Romanian Statistical Review - INSSE · Prof. Stelian Stancu PhD. Bucharest University of Economic Studies FORMAL EDUCATION IN THE EUROPEAN UNION AND ITS IMPACT ON THE MACROECONOMIC

Romanian Statistical ReviewRevista Română de Statistică

1/2017

www.revistadestatistica.ro

THE JOURNAL OF NATIONAL INSTITUTE OF STATISTICS

EXPERT SYSTEM AND HEURISTICS ALGORITHM FOR CLOUD

RESOURCE SCHEDULING

GROWTH WITH ENDOGENOUS CAPITAL, KNOWLEDGE, AND

RENEWABLE RESOURCES

FIXED EFFECTS MODELS TO ASSESS THE EFFECTIVENESS OF

ENTREPRENEURIAL DIVERSIFICATION STRATEGY IN SMES

EMPIRICAL RESULTS OF MODELING EUR/RON EXCHANGE

RATE USING ARCH, GARCH, EGARCH, TARCH AND PARCH

MODELS

FORMAL EDUCATION IN THE EUROPEAN UNION AND ITS

IMPACT ON THE MACROECONOMIC DEVELOPMENT

EXPERT SYSTEM AND HEURISTICS ALGORITHM FOR CLOUD RESOURCE SCHEDULING 3Mamatha E.Sasritha S.Dept of Engineering Mathematics, GITAM University, Bangalore, IndiaCS ReddySchool of Computing, SASTRA University, Thanjavur, India

GROWTH WITH ENDOGENOUS CAPITAL, KNOWLEDGE, AND RENEWABLE RESOURCES 19Prof. Wei-Bin ZhangRitsumeikan Asia Pacifi c University, Japan

FIXED EFFECTS MODELS TO ASSESS THE EFFECTIVENESS OF ENTREPRENEURIAL DIVERSIFICATION STRATEGY IN SMES 39Elena DruicăAna-Maria GrigoreUniversity of Bucharest, Faculty of Business and Administration

EMPIRICAL RESULTS OF MODELING EUR/RON EXCHANGE RATE USING ARCH, GARCH, EGARCH, TARCH AND PARCH MODELS 57Andreea - Cristina Petrică PhD. StudentProf. Stelian Stancu PhD.Bucharest University of Economic Studies

FORMAL EDUCATION IN THE EUROPEAN UNION AND ITS IMPACT ON THE MACROECONOMIC DEVELOPMENT 73 Sandra Teodorescu”Nicolae Titulescu” University

Romanian Statistical Review nr. 1 / 2017

CONTENTS 1/2017

ROMANIAN STATISTICAL REVIEW www.revistadestatistica.ro


Romanian Statistical Review nr. 1 / 2017 3

Expert System and Heuristics Algorithm for Cloud Resource SchedulingMamatha E ([email protected])Dept of Engineering Mathematics, GITAM University, Bangalore, India

Sasritha SDept of Engineering Mathematics, GITAM University, Bangalore, India

CS ReddySchool of Computing, SASTRA University, Thanjavur, India

ABSTRACT Rule-based scheduling algorithms have been widely used on cloud comput-ing systems and there is still plenty of room to improve their performance. This paper proposes to develop an expert system to allocate resources in cloud by using Rule based Algorithm, thereby measuring the performance of the system by letting the sys-tem adapt new rules based on the feedback. Here performance of the action helps to make better allocation of the resources to improve quality of services, scalability and fl exibility. The performance measure is based on how the allocation of the resources is dynamically optimized and how the resources are utilized properly. It aims to maxi-mize the utilization of the resources. The data and resource are given to the algorithm which allocates the data to resources and an output is obtained based on the action occurred. Once the action is completed, the performance of every action is measured that contains how the resources are allocated and how effi ciently it worked. In addition to performance, resource allocation in cloud environment is also considered. Keywords: Cloud computing, Scheduling and Expert System, Heuristic Models JEL Classifi cation: C87

INTRODUCTION

Cloud Computing, the long-held dream of computing industry, has the capability to change large IT industry, making software even more usable as a service and changing the way IT hardware is made and purchased. Developers with creative ideas for new Internet services no longer need the large capital costs in hardware to install their service or the human expense to operate it [1-5]. They need not be bothered about over-provisioning for a service whose attractiveness does not meet their predictions, thus wasting the


resources, or under-provisioning for one that becomes wildly accepted, thus missing potential customers and revenue. The prominent feature of cloud computing that it allows the consumption of services over internet with subscription based model. Based on the level of abstraction, various models for cloud computing like Infrastructure-as-a-Service (IaaS), Platform-as-a-Service (PaaS) and Software-as-a-Service (SaaS). This model of service consumption is extremely suitable for many workloads and cloud computing has become highly successful technology [5]. It allows its users to pay for what they use and also remove the upfront infrastructure cost. Cloud service providers receive resource requests from a number of users through the use of virtualization. It is very essential for cloud providers to operate very effi ciently in multiplexing at the scale to remain profi table. The increase in the use of cloud computing has risen to develop massive data centers with very large number of servers. The resource management at this scale is the concerned issue. Scheduling is responsible for arbitrate of resources and is at the center of resource management. The issue of effi ciency at this rate and developing model of consumption of cloud providers needs new approaches and techniques to be applied to the age old problem of scheduling. Virtual machine is the primary unit of scheduling in this model. In this study, we deal with problem of virtual machine scheduling over physical machines. We aim to understand and solve the various aspect of scheduling in cloud environments [6,7]. Specifi cally, we leverage different fi ne grained monitoring information to make better scheduling decisions and used learning based approach of scheduling in widely different environments. There is increasing concern over energy consumption by cloud data centers and cloud operators are focusing on energy savings through effective utilization of resources [8,9]. SLAs is also very important for them for the performance of applications running. We propose algorithms which try to minimize the energy consumption in the data center duly maintaining the SLA ensures. The algorithms try to use very less number of physical machines in the data center by dynamically rebalancing the physical machines based on their resource utilization. The algorithms also do an optimization of virtual machines on a physical machine, reducing SLA violations. For large scale distributed system autonomic management [10,11] is one of the most wanted features and even more important in dynamic infrastructures such as Clouds. This is self-managing such as self-healing, self-regulating, self-protecting, and self-improving. Good work in both academia and industry has been already carried out. Tsai [12] reported an overview of the early efforts in developing Metaheuristic scheduling for autonomic systems for storage management. Computing Grids have benefi ted


from the application of autonomic models for management of resources and the scheduling of applications [13,14,15]. Solutions for secure Cloud platforms have been proposed in the literature [16,17]. However, existing works are yet to address issues related to recognition of attacks against SaaS with the aim of exploiting elasticity. The basic idea of the proposed algorithm is to leverage the strengths of heuristic algorithms, such as swarm optimization [18], Scheduling Computer and Manufacturing Processes [19], Hadoop map-task scheduling [21,22] and ant colony optimization [20], by integrating them into a single algorithm. One of the important tasks for cloud provider is scheduling data packets for better achievement and effi cient resource pooling along with elasticity. In cloud computing scenarios scheduling algorithm becomes very signifi cant where the cloud service providers have to operate at very much competent to be competitive and take advantage at scale[23,24]. The wide acceptance of cloud computing means data centers with many more machines and the usage model is much different than traditional clusters, like hour boundaries, auction based prices are to name a few. Thus scheduling in cloud data center is more challenging than traditional cluster schedulers. Also, these data center run many different kinds of applications with varying expectations from infrastructure. Resource usage patterns in traditional data centers are have less variance in than the unpredictability faced by cloud data centers.

PROBLEM ANALYSIS AND DEFINITION

Since Rule based algorithms are straight forward and can be easily implemented, so there is lot of possibility to improve the performance of these algorithms especially in cloud environments. Conventional models and its corresponding algorithms are pretty good for small scale environments, however owing to the advent improvement of computer and related internet technological improvements; there is a huge range to enhancements in these algorithms to get better performance in large scale system. Extreme use of number of servers in the recent period has reduced the usage of traditional scheduling techniques. The resource management at this scale is the concerned as an issue. Scheduling is responsible for arbitrate of resources and is at the center of resource management. The issue of effi ciency at this rate and developing model of consumption of cloud providers wants new methodologies and techniques that to be extended to apply to presently available old algorithms of scheduling. The main objective of the paper is to develop and implement more effi cient scheduling algorithm suitable for cloud system. Since parallel and


distributed computing technologies was widely used to improve the diversity performance of computer systems, a number of models and thoughts have been anticipated for different approaches and congenital limitations in diverse eras. Whatever it may be the contemplation it is for; the way to competently use computer resources is a key research matter. Among all of them, scheduling is indispensable in the success of escalating the performance of the computing system. The wide acceptance of cloud computing means data centers with many more machines and the usage model is much different than traditional clusters, like hour boundaries, auction based prices are to name a few. Thus scheduling in cloud data center is more challenging than traditional cluster schedulers.

PRESENT SYSTEM AND PROPOSED SCHEDULING ALGORITHM

In this research paper, by the simple scheduling problems, we mean problems for which all the solutions can be checked in a reasonable time by using classical exhaustive algorithms running on modern computer systems. In comparison, with the large scale scheduling problems, like the problems for which not all the solutions can be examined in a reasonable time by using the same algorithms running on the same computer systems. These observations make it easy to understand that exhaustive algorithms will take a prohibitive amount of time to check all the candidate solutions for large scheduling problems because the number of candidate solutions is simply way too large to be checked in a reasonable time. As a result, researchers have paid their attention to the development of scheduling algorithms that are effi cient and effective, such as heuristics. Workfl ow is used with the automation of procedures where by fi les and data are passed between participants according to a defi ned set of rules to achieve an overall goal. A workfl ow management system is the one which manages and executes workfl ows on computing resources. Workfl ow Scheduling: It is a kind of global task scheduling as it focuses on mapping and managing the execution of inter-dependent tasks on shared resources that are not directly under its control. The authors classify and review hyper-heuristic approaches into the following four categories: based on the random choice of low level heuristics, greedy and puckish, meta heuristic-based, and those employing learning mechanisms to manage low level heuristics. The hyper heuristics can be used to operate at a higher level of abstraction. Meta heuristic techniques are expensive techniques that require knowledge in problem domain and heuristic technique. Hyper heuristic technique does not require problem


specifi c knowledge. In order to solve hard computational search problems the hyper heuristic techniques can be used. The hyper heuristic techniques can be operated on the search space of heuristics. Proposed System: The basic idea of the proposed algorithm is to use the diversity detection and improvement detection operators to balance the intensifi cation and diversifi cation in the search of the solutions during the convergence process. The proposed algorithm, called hyper-heuristic scheduling algorithm (HHSA).The parameters max and ni, where max denotes the maximum number of iterations the selected low-level heuristic algorithm is to be run; ni the number of iterations the solutions of the selected low-level heuristic algorithm are not improved. Line 2 reads in the tasks and jobs to be scheduled, i.e., the problem question. Line 3 initializes the population of solutions Z = fz1; z2;:::; zNg, where N is the population size. Online 4, a heuristic algorithm Hi is randomly selected from the candidate pool H = fH1;H2; :::;Hng. Hyper-heuristics are high level problem independent heuristics that work with any set of problem dependent heuristics and adaptively apply and combine them to solve a specifi c problem. This could be due to the fact that variants of differential evolution, which we mainly use as basic heuristics due to their competitive performance and simple confi guration, strongly depend on the population distribution. Hyper-heuristics might be regarded as a special form of genetic programming, the key intuition underlying research in this area is that, for a given type of problem, there are often a number of straightforward heuristics already in existence that can work well (but perhaps not optimally) for certain sorts of instances of that type of problem. Perhaps it is possible to combine those existing heuristics into some more elaborate algorithm that will work well across a range of problems. Cloud Computing denotes both the applications delivered as services, the hardware and systems software in the datacenters that provide those services. The services has been refered to as Software as a Service (SaaS). The datacenter hardware and software together combinedly called a Cloud. When a Cloud is of the kind pay-as-you-go manner to the public, then it is a Public Cloud; if the service is being sold then it is a Utility Computing. The term Private Cloud refers to internal datacenters of a business or other organizations, thart are not made available to the public. Thus, Cloud Computing is the combination of SaaS and Utility Computing, but does not comprise Private Clouds. Anyone can be users or providers of Software as a Service, and users or providers of Utility Computing.


Advantage: Statistical multiplexing is a method that can be used to maximize

utilization when compared to a private cloud. Cloud computing can also offer services at a cost of a medium-

sized datacenter and can even make a good profi t. Disadvantage: The one important disadvantage is the chance of data loss. User can leave the site permanently after facing a poor service;

this negative feedback may result in a permanent loss of a portion of the revenue stream.

WORKFLOW ENGINE:

A Workfl ow engine is a software service that is used to provide the run-time environment in order to create, maintain and develop workfl ow instances. The representation of a workfl ow process is in a form which supports automated manipulation. Invoked Applications: Interfaces to support interaction with a variety of IT applications Workfl ow Client Applications: Interfaces to support interaction with the user interface. Administration and Monitoring: Interfaces to provide system monitoring and metric functions to facilitate the management of composite workfl ow application environments. It can be seen that scheduling is a functional module of a Workfl ow Engine, becoming a signifi cant part of workfl ow management systems. Workfl ow is concerned with the automation of procedures whereby fi les and data are passed between Participants according to a defi ned set of rules to achieve an overall goal. A workfl ow management system defi nes, maintains and develops workfl ows on computing resources.

VIRTUAL GRID EXECUTION SYSTEM (VGES):

vgES provides an uniform qualitative resource abstraction over grid and cloud systems. We apply vgES for scheduling a set of deadline sensitive weather forecasting workfl ows. Specifi cally, this paper reports on our experiences with: 1. Virtualized reservations for batch queue systems, 2. Coordinated usage of Tera Grid (batch queue),Amazon EC2

(cloud), our own clusters (batch queue) and Eucalyptus(cloud) resources, and


3. Fault tolerance through automated task replication. The combined effect of these techniques was to enable a new workfl ow planning method to balance the performance, reliability and the cost considerations. These results point toward improved resource selection and execution management support for a variety of e-Science applications over grids and cloud systems.

This paper brings together many of the results from the VGrADS project demonstrating the effectiveness of virtual grids for scheduling LEAD workfl ows. In the process, it demonstrates a seamless merging of cloud and HPC resources in service of a scientifi c application. It also applies advanced scheduling techniques for both performance improvement and fault tolerance in a realistic context. LEAD has been run as a distributed application since its inception, but VGrADS methods have opened new capabilities for resource management and adaptation in its execution. This paper details the vgES implementation of virtual grids and their use in fault tolerant workfl ow planning of workfl ow sets with time and accuracy constraints. Our experiments show the effi ciency of the implementation and the effectiveness of the overall approach. Modules Description: A simple random method is used to select the low-level heuristic Hi from the candidate pool H. The diversity detection operator is used by HHSA to decide “when” to change the low-level heuristic algorithm Hi. This mechanism implies that the higher the temperature, the higher the opportunity to escape from the local search space to fi nd better solutions. The timer is fi xed at startup and end up mode of an application. We associate with such an event the workload dependent. Hyper heuristic Algorithm: Time-based consists in setting a timer that schedules the time instant when the Scheduled task has to be performed. The timer is fi xed at startup mode of an application. Hyper-heuristic algorithms can then maintain a high search diversity to increase the chance of fi nding better solutions at later iterations while not increasing the computation time. A time-based rejuvenation policy intends to identify the optimal time to rejuvenate with respect to one or more performance indices. The VMM does not degrade, and therefore, it is only necessary to keep memory of the age that was reached at the workload changing point.


Class Diagram to Scheduling Algorithm

Sequence Diagram for Cloud Scheduling Algorithm


ALGORITHM DESCRIPTION:

A hyper-heuristic is a heuristic search method that learns to automate, repeatedly by the incorporation of machine learning techniques, in which the process of selecting, combining, and generating or adapting a number of simpler heuristics (or components of such heuristics) to effi ciently solve the computational search problems. One of the main motivations for studying the hyper-heuristics is to build systems that which can handle the classes of problems rather than solving just a single problem. There might be multiple heuristics from which one can choose for solving the problem, and then the each heuristic has its own strength and also the weakness. The idea is to automatically devise algorithms by combining the strength and compensating for the weakness which are known heuristics. In the typical hyper-heuristic framework there consists of the high-level methodologies and a set of low-level heuristics (either constructive or perturbative heuristics). When a problem instance is given, the high-level method selects which low-level heuristic should be applied at any of the given time, based upon the current problem state, or the search stage.


Scheduling Flow Diagram

Primitive model of Server Side Sample Code: using System; using System.Collections.Generic; using System.ComponentModel; using System.Data; using System.Drawing; using System.Linq; using System.Text; using System.Windows.Forms; using System.Data.SqlClient; namespace server {


public partial class Form2 : Form { SqlConnection cn = new SqlConnection(“Data Source=SRUJAN\\SQLEXPRESS;Initial Catalog=schedule;Integrated Security=True”); SqlCommand cmd; SqlDataReader dr, dr1; public Form2() { InitializeComponent(); } private void Form2_Load(object sender, EventArgs e) { cn.Open(); } private void button6_Click(object sender, EventArgs e) { //+cal1(); //string sta = rsc + “N State”; //textBox6.Text = sta.ToString(); } private void button4_Click(object sender, EventArgs e) { } string t, t1, t2; private void button2_Click(object sender, EventArgs e) { SqlCommand cmd = new SqlCommand(“select * from vm1load”, cn); SqlDataReader dr = cmd.ExecuteReader(); while (dr.Read()) { t1 = dr[0].ToString(); } dr.Dispose(); cmd.Dispose(); if (t1 == null)

{MessageBox.Show(“Start sharinf fi le”); } else


{ textBox7.Text = t1.ToString(); } }private void button3_Click(object sender, EventArgs e) { cmd = new SqlCommand(“select * from vm2load”, cn); dr = cmd.ExecuteReader(); while (dr.Read()) { t2 = dr[0].ToString(); } dr.Dispose(); cmd.Dispose(); if (t2 == null) { MessageBox.Show(“Start sharinf fi le”); } else { textBox1.Text = t2.ToString(); } } private void button1_Click(object sender, EventArgs e) { //int v=Convert.ToInt32(textBox1.Text); int v1 = Convert.ToInt32(textBox7.Text); int v2 = Convert.ToInt32(textBox1.Text); if (v1 < 100) { label1.Visible = true; label1.Text = “ Failure Occured Unable to Load”; } if (v2 < 100) { label2.Visible = true; label2.Text = “Failure Occured Unable to Load”; } } private void pictureBox1_Click(object sender, EventArgs e)


{ if (textBox7.Text == “” && textBox1.Text == “”) { MessageBox.Show(“Start any of Your Server And Proceed”); } else { Form2 f2 = new Form2(); f2.Show();} } private void button4_Click_1(object sender, EventArgs e) { Form4 f4 = new Form4(); f4.Show(); this.Hide(); } private void label9_Click(object sender, EventArgs e) { } } }

CONCLUSION

The proposed algorithm uses two detection operators to automatically determine when to change the low level heuristic algorithm and a perturbation operator to fi ne tune the solutions obtained by each low-level algorithm to further improve the scheduling results in terms of make span. As the simulation results show, the proposed algorithm can not only provide better results than the traditional rule-based scheduling algorithms, it also outperforms the other heuristic scheduling algorithms, in solving the workfl ow scheduling and Hadoop map-task scheduling problems on cloud computing environments. With the incorporation of genetic programming into hyper-heuristic research, a new level of approaches are found that we have termed ‘heuristics to generate heuristics’. These approaches provide richer heuristic search spaces, and thus the freedom to create new methodologies for solving the underlying combinatorial problems. In addition, the simulation results show further that the proposed algorithm converges faster than the other heuristic algorithms evaluated in this


study for most of the datasets. In brief, the basic idea of the proposed hyper heuristic algorithm is to leverage the strengths of all the low level algorithms while not increasing the computation time, by running one and only one low-level algorithm at each iteration. This is fundamentally different from the so-called hybrid heuristic algorithm, which runs more than one low level algorithm for each iteration; thus requiring a much longer computation time.

REFERENCES

1. P. Chr´etienne, E. G. Coffman, J. K. Lenstra, and Z. Liu, Eds., 1995, Scheduling Theory and Its Applications. John Wiely & Sons Ltd.

2. A. Allahverdi, C. T. Ng, T. C. E. Cheng, and M. Y. Kovalyov, 2008, “A survey of scheduling problems with setup times or costs,” European Journal of Operational Research, vol. 187, no. 3, pp. 985–1032.

3. M. Armbrust, A. Fox, R. Griffi th, A. D. Joseph, R. Katz, A. Konwinski, G. Lee, D. Patterson, A. Rabkin, I. Stoica, and M. Zaharia, “A view of cloud computing,” Communications of the ACM, vol. 53, no. 4, pp. 50–58, 2010.

4. Reddy, C. S., et al., 2016, “Obtaining Description for Simple Images using Surface Realization Techniques and Natural Language Processing” Indian Journal of Science and Technology 9.22.

5. I. Foster, Y. Zhao, I. Raicu, and S. Lu, 2008 , “Cloud computing and grid computing 360-degree compared” in Proceedings of the Grid Computing Environments Workshop, pp. 1–10.

6. Mamatha, E., C. S. Reddy and Ramakrishna Prasad,, 2012, “Mathematical Modeling of Markovian Queuing Network with Repairs, Breakdown and fi xed Buffer” i-Manager’s Journal on Software Engineering 6.3 (2012): 21.

7. Tsai, Chun-Wei, et al., 2014, “A hyper-heuristic scheduling algorithm for cloud” IEEE Transactions on Cloud Computing 2.2 (2014): 236-250.

8. X. Lei, X. Liao, T. Huang, H. Li, and C. Hu, 2013, “Outsourcing large matrix inversion computation to a public cloud” IEEE Transactions on Cloud Computing, vol. 1, no. 1, pp. 78–87

9. Mamatha, E., C. S. Reddy, and K. R. Prasad, 2016, “Antialiased Digital Pixel Plotting for Raster Scan Lines Using Area Evaluation”, Emerging Research in Computing, Information, Communication and Applications. Springer Singapore, 461-468

10. J. H. Holland, 1975, Adaptation in Natural and Artifi cial Systems: An Introductory Analysis with Applications to Biology, Control, and Artifi cial Intelligence. University of Michigan Press.

11. Mamatha et al., An Effi cient Line Clipping Algorithm in 2D Space, in press, International Arab Journal of Information Technology,

12. C. W. Tsai and J. Rodrigues, “Metaheuristic scheduling for cloud: A survey”, 2014, IEEE Systems Journal, vol. 8, no. 1, pp. 279–297.

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14. K. M. Elsayed and A. K. Khattab, 2006, “Channel-aware earliest deadline due fair scheduling for wireless multimedia networks” Wireless Personal Communications, vol. 38, no. 2, pp. 233–252.

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16. Z. Wu, X. Liu, Z. Ni, D. Yuan and Y. Yang, 2011, “A market-oriented hierarchical scheduling strategy in cloud workfl ow systems” The Journal of Supercomputing, pp. 1–38.

17. M. R. Garey, D. S. Johnson and R. Sethi, 1976, “The complexity of fl owshop and jobshop scheduling” Mathematics of Operations Research, vol. 1, no. 2, pp. 117–129.


18. J. Bła˙zewicz, K. H. Ecker, E. Pesch, G. Schmidt and J. We¸glarz, 2001, Scheduling Computer and Manufacturing Processes. Springer-Verlag New York, Inc.

19. D. Shi and T. Chen, 2013, “Optimal periodic scheduling of sensor networks: A branch and bound approach” Systems & Control Letters, vol. 62, no. 9, pp. 732–738.

20. M. Dorigo and L. M. Gambardella, 1997, “Ant colony system: A cooperative learning approach to the traveling salesman problem” IEEE Transactions on Evolutionary Computation, vol. 1, no. 1, pp. 53–66.

21. Apache Hadoop. [Online]. Available: http://hadoop.apache.org 22. Y. M. Huang and Z. H. Nie, “Cloud computing with Linux and Apache Hadoop”

[Online]. Available: http://www.ibm.com/developerworks/aix/library/au-cloud apache. 23. Mamatha, E., C. S. Reddy and S. Krishna Anand, 2016, “Focal point computation

and homogeneous geometrical transformation for linear curves” Perspectives in Science

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RESULTS AND DIAGRAMS



Growth with Endogenous Capital, Knowledge, and Renewable ResourcesProf. Wei-Bin Zhang ([email protected])Ritsumeikan Asia Pacifi c University, Japan

ABSTRACT This paper proposes a dynamic economic model with endogenous technological change, physical capital and renewable resources. The model is a synthesis of the neo-classical growth theory, Arrow’s learning by doing, and some traditional dynamic models of renewable resources with an alternative approach to household behavior. The model describes a dynamic interdependence between technological change, physical accumu-lation, resource change, and division of labor under perfect competition. Because of its refi ned economic structure, the model analyzes some interactions between economic variables which are not found in the existing literature of economic growth. We simulate the model to demonstrate existence of equilibrium points and motion of the dynamic system. Our comparative dynamic analysis shows, for instance, that a rise in the capacity of the renewable resource increases the stock and reduces the price of the resource of the resource over time; the output levels of the two sectors, the total capital stock, and capital inputs of the two sectors are all increased; the labor distribution between the two sectors is slightly affected initially but is not affected in the long term; the rate of interest rises initially rise and is almost not affected in the long term; the per capita consumption levels of the good and the resource and the wage rate are increased. Keywords: renewable resource, harvesting, knowledge, Arrow’s learning by doing, capital accumulation, economic growth JEL CLassifi cation: Q2

INTRODUCTION

The purpose of this study is to build a dynamic model to describe interdependence between wealth accumulation, knowledge creation and utilization, and resource dynamics with a new approach to consumers’ behavior proposed by Zhang (1993). The model is built upon Solow’s one-sector growth model, Arrow’s learning by doing model, and some dynamic models of renewable resources. The main mechanisms of economic growth in these theories are integrated into a single framework. The neoclassical growth theory model is extensions and generalizations of the pioneering works of Solow (1956). The Solow model is sometimes referred as to the Solow-Swan model because Swan (1956) proposed a model


similar to the Solow model. The one-sector neoclassical growth model has played an important role in the development of economic growth theory by using the neoclassical production function and neoclassical production theory. The model has been extended and generalized in numerous directions (e.g., Burmeister and Dobell, 1970; Azariadis, 1993; Barro and Sala-i-Martin, 1995; Zhang, 2005). As far as economic structure is concerned, our model is based on the Solow model. Our approach to technological change is based on Arrow’s learning-by-doing. One of the fi rst seminal attempts to render technical progress endogenous in growth models was made by Arrow (1962). He takes account of learning by doing in modelling knowledge accumulation. Another earlier contribution to modelling knowledge accumulation is carried out by Uzawa (1965) who introduces education section to the growth theory. There are many other studies on endogenous technical progresses. But on the whole theoretical economists had been relatively silent on the topic from the end of the 70s until the publication of Romer’s 1986 paper. The literature on endogenous knowledge and economic growth have increasingly expanded since Romer’s 1986’s paper (Romer, 1986; Lucas, 1988; Grossman and Helpman, 1991; Aghion and Howitt, 1998; Zhang, 2005). Various other issues related to education, trade, R&D policies, entrepreneurship, division of labor, learning through trading, brain drain, economic geography, innovation, diffusion of technology, and behavior of economic agents under various institutions have been discussed in the literature. Nevertheless, there are only a few growth models with endogenous renewable resources, capital and knowledge. Changes of renewable resource are now considered as a part of economic evolution in many studies in the literature of economic dynamics. But there are only a few models of growth and renewable resources which treat the renewable resource as both input of production and a source of utility (e.g., Beltratti, et al., 1994, Solow, 1999, Ayong Le Kama, 2001). Our model contains renewable resources as sources of utility and input of production. It has been empirically demonstrated that natural resources may have either an adverse or positive effect on the equilibrium growth rate (e.g., Habbakuk, 1962; Gylfason, et al. 1999; Sachs and Warner, 2001; and Chen and Lu, 2009). It is argued that if population growth is faster and capital and labor show jointly diminishing returns, the limited resource may reduce per capita growth. Abundance of natural resources may also cause economies to reallocate resources and inputs from effi cient use to less effi cient use. If the government controls resources, the distribution of resources may encourage rent-seeking rather than growth-enhancing behavior. It is also suggested that resource-rich countries are likely to have a life-style which is beyond its means during a transitional phase when the resource is depleted. But some economists argue that there are positive


interactions between resources and economic development (e.g., Habbakuk, 1962). To examine dynamic interdependence between renewable resource and economic growth, we introduce renewable resource and endogenous knowledge into the neoclassical growth theory. We demonstrate that if the economic system functions effectively, an economy with richer natural resources should have faster economic growth and better steady state. It should be noted that the paper is based on Zhang (2011). It generalizes Zhang’s model in that knowledge is endogenous, while Zhang’s model does not explicitly consider knowledge. The paper is organized as follows. Section 2 introduces the basic model with wealth accumulation, technological change and dynamics of renewable resources. Section 3 examines dynamic properties of the model. Section 4 conducts comparative dynamic analysis with regard to some parameters. Section 5 concludes the study.

THE BASIC MODEL

The economy has one production sector and one resource sector. Most aspects of the production sector are similar to the standard one-sector growth model (Burmeister and Dobell, 1970; Azariadis, 1993; Barro and Sala-i-Martin, 1995). It is assumed that there is only one (durable) good in the economy. Households own assets of the economy and distribute their incomes to consume and save. Production sectors or fi rms use inputs such as labor with varied levels of human capital, different kinds of capital, knowledge and natural resources to produce material goods or services. Exchanges take place in perfectly competitive markets. Factor markets work well; factors are inelastically supplied and the available factors are fully utilized at every moment. Saving is undertaken only by households. All earnings of fi rms are distributed in the form of payments to factors of production, labor, managerial skill and capital ownership. We assume a homogenous and fi xed population, .N The labor force is distributed between the two sectors. We select commodity to serve as numeraire. The price of commodity is normalized to 1, with all the other prices being measured relative to its price. We assume that wage rates are identical between professions.

The production sector We assume that production is to combine labor force ,tNi and physical capital ,tKi and renewable resource, .tKR The production is also affected by knowledge. Let )0(tZ stand for the knowledge stock at time .t We use the conventional production function to describe a relationship between inputs and output. The production function tFi is specifi ed as follows


,1,0,,,,, iiiiiiiiRiim

ii mAtKtNtKtZAtF iiii (1)

where ,iA ,, iim i and i are positive parameters. If we interpret tZ iim / as the level of human capital, then the term i

m NZ ii / is the human capital or qualifi ed labor force employed by the industrial sector. The production function is a neoclassical one and homogeneous of degree one with the inputs. Here, we call jm country s'j knowledge utilization effi ciency parameter. Markets are competitive; thus labor and capital earn their marginal products. The rate of interest tr and wage rate ,tw and the price of the resource tp are determined by markets. The marginal conditions are given by

,,,tKtFtp

tNtFtw

tKtFtr

R

ii

i

ii

i

iik

(2)

where k is the given depreciation rate of physical capital.

Change of renewable resources We now model dynamics of renewable resources. It is well known that the logistic model has been frequently used in the literature of growth with renewable resource (e.g., Brander and Taylor, 1997; Brown, 2000; Hannesson, 2000; Cairns and Tian, 2010; Farmer and Bednar-Friedl, 2011). It was proposed early in the nineteenth century. Its wide success in different fi elds of biological and social sciences is its apparent empirical success. Let tX stand for the stock of the resource. The natural growth rate of the resource is assumed to be a logistic function of the existing stock

,10

tXtX

where the variable is the maximum possible size for the resource stock, called the carrying capacity of the resource, and , the variable 0 is “uncongested” or “intrinsic” growth rate of the renewable resource. If the stock is equal to , then the growth rate should equal zero. If the carrying capacity is much larger than the current stock, then the growth rate per unit of the stock is approximately equal to the intrinsic growth rate. That is, the congestion effect is negligible. There are some alternative approaches to renewable resources. For instance, Tornell and Velasco (1992), Long and Wang (2009), and Fujiwara (2011) use linear resource dynamics. In this study, for simplicity we assume both the carrying capacity and the intrinsic growth rate constant. This is a strict assumption as the two variables may change due to changes in other conditions. For instance, in Jinni (2006), the carrying capacity changes as a function of the stock of


a renewable resource. Benchekroun (2003, 2008) assumes an inversed-V shaped dynamics of resource accumulation, namely, the resource decreases if its stock is suffi ciently large. We may consider the capacity dependent on some factors such as efforts. For instance, in the case of forestry fertilizers or cleaning activities of the soil may affect the parameter. With aquaculture, we can also refer to feedings schemes, water temperature, or oxygen levels (Long, 1977; Berck, 1981; Levhari and Withagen, 1992; Ayong Le Kama, 2001; Wirl, 2004). It should also be mentioned that Munro and Scott (1985), Koskela et al. (2002) and Uzawa (2005: Chap. 2) use a more general growth function in their analysis of renewable resources in growth models. Let tF x stand for the harvest rate of the resource. The change rate in the stock is then equal to the natural growth rate minus the harvest rate, that is

.10 tFtXtXtX x

(3)

We assume a nationally owned open-access renewable resource. The open-access case was initially examined by Gordon (1954). With open access, harvesting occurs up to the point at which the current return to a representative entrant equals the entrant’s cost. This condition may not be satisfi ed, for instance, when property rights of the resource are incomplete. Aside from the stock of the renewable resources, like the good sector there are two factors of production. We use tNx and tKx to stand for the labor force and capital stocks employed by the resource sector. We assume that harvesting of the resource is carried out according to the following harvesting production function

,1,0,,,,, xxxxxxxxbm

xx bmAtNtKtXtZAtF xxx (4)

where xxx bmA ,,, and x are parameters. The specifi ed form implies that if the capital (like machine) and labor inputs are simultaneously doubled, then harvest is also doubled for a given stock of the resource at a given time. It should be noted that there are other approaches to growth with renewable resources with different property-rights regimes (e.g., Alvarez-Guadrado and VonLong, 2011). Schaefer (1957) uses the following Schaefer harvesting production function to describe the production process

.tNtXAtF xxx

This is a special case of (4). The Schaefer production function does not take account of capital. The function with fi xed capital and technology is widely applied to fi shing (e.g., Paterson and Wilen, 1977; Milner-Gulland


and Leader-Williams, 1992; Bulter and van Kooten, 1999). As machines and knowledge are important inputs in harvesting, we explicitly take account of knowledge and capital inputs. Harvesting is carried out by competitive profi t-maximizing fi rms. The profi t is .tNtwtKtrtFtp xxkx

Firms choose the capital and labor inputs. The marginal conditions are

.,tN

tFtptwtK

tFtptrx

xx

x

xxk

(5)

Full employment of capital and labor Let N and tK stand for respectively the (fi xed) the population and total capital stock. The labor force is allocated between the two sectors. As full employment of labor and capital is assumed, we have

,tKtKtK xi .NtNtN xi (6)

Consumer behaviors We apply an alternative approach to household behavior proposed by Zhang (1993, 2005). Consumers decide consumption levels of resources and commodities as well as on how much to save. We denote per capita wealth by ,tk where ./ NtKtk Per capita current income from the interest payment tktr and the wage payment tw is given by

twtktrty . We call ty the current income in the sense that it comes from consumers’ daily work and consumers’ current earnings from ownership of wealth. The total value of wealth that consumers can sell to purchase goods and then to save is equal to .tk Here, we assume that selling and buying wealth can be conducted instantaneously without any transaction cost. The per capita disposable income is then given by .1ˆ twtktrtktyty (7)

The disposable income is used for saving and consumption. At each point in time, a consumer would distribute the disposable income between saving ,ts consumption of commodities ,tc and consumption of resources .tcx The budget constraint is


.ˆ tytctptstc x (8)

In our model, at each point in time, consumers have three variables, ,ts ,tc and ,tcx to decide. We assume that consumers’ utility function is

a function of ,ts ,tc and tcx as follows .,, tctstcUtU x

For simplicity of analysis, we specify the utility function as follows ,0,,, 000

000 tctstctU x (9)

where 0 is called the propensity to consume commodities, 0 the propensity to own wealth, and 0 the propensity to consume resources. Maximizing tU in (9) subject to the budget constraint (8) yields

,ˆ,ˆ,ˆ tytctptytstytc x (10)where

.1,,,000

000

The demand for resources is given by ./ˆ tptytcx The demand decreases in its price and increases in the disposable income. An increase in the propensity to consume resources increases the consumption when the other conditions are fi xed. We now fi nd dynamics of capital accumulation. According to the defi nition of ,ts the change in the household’s wealth is given by .tktstk (11)

The equation simply states that the change in wealth is equal to saving minus dissaving. The demand for and supply of resource balance at any point in time .tFtKNtc xRx (12)

Knowledge creation with learning by doing Like capital, a refi ned classifi cation of knowledge and technologies tend to lead new conceptions and modeling strategies. Some major new knowledge and inventions that had far reaching and prolonged implications, such as Newton’s mechanics, Einstein’s theory of relativity, steam engine, electricity, and computer. Small improvements and non-lasting improvements take place everywhere, serendipitously and intentionally. Innovations may also happen in a drastic, discontinuous fashion or in a slow, continuous manner. The introduction


of the fi rst steam engine rapidly triggered a sequence of innovations. The same is true about electricity and computer. Bresnahan and Trajtenberg (1995) argued that technologies have a treelike structure, with a few prime movers located at the top and all other technologies radiating out from them. They characterize general purpose technologies by pervasiveness (which means that such a technology can be used in many downstream sectors), technological dynamism (which means that it can support continuous innovational efforts and learning), and innovational complementarities (which exist because productivity of R&D in downstream sectors increases as a consequence of innovation in the general purpose technology, and vice versa). This study uses knowledge in a highly aggregated sense. We assume that knowledge growth is through the so-called learning by doing. We propose the following equation for knowledge growth (Zhang, 1993)

,tZtZtF

tZtFtZ z

xxiixi

(13)

in which )0(z is the depreciation rate of knowledge, and ,j and ,j ,, xij are parameters. Equation (13) implies that knowledge accumulation

is through learning by doing. The parameters j and z are non-negative. We interpret, for instance, iZFii

/ as the contribution to knowledge accumulation through learning by doing by the industrial sector. To see how learning by doing occurs, assume that knowledge is a function of the sector's total industrial output during some period

,301

2

adFatZat

i

in which a a1 2, and a3 are positive parameters. The above equation implies that the knowledge accumulation through learning by doing exhibits decreasing (increasing) returns to scale in the case of 1)(2 a . We interpret

1a and 3a as the measurements of the effi ciency of learning by doing by the production sector. Taking the derivatives of the equation yields ,/ iZFZ ii

in which 21 aai and .1 2ai We have thus built the dynamic model. We now examine dynamic properties of the model.

THE DYNAMICS AND ITS PROPERTIES

This section examines dynamic properties of the model. First, we introduce a new variable by ./ tKtKtz xi We now show that the dynamics can be expressed by the three differential equations with tZtz , and tX as the variables.


Lemma The mo tion of the system is determined by the 3 differential equations

,~ˆ

1

tzt

tXtt

tXttttyNtz

,,, tXtZtztX (14)

,,,~ tXtZtztZ

where the functions in (14) are functions of tZtz , and tX defi ned in the appendix. Moreover, all the other variables can be determined as functions of tZtz , and tX at any point in time by the following procedure: tXtZtztK ,, → tKi and tKx by (A2) → tNi and tNx by (A3) → tFx by (4) → tKR by (A9) → tFi by (1) → tr and tw by (2) → tp by (5) → ty by (7) → tctc x, and ts by (10).

The differential equations system (14) contains three variables, ,tz ,tX and .tZ The lemma is important as it provides a procedure to follow

the motion of the system with computer with a given initial condition. A steady state of (14) is determined by

,0ˆ yN ,0,, XZz (15) ,0,,~ XZz

As the expressions of the analytical results are tedious, for illustration we specify the parameter values and simulate the model. We specify the parameters as follows

,4.0,3,1,5.0,3.0,1,6.0,3.0,5 000 mAAN xxiii ,03.0,15.0,6.0,6.0,01.0,3.0,03.0,2.0 000xxiixm

.04.0,05.0,7.0 zkb (16)

The capacity is unity and the adjustment speed 0 is fi xed at .3 The population is fi xed at .5 The propensity to save is much higher than the propensity to consume the commodity and the propensity to consume the renewable resource. Some empirical studies on the US economy demonstrate that the value of the parameter, , in the Cobb-Douglas production is approximately equal to 3.0 (for instance, Miles and Scott, 2005, Abel et al, 2007). The knowledge utility effi ciency parameters of the industrial and environmental sectors are respectively 4.0 and .2.0 With regard to the technological parameters, what are important in our study are their relative values.


Under (16), the dynamic system has a unique equilibrium point. The equilibrium values of the variables are given as follows

,19.1,81.3,98.0,20.10,61.0,86.4,01.34 xixi NNFFXZK

,61.1,064.0,77.2,37.0,16.7,85.26 wrpKKK Rxi

.70.1,12.0 ccx With the initial conditions, ,4.30 z ,6.40 Z and ,7.00 X we plot the motion of the system as in Figure 1. We see that

the level of the resource stocks falls initially and then rises in the long term; correspondingly its price rises initially and falls in the long term. The knowledge stock falls over time. The total capital and capital input employed by the industrial sector fall over time. The rate of interest rises over time. The capital stock employed by the resource sector falls initially and then rises in the long term. The labor input employed by the resource sector falls and the labor input employed by the industrial sector rises over time. The wage rate and consumption levels of the resource and goods fall over time. It is straightforward to calculate the three eigenvalues as:

g03.0,17.0,74.1 .

This guarantees the stability of the steady state. Hence, the dynamic system has a unique stable steady state.

Motion of the Economic System Figure 1

20 40 60 80 100

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20 40 60 80 100

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20 40 60 80 100

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ciN

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xF

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t

tt

t

t tt

t

t


COMPARATIVE DYNAMIC ANALYSIS

We now examine effects of changes in some parameters on the motion of the economic system. We introduce a variable tx to stand for the change of the variable tx in percentage due to the change in a parameter value.

A Rise in the propensity to consume resources First, we study the case that all the parameters, except the propensity to consume resources, are the same as in (16). The propensity to consume resources is increased as follows: .031.003.00

We plot the simulation result in Figure 2. The rise in the propensity to consume resources reduces the industrial sector’s output and capital input, the total capital, the wage rate and level of the consumption good. The interest rate rises over time. The level of the resource stock rises initially but falls in the long term. The consumption level of the resource is increased over time. The output of the resource sector rises initially but falls in the long term. The price of the renewable resource is reduced initially but increased in the long term. Some of the workers employed by the industrial sector are shifted to the resource sector. The wage rate and the consumption level of commodities fall over time.

A Rise in the Propensity to Consume Resources Figure 2

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A rise in the propensity to consume commodities We now allow the propensity to consume commodities to be increased as follows: .16.015.00 The rise in the propensity to consume commodities initially increases the industrial sector’s output and capital input and national capital stock and reduces these variables in the long term. The capital input employed by the resource sector is increased over time. The price of the resource is reduced. The per capita consumption level of the resource falls initially, then rises, and fi nally approaches to its original value in the long term. The wage rate rises initially but falls late on. The interest rate falls initially but rises in the long term. The level of the resource stock rises over time. Some workers move their jobs from the industrial sector to the resource sector. The knowledge stock rises initially but soon begins to fall.

A Rise in the Propensity to Consume Commodities Figure 3

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A rise in the resource capacity We now allow the resource capacity to be increases as follows:

.05.11 As the capacity is increased, the stock of the resource is increased. In association with the increase in the resource stock, the price of the resource is reduced. The output levels of the two sectors, the total capital stock, and capital inputs of the two sectors are all increased. The labor distribution between the two sectors is slightly affected initially but is not affected in the long term. The rate of interest rises initially rise and is almost not affected in


the long term. The per capita consumption levels of the good and the resource and the wage rate are increased. As mentioned in the introduction, some empirical studies demonstrate that natural resources have an adverse effect on the equilibrium growth rate. If we interpret a rise in the capacity as a rise of natural resources, our result implies that if we don’t neglect possible effects of rent-seeking and misallocation of natural resources, then economies may benefi t from rich natural resources.

A Rise in the Resource Capacity Figure 4

20 40 60 80 100

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20 40 60 80 100

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20 40 60 80 100

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t t

A rise in the population We increase the population as follows: .1.55 N As the population is increased, the labor inputs of the both sectors are increased. The total capital stock, the capital input employed by the industrial sector and the industrial sector’s output are all increased. The stock of the resource is reduced and the price of the resource is increased. The rate of interest rises initially, and falls late on, and is not affected in the long term. The output level of the resource sector and per capita consumption level of the resource are reduced. The wage rate and per capita consumption of the good are reduced initially but increased in the long term. It should be noted that in the Solow growth theory, a rise in the population reduces the per capita consumption and wage rate, while our model predicts that a rise in the population reduces the consumption level and wage rate initially, but the variables are increased in the long term.


We see that the increase in the population reduces the consumption level of the resource but increases the per capita consumption level of commodities in the long term.

A Rise in the Population Figure 5

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CONCLUDING REMARKS

This study built a dynamic economic model with wealth accumulation, change of renewable resource, and technological change. The economic system consists of one production sector and one resource sector. Our approach is different from most of the neoclassical growth models with renewable resources based on microeconomic foundation which neglect physical capital accumulation and technological change. The model is a synthesis of the neoclassical growth theory, Arrow’s learning by doing, and the traditional dynamic models of renewable resources with an alternative approach to household behavior. The study examines the interdependence among economic variables which are not found in the existing literature of economic growth with renewable resources. We also simulated the model to demonstrate existence of equilibrium points, stability and motion of the dynamic system. The model may be extended in some directions. For instance, we may introduce economic structure and research into the model.


Appendix: Proving the Lemma

The appendix shows that the dynamics can be expressed by the three differential equations in the lemma. From (2) and (5), we obtain

,x

i

x

i

NN

KKz (A1)

where we omit time index and ./ ixix By (A1) and (6), we solve

,1

,1

z

KKz

KzK xi (A2)

.,

z

NNz

NzN xi (A3)

By (2), (12) and ycp x ˆ in (10), we have

.ˆ xii FpFyN (A4)

By the defi nition of ,y we have

,ˆx

xx

x

xx

NNFpK

KFpyN

(A5)

where we use (5) and .1 k By (2) and (5), we have

,zFFp

x

iix

(A6)

where we also use (A1). Insert the above equation and (A5) in (A4)

,11 KFpzzz xi

ixxx

(A7)

where we use (A2) and (A3). Substituting (A6) into (A7) yields

.11 KzFzzz

x

ii

i

ixxx

(A8)

From (2), (5) and (A1), we solve

.i

xxiR

FzK

(A9)

Substituting (1), (A3) and (A2) into (A8), we solve


,1

~,,

00

00021

ixiixi

ixii

zzzXZnXZzK

bmm

(A10)

where we use (A9) and

,~,1

1 00 1

0

x

ixi

i

xi

ixi

ixixiii NAAn

.,1121

i

ixxx

We express K as a function of Zz , and .X From (A2), iK and xK are functions of Zz , and .X From (A3), iN and xN are functions of Zz , and .X By the following procedure, we can express other variables as

functions of tZtz , and tX at any point of time: iF by (1) → r and w by (2) → xF by (4) → p by (5) → y by (7) → xcc , and s by (10). It is straightforward to see that the right-hand side of (3) is a function of tZtz , and .tX Hence, we have

,,, XZztX (A11)

where we do not explicitly express XZz ,, as it straightforward but its expression is tedious. The right-hand side of (13) is a function of tZtz , and .tX We have

,,,~ XZztZ (A12)

Taking derivatives of (A10) with respect to t yields

,XX

ZZ

zz

K

(A13)

where

,

100

21

2

zzzzixixii

., 00

Xb

XZmm

Zixii

Multiplying the two sides of (11) with N and using (10), we have

.,,ˆ KXZzyNK (A14)


From (A13) and (A14), we solve

.~ˆ1

zXX

yNz (A15)

where we also use (A11) and (A12). We have thus proved the lemma.

Acknowledgements The author is grateful to the constructive comments of the anonymous referee. The author thanks the fi nancial support from the Grants-in-Aid for Scientifi c Research (C), Project No. 25380246, Japan Society for the Promotion of Science.

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Fixed effects models to assess the effectiveness of entrepreneurial diversifi cation strategy in SMEsElena Druică ([email protected])University of Bucharest, Faculty of Business and Administration

Ana-Maria Grigore ([email protected])University of Bucharest, Faculty of Business and Administration

ABSTRACT The purpose of this paper is to analyze the business environment, before and after 2009, and see if the divesifi cation strategy for types of activity, chosen by Romanian SMEs, was effi cient, similarly to porfolio divesifi cation. We explore multiple types of models aiming to differentiate between two categories of companies: those with only one type of activity and those who kept their options open by having multiple types of activities. The studied companies are from the Bucharest-Ilfov metropolitan area, the variables taken into consideration are profi t, number of employees, geo-graphical position, type of activity, revenues, losses, and the time period is 2000-2012, so as to properly capture the events in 2008 without straying too far from that point in time. We fi tted fi xed linear regression models for panel data, with and without an interaction variable to represent the crysis, as a dummy variable, and the total number of companies as a proxy variable for the level of competition in a certain type of activity and geographical position. As a matter of expectations, we departred from a similarity with the portfolio theory, and anticipated that we ought to fi nd signifi cant differences in favor of those companies which allow themselves multiple types of activities, more exactly the sec-ond category. The results confi rmed that there are many differences between the two categories, that companies with multiple types of activity have not been affected by the crysis as much, and they seem to have more stable profi ts. Keywords: fi xed effects models, models with interaction term, panel data, SMEs, Romania, economic crisis, entrepreneurial strategies JEL Classifi cation: C33, D22, D81, L25, L26


INTRODUCTION

Turbulence in business is unavoidable, but companies can most certainly choose how to deal with it. They can navigate between the vortexes or they can be swallowed up. When the economy returns to normal, it does not do so for each branch, market or individual company. Even in the absence of a global fi nancial crisis, the times can be troublesome for certain industries or organizations (Kotler and Casione, 2009). An answer to the rise in uncertainty and complexity in the environment in which fi rms operate is strategic planning. The word strategy can sound pretentious, even sophisticated, for SMEs, with most of these types of companies being led with a focus on the day to day activities. One of the important features of the small fi rm sector is its lack of homogeneity in what concerns size and age of business, sector, location, growth and decline, economic and market conditions, but also their management (Burns, 2011). The company is, in many ways, an extension of the entrepreneur, such as: the main goal of the company (profi t, growth, stability, work satisfaction); orientation (technical, commercial, social); style of internal and external communication, working conditions etc. Some business owners are motivated by “true” Schumpeterian entrepreneurship, while others tend towards more traditional models, seeking independence, staying small and having a more comfortable life (Nooteboom, 1993). This might explain the heterogeneity in SME’s organizational strategies. Developing a strategy and following it through can lead to less risk when working in a competitive environment and, as a consequence, an increase in profi tability. An OECD report from 2009 warns that in order to survive and grow SMEs need specifi c policies and programmes even in balanced time. It is even more that in times of crisis SMEs are generally more vulnerable for: “it is more diffi cult for them to downsize as they are already small; they are individually less diversifi ed in their economic activities; they have a weaker fi nancial structure; they have a lower or no credit rating; they are heavily dependent on credit and they have fewer fi nancing options” (OECD, 2009). Dedicated policies and programs are even more important in the case of a transitional economy, such as Romania, and this report was our source of inspiration in choosing the variables of the research. After many years of centralized economy, a large part of the population viewed the newly developed SME sector with suspicion. Until 2000 it was impossible to talk about a working market economy, there was chaos because companies worked in a legislative, political and social void which characterized the post revolutionary decade a situation which was enhanced


by the transfer of state property to certain groups without any legal oversight or control. This led to a chaotic and uneven development of the SME sector. After the year 2000 the economy started on an upward trend, fueled by the desire to join political, economic and military trans-atlantic structures. Everything evolved as expected, dragged back by inertia, but with certain coherence in the integration process and response to the eventual crisis of the latter part of the decade, with an expectation for its effects to end in 2012. That year, however, was one of great political crisis in Romania which lowered confi dence and may have led to less foreign direct investments in the country. The research period is therefore relevant, as it was not marred by any other type of event, other than those already familiar to the market economy, as we know it. Concerning the geographical research area, Bucharest-Ilfov, it represents approximately 40% of the Romanian economy. Many large national and international companies are located here and, obviously, SMEs are fl ourishing around them. Furthermore, 60% of total FDIs are directed to this area, the local economy being especially attractive due to the R&D activities. The level of entrepreneurship diversity, effervescence and density in this area is the only example in the country that is at the same level as the EU average. We intent to determine the infl uence of certain important variables – revenues, number of employees, geographical position, and type of activity – on the profi t of two types of SMEs: companies with only one type of activity and companies with more than one type of activity, as recorded at the Registry of Commerce. Most of the Romanian literature on SMEs has taken a descriptive or qualitative approach to the problem, therefore the objective of this paper is to quantify the ability of SMEs to obtain a profi t in a normal situation as well as in a crisis, in other words, their ability to innovate and to create added value. We use fi xed linear regression models for panel data and the statistical data available for the Romanian economy, in the period 2000-2012 and the geographical region of Bucharest-Ilfov. The paper is organized as follows: the next section provides a literature review on SMEs, both at an international level and in Romania. Section three describes the data, the research methodology and the main results. The last section provides the principal conclusions of the paper.

LITERATURE REVIEW

Considering the important role played by SMEs (statistics show that in most countries they represent the vast majority of the total number of companies, a substantial percentage of GDP and employ the greatest number of people), the institutional and market ineffi ciencies that they face must


be addressed by the relevant authorities (Pîslaru and Modreanu, 2012). The Small Business Act, adopted in 2008 by the European Union, was the fi rst step in creating a strategic agenda in order to foster an environment in which SMEs can grow. This strategy was further developed in the Horizon 2020 EU Strategy. In spite of the large amounts of money invested in this direction, there is no consensus in terms of results or performance. The link between entrepreneurship, SMEs and economic growth in Romania (see Marchiş, 2011; Pîslaru and Modreanu, 2012; Nicolescu, 2015; Grigore and Dragan, 2014) has shown that fi nancial and institutional diffi culties, a lack of political willpower, the economic crisis (and its effects on the budget), European constraints as well as educational and human resource limitations, have not allowed SMEs to develop to their full potential and have limited their contribution to the GDP. This phenomenon is easy to notice even now, when policy makers do not perceive the importance of entrepreneurship to its full extent. All this has overshadowed the traditional advantages of SMES, such as quick decision process, great ability to adapt and to generate economic innovations that can be applied in the economy, as well as their great potential to create added value. In Romania, one must make the distinction between the “political entrepreneur”, someone who uses political connections in order to obtain a profi t, and the “market entrepreneur”, who does not use political connections. Ciucan-Rusu and Szabo (2013, see also Armeanu et al., 2014) identify an additional problem of our business environment in general, and SMEs in particular: the transfer of activities, normally done by the public sector, to the politically dominated private sector, to be done by companies which have just one employee, no desire to innovate and don’t produce any added value for the client. In a quantitative approach, Armeanu et al. (2014) wants to measure the contribution of entrepreneurship, expressed as SMEs, to the GDP, as a whole and divided by sectors of the economy. Their message is clear “the Romanian entrepreneurship environment was severely affected by the crisis, SME productivity, for the most important six economic sectors, has been reduced substantially. The factors which have led to this have been a lack of ability to innovate, a high concentration of SMEs in sectors with a low added value, diffi cult access to fi nancing and inadequate management.” The international literature has shown great interest for the connection between entrepreneurship, SMEs and the economic crisis. Among the most important ones are: Ács et al., 2013; Szirmai et al., 2011; Naudé, 2011; Caree and Thurik, 2010; Walzer, 2009; Audretsch et al. 2006; Dejardin, 2000, Klepper, 1996. Pîslaru and Modreanu (2012) consider that: “any attempt at estimating SMEs contribution to economic growth must be based on the reality that there is a


strong variation in the companies’ rhythm of growth. Some companies perform better because they make better use of opportunities and create competitive advantages, either by introducing new technologies and radical innovations, or by incremental innovations, reducing costs, improving quality, processes and increasing organizational fl exibility. There are multiple scenarios concerning companies’ behavior in a period of crisis, depending on their structure and commercial policy. The entrepreneur’s appetite for risk has a signifi cant infl uence on strategy. Those with a low appetite will prefer so-called “safe” strategies, which minimize outside threats, ensuring low but acceptable profi ts. On the other hand, an entrepreneur with a high tolerance for risk will choose a more “aggressive” strategy, a more demanding one, with greater risk and greater reward. In this case, innovation is preferable to imitation and offense to defense. Bourletidis & Triantafyllopoulos (2014) states that there are companies, which show a remarkable yield and it seems that they get a benefi t from the crisis and make use of chances. The difference of the companies’ attribution still observed in the same geographical region even though to the same local market. Penrose (2000) says that a company’s perceptions of crises have a profound effect on primary crisis management activities, in other words the way decision makers perceive the crisis directly affects the way they will respond to it and they will involve in any activity. Soininen et al.(2010) asked the question “Does entrepreneurial orientation matter?” for SMEs in a period of crisis. Their results show that the different dimensions of the entrepreneurial orientation can have diverging effects on how fi rms are impacted by the recession. In general, the more innovative and proactive the fi rm is, the less its operations are affected by the recession and the more risk taking the fi rm is, the more its profi tability is affected by recession. Another type of pressure that companies, working in a dynamic environment, must endure is choosing between their main activity and new business alternatives (Fauchart &Keilback, 2009). The literature speaks of “ambidexterity” as a strategic option to improve performance. Ambidexterity is when fi rm`s managers aim simultaneously to improve their current operations and to expand them by implementing breakthrough new ideas (Gibson and Birkinshaw, 2004; Jansen et al, 2012). De Clercq et al. (2014), in a study conducted on a sample of SMEs, have shown that “the contextual ambidexterity–performance relationship is suppressed at higher levels of internal rivalry and amplifi ed at higher levels of external rivalry. The same authors suggest, based on their fi ndings, that “developing an ambidextrous posture should not be an end by itself, and they point to the need for SMEs to understand how the features of their internal and


external environments affect the performance consequences of such posture”. A similar study could be relevant for Romania as well because, to the best of our knowledge, it has not been conducted yet. Some investigations in this area would allow understanding how entrepreneurs can choose to behave so as to be competitive in an ever-changing environment.

DATA AND METHODOLOGY

Data and variable description The dataset analyzed in this paper contains 132929 observations concerning companies set up at the Registry of Commerce, during the period 2000-2012, corresponding to the different geographic positions and types of activity in the Bucharest-Ilfov area. The following variables are taken into consideration: 1. SIRUTA Code – indicating the geographical position of the

company. 2. NACE Code – indicating the activity for each SIRUTA code,

meaning that there may be more than one NACE code for each SIRUTA code. SIRUTA - NACE combinations identify unique observations in the dataset.

3. Total number of companies registered each year for each NACE - SIRUTA combination.

4. Total revenues – the sum of all the revenues for all the companies in each NACE - SIRUTA combination.

5. Total losses – the sum of all the losses for all the companies in each NACE - SIRUTA combination.

6. Total employees – the total number of people working for all the companies in each NACE - SIRUTA combination.

7. Total profi t – the sum of all the profi ts recorded by all the companies in each NACE - SIRUTA combination.

In total there are 1728077 observations, resulting from 132929 NACE - SIRUTA combinations taken into account for 13 years. The main characteristic of this data is that it contains only aggregated information, grouped by geographical position and business activity, and there is no information pertaining to individual companies. The data has a cross-sectional component, given by the fact that it is grouped into NACE - SIRUTA combinations, as well as a time series component, given by the 13 years taken into consideration. Therefore, we will use an econometric approach specifi c to panel data which will allow us to take into account the autoregressive nature of the data as well as the fi xed component specifi c to each observation.


An important characteristic of the dataset is the absence of companies for certain NACE-SIRUTA combinations. In order to avoid the 0 values in the data to affect the fi nal results, we only took into consideration those combinations where the number of companies is greater than zero. This resulted in an unbalanced panel dataset. Even though it would have been ideal to work with a balanced dataset, modern data analysis software can handle unbalanced data, and so does R. Furthermore, the descriptive statistics revealed asymmetry in the distribution of the data; the literature recommend a log transformation in order to account for the consequences, however, a signifi cant amount of the data is zero, be it profi t, number of employees or another variable in the dataset. Eliminating them would have been useful in order to abide by the requirements of the theoretical model, but it also would have obfuscated the phenomena as it manifests itself in reality. Therefore, we have chosen to keep the data in its original format and accepted the possible problems regarding the accuracy of the results. For the purposes of our analysis, the dataset has been split in two categories: companies with a single main activity (these will be referred to as companies with only one stated NACE and denoted by “NACE = 1”) and those companies which have chosen to keep their options open and have the prospect to run multiple types of main activity. In this case, the category was identifi ed as “NACE = 0”, or multiple NACE codes category. We will fi t two different models for each category, with and without an interaction term, and then compare the results.

Methodology In order to explain the variation in profi t for each NACE-SIRUTA combination, as it can be associated to the number of companies, total revenues, number of employees and the total losses, we fi tted a fi xed effects linear regression model for panel data. To account for the effects of the crisis, a dummy variable was introduced in the model: it takes the value 0 for every year up to and including 2008, and 1 for every year starting with 2009. The fi rst step is to apply the following model for both categories: Profi t = No. of companies, Total revenues, No. of employees, Total losses, Crisis (1)

After testing for multicollinearity, we resume to the following model for multiple NACE codes companies and discuss the fi ndings:

Profi t = No. of companies, Crisis (2)


The fi nal part of the analysis involves a model with interaction for both types of companies. For the single NACE code companies we use model (3) and, for the multiple NACE codes companies, model (4):

Profi t = No. of companies, Total revenues, No. of employees, Total losses, Crisis, No. of companies*Crisis (3)Profi t = No. of companies, Crisis, No. of companies*Crisis (4)

Our expectation regarding the chosen variables is still unclear in the fi rst phase of the investigation. On the one hand, we expect that a larger number of companies will lead to higher values in profi t. However, the increased level of competition in certain areas may have the opposite effect. Total revenues are expected to have a positive impact on profi t, the reasoning behind this being in the very defi nition of profi t, however our expectations can be deceived by having companies which record very high costs. At this stage, however, there is the clear expectation that there is a direct relationship between total revenues and profi t. The number of employees can be expected to have a negative impact on profi t because they represent a cost for the company, but we cannot be sure for now: it may also be the case that an increased number of employees may end up in higher levels of production and potentially a to a higher profi ts. Losses, naturally, are expected to have a negative impact on profi t, when talking about a single economic entity. In this case, however, we are working with aggregated data from all the companies in a region. As a consequence, it is possible to have profi t at the regional level, yet experience a signifi cant level of losses for some individual companies. Therefore, even if we expect a negative relationship between losses and profi ts, we cannot outright eliminate the possibility that there might be a different result, which might indicate a fl ow in revenues from those experiencing losses towards those with profi ts. At last, the dummy variable records the year and allows us to differentiate between results before and after the economic crisis. We expect it to have a signifi cant negative impact on the profi t during the period after 2008.

The model with all the variables, for companies with “NACE=1” (single NACE code)

We extracted, from the original dataset, only those NACE-SIRUTA combinations which have a positive number of companies and obtained an unbalanced panel with a total of 1052771 recordings for a total number of 129773 combinations for which there has been at least one company recorded for at least 1 of the 13 years taken into consideration, specifi cally between 2000 and 2012.


To test for multicoliniarity we used the pooled OLS model, in which we used the data as they are, without taking into consideration the longitudinal structure. This is justifi ed, in the literature, by the fact that multicollinearity is checked in relation to the other independent variables and there is no need to take into account the fi xed effects specifi c to panel data. We can see, in Table 1, that none of the variables has a variance infl ation factor above the acceptable limit; therefore we will keep all the variables in the fi xed model.

VIF for the OLS model with the afformendioned variables, “NACE=1” category

Table 1 Variable No. of companies Total revenues No. of employees Total losses Crisis

VIF 1.37 1.44 1.39 1.21 1

The second column in Table 2 shows that the signs for all the coeffi cients involved in the estimate are as expected. The number of companies, and total revenues, impact positively the profi t, whereas the number of employees, along with the crisis variable, have a negative impact. The coeffi cient for losses is positive, however, due to the way in which the values are recorded, it actually denotes a negative relationship with profi t. All the variables are signifi cant at the 0.1% level and the F-value shows that the model, as a whole, is signifi cant as well. The explanatory power of the model is 11.31%. It’s not clear whether this is due to the fact that, in general, fi xed effect models have a lower explanatory power than their corresponding OLS models, or if this is actually the real explanatory power of the model with the variables that have been taken into consideration.

The model with all the variables for companies with “NACE=1” (multiple NACE code)

For the second model, we only kept the companies with multiple NACE codes, or those “zero” NACE codes observations, where the number of companies was positive. This resulted in an unbalanced panel with 3156 regional observations with periods between 1 and 13 years, for a total of 23523 observations. We fi tted a similar model as before; the results can be found in the third column of Table 2. Once again, the relationships between the independent variables and profi t are as expected, they are statistically signifi cant, as is the model as a whole. However, for companies with multiple NACE codes, the crisis variable is not statistically signifi cant. In different words, although crisis years seem to be associated with lower profi ts, the differences before and after 2008 are not themselves signifi cant. Another aspect that is worth pointing out


is that the model has a much higher explanatory power, 75.82%. This time, the variations in the predictors taken into consideration are able to explain a higher proportion of the variations in profi t, than for the previous category. Because the models were applied on distinct sets of data, we cannot compare the differences between the coeffi cients we obtained. However, we can compare the specifi c infl uence that each variable has on profi t. Concerning the number of companies registered in a certain region, the marginal contributions of another company are similar in both cases: 26729 thousand lei for companies with a single NACE and 22680 thousand lei for those with multiple NACE-codes. Even though, as stated, we cannot speculate with regard to the difference between the coeffi cients, we can discuss the fact that the companies in the fi rst category seem to contribute more, possible as a result of the heterogeneity of their activity (different industries, opportunities). Another particularity of the two groups is that, for fi rms with a single NACE code, a single unit of revenue will contribute more to profi t than the same unit for a multiple NACE codes company: for 1000 units of revenue, the profi t of single NACE code companies will rise by 85, but only by 59 for the other group.

A comparisson between the results obtained for the fi xed effects models fi tted on the categories, illustrating the infl uence that each independent

variable has on profi tTable 2

Model Model for single NACE code Model for multiple NACE code

No. of companies 26729 ***(t-value = 27.34)

22680 ***(t-value = 109.35)

Total revenues 0.085 ***(t-value = 349.05)

0.059 ***(t-value =88.29)

No. of employees -581.42 ***(t-value = -12.30)

- 6514.00 ***(t-value =-123.25)

Total losses 0.067 ***(t-value = 30.615)

0.033 ***(t-value = 7.98)

Crisis After 2008: 1 Before 2009:

0

-298300 ***Reference(t-value = -7.8671)

-64155 Reference(t-value = 1.177)

Adjusted R2 11,311% 75,82%

F - statistic 27344.4(p-value: < 2.22e-16)

28760.2(p-value: < 2.22e-16)

Losses have and adverse impact, although it seems to be more pronounced for companies with a single NACE code. There are signifi cant differences when discussing the impact that employees have on a company.


For both groups there is an inverse relationship between the number of employees and profi t, however, for companies with a single NACE code, the marginal infl uence of a single employee is much higher than for fi rms in the other category. The impact of the fi nancial crisis represents another notable difference between the two categories. For the fi rst group, the crisis had statistically signifi cant impact, and much higher in magnitude than the second group: 298300 thousand lei, compared to 64155 thousand lei. Finally, the explanatory power of the models is signifi cantly different between the two groups. Another aspect which is worth pointing out is that the variable with the greatest impact on profi t is different between the two: total revenues (t-value=349.05) has the greatest impact on profi t for single NACE code companies, whereas, in the case of multiple NACE codes companies the number of employees seems to have the greatest impact (t-value= -123.25). Although the analysis presented in Table 2 is fairly eloquent, we cannot ignore the problem put forward by the information present in Table 3, which shows the existence of a strong multicollinearity between the independent variables in the multiple NACE codes model (“NACE=1”). From an econometric point of view, multicollinearity infl uences estimator values, but it is usually considered a problem related to the structure of the data and some author recommend no measures to correct it in any way, especially when the different variables included in the model are economically relevant in the model. In our case, however, it means that the number of companies in each NACE – SIRUTA combination is strongly correlated with total revenues, the number of employees or total losses, and this is not something which happens for the single NACE code category.

VIF for the OLS model with the afformendioned variables, “NACE=0” category

Table 3Variable No. of companies Total revenues No. of employees Total losses Crisis

VIF 18.38 14.26 12.72 4.30 1


Fixed effects model explaining variations in profi t as determined by variations in the number of companies and the year of the result, for

companies with “zero” NACETable 4

Model Estimator Standard Error t-value Pr(>|t|) Signif.No. of companies 20890.219 79.368 263.2068 < 2.2e-16 ***CrisisAfter 2008: 1Before 2009: 0

554822.1

Reference

73225.72 7.58 3.691e-14 ***

Adjusted R2 66,984%

F - statistic34816.6(p-value: < 2.22e-16)

This aspect will be discussed in more detail in the results section, but, for now, we will eliminate this phenomenon by keeping only the total number of companies as an independent variable. Table 4 shows the results obtained from model (2), presented at the beginning of this section. Both variables are statistically signifi cant, and so is the model as a whole. The coeffi cient for the “number of companies” variable is positive, as before. What is different, when compared to Table 2, is the impact of the dummy variable that is now statistically signifi cant and has a positive, direct infl uence: the impact of the crisis on the profi t of single NACE code companies was a rise in profi t. This result will be discussed as well in the fi nal section. Another difference, in comparison to Table 2, is the lowered explanatory power of the model. This is not surprising: a decrease in the coeffi cient of determination is to be expected when eliminating variables; therefore it will not be considered a problem for the new model.

Models with interaction betweem the crysis and the number of companies

The last step of this investigation involves a model with interaction term meant to investigate the nature of the positive infl uence the crisis had on companies with a multiple objects of activity. The results reported in the second column of Table 5 show that a rise in the number of companies during the crisis has an adverse effect on profi t, even though otherwise the number of companies was positively associated with the profi t. In other words, when the number of companies and the crysis are taken separately, neither of them have an adverse effect on profi t. However, when a new company is accounted during a crysis year, the overall profi t suffers. An interesting observation can be derrived as a result of the function


obtained from the econometric model presented in Table 5. Presented below are the two forms of the model – before and after 2008:

Estimated total profi t = 20890.219 * No. of companies + 554822.1 * 1 - 13219.6 * No. of companies * 1, for the years after 2008 (5)

Estimated total profi t = 20890.219 * No. of companies + 554822.1 * 0 - 13219.6 * No. of companies * 0, for the years up to and including 2008 (6)

For the same NACE – SIRUTA observation, the difference in average profi t for a year up to and including 2008 differs from those after 2008 by 554822.1 - 13219.6 * No. of companies, a value obtained from the difference between (5) and (6). That means that profi t is improved in a year after 2008 only if the number of companies in that specifi c NACE – SIRUTA combination is smaller than 42, a value obtained from the condition 554822.1 - 13219.6 * No. of companies > 0.

Fixed effects model with and without interaction, for companies with multiple NACE codes (“NACE=0”)

Table 5 Model Results without interaction Results with interaction

No. of companies20890.219 ***(t-value = 263.207)

20890.219 ***(t-value = 263.2068)

CrisisAfter 2008: 1Before 2009

554822.1 *** Reference(t-value = 7.58)

554822.1 ***Reference(t-value = 7.57)

(No. of companies)* (Crisis)After 2008: 1Before 2009 - -13219.6 ***

Reference (t-value = -16.179)

Adjusted R2 66,984% 67.23%F - statistic 34816.6

(p-value: < 2.22e-16)23595.5 (p-value: < 2.22e-16)


A comparisson between the results obtained for the fi xed model without the interaction and the one with the interaction between the number of companies and the year of the result, for companies with single NACE

code (“NACE=1”)Table 6

Model Results without interaction Results with interaction

No. of companies 26729 ***(t-value = 27.34)

68672 ***(t-value = 59.98)

Total revenues 0.085 ***(t-value = 349.05)

0.087***(t-value = 355.32)

No. of employees -581.42 ***(t-value = -12.30)

-543.75 ***(t-value = -11.54)

Total losses 0.067 ***(t-value = 30.615)

0.054 ***(t-value = 23.772)

CrisisAfter 2008: 1Before 2009: 0

-298300 ***Reference(t-value = -7.8671)

-28890Reference(t-value = -0.760)

(No. of companies)* (Crisis)After 2008: 1Before 2009: 0

- - 50955 ***(t-value = 69.857 )

Adjusted R2 11,311% 11,713%

F - statistic 27344.4(p-value: < 2.22e-16)

23720.8(p-value: < 2.22e-16)

Therefore, the interaction model allows us to determine that the positive effects of a larger number of companies manifest themselves only up to a certain point. Beyond that threshold however, the crowding on the market leads to worse results. It terms of performance, the model with interaction is not signifi cantly better compared to the one without interaction. A model with a similar interaction, but for companies with single NACE codes, can be found in the third column of Table 6. Table 6 helps us make an effi cient comparison between the model without the interaction and the one with the interaction between the number of companies and the year of the result, for companies with a single NACE code: the estimated coeffi cients are similar, with the exception of the total number of companies: for the interaction model, the estimated coeffi cient in much larger, but it is compensated by the value of the interaction coeffi cient. Using an approach similar to the one used for the relationship between (5) and (6), the results in Table 6 tell us that, ceteris paribus, the difference between


the average profi t for a crysis year (starting with 2009) and any year before the crysis (up to and including 2008) is:

-28890 - 50955 * No. of companies (7)

The interaction model, compared to the one without itnteraction, shows that increasing the number of companies does not have a positive effect on profi t unless this growth is associated with a year up to or including 2008. The coeffi cient for the interaction term tells us that during a crysis year, under no circumstance, will an increase in the number of companies lead to an increase in profi t. This result will be discussed in the last section.

CONCLUSIONS, DISCUSSIONS AND INTERPRETATIONS

Concerning the debate between those who claim that the best strategy for the development of a company is to specialize on a single type of activity, intensive development, versus developing several activities – be they complementary or not, extensive development, the result presented in this paper, surprisingly for some, is that during a period of crisis, companies with multiple NACE codes fare better. The result is based on data for the Bucharest-Ilfov region, in the aforementioned time period and analyzed using linear regression models. We found that there are real differences between the two categories taken into account: the total number of companies in a NACE – SIRUTA combination for the multiple NACE codes category is strongly correlated with total revenues, total number of employees, or total losses. This is something that does not happen in the single NACE code category. One possible interpretation could be that profi t, for companies with a single type of activity, is strongly connected with revenues because these fl ows are well known and, just like costs, very specialized, with the number of employees adjusted to the dimension of the company. For a company with a single activity, fi xed costs are known, therefore, when revenues drop so does profi t. The number of employees has a negative effect on profi t in both situations, but it is much more profound for companies with multiple types of activity. First of all, the fact that it has a negative impact is an anomaly in itself: if the number of employees was better adjusted to the size of the company, and should the company be better organized, then each employee would have to create added value, meaning profi t. Unfortunately, the technological, industrial and cultural level of Romanians is low – labor productivity is among


the lowest in the EU. If a company can develop in different directions while keeping employment at a minimum, there is a chance for profi t. But if the company starts to hire new people in order to cover as many competencies as possible then, as the model demonstrates for this geographical area, profi t disappears. Model (2), obtained after eliminating multicollinearity between variables in the multiple NACE dataset, showed that profi t could be increased during a crisis, as opposed to companies with a stated NACE code that recorded worse results than in the years prior to 2009. A company that specializes in an area has more expertise when it comes to the available technology and management practices. But it also has a well-defi ned market, which shrinks during a period of crisis. It makes quality products, but during a period of crisis there isn’t enough money for this to be a key factor. A multidextrous company can, usually, optimize its expenses by reducing its fi xed costs and it can access multiple markets. At the same time, in a crisis period there are certain situations that can be better exploited by a more opportunistic fi rm. The two interaction models show that the crisis is not the only one to have negative effects, in the same sense that increasing the number of companies is not a solution for unlimited growth in profi t, irrespective of the external economic environment. The introduction of the interaction term helped clarify the limits of growth for companies in the multiple NACE codes category and showed how they differ from those with a single NACE code. As we have seen, companies with multiple types of activity have the potential to pass relatively unscathed through a crisis: smaller fi xed costs, diversifi ed markets, elastic and opportunistic management, and this study have proven this beyond doubt.

REFERENCES

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3. Audretsch, D. B., Keilbach, M. C., Lehman, E., 2006, „Entrepreneurship and Economic Growth“, Oxford: Oxford University Press.

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5. Carree, M. A., Thurik, A. R., 2010, The Impact of Entrepreneurship on Economic Growth, in Acs, Z. J., Audretsch, D. B. (eds.), “Handbook of Entrepreneurship Research”, New York: Springer Science.

6. Ciucan-Rusu, L., Szabo, Z., 2013, The Pyramid of Entrepreneurship in Romania: Towards New Approach. In: Ramadani, B. and Schneider, C., eds., 2013. Entrepreneurship in the Balkans. Berlin Heidelberg: Springer-Verlag.


7. De Clercq , D., Thongpapanl, N., Dimov, D., 2014, Contextual ambidexterity in SMEs: the roles of internal and external rivalry, Small Business Economics , 42(1), pp. 191–205

8. Dejardin, M., 2000, Entrepreneurship and Economic Growth: An Obvious Conjunction?, [Online], Available at: http://www.spea.indiana.edu/ids/pdfholder/IDSissn00-8.pdf,

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13. Kotler, Ph., Casione, J., Chaotics, 2009, Management si marketing in era turbulentelor, Publica House

14. Jansen, J., Simsek, Z., & Cao, Q., 2012, Ambidexterity and performance in multiunit contexts: Cross-level moderating effects of structural and resource attributes. Strategic Management Journal, 33, 1286–1303.

15. Marchiş, G., 2011, Study Regarding Romanian Entrepreneurship. EuroEconomica, 30(5).

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Empirical Results of Modeling EUR/RON Exchange Rate using ARCH, GARCH, EGARCH, TARCH and PARCH modelsAndreea - Cristina PETRICĂ PhD. Student([email protected])Bucharest University of Economic Studies

Prof. Stelian STANCU PhD.([email protected])Bucharest University of Economic Studies

ABSTRACT The aim of this study consists in examining the changes in the volatility of daily returns of EUR/RON exchange rate using on the one hand symmetric GARCH models (ARCH and GARCH) and on the other hand the asymmetric GARCH mod-els (EGARCH, TARCH and PARCH), since the conditional variance is time-varying. The analysis takes into account daily quotations of EUR/RON exchange rate over the period of 04th January 1999 to 13th June 2016. Thus, we are modeling heterosce-dasticity by applying different specifi cations of GARCH models followed by looking for signifi cant parameters and low information criteria (minimum Akaike Information Criterion). All models are estimated using the maximum likelihood method under the assumption of several distributions of the innovation terms such as: Normal (Gaussian) distribution, Student’s t distribution, Generalized Error distribution (GED), Student’s with fi xed df. Distribution, and GED with fi xed parameter distribution. The predominant models turned out to be EGARCH and PARCH models, and the empirical results point out that the best model for estimating daily returns of EUR/RON exchange rate is EGARCH(2,1) with Asymmetric order 2 under the assumption of Student’s t distributed innovation terms. This can be explained by the fact that in case of EGARCH model, the restriction regarding the positivity of the conditional variance is automatically satisfi ed. Keywords: Exchange Rate Volatility, Heteroscedasticity, Symmetric GARCH Models, Asymmetric GARCH Models, Fat-tails, Volatility Clustering, Leverage Effect JEL Classifi cation: C13, C22, C26, C51, C52, C55, C58


1. INTRODUCTION

Nowadays, volatility represents an important tool in Economy and plays an important role in the area of risk management. A disadvantage of stationary linear models is given by not taking into account the fact that volatility is time-varying, and so the length of the forecast intervals remains constant as long as the model parameters are not changed, even if new data become disposable, something that is unlikely in the case of ARCH family models where the forecast intervals include any sudden changes in volatility, keeping all the parameters unchanged. This characteristic makes ARCH family models such important tool in analyzing fi nancial and monetary time series. From this point of view, the main aim of this paper is to investigate the volatility of EUR/RON exchange rate using non-linear processes, so we proceed to apply ARMA models with different Generalized Autoregressive Conditionally Heteroscedastic (GARCH) errors, including both symmetric and asymmetric models. The main feature of analyzing the conditional variance of exchange rates - and fi nancial time series in general - is given by the fact that it is not directly observable. Starting with the 1980s, there were developed many models for estimating the conditional volatility of fi nancial series. Thus, the starting point is given by Engle (1982), who introduced in the literature the Autoregressive Conditionally Heteroscedastic process (ARCH). Four years later, the ARCH model is extended by Bollerslev (1986) to the so-called the Generalized Autoregressive Conditionally Heteroscedastic model (GARCH). Since both processes have symmetric distribution, so they fail with respect to leverage effect, Nelson (1991), Zakoian (1994), Glosten et al. (1993) and Ding et al. (1993) provide an extended methodological framework to allow for asymmetric effects of positive and negative innovations. For a short overview of recent literature, we bring up the following recent studies: Elsheikh and Zakaria (2011) estimate the volatility of Khartoum Stock Exchange1 over the period January 2006 – November 2010 using both symmetric and asymmetric GARCH models. The results reveal the presence of leverage effect leading to the better fi t of the asymmetric models. Begu et al. (2012) estimated the daily returns of RON/EUR exchange rates from 05.01.2009 to 12.10.2012 using the following models: ARCH, GARCH, EGARCH and TGARCH. They have reached the conclusion that GARCH model is the most promising for investigating the volatility and “fi t the sample data good enough”2. Ignat et al.

1. The Khartoum Stock Exchange represents the principal stock exchange of Sudan.2. Begu et al. (2012), pp. 38-39.


(2013) pointed out the effects of currency depreciation in case of Romania, where the exchange rate is considered an infl uencing factor of the economy used by some countries to correct certain disequilibrium produced as a result of the fi nancial crisis who “hit” in many areas considered previously to be infallible. Damianova (2014) applies GARCH methodology using the dollar-adjusted daily return of the Bucharest Exchange Trading Index and fi nds out the market ineffi ciency from the Bucharest Stock Exchange. Dutta (2014) investigated the U.S. – Japan exchange rate (daily observations) by using and comparing the symmetric and asymmetric GARCH models taking into account two distributions (normal and heavy-tailed) and the results of the analysis indicate that the second distribution gives a reduced persistence. Dineată and Anghelache (2015) analyzed the Romanian capital market sensitivity to exchange rate fl uctuation through a GARCH model, using daily returns of BET-C Index and EUR/RON exchange rate over the period of 03th January 2005 to 20th June 2014. The empirical results showed that the exchange rate has a strong impact on both the average return on capital market, and on its volatility.

2. METHODOLOGY

The goal of this section is to describe the volatility modeling techniques in terms of symmetry (ARCH and GARCH processes) and asymmetry (EGARCH, TARCH/GJR-GARCH and PARCH processes) concepts, giving an overview of the processes used in this paper for modeling the daily returns of EUR/RON exchange rate. Thus, the key concept in autoregressive conditionally heteroscedastic model and its extensions is represented by the conditional variance. Furthermore, their mathematical representation is given by two equations, one for conditional mean (the predictable component) - where the Box-Jenkins approach can be used, and another one for conditional variance which represents the unpredictable component – where the innovation terms from the conditional mean are modeled using symmetric and asymmetric GARCH models. The fi rst equation is a function of the expected value conditional on the information available at time t-1 and the current value of the innovation term. The second equation can be described as a quadratic function of past values of the innovations {εt}. Another thing worth mentioning is that the difference between the symmetric and asymmetric GARCH models is given by the impact of good and bad news on volatility. In case of symmetric models good and bad news have the same impact on volatility, while in case of asymmetric models bad news affect more the volatility than the good news. In other words, the symmetric models can’t explain the leverage effect.


2.1. The Autoregressive Conditionally Heteroscedastic Model (ARCH)

The Autoregressive Conditionally Heteroscedastic process for the series {εt}, ARCH(q), is expressed by allowing the conditional variance to be described by its past q squared innovations as follows:

[1] where: – the conditional variance of the innovations(errors) at time t; – the constant term; – the squared error at time t-q; – ARCH terms i.e. volatility shocks from prior periods. To ensure that is positive we have to impose some restrictions with respect to the parameters in the conditional variance equation: and for , and . If we rewrite eqn[1] in terms of the lag operator (L), we get the following representation of the ARCH(q) model:

[2]

2.2. The Generalized Autoregressive Conditionally Heteroscedastic Model (GARCH)

The generalized autoregressive conditionally heteroscedastic process, GARCH(p,q), is expressed by allowing the conditional variance to be described by both past q squared errors and p conditional variances as follows:

[3]

where:

– the constant term; – ARCH terms i.e. volatility shocks from prior periods. – GARCH terms i.e. the persistence of volatility; – the number of lagged conditional variance terms ( ); – the number of lagged errors ( ). To ensure that is strictly positive we have to impose some restrictions with respect to the parameters in the conditional variance equation:

, , for , , for and


(i.e. good news and bad news have a declining impact on future volatility). If we rewrite eqn[3] in terms of the lag operator (L), we get:

[4]

2.3. The Exponential Generalized Autoregressive Conditionally Heteroscedastic Model (EGARCH)

The Exponential GARCH model (EGARCH) introduced by Nelson (1991) models the logarithm of conditional variance and it captures asymmetric responses of the conditional variance to good and bad news. The equation of the EGARCH model can be written in the following form:

[5]

where represents the asymmetry parameter (leverage effect). points out the presence of asymmetry, while

) shows that volatility

rises more after bad news ( ) than after good news ( ).

2.4. The Exponential Generalized Autoregressive Conditionally Heteroscedastic Model (TARCH and GJR-GARCH)

The difference between the Threshold ARCH (TARCH) model introduced by Zakoian (1994) and the GJR-GARCH model introduced by Glosten et al. (1993) is given by using the specifi cation on the conditional standard deviation instead of conditional variance. Hence, the conditional variance for the TARCH model is represented by eqn[6], while the conditional variance for the GJR-GARCH model is represented by eqn[7]:

[6]

where and .

[7]


where - represents the indicator function, .

2.5. Power ARCH (PARCH) The Power ARCH model (PARCH) introduced by Ding et al. (1993) is an asymmetric model and it has the following representation:

[8]

where:

; –

– – – t

the standard ARCH term; the standard GARCH term; the leverage parameter ( ); the parameter for the power term ( ).

To ensure that is strictly positive we have to impose some restrictions with respect to the parameters in the conditional variance equation:

, , with at least one p

, ( ) and ( ). It is worth mentioning that for , PARCH model becomes a classic GARCH model that allows for asymmetry, while leads to the estimation of the conditional standard deviation.

3. DATA AND EMPIRICAL RESULTS

This section reveals and provides with graphs the empirical results obtained by employing the symmetric and asymmetric GARCH models to the percentage daily returns of the EUR/RON exchange rate

, respectively: ARCH, GARCH, TARCH,

EGARCH and PARCH models. The data were collected from the offi cial website of the National Bank of Romania and consist of 4439 daily quotations of EUR/RON exchange rate over the period of 04th January 1999 to 13th June 2016. The evolution of daily price and return series for EUR/RON exchange rate during the analyzed period is presented in Figure 1.


Daily prices and returns for the EUR/RON exchange rate (January 04, 1999 – June 13, 2016)

Figure 1

1.2

1.6

2.0

2.4

2.8

3.2

3.6

4.0

4.4

4.8

1000 2000 3000 4000

EUR/RON exchange rate

-6

-4

-2

0

2

4

6

8

1000 2000 3000 4000

Percentage daily EUR/RON exchange rate return

The evolution of the daily EUR/RON exchange rate presented in Figure 1 denotes that the series has constant and trend. Likewise, the correlogram reveals very high autocorrelations for all lags, with values decreasing very slowly and reaching a value of 0.959 at the 36th lag. This leads together with High Q-Stat test values (Prob. < 0.05) to the conclusion that the aforementioned series is non-stationary. On the other hand, the ACF and PACF coeffi cients of daily returns of EUR/RON exchange rate are close to zero at all lags, starting from 0.104 at lag 1 and decreasing quickly at lag 2 (ACF= -0.068 and PACF= -0.080), this indicates that the series of daily returns is generated by a random walk process. Thus, to investigate stationarity, besides visual inspection given by graphs which represents the fi rst step of making an idea if our series are stationary or not, we also have statistical tools for investigating the stationarity of the series. Taking these into account, Table 1 summarizes the fi ndings of the Augmented Dickey-Fuller (ADF) and Phillips-Perron (PP) tests which confi rm that daily EUR/RON exchange rate series is not stationary, but in terms of daily percentage returns we fi nd stationarity at all conventional confi dence levels (1%, 5% and 10%).


Augumented Dickey-Fuller and Phillips-Perron Tests for both series – prices and returns

Table 1ADF Test

(Probability)Critical Values

1% 5% 10%Daily EUR/RON exchange rate

-2.377248(0.3915) -3.960107 -3.410818 -3.127206

Daily EUR/RON return series

-41.39923(0.0000) -2.565484 -1.940895 -1.616652

PP Test(Probability)

Critical Values1% 5% 10%

Daily EUR/RON exchange rate

-2.371825 (0.3944) -3.960106 -3.410817 -3.127205

Daily EUR/RON return series

-59.48531(0.0001) -2.565483 -1.940895 -1.616652

Source: Authors’ calculations.Note: The results presented above correspond to the ADF and PP Tests including intercept and trend in case of EUR/RON exchange rate series and ADF and PP Tests without intercept and trend in case of daily returns of EUR/RON exchange rate.

The descriptive statistics reported in Figures 2-3 show: - negative asymmetry (Skewness= -1.107702) for daily EUR/RON

exchange rates and positive asymmetry (Skewness = 0.884889) for returns;

- leptokurtic distribution for both daily EUR/RON exchange rates and returns (Kurtosis= 3.235483 and 17.01422, respectively);

- non-normal distribution for both series (Jarque-Bera= 918.03 and 36896.51, respectively, with zero probability in both cases).

Descriptive Statistics for daily EUR/RON exchange rateFigure 2


Descriptive Statistics for daily returns of EUR/RON exchange rateFigure 3

As we said in the Introduction section, the main disadvantage of stationary linear models is given by not taking into account the fact that volatility is time-varying, which in the case of ARCH family models the forecast intervals include any sudden changes in volatility, keeping all the parameters unchanged. This characteristic makes these models such important tool in analyzing time series. Therefore, using Box-Jenkins approach we employ the Autoregressive Moving Average models (ARMA) for the conditional mean in order to fi nd the adequate model. Based on the correlogram of daily returns the maximum orders of the AR and MA processes is 3, so using EViews 9 software we estimated 10 models and the results are presented in Table 2. As can be seen, according to the all three used criterions (Akaike Information Criterion, Schwarz Criterion and Hannan-Quinn Criterion) the adequate model achieved for modeling the conditional mean is AR(3) model (AIC=1.463956).


The estimated ARMA models for the conditional mean of the daily returns of EUR/RON exchange rate

Table 2The estimated

modelAdjusted R-squared

Akaike info criterion Schwarz criterion Hannan-Quinn

criterionAR(1) 0.010474 1.473531 1.477856 1.475056AR(2) 0.016628 1.467521 1.473287 1.469554AR(3) 0.020350 1.463956 1.471164 1.466498MA(1) 0.012118 1.471869 1.476193 1.473394

MA(2) 0.014555 1.469625 1.475391 1.471658MA(3) 0.020064 1.464248 1.471456 1.466789

ARMA(1,1) 0.012982 1.471219 1.476985 1.473252ARMA(1,2) 0.017356 1.467005 1.474213 1.469546ARMA(2,1) 0.018880 1.465455 1.472663 1.467996ARMA(2,2) 0.020182 1.464353 1.473003 1.467403

Source: Authors’ calculations.

Consider the mean equation as being given by the econometric model AR(3) since previous results. Given the fact that we are interested in analyzing the volatility of daily returns of EUR/RON exchange rate, we use the residuals of the autoregressive process of order 3 to test for ARCH effects using ARCH LM Test. The number of observations times R-squared is evaluated against Chi-Square distribution, and the Obs*R-squared of 88.14303 with a probability less than 5% indicates that the null hypothesis is rejected, case in which we can run the ARCH family models. This means that we have established that the conditional variance is time-varying. The results are summarized in Table 3.

Testing residuals for ARCH effectsTable 3

Obs*R-squared 88.14303Prob. Chi-Square(1) 0.0000

Source: Authors’ calculations. Note: H0 : There are no ARCH effects in the residual series.

Next, the diffi culty is given by the construction of the models that “accommodate heteroskedasticity so that valid coeffi cient estimates and models are obtained for the variance of the error terms”.1 We continue this study by examining the changes in the volatility of daily returns of EUR/RON exchange rate using symmetric GARCH models (ARCH and GARCH) and asymmetricGARCH models (EGARCH, TARCH and PARCH). The fi rst

1. Rachev et al. (2007), pp. 279


class treats the shocks/errors/innovations as symmetric, meaning that shocks affect the conditional variance in the same way whether they are positive or negative, whereas the second class treats them as having an asymmetric effect on the conditional variance. Therefore, having set up that the conditional variance is time-varying, the next step in this study consists in model this heteroscedasticity by applying the symmetric and asymmetric GARCH models. For this we are trying different specifi cations followed by looking for signifi cant parameters and low information criteria (minimum Akaike Information Criterion). All models are estimated using the maximum likelihood method under the assumption of several distributions of the innovation terms such as: Normal (Gaussian) distribution, Student’s t distribution, Generalized Error distribution (GED), Student’s with fi xed df. Distribution, and GED with fi xed parameter distribution.

Akaike Information Criterion results of different GARCH modelsTable 4

ModelError Distribution

Normal (Gaussian) Student’s t Generalized

Error (GED)Student’s with fi xed df.

GED with fi xed parameter

ARCH(1) 1.233917 1.007439 1.001994 1.093013 1.094990ARCH(2) 1.135639 0.948401 0.948893 1.011676 1.015676GARCH(1,1) 0.882523* 0.797746 0.803225 0.813491* 0.817117GARCH(1,2) 0.876557** 0.795905 0.800829 0.810915 0.813683GARCH(2,1) 0.876426*** 0.795377 0.800473 0.810694* 0.813423GARCH(2,2) 0.876780*** 0.795822 * 0.800924* 0.811143* 0.813872*EGARCH(1,1)Asymmetric order 1

0.884665 0.794197 ** 0.801765 ** 0.810639 ** 0.816702****

EGARCH(1,1)Asymmetric order 2

0.881407 0.791276 0.799337 0.807424 0.813924

EGARCH(1,2)Asymmetric order 2

0.875815 0.789429**** 0.797095 ** 0.805045**** 0.810718 **

EGARCH(2,1)Asymmetricorder 2

0.875409 0.787957 0.796127*|* 0.803903 0.809881

TARCH(1,1)Threshold order 1

0.881618 0.797612 *** 0.802645 0.813216 0.816440

TARCH(1,2)Thresholdorder 1

0.876095*** 0.795939 *** 0.800526*|** 0.810863*|** 0.813339

PARCH(1,1) 0.880366* 0.794487 0.800920 0.810265 0.814731PARCH(1,2) 0.872975 0.791853 0.797705 0.806716 0.810271PARCH(2,1) 0.872857* 0.790706 0.797079 0.806048* 0.809813PARCH(2,2) 0.873193 0.790876 0.797517 **** 0.805896* 0.810264 ****Source: Authors’ calculations.


Note: * The coeffi cient of AR(2) term in the conditional mean equation is statistically signifi cant at 10% confi dence level.**The coeffi cient of AR(3) term in the conditional mean equation is statistically signifi cant at 10% confi dence level.*** The coeffi cients of AR(2) and AR(3) terms in the conditional mean equation is statistically signifi cant at 10% confi dence level.* The coeffi cient of GARCH(-2) term is not statistically signifi cant at any confi dence level.** The coeffi cient of RESID(-1)/@SQRT(GARCH(-1)) term is not statistically signifi cant at any confi dence level.****The coeffi cient of RESID(-1)/@SQRT(GARCH(-1)) term is statistically signifi cant at 10% confi dence level.*|* The coeffi cient of RESID(-1)/@SQRT(GARCH(-1)) term is statistically signifi cant at 10% confi dence level.*** The coeffi cient of RESID(-1)^2 (resid<0) term is not statistically signifi cant at any confi dence level.*|** The coeffi cient of RESID(-1)^2 (resid<0) term is statistically signifi cant at 10% confi dence level.**** The coeffi cient of @SQRT(GARCH(-2))^C(10) term is not statistically signifi cant at any confi dence level.

As reported in Table 4, we achived based on Akaike Information Criterion that the best models have proved to be EGARCH and PARCH. Moreover, Table 5 summarizes the best GARCH model obtained for each error distribution separately. Comparing all the results presented in Table 5, we notice that daily returns of EUR/RON exchange rate could be modeled using EGARCH(2,1) with Asymmetric order 2 under the assumption of Student’s t distributed innovation terms.

The best GARCH model achived under different error distributionTable 5

Error Distribution

Normal (Gaussian) Student’s t

Generalized Error

(GED)

Student’s with fi xed df.

GED with fi xed parameter

Model PARCH(1,2)EGARCH(2,1)

asymmetric order 2

PARCH(2,1) EGARCH(2,1) PARCH(2,1)

Minimum AIC 0.872975 0.787957 0.797079 0.803903 0.809813

Source: Authors’ calculations.Note: All the estimated parameters in the conditional variance equation are statistically signifi cant at all confi dence levels (1%, 5% and 10%).

Table 6 points out that AR(3)-EGARCH(2,1) with Asymmetric order 2 and Student’s t error distribution is the most adequate model for estimating


the conditional variance (having the minimum AIC, which is 0.787957). The presence of asymmetry in the returns of EUR/RON exchange rate is confi rmed by the non-zero leverage parameters ( and

). A negative leverage parameter indicates an asymmetric response for positive returns in the conditional variance equation, while a positive leverage parameter indicates that bad news leads to increased volatility. In case of volatility persistence, Table 6 reveals a very large value of the estimated persistence parameter ( ) resulting in a slowly decreasing of the rises in the conditional variance due to shocks.

Estimation results of EGARCH(2,1) Asymmetric order 2 – Student’s t error distribution

Table 6Variable Coeffi cient Std. Error z-Statistic Prob.

Conditional Mean EquationC 0.001358 0.003377 0.402083 0.6876*

AR(1) 0.047834 0.016246 2.944421 0.0032AR(2) -0.036291 0.014342 -2.530440 0.0114AR(3) -0.041527 0.014480 -2.867885 0.0041

Conditional Variance Equation-0.193853 0.015252 -12.71001 0.00000.416476 0.043840 9.499823 0.0000-0.167695 0.042571 -3.939215 0.00010.059061 0.029140 2.026764 0.0427-0.078136 0.028240 -2.766824 0.00570.993305 0.002386 416.3580 0.0000

*The coeffi cient is not signifi cant at any confi dence level (1%, 5% and 10%).Source: Authors’ calculations.

Withal, ARCH-LM Test indicates that the conditional variance equation found is well specifi ed as there is no ARCH effect left in the innovations (Obs.* R-squared= 0.238921with Prob. Chi-Square(1)= 0.6250).

4. CONCLUSIONS

This study consists in examining the changes in the volatility of daily returns of EUR/RON exchange rate using both symmetric and asymmetric GARCH models. The analysis takes into account daily quotations of EUR/RON exchange rate over the period of 04th January 1999 to 13th June 2016. Thus, we are modeling heteroscedasticity by applying different specifi cations of GARCH models (16 models as can be seen from Table 4) followed by looking for signifi cant parameters and low information criteria


(minimum Akaike Information Criterion). All models are estimated using the maximum likelihood method under the assumption of several distributions of the innovation terms such as: Normal (Gaussian) distribution, Student’s t distribution, Generalized Error distribution (GED), Student’s with fi xed df. Distribution, and GED with fi xed parameter distribution. The predominant models turned out to be EGARCH and PARCH models, but the empirical results point out that the best model for estimating daily returns of EUR/RON exchange rate is EGARCH(2,1) with Asymmetric order 2 under the assumption of Student’s t distributed innovation terms (having the minimum AIC, which is 0.787957). This can be explained on the one hand by the fact that the volatility reacts asymmetrically to the good and bad news and on the other hand by the fact that in case of EGARCH model, the restriction regarding the positivity of the conditional variance is automatically satisfi ed. The presence of leverage effect in the returns of EUR/RON exchange rate is confi rmed by the non-zero asymmetry coeffi cients and . Thus, a negative asymmetry coeffi cient indicates an asymmetric response for positive returns in the conditional variance equation, while a positive asymmetry coeffi cient indicates that bad news leads to increased volatility. Moreover, volatility persistence reveals a slowly decreasing of the rises in the conditional variance due to shocks given the value of the b parameter of 0.993305, and the ARCH-LM Test indicates that there is no ARCH effect left in the innovations - so the conditional variance equation found is well specifi ed.

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Formal Education in the European Union and Its Impact on the Macroeconomic Development Sandra TEODORESCU ([email protected])”Nicolae Titulescu” University

ABSTRACT This paper focuses on various statistical methods to analyze the impact of formal education on the macroeconomic development in Romania and in other EU member states. Generally speaking, the research reveals two trends which are driven, on the one hand, by the need for increased investments in education that generates further benefi ts and revenue on the long time and contributes to social development, too, and, on the other hand, by the need for quality education, since knowledge plays a key role in the modern society, leading to growth and prosperity. The study begins with the presentation of international developments and challenges in today’s world, especially in the education sector. In order to analyze the relationship between the economic and the educational indicators provided by EURO-STAT and to focus on developments in certain countries, we used data for 28 countries, i.e. 27 EU member states and the EU average, during 2001-2015. The study uses two statistical methods, i.e. the exploratory method (Principal Components Analysis) and the inferential method (multiple regression). Performing PCA, we came to the conclu-sion that gross domestic product is strongly infl uenced by total public expenditure on education and employment rates of tertiary graduates. Keywords: formal education, economic growth, exploratory statistical meth-od, inferential method, Principal Components Analysis JEL Classifi cation: C38 , O15, O47

1. INTRODUCTION Given the international context in today’s world, i.e. the second decade of the 21st century, the following relevant assumptions can be issued: 1. The economic cycle is defi ned by recurrent crises and growth,

which often has a dramatic effect on national living standards. 2. Political uncertainty has deepened, posing a major challenge. Thus,

in the past few years, the confl icts in the Middle East have intensifi ed, and the negative impact of the “Arab Spring” phenomenon has been felt. Radicalism has grown in the Islamic world, triggering immediate consequences, such as increasing terrorism in the world, wartime migration and economic migration as well.


3. As a result, the European Union has witnessed the rise of populism, while radical, anti-democratic and anti-European movements seem to be ready to take power.

4. Countries that have recently joined the European Union, following the fall of Communism, are facing complex challenges, which have revealed that democracy and prosperity could hardly be achieved unless sustained efforts are undertaken on the long term, implying a change both in mental patterns and in attitude, despite the structural reforms implemented across Europe.

This short overview refers to key issues and complex challenges we face in today’s world. As a result, adequate solutions should be identifi ed to cope with such challenges. The strategies adopted by the European Union in the 21st century contain major guidelines which could offer us a solution, namely providing universal access to education and equal opportunities, in order to ensure sustainable development worldwide, reduce inequality and poverty, and spread knowledge. Reliable surveys drafted by OECD (“Education at a Glance”, 2011) show that the net public return on an investment in tertiary education is 91,036 dollars per year, not to mention the new jobs created and the economic development fueled by innovation. On the other hand, dramatic fi gures refl ect low education levels: high school dropout rates, the lack of skilled workforce, including low literacy rates, i.e. 20% of the European workforce, and poor access to technology, i.e. 25% (”Education for economic growth and inclusion”, European Council). The need to improve education is a must, not just a luxury or a caprice, since it is essential for achieving economic growth and social inclusion, promoting a healthy state and the active involvement of civil society in the decision-making process, reducing crime and violence, and last, but not least, increasing life expectancy rates. In addition, the constant increase in the number of higher education graduates that could identify adequate solutions in today’s changing world sets up the basis for solving key issues and brings about social equity. In the past 15 years, the meetings of EU ministers of education focused on efforts to draft a comprehensive reform strategy, to be implemented by member states, the European offi cials repeatedly stressing the need to ensure a signifi cant amount of funding to states for education in order to reduce school dropout rates, improve the quality of education, and develop skilled workforce. This would also help decrease poverty and reduce social exclusion.


Recent research reveals two dominant trends: on the one hand, investments in education have increased since the beginning of the century, and, on the other hand, despite this positive development, which has varied across Europe, there is room for further improvement. Although geographic criteria is irrelevant, small North and South European countries top the list of states by spending on education (% of GDP), as follows: Ireland – 7.9%, Denmark – 7.8%, and Cyprus – 7.2%. Central, South-East and South European countries ranked the lowest in terms of education expenditure, i.e. Slovakia – 4.1%, Greece and Romania – 4.4%, each, and Bulgaria – 3.6%. We all know very well the situation in our country, that’s why I’ll only mention that, despite gradual annual increase, spending on education has failed to reach the 6% target set in the 1995 Education Law. Europe 2020 strategy elaborated by Brussels show that sustained efforts have been undertaken to improve the situation in this sector. The document defi nes top priorities and goals in the fi eld of education and training, for the next decade (2011-2020). A halfway report on the implementation of the Strategic framework for European cooperation in education and training was drafted in 2015 to assess the progress achieved and set new priorities in 6 key areas, namely: the quality of learning outcomes to be stimulated in a lifetime perspective, fostering inclusion and equality, developing digital skills, providing support to trainers, ensuring validation and recognition of skills and qualifi cations, as well as effective investment in quality education and training. At the same time, the European Commission has recently submitted its Annual Growth Survey 2016 to the Council, kicking-off the 2016 European Semester. The document sets out the economic and social policy priorities and urges EU countries to re-launch investment and focus on innovation, increase competitiveness and reduce unemployment (”Education for Economic Growth and Inclusion”, European Council). In 2015, the European Council adopted new guidelines to reduce school dropout rates, inviting member states and the European Commission to increase funding to that end. In addition, amid the fl ow of migrants to Europe, in the summer of 2015, the Council shifted attention to key issues, such as language learning by migrants and their families, migration skills assessment, as well as quality education and training to ensure diversity in schools.

2. LITERATURE REVIEW

The standard method of estimating the effect of education on economic growth is to estimate cross-country growth regressions where average annual growth in GDP per capita over several decades is expressed as a function


of measures of schooling and a set of other variables deemed important for economic growth. Regarding literature review, one of the promoters of the role of education in economics is Robert Barro. Following the classical contributions by (Barro,1991) and (Barro,1996) a vast early literature of cross-country growth regressions tended to fi nd a signifi cant positive association between quantitative measures of schooling and economic growth. În another work of (Barro, 1999) the schooling quality infl uence, using test scores, over economic growth, is measured. The study (Hanushek and Kimko, 2000) concludes that the results in mathematics and science, in 31 countries, are strongly correlated with indicators of economic growth. In (Sala-i-Martin et al, 2004) primary schooling turns out to be the most robust infl uence factor on growth in GDP per capita in 1960-1996 in the extensive robustness analysis of 67 explanatory variables in growth regressions on a sample of 88 countries. (Khattak and Khan, 2012) investigates the contribution of education on economic growth in Pakistan. To this end, the author used as Ordinary Least Squares estimation techniques and Johansen Cointegration test. The study shows that elementary as well secondary education contributes to real GDP per capita in Pakistan. In (Ciucu and Dragoescu, 2014) the infl uence of primary, secondary and tertiary education over the GDP growth was analized for Bulgaria, Czech Republic and the Netherlands, using regression models.

3. METHODOLOGY

The specifi c, educational indicators used in this paper are the predictors, i.e.: 1) School expectancy – SE 2) Total public expenditure on education- PEE 3) At least upper secondary educational attainment, age group 20-24

years - % - USEA 4) Tertiary educational attainment, age group 30-34 years- TEA 5) Employment rates of recent graduates - % - ERRG 6) Employment by educational attainment level, annual data, age

class-15-64 years, tertiary education - EEAL 7) Population by educational attainment level, sex and age -% -PEAL The broadest indicator of economic output and growth is the Gross Domestic Product or GDP, expressed in million of Euros, which represents the


dependent variable. To illustrate the impact of education on the long term, the relationship between variables is considered as asynchronous (for example, there is a 4-year gap between GDP and PEE). To analyze the impact of education, statistical data provided by EUROSTAT are processed by STATISTICA software, following logarithmic transformations. In order to analyze the relationship between the economic and educational indicators in EU member states, I resorted to an exploratory, multidimensional scaling method, i.e. Principal Components Analysis or PCA. The study uses also a statistical method, i.e. the inferential method, multiple regression estimation. As you know, in multiple regression, main source in β-coeffi cient is represented by the redundancy of the predictors. In statistical analysis, it is revealed by the strong correlation between explanatory variables. Regression coeffi cients get affected by the strong correlation between the predictors, i.e. the estimation Ey, will be achieved with signifi cant errors, although R2 is close to 1. Ridge regression helps us get stable and accurate coeffi cients, as it follows, b(k)=(X'X + kI)-1X'y, where k is a positive constant to be determined.

4. EMPIRICAL RESEARCH AND COMMENTS

In order to analyze the relationship between economic and educational indicators as well as the developments and trends in countries by average growth, I report a study of 11 groups of 28 individuals, i.e. 27 EU member states and, respectively, the EU average. The cases used in analysis are assigned values recorded during 2001-2011 (actually, the period analyzed is 2001-2015, showing a 4-year gap between values), i.e. 2464 log-transformations are applied for further PCA analysis. We use: • active variables (which participate to the construction of the factorial

axes): SEA; PEE; USEA; TEA; ERRG; EEAL; PEAL; • supplementary variable (which does not participate to the construction

of the factorial axes but is used for cross-validation): GDP ; • The countries were grouped, according to the year, into active and

supplementary cases. Active cases are the EU countries with values assigned to variables in 2001 - the starting year for this study. The rest of the cases covered for further observation and analysis until 2015, as compared to 2001, are supplementary cases.


The situation in EU member states in 2001 To get the dimension of the projective space and where the relationship between variables will be more easier to observe, we can examine the Eigenvalues, resulting from the diagonalized correlation matrix of the active variables (Table 2.1). Eigenvalues of the correlation matrix of the active variables play an important role in computing the principal components. In the eigenvalues table, the fi rst two dimensions offer a quality of representation, in the new space, of 68,04%. Thus, the projection will be the factor plane (the subspace of 2 dimensions which we are looking for is spanned by the fi rst 2 eigenvectors of the matrix A associated with the largest eigenvalues) and 68,04% of cumulative variance (explained) can be attributed to the number of factors.

Eigenvalues of correlation matrixTable 2.1

Eigenvalues of correlation matrix, and related statistics. Active variables only Include condition: Cod_1=1

Eigenvalue % Total - variance Cumulative - Eigenvalue Cumulative - %

1 2.848527 40.69324 2.848527 40.69322 1.914830 27.35472 4.763357 68.04803 1.247682 17.82403 6.011039 85.87204 0.530896 7.58423 6.541936 93.45625 0.372439 5.32056 6.914375 98.77686 0.064669 0.92384 6.979044 99.70067 0.020956 0.29937 7.000000 100.0000

Data source: EUROSTAT database, processed by author with Statistica software According to the methodology used in this study, the role of PCA is to illustrate the relationship between variables (economic and educational indicators), groups of individuals (countries) and corresponding developments. As a result, we analyze Table 2.2, which shows the factor coordinates referred to as “factor loadings”. This further implies that the factor coordinates of a variable are the correlations between the variable and the factor axes. There is a strong negative correlation between the fi rst factor and PEE and EEAL variables, i.e. the fi rst factor is a linear combination of these two variables that are most correlated with it. Similar, the second is a linear combination between TEA and PEAL variables.


Factor-variable correlationsTable 2.2.

Factor-variable correlations (factor loadings) Active and Supplementary variables *Supplementary variable Include condition: Cod_1=1

Factor 1 Factor 2SE -0.800131 -0.099922

PEE -0.737424 -0.597408USEA -0.159949 0.023473TEA -0.713525 0.609765

ERRG -0.155623 0.659506EEAL -0.734255 -0.629784PEAL -0.752644 0.586524*GDP -0.742212 -0.528789

Data source: EUROSTAT database, processed by author with Statistica software

Projection of the variables on the factor plane Graph 2.1

Projection of the v ariables on the f actor-plane ( 1 x 2)

Activ e and Supplementary v ariables

*Supplementary v ariable

Include condition: Cod_1=1

Activ e Suppl.

SE

PEE

USEA

TEA ERRG

EEAL

PEAL

*GDP

-1.0 -0.5 0.0 0.5 1.0

Factor 1 : 40,69%

-1.0

-0.5

0.0

0.5

1.0

Fac

tor

2 :

27,3

5%

SE

PEE

USEA

TEA ERRG

EEAL

PEAL

*GDP

Data source: EUROSTAT database, graphical representation by author

The variable representation onto factor plane is made in Graph 2.1. According to the neighborhoods system between the two variables, the strongly correlated variables are very close to each other and determine, essentially, two factors. Approaching GDP by PEE and EEAL suggests that GDP is strongly infl uenced by PEE and EEAL, so we resort to multiple regression.


Projection of the cases on the factor plane. Cases with sum of cosine square>=0.5

Graph 2.2Active cases variable: Cod_1Include condition: Cod_1=1

Active

RO_01

DE_01

IT_01

HU_01

PL_01

UK_01BE_01

DK_01 IE_01

FR_01

CY_01

LV_01

LT_01

LU_01

MT_01

NL_01

SK_01

SE_01

-5 -4 -3 -2 -1 0 1 2 3 4 5 6

Factor 1: 40,69%

-5

-4

-3

-2

-1

0

1

2

3

4

5

Fact

or 2

: 27,

35%

RO_01

DE_01

IT_01

HU_01

PL_01

UK_01BE_01

DK_01 IE_01

FR_01

CY_01

LV_01

LT_01

LU_01

MT_01

NL_01

SK_01

SE_01


For the quality of representation, Graph 2.2 shows the dynamics of the EU member states or individuals which, in 2001, formed an angle that was less than 45 degrees on the factor plane (i.e. cosine square is greater than 0.5), namely: Romania, Hungary, Slovakia, Italy, Poland, Germany, France, Great Britain, Sweden, Belgium, Netherlands, Denmark, Ireland, Lithuania, Cyprus, Latvia, Malta, and Luxembourg. The graph 2.2. shows that countries in the second and third quadrants have the highest GDP, PEE, EEAL, TEA, and PEAL values, i.e. countries with high quality education, such as Denmark, Sweden, Netherlands, Belgium, and Great Britain. Countries in the fi rst and fourth quadrants, such as Romania, Bulgaria Slovakia, Hungary, Greece, Cyprus or Malta, ranked low.


Dynamics of EU member states during 2001-2015 Graph 2.3 illustrates a special case, i.e. the projection of a few EU member states observed during 2001-2015 and active variables in 2001, which form an angle that is less than 45 degrees on the factor plane.

Projection of the cases on the factor plane Graph 2.3

Projection of the cases on the factor-plane ( 1 x 2)Cases with sum of cosine square >= ,50

Active cases variable: Cod_1Include condition: Cod_2=1

Active Suppl.

RO_01

DE_01

IT_01

HU_01

PL_01

UK_01

BE_01

DK_01 IE_01

FR_01

CY_01

LV_01

LT_01

LU_01

MT_01

NL_01

SK_01

SE_01

UE_01

RO_02UE_02

DE_02

IT_02

UK_02FR_02

SE_02

RO_03

UE_03

DE_03

IT_03

UK_03 FR_03

SE_03

RO_04

UE_04

DE_04

IT_04

UK_04 FR_04

SE_04

RO_05

UE_05

DE_05

IT_05

UK_05 FR_05

SE_05

UE_06

DE_06

IT_06

UK_06FR_06

SE_06

RO_07

UE_07

DE_07

IT_07

UK_07FR_07

SE_07

UE_08

DE_08

IT_08

UK_08FR_08

SE_08

RO_09UE_09

DE_09

IT_09

UK_09FR_09

SE_09

RO_10UE_10

DE_10

IT_10

HU_10UK_10

FR_10

SE_10

RO_11

UE_11

DE_11

IT_11

HU_11UK_11

FR_11

SE_11

-4 -3 -2 -1 0 1 2 3 4

Factor 1: 40,69%

-4

-3

-2

-1

0

1

2

3

Fact

or 2

: 27,

35%

RO_01

DE_01

IT_01

HU_01

PL_01

UK_01

BE_01

DK_01 IE_01

FR_01

CY_01

LV_01

LT_01

LU_01

MT_01

NL_01

SK_01

SE_01

UE_01

RO_02UE_02

DE_02

IT_02

UK_02FR_02

SE_02

RO_03

UE_03

DE_03

IT_03

UK_03 FR_03

SE_03

RO_04

UE_04

DE_04

IT_04

UK_04 FR_04

SE_04

RO_05

UE_05

DE_05

IT_05

UK_05 FR_05

SE_05

UE_06

DE_06

IT_06

UK_06FR_06

SE_06

RO_07

UE_07

DE_07

IT_07

UK_07FR_07

SE_07

UE_08

DE_08

IT_08

UK_08FR_08

SE_08

RO_09UE_09

DE_09

IT_09

UK_09FR_09

SE_09

RO_10UE_10

DE_10

IT_10

HU_10UK_10

FR_10

SE_10

RO_11

UE_11

DE_11

IT_11

HU_11UK_11

FR_11

SE_11


One can easily notice that countries in the second and third quadrants have the highest PEE, EEAL, PEAL and TEA values, namely the EU, Great Britain, Sweden, Germany, and France. Although it is placed on the third quadrant, Italy is an outlier, and therefore, its position should be explained. To perform a comprehensive analysis and a better visibility of individuals clouds, I will focus on the situation in EU member states with opposite GDP, and, respectively, educational values. As a result, I will perform a separate analysis for each case, including, of course, Romania, and its neighbors Hungary and Bulgaria. Given the current international context, European resources and work force strongly depend on political stability and the ability to identify


solutions to cope with challenges in today’s world, i.e. Brexit, terrorism, and widespread confl icts. One thing is clear: there are major gaps between industrialized, Western countries, and the former Communist states located in Eastern Europe. As for Romania, our country should strongly promote its Western orientation, i.e. strengthen cooperation with EU member states and increase its role in ensuring security and peace at the international and the European levels.

The EU Graph 2.4 shows that the European Union faced an upward trend during 2001-2015, see the third quadrant, with the highest PEE and EEAL values. We can draw two conclusions: the direction of GDP growth, by increasing total public expenditure on education and the employment by tertiary education, is indicated by the major economic powers of the continent. Although the EU member states have been trying to follow this example, despite their efforts, the gap still remains and will most likely remain on the short term.

Projection of the European Union, during 2001- 2015, on the factor plane

Graph 2.4

Cases with sum of cosine square >= ,50

Activ e cases v ariable: Cod_1


Activ e Suppl.

UE_01UE_02

UE_03UE_04

_

UE_05UE_06UE_07UE_08UE_09UE_10

UE_11

-4.0 -3.8 -3.6 -3.4 -3.2 -3.0 -2.8 -2.6 -2.4 -2.2

Factor 1: 40,69%

-2.8

-2.6

-2.4

-2.2

-2.0

-1.8

-1.6

-1.4

-1.2

-1.0

Fac

tor

2: 2

7,35

%

UE_01UE_02

UE_03UE_04

UE_05

DE_05

UE_06UE_07UE_08UE_09UE_10UE_11



Italy Italy, is an outlier, since despite its low PEE as a proportion of GDP and a high tertiary education leavers rate, as well as its diffi culties in entering to the labour market for highly-skilled people, which confi rm the conclusion drawn by EC in its report on Education and training 2015, it is nevertheless placed on the third quadrant. However, following the recent withdrawal of Great Britain from the EU, Italy will most likely become the third economic power in Europe, as recent negotiations aimed at reshaping the EU, carried out after Brexit by the German Chancellor, the French President, and Italian Prime Minister, do show.

Projection of Italy during 2001- 2015, on the factor plane Graph 2.5.

Cases with sum of cosine square >= 0,00

Activ e cases v ariable: Cod_1


Activ e Suppl.

IT_01

IT_02IT_03IT_04

IT_05

IT_06IT_07IT_08

IT_09

IT_10

IT_11

-1.2 -1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0

Factor 1: 40,69%

-4.0

-3.8

-3.6

-3.4

-3.2

-3.0

-2.8

-2.6

-2.4

-2.2

-2.0

Fac

tor

2: 2

7,35

%

IT_01

IT_02IT_03IT_04

IT_05

IT_06IT_07IT_08

IT_09

IT_10

IT_11


Hungary and Bulgaria Although our neighbors, Bulgaria and Hungary, have a parallel trajectory following the EU model, Hungary has higher PEE and EEAL as compared to Bulgaria. While in Bulgaria stands a little relevance of tertiary education to the labor market and low levels of PEE, in Hungary, higher technical education recorded numerous leavers and PEE remains at one of the lowest levels in the EU. Nevertheless, Hungary experiences high school


dropout rates, and its spending on education is among the lowest in the EU. This fi nding confi rms the conclusion drawn by EC in its report on Education and training 2015.

Projection of Hungary and Bulgaria, during 2001- 2015, on the factor plane

Graph 2.6

Cases with sum of cosine square >= 0,00Active cases variable: Cod_1Include condition: Cod_2=1

Active Suppl.

BG_01

HU_01

LV_01

_

AT_01

PT_01

SI_01

RO_04

BG_06

HU_06

BG_11HU_11

-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8

Factor 1: 40,69%

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

1.2

Fact

or 2

: 27,

35%

BG_01

HU_01

LV_01

LT_01

AT_01

PT_01

SI_01

RO_04

BG_06

HU_06

BG_11HU_11


Sweden, Great Britain, France and Germany Graph 2.7 shows the projection of Germany and Sweden, which have quite a parallel trajectory, being placed in the second and third quadrants. Although it has high PEE, France stagnates and faces major challenges, i.e. migrants from the former French colonies. As for Great Britain, the graph shows a major decline in PEE, which explains the discontent of the British at the work force migration within the EU that has led to Brexit. Germany is the only European power which ranks highest.


Projection of Sweden, Great Britain, France and Germany, during 2001- 2015, on the factor plane

Graph 2.7

Cases with sum of cosine square >= 0,00Active cases variable: Cod_1Include condition: Cod_2=1

Active Suppl.

DE_01

ES_01UK_01

BE_01

FR_01

NL_01

SE_01

DE_06

UK_06

FR_06

SE_06

DE_11

UK_11

FR_11

SE_11

-3.4 -3.2 -3.0 -2.8 -2.6 -2.4 -2.2 -2.0 -1.8 -1.6

Factor 1: 40,69%

-1.2-1.0-0.8-0.6-0.4-0.20.00.20.40.60.81.0

Fact

or 2

: 27,

35%

DE_01

ES_01UK_01

BE_01

FR_01

NL_01

SE_01

DE_06

UK_06

FR_06

SE_06

DE_11

UK_11

FR_11

SE_11


Romania Graph 2.8 shows Romania has a pronounced convergence trajectory to the origin of axes (the centroid of data cloud) during 2001 until 2004, and, respectively, to approach the countries with average values during 2005-2009, and, subsequently, to growing faster and evolve on a parallel trajectory. Romania has high TEA, EEAL and PEE, which have triggered GDP growth. The upward trend is experienced by European powers, such as Germany, France, and Great Britain.


Projection of Romania, during 2001- 2015, on the factor plane Graph 2.8.

Cases with sum of cosine square >= ,50Active cases variable: Cod_1Include condition: Cod_2=1

Active Suppl.

RO_01

HU_01

PL_01

SK_01

RO_02

RO_03

RO_04

RO_05RO_07

RO_09RO_10

RO_11

-1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5

Factor 1: 40,69%

-2.4-2.2-2.0-1.8-1.6-1.4-1.2-1.0-0.8-0.6-0.4-0.20.0

Fact

or 2

: 27,

35%

RO_01

HU_01

PL_01

SK_01

RO_02

RO_03

RO_04

RO_05RO_07

RO_09RO_10

RO_11


CorrelationsTable 2.3

Correlations (Date UE) Marked correlations are signifi cant at p < .05000 N=268 (Casewise deletion of missing data) Exclude condition: Cod_1>100

GDP SE PEE USEA TEA ERRG EEAL PEALGDP 1.00 0.33 0.99 -0.18 0.12 -0.08 0.94 0.14SE 0.33 1.00 0.38 0.02 0.35 -0.01 0.38 0.34

PEE 0.99 0.38 1.00 -0.15 0.13 -0.12 0.96 0.14USEA -0.18 0.02 -0.15 1.00 0.09 -0.15 -0.08 0.12TEA 0.12 0.35 0.13 0.09 1.00 0.11 0.14 0.95

ERRG -0.08 -0.01 -0.12 -0.15 0.11 1.00 -0.19 0.12EEAL 0.94 0.38 0.96 -0.08 0.14 -0.19 1.00 0.17PEAL 0.14 0.34 0.14 0.12 0.95 0.12 0.17 1.00

Data source: EUROSTAT database, processed by author with Statistica software


Correlations between variables, histograms, scatterplotsGraph 2.9.

SE

PEE

USEA

TEA

ERRG

EEAL

PEAL

GDP

PCA clearly shows that GDP is infl uenced by education expenditure and EEAL. The same offers us, the fi gure 2.9, where on one hand we see, from examining the histograms, that the normality or close to it have only variables PEE, EEAL and GDP. On the other hand, considering the variable GDP on OY and PEE respectively EEAL, on OX is noted that these are the only Scatterplots showing a linear regression. Regression analysis can be performed based on the above-mentioned conclusions, i.e. calculating regression coeffi cients and defi ning the quality of the model. Thus, we get the standardized Ridge regression equation: (2.9)


To see how independent variables contribute to the GDP prediction we analyze the following non-standardized or standardized coeffi cients:

Ridge regression summaryTable 2.4

Ridge Regression Summary for Dependent Variable: PIB (Date UE) l=.10000 R= .95375675 R²= .90965193 Adjusted R²= .90898516 F(2,271)=1364.3 p100Beta Std.Err. - of Beta B Std.Err. - of B t(271) p-level

Intercept 3.427957 0.173833 19.71986 0.000000PEE 0.646684 0.035710 0.696523 0.038462 18.10923 0.000000

EEAL 0.288343 0.035710 0.329859 0.040852 8.07452 0.000000Data source: EUROSTAT database, processed by author with Statistica software

Adjusted quality indicatorsTable 2.5

Summary Statistics; DV: GDP (Date UE) Exclude condition: Cod_1>100Value

Multiple R 0.954Multiple R² 0.910Adjusted R² 0.909

F(2,271) 1364.255p 0.000

Std.Err. of Estimate 0.508Data source: EUROSTAT database, processed by author with Statistica software

High R squared value (0.95) – where R is the coeffi cient of multiple correlation, shows the strong correlation between PEE and GDP, on the one hand, and EEAL and GDP on the other hand, i.e. they have a strong infl uence on GDP. Multiple shows that PEE and EEAL infl uences economic growth, i.e. 91%, and the rest of 9% - other factors. Thus, we can further elaborate and predict GDP values.

5. CONCLUSIONS

To perform a comprehensive analysis, I took into consideration an exploratory approach, i.e. factor analysis, that is viewed as a data-reduction technique as it reduces the number of selected educational indicators which are strongly correlated, in order to conduct multiple regression. The exploratory analysis and inferential statistical methods used in this study have shown us that GDP is strongly infl uenced by education expenditure and EEAL, and that is one of the main conclusions of my research.


Also, the review on the dynamics of the EU member states during 2001-2015 has led to clear fi ndings shortly presented below. Despite major gaps within the EU, European countries face the same challenges and have to cope with them in order to ensure prosperity and comply with democratic standards. It seems that there is only one solution, i.e. to perform an accurate assessment of the situation, apply coherent reforms, and strengthen cooperation, based on mutual benefi ts. Romania should increase its role within the EU, and capitalize upon its resources, encouraging sustainable development, improving its situation, and reducing its vulnerabilities. To that end, a key role is played by quality education and training in order to assert traditional values and make our dream come true.

Acknowledgement This paper has been developed within the period of sustainability of the project entitled “Horizon 2020 - Doctoral and Postdoctoral Studies: Promoting the National Interest through Excellence, Competitiveness and Responsibility in the Field of Romanian Fundamental and Applied Scientifi c Research”, contract number POSDRU/159/1.5/S/140106. This project is co-fi nanced by European Social Fund through Sectoral Operational Programme for Human Resources Development 2007-2013. Investing in people!

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Documents

Romanian Statistical Review - INSSE · Prof. Stelian Stancu PhD. Bucharest University of Economic Studies FORMAL EDUCATION IN THE EUROPEAN UNION AND ITS IMPACT ON THE MACROECONOMIC