2},\dots ,N \, and \, t=\text{1,2},\dots ,T$$
(9)

where yit is the value of constructed food security indicator of i-th country in time t, and x1it, to x5it represent food security factors described in Table 2, for i-th country in time t.

Model assumes linear relationship between food security and its factors. Logarithmic transformation was not suitable due to percentage nature of the most explanatory variables. Standardization of all explanatory variables allowed comparability of estimated coefficients.

The analysis assumed a basic relationship between variables:

$${y}_{it}={b}_{0}+{b}_{1}{x}_{1it}+{b}_{2}{x}_{2it}+{b}_{3}{x}_{3it}+{b}_{4}{x}_{4it}+{b}_{5}{x}_{5it}+{u}_{it}$$
(10)

where b0, b1, …b5 are functional parameters and uit random error component.

The standard approach to panel data analysis is a model with fixed effects or random effects which assume homogenous values of b coefficients, which are the same for all countries.

The fixed effects model assumes that slope coefficients are the same for all analyzed countries, but functions differ in constant b0, which denotes the fixed effect. This could be obtained by following substitution in Eq. 2:

$${b}_{0}={\alpha }_{i}$$
(11)

where αi is the time-invariant individual effect. In practice, could be fixed effects estimated by introducing N-1 dummy variables.

The alternative panel approach assuming homogenous values of estimated parameters is the random effects model. In contrast with the fixed effects model, it estimates individual effects as specific error components. The following modification of Eq. 2 creates the random effect model:

$${u}_{it}={{e}_{it}+v}_{it}$$
(12)

where eij is the common random error component and vit is the random error specific for every cross-sectional unit which expresses the individual heterogeneity of the panel. The decision between the fixed and random effects model was based on the result of the Hausman test, which verifies if the random effects model estimate is consistent. In case of null hypothesis acceptance is suitable the random effects model, otherwise is adequate fixed effects model.

The alternative to the fixed and random effects model is Pooled mean group model, which allows to estimate of heterogenous functional parameters in the short run, which are specific for every cross-sectional unit. A common approach to modelling panel data is to estimate N separate regression and calculate the mean value of coefficients called the Mean Group estimator. An approach introduced by Pesaran et al. (1999) called the Pooled Mean Group estimator allows the long-run coefficients to be the same and short-run coefficients and error variances to differ across groups. It assumes that there are often good reasons to expect long-run equilibrium relationships between variables to be the same, but short-run dynamics and error variances tend to be different.

We assume that Eq. 2 expresses long-run relationships with heterogeneous functional parameters. But in the short run can be estimated relationship in equations with slope coefficients specific for each cross-sectional unit according to Eq. 5.

$${\Delta y}_{it}={\varphi }_{i}\left({y}_{it-1}-{b}_{0}-{b}_{1}{x}_{1it}-{b}_{2}{x}_{2it}-\dots -{b}_{5}{x}_{5it}\right)+{\delta }_{1i}\Delta {x}_{1it}+{\delta }_{2i}\Delta {x}_{2it}+\dots +{\delta }_{5i}\Delta {x}_{5it}+{\varepsilon }_{it}$$
(13)

where \({\Delta y}_{it}, {\Delta x}_{1it},\dots ,{\Delta x}_{5it}\) are the first differences of dependent and independent variables.

\({\varphi }_{i}\) denotes the error correction term, which expresses how fast the cross-sectional unit converges to long-run equilibrium Significance of this term also confirms the significance of the long-run relationship.

\({\delta }_{1i}, {\delta }_{2i}, \dots , {\delta }_{5i}\) are short-run coefficients specific for each analyzed cross-sectional unit.

Interpreted results include a comparison of long-run coefficients estimated with different methods and short-run dynamics estimated with the use of the Pooled mean group model.

3 Results

The food security situation in European countries over the 20 years significantly improved. Figure 1 shows the average value of the food security index produced by DEA analysis in European countries (blue line, values on the left axis) and its variability measured by the coefficient of variation (orange line, values on the right axis). The values of the calculated food security index every year depend on the performance of all European countries included in the analysis. All countries were benchmarked with the best performance in the actual year. The average value of the food security index improved from 0.65 in 2001 to 0.74 in 2020 which suggests a significant increase. On the other side, differences between countries measured by coefficient of variation decreased from 16% in 2001 to 12% in 2020. This suggests substantial improvement and convergence between countries concerning the food security situation in the region. However, with a closer look at the end of the analyzed period, the deterioration of the food security situation between 2014 and 2015 is apparent. The average value of the food security index stopped growing and stabilized at value 0.73. Variability of index recorded a similar development. The decrease in variability between countries stopped in 2014 and the coefficient of variability in upcoming years oscillated around 13%.

Fig. 1
figure 1

Source: Author´s work based on FAOstat data

Development of constructed food security index and its variability.

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This explains the deterioration of the average score for indicators of consumer price index, political stability, food supply variability and minimum dietary energy requirement, which were mostly stable for the rest of the analyzed period. In 2014 also started first armed Russian operations in Ukraine. Alongside the increase in the average value of food security indicators in 2020 also increased its variability which suggests the deepening of food security disparities between European countries. The spread of Covid 19 which started in 2020 may significantly influenced this development. The Covid crisis and escalation of the war in Ukraine in recent years led to further deterioration of the food security situation in European countries and an increase of disparities between European countries. Unfortunately, it was not possible to verify this assumption, due to the unavailability of data for the input variables after the year 2020. This could be the subject of further research conducted when data is available. Despite the stable food security situation in European countries, results indicate its decrease since 2014. In 2020 the average performance of analyzed European countries was still slightly smaller compared to 2014, despite its continuous growth since 2015.

3.1 Food security situation in Europe in 2020

The food security situation of European countries in 2020 is in Fig. 2 (the latest available year, significantly influenced by the COVID-19 pandemic). Values of food security index produced as the result of DEA analysis divided countries into six groups. They vary between 0 and 1. A higher value means a better result. The best food security situation in Europe recorded Switzerland, Benelux countries, Ireland, Austria, Germany, Iceland, Sweden, and Norway. On the other side, the worst situation was in Ukraine, North Macedonia, Albania, and Montenegro.

Fig. 2
figure 2

Source: Author´s work in Data wrapper based on data from FAOstat

Food security situation in 2020 according to produced DEA indicator.

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Only slightly better food security performance was in Belarus, Serbia, and Croatia. The worst performing countries are in the east and south-east of Europe. Surprisingly, deficient performance recorded France and Slovakia, which ranked 25th and 28th respectively in the analyzed set of 38 European countries.

The worst performance regarding the availability of food was in Bulgaria, Serbia, and Slovakia. In the second pillar- accessibility of food were the worst performing countries Ukraine and Albania. The third pillar-stability consisted of political stability, food supply and caloric consumption variability. From a political perspective was worst result recorded in Ukraine, Belarus, and the Russian Federation. On the other hand, food supply variability was surprisingly the worst in Montenegro, Czechia, and Slovakia. Habitual consumption had the highest variability in Albania, North Macedonia, and Ukraine. In the last pillar-Utility was the worst performing in Belarus and Albania.

The deficient performance of France can be a consequence of the country's bad result according to the food production index and food supply variability, where it ranked among the worst countries. The pandemic situation in Europe significantly influenced condition in 2020.

3.2 Long run influence of food security factors

The further analysis of factors influencing countries' food security performance used the constructed food security index as a dependent variable, which is related to factors described in Table 2. Panel data analysis involved fixed effects, random effects, and pooled mean group model, which allowed us to estimate also short run dynamic in every country. The random effects estimator was not consistent according to the Hausman test, in which a p-value was 7.5 e–10. For this reason, Table 3, which shows the long-run influence of food security factors estimated using the Pooled mean group and fixed effects model, does not include the random effects model. The table contains both point and interval estimates. The R-squared value of the fixed effects model was equal to 0.91. This value is not directly comparable with the Pooled mean group model, where it is not possible to estimate the R-squared value for its long-run coefficients.

Table 3 Long-run influence of food security factors
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The fixed effects model included two insignificant variables: agriculture, forestry and fishing value added and gross capital formation. Significant variables were trade openness, temperature change and urbanization. According to the pooled mean group model all considered variables significant. This difference comes from the nature of both estimators. The fixed effects model is a pooled estimator assuming different intercepts for each country, and the Pooled mean group model estimates the mean coefficient value in panel data. An interesting fact is that in the initial pre-analysis of input variables arable land was an insignificant factor according to all considered models. This suggests that the intensity of food production became more important than its extensity. Standardization of all explanatory variables ensured direct comparability of factors´ influence.

Both models confirmed the significant positive influence of trade following expectations. The mean coefficient is slightly higher than pooled in the fixed effects model. Trade is therefore a significant factor in food security. Goods and commodities flow in both ways, but in general trade openness is a significant factor in ensuring a stable and sufficient food supply. A positive influence on the food security situation according to both models was in the case of urbanization (slightly higher according to the PMG model). Despite negative expectations, this result follows other authors. Urbanization can be also a measure of development and concentration of capital and human resources. For developed countries with elevated levels of urbanization is characteristic open economy with intensive technologically advanced agriculture. This can be the reason for the positive value of the urbanization coefficient.

Different results recorded temperature change influence on the food security situation. Climate change has a significant impact on food security according to both models, however estimated direction of its impact was different. This can be due to the difference between the average effect (PMG estimate) and aggregated effect (fixed effects) of climate change in European countries. The fixed effects model suggests a small positive impact, on the other side pooled mean group estimation suggests a significant negative impact. This could mean different effects on food security situations across individual regions, which will depend on the character and geographical position of each country.

Different results recorded in the fixed effects model and pooled mean group model for agriculture, fishing and forestry added value and gross capital formation could be explained by the lack of relationship between variables in a pooled set of data, but its significance in separately estimated country-specific models. According to the pooled mean group estimator for the agriculture, forestry and fishing value added is this factor significant, but the fixed effect model evaluated it as an insignificant factor. Better understanding could offer country-specific short-run models shown in Figs. 3, 4, 5, 6, 7, 8 and 9. This confirms the hypothesis, that the pooled mean group model can show deeper insight into the impact of food security factors in comparison to the fixed effects model.

Fig. 3
figure 3

R Squared values in short run estimation

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Fig. 4
figure 4

Error correction term coefficient -speed of convergence to long-run relationship

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Fig. 5
figure 5

Agricultural, fishing and forestry value-added long-run and short-run coefficient values

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Fig. 6
figure 6

Short run and long run coefficient for trade

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Fig. 7
figure 7

Short run and long run coefficients for Gross capital formation

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Fig. 8
figure 8

Short-run and long-run effects of urbanization

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Fig. 9
figure 9

Estimated short-run effect of temperature change

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3.3 Short-run influence of food security factors

The food insecurity in the most endangered segments of the population was not possible to identify in aggregated data at the country level. Even in countries with good overall situations, food insecurity endangers specific groups of people. However, conducted analysis can help to identify endangered regions and the direction of influence of food security factors which helps to predict further development of the food security situation in the region.

The explanatory ability of each model measured by the R-squared value is in Fig. 3. The highest proportion of explained variability was in Slovakia, Ireland, Portugal, Germany, and North Macedonia. Factors in Table 3 influenced the most the food security situation in countries with the highest R-squared value. On the other hand, in countries with the smallest R-squared value is food security determined by other factors, or they are in specific conditions, which is the case of Romania, Lithuania and Ukraine. More than 55% of estimated short-run relationships recorded R squared value higher than 50%. This suggests, that selected factors significantly influence the food security situation in most European countries.

The pooled mean group model allowed us to estimate long-run relationship coefficients common for all analyzed countries and country-specific short-run effects. Error correction terms in short-run models shows how fast countries converge toward long-run equilibrium and its significance and negative value confirm the existence of the long-run relationship. Figure 4 shows estimated error correction coefficients in country-specific short-run models. Bars in blue denote significant coefficients. Slovakia, Serbia, and Portugal converge fastest to long-run equilibrium, which suggests, that these European countries are the most flexible. On the other hand, Ukraine, Romania, Luxembourg, Austria, and Norway were on the other side of the distribution with the smallest values estimated values and insignificant error correction terms. This suggests just an exceedingly small speed of adjustment of their food security toward long-run equilibrium in Europe, or that long-run equilibrium in these countries does not correspond to the rest of Europe. This may be the case in Luxembourg, Austria, and Norway with remarkably prominent levels of food security. In the case of Romania and Ukraine with poor food security performance, it indicates even further deepening of disparities compared to other countries.

The next figures show the short run influence of food security factors estimated as country specific. Figure 5 shows a comparison of estimated short run coefficients for agriculture, forestry, and fishing value added. Coloured bars denote significant coefficients, and the orange line shows the long-run coefficient according to the pooled mean group estimator. The highest impact of agriculture value added on food security was in Austria, Spain, and Czechia. The high value of the coefficient was also in Switzerland and Bosnia and Herzegovina, but it was insignificant. In these countries, agriculture plays a vital role in ensuring food security. On the other hand, countries like Portugal, Norway and Malta have their food security based on other sources than agriculture, forestry, and fishing. Significant negative influence in North Macedonia, Malta, Norway, and Portugal suggests a negative relationship between food security and agricultural value added. For example, Sweden and Portugal improved food security despite a decrease in agriculture, forestry and fishing value added on the other hand, the food security position of Malta and Norway worsened despite the increase in this variable.

In general, agriculture has a key role in food security environment. In the long run, it was the second most influential variable according to the results of the pooled mean group model. Its significance is smaller in countries with specific conditions. Interestingly, variables like land, or arable land expressed in various indicators turned out to be insignificant in the initial pre-analysis of this paper. In contrast with the significance of agriculture, forestry and fishing value added it seems, that rather than the extensity of agriculture becomes important intensity of agriculture and efficient use of resources. A slightly smaller long-run impact on the food security situation was in the case of trade (expressed as % of GDP). However, trade was significant in both PMG and Fixed effects models, but agriculture value added only in PMG.

There are two ways it can impact the food security. With the import of food-related goods, it can improve the food security situation. On the other hand, with excessive export of food commodities be food security situation deteriorated. The long-run impact of trade on food security was positive. Country-specific short-run results were heterogeneous. Similarly, to agriculture, forestry and fishing value-added, also in the case of trade was its effect in the long run higher than in the short run in the most of analyzed countries.

The estimated short-run coefficient for the impact of trade on food security shows Fig. 6. Significant positive short-run impact of trade was only in the case of Portugal. In this country, significant negative effects of agriculture fishing and forestry value added. Its food security is based on trade and food security risk will be associated more with factors influencing trade than agricultural-related conditions.

Countries with significant negative values of short run influence of trade can be divided into two groups. For example, the United Kingdom, Sweden, Slovakia, and Finland worsened their food security positions despite of slight increase in the share of trade on GDP over the analyzed period. The second group are countries like Latvia, Ireland, Iceland, and Hungary, which improved their food security position in Europe despite a slightly decreasing share of trade in GDP. Therefore, for both groups with significant negative short-run coefficients trade is crucial in the short run to ensure their food security and for most analyzed countries. However, unexpected changes in trade can significantly decrease food security in Belarus, Estonia, and Iceland. Also, the significance of this variable in short-run equations suggests that for many European countries trade is a more important food security factor in the long run, as it was insignificant in most of the short-run equations.

Another factor considered in the analysis performed was gross capital formation. This was the only variable related to food security level as an absolute cumulative indicator. It is interesting that in case of gross capital formation expressed as percentage of GDP or per capita, was its effect in the long run insignificant. It was also insignificant in the estimated fixed effects model, but in the PMG model, it was the most influential variable with an estimated value of coefficient 1.549. The absolute value of an indicator includes not only information about investments in the country but also about its size. Even with the standardized value of a variable, a consequence of its cumulative absolute value was some extremely high short-run coefficient. The influence of Gross capital formation is in Fig. 7, extreme values of estimated short-run coefficients are out of scale in the figure. Full-coloured columns denote significant short-run coefficients.

Results suggest a significant short run impact of Gross capital formation on food security. It is interesting, that in contrast with the previously analyzed two factors is short-run effect in most countries is higher than long run. Especially food security in countries with large significant values of short run coefficients will depend on Gross capital formation. The most significant positive impact was in Latvia, North Macedonia, and the United Kingdom. On the other hand, negative values of short-run coefficients are in countries that improved their food security position despite a decrease in gross capital formation, such as Belgium or Portugal. On the other hand, in Slovenia or Malta, the food security situation got worse even with the increase in Gross capital formation. Therefore, other factors influenced food security in these countries more significantly. A sudden change in Gross capital formation would worsen the food security situation in European countries mostly in the short run. Still, the long run effect would be smaller than in the case of agriculture value added or change in trade conditions.

The long-run and short-run effects of urbanization on food security are in Fig. 8. Similarly, to Gross capital formation, also in the case of urbanization (expressed as % of urban population) was effect in the long run was much smaller than the short-run effect. But compared to the influence of other considered factors, the effect of urbanization in the long run was the fourth principal factor. Result suggests that a high degree of urbanization could negatively affect the food security situation. On the other hand, in some regions, it also means a high concentration of human resources and capital.

Another interesting fact is that urbanization was significant in a substantial share of analyzed countries, compared to previously analyzed factors. Especially in the Russian Federation, Greece, North Macedonia, Malta, and the Netherlands is urbanization a crucial factor influencing food security positively. Much more interesting are countries in the right part of Fig. 8, such as France, Bulgaria, and Italy, with a significant negative influence of urbanization on food security in the short run. Food security in these countries got worse despite the increased level of urbanization. It could mean that food security in these countries is related strongly to other factors. Another reason could be that the increased level of urbanization in these countries was not related to economic and income growth.

The short-run effect in this case means the relationship between the first differences of variables in annual time series data. Compared to other analyzed factors, in this case, there is not a large probability of a large sudden change in urbanization with an instant significant impact on food security. Change in urbanization is usually slower and it can have two direct effects on food security. In one case, it can be increased urbanization with growing city area at the expense of agricultural land and production which would decrease the availability of food, in another case it can be increased urbanization with increasing density of population in cities as the result of economic development related to the change in economic structures, which may lead to increased income of population and improve accessibility and utilization of food.

The last factor investigated in the performed analysis was climate change measured as a change in temperature. Results in the case of this variable were the most controversial, however, it was significant in both the PMG and fixed effects models. In the case of the panel fixed effects model had this variable small significant positive influence on food security, on the other hand, in pooled mean group model was negative significant long-run coefficient with an absolute value slightly higher than in the fixed effects model. Therefore, results of the pooled mean group model indicate negative long-run effect of climate change on food security in Europe.

On the other hand, Fig. 9 shows, that most of the analyzed countries were estimated positive short-run impacts of temperature change on food security. This variable was significant in equations for twenty-two countries in the short run. The largest positive short-run effect was in North Macedonia, Albania, Bosnia and Herzegovina, Germany, and Italy. The positive short-run effect can be related to improved conditions for agriculture in some countries and can support tourism during holiday periods, especially in coastal regions, which helps to increase population income and the local economy. On the other hand, extreme weather conditions linked with climate change can significantly decrease food security in the long run. The largest negative effects were in Iceland, Bulgaria, Romania, and Montenegro; however, these coefficients were insignificant.

3.4 Discussion

The result of the analysis conducted confirmed the significant role of agriculture in achieving food security. It is to the findings of Fan and Brzeska (2016) and Poudel and Gopinath (2021). There are more ways to express agriculture. Some authors used arable land, land productivity or added value of agriculture, fishing, and forestry. Arable land was not significant in the conducted pre analysis, so the paper´s results do not include it. This is in contrast with Poudel and Gopinath (2021) who found its influence significant, on the other side results confirmed their conclusion about the significance of agricultural value added. Their research focused especially on developing countries, which may explain the difference in results. This variable used also Matkovski et al. (2020) which confirmed its significance but concluded a negative impact on food security which is in contrast with the presented paper. However, it is on the results of the estimated fixed effects model.

According to expectations, analysis result confirmed significant influence of trade openness on food security. This supported the conclusions of Feleke et al., (2005), Dorosh et al. (2016), Pyakuryal et al., (2010), Dithmer and Abdulai (2017) and Poudel and Gopinath (2021).

The case of urbanization also confirmed a significant positive effect on food security, which is in contrast with conclusions by Farrukh et al. (2022) made for Pakistan. But it supports findings by Poudel and Gopinath (2021) and Li et al. (2023). about the significant effect of urbanization which is different for low-income and high-income countries. The significance of gross capital formation also supports findings by Poudel and Gopinath (2021).

The negative impact of climate change on food security is also following results published by Lee et al. (2024), Hadley et al. (2023), Mirzabaev et al. (2023), Mekonnen et al. (2021) which concluded its negative impact on food security. However, this study suggests dividing analysis of climate change effects separately into its short-run and long-run influence.

4 Conclusion

The presented paper contributes to actual food security discussion from both theoretical and practical perspectives. It demonstrates the application of general methods to evaluate food security and investigate its determinants, not only in European regions. Results suggest that also Europe has food security issues, and its level has not improved since 2014. Many fluctuations caused by the COVID-19 pandemic and military conflict in Ukraine affected the food security situation in Europe last year. The most endangered region is in the Eastern and South-eastern parts of Europe, but the volatility of food supply negatively also influenced countries of central Europe. The availability of relevant data limited presented analysis, but in recent years with unavailable data is probable further decline in food security indicators.

Conducted analysis showed that the added value of agriculture, fishing forestry and trade openness significantly influenced food security in the long run. Significant role plays especially intensity of agriculture and its technological development. It has an essential role, especially in countries with good natural conditions. Food security in countries with smaller food productivity depends on trade and its influence is significant, especially in the long run. But the short run of trade was also significant, especially in countries with direct access to the sea.

Other considered factors were gross capital formation and urbanization which is important, especially in the short run. Gross capital formation is a measure of the economic development and influence of a country, and it has an essential role in ensuring food security in the short run, especially in less-developed European countries. However, this variable turned out to be the most significant factor even in the long run. Discussion about urbanization evaluates its positive and negative aspects. In less developed countries it can bring positive externalities in higher income and resource concentration, but it can have also negative externalities in the form of price growth and environmental pollution. The analysis showed, that along with traditional sources of food security, the effect of climate change is also significantly influencing it with expectation to its intensification in upcoming years. Results suggested that climate change's effect on food security depends on the current character of each country, and its study should distinguish its long-run and short-run effects. Pooled mean group estimates confirmed the negative effect of climate change on food security in the long run, however in short run was its effect positive in most European countries. A significant limitation of this study was yearly data only for 20 years, which decreased flexibility of using more variables and lagged values in the short run equation of pooled mean group models.