USING THE MONTE CARLO METHOD TO ESTIMATE THE EUROPEAN FUNDS ABSORBED BY THE ROMANIAN ECONOMY FROM THE EU IN

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1 USING THE MONTE CARLO METHOD TO ESTIMATE THE EUROPEAN FUNDS ABSORBED BY THE ROMANIAN ECONOMY FROM THE EU IN Prof. habil. Gheorghe Săvoiu PhD., Ligian Tudoroiu, PhD. candidate Assoc. prof. Emil Burtescu, PhD. Abstract This paper describes a concrete application of the Monte Carlo method for the way the European funds were accessed between 2007 and 2013 by the Romanian economy the economy of a member state of the European Union (EU). In all analyses of simulations there are two waiting areas, placed either at the level of January (16.98 billion Euros), or slightly upward in value, and even above the level of that month (17.09 billion Euros) for the period remained between 31 January 2017 and 31 March 2017, i.e. the last reporting, or the closing of accessing funds by Romania for the period Keywords: probability, random draws, the Monte Carlo method, statistical test, normal distribution, European funds. 1. INTRODUCTION Romania s economy, in its new capacity, acquired on 1 January 2007, that of an economy of a member state of the European Union (EU), benefi ted from the support of European funds accessed between , thus ensuring sustained post-accession development, except during the global fi nancial downturn. The European funds absorbed ensured some elements of institutional infrastructure, improving standards and competitive labour market, the survival and modern development of scientifi c research, educational harmonization, regional convergence, and reducing disparities in socio-economic development compared to other EU member states, etc. Unfortunately, the Romanian economy failed to achieve the current absorption rate for 2015, reaching a level of merely 69.9%, far below the 80.0% estimate, but managed to improve it signifi cantly during the next year. A sustained and, especially remarkable effort over the year 2016 brought Romania to a general absorption level of 89% at the end of that year, but still placed it below the European average of 93%. On 31 January 2017, the national economy recorded an effective absorption rate of only 79.23%, a rate of current absorption of 82.93%, and an overall absorption 110 Romanian Statistical Review - Supplement nr. 3 / 2017

2 rate of 90.44%, which also included the amounts of money received from the EC in advance. This article attempts a simulation of European funds accessed by Romania as of 31 March 2017, capitalizing on the Monte Carlo method, or in simpler words, trying a calibration of an optimal number of draws that could maintain the allure of a final normal distribution. 2. THE MONTE CARLO METHOD, APPLIED TO THE SIMULATION OF THE VALUE OF THE EUROPEAN FUNDS ACCESSED BY ROMANIA BETWEEN 2007 AND 2013 The data necessary for the simulation by the Monte Carlo method applied to the funds accessed from the European Union take into consideration two variables: I. Variable 1 is defined by the amounts allocated in keeping with the existing data on the official website of Romania, i.e. ro/, but also in relation to the probability resulting from the careful analysis of the importance and impact of each variable in part. Variable 1 AMOUNTS ALLOCATED (SA) (in billions Euro) Variable 1 = SAk where k = 3 Probabilities (expressed classically, between 0 and 1) Probabilities (expressed in %) Source: The data available at stadiul-absorbtiei were analyzed by the authors. II. Variable 2 represents the absorption rate of EU funds allocated for Variable 2 is defined by the rates of absorption according to the existing data on the official website of Romania, but also in relation to the probability resulting from the careful analysis of the importance and impact of each variant. Variable 2. ABSORPTION RATE OF EU FUNDS (in ratios and percentages) Variable 2 = Rak where k = 5 Probabilities (expressed Probabilities classically, between 0 and 1) (expressed in %) (in % = 88.60) % (in % = 89.00) % (in % = 90.44) % (in % = 91.00) % (in % = 93.00) % The relationship between Variable 1 and Variable 2 generates, through aggregation, the funds accessed by Romania, and is expressed as the following aggregate: Revista Română de Statistică - Supliment nr. 3 /

3 (1) The result of this simulation predicts the final absorption of funds by Romania as of 31 March 2017, for the 2007 to 2013 period. In subsequent figures and graphs (Figs 1-12) there appear the results of the first calibration simulations (100, 200, 300, and then 1,000 random draws, in keeping with the Monte Carlo method) for the funds accessed by Romania from the EU (including the earnest money given by the EU). Monte Carlo simulation for 100 draws and the series of results Figura no. 1 EU Accessed funds Number of draws Source: data processed by the authors Total 100 Histogram of the data series and the descriptive statistics (100 draws) Figura no Romanian Statistical Review - Supplement nr. 3 / 2017

4 The resulting distribution is a normal type, as seen in its graphical curve, based on a Kernel type diagram drawn by means of the Eviews software package. The Kernel type chart of the 100 resulting draws Figure no. 3 Monte Carlo simulation for 200 draws and the series of results Figure no. 4 Source: data processed by the authors EU Accessed funds Number of draws Total 200 Revista Română de Statistică - Supliment nr. 3 /

5 Histogram of the data series and the descriptive statistics (200 draws) Figure no. 5 The resulting distribution is again of the normal type, apparently more distorted, and is closer to the perfect symmetry (according to the Skewness coefficient of -0.03, the value that clearly approaches 0). The distribution remains normal, as can be seen in its graphical curve, based on the Kernel type chart, made with the Eviews software package for 200 draws. The Kernel type diagram of the 200 resulting draws Figure no Romanian Statistical Review - Supplement nr. 3 / 2017

6 Monte Carlo simulation for 300 draws and the series of results Figure no. 7 EU Accessed funds Number of draws Total 300 Source: data processed by the authors. Histogram of the data series and the descriptive statistics (300 draws) Figure no. 8 The resulting distribution is again of the normal type, and it became more homogenous, naturally, in keeping with the very small amount of the standard deviation (std dev = 0.26). The distribuţia remains normal, as can be seen in its graphical curve, based on a Kernel type diagram made with the Eviews software package for 300 draws. Revista Română de Statistică - Supliment nr. 3 /

7 The Kernel type diagram of the 300 resulting draws Figure no. 9 Monte Carlo simulation for 1,000 draws and the series of results Figure no. 10 Source: data processed by the authors EUAccessed funds Number of draws Total Romanian Statistical Review - Supplement nr. 3 / 2017

8 Histogram of the data series and the descriptive statistics (1000 draws) Figure no. 11 The resulting distribution tends to the limit of abnormality (according to the value of the Jarque Bera test = 8.44). The distribution remains within the normal range (graphically, two relative profiles of distinct curves begin to be distinct), as can be seen in its graphical curve, based on the Kernel type chart made with the Eviews software package for 1,000 draws. A Kernel type diagram of the 1,000 resulting draws Figure no. 12 Revista Română de Statistică - Supliment nr. 3 /

9 The optimal statistical option should be placed between 100 and 300 draws, with a tendency of stationarity around the value of 200 draws (a sample with favourable implications related to stability) In all analyses there are two waiting areas, placed either at the level of January (16.98 billion euros), or with a slightly upward value (17.09 billion euros) for the period left between 31 January 2017 and 31 March 2017, i.e. the last reporting, or the closing of the accessing of funds by Romania for the period The method can be made use of for other simulations with a similar theme, e.g. for the period CONCLUSIONS In simulation, in order to mimic or replicate what happens in a stochastic system, it is necessary to randomly generate the values of the probabilistic variables that occur in the question under examination. The process of randomly generating the values of a probabilistic variable is known in the literature as the Monte Carlo method, and consists in using a generator of random numbers, uniformly distributed within the interval [0, 1], and the function of the cumulative distribution associated with that probabilistic variable, as the authors did in this article with the variables amounts allocated (SA) and the EU funds absorption rate (RA). The statistical analysis of each distribution in relation to the number of the draws enabled us to identify a number of aspects and tendencies of distributional normality and abnormality. The analysis of the values of the variables described by a probability distribution was conducted statistically, both graphically and in a tabulated form, exploiting several software packages (especially Microsoft Excel and Eviews). The authors intention is to continue research, by capitalizing the Monte Carlo method in simulating the absorption and accessing of European funds by Romania for the European budget programming period , too. REFERENCES 1. Burtescu, Emil (2010). Sisteme informatice în afaceri, Editura Sitech, Craiova. 2. Cache, C., Cache, S., Nicolăescu, V. (2011). Absorption of the Structural Funds in Romania, Romanian Journal of Economic Forecasting, vol. 14, no. 2, pp Crăciun Claudiu, Collins E. Paul (2008). Managementul politicilor publice. Transformări și perspective, Editura Polirom, Iași. 4. Dinu Vasile, Săvoiu Gheorghe, Dabija Dan Cristian, (2016). A concepe, a redacta și a publica un articol științifi c. O abordare în contextul cercetării economice, Editura ASE Bucuresti. 5. Gobet, Emmanuel (2013). Méthodes de Monte-Carlo et processus stochastiques: du linéaire au non-linéaire, Éditions de l École polytechnique, Paris. 6. Horvat, Romana Vajde (2010). EU Projects - Understand them before applying for 118 Romanian Statistical Review - Supplement nr. 3 / 2017

10 one, published at [on-line] Available at: org/uploads/ media/ecqa-eu_projects-understand_them_before_apply_for_ one Vajde_Horvat_.pdf Accessed 10 February, Iancu Diana-Camelia (2010). Uniunea Europeana și administrația publică, Ed. Polirom, Iași. 8. ICF, (2016). Raportul fi scal anual [on-line] Available at: ro/ RaportanualCF2015.pdf Accessed 10 February, Matejun, M. (2015). Absorpcja wsparcia w zarządzaniu rozwojem mikro, małych i średnich przedsiębiorstw podejście strategiczne. 10. Săvoiu Gheorghe, (2013). Modelarea Economico Financiară: Gândirea econometrică aplicată în domeniul fi nanciar, Editura Universitară, Bucureşti. 11. Săvoiu,G., Jaško, O., Dulanović, Ž., Čudanov, M., Craciuneanu, V.,(2008). The value of general methods, quantitative techniques and management models in professionalizing management, Management vol 49-50, pp Revista Română de Statistică - Supliment nr. 3 /