Effectiveness of the global banking system in 2010 a data envolopment analysis approach

Based on available data from 64 countries over the world, the author tried to evaluate the effectiveness of the banking sectors in those countries through the view point of the data enve

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Chinese Business Review, ISSN 1537-1506

November 2011, Vol 10, No 11, 961-973

Effectiveness of the Global Banking System in 2010:

Ngo Dang-Thanh

University of Economics and Business (Vietnam National University), Hanoi, Vietnam

Massey University, Palmerston North, New Zealand

The current crisis has revealed the weaknesses of the global financial in general and its banking system in particular, and puts forward a requirement for assessing the effectiveness and stability of the banking sectors across countries Based on available data from 64 countries over the world, the author tried to evaluate the effectiveness of the banking sectors in those countries through the view point of the data envelopment analysis approach to define how the global banking systems is under the effect of the current crisis Findings from the research showed that banking systems in advanced economies are still more effective than in developing countries Moreover, it explained the effect of the current financial crisis, the role of public finance (and the government), and the development of the (privately) commercial banks to the effectiveness of the banking sectors The research also explained some determinants that can affect the effectiveness of the banking system, including inflation, bank concentration, and level of economic development

Keywords: data envelopment analysis, effectiveness, efficiency, banking, cross countries

Introduction

Because of the important role of the banking and financial system in the rapid development of new industrial economies (NIEs) in the 1960s-1970s, there were renewed interests in the relationship between financial and economic growth Schumpeter (1911) argued that the role of financial intermediaries in savings mobilization, projects evaluation and selection, risk management, entrepreneurs monitor, and facilitating transactions is important to technological innovation and economic growth Following this argument, many other leading economists continuing emphasized the positively essential role of the financial sector in economic development, including Goldsmith (1969), Shaw (1973), McKinnon (1973), King and Levine (1993a, 1993b)

Banks are the core of the financial system They accept deposits from savers and lend them to borrowers

∗

Acknowledgement: The author would like to offer special thanks to Professor David Tripe at Centre for Banking studies,

Massey University, New Zealand for his supports, encouragement and useful comments The author also thanks participants at the 18th Annual Global Finance Conference in Bangkok, Thailand, April 2011 for their constructive comments and feedback to improve the quality of the paper The usual disclaimer applies

Ngo Dang-Thanh, Ph.D candidate, Lecturer, Faculty of Political Economy, University of Economics and Business (Vietnam National University), Centre for Banking Studies, Massey University

Correspondence concerning this article should be addressed to Ngo Dang-Thanh, Faculty of Political Economy, University of Economics and Business (Vietnam National University) E-mail: ndthanhf@yahoo.com

EFFECTIVENESS OF THE GLOBAL BANKING SYSTEM IN 2010

962

They hold liquid reserves which allowing predictable withdrawal demand They issue liabilities which are more liquid than the deposits They also reduce (or some times eliminate) the need of self-finance (Bencivenga & Smith, 1991, p 195) Banks hold an important role within the financial system, and to some certain level, researching the banking system therefore means researching the financial system

Started from the bankruptcy of the Northern Rock Bank in the UK (2008, February), however, the global financial crisis and its heavily impacts have put researchers and policy makers under the requirement of re-assessment and re-evaluation the stability and performance of the global financial and banking system1

A firm is effective when it reaches its target outputs Similarly, a banking system is defined as effectiveness

if it can fulfill its missions of providing banking services and monitoring the stability of the system Meanwhile,

if banking systems are set under similar conditions of macro- and micro-economic, the level of outcomes that a banking system can provide (in term of services and stability) is indeed its efficiency In this sense, the problem

of calculating effectiveness of banking systems all over the world becomes the problem of evaluating its efficiency with a (dummy) similar and equal input This research is trying to define the effectiveness of the global banking system in 2010 through analysing cross-country data observed from 64 countries, using the data envelopment analysis (DEA) approach The remainder of this paper is organized as follows Section 2 gives some reviews on efficiency and effectiveness evaluation in the banking sector using DEA approach Section 3 explains the methodologies and technical will be applied in the research Section 4 shows empirical results and section 5 concludes

Literature Review

To evaluate the efficiency of a set of firms (or banks), the most popular approaches are ratio analysis, parametric analysis and nonparametric analysis (the latter two methods belongs to the X-efficiency approach) While ratio analysis focuses on ratios between two variables (of inputs or outputs) to define the productivity and efficiency, X-efficiency analysis evaluates the efficiency of a bank through a multi-variables aspect

DEA is a popular nonparametric method applied in evaluating efficiency in finance and banking area After Farrell (1957) laid the foundation for a new approach in evaluating efficiency and productivity at micro-level, Charnes, Cooper and Rhodes (1978) and then Banker, Charnes and Cooper (1984) developed the CCR and BCC-DEA model, respectively, to evaluate the (relative) efficiencies of the researched decision making units (DMUs) Since then, DEA was increasingly applied in efficiency evaluation, especially in social sciences2 There are a limited number of researches using DEA to examine banking performance at cross-country level

A study in 1997 showed that out of 130 studies on banking performance and efficiency, only six were focused on comparing the efficiency level of banking systems across countries (Berger & Humphrey, 1997, pp 182-184) As shown in Table 1, all three DEA studies were using small sample data at institutional (bank) level to define the benchmark frontier, hence, the global banking system was left untouched

In the 2000s, further studies which used common frontier approach were developed by add in the model

1 According to Science Direct, since 2010, there are more than 2,200 journal articles regarding banking performance after the crisis of 2007-2008 (Retrieved December 20, 2010, from http://www.sciencedirect.com)

2 Recent study of Avkiran (2010) showed that there are more than 170 articles using DEA as a main methodology to analyse the efficiency of banks and banks branches, including Sherman and Gold (1985), Peristiani (1997), Schaffnit, Rosen and Paradi (1997), and Pastor, Knox Lovell and Tulkens (2006)

EFFECTIVENESS OF THE GLOBAL BANKING SYSTEM IN 2010 963

some environmental/controllable variables such as banking market conditions or market structure and regulation (Kwan, 2003; Lozano-Vivas, Pastor, & Hasan, 2001; Maudos, Pastor, Perez, & Quesada, 2002; Sathye, 2005) However, as they are also mainly focused on institutional level data while macro-environment is different from country to country, they ignored that banks which are efficient in this country may not performance well if they run as foreign-owned banks in other countries (Berger, 2007, p 125) Hence, while trying to examine the whole banking systems across countries, this study attempts to overcome the above problem

Table 1

Studies on Banking Performance at Cross-Country Level (Prior to 1997)

Berg, Forsund, Hjalmarsson, &

Fecher & Pestieau (1993) Distribution free approach 11 OECD countries Financial service

Ruthenberg & Elias (1996) Thick frontier approach 15 developed countries Bank

Bukh, Berg, & Forsund (1995) Data envelopment analysis Norway, Sweden, Finland, Denmark Bank

J Pastor, Perez, & Quesada (1997) Data envelopment analysis 08 developed countries Bank

Note Source: Berger and Humphrey (1997)

As DEA evaluates the efficiency of each DMU based on the optimal multipliers (or weights) of inputs and outputs factors, it allows us to examine the effectiveness of a banking system by looking at the achievements of the banking sector, including both quantity (assets, deposits, credits, etc.) and quality (overhead cost, nonperforming loans, frequency of bank crises, etc.) factors of commercial banks in the economy3 They are chosen following 122 variables represent the stability of the global financial system (WEF, 2010, Appendix A) However, since DEA treats those factors dynamically (meaning each country can have its own preference on them), to be understandable in evaluating and comparing the effectiveness of the banking systems between countries, a common preference (or common set of weights) for the above analyzed factors is required Therefore,

in this research, the DEA model will be divided into three stages, in which the first stage conducts a dynamic DEA model (DSW model) to define the relatively efficiencies of the banking systems from these 64 countries; the second stage examines the determinants affecting that efficiencies (Tobit model); and the third stage defines the common set of weights for those analyzed factors (CSW model) in order to conduct the final banking effectiveness scores

Technical Methodologies

In the first step, DSW model is produced to calculate the maximum effectiveness scores that each country can achieve with the observed (achievement) factors Mahlberg and Obersteiner (2001) and Depotis (2004) developed an input-oriented DEA-like model which treats all factors as outputs, while input is a dummy variable (values equal to 1 for all countries) Therefore, the DSW model in this research is in fact a

constant-returns-to-scale (CRS) and input-oriented DEA model For an evaluated country j 0-th, its efficiency

score (DSWj 0) can be expressed by the following non-negative linear problem:

3

It is important to notice that these factors are outcomes that a banking system is aiming for; hence, the DEA model in this paper will use them all as output variables

EFFECTIVENESS OF THE GLOBAL BANKING SYSTEM IN 2010

kj k

mj m

x v

y u

u m : weight of m-th output factor;

v k : weight of k-th input factor;

In the next step, a Tobit regression (for more details, see Tobin, 1958) is used to determine the factors affecting the country’s banking efficiencies (Tobit model) Since the CSW scores are bounded between 0 to 1, non-censored regression models could be biased (Fethi & Pasiouras, 2010), while Tobit regression is justify as in equation (2) Variables used in this model are ones that mainly related to the financial efficient of a banking system at micro-level and are expressed in Table 2

EF = + 1*CONC + 2*ROA + 3*ROE + 4*CIR + 5*INF

+ 6*CTA + 7*NIM + 8*CII + 9*GROUP (2)

Table 2

Variables of the Tobit Model

Variables Definition

CONC Bank concentration (assets of three largest banks as a share of assets of all commercial banks)

ROA Bank’s average return on assets (Net income/Total assets)

ROE Bank’s average return on equity (Net income/Total equity)

CIR Bank’s cost to income ratio (Total costs as a share of total income of all commercial banks)

INF Inflation, consumer prices (annual %)

CTA Bank’s capital to assets ratio (ratio of bank capital and reserves to total assets)

NIM Net interest margin of banks (value of bank’s net interest revenue as a share of its interest-bearing assets) CII Depth of credit information index (measures rules and practices affecting the coverage, scope and accessibility of

credit information)

GROUP Dummy variable of income group (equals to 0 if country belongs to lower income, 1 if middle income, and 2 if high income group)

EFFECTIVENESS OF THE GLOBAL BANKING SYSTEM IN 2010 965

The last step is to define the optimal common set of weights which should be used for compare and ranking countries based on their banking systems’ effectiveness It is done by applying the CSW model It is believed that the efficient frontier found in the DSW model in the first step is the “best practice frontier” (Grosskopf & Valdmanis, 1987; Schaffnit, Rosen, & Paradi, 1997); hence, the optimal common weight set will be the one that get every countries’ performances closest to that frontier There are several ways to define that common set of weights is based on this idea While imposing bounds for factor weights, Roll and Golany (1993) found out that the common set of weights can be defined by maximizing the average efficiency of all DMUs or maximizing the number of efficient DMUs Kao and Hung (2005) applied a compromise solution approach to minimize the total squared distances between the optimal objective values (found by DEA) and the common weighted values (found

by using common set of weights) Jahanshahloo, Memariani, Lotfi and Rezai (2005) applied the multiple objective programming approach to simultaneously maximize the performance scores to get it closes to the “best practice frontier” Liu and Peng (2008) applied the common weights analysis to minimize the vertical and horizontal virtual gaps between the benchmark line (slope equals to 1.0, or performance scores equal to 1.0) and the coordinate of common weighted DMUs In this paper, we modified the model of Kao and Hung (2005) into a minimum distance efficiencies model, in which the common set of weights can be defined as the one minimizing the total distances between optimal efficiencies (DSW scores) and common weighted scores (CSW scores) of all DMUs, under the condition that each DMU’s efficiency cannot exceed its DSW efficiency4 To understand the role of each factor in CSW scores, another condition was added where the total sum of weights is equal to 1 (or 100%) The country’s banking effectiveness scores will be constructed based on that CSW scores and findings from the super efficiency DEA results in the previous step This CSW model can be expressed as a non-negatively linear problem as follows:

mj m j

x v

y u

EFFECTIVENESS OF THE GLOBAL BANKING SYSTEM IN 2010

ES j : Effectiveness score of country j-th;

u m CSW : Common weight of factor m-th;

y mj : Value of factor m-th of country j-th

Empirical Results

In the first stage, countries and factors are collected from the database of Beck, Demirgüç-Kunt and Levine

(2000), Laeven and Valencia (2010), the World Bank (World Development Indicator, Global Development

Financial, and Doing Business databases), the International Monetary Fund (IMF, 2010), the Consultative Group

to Assist the Poor (CGAP, 2010) and Annual Reports from Central Banks of such researched countries Ten

factors6 are included in this research, covering both quantitative (the first 5 factors) and qualitative (the last 5

factors) aspect of the banking sectors (see Table 3) It is important to notice that the last 3 factors are undesirable

factors (as they have negative effect to the banking effectiveness), hence, they was transformed into desirable

ones through the linear monotone decreasing transformation method7

Table 3

Descriptive Statistics of Factors

Domestic credit provided by banking sector (% of GDP) 80.21 8.74 69.92 -11.17 379.30

Note Data of the last three variables are already transformed.

As mentioned in section 3, those factors will be treated as output variables, while a dummy-input (equals to

1) will be set for the whole 64 countries The DSW model then produces an effective frontier built from 25

countries, while the other 39 are ineffective (see Appendix A Table A2)

Within the ineffective ones, none of them is developed countries, suggesting that the banking systems in

6 According to Dyson et al (2001, p 248) and Avkiran (2001, p 68), one rule of thumb in using DEA is that the sample size has

to be at least 3 times bigger than the number of total inputs and outputs to overcome the discrimination problem As we have 64

samples over 10 variables, hence, this research is justified

7

In this method, the transformed values will be calculated by the difference between a proper translation vector w with the

original values of those undesirable factors For more details, see Seiford and Zhu (2002) and Fare and Grosskopf (2004)

EFFECTIVENESS OF THE GLOBAL BANKING SYSTEM IN 2010 967

advanced economies still run better than in developing countries although they had to bear stronger effect from

the current crisis This can be explained by the difference between projected values and original values of these

factors (in percentage of original values), in which the biggest differences are mainly for quantity factors, except

for the case of private credit bureau coverage The results show that, major weaknesses of ineffective countries in

banking system development are the ATM network, bank deposits to GDP, private credit coverage, bank assets,

and bank’s domestic credits Those are the disadvantage of developing countries as they are still on their way

developing their financial and banking systems (see Table 4)

Table 4

Differences Between Projected and Original Values for Inefficient Countries

In value In percentage of original value

In the second stage, the results from Tobit model show the relation between the banking systems’

effectiveness and various variables such as inflation level of the economy, income group that the country belongs

to, concentration of the banking system, etc., as summarized in Figure 1 It is obvious that higher inflation,

banking concentration, and bank’s cost-income ratio can reduce the effectiveness of the banking sector

(respectively significant at 1, 5 and 10 percent), while the high level of economic development (improving to

higher income group) can help increase the effectiveness of the banking system (5% significant level)

Figure 1 Determinants of the global banking effectiveness

EFFECTIVENESS OF THE GLOBAL BANKING SYSTEM IN 2010

968

In the last stage, solving the non-linear problem of the CSW model (equation (3)) helped us defining a

common set weight for the ten factors of every country in the research (see Table 5) Noticeably, important

factors which strongly affect the performance of the banking sector in those countries are non-performing loans

ratio (79.49%), public credit bureau coverage (10.47%), and number of branches per 100,000 people (3.03%)

The other factors only keep minimum role (1% weight) in the final results It shows that the effectiveness of the

banking sector is mainly affected by the damage of the global crisis, the (financial) public policy of the

government, and the development of the commercial bank system of each country respectively It also suggests

that the quality of the banking sector is now becoming more important than the quantity aspect, not only for

countries with developed banking systems but for developing countries as well Thus, country which focuses on

improving the quality of its banking sector can have higher effectiveness and is more stable

Table 5

Common Set of Weights for the Effectiveness Scores

Factors Weight

By applying this common set of weights, the effectiveness scores of country’s banking systems can be

calculated and countries can be ranked as in Table 6 Since non-performing loans ratio became the most

important factor, countries having problems with NPLs became less efficient and ranked bottom in the list,

including even Denmark and New Zealand

Table 6

The Global Banking Effectiveness in 2010

EFFECTIVENESS OF THE GLOBAL BANKING SYSTEM IN 2010 969 (Table 6 continued)

Conclusions

Using data from 64 countries in the world, this research applied the data envelopment analysis (DEA) to evaluate the effectiveness of banking systems in the World in 2010 The research was divided into three steps, in which the first stage applied data envelopment analysis method to build a common frontier for these 64 countries; the second step detected the determinants of the banking sector’s effective; and the last step defined a common set

of weights for analyzing factors helping in ranking the effectiveness of the global banking system in 2010 The research evaluated the effectiveness of the global banking systems using a dummy input and ten outputs

to create a common frontier for the whole banking systems of 64 countries (while previous studies used institutional level data of smaller sample size); and after that building a common set of weights to calculate the effectiveness scores of the global banking system, applied to the DEA method This proposes an interesting function for using DEA in examining the effectiveness (and efficiency) in the banking sector

Findings from the research showed that banking systems in advanced economies are still more effective than

in developing countries Reasons seem to be related to the development of the banking sector in quantity (number

of bank branches) and more importantly in quality aspects (including the NPL ratio, public credit bureau coverage, bank concentration, bank’s capital, and cost-income ratio) It is also included the effect of economic development, expresses through level of income (group) and inflation rates These results partly explained the effect of the current financial crisis to the banking sector, the role of public finance (and the government) in this kind of situation, and the important role of developing commercial banking system to its efficiency and effectiveness

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EFFECTIVENESS OF THE GLOBAL BANKING SYSTEM IN 2010

EFFECTIVENESS OF THE GLOBAL BANKING SYSTEM IN 2010 973

Table A2

Dynamic DEA Efficiencies

Note First 25 countries are ranked based on super-efficiency DEA results

Chinese Business Review, ISSN 1537-1506

November 2011, Vol 10, No 11, 974-984

Diana Bílková

University of Economics in Prague, Prague, Czech Republic

This paper deals with the use of Pareto distribution in models of wage distribution Pareto distribution cannot generally be used as a model of the whole wage distribution, but only as a model for the distribution of higher or of

the highest wages It is usually about wages higher than the median The parameter b is called the Pareto coefficient

and it is often used as a characteristic of differentiation of fifty percent of the highest wages Pareto distribution is

so much the more applicable model of a specific wage distribution, the more specific differentiation of fifty percent

of the highest wages will resemble to differentiation that is expected by Pareto distribution Pareto distribution assumes a differentiation of wages, in which the following ratios are the same: ratio of the upper quartile to the median; ratio of the eighth decile to the sixth decile; ratio of the ninth decile to the eighth decile This finding may serve as one of the empirical criterions for assessing, whether Pareto distribution is a suitable or less suitable model

of a particular wage distribution If we find only small differences between the ratios of these quantiles in a specific wage distribution, Pareto distribution is a good model of a specific wage distribution Approximation of a specific wage distribution by Pareto distribution will be less suitable or even unsuitable when more expressive differences

of mentioned ratios If we choose Pareto distribution as a model of a specific wage distribution, we must reckon with the fact that the model is always only an approximation It will describe only approximately the actual wage distribution and the relationships in the model will only partially reflect the relationships in a specific wage distribution

Keywords: Pareto distribution, Pareto coefficient, estimation methods for parameters, least squares method, wage

distributions

Pareto Distribution

The question of income and wage distributions and their models is quite extensively treated in the statistical literature (Bartošová, 2006; Bartošová & Bína, 2009; Bílková, 2007; Dutta, Sefton, & Weale, 2001; Majumder & Chakravarty, 1990; McDonald & Snooks, 1985; McDonald, 1984; McDonald & Butler, 1987)

∗

Acknowledgment: The paper was supported by grant project IGS 24/2010 called “Analysis of the Development of Income

Distribution in the Czech Republic Since 1990 to the Financial Crisis and Comparison of This Development With the Development of the Income Distribution in Times of Financial Crisis, According to Sociological Groups, Gender, Age, Education, Profession Field and Region” from the University of Economics in Prague

Diana Bílková, Ing./Dr., Department of Statistics and Probability, Faculty of Informatics and Statistics, University of Economics

in Prague

Correspondence concerning this article should be addressed to Diana Bílková, Department of Statistics and Probability, Faculty

of Informatics and Statistics, University of Economics in Prague, Sq W Churchill 1938/4, Prague 3, Czech Republic, post code:

130 67 E-mail: bilkova@vse.cz

APPLICATION OF PARETO DISTRIBUTION IN WAGE MODELS 975

Pareto distribution is usually used as a model of the distribution of the largest wages, not for the whole wage distribution In this article, we will consider using the Pareto distribution to model wages higher than median

The 100·P% quantile of the wage distribution will be denoted by x P , 0 < P < 1 This value represents the upper bound of 100·P% lowest wages and also the lower bound of 100(1 – P) % highest wages A particular quantile (denoted as x P0) which will be the lower bound of some small number of the highest wages is usually set to be the

maximum wage If the following formula (1) holds for any quantile x P, the wage distribution is Pareto distribution

0

0

1 1

b P

P

P x

The parameter b of the Pareto distribution (1) is called the Pareto coefficient It can be used as a

characteristic of differentiation of 50% highest wages

We will now consider a pair of quantiles x P1 and x P2 , P1 < P2 It follows from equation (1) that:

1 1

b P

P

P x

P x

The rate is an increasing function of the Pareto coefficient b If the rate of quantiles increases, the

relative differentiation of wages increases too If only absolute differences between quantiles increase, only the absolute differentiation of wages increases

It follows from the equation (1) that once the values x P0 and b are chosen, we can determine the quantile x P for any chosen P or the other way around for any value x P we can find the corresponding value of P In the first

case, it is advantageous to write the equation (1) as:

P

x

x P

APPLICATION OF PARETO DISTRIBUTION IN WAGE MODELS

976

or after logarithmic transformation as:

)loglog

(

1)1(log)(1

b P

P0−+

0 1 1 0

P P x x

2 1 1 2

P P x x

It follows from the equation (9) that instead of the Pareto coefficient b we can use any other quantile x P1 of

the Pareto distribution and it follows from the equation (10) that the Pareto coefficient b can be calculated using any known quantiles x P1 and x P2 Then we can also determine the value x P0 using the formulas:

, 1

1

0

1 1

x

b P

0= x ⎜⎜ ⎝ ⎛ − − P P ⎟⎟ ⎠ ⎞

x

b P

The model characterized with the relationship (1) will be practically applicable if the following is known:

 The value of the quantile that characterizes the assumed wage maximum and the value of the Pareto

coefficient b;

 The value of the quantile that characterizes the assumed wage maximum and the value of any other quantile;

 The values of any two quantiles of the Pareto distribution

Any two quantiles can be written as x P and x P+k , where 0 < k < 1 – P Using the equation (4), we can derive

for the rate of these two quantiles:

k P

P x

x b

P

k P

1

c k P

1

P c

c

We will use the constant c = 2 in equation (15) and we will choose gradually P = 0.5; 0.6; 0.8 Then using the

equation (13) we can show the equality of rates of some frequently used quantiles:

APPLICATION OF PARETO DISTRIBUTION IN WAGE MODELS 977

0.75 0.8 0.9 0.5 0.6 0.8

From the relationship (16) we can conclude that Pareto distribution assumes such a wage differentiation for which the rate of the upper quartile to median is the same as:

 The rate of the 8th to the 6th decile;

 And as the rate of the 9th to the 8th decile

If in a particular case, the observed differences of the rates of the above mentioned quantiles are negligible, Pareto distribution will be an appropriate model of the considered wage distribution In the case, the differences are quite material, the approximation of the considered wage distribution with Pareto distribution will be more or less inappropriate More about the theory of Pareto distribution is described in statistical literature (Forbes, Evans, Hastings, & Peacock, 2011; Johnson, Kotz, & Balakrishnan, 1994; Kleiber & Kotz, 2003; Krishnamoorthy, 2006)

Parameter Estimates

If the Pareto distribution is chosen as a model for a particular distribution we have to keep in mind that this model is only an approximation The wage distribution will be only approximated and the relations derived from the model will also hold for the “true distribution” only approximately Which relations will hold more precisely and for which the precision will be lower will be mostly dependent on the method of parameter estimates There are many possibilities to choose from In the following text the quantiles of Pareto distribution will be

denoted as x P and the quantiles of the observed wage distribution will be denoted as y P

First we need to decide which quantile to choose as x P0 It this article we will assume that x P0 = x0.99 From the equation (1) we can see that the considered Pareto distribution will be defined by the equation:

0.99 10.01

b

P

P x

x

−

Then we need to determine the value x0.99 and the value of the Pareto coefficient b Because it is necessary to

estimate the values of two parameters we need to choose two equations to estimate from

A natural choice is the equation x P0 = y P0 ; that is in our case x0.99 = y0.99. As the other equation we set a

quantile x P1 equal to the corresponding observed quantile, i.e., x P1 = y P1 In this case, the parameters of the model will be:

y

x P0= P0 (18)

and using equation (9):

P0 1 1 0

log

1 Plog1

P

y y b

P

−

(19)

We can get different modifications using different choice of the maximum wage and the second quantile If we

use equation x0.99 = y0.99 and we use the median in the second equation, i.e., x0.5 = y0.5 we get a model with

APPLICATION OF PARETO DISTRIBUTION IN WAGE MODELS

log0.5log0.01

y y

1loglog

2 1 1 2

With this alternative we can also get numerous modifications depending on the choice of quantiles y P1 and

y P2 that are used

The third possibility is based on the request that x P0 = y P0 and that the rate of some other two quantiles of the

Pareto distribution x P2 /x P1 is equal to the rate y P2 /y P1 of correspoding quantiles of the wage distribution observed

In this case we will estimate the parameters using equation (10):

P y P

P2 1 1 2

log

1 Plog1

P

y y b

chosen and what quantiles y P1 and y P2 are chosen

For all of the above methods the equality of two characteristics of the model and the observed distribution was required There are also different approaches to the parameter estimates

The least squares method is frequently used for the Pareto distribution parameter estimates as well We will

consider the following quantiles of the observed wage distribution y P1 , y P2 , …, y Pk and corresponding quantiles of the

APPLICATION OF PARETO DISTRIBUTION IN WAGE MODELS 979

Pareto distribution x P1 , x P2 , …, x Pk The model distribution will be most precise when the sum of squared differences:

1 0

1 log

log

k k

i Pi

P

P P b

In the case we use this estimating method, it is needed to keep in mind that the equality of model quantiles

and observed quantiles is not guaranteed for any P Again we can arrive to different results depending on what quantiles y P1 , y P2 , …, y Pk are used for the calculations Furthermore the parameter estimates also depend on the

choice of the maximum wage

Characteristics of the Appropriateness of the Pareto Distribution

For the application of Pareto distribution as a model of the wage distribution, it is crucial that the model fits the observed distribution as close as possible It is important that the observed relative frequencies in particular wage intervals are as close to the theoretical probabilities assigned to these intervals by the model as possible

It is needed to note that the same parameter estimation method does not always lead to the best results It is

of particular importance in “what direction” is the observed wage distribution different from Pareto distribution Pareto distribution assumes such wage differentiation that the relations (16) hold With real data we can encounter many different situations:

0.75 0.8 0.9 0.5 0.6 0.8

0.75 0.8 0.9 0.5 0.6 0.8

0.75 0.9 0.8 0.5 0.8 0.6

y y y

y < y < y (34)

0.75 0.9 0.8 0.5 0.8 0.6

0.8 0.75 0.9 0.6 0.5 0.8

APPLICATION OF PARETO DISTRIBUTION IN WAGE MODELS

980

0.8 0.75 0.9 0.6 0.5 0.8

It follows from equations (32)-(37) that the observed distributions will more or less systematically differ from the Pareto distribution In the case of equation (32) the differentiation of the observed wage distribution is higher; in the case of equation (33) the differentiation will be lower than in the case of Pareto distribution Some bias occurs in cases equations (34)-(37) as well (but cannot be so specified) Systematical bias should be a signal for potential adjustment of the model which could be based for example on adding one or more parameters into the model These adjustments usually lead to more complicated models Therefore, the above mentioned bias is often neglected and simple models are preferred even though they lead to some bias

Wage Distribution of Males and Females in the Czech Republic in 2001-2008

The data used in this article is the gross monthly wage of male and female in CZK in the Czech Republic in the years 2001-2008 Data were sorted in the table of interval distribution with opened lower and upper bound in the lowest and highest interval respectively The source is the web page of the Czech statistical office The following quantiles were calculated (see Table 1)

Table 1

2001-2008 (Total and Split up to Male and Female Separated)

14,042 17,125 18,458 19,557 20,566 21,564 23,227 24,696

16,987 20,215 22,224 23,077 24,470 25,675 27,590 29,553

18,254 22,193 23,797 24,849 26,328 27,693 29,900 31,769

23,319 27,754 29,590 31,082 33,292 35,230 37,892 40,541

44,921 47,172 47,719 56,369 56,852 57,326 66,395 68,828

15,781 18,667 20,116 21,321 22,446 23,460 25,366 27,115

19,037 22,604 24,145 25,306 26,822 28,090 30,284 32,343

20,697 24,199 26,041 27,286 28,989 30,525 32,663 35,105

26,264 31,101 34,564 34,819 37,211 39,381 42,815 46,375

46,781 48,047 48,417 57,514 57,808 58,104 70,522 72,338

12,187 15,181 16,453 17,303 18,211 19,202 20,392 21,600

14,655 17,727 19,281 20,293 21,426 22,530 24,024 25,558

15,700 18,903 20,628 21,560 22,804 23,966 25,924 27,215

18,904 23,291 24,637 25,776 27,503 29,082 31,338 33,405

37,526 43,339 44,883 50,776 52,508 54,054 58,649 63,628

APPLICATION OF PARETO DISTRIBUTION IN WAGE MODELS 981

From Table 2, we can see that, with the exception of male in the year 2003, 2007 and 2008, all other wage distributions have lower differentiation than Pareto distribution The systematical error occurred also in the case

of male in the year 2003, 2007 and 2008 It follows from the empirical criterion (16) and from Table 2 that in all cases the differences between the rates of the considered quantiles are negligible and therefore Pareto distribution can be used as the model of the distribution

The 99th percentile will be considered as a characteristic of the maximum wage The parameters of the Pareto distribution are estimated using the above described methods

First we consider the conditions x P0 = y P0 a x P1 = y P1 and we chose median as the second quantile, i.e.,

x0.99 = y0.99 and x0.5 = y0.5 We estimate the parameter b using the formula (21) The summary of the parameter

0.80 0.60

y y

0.90 0.80

Parameters of the Pareto distribution can also be estimated using the equations x P0 = y P0 and x P2/x P1 = y P2/y P1

We choose the 9th and 6th decile in the rate y P2/y P1 In this case we use the relations (26) and (27) to estimate the parameters The summary of the parameter estimates is also in Table 3

APPLICATION OF PARETO DISTRIBUTION IN WAGE MODELS

0.6 0.6

y x

y x

0.326952 0.283758 0.267846 0.295969 0.299456 0.275468 0.294405 0.287978

54,143 61,890 64,800 67,096 74,095 79,614 85,426 92,352

0.365843 0.348293 0.340425 0.334192 0.347455 0.354083 0.353045 0.357552

44,921 47,172 47,719 56,369 56,852 57,326 66,395 68,828

0.365843 0.348293 0.340425 0.334192 0.347455 0.354083 0.353045 0.357552

0.305624 0.265814 0.249540 0.278536 0.267749 0.257739 0.287153 0.276777

61,207 72,613 84,934 78,632 86,165 93,098 102,142 113,087

0.367449 0.368246 0.390464 0.353784 0.364658 0.373653 0.377610 0.387128

46,781 48,047 48,417 57,514 57,808 58,104 70,522 72,338

0.367449 0.368246 0.390464 0.353784 0.364658 0.373653 0.377610 0.387128 Females 2001

0.319087 0.293539 0.283055 0.300989 0.296625 0.291062 0.296461 0.303636

39,196 47,418 48,172 49,971 54,551 57,954 63,977 68,917

0.316679 0.308749 0.291217 0.287505 0.297414 0.299456 0.309955 0.314516

37,526 43,339 44,883 50,776 52,508 54,054 58,649 63,628

0.316679 0.308749 0.291217 0.287505 0.297414 0.299456 0.309955 0.314516

In the end we also estimate the parameters of the Pareto distribution using the least squares method We use

the relations (30) and (31) In this method, we choose 5th, 6th, 7th, 8th and 9th deciles of the observed wage

distribution, i.e., k = 5 Parameters estimated using the least squares method are summarized in Table 4

94.849

0.379911 0.358469 0.351034 0.344615 0.356935 0.362626 0.362359

0.366387

63.774 73.770 85.080 80.310 88.251 95.225 103.405

114.131

0.379912 0.372825 0.391617 0.360986 0.372535 0.381012 0.383183 0.391293

42.520 49.188 51.125 52.763 57.413 60.917 67.572

72.463

0.341047 0.320682 0.309187 0.303849 0.312826 0.315022 0.325878 0.330659

The values of the sum of absolute differences of observed and theoretical absolute frequencies of all

APPLICATION OF PARETO DISTRIBUTION IN WAGE MODELS 983

intervals calculated for all cases considered wage distributions are in Table 5 In the case of the theoretical frequencies at first we determined theoretical probabilities using the formula (8) From these, we determined theoretical absolute frequencies

y x y

23,255 27,327 36,520 64,422 69,930 68,849 260,786 253,373

85,795 171,404 204,535 249,348 353,661 426,442 322,437 372,117

23,859 31,658 39,722 66,249 68,679 69,104 262,224 257,050

10,089 19,711 23,576 32,457 35,349 37,737 138,678 133,953

56,291 111,796 96,863 178,858 220,276 250,764 202,143 173,262

9,959 20,298 23,747 33,076 36,321 37,653 139,428 135,089

23,926 16,716 30,902 41,416 41,615 41,137 128,854 132,125

23,687 42,148 40,237 45,460 52,493 74,302 150,258 155,071

21,270 18,595 30,011 40,957 41,449 41,812 127,313 131,224

Conclusions

The appropriateness of particular modifications of the Pareto distribution can be evaluated comparing the theoretic and empirical frequencies It is possible to compare both the absolute and relative differences between the theoretic and observed empirical distributions In this article we used the absolute differences The values sums these differences are in Table 5 The values seem to be relatively high The question of appropriateness of a given theoretic wage distribution in the case of large samples was described in statistical literature (Bílková, 2007) Some more general conclusions can be made from the values of the absolute differences of observed and theoretic distributions

With the exception of the wage distribution of women in 2001, the worst results are achieved using the

equation x0.99 = y0.99 and setting the ratio of other two quantiles of the Pareto distribution x0.9/x0.6 equal to the ratio

y0.9/y0.6 of the corresponding empirical quantiles This fact is less obvious for female distribution and most obvious for total distribution This is also due to the larger sample size of the total sample (in comparison with the

APPLICATION OF PARETO DISTRIBUTION IN WAGE MODELS

984

sample size of the sub-groups of male and female) Again with the exception of the wage distribution of women

in 2001 the second worst model is the estimate based on the equations x0.99 = y0.99 and x0.5 = y0.5 This fact is again less obvious for female distribution and most obvious for total distribution In the case of the wage distribution of

women in 2001, the worst estimate is based on the equations x0.99 = y0.99 and x0.5 = y0.5. In the case of the total group is the third worst (second best) method the least squares method (with the exception of 2005) The best

results are achieved with the method based on the equations x0.6 = y0.6 and x0.9 = y0.9 In the case of the total wage

distribution in 2005 is the third worst method based on the equations x0.6 = y0.6 and x0.9 = y0.9 and the best method

is the least squares method In the case of the wage distribution of male (with the exception of the years 2001 and 2006), the third worst (second best) results are again achieved using the least squares method The best results are

achieved with the method based on the equations x0.6 = y0.6 and x0.9 = y0.9 In the years 2001 and 2006 (set of men)

is the third worst method the method based on the equations x0.6 = y0.6 and x0.9 = y0.9 and the best is the least squares method In the case of the female group (with the exception of the years 2001, 2002 and 2006) is the third

worst (second best) method based on the equations x0.6 = y0.6 and x0.9 = y0.9 and the most precise results are achieved with the least squares method In the years 2001, 2003, 2004 and 2005 was for the group of women the most precise the least squares method The very best method for the group of male in 2001 was the least squares method In this case other methods had much higher values of the above mentioned sum of absolute differences From the above described comparison, it is obvious that the simplest parameter estimating methods can be

in the case of the Pareto distribution competing with more advanced methods

Bílková, D (2007) Modeling of income distributions using lognormal distribution In 10th International Scientific Conference

AMSE—Applications of matematics and statistics in Ekonomy Poprad-Tatry, Slovakia, August 29-September 1, 2007, CD

Dutta, J., Sefton, J A., & Weale, M R (2001) Income distribution and income dynamics in the United Kingdom Journal of

Majumder, A., & Chakravarty, S R (1990) Distribution of personal income: Development of a new model and its application to

U S income data Journal of Applied Econometrics, 5(2), 189-196

McDonald, J B (1984) Some generalized functions for the size distribution of income Econometrica, 52(3), 647-665

McDonald, J B., & Butler, R J (1987) Some generalized mixture distributions with an application to unemployment duration The

Review of Economics and Statistics, 69(2), 232-240

McDonald, J B., & Snooks, G D (1985) The determinants of manorial income in domesday England: Evidence from Essex The

Journal of Economic History, 45(3), 541-556

Chinese Business Review, ISSN 1537-1506

November 2011, Vol 10, No 11, 985-989

The Chaotic Monopoly Price Growth Model

Vesna D Jablanovic

University of Belgrade, Belgrade, Serbia

Deterministic chaos refers to an irregular or chaotic motion that is generated by nonlinear systems The chaotic behavior is not to quantum-mechanical-like uncertainty Chaos theory is used to prove that erratic and chaotic fluctuations can indeed arise in completely deterministic models Chaotic systems exhibit a sensitive dependence

on initial conditions Seemingly insignificant changes in the initial conditions produce large differences in outcomes To maximize profit, the monopolist must first determine its costs and the characteristics of market demand Given this knowledge, the monopoly firm must then decide how much to produce The monopoly firm can determine price, and the quantity it will sell at that price follows from the market demand curve The basic aim of this paper is to construct a relatively simple chaotic growth model of the monopoly price that is capable of generating stable equilibria, cycles, or chaos A key hypothesis of this work is based on the idea that the coefficient,

⎣ ⎦ plays a crucial role in explaining local stability of the monopoly price, where,

b—the coefficient of the marginal cost function of the monopoly firm, m—the coefficient of the inverse demand

function, e—the coefficient of the price elasticity of the monopoly demand, α—the coefficient

Keywords: monopoly, price, chaos

Introduction

Chaos theory attempts to reveal structure in unpredictable dynamic systems It is important to construct deterministic, nonlinear economic dynamic models that elucidate irregular, unpredictable economic behavior Deterministic chaos refers to irregular or chaotic motion that is generated by nonlinear systems evolving according to dynamical laws that uniquely determine the state of the system at all times from the knowledge of the system’s previous history Chaos embodies three important principles: (1) extreme sensitivity to initial conditions; (2) cause and effect are not proportional; and (3) nonlinearity

Chaos theory can explain effectively unpredictable economic long time behavior arising in a deterministic dynamical system because of sensitivity to initial conditions A deterministic dynamical system is perfectly predictable given perfect knowledge of the initial condition, and is in practice always predictable in the short term The key to long-term unpredictability is a property known as sensitivity to (or sensitive dependence on) initial conditions

Chaos theory started with Lorenz’s (1963) discovery of complex dynamics arising from three nonlinear

Vesna D Jablanovic, Associate Professor of Eonomics, Faculty of Agriculture, University of Belgrade

Correspondence about this article should be sent to Vesna D Jablanovic, Vinogradski venac 20, 11000 Belgrade, Serbia E-mail: vesnajab@ptt.rs

THE CHAOTIC MONOPOLY PRICE GROWTH MODEL

986

differential equations leading to turbulence in the weather system Li and Yorke (1975) discovered that the simple logistic curve can exibit very complex behavior Further, May (1976) described chaos in population biology Chaos theory has been applied in economics by Benhabib and Day (1981, 1982), Day (1982, 1983, 1997), Grandmont (1985), Goodwin (1990), Medio (1993, 1996), Lorenz (1993), Jablanovic (2010, 2011), among many others

The basic aim of this paper is to provide a relatively simple chaotic the monopoly price growth model that is capable of generating stable equilibria, cycles, or chaos

A Simple Chaotic Price Growth Model of a Profit-Maximizing Monopoly

In the model of a profit-maximizing monopoly, take the inverse demand function:

P t = n – mQ t (1)

Where P—monopoly price; Q—monopoly output; n, m—coefficients of the inverse demand function

Further, suppose the quadratic marginal-cost function for a monopoly is:

MC t = a + bQ t + cQ t 2 (2)

MC—marginal cost; Q—monopoly output ; a, b, c—coefficients of the quadratic marginal-cost function

Marginal revenue is:

=

e P

MR t t 1 1 (3)

MR—marginal revenue; P—monopoly price; e—the coefficient of the price elasticity of demand

A monopoly firm maximizes profit by producing the quantity at which marginal revenue equals marginal cost Thus the profit-maximizing condition is that:

MR t = MC t (4) Further,

MC t+1 = MC t + ΔMC (5)

Or

MC t+1 = MC t + αMC t+1 (6) i.e.,

(1-α ) MC t+1 = MC t (7) Thus, the chaotic model of the profit-maximizing monopoly is presented by the equations (1)-(4) and (7)

Where: Q—output of the monopoly firm; MC—marginal cost; MR—marginal revenue; P—monopoly price;

e—the coefficient of the price elasticity of demand; n, m—coefficients of the inverse demand function; a, b, c—coefficients of the quadratic marginal-cost function

Firstly, it is supposed that a = 0 and n = 0

By substitution one derives:

size of the monopoly price, P, relative to its maximal size in its time series P m We introduce p as p = P/P m Thus,

Now, growth rate of the monopoly price is measured as:

THE CHAOTIC MONOPOLY PRICE GROWTH MODEL 987

1

111

e m

c e p

e m

b e p

+

−

−+

This kind of difference equation (9) can lead to a very interesting dynamic behavior, such as cycles that repeat themselves every two or more periods, and even chaos, in which there is no apparent regularity in the

behavior of p t This difference in equation (9) will possess a chaotic region Two properties of the chaotic

solution are important: firstly, given a starting point p 0 the solution is highly sensitive to variations of the

parameters b, c, m, and e; secondly, given the parameters b, c, m, and e the solution is highly sensitive to variations of the initial point p 0 In both cases the two solutions are for the first few periods rather close to each other, but later on they behave in a chaotic manner

Logistic Equation

The logistic map is often cited as an example of how complex, chaotic behavior can arise from very simple non-linear dynamical equations The logistic model was originally introduced as a demographic model by Pierre François Verhulst It is possible to show that iteration process for the logistic equation:

b e

α

π (12) Using equation (9) and equation (11) we obtain:

p1e12m

ce

THE CHAOTIC MONOPOLY PRICE GROWTH MODEL

(1) For parameter values 0 < π < 1 all solutions will converge to z = 0;

(2) For 1 < π < 3.57, there exist fixed points the number of which depends on π;

(3) For 1 < π < 2, all solutions monotnically increase to z = (π - 1)/π;

(4) For 2 < π < 3, fluctuations will converge to z = (π - 1)/π;

(5) For 3 < π < 4, all solutions will continously fluctuate;

(6) For 3.57 < π < 4, the solution become “chaotic” wihch means that there exist a totally aperiodic solution

or periodic solutions with a very large, complicated period This means that the path of z t fluctuates in an apparently random fashion over time, not settling down into any regular pattern whatsoever

Conclusion

This paper suggests conclusion for the use of the simple chaotic model of a profit—maximizing monopoly

in predicting the fluctuations of the monopoly price The model (9) has to rely on specified parameters b, c, m, and e, and initial value of the monopoly price, p 0 But even slight deviations from the values of parameters

parameters b, c, m, and e and initial value of the monopoly price, show the difficulty of predicting a long-term behavior of the monopoly price, p 0

A key hypothesis of this work is based on the idea that the coefficient plays a crucial role in explaining local stability of the monopoly price:

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THE CHAOTIC MONOPOLY PRICE GROWTH MODEL 989

Goodwin, R M (1990) Chaotic economic dynamics Oxford: Clarendon Press

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Chinese Business Review, ISSN 1537-1506

November 2011, Vol 10, No 11, 990-997

Analysis of the Relationship Between Perceived Security and Customer Trust and Loyalty in Online Shopping

Nihan Özgüven

Dokuz Eylul University, Izmir, Turkey

Advancements in the internet technology triggered a line of developments in the field of marketing As an alternative to the conventional shopping, online shopping over the internet has gained substantial share of retail market Customers get used to this new shopping venue and nowadays prefer it more and more according to the researchers, ten percent of the global population now uses internet for shopping In this research, the author explored the relationship between the security measures implemented by a company, very active in the online shopping domain, and the customer trust and loyalty on the online services provided by this company Findings of this research are based on survey data analyzed in SPSS This research supports the existence of a relationship between the security of a company’s website and customer trust and loyalty on the online services of this company When the perception of security measures improves, customer trust and loyalty increases accordingly

Keywords: customers, customer trust, perceived security, loyalty, online shopping, websites

Introduction

Today’s companies have to take advantage of the opportunities offered by the internet in order to be one step ahead of its competitors Leaving aside the traditional shopping, they need to differentiate themselves via this modern communication channel as online shopping emerges as a new domain

However, customers are confused with the increasing numbers of websites day by day In this context, companies have to generate publicity, create user blogs and provide the most honest information about their products and services in order to shine out among the realm of websites Only then, they can attract the attention and interest of the customers, according to Faks (2008)

Only after companies fully meet the customers’ needs and expectations, customer trust starts to build-up, according to Ural (2009) Online shopping turnover is increasing year by year, and the main drivers of this increase include the form of payment options offered to ease up the process and value-added services provided to increase the customer satisfaction With these advancements, online shopping today has reached about four times the size of the traditional shopping for certain goods and services

Today, from the electronic goods to car rentals to all kinds of sports materials, a wide range of goods and

Nihan Özgüven, Ph.D., Department of Business Administration, Dokuz Eylul University

Correspondence about this article should be sent to Nihan Özgüven, Dokuz Eylul University, Faculty of Economics and Administrative Sciences, Department of Business Administration, Dokuzcesmeler Campus, 35160, Buca-Izmir/Turkey E-mail: nozguven@hotmail.com

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services can be purchased over the internet Traditional retail companies are under continuous pressure of pleasing their customers and following the advancements in business to maintain their position in the market From this perspective, easy and secure online payment applications facilitate the everyday business of these companies A list of companies, including banks and credit card companies, have lost market share in this dynamic era as they failed to carry over the customer loyalty, brand awareness and thereby, the share of mind they used to own to the online media Even if these companies make online payment available, their brands can get lost among numerous e-wallets In particular, credit card and payment companies remain behind the competition when the customer accounts are linked directly to e-wallets

In the study, the literature reviewed is primarily about online shopping and its effects on the perceived reliability, and the trust and loyalty variables are explained and the relationship between these variables and online shopping are revealed

Literature Overview

In the study which researched the impact of customer trust on e-commerce, Kim, Chung and Lee (2011) concluded that internet security measures have positive impact on customer trust and no impact on transportation costs while customer satisfaction has positive impact on trust and commitment Bellman, Lohse and Johnson (1999) explored the relationship between customers’ demographic characteristics, personality traits and attitude towards online shopping; they identified that customer lifestyle is effective on attitude towards online shopping and customers with time limitations tend to do more online shopping Separately, Jarvenpaa, Tractinsky and Vitale (2000) explored the setup of online shopping website and company reputation in relation to risk perception, customer trust and attitude and demand; they emphasized that there is a positive relationship between company reputation and consumer trust and as trust improves, risk perception decreases

Ou, SIA and Banerjee (2007) explored the Chinese market and identified the mistrust in the websites, lack of regulatory framework and limited product offer as the reasons behind the slow development of online shopping over there Teo (2002) examined customer attitude towards online shopping and Internet and concluded that companies do not encourage customers to shop online and customers do not embrace the idea of online shopping

In addition, he emphasized that customers do use internet to collect information, rather than shopping

Perceived Security, Trust and Loyalty

In the online shopping domain, website security is important for the sense of trust and loyalty The security

of the website is essential to attract customer traffic and this is only possible with the security measures put in place

Perceived security Security is the fundamental concern of the customers who want to shop over the

internet, according to Suh and Han (2003) Failure to put in place adequate security measures that assure the confidentiality of the customer data is the major barrier in front of the e-commerce development, according to Furnell and Karweni (1999) In the online shopping domain, perceived security depends on the reliability of the payment methods as well as the data transmission and storage In other words, perceived security is the customer perception on the quality of tools and processes used for personal information transmission and storage, according to Kolsaker and Payne (2002)

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Trust In the online shopping, companies with online sales services thorough their websites focus on the

customer trust and online purchasing experience In traditional shopping, customer trust depends on the salesperson and company image whereas in online shopping, it depends on the reaction of buyers, their e-commerce experience and purchasing style, according to Kim, Ferriand and Rao (2008) Trust is a relationship

of exchange between the uncertainty, sensitivity and commitment, according to Jarvenpaa, Noam, and Vitale (2000) Trust is also considered in connection with the communication, commitment, satisfaction and relationship marketing theories, according to Flavian and Guinaliu (2006)

Loyalty Loyalty in online shopping means customers continuing to shop at a website that they have

shopped before and recommending it to their friends, according to Cyr (2008) Loyalty is a result of consistent satisfaction the customer gets from a product or service the purchases for himself and his family, according to Assael (1990) loyalty is also defined as a “saturation in satisfaction”, according to Altıntas (2000) to develop loyal customers, companies create online virtual communities; by focusing on online virtual communities, they both gain potential customers and retain the existing ones, according to Kim, Lee, and Hiemstra (2004, p 343)

Methodology

As part of this study, a questionnaire was prepared, collected data were analyzed using SPSS 16 program and the results were interpreted Studies of Chen (2006), Kim, Chung and Lee (2011), Wu and Chang (2003) were used as references while preparing the basic scale expressions in the survey form

Objective of the study This research aims to understand the relationship between perceived security and

customer trust and loyalty towards online shopping and different websites The study covers online shopping

customers in Turkey

Findings of the study Findings of the research, as the outcome of the analysis conducted, are shown below

Reliability of the scale statements has been also analyzed

As the result of reliability analysis, the overall average of the scale statements is found as 2.8670 and the correlation between questions is 0.4501 These findings show that the correlation between questions is low The analysis of the reliability value is obtained as 0.8986 accordingly, indicating a high reliable scale (0.80 < <1) Table 1 shows the demographic characteristics of people who filled in the questionnaire

Among the participants of this survey, 42% were female and 58% were male According to the data collected, the larger portion of the survey respondents were male and men use online shopping more The distribution of respondents by age groups are as follows: 33% of respondents are aged 18-25 years, 23% are aged 26-35 years, 21% are aged 36-45 years, 8% are aged 46-55 years, 8% are aged 56-65 years and 7% are more than

65 years old According to these findings, most respondents are aged 18-25 years and young This is a well-expected finding as younger people use the Internet more frequently Seven percent of survey respondents are primary school graduates, 7% are secondary school graduates, 22% are middle school graduates, 13% are associate degree graduates, 40% have undergraduate and 11% have graduate degrees Accordingly, most respondents have a graduate degree which indicates that online shoppers have relatively high levels of education Sixty percent of respondents are married and 40% of them are unmarried Among the respondents of survey, 3% earn 500-1,000 TL, 14% earn 1,001-1,500 TL and 1,501-2,000 TL, 9%, earn 2,001-2,500 TL, 15% earn 2,501-3,000 TL, 18% earn 3,001-3,500 TL, 8% earn 3,501-4,000 TL, 9% earn 4,001-4,500 TL, 4% earn

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4,501-5,000 TL and 6% earn 5,001 TL or more than on monthly basis This finding shows that the majority of the

respondents in the range of 3,001-3,500 TL income level have a high level of income compared to the overall

country average Six percent of the surveyed work in public sector, 19% of them work in private sector, 5% are

housewives, 8% are retired, 12% of them are students, 32% are self-employed and 13% are trader Most of the

participants are self-employed

Table 1

Demographic Characteristics

Results of Factor Analysis

As shown in Table 2, the first factor, trust has 3; the second factor, perceived security has 4 and the last

factor, loyalty has 4 questions Factor loadings of the questions for the first factor are between 0.604 and 0.779;

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for the second factor are between 0.637 and 0.753 and for the third factor are between 0.888 and 0.823 All factor load values high The first factor explains 30.566% of the total variance, the second factor explains 23.747% and the third factor explains 25.277% of the total variance According to the obtained findings, the first factor, trust is more explanatory than the other factors

Table 3 shows the correlation between the scale dimensions

Table 3

The Correlation on the Scale Dimensions

T-test Results of the Scale on the Statements

Trust

The web sites which provides online shopping are honest 415 2.7590 1.00470 0.04932

The web sites that offer online shopping are reliable 415 2.7012 0.94146 0.04621

Perceived security

The web site which I give credit card number to get my product, is safe 415 2.8627 1.08031 0.05303

Online sales firms, honest about my personal data is kept private 415 2.9012 0.98901 0.04855

Online sales firms offer a guarantee of confidentiality in all matters 415 2.9205 1.02667 0.05040

Loyalty

Web sites easy to think that the process of purchasing 415 3.6241 1.03951 0.05103

I prefer online shopping and traditional shopping methods 415 2.6096 1.16590 0.05723

When the scale expressions are evaluated in 5-point Likert scale, response 3 means that customers are undecided on this specific point Accordingly, test value was taken as 3 In Table 3, the average values of the scale are given If the average value of the expressions is more than 3, then it means that the respondents agree

However, when the t values in Table 4 interpreted together with the values in Table 5, respondents do agree in the

statements 8 and 9 These statements are as follows: “I think the online purchasing process is easy” and “I would recommend online shopping to my friends” Respondents do not agree on the other statements about perceived

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security and trust The two expressions respondents agree are about with loyalty Accordingly, it can be concluded that respondents are more loyal to the online shopping than the average

H1: There is a relationship between trust and perceived security;

H2: There is a relationship between trust and loyalty;

H3: There is a relationship between perceived security and loyalty

When the hypotheses were tested with regression analysis, the relationship between trust and perceived

security was found to be statistically significant (p < 0.05) The relationship between trust and perceived security

is a very strong and positive one (r = 0.890) In addition, the correlation coefficient (r 2) was calculated as 0.792, which means that 79.2% of the variation in trust depends on the perceived security As the perceived security of online shopping improves, customer loyalty increases Hypothesis H1 is accepted

The relationship between trust and loyalty was significant (p < 0.05) The relationship between trust and loyalty is a positive one (r = 0.737) However, the correlation coefficient (r 2) was calculated as 0.543; i.e., 54% trust variability depends on the loyalty H2 hypothesis was also accepted Customer loyalty in online shopping increases in line with the trust

The relationship between perceived security and loyalty variables found to be significant (p < 0.05) There is

a positive relationship between perceived security and loyalty (r = 0.871) In addition, the correlation coefficient (r 2) was found to be 0.75, i.e., 75% of variation in the loyalty depends on the perceived security Accordingly, customer trust towards online shopping depends on perceived security and trust leads to loyalty

In the online shopping domain, website security measures improve customer trust and this trust results in a customer loyalty

Results

This study considered three factors associated with online shopping: perceived security, trust and loyalty