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23ECONOMIC SCIENCES
THE MALMQUIST PRODUCTIVITY INDEX AND ITS ANALYSIS ON THE EXAMPLE OF THE RA
Avagyan G.,
Associate Professor, PhD in Economics Armenian State University of Economics (ASUE) https://orcid. org/0000-0003-3395-24 73 Vardanyan Q., Associate Professor, PhD in Economics Armenian State University of Economics (ASUE) https://orcid.org/0000-0002-7198-3740 Petrosyan G.,
Armenian State University of Economics (ASUE) https://orcid.org/0000-0002-4711-7615 Navasardyan M., PhD Student
Armenian State University of Economics (ASUE) https://orcid. org/0000-0002-54 74-6401 Margaryan A.
PhD Student
Armenian State University of Economics (ASUE)
ABSTRACT
One of the pillars of assessing the competitiveness of the country's economy is the degree of efficiency of its output, which mostly depends on the productivity of factors used in the production process, as well as on the effectiveness of production, organization and control. The professional literature has repeatedly referred to the evaluation of competitiveness and effectiveness. In this context, the Malmquist index is one of the most commonly used and comprehensive indicators for measuring productivity and efficiency. The contribution of this paper is the Malmquist index application in calculation of gross domestic production efficiency for a group of more than hundred countries, which will let us to reveal the trends in the dynamics of the country's competitiveness. Besides, that will help to identify the underlying issues that hinder the economic productivity of the observing country, in particular, the Republic of Armenia, and, consequently, its competitiveness. The explorations showed that the index in the context of economic efficiency is capable of detecting competitive advantage and disadvantage of any decision-making unit over other ones: in the RA they are pure efficiency change and scale efficiency change accordingly. Besides, the results indicated oscillatory nature of Armenia GDP efficiency change of production process and stable nature of production frontier shift.
Keywords: competitiveness, Malmquist index, total factor productivity, technical efficiency, scale efficiency
JEL classification: O47
Introduction
Many researchers put the efficiency of the production and the productivity of the resources used in this process among the pillars that form the competitiveness of the country's economy, or at the basis of the assessment of competitiveness. The "iceberg" model of competition (Peneder, 2017) offers a vertical classification of competitiveness targets and engines, the starting point of which is productivity. On the other hand, all the economic agents in the world are struggling to manage the allocation of resources, thus, in this study, the terms "competitiveness" and "efficiency" are interconnected with each other.
The current geopolitical and socio-economic situation in the Republic of Armenia contains great risks of a negative impact on the country's production potential. The consequences of a further decline in the country's attractiveness for labor emigration and investment could lead to a long-term decline in the country's economic resources. Therefore, it is generally very im-
portant to find out and keep issues of resources and production efficiency in the center of attention on an ongoing basis.
Determining the level of efficiency of the output produced in a country provides a valuable insight into economic behavior and provides an opportunity to compare it with other economies. If countries do not use their resources properly, it is definitely an indication of the need of making adjustments in the measures of production organization and improvement of its efficiency.
Normally, the growth rate of the output for a certain period of time differs from the growth rate of the labour force and the capital participation in that process in the same period of time. This can be explained by change in total factor productivity (TFP), that is, the ability to use and combine factors more efficiently over time. This may be due to changes in certain qualities (more relevant skills or new technologies introduced) or to more optimal methods of enterprise production management. TFP is directly associated with the real driving force behind product growth, which is related
to technological innovation and efficiency improvement. It can be achieved by improving labor skills and capital management. TFP plays a critical role on economic fluctuations, economic growth and cross-country per capita income differences. At business cycle frequencies, TFP strongly correlates with output and hours worked (Comin, 2006). It plays a significant role in improving the country's competitiveness, especially in the current context of severe resource constraints.
The economic literature has repeatedly referred to the assessment of the efficiency. Different authors have developed and have even separated several components in the nature of this concept in order to analyze it in more detail. Hawdon (2003) attributed efficiency to three main properties: technical, economic, and distributional. Melecky and Stanickova (2012) analyzed efficiency by the example of European countries, describing it as a reflection of the level of potential competitiveness.
The original idea of the Malmquist index proposed Swedish economist-statistician Stan Malmquist in 1953. He suggested comparing the input of a firm at two different points of time in terms of the maximum factor by which the input in one period could be decreased such that the firm could still produce the same output level of the other period. Later, this idea of input-reducing ratio expanded and became Malmquist Productivity Index (Caves et al., 1982). There was a resurgence of interest in its application in 1994, when the Malmquist index of improvement of output was calculated on the panel data basis, assuming a stable return on production. The calculated index was the average geometric mean of the two TFP indices.
For example, Dai and Liu (2009) estimated the efficiency and productivity growth of 16 major high-tech companies in China in 2002-2007. Sharma and Thomas (2008) calculated the same index for 20 OECD member countries, the Russian Federation and China. Lu and Liu (2010) employed the Malmquist index, to decompose productivity growth into technical efficiency and technological change. The results indicate that the increase in R&D productivity is mainly attributed to the increase in technical change, and the efficiency gain found is largely the result of improvements in scale efficiency: Park (2014) analyzed the efficiency and productivity change within government subsidy recipients of a national technology innovation research and development (R&D) program.
Another attempt to calculate the Malmquist index revealed the trends in productivity growth of OECD member countries in 1981-2006. The assessment was carried out for each 5 years period, calculating the average of total factor productivity. The results show that the annual growth of TFP varies considerably, as significant fluctuations have been observed over time in the member countries. In most of them, the annual TFP has significantly deteriorated. In particular, the decline in productivity has been more perceptible since 2001. During 2001-2006, the average annual change in the TFP in the OECD area was negative. Only Germany and Japan from the Group of the Seven recorded a positive change of the TFP during that period. The results did not provide strong evidence that huge investments
in information technology, particularly in the second half of the 1990s, clearly boosted the productivity of large industrialized countries. In fact, in many of the surveyed countries the growth of TFP has slowed significantly during the 1990s compared to the 1980s. Of the Scandinavian countries, only Finland, Norway and Sweden have been able to record leading productivity growth in this comparison. Australia and New Zealand also experienced relatively higher productivity growth, but mainly in the early 1990s. With the exception of these countries, GDP growth was relatively weak in most of the OECD area in the 1990s, including the G7 countries. As mentioned above, such a weak increase in productivity continued and sometimes even became negative after 2000.
Another interesting example of the application of the Malmquist index is the assessment of the productivity of the construction sector in eight Australian states in 1990-2007. As input factors of construction were used the construction work and the number of people working in that field. The first of these is a composite indicator, which includes payments for the supply of raw materials, labor prices and speculative contracts. As an output of the production, the value added in the construction sector in the respective state was used. The results of the research describe how the technology of this field, the net technical efficiency and the scale of the economy affect the change of construction productivity. The analysis is carried out not only at the state level, but also at the national level. The study shows how the technology, technological efficiency and scale of economy affect on the change of overall productivity. Although the growth rates of construction productivity in the Australian states did not show obvious differences, the growth factors were to some extent different (Li & Liu, 2010).
Thus, one of the theoretically substantiated and the most common indicators measuring total factor productivity and the quality of production organization is the Malmquist productivity index, which stands out for its unique and meaningful nature among other estimates.
During the calculation and interpretation of the index, the keyword "change" is not stressed accidentally. The point is that the calculated index is obtained for each period by comparing the end and beginning of the period, or that it is the same, through change.
The Malmquist index for the period is the ratio of two distance functions that, under stable conditions of production technology, measure the maximum proportional change in factors-output combination from the previous (t-1) to the observed (t) period. The Malmquist TFP index is a geometric mean of two Malmquist indices (Karmann & Roesel, 2016). The difference between them lies in the production technologies: in one case, it refers to the previous period, and in the other to the observed one.
M(yt,xt,yt-I,xt-1)
N
Dt-1 (xt,yt) v Dt (xt,yt)
X
Dt-i O^t-u yt-i) Dt (xt-i yt-i)
(1)
The index introduces TFP of current DMU at point (xt,yt) in comparision with (xt-1,yt-1) point. If the
value of the index is greater than, less or equal to 1, then the TFP has either progressed (increased productivity) or experienced a decline (decreased productivity), or the TFP change, respectively has missed. Thus, to calculate the index describing the change in TFP for each DMU, four distance functions must be calculated to measure the TFP change between two periods, t and t+1. This requires solving four LP problems (Li, 2009).
After some mathematical modifications the Malmquist TFP index can be divided into two components, which are meaningful in context of economic
The discussed TFP evaluation criterion includes another stage of separation, which follows in the "footsteps" of the primary sources of the efficiency of resources involved in the production process: the change
Malmquist TFP indices calculations research for the period 1995-2019 covers 123 countries and groups of countries, including the whole world, as one DMU. The calculations are based on GDP (World Bank, 2020a) as an output, gross fixed capital formation (World Bank, 2020b) and labor force (International Labor Organization, 2021) as factors of production.
1,04
1,02
1
0,98
0,96
In Figure 1, there are introduced the average values of the first-degree decomposition of the studied countries' Malmquist index, which are the geometric means of each DMU. The highlighted numbers represent the average of the corresponding type of efficiency for the whole world as one DMU (more than 200 countries). It should be noted that the change in technical efficiency level in the world has generally declined, decreasing by 0.4 percent in the observed period, while the ECH has been positive by the same amount as
logic: efficiency change (ECH) and technological efficiency change (TECH). The first refers to the change in the efficiency of the factors and the change in the optimal operation of the existing factors. The second describes the change in production frontier, in other words, technological progress. It should be noted that now in the professional literature such a decomposition of the Malmquist TFP index appears as a generally agreed approach.
(2)
in factor efficiency is explained by two circumstances: a pure change in efficiency (PECH) and a change in efficiency from scale (SECH).
(3)
The research carried out within the framework of the "Comprehensive and Enhanced Partnership Agreement" involves the development and maintenance of a number of trendy statistical software packages. The technical solutions for Malmquist index study were provided through one of those programs (CEPA, 1996), which allows to calculate the indicators presented in Equation 2.
TECH. As a counterargument to this, more unstable nature of the ECH variance is determined, while the TECH mainly fluctuates in the range much closer to unit. The highest level of TECH was registered in 2009 (Figure 2), increasing by 11.4 percent, and the lowest in 2018 (-14.5 percent). It is interesting that the Malmquist TFP index also showed its highest level in 2009 (7.7 percent) and the lowest in 2019 (-7.3 percent). On the other hand, the highest level of ECH was in 2018 (16.6 percent), and the lowest in 2000 (-9.2 percent).
M(yt,Xt,yt-i,Xt-i) =
Dt (xt,yt) Dt-i (xt-i,yt-i)
Dt-i (xt,yt) Dt-i (xt,yt)
/ Dt-i (x (Dt(xt_i,
-i,yt-i) Dt (xt_i,yt_i)
x
Malmquist TFP index = PECH x TECH = PECH x SECH x TECH
Armenia; 1,017
□°D
World; 1,004
cP
□ III
o o oo
o o
□ □
^ UP
9> D Q
□ OQO O O
DEfïiciency change O Technical efficiency change
Figure 1. The scatter of efficiency and technical efficiency changes means of observed 123 DMUs
0,8
2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 — — ■ Efficiency change Technical efficiency change —Total factor productivity
Figure 2 .Average Total factor productivity and scale efficiency changes in the world during 1996-2019
The dynamics of production process efficiency and technical efficiency changes illustrates some interesting facts about the nature and the causes of production efficiency in the world during last two decades. At first, it is noticable that almost every year during the observed period, trends of two main characteristics describing TFP are opposite. That is, for example, in case of efficiency positive change, technical efficiency declines. Although it is an expected scenario (as if efforts are aimed to improve production process efficiency and productivity of factors, may lead the DMU to lag behind the global trends of research and technological development), it is possible for DMU to simultaneously improve both types of efficiency (as in 2009). Otherwise, such a contraindication can occur due to the lag
1,3
1,2
1,1
between achievements of scientific and technical progress with production process efficiency. This means, that when technical efficiency increases (TECH), that is production frontier shifts, current level of organizational efficiency of production process does not react to it simultaneusly. Therefore, that opposite thrends have to be handled by synchronizing two main types of efficiency changes.
An interesting behaviour of efficiency indicators is noticable In Figure 2: there are large amplitude fluctuations of Malmquist index first level components noticed after 2008, which is probably caused by the global financial and economic crisis and its consequences.
0,9
0,8
0,7
2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 Armenia ••••• ■ Belarus —Kazakhstan Kyrgyzstan Russia
Figure 3. Dynamics of Malmquist TFP indices of members of Eurasian Economic Union (EAEU)
1
Let us make a transition to the indicators of specific countries, in particular, further analysis will be on the example of the Republic of Armenia (RA), though the calculations allow to do the same for all of the observed DMUs (Authours' calculations, 2021).' Taking into account the economic and mathematical nature of the index, in the professional literature it is accepted to analyze indices in some comparison edges. Therefore, before getting acquainted with all the index components of the Republic of Armenia separately, let us make some comparative analysis of Armenia and other DMUs.
Thus, from the presented Figure 3, we can first notice that in the observed period, according to the change of the TFP, there are no highlighted leaders among EAEU members. The sharp fluctuations of the change in TFP of RA in 2002 and 2011 are noticeable: in the
first case the negative change was more than 20 percent, but in the second case the difference was positive (25.2 percent). Note that not only for those years the trends of the EAEU member states coincide to some extent, but also for the years after the founding of the union (2015). In recent years, the changes in their TFP are almost identical, though in the case of the last observation only Armenia registered a positive result in the list of those DMUs, with a 4.6 percent change. In addition, the Malmquist TFP index of RA was the best among the members of the union in 2007, 2009, 2011, as we have already mentioned, in 2019, and the lowest only in 2002. The main reason for that decline was 33 . 2 percent increase in investment (a slight increase in labor force), which significantly exceeded the economic growth based on it (13.2 percent).
1,7
1,5
1,3
1,1
0,9
0,7
2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 Armenia ■ ■ ■ ■ ■ ■ Moldova —H— Ukraine Iran Lebanon
Figure 4. Dynamics of Malmquist TFP indices of Armenia and countries comparable to it
In Figure 4 there are represented discussing index of Armenia and other comparable by GDP per capita countries. In this group of countries, too, according to the assessed index, there is no emphasized leader. Only Ukraine has obvious fluctuations: more than 30 percent, and this can be seen in several year indicators. As for the position of the Republic of Armenia in such a framework of monitoring the index, it should be noted
that it was the lowest not only in 2002, as in the previous group of countries, but also in 2004, 2005 and 2015.
The noticeable negative shift in 2015 (0.984) was mainly due not to the low level of that year's components decline, but to the high ranks of ECH and TECH in 2014, as a result of which the index in 2015 was the lowest among negative and comparable countries. It should also be noted that Armenia was the leader in this list in 2007, 2011, 2017 and 2018.
1 Authours' calculations. (2021). Malmquist TFP indices and their components [database]. Available in
https://docs.google.com/spreadsheetsAi/1mi-hYj2rV5lWWYA54BvfTFaad-upUNajl8cF5s-KcIZk
1,3
0,7
2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019
Efficiency change ...... Technical efficiency change —It— Pure efficiency change
Scale efficiency change Total factor productivity
Figure 5. Malmquist TFP index and its components dynamics of Armenia
In order to explain the dynamics of the Malmquist TFP index of the RA and to justify its movement objectively, we have also observed the components of the index. Looking at Figure 5 we can notice the shift in the index of Armenia is generally caused by the ECH, that is, the change in resources and their management efficiency. Its change, in its turn, is due to more PECH, which fluctuates in the range 0.788-1.255, while SECH, which is the other component of ECH, is in the narrow range 0. 983-1. 068 during the observed period. Such a small difference of efficiency gained from production scale change in Armenia hints about the need to enter new markets, especially outside, as satisfaction of internal demand is already quite saturated.
The maximum value that Armenia scored in the period under review is 1.172 in 2011, which means that the country has improved its TFP by 17.2 percent compared to 2010, while the TFP change of the whole world for the same year was negative (-11.3 percent). There is also a significant difference with the index calculated for the world - in the case of the lowest index registered
in the last 20 years of the Republic of Armenia (in 2002 was 0.896), the rather deep negative index of our country is opposed to the positive tendency of the same index in the world (1.027).
Thus, Malmquist TFP index provides extensive information about DMU's effectiveness, as well as competitiveness. It allows to explain the fluctuations of the TFP dynamics and the obstacles to improving competitiveness. Thanks to index decomposition into interpretable in macroeconomic context indicators it is possible to separate efficiency types observed during production process.
Malmquist TFP index in the world has been generally close to 1 during the years 1996-2019, that is the change in TFP has been missing. The reasing are the contradictory tendencies of the two components of the index, which represent the change in the shift in production frontier (TECH) and in change of efficiency of production factors or production organization process (ECH). In particular, TECH has decreased, but a positive shift has been recorded in ECH, and both to the same extent.
Lebanon Moldova ArmeMa Kyrgyzstan World
Bel"108
Kazakhstan
„an
Russia
Ukraine
0,95 0,96 0,97 0,98 0,99 1 1,01 1,02
■ Total factor productivity change ^ Scale efficiency change
Figure 6.
Average Total factor productivity and scale efficiency changes of compared countries during 1996-2019
As the analysis of the observed period showed, the TFP of the RA increased by an average of 1.2 percentage. The change in the TFP of the country was mainly because of the change in factor efficiency, which was largely motivated by a change in net efficiency change. Main barriers of the competitiveness shift of Armenia are TECH and SECH: change in scale efficiency is almost zero, averaging only 0.2 percentage. Expanding export opportunities and entering foreign markets will ensure improved efficiency from scale.
Finally, the calculated components and comparative analysis of EAEU members and countries comparable with Armenia confirm that competitive advantage of the RA in the context of production efficiency is the production process efficiency. On the contrary, the main obstacle to the increasing its TFP is the low level of scale efficiency. That indicates Figure 6. where are introduced TFPCH and SECH of all the countries compared with Armenia in this paper, as well as the same changes in the world in average. Here we can find the RA to be the lowest after Moldova and Lebanon in the ranking by scale efficiency change. That is scale efficiency changes in Armenia are not only almost static, but also its level is less than the average in the world. On the other hand, only in Armenia and Lebanon the SECH is inferior to TFPCH. This fact threatens the TFP positive dynamics of Armenia, because at such an almost constant pace of SECH theoretically once the country will exhaust its potential of improving pure efficiency, and in that case, it can only increase its production efficiency only due to TECH, which is too expensive to be always applied to improve TFP.
The nature of scale efficiency can describe how expedient the expansion of production will be, from the point of view of efficiency. That indicator therefore is one of the most important indicators figuring the competitiveness of the country.
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МЕТОДИ ХЕДЖУВАННЯ ВАЛЮТНОГО РИЗИКУ БАНКАМИ
Краснова 1.В.,
д.е.н., професор, професор кафедри банювсько'1 справи та страхування КНЕУ iM. В.Гетьмана
Шевалдша В.Г. к.е.н., доцент, доцент
кафедри банювсько'1 справи та страхування КНЕУ iM. В.Гетьмана
METHODS OF HEDGING CURRENCY RISK BY BANKS
Krasnova I.,
Doctor of Economics, Professor, Professor Department of Banking and Insurance Kyiv National Economic University named after Vadym Hetman
Kyiv, Ukraine Shevaldina V.
Ph. D. in Economics, Associate Professor of the Department of Banking and Insurance Kyiv National Economic University named after Vadym Hetman
Kyiv, Ukraine
АНОТАЦ1Я
Не зважаючи на велику шльшсть робгг присвячених питанням валютного ризику та методам його хе-джування, деяш питання залишаються не визначеними. Не мае стало! класифжацп методiв та стратегш хеджування. У статп розглянуто концептуальш щдходи до класифжацп видiв валютного ризику. Запро-поновано авторський шдхщ до структуризаци методiв хеджування валютного ризику та виокремлено ш-струменти хеджування валютного ризику банками ктенпв. Проаналiзовано впчизняну практику хеджування валютного ризику та визначено можливосп застосування форвардних контракпв в сучасних умовах.
ABSTRACT
Despite the large number of papers on currency risk and methods of it's hedging, some issues remain unresolved. There is no permanent classification of hedging methods and strategies. The article considers conceptual approaches to the classification of currency risk types. The author's approach to the structuring of currency risk hedging methods is proposed and the tools of currency risk hedging by clients' banks are singled out. The domestic practice of currency risk hedging is analyzed and the possibilities of using forward contracts in modern conditions are determined.
Ключовi слова: валютний ризик, банк, хеджування, класифжащя, метод, деривативи, форвард.
Keywords: currency risk, bank, hedging, classification, method, derivatives, forward.
Актуальшсть. Валютний ризик е частиною транснацюнальних компанш та баншвських уста-
ландшафту ризишв баншвсько! установи. Вш пов'- нов, диверсифжащею !х дiяльностi, i представляе
язаний з глобалiзацiею та штегращею, штернацю- ситуащю, яка допускае потенцшш грошовi втрати налiзацiею ринку баншвських послуг, створенням
