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Explaining Uzbek firms’ growth: The Cobb-Douglas production function using
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ISSN 2225-9538
Научно-аналитический журнал
Наука и практика
Российского экономического университета имени Г. В. Плеханова
Т. 13. № 3 (43). 2021
Scientific and Analytical Journal
Science and Practice
of the Plekhanov Russian University of Economics
Vol. 13. No. 3 (43). 2021
УЧРЕДИТЕЛЬ
Федеральное государственное бюджетное образовательное учреждение высшего образования
«Российский экономический университет имени Г. В. Плеханова»
(ФГБОУ ВО «РЭУ им. Г. В. Плеханова»)
Главный редактор:
Научный редактор:
Гретченко Анатолий Иванович – д-р экон.
Кулапов Михаил Николаевич – д-р экон.
наук, проф., заслуженный деятель науки РФ наук, проф., заслуженный работник высшей
школы Российской Федерации
Ответственный секретарь:
Сорокина Наталья Юрьевна, канд. экон.
наук, доц.
МЕЖДУНАРОДНЫЙ СОВЕТ ЖУРНАЛА
Гретченко Анатолий Иванович, доктор экономических наук, профессор. Директор НИИ
«Новая экономика и бизнес» Российского экономического университета имени Г. В. Плеханова (Россия).
Драшкович Веселин, доктор экономических наук, профессор Университета Черногории (Черногория).
Юань Лунгу, профессор, Школа экономики и управления Пекинского Университета Цзяотун
(Китай).
Масато Хиватари, профессор Университета Хоккайдо (Япония).
Герхард Фелдмайер, профессор Бремерхафенского университета прикладных наук
(Германия).
Эко Сри Маргианти, профессор, ректор университета Гунадарма (Индонезия).
Абдурахманов Каландар Ходжаевич, профессор, академик Академии наук Республики Узбекистан, директор филиала Российского экономического университета имени Г. В. Плеханова
в г. Ташкенте (Узбекистан).
Короленок Геннадий Антонович, доктор экономических наук, профессор. Белорусский государственный экономический университет (Беларусь).
Бейсенбек Зиябеков, доктор экономических наук, профессор. Казахстанско-Немецкий университет (Казахстан).
РЕДАКЦИОННАЯ КОЛЛЕГИЯ:
Беляков Геннадий Павлович, доктор экономических наук, профессор. Сибирский государственный аэрокосмический университет имени академика М. Ф. Решетнева (СибГУ), профессор кафедры организации и управления наукоемкими производствами.
Борисов Владимир Николаевич, доктор экономических наук, профессор. Лаборатория прогнозирования машиностроительного комплекса Института народнохозяйственного прогнозирования РАН (ИНП РАН), заведующий лабораторией.
Бородин Владимир Андреевич, доктор экономических наук, профессор. Алтайский государственный технический университет им. И. И. Ползунова (АлтГТУ), профессор кафедры международных экономических отношений.
Валентей Сергей Дмитриевич, доктор экономических наук, профессор. Научно-исследовательское объединение Российского экономического университета имени Г. В. Плеханова
(РЭУ), научный руководитель.
Гагарина Галина Юрьевна, доктор экономических наук, профессор. Российский экономический университет имени Г. В. Плеханова (РЭУ), заведующая кафедрой национальной и региональной экономики.
Гретченко Анатолий Иванович, доктор экономических наук, профессор. Директор НИИ
«Новая экономика и бизнес» Российского экономического университета имени Г. В. Плеханова (Россия).
Горбашко Елена Анатольевна, доктор экономических наук, профессор. Санкт-Петербургский государственный экономический университета (СПбГЭУ), проректор по научной работе.
Гаибназарова Зумрат Талатовна, доктор экономических наук, профессор кафедры «Экономика и менеджмент промышленности» ТГТУ им. И. Каримова (г. Ташкент).
Журавлева Галина Петровна, доктор экономических наук, профессор. Научная школа «Экономическая теория» Российского экономического университета имени Г. В. Плеханова (РЭУ),
руководитель.
Иванкина Елена Владимировна, доктор экономических наук, профессор. Институт отраслевого менеджмента Российской Академии народного хозяйства и государственной службы при
Президенте РФ (РАНХиГС), декан.
Кулапов Михаил Николаевич, доктор экономических наук, профессор, заслуженный работник высшей школы Российской Федерации, лауреат премии Правительства РФ в области образования.
Катабай Павел Хафизуллович, начальник Отдела по работе с диссертационными советами
Управления аттестации и подготовки научных кадров РЭУ им. Г. В. Плеханова.
Манахов Сергей Владимирович, кандидат экономических наук. Управление организации
научно-исследовательских работ Российского экономического университета имени
Г. В. Плеханова (РЭУ), начальник управления.
Одегов Юрий Геннадьевич, доктор экономических наук, профессор. Научная школа «Управление человеческими ресурсами» Российского экономического университета имени
Г. В. Плеханова (РЭУ), руководитель.
Полевая Марина Владимировна, доктор экономических наук, профессор. Финансовый университет при Правительстве Российской Федерации (ФУ), заведующая кафедрой управления
персоналом и психологии.
Половинко Владимир Семенович, доктор экономических наук, профессор. Омский государственный университет имени Ф. М. Достоевского (ОмГУ), заведующий кафедрой экономики
и управления человеческими ресурсами.
Наумов Сергей Николаевич, кандидат экономических наук, доцент, Центр развития программно-целевого управления Всероссийской академии внешней торговли Минэкономразвития
России, заместитель руководителя.
Тихомиров Николай Петрович, доктор экономических наук, профессор. Российский экономический университет имени Г. В. Плеханова (РЭУ), заведующий кафедрой математических
методов в экономике.
Фалько Сергей Григорьевич, доктор экономических наук, профессор. Московский государственный технический университет им. Н.Э. Баумана, заведующий кафедрой экономики и организации производства.
Хасбулатов Руслан Имранович, член-корреспондент РАН, доктор экономических наук, профессор. Российский экономический университет имени Г. В. Плеханова (РЭУ), заведующий
кафедрой мировой экономики.
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СОДЕРЖАНИЕ
КОЛОНКА ГЛАВНОГО РЕДАКТОРА
8
ЦИФРОВАЯ ЭКОНОМИКА
Тихонова О. Б., Журавлева Г. П., Александрова Е. В. Цифровая
экономика – необходимость, обусловленная временем
9
РЕГИОНАЛЬНАЯ ЭКОНОМИКА
Лысенко А. А. Оценка влияния государственных программ Российской
Федерации на изменение ключевых параметров государственного
потребления, инвестиционный климат и рост доходов населения
28
Белякова Г. Я., Чистякова Н. О. Потенциал имплементация стратегии
умной специализации для регионов СФО: перспективы и ограничения
37
УНИВЕРСИТЕТСКИЕ ИССЛЕДОВАНИЯ
Наумов С. Н., Швец Ю. Ю., Гретченко А. А. Большие данные
в отечественном здравоохранении
57
Гретченко А. И. Устойчивость социально-экономических систем
и регулирование рынка труда в условиях коронавирусной инфекции
71
НАУКА ЗА РУБЕЖОМ
Гаибназарова З. Т. Анализ инвестиционной деятельности
железнодорожной системы Республики Узбекистан
79
Юлдашев С. Ф. Направление для привлечения иностранных инвестиций
в АО «Узбекнефтегаз» в условиях модернизации национальной экономики 92
Махсудов Мухаммадбек Дилшодбек угли Регулирование диверсификации
использования земельного фонда через генеральную схему
107
Суюнов А. Объяснение роста узбекских фирм: производственная
функция Кобба – Дугласа с использованием данных на уровне фирм
120
ОБ АВТОРАХ
132
УСЛОВИЯ ПОДАЧИ МАТЕРИАЛОВ В ЖУРНАЛ
135
Scientific and analytical journal «Science and Practice» of Plekhanov University.Vol.11.No.3 (35)2019
6
CONTENTS
CHIEF EDITOR’S COLUMN
8
DIGITAL ECONOMY
Tikhonova O. B., Zhuravleva G. P., Aleksandrova E. V. The digital economy
is a time-bound necessity
9
REGIONAL ECONOMY
Lysenko A. A. Assessment of the impact of state programs of the
Russian Federation on changes in key parameters of state consumption,
investment climate and income growth of the population
28
Belyakova G. Ya., Chistyakova N. O. Implementation of smart specialization
strategy for the regions of Siberian Federal district: prospects and limitations
37
UNIVERSITY RESEARCH
Naumov S. N., Shvets Y. Yu., Gretchenko A. A. Big data in domestic
healthcare
57
Gretchenko A. I. Stability of socio-economic systems and regulation
of the labor market in the conditions of coronavirus infection
71
SCIENCE ABROAD
Gaibnazarova Z. T. Analysis pf investment activity in the railway system
of The Republic of Uzbekistan
79
Yuldashev S. F. Directions of attracting foreign investments to JSC
"Uzbekneftegaz" in the conditions of modernization of the national economy
92
Mahsudov Muhammadbek Dilshodbek ugli Regulation of the diversification
of the use of the land fund through the general scheme
107
Suyunov A. Explaining Uzbek firms’ growth: The Cobb – Douglas production
function using firm-level data
120
ABOUT THE AUTHORS
132
PAPER SUBMISSION GUIDELINES
135
Scientific and analytical journal «Science and Practice» of Plekhanov University. Vol. 13. No. 3 (43) 2021
7
НАУКА ЗА РУБЕЖОМ/SCIENCE ABROAD
ОБЪЯСНЕНИЕ РОСТА УЗБЕКСКИХ ФИРМ:
ПРОИЗВОДСТВЕННАЯ ФУНКЦИЯ КОББА – ДУГЛАСА
С ИСПОЛЬЗОВАНИЕМ ДАННЫХ НА УРОВНЕ ФИРМ
EXPLAINING UZBEK FIRMS’ GROWTH: THE COBB – DOUGLAS
PRODUCTION FUNCTION USING FIRM-LEVEL DATA
Суюнов Алишер
исследователь
Международный Вестминстерский Университет в Ташкенте
Suyunov Alisher
Researcher
Westminster International University in Tashkent, Tashkent
Являясь индикатором экономического благосостояния, экономический
рост отображает объем производства, достигнутый экономическим сообществом. Несмотря на то, что темпы экономического роста в Узбекистане
колебались в пределах 4–7% в течение 2000–2020 гг., позитивные темпы экономического роста в течение всего периода недостаточно отражались на
уровне занятости. Несмотря на ежегодные программы правительства Узбекистана по созданию рабочих мест и повышению занятости, в Узбекской экономике сохраняется феномен высокого уровня безработицы. Одним из способов понимания механизма экономического роста и его измерения является производственная функция – одна из важнейших концепций неоклассической экономической теории, которая определяет фирму, отрасли, мощность/производительность всей экономики для всех комбинаций факторов производства.
На основе данных Обследования предприятий Всемирного банка в этом
исследовании мы построили производственную функцию Кобба – Дугласа на
уровне фирм для частного сектора Узбекистана, определяя доли факторов и
общую производительность факторов производства.
В соответствии с различными спецификациями моделей мы обнаружили, что в среднем узбекские фирмы трудоемки, где доля капитала составляет 0,248, а доля рабочей силы оценивается в 0,729. Наша оценка общефакторной производительности в Узбекистане в 2019 г. составляет 1,94, что
выше оценок за 2008 г. Наши результаты показывают, что рост безработицы
в Узбекистане, наблюдавшийся в период 2000–2020 гг., может быть результатом роста производительности. Также предлагаемая аппроксимация производственной функции показывает, что малые фирмы в Узбекистане
склонны нанимать дополнительных работников для увеличения производства
в отличии от средних и крупных фирм.
Being an indicator of economic welfare, economic growth reflects production
output achieved by an economic community. Although economic growth in
Uzbekistan fluctuated around 4–7% rate over the course of 2000–2020, the positive
economic growth rate throughout the period is not reflected upon employment rate
sufficiently. In spite of Uzbek government’s annual programs on job creation and
Scientific and analytical journal «Science and Practice» of Plekhanov University. Vol. 13. No. 3 (43) 2021 120
НАУКА ЗА РУБЕЖОМ/SCIENCE ABROAD
enhancing employment, high unemployment rate phenomenon has been persistent
for Uzbek economy. One way of understanding the mechanism of economic growth
and its measurement is a production function. Being the one of the most important
concepts of neoclassical economic theory, a production function specifies a firm,
industry, whole economy’s output for all combinations of inputs.
Based on the firm-level dataset – World Bank Enterprise Survey, in this
research study, we construct a firm-level Cobb – Douglas production function for
private sector of Uzbekistan identifying factor shares and total factor productivity.
Under different model specifications, we found on average Uzbek firms are
labour intensive having the share of capital is 0,248, while the share of labour has
been estimated to be 0,729. Our estimate of total factor productivity for Uzbekistan
is 1,94 in 2019 which is greater than TFP estimates for 2008. Our results show
Uzbekistan’s jobless growth observed over 2000–2020 could be attributed to a
productivity growth. The approximation of firm-level production function confirms
small firms in Uzbekistan are inclined to hire additional workers to increase
production compared to medium-and large-firms.
Ключевые слова: частный сектор, производственная функция, YAKL,
YAKLM, продуктивность, Узбекистан.
Keywords: private sector, production function, YAKL, YAKLM, productivity,
Uzbekistan.
Introduction
Over the course of 2000–2020 (Figure 1), economic growth in Uzbekistan
fluctuated around 4–7% rate. This positive economic growth rate throughout the
period is not reflected upon employment rate sufficiently. Moreover, despite the
Uzbek government’s annual programs on job creation and enhancing employment,
high unemployment rate phenomenon has been persistent for Uzbek economy. As
Figure 2 presents, over 2007–2017 unemployment rate in Uzbekistan was accounted
for around 5%, while it has been increasing steadily since 2018, arising a significant
concern. This trend has been exacerbated the recent COVID-19 outbreak in 2020,
increasing the unemployment rate up to 10,5% and decreasing national economic
growth to 1,6%.
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12 %
10
Unemployment
rate
8
6
4
2
Real GDP
growth
0
2000 2002 2004 2006 2008 2010 2012 2014 2016 2018 2020
* Data source: The State Committee of Uzbekistan on Statistics
Figure 2. Real GDP growth and unemployment rate of Uzbekistan over 2000–2020
Under these circumstances, it is important for the Uzbek government to take
decisive actions to combat increasing unemployment rate. Therefore, the state is
beginning reforms in business development and enhancing entrepreneurship aim to
strengthen entrepreneurial activities, reducing inefficient bureaucratic procedures
and outdated laws to enhance business ecosystems. Private sector development
initiatives are reflected upon the reduction of illegal or irrational government
interventions to private firms’ operations and regulation across sectors. In addition,
reforms on decreasing government share and sectoral deregulation create ample
opportunities for businesses to acquire provision of government functions and reap
benefits from state-owned enterprises’ transparent privatisation. These initiatives can
be early signs of Uzbekistan’s transition from state-led to market-driven growth.
However, it is essential employment growth should be maintained through
business-friendly macroeconomic policies, not solely administrative measures.
Otherwise, those actions turn out to be harmful because inefficient allocation of
resources, excessive bureaucracy, overstaffing, and hidden unemployment make the
situation even worse. To avoid poor decisions, it is important to understand how
private firms decide the combination of production factors and output to achieve their
goals.
Being an indicator of economic welfare, economic growth is an increase in
production output achieved by an economic community [3]. One way of
understanding the mechanism of economic growth and measuring production growth
is constructing a production function. As Saari and Oy [3] pointed out under the
production function, it is important to maximise real income formation since
maximising productivity may not be an optimal solution. The reason is when
productivity is maximised, current output increases without new job creation, i. e.
jobless growth. Therefore, in the economy with considerable unemployment rate,
output growth does not contribute to employment growth. In other words,
unemployed people remain to be unemployment in spite of positive economic growth
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rates. Saari and Oy [3], therefore, emphasised the importance of maximising real
income. In this case, jobless people are provided with jobs having relatively low
productivity, resulting in a decline in average productivity. However, despite a
reduction in productivity, real income per capita and whole society’s well-being
increases. Although average productivity plays a major role in income generation, it
should not necessarily be maximised due to reasons we discussed above.
Methodology
Being the one of the most important concepts of neoclassical economic
theory, a production function specifies a firm, industry, whole economy’s output for
all combinations of inputs [1; 6]. In this context, a profit maximising firms should
obtain the maximum level of output by using various combinations of factors of
production [1].
The widespread two-factor production function was introduced by Cobb and
Douglas in 1928 [6]. As Cobb – Douglas argued, a true production function of a firm
can be approximated using the following equation [6], cited in [1; 5]:
𝑓(𝑥, 𝑦) = 𝐴𝑥 ! 𝑦"#!
(𝐴 > 0 𝑎𝑛𝑑 0 < 𝛼 < 1)
(1)
or
𝑌 = 𝐴𝐾 ! 𝐿$ ,
(2)
where 𝐴 denotes total factor productivity, 𝑥 (or 𝐿) and 𝑦 (or 𝐾) stand for labour and
capital respectively.
There are several research studies which presents factor shares in the context
of Central Asian countries, including Uzbekistan. Şeker and Saliola [4]’s study
obtained the following share of inputs for four Central Asian countries:
Table 1
Factor shares estimated using YAKLM framework in Şeker and Saliola [5]’s study
Country
Kazakhstan
Kyrgyzstan
Tajikistan
Uzbekistan
2009
2009
2009
2008
2008
0,07
0,07
0,12
0,07
0,19
0,38
0,38
0,33
0,32
0,55
0,68
0,68
0,74
0,70
0,44
According to their estimates in Table 1, out of four Central Asian countries,
the highest share of capital and labour is observed in Uzbekistan. However, the share
of intermediate materials is the lowest in Uzbekistan, while the highest is accounted
for Kyrgyzstan.
Unlike labour and capital, measuring total factor productivity is not as easy
as it sounds. In usual single-factor productivity estimates, the units of output per unit
of input are calculated, such as labour productivity which varies depending on the
intensity of use of capital [5]. Total factor productivity, however, is independent from
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observable production factors. In this context, firms having high TFP produce higher
outputs than their counterparts having relatively lower TFP using the same quantity
of inputs. As Syverson [5] argued TFP can be estimated easily using a production
function with observable inputs and a factor-neutral shifter, which is 𝐴. The 𝐴
captures a variation in output not explained by variation in inputs, which is a residual.
By itself, a residual captures a variation in output unexplained by observable inputs.
For our study, we employ a Cobb – Douglas production function as the
following functional form:
𝑌 = 𝐴𝐾 ! 𝐿$ .
(3)
Where, 𝑌 is the output measured using annual total sales, 𝐴 is total factor
productivity, 𝐾 is replacement value of capital – machinery, vehicles, and equipment,
𝐿 stands for annual labour costs. We call the first model specification as YAKL.
Meanwhile, 𝛼 and 𝛽 represent the share of capital and labour respectively. As
equation (3) is intrinsically linear, we calculate the natural logarithm of the equation
to obtain the following linear expression:
𝑙𝑛𝑌 = 𝑙𝑛𝐴 + 𝛼𝑙𝑛𝐾 + 𝛽𝑙𝑛𝐿.
(4)
In our second specification, in addition to the variables above, we include 𝑀
which represents total annual cost of materials and intermediate goods as well as 𝜙
indicating the share of intermediate goods and materials:
𝑌 = 𝐴𝐾 ! 𝐿$ 𝑀%
(5)
𝑙𝑛𝑌 = 𝑙𝑛𝐴 + 𝛼𝑙𝑛𝐾 + 𝛽𝑙𝑛𝐿 + 𝜙𝑙𝑛𝑀.
(6)
As the third model specification, as Şeker and Saliola [5] suggested, we use
value added (7) instead of total annual sales by calculating total annual sales minus
total annual cost of intermediate goods and materials.
𝑉𝐴 = 𝑌 − 𝑀.
(7)
Turning to the measurement of total factor productivity, as Syverson [5]
suggested, the approximation of Cobb-Douglas production is:
𝑙𝑛𝑌 = 𝛼& + 𝛼𝑙𝑛𝐾 + 𝛽𝑙𝑛𝐿 + 𝜙𝑙𝑛𝑀 + 𝜖.
(8)
In equation (8), 𝛼
>& + 𝜖̂ is the logged TFP estimate we are looking for. The
𝛼
>& term is a constant across firms in the sample, while the 𝜖̂ term varies depending
on a firm’s characteristics.
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Data
In our study, we use a secondary data source – World Bank Enterprise Survey.
The firm-level survey provides a valuable information on private firm’s
characteristics, gender and workforce composition, access to finance, annual sales,
cost of inputs and labour, bribery, licensing, infrastructure, trade, crime, competition,
capacity utilisation, innovation and technology, and performance indicators [7].
The survey uses a stratified random sampling to ensure representativeness of
the dataset. The sample of firms are obtained from the pool of eligible firms provided
by the country’s statistical authority or other reliable authorities, including tax and
licensing authorities, associations. The stratification is used at industry, firm size, and
region. Considering the aforementioned, we carry out our research study based on
2019 round of the study.
Results
The Table 2 presents the descriptive statistics of selected variables. As we can
observe, around 33,3% of firms in the sample have outliers which are three standard
deviations above or below from mean.
Table 2
Summary statistics of variables of interest
Variables
(1)
N
(2)
Mean
(3)
Standard
Deviation
(4)
Min
(5)
Max
1,239
1,239
3,785e+10
7,375e+08
6,367e+11
3,090e+09
-9
-9
2,100e+13
6,020e+10
841
6,070e+09
3,632e+10
-9
9,050e+11
841
3,567e+15
1,034e+17
-9
3,000e+18
1,239
0,333
0,472
0
1
… in Last Fiscal Year
Total Annual Sales
Total Labour Cost
(inc. Wages, Salaries,
Bonuses, etc)
Cost of Raw Materials
and Intermediate Goods
Used in Production
Cost for Establishment
to Re-Purchase All
of its Machinery
isOutlier
Following this, we check our model for multicollinearity and
heteroskedasticity issues. In general, the diagnostic test results suggest that the
degree of multicollinearity is considerably low since average variance inflation factor
has been estimated to be 1,88. In contrast, the White’s test for heteroskedasticity
suggests the presence of the heteroskedasticity. To overcome its adverse effects and
account for the heteroskedasticity, we employ robust variance estimator in our
regression models.
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As Table 3 results suggest, in the context of Uzbekistan, the share of capital
is estimated to be 0,248, the share of labour is 0,729 in the YAKL model. While the
second model suggests the share of capital is 0,19, the share of labour is 0,4, and
share of intermediate goods and materials is 0,423. Meanwhile, the models excluding
extreme observations demonstrated slightly different estimates than their
counterparts with outliers. In YAKL model, the share of capital has been found to be
0,263, while the share of labour is 0,709. Under YAKLM specification without
outliers, the share of capital is accounted for 0,187, while share of labour and
intermediate goods/materials are 0,358 and 0,443 respectively. However, under
YAKLM models regardless the presence of outliers, the magnitude of intermediate
goods and materials (M) tended to be the highest. This stresses out the high
importance of intermediate goods and materials for production.
Table 3
Regression results under YAKL (1–2) and YAKLM (3–4) specifications
Variables
Log of Replacement value
of machinery, vehicles
and equipment
Log of Total labor cost
Log of Total annual cost
of materials and intermediate goods
Constant
Observations
R-squared
Outliers
F-statistics
(1)
Model 1
(2)
Model 1
(3)
Model 2
(4)
Model 2
0,248***
(0,0496)
0,263***
(0,0495)
0,190***
(0,0440)
0,187***
(0,0439)
0,729***
(0,0619)
0,709***
(0,0649)
2,296***
(0,843)
2,332**
(0,906)
0,400***
(0,0726)
0,423***
(0,0599)
1,161*
(0,645)
0,358***
(0,0756)
0,443***
(0,0632)
1,594**
(0,620)
408
0,627
Included
257,4
377
0,628
Excluded
222,9
366
0,749
Included
353,4
358
0,755
Excluded
388
Robust standard errors in parentheses
*** p < 0,01, ** p < 0,05, * p < 0,1
In general, our results are quite similar to Şeker and Saliola [4]’s estimates of
factor shares for Uzbekistan in 2008 using YAKLM specification. Their estimates
were 0,19 for the share of capital and 0,55 for the share of labour, and 0,44 for the
share of intermediate goods and materials. However, the share of labour we obtained
for 2019 is lower than Şeker and Saliola [4]’s estimate for 2008. Such distinction in
magnitude may indicate Uzbek firms have become less labour-intensive since 2008.
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Table 4
Regression result of an econometric model with VAKL specification
Variables
Log of Replacement value of machinery,
vehicles and equipment
Log of Total labor cost
Constant
Observations
R-squared
Outliers
F-statistics
(1)
Value Added
(2)
Value Added
0,270***
(0,0528)
0,698***
(0,0621)
1,721*
(0,882)
0,280***
(0,0543)
0,674***
(0,0654)
1,895**
(0,953)
390
0,601
Included
231,2
360
0,599
Excluded
192,8
Robust standard errors in parentheses
*** p < 0,01, ** p < 0,05, * p < 0,1
Based on our model specifications expressed in equations (6) and (8), we
estimate the average TFP in the context of Uzbekistan. TFP estimates in Table 5 are
quite similar to those obtained by Şeker and Saliola [4]’s study for Uzbekistan in
2008, with the exception of TFP estimates obtained under VAKL specification. The
TFP estimates obtained using YAKL and YAKLM models imply that Uzbek firms
experienced a total factor productivity growth compared to 2008. In contrast, VAKL
TFP values are lower than those obtained for 2008. We attribute such variation in
VAKL TFP estimates to methodological differences in value added calculation.
Table 5
A comparison of TFP estimates for Uzbekistan
Model
YAKL
YAKLM
VAKL
TFP estimate
2,53
1,94
2,84
Şeker and Saliola
[5]’s TFP estimate
2,30
1,77
4,15
Having estimated coefficients for the production function for Uzbek firms,
we plot isoquant curves (Figure 3) which illustrate various combinations of inputs
(labour and capital) resulting in the same output. We use the following functional
form of production function:
𝑓(𝐾, 𝐿) = 𝐴𝐾 ! 𝐿$ = 2,53𝐾 &,()* 𝐿&,+(, .
(9)
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Firms try to maximise their profits by choosing the most lucrative
combination of capital and labour, especially labour costs are arguably one of key
determinants of firms’ demand to labour. We, therefore, estimate marginal rate of
technical substitution (MRTS). MRTS shows the degree of which one can replace
one input with another one. The slope of the isoquant curve at the given point 𝑋
represents MRTS for that combination of labour and capital implying the quantity of
capital required to substitute a unit of labour at the point 𝑋(𝐿& ; 𝐾& ).
* Source: The author’s own estimates
Figure 4. Isoquant curves using YAKL (model 1) parameters
Let 𝑀𝑃𝐾 and 𝑀𝑃𝐿 be the marginal product of capital (10) and labour (11)
respectively:
𝜕𝑌 𝜕(𝐴𝐾 ! 𝐿"#! )
𝐿"#!
𝐿 "#!
𝑀𝑃𝐾 =
=
= 𝛼 ⋅ 𝐴 ⋅ "#! = 𝛼 ⋅ 𝐴 ⋅ H I ,
𝜕𝐾
𝜕𝐾
𝐾
𝐾
𝑀𝑃𝐿 =
𝜕𝑌 𝜕(𝐴𝐾 ! 𝐿"#! )
=
= (1 − 𝛼) ⋅ 𝐴 ⋅ 𝐾 ! 𝐿#!
𝜕𝐿
𝜕𝐿
𝐾 !
= (1 − 𝛼) ⋅ 𝐴 ⋅ H 𝐿 I .
(10)
(11)
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In our case, it is the replacement of labour for capital given that output
remains unchanged:
-./
𝑀𝑅𝑇𝑆(𝐿, 𝐾) = − -.0 =
! #
"
" $%#
!⋅4⋅5 6
!
("#!)⋅4⋅5 6
=
"#!
!
0 !#!8"
⋅ M/N
=
"#!
!
0
⋅ /.
(12)
The estimated production function suggests that, for example, at the given
point of 𝐿& = 100, i. e., medium-sized firm, 𝑀𝑅𝑇𝑆 = 0,08. This indicates given that
output remains unchanged and production technology is the same, the firm should
give up roughly 13 workers and increase capital by an additional unit (Figure 3a).
Meanwhile, for the small firm with 𝐿& = 30 and 𝑀𝑅𝑇𝑆 = 9,14 – an additional
worker can substitute approximately 10 units of capital (Figure 3b). These results
imply in small firms, labour is relatively more productive than capital compared to
medium-sized firm (Figure 3a) in which capital productivity is much higher than
labour productivity. Our findings in the context of Uzbekistan is in line with Heyman
et al. [2]’s results who reported small firms were inclined to create more jobs than
medium- or large-firms, while, in contrast, larger firms are able to drive productivity
growth.
(a)
𝐿& = 100; 𝐾& = 2,71;
𝑀𝑃𝐾 ≈ 9,46; 𝑀𝑃𝐿 ≈ 0,75; 𝑀𝑅𝑇𝑆&
≈ −0,08
(b)
𝐿& = 30; 𝐾& = 93,309;
𝑀𝑃𝐾 ≈ 0,27; 𝑀𝑃𝐿 ≈ 2,44; 𝑀𝑅𝑇𝑆&
≈ −9,14
* Source: The author’s own estimates
Figure 5. MRTS estimates at the point (a) and (b)
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Concluding remarks
The research study provides a Cobb – Douglas production function to identify
the factor shares and total factor productivity in the context of Uzbekistan using firmlevel data. Our results show that under YAKLM and YAKL model specifications
without outliers, the share of capital is found to be 0,187 and 0,263, while share of
labour is accounted for 0,358 and 0,709 respectively. Such distinction in magnitude
of share of labour between models is attributed to the high share of intermediate
goods and materials (0,443) in YAKLM model.
Following this, we found total factor productivity in Uzbekistan for 2019
estimated using YAKL and YAKLM models to be greater than similar studies
conducted for 2008. Our estimates suggest that total factor productivity obtained
using YAKL and YAKLM are 2,53 and 1,94.
We found that our approximation of production function confirms other
research studies’ findings on firms’ demand to labour resources. The production
function shows small firms are inclined to hire additional workers to increase
production compared to medium- and large- firms due to the difference in magnitude
of MRTS.
In general, our results show Uzbekistan experienced a productivity growth
which could have resulted in a jobless growth. In other words, output increased due
to efficient use of factors of production, not through recruitment of additional
workers.
Acknowledgements
We would like to thank Dr. Prof. Tursun Shodiev, and other referees for their
valuable comments and suggestions.
Funding
The author received no specific funding for this work.
Data availability statement
Data is available
enterprisesurveys
on
URL:
https://www.enterprisesurveys.org/en/
Conflict of interest
The authors declare that there is no conflict of interest.
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Scientific and analytical journal «Science and Practice» of Plekhanov University. Vol. 13. No. 3 (43) 2021 130
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