statistical-econometric models used to study the ... · statistical - econometric models 7 included...

Institutul Na�ional Societatea Român� de Statistic� de Statistic�

Prof. Constantin Anghelache PhD.1,2

(coordonator) Prof. Dan Cruceru PhD.1 Prof. Gabriela Anghelache PhD.2

Prof. Constantin Mitru� PhD.2 Prof. Vergil Voineagu PhD.2Prof. Radu Titus Marinescu PhD.1 Prof. Mario G.R. Pagliacci PhD.3

Prof. Ioan Partachi PhD.4 Assoc.prof. Alexandru Manole PhD.1Assoc. prof. Aurelian Diaconu PhD.1 Lecturer M�d�lina Anghel PhD.1Assoc. prof. Emanuela Ionescu PhD.1 Ligia Prodan PhD. student 2

Alexandru Ursache PhD. student 2 Marius Popovici PhD. Student2

Andreea Gabriela Baltac PhD. student 1,2 Zoica Dinc�� (Nicola) PhD. student 1,2

Bogdan Dragomir PhD. student 2 Daniel Dumitrescu PhD. student 2

Cristina Sacal� PhD. student 2 Diana Valentina Soare PhD.student 2

Emilia Stanciu PhD. Student2 Georgeta Barda�u PhD. Student2

Ec. Ionu� Negoi��5 Adina Mihaela Dinu PhD. Student2

STATISTICAL-ECONOMETRIC MODELS USED TO STUDY THE MACROECONOMIC

CORRELATIONS

ROMANIAN STATISTICAL REVIEW - SUPPLEMENT -

December 2014

1 „Artifex” University of Bucharest2 Bucharest University of Economic Studies 3 Universita degli Studi di Perugia 4 Academy of Economic Studies of Moldavia5 Manager

Autorii poart� întreaga r�spundere pentru con�inutul materialelor publicate, revista �i Societatea Român�

de Statistic� fiind exonerate de orice r�spundere.

ISSN 2359-8972

TABLE OF CONTENTS

Introduction .................................................................................................. 5

Chapter 1. Statistical-Econometric Models used in Economic Analysis ................................................................................... 9

Chapter 2. Testing of the Significance of the Regression Model ........... 16

Chapter 3. Econometric models utilized for the portfolio selection ...... 19

Chapter 4. The Verification of the Residual Normality and the Prediction of the Regression Model .......................................................... 22

Chapter 5. Elements concerning the Use of Multiple Regression Models ...................................................................................... 27

Chapter 6. Macroeconomic Correlations Analyzed Multiple Regression Model ...................................................................................... 30

Chapter 7. Correlation between Production and Labor based on Regression Model ...................................................................................... 36

Chapter 8. Multiple Regression Used in Macro-economic Analysis ....................................................................................................... 40

Chapter 9. Linear Regression Model ...................................................... 48

Chapter 10. Models used in Macroeconomic Analyses .......................... 53

Chapter 11. Econometric Models used in Macro-economic Analysis ....................................................................................................... 58

Statistical - Econometric Models �4

Chapter 12. Index of Population Consumption Prices ........................... 65

Chapter 13. The monetary evolution, placements and resources ......... 72

References ................................................................................................... 81

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�In the contents of this paper, there are presented the results of

the research developed by a group of teachers and researchers on the subject of identifying the statistical-econometrical models used in the study of macroeconomic correlations. The research took into account the solving of the issue within the framework of a research contract closed with the foreign business environment, preoccupied to know the social-economic evolution in our country. The models identified are used in the studies aimed towards the interest of the foreign partner. At the same time, some aspects of the indicators related to the macroeconomic development of Romania during the last period were outlined. The main aspects of this work were disseminated by publishing articles and presenting scientific papers at international scientific sessions. A series of articles are to be published in nationally or internationally recognized journals, registered at least as B+ or indexed in international databases. The final elaboration of the work is based on the material, with research report contents for the specified contract, which includes elements from the disseminated articles, by mentioning, in each case, the persons from the research team who have published or presented scientific papers. Also, the references include the main theoretical or research materials taken into account as bases of research. There were used data and conclusions drawn from reunions on the subject of using statistical-econometric models in economic studies. Elements of interest are used in the synthesized materials. The emphasis was put on the capitalization of data related to Romania. In this study, we consider important the following aspects:

• Statistical-Econometric Models used in Economic Analysis (Introductory aspects regarding statistical – econometric models, Some aspects regarding the regression model, Elements regarding linearization models for the non-linear models, Some aspects of the hyperbolic and parabolic model);


•• Testing of the Significance of the Regression Model (the dispersion of the residual variable, Testing the null hypothesis, Defining the interval of confidence);

• Econometric models utilized for the portfolio selection • The Verification of the Residual Normality and the

Prediction of the Regression Model (Aspects regarding the verification of residual normality, Some aspects concerning the prediction through the regression model);

• Elements concerning the Use of Multiple Regression Models (Some theoretical aspects regarding multiple regression model, Aspects regarding determination in multiple regression, Akaike criterion as base in econometric models);

• Macroeconomic Correlations Analyzed Multiple Regression Model (Theoretical Aspects, Analysis of correlation between Total Production and Services);

• Correlation between Production and Labor based on Regression Model (Theoretical Aspects, The correlation between Production and Labor);

• Multiple Regression Used in Macro-economic Analysis; • Linear Regression Model; • Models used in Macroeconomic Analyses; • Econometric Models used in Macro-economic Analysis

(Characteristics of the regression model, The Linear and Non-displaced Estimator, Additional properties of the model, Inference in multiple regression

• Index of Population Consumption Prices); • The monetary evolution, placements and resources. Conclusions that were reached are mentioned in each

chapter/subchapter of the work. Being a wide array of problems, we pursued to synthesize as much as possible, so the research is to be further pursued and expanded. Some results of the research were presented and debated in the sessions of the „Octav Onicescu” Scientific Seminary. The debates emphasized items of interest, adequately taken and used in the work. Many elements were also

Statistical - Econometric Models� 7

included in papers presented at international scientific symposiums in Bucharest or other academic centers.

The final form of the presentations in the work was realized by the coordinator of the collective of specialists. The bibliographic reference included studies and materials used in the research, which can help the persons interested to expand their studies and argument some viewpoints presented in the paper.

Coordinator, Prof. Constantin Anghelache PhD.

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• Introductory aspects regarding statistical – econometric models∗

Regression and correlation method indicates how the characteristic result of „Y” changes in conditions where the characteristics of values „X” changes. The goal of regression is to identify the mathematical relationship that exist between two variables1.

• Some aspects regarding the regression model Linear regression model involves the identification of variables

for defining specification for variable and model residuals; the context in which the regression model is used. Analysis of chronological (time) using a temporal function which, in essence, is also a regression, with a variable time (t).

This model is recommended when the points are located, that the cloud of points around a line.

This requires completion of the methods used for the estimation of the two parameters.

In defining the function of linear regression are consideredthe following hypotheses2:

- data series are not affected by the errors. ∗ Those aspects were also presented in the article Economic Analysis through the Use of Statistical – Econometric Models, published in Romanian Statistical Review - Supplement no. 4/2014, authors prof.. dr. Constantin Anghelache PhD, prof.. dr. Mario G.R. Pagliacci PhD, prof. Constantin Mitru� PhD 1 Anghelache, C. (coord., 2012) – „Modele statistico – econometrice de analiz�economic� – utilizarea modelelor în studiul economiei României”, Revista Român�de Statistic�, Supliment Noiembrie 2 Anghelache, C. (2013) – „Elemente de econometrie teoretic�”, Editura Artifex, Bucure�ti


- for each fixed value of the characteristic factorial, residual variable is zero, i.e. on average: ��

- the lack of correlation between residues expressed that the terms do not exhibit the phenomenon of covariance, which means the variable correlation hypothesis

- residuals with the independent, which means that � �� for any j, showing an increase in the value of the variable factorial does not automatically lead to an increase of the values of the variable. On the basis of the four assumptions define the linear

regression model through the function:�� , i = 1,..,n In the theoretical analysis, dependency of variables is

stochastic. Consideration of the residual variable within such a model is needed. Other factors that influence the score variable are grouped in the residual3.

Uni-factorial nonlinear models are linearized. A model of the form turns into a linear model by logarithm the two terms of the above equality, resulting in linear function.

Sometimes, for estimating parameters using other techniques of estimation, which cannot be incremental transformations, linear estimation of parameters is made by numerical methods.

Linear regression model is based on the series of data for the two features, represented by vectors „x” (the variable factor) and „y” (variable score).

The evolution of the economic phenomena does not develop according linear trajectories but can take non-linear trajectories as well4. Thus, if the dependence between two variables is shown by the non-linear model of regression �� , through logarithmic procedure, we get the regression linear model �� 3 Fernandez-Villaverde J. & Rubio-Ramirez J. (2009) – “Two Books on the New Macroeconometrics”, Taylor and Francis Journals, Econometric Reviews4 Anghelache, C. (coord., 2012) – „Modele statistico – econometrice de analiz�economic� – utilizarea modelelor în studiul economiei României”, Revista Român�de Statistic�, Supliment Noiembrie 2012


When estimating a regression non-linear model we proceed as follows:

− we estimate the parameters applying the method of the smallest squares;

− through transformations, we linearize the non-linear function and then we estimate the parameters applying the method of the smallest squares;

− we establish the parameters through numerical methods. •• Elements regarding linearization models for the non-

linear models We submit the semi-logarithmic and the double logarithmic

models which can be linearized5: − The logarithmic model can be either without free term or with

free term. − The free term model (log-log) is of the dependence form; − The exponential equation maight use the model: ��

In this model � � !" and � � . Depending of the sign of the parameter b the properties of the resulting characteristic are set up.

Applying the logarithms the double logarithmic model results6�� #$ � �� % � & � �� '$ � ��($Using the substitutions,the regression linear model becomes: #$ � �" � ��" � ��"− The free term model (log-log) holds, in addition, a free

term and shows under the following form: #$ � �) � � � �� In order to estimate the parameters, one of the following two

methods applies7:

5 Anghel M.G. (2010) – Utilizarea modelelor econometrice în analizele economice, Simpozionul �tiin�ific interna�ional „Necesitatea reformei economico – sociale a României în contextul crizei globale”, Editura Artifex, Bucure�ti 6 Anghelache, C. (2013) – „Elemente de econometrie teoretic�”, Editura Artifex, Bucure�ti


- when a value of the free term of the model is specified, then, using the notations *� � �� + �) and ,� � �, we get the regression model�� . In this respect, parameters are estimated according to the case of the double logarithmic model;

- then we estimate the three parameters of the model through numerical models. The model might be transformed into a linear one using the development of the Taylor series.

The interpretations are achieved in the context of using the model �� . For this model we must consider:

- if � < 0, the function log-log is down warding as against the factorial characteristic. In this case, -./�01 �� 2�3 � �. In the situation of the free term model r, -./�01 �� 2�3 � �);

- if � > 0, the non-linear function is up warding and -./�01 �� 2�3 � 4;- irrespectively of the sign of the parameter �, this is equal

with the elasticity of the resulting variable, calculated in connection with the factorial variable: � � 5��5� 6 7 ��

- when the differential of second order is 89:�8��9 � ��2� +;3��<=, is results that: & � 2��;3, the analytic function is up warding and concave; � = 1, the regression model gets reduced to the simple linear model, without free term; � > 1, the function is up warding and convex .

− The exponential model is used when the points cloud resulting from the graphical representation of the series of values 2�� 3�>?�@AAAAA is directed along the curve of an exponential function8.

7 Anghelache, C. (2013) – „Elemente de econometrie teoretic�”, Editura Artifex, Bucure�ti 8 Dougherty, C. (2008) – “Introduction to econometrics. Fourth edition”, Oxford University Press


The exponential model, is defined through the relation: �� !"When the parameters of the exponential model are to be

estimated through data transformations by logarithms, there must be considered that:

- by logarithms applied to the equality terms we get the regression linear model: -B �� -B � � -B� � � � -B��

The model becomes a linear by the substitution. - we estimate the parameters of the regression linear model,

using the smallest squares method; we get the estimators �C"and �D";

- the estimators of the parameters of the regression non-linear model are established: �C � EFG" and �D � E�H"

Then, we calculate the values adjusted on the basis of the estimates regression non-linear model: �C� � �C��D�� . � ;� BAAAAA

In order to interpret the meaning of the parameter � we take into account that � � ;� � 5�5

In the case of the exponential model, there are the following situations:

- � is the rate of increasing or decreasing of the characteristic Y as against X;

- if � > 1, he evolution of the characteristic Y is up warding - if & � 2��;3, the characteristic Y records a decrease as

against the variable X; - the values of the characteristic Y are positive only and the

parameter a satisfies the positivity property.

•• Some aspects of the hyperbolic and parabolic model For example, the regression model is used also to study the

correlation between the unemployment rate and the inflation rate.


The value –�/� is the abscise of the point in which the graph crosses the Ox axis. The value corresponds to the minimum income allowing the acquisition of the requested product for consumption9. The reciprocal model has the equality: ��

The interpretation of the hyperbolic model parameters is: - We calculate the curve slope by the relation: 5��5� � +��=The function is down warding when the parameter � is positive

and up warding if � is negative. - Irrespectively of the sign of the parameter b, for the

hyperbolic model: �IJ�01 �23 � � The estimation of the parameters is done by following the stages:

- the parameters �, � are estimated through the smallest squares method. Out of the condition K 2�� +7�C + �D ?��3=� = minimum, we get the linear system of equations:

LMNMO B�C � �DP ;�

@�>? �P��@

�>?�CP ;�

@�>? � �DP ;�=

@�>? �P��

@�>? QMR

MS

From the linear system, we calculate the value of �C and �D . - then when determine adjusted values �C� � �C � �H��, and the

series of the adjusting errors.

9 Anghelache, C. (coord., 2012) – „Modele statistico – econometrice de analiz�economic� – utilizarea modelelor în studiul economiei României”, Revista Român�de Statistic�, Supliment Noiembrie


The parabolic model is used in the case that the characteristic rhythm of evolution follows a linear function, having the slope coefficient equal to the constant �. The points 2�� 3�>?�@AAAAA are placed around the curve described by a parabola10.

For example, the Laffer curve is represented in the form of a parabola and defines the relation between the government income and the taxation rate. We underline certain characteristics of the Laffer curve:

- The state income = y (taxation rate); - The Laffer curve is decomposed in two regions: one of

normal behavior, comprised between 0 and that level of the taxation rate (t%) where the state income is maximum; the region comprised between t% and 100% known as the inadmissible zone where, at an increase of the taxation rate, a corresponding increase of the state income is not achieved.

- Between the income out of the inflation taxation and the inflation rate there is a dependence of parabolic type. In this case, it is stated out that there is a level of the inflation up to which it is estimated that state increases its income after which, an increase of the inflation rate leads to the state income diminishing.

The regression parabolic model which is defined by the �� T � is �� T � �� = � ��Being a linear function as against the three parameters, �, � and

�, in order to estimate them the smallest squares method is utilized. It is required as a condition that the value of the expression is a K 2�� + TC + �D� + �C�=3=� minimum one, resulting a system of equations11.

10 Anghelache, C. (coord., 2012) – „Modele statistico – econometrice de analiz�economic� – utilizarea modelelor în studiul economiei României”, Revista Român�de Statistic�, Supliment Noiembrie 2012 11 Anghelache, C. (2013) – „Elemente de econometrie teoretic�”, Editura Artifex, Bucure�ti

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In submitting the two procedures applied to testing the hypotheses formulated on the parameters of the regression model, the following emphasizes are to be considered: - the estimators of the parameters of the regression linear model are of minimum dispersion; - if the parameters of the model are estimated by means of the least squares method, then the dispersion of the residual is estimated through the relation:

UAV= � ;B + WPE�=@�>?

- the residual variable is following up a normal repartition X2�� UAV=3. Starting from the properties of the estimators of the regression

linear model, the estimators %G and &Y are linear combinations of randomly variable normally distributed1.

• the dispersion of the residual variable is known. Considering the expressions of the two estimators, it is

resulting that these ones are meeting the two properties. • the dispersion of the residual variable is unknown.

In order to define the statistics used for testing the significance of the parameters of the regression linear models we have to keep in mind that:

- if � 0 X2��;3� . � ;� BAAAAA then ∗ Such aspects are also presented in the article Theoretical Aspects Concerning the Testing of the Significance of the Regression Model, Revista Român� de Statistic�– Supliment nr. 7/2014, autori prof. univ. dr. Constantin Anghelache, drd. Alexandru Ursache, drd. Bogdan Dragomir, drd. Georgeta Barda�u (Lixandru), drd. Marius Popovici 1 Anghel, M.G. (2014) – “Econometric Model Applied in the Analysis of the Correlation between Some of the Macroeconomic Variables”, Revista Român� de Statistic� – Supliment/Nr. 1


Z �P�= 0 [@=@�>?

- if � 0 X2�� U=3� . � ;� BAAAAA then

Z �P\�U]=@�>? 0 [@=

-- if � 0 X2��;3 and Z 0 ^_=, then

`Za 0 b_In terms of practical analysis, the dispersion of the residual

variable is not known. Taking into consideration the calculation relationship of the Student statistics and applying the three properties, the following results are obtained:

- for the coefficient of the slope of the regression line:In order to test H0: � � �C, with the alternative H0:7� c �C,, we

have to keep in mind the fact that: �C + �UCFG � dK 2� + e3=�2fGgf3UV � 2�C + �3U�UV hB + W 0 b@<=

- for the free term In order to test the null hypothesis H0: � � �D , with the alternative : H1: � c �D , we have to keep in mind the fact that: �D + �UC�H � ��D + ��

i;B � e=K 2� + e3=�jGk 0 b@<=

These two outcomes are useful for testing the significance and defining the intervals of confidence for the two parameters of the regression line2.

2 Manole, A. et. al. (2013) – “Conditional Probability and Econometric Models”, Romanian Statistical Review Supplement., Issue 1


• Testing the null hypothesis when there is an established significance threshold, if lFG<FmGfG l n bFo=p@<=, then the null hypothesis is rejected. This test is used in order to set up whether the linear dependence between the two characteristics is a significant one. In this case the testing goes for H0: a=0, with the alternative H1: � c �. The null hypothesis is rejected if l FGmGfGl n bFo=p@<=.

• Defining the interval of confidence: For a threshold of significance � established out of the Student repartition table the value bFo=p@<= is set up for n-2 degrees of liberty.

Each parameter of the regression model would be separately tested or a procedure of a simultaneous testing could be applied. As the two estimators,7�C and �D , are not independent alleatory variables, it is considered that the successive testing of the two parameters is not exactly correct. Therefore, the simultaneous testing of the two parameters is recommended. The utilisation of the regression model is giving very good results for the economic analyses. In practice, there is an issue to be considered, namely, in case there are various regression models which statistical significance has been checked up, which one should we apply to? We are interested to get close positions for the parameters estimated for the recorded data In case they are significantly daggering, we use the test „t” given by the relation: b � �C + �CqdUFG= � UFGr=

Then, we use the null hypothesis and finally we analyse the inequality: F > T1-�� -2)

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In order to make the choice of the regression function, the points (Rt, �it) for all the periods t are graphically represented, in the Cartesian of axis, the points (Rt, �it) for all the periods t. A points cloud is thus generated which stands at the basis of forming the dependence between the two variables. If these points aligned along a line, then the dependence between the two variables is a linear one: s � � � �t.s � �swhere:

- the parameter � is quantifying the component of the total yield of the independent equity as against the fluctuation of the index of the exogenous characteristic from the regression linear model;

- the parameter � is fixing the extent to which the alteration by one per cent of the index of the exogenous characteristic is generating the increase or the decrease of the equity yield;

- �t is representing the residual variable of the regression linear model, which quantifies the alleatory fluctuation of the equity yield under the influence of factors other than the recorded one.

- through the intermediary of this model, the factors acting on the equities yield are divided into two classes: macroeconomic factors, acting to a larger or a smaller extent on all the equities: the inflation rate of the economy, the performance indicators of the economic environment or financial markets etc. Out of these factors, the choice goes

∗ Aspects inserted in this chapter were described in the article The model of W.F. Sharpe and the model of the global regression utilized for the portfolio selectionRRS supplement no. 7/2014, prof. Constantin Anghelache PhD, lecturer M�d�lina Anghel PhD


to that one depending on which we want to define the regression linear model and microeconomic factors, acting on the yield of an equity or group of equities. These factors are quantified in the frame of the model through the residual variable.

In order to estimate the two parameters of the regression line, the method of the least squares is resorted to. For defining the estimators, we have to keep in mind that the residual variable (�t) is satisfying the following hypotheses1:

- each residual has a null mathematical expectation so that E(�t) = 0;

- the variables �’t �i �t are not correlated since the hypothesis of non-correlation for the specific risks of the equities, taken two by two, is admitted;

- the residual variables are normally distributed: �s �X2�� UV3� 2u2b3 � ;�/AAAAAA3.Following the application of the least squares method, an

estimator of the volatility coefficient (�) is established through the relation: �D � � �2 s�t.3Ut= � vst UsUtwhere: - vst is the linear coefficient of correlation calculated in order to measure the linear dependence between the equity yield and the market index: - Us represents the standard deviation calculated in the case of the equity yield; -Ut is the standard deviation of the financial market index;

Depending on the value of the parameter �, the following types of equities are identified2: 1 Anghel M.G. (2014) – Econometric Model Applied in the Analysis of the Correlation between Some of the Macroeconomic Variables, Revista Român� de Statistic� – Supliment Nr. 1 2 Anghel, M.G. (2010) – “Utilizarea modelelor econometrice în analizele economice”, Simpozionul �tiin�ific interna�ional „Necesitatea reformei economico – sociale a României în contextul crizei globale”, Editura Artifex, Bucure�ti


- if � < 0, then the equity yield is developing differently as against the general tendency of the financial market;

- in the situation of � � 2��;3, then the equity has a low volatility. In this case, the variation of the equity yield is lower as against the changes of market index from one period to another. Thus, an example of equity of low volatility is given by the case when the market index changes by 8% in the conditions of a variation of the equity yield of 5% only;

- in case that � = 1 the equity is neutral. For a neutral equity the yield changes to the same extent as the financial market index. For instance, if the index of the financial market is recording a fluctuation of 2% then the equity yield will record the same increase;

- if � > 1, then the equities bear a high volatility. The equities of this class have a high sensitivity to the overall fluctuations of the financial market. These equities are of an increased interest for the speculators on the financial markets. In this case, the equity risk is extremely high. For instance, for a fluctuation of 3% of the market price, a fluctuation of the yield higher than 3% is recorded for the equities of this class.

- In the financial practice, the outcomes given by this method are regarded with certain reluctance since, while the parameter � is calculated on the basis of a data series from the past, the risk refers to a period in the future.

This method is substantiated on the hypothesis that the yield of equity is fluctuating as against the global yield of the market where it is transacted or as against the overall performances of the economic environment. Through the intermediary of the global regression, the number of the operations involved by the calculation of the global yield and the total risk is getting significantly reduced.

�� "�

� ��#�� $�� %�� ∗�

�• Aspects regarding the verification of residual normality The relations applied for testing the characteristics of the

residual distribution are defined by taking into account the asymmetry and the trimming of the normal distribution. For an alleatory variable with a normal distribution, the asymmetry coefficient is zero while the trimming one is three.

Let’s consider the regression linear model: �� , i = 1,..,n and the series of the estimated residual E� � �� +��D � �C��. For the residual series there are two indicators to define, used by the descriptive statistics in order to analyze the asymmetry and the trimming of a distribution series:

- asymmetry coefficient

�? � wx=w=x- trimming coefficient �= � wyw=

In order to define the statistical tests used for the verification of the residual distribution according to a normal distribution, the following property of the symmetry and trimming coefficients: „Consider the alleatory variable � 0 X2/� U�=3. The asymmetry and trimming coefficients calculated for a series of data with n values, which is defined for this variable, are meeting the following properties:

∗ The concepts included in this chapter were also presented in the article Aspects Concerning the Verification of the Residual Normality and the Prediction of the Regression Model, RRS Supplement no. 7/2014, prof. Constantin Anghelache PhD, prof. Radu Titus Marinescu PhD, assoc. prof. Alexandru Manole PhD, ec. Emilia Stanciu


�D??o= 0 Xz��i{B|�D= 0 Xz}�iW~B | In order to verify the null hypothesis of the normal distribution of the residual 2E�3�>?�@ we have to resort to one of the tests:

- tests for verifying the asymmetry and trimming for the distribution of the estimated residual;

- tests for verifying the asymmetry and the test Jarque – Bera.

On the ground of the estimated series it is verified whether this distribution is normally divided. By using this series, the two coefficients are estimated as �D??o=, respectively �D=. Under the null hypothesis H0: �1 = 0, it is resulting:

� � �D??o=`{B0 X2��;3�

Similarly, if defining the null hypothesis on the second coefficient, as H0:�2=3, then:

� � �D= + }`W~B

0 X2��;3 The null hypothesis according to which the residual is uniformly distributed is accepted provided the following inequities are simultaneously met: �� b?<f9 and �� b?<f9, where b?<f97is the value of the distribution quartile N(0,1)for the significance threshold �.


• Some aspects concerning the prediction through the regression model

On the basis of the data series 2�� 3�>?�@AAAAA the parameters of the regression line have been estimated. Thus we get the series of the estimated values for the endogenous variable through the relation: �C� � �D � �C � �, . � ;� BAAAAA� Within the prediction process, using the regression linear model, there is the question mark on how to solve the following two aspects:

- accomplishing predictions either punctually or through intervals of confidence;

- verifying the framing of certain points within the tendency postulated by a regression model.

We shall make punctual or through an interval of confidence predictions for a value of the endogenous characteristic y0 or for its mean, E(y0). For each and every case there are various calculation formulas being established for the punctual prediction and the prediction through an interval of confidence. For the regression linear model, the real value of the endogenous characteristic is specified through the relation: �) � � � � � ) � �), where is the accomplishment of a normal distribution of mean zero and dispersion equal to one. The punctual value estimated through the regression linear model is defined by the relation: �) � �D � �C � ) As a rule, this value is utilized for defining an interval of confidence. In order to define the interval of confidence, in the conditions that a level of the significance threshold is specified, we must take into consideration the fact that, by utilizing the regression linear model for defining the punctual prediction, a prediction error is made, equalling to: E) � �) + �C) � �� + �D� � 2� + �C3) � �)

0ε


Considering the properties of the two estimators of the regression line estimators, we can consider the main properties of the prediction error. The mean of the prediction error equals to zero. We define the equality: E(e0)=0 The above result is obvious if applying the mean operator to the terms of the equality, taking into account the properties of the two estimators and the hypothesis formulated on the residual variable. The dispersion of the prediction error made in the case when the purpose is to make a prediction for the value of the endogenous characteristic y0 is:

��2E)3 � UV= �; � ;B � 2 + )3=K 2� + 3=� � In order to obtain the expression of the variance of the prediction error, the dispersion of the terms of the equality is applied. The following outcomes are obtained: ��2E)3 � �2E)=3 � ��D� � )=��2�C3 � ��2E�)3 � W)� �2�C� �D3� UV= � ;�� )= �;B � e=�� + W) e�� UV= �;B � 2 + )3=K 2� + 3=� � For building up an interval of prediction for the value of the endogenous variable, in the conditions of a fixed level of the exogenous characteristic, the following two results are to be taken into consideration: �) + �C)U 0 X2��;3�) + �C)UC� 0 b@<=

For a stable significance threshold, the size of the prediction interval is function of the following measurements:

- the value of the exogenous for which the value of the endogenous characteristic is predicted. This factor is quantified through the term 2) + 3=;


- the number of terms of the series which have been used for estimating the parameters of the regression linear model. The prediction error is proportionally inverse to n;

- the quality of the regression model being quantified through the dispersion of the residual variable;

- the value of the significance threshold. In the situation where a prediction on the average values E(y0) is made, under the conditions of an established values for the exogenous characteristic, the dispersion of the prediction error is:

��2E)3 � UV= �;B � 2) + 3=K 2� + 3=� � By applying the mean operator to the terms of the equality above, we get the above formula.

�� &�

�� '��∗�

• Some theoretical aspects regarding multiple regression model

The situation in which economic correlations involve only two variables are very rare. Rather we have a situation where a dependent variable, Y, can depend on a whole series of factorial variables or regressions. For example, the demand for a commodity depends not only on price but also on the prices of substitutes or complementary goods, the general level of consumer prices and resources. Thus, in practice, there are normally correlations as: � � �) � �?? � �== � �� @@ � �

The equation is known as the multiple regression equation. For moment, conventionally, we consider that it is of linear form. Unlike the case of two-variable regression, we cannot represent the equation by means of a two-dimensional diagram.

ai are the regression parameters. Sometimes they are also called regression coefficients. a0 is a constant (intercept) and a1 , a2 and so on, are the parameters of the regression slope.

As the population regression equation is unknown, it will be estimated based on a sample. Suppose that we have available a sample of n observations, each observation containing values for dependent variable Y and for each factorial variables X.

Given that it is assumed that the sample data were generated by the correlation of the population, each observation has to involve a set of values as the initial model.

∗ This chapter is based on some elements from the study Multiple Linear Regression Model Used in Economic Analyses, RRS Supplement no. 10/2014, authors prof. Constantin Anghelache PhD, lecturer M�d�lina Gabriela Anghel PhD, Ligia Prodan PhD student, Cristina Sacal� PhD student, Marius Popovici PhD student


The above equation is in fact identical to that of the two-variable regression but in general we were not able to illustrate the graphic of ei.

Summarizing, we can calculate the OLS estimators in two ways. The first is to use the �C(x’x)-1x’y function but involves working with a matrix of order k x k. Alternatively, we can work in terms of deviations from the average of the variables, which only requires inverse of the matrix of order (k – 1) x (k – 1).

• Aspects regarding determination in multiple regression In approach of the two variables of regression we defined the

coefficient of determination, which measures the proportion of variation due to the X explanatory variable in total variation of the variable Y.

A similar measurement of harmonization accuracy can be defined also for the multiple regression.

We consider the equation �� C� � E�. By removing �A from each side of the equation we get �� + �A � �C� + �A � E� for each value i.

Thus, if we measure the deviations of Y around its average,7�A, we can say that for each observation, the total deviation of Y can be divided into an explained deviation,7�C� + �A and residual deviation, ei. The above equation is identical to that of the two-variable regression.

As in the case of two-variable regression, first we square and then proceed to the adding of all observations.

The last equation is identical to that of the two-variable regression. It means that, during the entire measurement, the measurement result of the total variance of Y, SST, can again be divived into a measure of the variation factor of Y, SSE, and a residual variation, SSR. We have to emphasize that the relationship is available, as in the two-variable regression, only if the estimation method is OLS, because the correlation is only support for this form of estimation.

We can define the coefficient of multiple determination, R2, as the proportion of total variation of Y that can be attributed to variations in all variables factor acting focused.

Given the equation SST = SSE + SSR, it means that:


= � E�-.�.b7�,/7 �7��,��E�b b�-7�,/7 �7��,��E� � ��We can consider the principle like in two-variable regression

and so results:

= � ; + KE�=K ��=Sum of squares of residues from above relation can then be

calculated by expansion, which demonstrably is supported for multiple regression, like: PE�= �P��= + �C?P?�� + �C=P=�� +�+ �C_P_��

• Akaike criterion as base in econometric models The Akaike information criterion (AIC) is defined as:

�� K E�=B � � WaBIn this case we are not concerned with the theoretical basis of

AIC, we will only mention that in this case the criterion is to include an additional variable only if it leads to lower AIC. Like, A=, AIC depends on the residual sum of squares, KE�= and the number of parameters to be estimated, k. However, in the case of a decrease in the level KE�=, which occurs when it includes an additional explanatory variable, it is possible that this does not necessarily lead to a decrease and AIC. Additional variable represents an increase of k, respectively the number of parameters to be estimated, and this leads to increased AIC. Therefore, AIC is reduced only if the decrease recorded of KE�= is large enough to counteract the increase of k.

Among the measurements of accuracy of harmonization in relation to the inclusion of additional factors variables, the Schwartz criterion and the Amemiya criterion are included.

�� (�

��!��∗��

�• Some Theoretical Aspects There are many transformations which can be considered but

we shall focus on a specific class characterized by the relation: [ � ��2Z3�2Z3 �ZIn this formula,7�2Z3 � �2��Z� � Z3 and w(z) is a weight

function which is either scalar or vectorial and satisfies w(z )=0 if ��2Z3 � �, which is natural since g (z ) is defined only if ��2Z3 n �. The parameter of interest � is scalar or vectorial. This class of transformation is justified by the properties of the

resulting estimator � and, meantime, by its relevance as regards many issues of applied econometrics, which are special situations of these analyses.

Before entering into details, we notice the fact that this transformation does not insert the over-determination of the conditions on the variables distribution.

We shall21 estimate the mean of the regression differentials. We have seen that the parametrical estimation of a regression erroneously specified does not allow us to consistently estimate the differentials of this function in a certain point. In many econometrical issues, the differentials are parameters of interest. The estimation is possible but its rate of convergence is very slow and, consequently, requires a large sample. Nevertheless, in many applications it is enough to estimate the mean of the regression differentials, namely:

∗ This chapter includes elements presented in the article Model of Regression used to Analyze the Macroeconomic Correlations, RRS Supplement no. 1/2014, authors prof. Constantin Anghelache PhD, prof. Radu Titus Marinescu PhD, Adina Mihaela Dinu PhD Student, Daniel Dumitrescu PhD Student, Diana Valentina Soare PhD Student 21 Romanian Statistical Review – Supplement December 2013


[ � �5F�2Z3*2Z3 �Zwhere � is a multiple index of the derivation and 5F is the derivation defined by this multiple index. The function *2Z3 is a density on the explanatory variable which can be equal to7��2Z3, the density of the actual explanatory variable being studied. We shall analyze the under-additively test.

In order to illustrate this situation, let’s assume that the function C is the function cost which associates an expected cost with the quantities of the different products z. The economic theory is interested in the under-additively C, namely it is:

� zPZ��>? | � zP�2Z�3�

�>? |• Which means that, the cost of a company producing K Z��>? , is lower than the cost of several companies each producing Z�. The above property must be true for each p and each sequence �Z?� � � Z��. It is easy to show that this property is equivalent to the

property which will be explicitly shown by the content. If is the density �Z?� � � Z��, � the density of the sumZ? � �� Z� and7 � the density7Z�, than, it is equivalent with the fact that for each , we have:

��2,3 �2,3�, �P��2Z�3��>? ��Z��Z�

The reciprocal is resulting by taking into account the distribution on focused in one point. Now, we shall approach the under-additively test. The previous relation suggests that there is a

defined, namely:

�2Z3 � �2Z3 +P �2Z3��>?

the sign of this parameter having to be tested. The estimation of � defined can be made in two modes.

),...,( 1 pzz

λ


The first variant consists of the estimation of g followed by the calculation.

The second approach avoids the estimation g and is based on the particularity given by the utilized (final) function: ;BP�s �2Z�3��2Z�3

@�>?

This condition is seldom satisfied. We can replace �� with a parametrical or non-parametrical estimation.

Implicitly, we assume that w is given. In practice, iv can be partially or totally unknown (since it is, for instance, a function of ��) and thus w must be replaced by an estimation.

The main asymptotic result is the convergence rate [D@ at �. Indeed, we know: hB�7[D@ + ¡� 0 X2�� ¢3, in the frame regularity conditionings and under the condition that the bands width have an adequate asymptotic behavior. In order to limit the problems of dimensioning or to impose certain restrictions originating in the economic theory, we often assume that the conditioned probability g(z), which is a function of the variables q, depends in fact on the functions of a reduced number of variables and, possibly, on certain parameters. In fact, there are two points of view being expressed: either we assume that g is actually restricted to this specific form or we are searching for the best approximation g through an element satisfying the considered restrictions.

• Analysis of correlation between Total Production and transport production computed using Eviews

-milions-

Year

Transport production (services)

Total production

x y 1990 13.39 102.831991 57.72 268.32


Year

Transport production (services)

Total production

x y 1992 178.62 788.971993 529.36 2478.451994 1095.77 6110.131995 1709.11 8770.971996 2928.51 13256.231997 6686.29 29947.451998 11170.9 43824.561999 16755.44 63554.662000 23628.67 93588.172001 32245.72 137906.862002 39167.05 177998.992003 52125.19 216582.992004 66274.65 287210.692005 81336.84 318079.842006 99362.38 376604.282007 122688.54 456099.282008 155534.21 596096.152009 148044.13 586272.832010 113817.86 606316.12011 106618.2 634053.162012 116453.35 665745.862013 121745.95 696002.332014 127038.67 726258.83

Another important branch in correlation with the total

production is represented by transport services. The period analyzed is 1990-2014 and we can observe that the

correlation between the two indicators is significant for 2008 and 2009, because the SERVICES evolution depends on the total production.


The evolution of labor force in the branch of services in Romania during 1990-2014, as drawn by Eviews:

Statistical tests over the correlations between total production and the labor force in the branch services in Romania 1990-2014 were calculated in Eviews:

To estimate the regression model parameters, we used the software Eiews in which we defined an equation that has as outcome


variables the labor force, and Total Production in the branch of services in Romania. Estimation method defined in the program is the method of least squares. Based on the above data, by using Eviews, we have obtained the following results:

From the above, simple regression model describing the relationship between the three macroeconomic indicators that are are the subject of previously determined may be given in the form of equation as follows: TOTAL_PRODUCTION = SERVICES * 4,702596 – 2468,326

�� )�

��*��+��%��,�*��*��∗�

• Some theoretical aspects In the theoretical analysis, dependency of variables is

stochastic. Consideration of the residual variable within such a model is needed. Other factors that influence the score variable are grouped in the residual22. Uni-factorial nonlinear models are linearized transformations that are applied to the variables, the regression model. So, for example, a model of the form turns into a linear model by logarithm the two terms of the above equality, resulting in linear function. This model is recommended when the points are located, that the cloud of points around a line.

Linear regression model is based on the series of data for the two features. They are represented by vectors x (the variable factor) and y (variable score).

Simple regression aim is to highlight the relationship between a dependent variable explained (endogeneous, score) and an independent variable (explanatory note, exogenous factor predictors).

To be able to build a linear regression model we defined total production as the independent variable, while labor force in financial intermediation and insurance; real estate was considered to be a dependent variable.

• The correlation between Production and Labor To determine the parameters of the linear regression model we

have considered a variety of data on the evolution of the macroeconomic indicators of outcomes in the period 1990-2014.

∗ This chapter is based on elements included in the article The Regression Model used to Analyze the Correlation between Production and Labor, RRS Supplement no. 1/2014, by prof. Constantin Anghelache et. al. 22 Anghelache, C. (2013) – „Elemente de econometrie teoretic�”, Editura Artifex,

Bucure�ti


By using EViews we realized an analysis of correlation between labor force in the financial intermediation and insurance; real estate branch and TOTAL PRODUCTION.

-milions-

Year

Labor force in Financial Intermediation and

insurance; real estate(BRANCH 5)

Total production

x y 1990 6.1 102.83 1991 14.4 268.32 1992 58.3 788.97 1993 185.4 2478.45 1994 453.4 6110.13 1995 704.1 8770.97 1996 911.4 13256.23 1997 3015.9 29947.45 1998 4907.7 43824.56 1999 7905.7 63554.66 2000 11674.3 93588.17 2001 17956.0 137906.86 2002 25415.5 177998.99 2003 29217.3 216582.99 2004 36531.5 287210.69 2005 35172.2 318079.84 2006 40984.9 376604.28 2007 51455.6 456099.28 2008 43078.8 596096.15 2009 43949.1 586272.83 2010 57931.9 606316.1 2011 60899.5 634053.16 2012 62448.0 665745.86 2013 65286.0 696002.33 2014 68124.3 726258.83


Financial intermediation and insurance, real estate branch has an important role in influencing the total production. Between the two indicators there is a direct and linear in shape. As we can see from the table above, the evolution of financial intermediation and insurance; real estate is more considerable starting with 2010 until 2014. The financial intermediation and insurance; real estate field recorded values on rise during this period, who caused the increased of total production. The validity of the regression model is confirmed by the F-test statistic values (value far superior to the table what level is considered to be a landmark in tests of validity of econometric models) and the degree of risk is zero (reflected by the value of Significance). The correlation between the two indicators can be analyzed using computer software Eviews. Multiple R is the coefficient of multiple correlation, in this case the simple correlation between x and y. It is noted that between the value of Branch 5 and that of total production registered in our country between 1990-2014 there is a direct and very strong conclusion expressed based on the value of Multiple R.

The evolution of labor in the financial intermediation and insurance; real estate branch in Romania, during 1990-2014 (as represented by Eviews tools):

Statistical tests regarding the value of BRANCH 5 in Romania, during 1990-2014 is represented as drawn from Eviews processing:


Characteristics of the regression model:

We can conclude that as much the value of labor in the financial intermediation and insurance, real estate branch is growing, the value of the total production also is growing.

Also the validity of the regression model is confirmed by the F test value - statistically superior value than the table level, considered to be the benchmark in the analysis of the validity of econometric models and by the value of the test Prob (F - statistic) that it is zero.

Based on observations made on the analysis of Romania's Branch 5, using simple regression model, we conclude that the value of this indicator is significantly influenced by the variation of Total Production.

�� -�

��'��∗�

The economic situation in which correlations involves only two variables are very rare. Rather we have a situation where a dependent variable, Y, can depend on a whole series of variables factorial or regressor. In practice, there are correlations of the form: Y = a1 + a2 X2 + a3X3 + a4X4 +...+ akXk + �where values Xj (j = 2, 3, ..., n) represents the variable factor or regressors, the values aj (j = 1, 2, 3, ...,k) are the regression parameters, and � is the residual factor. Residual factor reflects the random nature of human response and any other factors, others than Xj, which might influence the variable Y.

We adopted the usual notation, respectively assigned to the first factor notation X2, the second notation X3 and so on. Sometimes it is convenient that the parameter a to be considered that coefficient of one variable X1 whose value is always equal to unity. Then the relationship is rewritten as: Y = a1X1+a2X2 + a3X3 +...+ akXk + � In the case of regression with two variables (E(�) = 0), then, substituting, for given values of the variables X, we get: E(Y)=a1 + a2 X2 + a3X3 + a4X4 +...+ akXk The relationship is multiple regression equation. For now, conventional, we consider that it is the linear form. Unlike the case of two-variable regression, we cannot represent this equation in a two-dimensional diagram. aJ are regression parameters. Sometimes, they are also called regression coefficients. a1 is a constant (intercept) and a2 , a3 and so on, are the regression slope parameters. a4, measuring the effects of E(Y) produced by changing one unit of X4,considering that

∗ The study uses elements from the article Aspects Regarding the Multiple Regression Used in Macro-economic Analysis, RRS Supplement no. 1/2014, by prof. Constantin Anghelache PhD, assoc. prof. Alexandru Manole PhD, Ligia Prodan PhD Student, Andreea Gabriela Baltac PhD Student, Zoica Dinc� (Nicola) PhD Student


all other factor variables remain constant. a2 measures the effects on E(Y) produced by changing one unit of X2, considering that all other variables remain constant factor. As the population regression equation is unknown, it has to be estimated based on data sample. Suppose that we have available a sample of n observations, each observation containing the dependent variable values for both Y and for each factorial variables X. We write the values for observation i as: Yi , X2i , X3i , X4i ,..., Xki

For example, X37 is the value of X3 in the 7th observation and X24 is the value X2 taken in the 4th observation. For a similar manner, Y6 is the variable Y in the observation of 6 and so on. Given that it is assumed that the sample data were generated by the correlation of the population, each observation have to involve a set of values satisfy the multiple equation regression. We can rewrite the relationship in a simple matrix form, as follows: Y = Xa + � , where

X is a matrix the form of n x k with k column of values and then all sample values of the k – 1, X variables. Thus, the fourth column of X, for example, contains the values of X4 of the sample n, the seventh column contains the values of X7

and so on. a is a vector of k x 1 column containing the parameters aj

and � is an vector of n x 1 column containing the residual values. The effective values of Y will not coincide with the expected values of Y and, in the case of two-variable regression, the differences between them are known as residual values. The average number of employees, on the activities of the national

economy - thousand persons -

Year Agriculture, forestry and fishing

Industry, including

energy Constructio

ns Trade, repair of motor

vehicles and motorcycles; transport and storage; Hotels and

restaurants; Information and communications

Financial intermediation and insurance;

Real estate transactions

Other service

activitiesTotal

labour force

1990 762 3846 704 1427 429 988 81561991 70S 3643 486 1344 338 1055 7S741992 654 3245 459 1200 308 1022 68881991 648 3017 536 1152 294 1025 6672


Year Agriculture, forestry and fishing

Industry, including

energy Constructio

ns Trade, repair of motor

vehicles and motorcycles; transport and storage; Hotels and

restaurants; Information and communications

Financial intermediation and insurance;

Real estate transactions

Other service

activitiesTotal

labour force

1994 575 2856 515 1160 289 1043 64381995 503 2615 443 1291 262 1046 61601996 442 2586 431 1191 254 1035 59391997 357 2443 387 1193 218 999 55971998 316 2272 378 1188 240 975 53691999 244 1991 309 1044 236 937 47612000 199 1873 316 1022 248 965 46232001 191 1901 309 1010 249 959 46192002 162 1891 300 986 277 952 45682003 155 1848 325 1013 288 962 45912004 145 1741 323 1006 297 957 44692005 147 1672 348 1086 317 989 45592006 136 1632 352 1159 371 1017 46672007 127 1615 406 1241 422 1074 48852008 105 1606 458 1373 139 1365 50462009 110 1371 404 1330 136 1423 47742010 95 1237 337 1224 128 1355 43762011 98 1259 334 1227 126 1305 43492012 104 1296 356 1246 121 1320 44432013 104 1285 345 1260 118 1200 4312

Source: Statistical Yearbook, the AVERAGE NUMBER of employees, on the ACTIVITIES of the NATIONAL ECONOMY Tempo Online Database

Agriculture, forestry and fisheries in the period 1990-1999, experienced a reduction in the number of employees. So if in 1990 762 th. persons were employed in this branch, in 1996 there were 442 th. employees, and in 1999 it was a number of 244 th. employees. The period between the years 2000-2013 is characterized by a significant drop in the number of employees, especially in 2010 when there were 95 th. employees and in 2011 - their number was 98 th. persons. In 2012 we notice a slight increase in the number of employees, 104, which holds also in 2013.

In the field of industry and energy, we are also witness to the reduction in the number of employees, which in 1990 was 3846 th. persons, and in 2013 the number fell to 1285. We find, as in the previous case, a serious fall of the number of employees since 2000.

Constructions, constitutes another branch of the national economy which has been confronted also with the reduction from one


year to another in the number of employees, with major discrepancies between 1990 and 2002, whereas the number of employees was reduced to more than half, from 704 to a total of 300 (both values as thousand persons). After an increase in the number of employees in 2007-2009, starting in 2010 their number begins again to fall, and in 2012 tends to increase timidly.

Trade, repair of motor vehicles and motorcycles; transport and storage; hotels and restaurants; information and communication constitutes a series of activities of the national economy which have recorded a large number of employees in the period 1990-1999, and after 2000 we are witnessing a decline in the number.

Financial Intermediation and insurance; real estate constitutes a branch of national economy who knows fluctuations - increasing and decreasing, and at the level of 2007 total number of employees was 422, very close to the total number of employees at the level of 1990, that is 429.

Other service activities (professional activities, Scientific and technical knowledge; service activities and administrative support services activities; public administration and defense; social security from the public system; education; health and social work; activities of performances, Cultural and recreational; repair of household products and other services) represents a branch with dramatic changes to the number of employees. Thus, in the period 1991 to 1995 the number of employees is increasing, and during the period 1996-2005, we are witnessing a reduction in their number. Starting with 2006, the number of employees begins to increase, the year with the highest number of employees being 2009.

In the case of total employment in the period 1990-2013 we are witnessing permanent fluctuations from one year to another marked by up and down movements in the number of employees. The largest discrepancy can be observed between 1990, when the total number of employees was 8156 and 2011, the total number of employees has reached 4349, thus reducing by about half their number. An extremely important factor of drastically reducing the number of employees highlighted in the year 2011 is the impact of the economic-financial crisis on employment.


The equation model for multiple linear regression will show in the following way: Y=a0+a1X1+a2X2+a3X3+a4X4+a5X5+a6X6+where : Y – Total labour force; a0,a1,a2, a3,a4,a5,a6 – the regression model parameters;

- variable, interpreted as error (disturbance, measurement error). Thus, the regression model can be cited under this equation maths: Total labour force = a0+a1B1+a2B2+a3B3+ +a4B4+a5B5+a6B6+ The results of the regression can be presented in the following diagram, as drawn from Eviews processing.

• Analysis of the correlation between GDP, final consumption and net investment

In the analysis of the factors that determine the variation of GDP, we started from specific component elements of using the final production method (expenditure method), considering that this is a significant source of information on the main correlations that influence the evolution of the main macroeconomic aggregate. Thus, according to the calculation method above, GDP involves

ε

ε

ε


adding components that express using of goods and services for final production, as follows: PIB = CF + FBC + EXN Based on the elements mentioned above we want to identify the existing relationship between the evolution of the country's final consumption (regarded as a sum of private and public consumption), net investment and GDP variation. In this regard, we used linear multiple regression analysis as a method in which we consider GDP as outcome variables and the variable factor the final consumption value and net investments in our country during 2006-2014. The three indicators can be presented in summary form as follows:

Evolution of GDP, final consumption and net investment in Romania during 2006-2014

Year GDP (mil. lei) Y

FINAL CONSUMPTION

(mil. lei) X1

NET INVESTMENT

(mil. lei) X22006 247,368.0 211,054.6 44,869.9 2007 288,954.6 251,038.1 54,566.0 2008 344,650.6 294,867.6 72,891.0 2009 416,006.8 344,937.0 98,417.7 2010 514,700.0 420,917.5 99,525.6 2011 501,139.4 404,275.5 74,939.3 2012 523,693.3 419,801.2 72,294.7 2013 556,708.4 436,485.0 87,815.8 2014* 600,899.8 468,689.3 93,950.9 TOTAL 3,393,221.1 - -

Source: Statistical Yearbook of Romania, Gross Domestic Product, categories of uses, NIS, Bucharest, 2008, 2009, 2010, 2011, 2012, 2013

* the authors estimated the data For an pertinent analyze of the correlation between the three

macroeconomic indicators presented in the table above, it is necessary in a first step of this research to identify a number of features aiming the evolution of each indicator considered in the period under review. To prove this, using the software Eviews, we studied in the first stage,


the evolution of the three indicators. As can be seen from analyzing the data series under investigation, especially as in the figure shown above, in the period considered, the three of our country's macroeconomic indicators have registered a steady growth from year to year. The purpose of multiple regression (term used by Pearson, 1908) is to highlight the relationship between a dependent variable (explained endogenous effect) and a lot of independent variables (explanatory factors, exogenous predictors).

Multiple linear regression model equation will look like this: Y=b0 + b1X1 + b2X2 + �

in which: Y = Gross Domestic Product (GDP); X1 = Final Consumption (CF); X2 = Net investments (INV); b0,b1,b2 = parameters of the regression model; � = variable, interpreted as error (disturbance, measurement error).

The regression model may be rewrite under the following mathematical equation: PIB= b0 + b1CF + b2INV + �

To estimate the regression model parameters we used the software Eiews in which we defined an equation that has as outcome variables GDP, and factor variables the final consumption and net investments. We also thought that this regression model will also include free term c, which is expected to influence dimming terms that were not taken into account when we building this model. Estimation method defined in the program is the method of least squares. Based on the above, using Eiews we obtained the following results:


• Characteristics of the regression model From the above, multiple regression model describing the

relationship between the three macroeconomic indicators that are are the subject of previously determined may be given in the form of equation as follows:

PIB = -8.927,569 + 1,165488 CF + 0,284958 INV Thus, we can say that an increasing with a monetary unit of

final consumption (with its two component - private consumption and public consumption) will lead to an increase of 1.165488 units monetary of gross domestic product value. In case of the net investment, the difference is more significant, we can see that every leu invested brings an increase of only 0.284958 lei of the level of gross domestic product. This situation corresponds with the reality economics of Romania because in the last twenty years the Romanian economy was based almost exclusively on stimulating consumption and less on promotion of an investment policy correctly.

The influence of the free term as a picture of the factors that were not included in the analysis model is one significant. In fact, it can be said, that the factors that were not included in the econometric model of analysis, they have an significant decrease in the value of gross domestic product.

The probability for this model to be correct is very high - about 98.89%, this conclusion can be formulated on the basis of statistical tests R-squared (0.988909) and Adjusted R-squared (0.986892).

Also the validity of the regression model is confirmed by the F test value - statistically superior value table level that is considered to be the benchmark in the analysis of the validity of econometric models and by the value of the test Prob (F - statistic) that it is zero.

Based on observations made on the analysis of Romania's GDP, using multiple regression model, we conclude that the value of this indicator is significantly influenced by the variation of final consumption and net investment less variation.

Using a multifactorial regression model allows to obtain more edifying results in macroeconomic analysis and conducting relevant research on the evolution of the national economy.

�� .�

,��∗�

Sometimes, for estimating parameters using other techniques of estimation, which cannot be incremental transformations, linear estimation of parameters is made by numerical methods. Linear regression model is based on the series of data for the two features. This requires completion of the methods used for the estimation of the two parameters; specify the methods to be used for testing the properties of the estimators of regression model and setting the framework for the use of the regression model in making predictions.

In defining the function of linear regression are considered, most commonly, four hypotheses:

- data series are not affected by the errors. - for each fixed value of the characteristic factorial, residual

variable is zero, i.e. on average: �� for all i, - the lack of correlation between residues expressed that the

terms do not exhibit the phenomenon of covariance, which means the variable correlation hypothesis;

- residuals with the independent, which means that � �� for any j, showing an increase in the value of the variable factorial does not automatically lead to an increase of the values of the variable. On the basis of the four assumptions define the linear

regression model through the function: :�� , I � ;� �AAAAA. Linear regression model involves the identification of variables

for defining specification for variable and model residuals; the context in which the regression model is used. Analysis of chronological

∗ This chapter includes elements presented in the article Model based on Linear Regression Function, RRS Supplement no. 1/2014, authors prof. Constantin Anghelache PhD, prof. Radu Titus Marinescu PhD, assoc. prof. Emanuela Ionescu PhD, Ligia Prodan PhD Student, Alexandru Ursache PhD Student


(time) using a temporal function which, in essence, is also a regression, with a variable time (t). Uni-factorial nonlinear models are linearized transformations that are applied to the variables, the regression model. Sometimes, for estimating parameters using other techniques of estimation, which cannot be incremental transformations, linear estimation of parameters is made by numerical methods. Linear regression model is based on the series of data for the two features. They are represented by vectors x (the variable factor) and y (variable score). Simple regression aim is to highlight the relationship between a dependent variable explained (endogeneous, score) and an independent variable (explanatory note, exogenous factor predictors). To be able to build a linear regression model we defined agriculture, forestry and fisheries as the independent variable, while the total production was considered to be a dependent variable. To determine the parameters of the linear regression model we have considered a variety of data on the evolution of the macroeconomic indicators of outcomes in the period 1990-2014. Correlation analysis of Total production and Agriculture, forestry

and fisheries -milions-

Year Agriculture, forestry and fisheries Total production

x y 1990 18.7 79.11991 41.6 206.41992 114.8 606.91993 420.6 1906.51994 989.8 4700.11995 1426.9 6746.91996 2094.9 10197.11997 4553.3 23036.51998 5377.3 33711.21999 7280.5 48888.22000 8901.5 71990.92001 15617.9 106082.22002 17289.3 136922.32003 22847.5 166602.3


Year Agriculture, forestry and fisheries Total production

x y 2004 31055.0 220931.32005 24291.8 244676.82006 26861.9 289695.62007 23992.2 350845.62008 34126.4 458535.52009 32297.8 450979.12010 29874.2 466397.02011 36341.6 487733.22012 28638.1 512112.22013 29938.9 535386.42014 31239.8 558660,6

From the analysis of correlation between total production and the first branch, namely agriculture, forestry and fisheries, have cost and then unearthed graphic that during the analysis period from 1990 to 2014 as the value of agriculture, forestry and fisheries is stronger. For this, from 2001 onwards and until the year 2014 the correlation between the two factors is significant, and the relationship of interdependence between those two factors.

Developments in the field of agriculture, forestry and fisheries in Romania in the period 1990 to 2014:

Graphical representation of the total production in Romania during 1990-2014 is as follows:


Statistic tests regarding Agriculture, forestry and fisheries of Romania during 1990-2014 is presented in the following chart:

Statistics tests upon the value of Total production of Romania between 1990-2014 are plotted:

Corelation between Agriculture, forestry and fisheries – Total production is represented:


Characteristics of regression model are:

�� /�

��∗�

The semi-logarithmic1 and the double logarithmic models are the two models which can be linearized:

− The logarithmic model can be either without free term or with free term.

− The free term model (log-log) is of the dependence form, respectively: ��

In this model � � !" and � � . Depending of the sign of the parameter b the properties of the resulting characteristic are set up.

If this parameter is positive, the resulting characteristic has an up warding trajectory. The down warding trajectory of the resulting characteristic is emphasized, in the case of the regression non-linear model, by the negative value of the resulting characteristic exponent.

Applying the logarithms the double logarithmic model results �� #$ � �� % � & � �� '$ � ��($Using the substitutions ��" � a � - ��, �" � - �� " � - ��, the regression linear

model becomes:#�" � �" � ��" � ��"The free term model (log-log) holds, in addition, a free term

and shows under the following form: �� ) � �� In the case of this model applying the previous procedure of

linearization is no more possible. In order to estimate the parameters, one of the following two methods applies:

∗ This chapter includes elements presented in the Using Linear and Non-linear Models in Macroeconomic Analyses, authors prof. Constantin Anghelache PhD, Ligia Prodan PhD student, Daniel Dumitrescu PhD student, Diana Valentina Soare PhD student, Georgeta Barda�u (Lixandru) PhD student, RRS Supplement no. 1/2014 1 Romanian Statistical Review – supliment – December 2013


- when a value of the free term of the model is specified, then, using the notations *� � �� + �) and ,� � �, we get the regression model �� . In this respect, parameters are estimated according to the case of the double logarithmic model;

- then we estimate the three parameters of the model through numerical models. It is possible to transform the model into a linear one using the development of the Taylor series.

The exponential model is used in the case when the points cloud resulting from the graphical representation of the series of values 2�� 3�>?�@AAAAA is directed along the curve of an exponential function.

The exponential model, with the parameters a and b, is defined through the relation: �� !"

The estimation of the parameters of the exponential model is made through data transformations by logarithms, following the stages:

- by logarithms applied to the equality terms we get the regression linear model: -B �� -B � � -B� � � � -B��

The model2 becomes a linear by the substitution of ,� � -B�� , £� � -B�, �" � -B� and �" � �; - we estimate the parameters of the regression linear model, - ,� � �" � �"� � £�7using the smallest squares method; we

get the estimators �C" and �D"; - the estimators of the parameters of the regression non-linear

model are established: �C � EFG" and �D � E�H"Finally, we calculate the values adjusted on the basis of the

estimates regression non-linear model:

2 Romanian Statistical Review – supliment – December 2013


�C� � �C2�D3�� , . � ;� BAAAAAThe exponential model is used when the values of the resulting

variable increase in an arithmetic progression while the values of the factorial variable increase in a geometrical progression.

In the case of the exponential model we consider the following situations:

- � is the rate of increasing or decreasing of the characteristic Y as against X;

- if � > 1, he evolution of the characteristic Y is up warding; - if: & � 2��;3, the characteristic Y records a decrease as

against the variable X; - the values of the characteristic Y are positive only and the

parameter a satisfies the positivity property. We have realized an analysis of the correlation between total

production and services branch using Eviews. -milions-

Year Services Total

production x y

1990 4.6 79.11991 12.9 206.41992 36.3 606.91993 111.2 1906.51994 287.1 4700.11995 454.6 6746.91996 613.2 10197.11997 1191.6 23036.51998 3109.0 33711.21999 4541.1 48888.22000 7362.5 71990.92001 9165.8 106082.22002 14344.7 136922.32003 14344.7 166602.32004 26088.1 220931.32005 32049.6 244676.8


Year Services Total

production x y

2006 35312.4 289695.62007 41950.2 350845.62008 87318.2 458535.52009 87405.3 450979.12010 94723.3 466397.02011 102884.4 487733.22012 115407.1 512112.22013 120652,4 535385.72014 125898.0 558659.9

The correlation between services – and the total production highlights that the evolution of two indicators can be related. And from the analysis using software Eviews we can establish that the correlation is significant for the period 2008-2014 when as services register values increasing to establish and increase the total production. The evolution of the labor in other activities and services branch

in Romania during 1990-2014

For an pertinent analyze of the evolution of labor in services it is necessary in a first step of this research to establish the growth of


other activities and services in the period under review. To prove this, using the software Eviews, we studied in the first stage, the evolution of this indicator. As can be seen from analyzing the data series under investigation, especially as in the figure shown above, in the period considered, the labor in services branch has registered a steady growth from year to year, except to this rule making the period between 2008 and 2014, when the growth kept getting bigger from an year to another.

Statistical tests performed on the value of labor in services branch in Romania in the period 1990-2014 are graphically represented:

Characteristics of the regression model, as drawn from Eviews, are described in the diagram below:

��

��∗∗

The economic situation in which correlations involves only two variables are very rare. Rather we have a situation where a dependent variable, Y, can depend on a whole series of variables factorial or regressor. In practice, there are correlations of the form: ¤ � ¥? � ¥=�= � ¥x�x � �� ¥_�@ � � where values Xj (j = 2, 3, ..., n) represents the variable factor or regressors, the values bj (j = 1, 2, 3, ...,k) are the regression parameters, and � is the residual factor. Residual factor reflects the random nature of human response and any other factors, others than Xj, which might influence the variable Y.

We adopted the usual notation, respectively assigned to the first factor notation X2, the second notation X3 and so on. Sometimes it is convenient that the parameter b to be considered that coefficient of one variable X1 whose value is always equal to unity. Then the relationship is rewritten as: ¤ � ¥?�? � ¥=�= � ¥x�x � �� ¥_�@ � �

In the case of regression with two variables (E(�) = 0), then, substituting, for given values of the variables X, we get: �2¤3 � ¥? � ¥=�= � ¥x�x � �� ¥_�@ The relationship is multiple regression equation. For now, conventional, we consider that it is the linear form. Unlike the case of two-variable regression, we cannot represent this equation in a two-dimensional diagram. bj are regression parameters. Sometimes, they are also called regression coefficients. b1 is a constant (intercept) and b2, b3 and so on, are the regression slope parameters. b4 measuring the effects of E(Y) produced by changing one unit of X4,considering that ∗∗ This chapter is based on some elements included in the article Macro-economic Analysis based on Econometric Models, authors prof. Constantin Anghelache PhD, prof. Gabriela Victoria Anghelache PhD, prof. Ioan Partachi PhD, Emilia Stanciu PhD student, Bogdan Dragomir PhD student, RRS Supplement nr. 10/2014


all other factor variables remain constant. b2 measures the effects on E(Y) produced by changing one unit of X2, considering that all other variables remain constant factor. As the population regression equation is unknown, it has to be estimated based on data sample. Suppose that we have available a sample of n observations, each observation containing the dependent variable values for both Y and for each factorial variables X. We write the values for observation i as: Yi , X2i , X3i , X4i ,..., Xki

For example, X26 is the value of X2 in the 6th observation and X35 is the value X3 taken in the 5th observation. For a similar manner, Y8 is the variable Y in the observation of 8 and so on1. Given that it is assumed that the sample data were generated by the correlation of the population, each observation have to involve a set of values satisfy the multiple equation regression. We can write the equation: Yi = b1 + b2X2i + b3X3i + ...+ bkXki

+ �i for all the values, where �i represents the residual value for the observation of the i. We can rewrite the relationship in a simple matrix form, as follows: Y = X� + �, where X is a matrix the form of n x k with k column of values and then all sample values of the k – 1, X variables. Thus, the fourth column of X, for example, contains the values of X4 of the sample n, the seventh column contains the values of X7

and so on. b is a vector of k x 1 column containing the parameters bj

and � is an vector of n x 1 column containing the residual values. The effective values of Y will not coincide with the expected values of Y and, in the case of two-variable regression, the differences between them are known as residual values. Like ¤� � ¤Y� � E�, for all values of i where ei is the residual corresponding to the observations of i. The relationship can be written

1 Anghelache, C., Negoi��, I. et. al. (2013) - „Inflation and Unemployment – a Correlative Analysis”, International Symposium “Romania and the Economic-Financial Crisis. Methods and Models for Macroeconomic Analysis”, May 2013, “Artifex” University of Bucharest, published in Romanian Statistical Review, Supplement no. 2/2013, pp.22 – 29


as: ¤� � ¥Y? � ¥Y=�=� � ¥Yx�x� � ¥Y_��_� � �� E�, for all values of i or on matrix form: ¤ � �¥Y � E, where X and Y are already defined. There are two issues to be retained on the residual values.

First, regardless of the method used to estimate the regression equation, we get such residual values - one for each of the sample observations. Second, as expected ¥Y� when it becomes known and can be used to calculate them. Now, we need to calculate the differential with the vector ¥Y and equalizer to zero the result. Such of this matrix lead to the following relation: 5�5¥Y � +W�r¤ � W�r�¥Y � �

The above equation is a set of k equations that can be written as �r�¥Y � �q¤.

• The Linear and Non-displaced Estimator A general matrix demonstration on the features BLUE in case

of multiple regression is outside the goal. We will limit ourselves only to find expressions for the

variations and covariance of OLS estimators. As we shall see, these expressions are important if we want to

develop inferences about the parameters of the multiple regression. The matrix is known as the matrix variation – covariation of the vector ¥Y, which generally is written in the form of ¢� �¥Y�. Note that in the bottom of its main diagonal, it contains variations vector ¥Y�. Outside the diagonal elements represents the covariance between different values ¥Y�that would result in case of more samples extraction. It is clear that if we need to develop inferences about the true value of ¥� , it is necessary to find an expression for this matrix. The equation is just the expression for the matrix variation – co-variation of vector OLS ¥Y.

We write the element of row i and column j of the (X’X)-1

inverse matrix as Xij. Since (X’X)-1 is symmetric, we have Xji = Xij. The comparison indicates that the variation of ¥Y�, which is written in the form U¦Y§= is given by: U¦Y§= � ¢� �¥Y�� U=�� ¨ � ;� a�AAAAA


Thus, to find the variation of ¥Y�, we have to take the j element of the diagonal matrix (X’X)-1 and to multiply it by the change in average residual values, �2. Square root of ¢� �¥Y�� is known as the standard error of ¥Y� and it is noted by U¦Y§.Comparing the two equations further, resulting that: � ��¥Y�� ¥Y�� U=�� for all values i � j

The expressions obtained are of considerable importance for inference in multiple regression.

It is possible to obtain equivalent expressions if we work in terms of deviations of variables from their average. It is merely necessary to work in terms of the inverted matrix (x’x)-1 instead of the matrix (X’X)-1. A complete derivation would prove repetitive but it is not difficult to prove that: U¦Y§= � ¢� �¥Y�� U=�� ¨ � ;� aAAAAA and � ��¥Y�� ¥Y�� U=�� for all values i � j where xij is the element from row (i – 1) and column (j – 1) of matrix (x’x)-1.

It should be noted that the relationship does not lead to an expression for7¢� �¥Y��.

In the particular case of two-variable regression, (x’x)-1 is only the scalar K== so that == � ;oK==, which leads to the relationship: ¢� �¥Y=� � U=oK==

This is identical to the corresponding expression for the variance estimator OLS for the slope regression parameter with two variables.

• Additional properties of the model As in the case of two-variable regression, where the OLS

estimators have to to be mainly but not only stationary and asymptotically efficient and effective, it is necessary that the IID assumption of classic model to self-sustain – that means the residual values have to be normally distributed2. Therefore, if OLS estimators 2 Anghelache, C., Negoi��, I. et. al. (2013) - „Inflation and Unemployment – a Correlative Analysis”, International Symposium “Romania and the Economic-Financial Crisis. Methods and Models for Macroeconomic Analysis”, May 2013, “Artifex” University of Bucharest, published in Romanian Statistical Review, Supplement no. 2/2013, pp.22 – 29


must have these properties, it is necessary that all classical assumptions are valid. A proof of ownership efficiency is outside the goal we have set. Remember only that efficiency implies that OLS estimators have the minimum variance of stationary estimators of all - not only of linear stationary estimators.

Normality residual values have other two important consequences for OLS regression. First, it means that the distributions of OLS estimators will be the selection of normal distributions. A demonstration of this statement is analogous to the case of two-variable regression. However, that, whereas under all classical assumptions, each ¥Y� is stationary with set variation: ¥Y� is X�¥�� U=��, ¨ � ;� aAAAAA.

A precise knowledge of the distributions of selection of OLS estimators, respectively ¥Y�, is of vital importance for inference. It is often helpful for the relationship to be expressed in an alternative form, working in terms of deviations from their average variables X, in which case we get:7¥Y� is X�¥�� U=��, ¨ � ;� aAAAAA.

The second consequence of the assumption of normality of the distribution of residual factors is, as in the case of two-variable regression, that OLS estimators are maximum probability estimator. As in the two-variable regression, MLE for �2 's proves:

U�= � KE�=Bwhere KE�= is the sum of squared residual factors. However, U�=proves to be an moved estimator of �2 real. In fact, it can be shown that if multiple regression: �2U�=3 � B + aB � U= c U=and is a generalization of the two-variable regression results.

Since, under classical assumptions, OLS and ML estimators of the parameters bj are identical at this point it may seem that ML estimation contribute little to our analysis of regression equations. Maximum probability estimation becomes most relevant when classical hypotheses are refused.


For example, this method is often used in cases where the regression equation is nonlinear.

There is also of great importance when classical assumptions on the variable factor and/or to the residuals are invalidated. As we have seen, if the classical assumptions are not valid, then the OLS estimators lose some, or all, of the desired properties. It proves that, in such circumstances, OLS estimators and ML estimators are not identical. In such a situation, ML estimators have the advantage that they still maintain their properties, namely compatibility and asymptotic efficiency.

• Inference in multiple regression By condition that all classical assumptions are valid, inferences

on the slope parameters in multiple regression can be based on the outcome ¥Y� � X�¥�� U=�� which implies that, for ¨ � ;� aAAAAA have: ¥Y� + ¥�U¦Y§

has a distribution N(0, 1). We will focus on the slope parameters that are of interest. The

inference on the parameter b1, it should be based on the set equation, with j = 1.

The problem that arises it is that the standard errors, U¦Y§, are unknown because the residuals variations, �2 is unknown.

When we substituting7U¦Y§ on stationary estimators, �¦Y§, as in the two-variable regression, we have to change the distribution of t. It can be shown that: ¥Y� + ¥��¦Y§has a distribution t, cu n – k g.l.

For example, at a 95% confidence interval for any value �j (j = 2, 3, ...,k) is:7¥Y� � b)�)=©�¦Y§the value of t0,025 depending on n – k and on the number of degrees of freedom. In order, to obtain a 99% interval are replaced t0,025 with t0,005.


Trustworthiness check can continue over the similar lines of the two-variable regression determined3.

To test the null hypothesis like H0 : bj = 0 (j = 2, 3, ...,k), we have to say that under the null hypothesis, which implies:7¥Y� �¦Y§ª have a t distribution with n - k degrees of freedom.

Therefore, we use ¥Y� �¦Y§« like test statistic and reject the null hypothesis that variable Xj does not influence the variable Y whether the absolute value of the test statistic is sufficiently large.

As in the case of two-variable regression, the statistical test is often called the coefficient t.

3 Anghelache, C., Voineagu, V., Negoi��, I. et. al., „The Features of the Chronological Series of Statistical Indices”, International Symposium “Romania and the Economic-Financial Crisis. Methods and Models for Macroeconomic Analysis”, May 2013, “Artifex” University of Bucharest, published in Romanian Statistical Review, Supplement no. 2/2013, pp. 55-61

��

��0��%��%��∗��

• Practically it is impossible to survey and record the prices for all the goods and services being consumed by the population during a given period of time. That’s why, for surveying and recording these statistic data, a sample of goods and services is utilized, which must be representative through the consumption and prices structure, so that the out coming results may be extended over the entire population, with an error margin as limited as possible.�

When analysing this index the following aspects, which are influencing its evolution from one to another period, should be considered1:

− The population cannot take advantage of a self-protection against a strong increase of the prices, in general or for certain categories of goods and services. Consequently, the simplest way to go for is to reduce the consumption, to substitute them with other goods or even to pull out of consumption of these categories of goods.

− On the Romanian market the prices for some goods and services consumed by the population do not evaluate in connection with the ratio between demand and offer, the sales being mainly directed by the level of the incomes available with the population at a given time. Or, these incomes are relatively smaller and smaller in comparison with the rhythm of the prices increase and the population’s consumption needs. Under the circumstances, the producers are diminishing the margin of risk or are freezing, for certain periods, the prices of certain goods, which results in getting a lower index of the inflation, far away of the economic reality;

∗ This chapter uses some elements included in the article The Evolution of the Index of Population Consumption Prices, RRS Supplement nr. 4/2014, authors prof. Constantin Anghelache PhD, prof. Gabriela Anghelache PhD, Daniel Dumitrescu PhD student, Bogdan Dragomir PhD student, Diana Valentina Soare PhD student. 1 Anghelache, C (2013). România 2013. Starea economic� sub povara efectelor crizei, Editura Economic�, Bucure�ti


− The new products entering the market have not a perfect degree of comparison with the previous periods, influencing thus the level of the inflation index;

− The inflation index is also influenced by certain goods or services which are no more produced (or sold) during the current period. As a rule, this kind of products, which get out of the market under normal conditions are replaced by other products, which leads to a diminished influence on the inflation index. In general terms, the index of the population consumption prices

is depending on: − The nature of the goods and services for which the prices are

considered; − The categories of population for which the purchases

(consumption) are considered; − The nature of the prices; − The limit of satisfying the population’s consumption needs

through purchases of goods and services; − The influence of the level of the population’s incomes on meeting

the consumptions needs through purchases of goods and services. The evolution of the population’s consumption prices and

of the average net wage gains indices during the period July 2012-July 2013

Data source: The National Institute of Statistics, Statistic Bulletin no, 7/2013


Consumption prices indices for the period 2001-2013 - December previous year = 100 -

*) Estimated data for the second half 2013. Data source: The National Institute of Statistics, Statistic

Bulletin no, 7/2013 Taking into consideration the above emphasized aspects, typical,

the average monthly rate of the calculated prices counted for 0.30%. The annual inflation rate in July 2013 counted for about 4.5%,

as against June 20122.

• Consumer prices index for foodstuffs Comparatively with December 2010, in December 2012, the

foodstuffs recorded price increases of 0.4%, which means insignificant monthly average increase of the prices3.

In December 2010, as against November same year, significant increases, within the category foodstuffs, have been recorded for eggs, vegetable, bakery products, butter, eatable oil and milk.

In July 2013, the prices index for foodstuffs counted for 3.9%, with a monthly average of 0.2%.

There were decreases as well, as against June 2013, recorded for citrus and other southern fruit, respectively potatoes.

2 Anghelache, C. (2013). România 2013. Starea economic� sub povara efectelor crizei, Editura Economic�, Bucure�ti 3 Anghelache, C. (2013). România 2013. Starea economic� sub povara efectelor crizei, Editura Economic�, Bucure�ti. See also Anghelache, C. (2012). România 2012. Starea economic� in criz� perpetu�, Editura Economic�, Bucure�ti

130,3

117,8

114,1

109,3108,6

104,9 106,6107,9

104,7

109

104,2 105,33104,4103

108

113

118

123

128

133

2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013*

- % -


As for the other products, the increases being recorded were somehow reasonable.

• The consumer prices index for non-foodstuffs As far as the non-foodstuffs are concerned, the prices increase

in July 2013, against July 2012, counted for 5.5%, significant increases being recorded for: fuels, cars, accessories and spare parts.

• The consumer prices index for services The increase by 3.0% of the tariffs, on the overall group of

services has been generated by the evolution of the tariffs for air transport, telephone and hygiene and cosmetics.

If considering the large industrial groups, in July 2013 as against July 2012, price increases have been recorded by the energetic industry, industry of goods for current use, industry of capital goods and industry of intermediary goods and industry of durable goods (4%).

• The nominal average wage gain When analysing the impact of the inflation on the living standard,

it is necessary to take into account also the average gains of the population during the analysed period. Thus, the nominal average gross wage at the economy level counted for 2,259 lei in July 20134.

In the industrial sector, the gross wage in July 2013 counted for 2,326 lei, with higher levels in the extractive industry and electric, thermic, water, gas sector. As to the manufacturing industry, the wages were below the average of the total industry.

The ratio between the index of the nominal net average gain and the index of the consumer prices in July 2013 counted for 104.3%, as against the previous month, 103.2% as against the corresponding month of the previous year and 124.8%, comparatively with October 1990.

4 Anghelache, C. (2013). România 2013. Starea economic� sub povara efectelor crizei, Editura Economic�, Bucure�ti. See also Anghelache, C-tin (2012). România 2012. Starea economic� in criz� perpetu�, Editura Economic�, Bucure�ti


The inflation keeps on playing a different role in evaluating the ratio between the index of the nominal net average wage and the index of the consumer prices.

It is rather difficult to come up with a conclusion as regards the evolution of the inflation for the forthcoming period.

At first sight, the level of the inflation rate of 2012 and the first seven months of 2013 leads to the conclusion that the social and economic situation in Romania is facing a more difficult moment than that of the period 2000-2010, but on a stabilizing trend.

For the year 2013 the estimated rate of inflation counts for about 4.3%, which I consider as being a realistic one in comparison with the very low incomes of the population.

There are some comments to be made also in connection with the real level of this indicator, recorded in 2012, as it is calculated according to a concrete methodology which implies a constant weight of participation of the foodstuffs, non-foodstuffs and services in the process to build up the index of the population’s consumer prices.

From this point of view, we can estimate that, probably, the prices index, mainly as for foodstuffs, would have been different under the conditions of an organized structure, according to criteria closer to the real situation and under the circumstances given by higher incomes to the population. As it has to be, in 2012 as well, a number of producers and traders have been obliged to diminish at maximum the margin of their profitableness with the hope of being in the position to sell their products instead of keeping them in stocks, in many situations these goods being sold even below their real market value. There is another aspect to underline5 as well namely the fact that, unfortunately, in Romania there is an underground economy which keeps on maintaining, “producing” or “offering” certain goods and services to the population at low levels of price which, although always of a suitable quality, represent an element of “temptation” for

5 Voineagu, V. et al. (2013) – “The Economy of Romania during the Period 2000-2012”, Romanian Statistical Review Supplement., Volume (Year): 61 (2013), Issue (Month): 1 (March), pp. 96-104


the consumers who go for these items from financial reasons (saving sense).

Thus, even if the payment for certain services will be reflected in the index of the population’s consumption price, as a percentage only, the increase of these prices in form of taxes and charges to be paid on properties, dwellings, terrains, transport means etc., by the population next year only, is already leading to difficulties in recording such an index for the respective year.

On the other hand, it would be recommendable to forecast some steps of social protection for the population so that the increase of the index of the inflation does not affect too profoundly, through pauperization, the situation of the population of our country. Of course, the reform must be continued but a minimum of protection steps must be secured to the population.

Incredible leaps of the gross average wage on the economy have been achieved in the years 2008 and 2009 but they could not be paid in 2010 and 2011, since, in fact, half of them had not a real fundament. This trend has been dictated by electoral interests, without cover in the market offer and economic capacities. We are presently at the border of the concealed scandal between the power and the opposition, “under the mediation of the IMF”. In fact, even if at different levels of responsibility, to be blamed are all those governing, as they could, during the period 01.09.2009-30.05.2012 but analysing the situation is not a subject of this work. This is only an introduction to the theme, so that the false illusion of “better in 2012” gets temperate. For the first time in Romania, the year 2012 marked the succession of three government teams, differing through doctrine and strategy. After the elections of December 9th, 2012 the situation stabilized and a process of significant changes. Nevertheless, until March 2013, marking one year since Boc left, we keep on talking about one year in which we have been greeted (this is the only way to put it in this analysis) by four governing teams. The economic and social effects are obvious while the prospects might be even worse unless one of the following three variants happens: accepting the co-habitation on the ground of strategies for economic and social development of Romania, not on the doctrinal basis; the president’s


withdrawal; obliging the president to either sticking with his attributions or withdrawing…. And the last but not the least, Romania must regain its “voice” as an European country without interferences from outside.

��

� ��1��2��∗�

• When analysing this situation, a full correlation with the the inflation rate must be considered as well as with the mode in which these monetary resources are placed in the frame of the consolidated balance sheet.

If considering the year 2013, such an analysis can be achieved on the basis of the statistic data published by the National Institute of Statistics (Statistical Bulletin no. 7/2013).

Thus, during the mentioned period, the total placements in the credit account amounted 474,121.1 million lei for the month of July 2013 as against 479,805.4 millio lei in December 2012.

Consequently, during the year 2013, the situation of the placements in assets kept on increasing in accordance with existing resources of the market1.

An aspect which has to be emphasized refers to the external assets chapter which, starting with the year 1997 up to July 2013, recorded a high value amounting 178,125.7 million lei.

As far as the internal assets are concerned, they amounted 295,995.4 million lei, out of which the non-governmental credits counted for 221,432.3 million lei.

The governmental credits counted for 9,573.8 million lei, while the negociable equities amounted 62,947.5 million lei in bonds and treasury bills, respectively 2,041.8 million lei in shares and other capital participation titles being held.

∗ Some aspects included in this chapter were also presented in the article Budgetary Execution, Monetary Market – Resources and Placements, RRS Supplement no. 4/2014, authors prof. Constantin Anghelache PhD, prof. Gabriela Victoria Anghelache PhD, lecturer M�d�lina Gabriela Anghel PhD 1 Anghelache, C. (2013) – “România 2013. Starea economic� sub povara efectelor crizei”, Editura Economic�, Bucure�ti. See also Anghelache, C. (2012) – “România 2012. Starea economic� în criz� perpetu�”, Editura Economic�, Bucure�ti


The external liabilities amounted 120,994 million lei, out of which 120,540.8 million lei as deposits. The internal liabilities counted for 353,128.7 million lei, out of which 101.895,3 million lei long term financial liabilities and 225.905,2 million lei money at large extent.

A more accurate picture on the monetary situation is given by the following table: From the point of view of the monetary situation (placements and resources), as a result of a careful strategy of the National Bank, the year 2013 recorded a good evolution.

By means of the system of treasury bills, public securities etc., as well as through the interests set up by the commercial banks or the lever of the exchange rate evolution, a significant amount is drawn from the population as well as from the savings in foreign currencies of the residents.

• During the year 2012, the execution of the state budget has been achieved quite difficultly so that by the end of the year it closed up with a deficit of 26,717.5 million lei. In the case of the budget of the state social securities, by the end of the month of July 2012, an excess of 175.3 million lei has been recorded and, by the same time, the local budgets have recorded an excess of 667.7 million lei2.

For the period 2001-2012, the Executive, through the Ministry of the Public Finances, paid all necessary efforts, drew up and submitted to the approval of the Parliament, the budgets (the state one and the state social securities one) for the following years.

The outcomes of the budgetary execution for the year 2012 has been somehow interesting since it would have been normal that, in the case of a correct collecting, the multitude of taxes and charges lead to additional incomes to support the expenses at the state budget level.

But if considering the chapter of the indirect taxes, mainly excises, charges, value added tax, these incomes have been not entirely achieved because of the fact that, on one hand, the activities involving

2 Penu, D. (2012) – “The Analysis of the Budget Deficit in Romania”, Romanian Statistical Review Supplement, Volume (Year): 60 (2012), Issue (Month): 1 (March), pp. 73-77


excises diminished and, on the other hand, in the case that these excises increased, the physical volume of the respective activity decreased. There is a similar forecast to consider for the years 2013 and 2014, when the government should reduce the excises for those products for which there are no taxes on consumption perceived in the frame of the European Union.

There has been also a, let’s say recklessness, to consider when considering the exemptions and re-spreading of payments being granted for the payment of taxes and charges for the benefit of a large number of economic agents.

Neither the incomes from capital, such as those resulting from the process of turning to account certain goods belonging to the state, recorded a significant level while the cashing from the reimbursement of the granted loans have been quite low.

The year 2013 counted for the tenth year of applying the unique taxation quota of 16%. As from July 2013, the diminished quota of taxation for the VAT on bakery products has been reinforced.

It is necessary that appropriate steps are taken in order to stimulate the economic activity and the development, mainly, of the small and medium companies (the middle stratum), so that these steps, correlated with the possibility to support certain branches of the national economy in the frame of the reform, allow new jobs to be generated and lead to the decrease of the expenses made by the state, mainly at the chapter of the state social securities, for sustaining the unemployment.

The fact that, from the point of view of the way in which the expenses from the state budget have been achieved, most of the activity sectors but mainly the education, health, culture, social security, defence, public order and national security, the expenses are low as comparatively with the resources available with the population, generally speaking, or with those running their activity in these domains, has to be underlined as an alarming situation3. 3 Man, M., Marin, R.M. (2011) - “Aspects Regarding the Evolution of Romania’s Public Debt in the Context of its Integration within The E.U. and of Worldwide Financial Crisis”, Annals of the University of Petrosani – Economics, Volume (Year): 11 (2011), Issue 1, pp 129-136


This means actually that the sources out of which the state budget incomes have been formed (fiscal, non-fiscal), were not collected always at the level forecasted when the state social securities budget had been drawn up.

Under the circumstances, the higher expenses required cover from other sources, involving difficulties for the forthcoming period if considering that up to now the main expenses from the state social security budget (allocations, pensions, supports and indemnities) have been not properly increased so that the next period will require new incomes sources4.

Since after the reinforcement of the Fiscal Code there are still certain persisting ambiguities, there will definitely be difficulties to face as far as the budgetary execution is concerned over the forthcoming period. Therefore, we take the liberty of considering that it is compulsory that the Ministry of Public Finances should proceed to take necessary steps meant to temper the effects of the financial crisis, such as:

- Collecting , from contributors, the observations concerning the Fiscal Code, a beforehand simulation of the forecasted steps and afterwards, accommodating this law to the needs and the economic conditions from our country;

- Intensifying the efforts meant to secure the collecting of the incomes to the state budget, local budgets and state social security budget;

- Correcting, towards a reduction of the taxation policy, certain taxes and charges, allowing thus an easier collecting of all due amounts, from individuals and juridical persons;

- Recovering the debts from the big debtors, by means of taking over quotas of shares packages of the private commercial companies being in this situation and of

4 Mitac, M. (2011) – “The Impact of the Current Financial Crisis on Romania’ Budget”, Ovidius University Annals, Economic Sciences Series. Volume (Year): XI (2011), Issue (Month): 2 (May), pp. 821-824


imposing an adequate management or the re-privatization of these companies (shares packages);

- Getting additional incomes out of privatization (with the hope that this will be the final outcome of finalizing the privatization), as well as out of new loans granted even if by the IMF.

Certainly, these steps could be considered within a larger context in the frame of the process of reform and the programme of social protection which the government should consider. One never should forget that when adding minus to minus a bigger, even abyssal minus could occur mainly when facing a deep financial crisis.

However, one must make the point on the fact that a plus can result only when “multiplying” minus by minus. This means that correcting the budgetary deficits for the years 2010 and 2011 excessively through the reduction of the salaries and the increase of taxes/charges was not advisable since such a policy would compulsory lead to the diminishing of the consumption, taxation basis etc. and would deepen profoundly the social crisis with hard to anticipate developments and effects.

• The deficit of –10,022.2 million lei, recorded by the state budget by the end of the month of July 2013 is representing a significant exceeding of the level planned for the entire year. Thus, the year 2013 failed to allow the fulfilment of long time aimed target, namely recording excesses.

If considering other categories of income, such as the incomes cashed from privatization, there are obviously difficulties which clearly lead to the conclusion that privatization by assets selling at any price proved to lack a major role all together, not even for achieving incomes for the state budget.

Irrespectively the extent of the need for incomes would be over the next period, it is necessary to pay an additional attention to evaluating the privatization reform steps on the basis of economic efficiency so that to avoid running the risk to alienate essential values of the national wealth against modest amounts, without any prospects to get them recovered during the next period.


The returns from excises, customs charges or the tax on crude and natural gas from the domestic production are by far lower as against the initial forecast, if comparing them with the programme set up for the year 2013. The situation is easily explainable by the fact that the above mentioned taxes have been increased by the unsubstantiated decision of the Ministry for Public Finances aiming to increase the incomes to the state budget. The outcome of such a step was contrary to the goal due to the fact that higher taxes led to prices increase, sales decline and, consequently, lower returns, not to mention that this policy involved an escalade of the general prices, all over the national economy, with an immediate effect on the deterioration of the population living standard.

Here we can consider that there is a subject to be analysed by those who conceived the state budget for the years 2011-2013, as they should indubitably focus on the effort to find out levers for quicker collecting of incomes to the state budget, to relax the fiscal system so that to collect little from many instead to aim collecting much from some few and, mainly, to reach an equilibrium as regards the process to let the entire economy come out from the underground by means of relaxing fiscal steps.

Otherwise, if theoretically, the steps taken by the time of the budget rectifications in the direction of increasing the taxes and charges might look beautifully on the paper matrix, they definitely would prove to be totally non-efficient for the practical activity of the economic process and, mainly, for the collecting activity, because of the clear danger to get some activities running to the “underground” and to lose any control on them.

The expenses category referring to interests paid on account of the public debt is just another element implying a proper attention view that it reaches a high level.

Although generating problems to the credit claimers from the budget, unable to cover the real expenses, the other categories of expenses have been made within the availability limits, as a rule. When drawing up the budget for 2013, the increase of the expenses directed to certain consuming sectors from the state budget has been emphasized.


However, taking into account the fact that there is a high level of dissatisfaction assuming that additional amounts are needed in the perspective of balancing the budget, it will be quite difficult to achieve the required equilibrium.

If considering the way of achieving the stipulations of the state social security budget, submitted by the following table, we have to face a kind of a delicate situation.

Based on the above analysis we can conclude that the level of achieving the state budget, the social state security budget and the local budgets has been reached with difficulty, mainly as far as the state budget is concerned which, despite the rectifications being applied, could not be entirely balanced and did not satisfied integrally the stringent needs of certain vital sectors of activity.

Certain evaluations and comments might be underlined as to the deficit of the consolidated budget as well but in this case there are no particular new aspects to consider and the basic grounds of the developments recorded in this case are the same as always.

• The internal public debt keeps accumulating under the circumstances of a national economy breathing with difficulty, lacking prospects to reach a steady status, even if at a very low level, so that it can meet the more and more higher requirements of the budgetary execution5.

The increase of the public debt in Romania would definitely not be a particularly tough issue if a prognosis, either on short or medium term, exists as regards the quantification of some real incomes to be drawn to the state budget.

Otherwise, under the existing conditions, when the incomes to the budget are flatly exceeded by the expenses set up through the state budget, one has to resort to the possibility to balance the budget by means of increasing the public debt, both internal and external.

As the internal public debt is bearing serious interests, particularly nowadays, in the context of the world financial crisis, over 5 Anghelache, C. (2013) – “România 2013. Starea economic� sub povara efectelor crizei”, Editura Economic�, Bucure�ti. See also Anghelache, C. (2012) – “România 2012. Starea economic� în criz� perpetu�”, Editura Economic�, Bucure�ti


the forthcoming period it will lead to the increase of the expenses from the state budget, on one side and, on the other side, will result in the rise in the price for the population life.

The fact that for the time being the internal public debt reached a higher level is essential, not to mention that the government has to pay interests as well.

In order to be in the position to pay back the internal debt, the government, through the Ministry for Public Finances, has no choice but to keep on borrowing from the commercial banks and on drawing money from the population by means of issuing treasury bills.

This mechanism allows the government to get the possibility of a break enabling it to meet the major requirements for sources meant to cover the expenses from the state budget.

The issue arising from such a situation consists of the fact that these being uncovered expenses, the government should go for several budgetary rectifications. Or, these budgetary rectifications could have been done by means of finding put “new solutions” only, meant to bring additional incomes to the state budget.

On one hand, such action might prove once again to be merely a theoretical one, if considering the fact that it led to stagnation for the volume of certain goods sale; on the other hand, one cannot disregard the fact that, in an immediate perspective, a share of the businesses with such products slips, slowly but certainly, to the uncontrolled zone of the market.

Simultaneously, in order to draw new financial sources, mainly from the population, the government will have to sell treasury bills which, on one side will lead to the increase of the internal public debt while, on the other hand, a kind of settling down the population requirements would be achieved as a consequence of the fact that some of the existing financial sources will be drawn and so the ratio between demand and offer will get “balanced”, in the sense of getting a diminished demand due to lack of financial possibilities. However, there is still the risk that the alterations of the excises for certain products lead, un-doubtfully, to a fan if not a real avalanche of price increasing for the other products as well, those including (sometimes not including) costs on the account of the excised products.


Under the event of economic and financial circumstances of the years 2011 and 2012, it would have been more efficient if the budgetary rectifications were not made on the basis of the two above mentioned sources only, but also by means of finding out concrete ways to stimulate the production so that to achieve a profitable activity, enabling the salaries to be reconsidered in a positive sense while the real taxes (taxes on profit, on wages etc.) to be cashed by the state increase.

Otherwise, allegations of the kind „we overpassed the top of the external debt reimbursement” are not bringing any satisfaction and, mainly, any comfort and peace for the majority of the population, as long as there are no allegations of the kind “a number of steps have been identified and taken concerning the security of the social protection”.

This is why the level presently recorded by the internal public debt in Romania is high enough if considering the fact that for the largest part of the population the incomes reached a hardly bearable level. It is almost impossible to figure how could the population deal with the chapter “expenses for two budgets” with “incomes for a single budget” when the internal public debt almost equals the budget for one year. The austerity steps taken in 2011, which kept on being applied over the first five months of the year 2012, as well as the loans with the IMF, World Bank and European Union, will weigh heavily for the internal financial strategy. 2012 is the year when the financial effects of the policy applied over the last three years have been negatively felt on the living standard of the population.

For the time being there is the possibility to find out solutions for freezing the wages only but no solutions to encourage activities which generate new jobs and secure at least decent incomes for the population, along with the limitation of the unemployment rate which will have a negative effect for Romania in 2013 (on the living standard of the population, mainly on the un-favoured categories.

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