ECONOMETRIC MODEL OF GROWTH LONG TERM GROWTH VIEW, CASE STUDY IN VIET NAM

This study uses the Cobb-Douglas production function with the assumption of the exponents of labor and capital inputs unchanged and includes dummy variables explaining Vietnam's economic

ECONOMETRIC MODEL OF GROWTH - LONG-TERM GROWTH VIEW,

CASE STUDY IN VIET NAM

Quyet Pham Dang Kinh Bac University, Bac Ninh City, Vietnam

Abstract

There have been many studies in Vietnam and abroad to identify the factors influencing economic growth with parametric or non-parametric approaches This study uses the Cobb-Douglas production function with the assumption of the exponents of labor and capital inputs unchanged and includes dummy variables explaining Vietnam's economic development stages from 1970 to 2020 to answer the question: what determines Vietnam's long-term growth rate The paper measures the contribution of capital stock, labor, and technological progress to the growth of the economy and contribution of increasing capital intensity and increasing total factor productivity (TFP) to increasing labor productivity The major findings are: the most important source of economic growth is capital accumulation, and although the TFP growth rate has gradually increased, capital intensity is still the main factor contributing to the increase in labor productivity, but the use of capital is not effective The main driver of economic growth is increasing labor productivity

The Cobb-Douglas Logarithmic function regression statistics revealed some interesting information and policy implications related to the Vietnam's economy as the market-oriented institutions have had a positive impact on economic growth, bringing about impressive progress in growth, but the growth efficiency is still low Among the transition directions, the institutional transformation orientation is the most important This is considered an important decisive factor of the national competitiveness so that the country's economy will move from an efficiency-driven stage to an innovation-driven economy

Key words: Econometric model of growth, production function, economic

growth, capital productivity, labor productivity, total factor productivity TFP

1 Problem

A country's Gross Domestic Product (GDP) provides a measure of the monetary value of the goods and services that are produced in a particular year This is an important statistics that tells whether an economy is growing or declining Providing quantitative GDP data helps the Government to make decisions such as stimulating the economy by injecting money in the case of an unimproved economy that needs such stimulus packages In case the economy is heating up, the Government can also act to prevent this from becoming too overheated Businesses can also use GDP data

as a guide to decide how to best expand or shrink their production and other business activities And investors also monitor GDP figures because these provide a framework for making investment decisions

Economic growth is the increase in the market value of the goods and services that an economy produces over time It is measured as the percentage rate change in the real gross domestic product (GDP) GDP growth is the goal to achieve improved

quality of life Gross domestic product per capita is an important indicator of the economic development level and living standards of the people

There is an important difference between the growth variation of an economic cycle (cyclical variation) and long-term growth (long-term trends) The economic cycle, also known as the business cycle, is the variation of real GDP in a three-phase order of recession, recovery and prosperity respectively There is also a view that the recovery phase is non-essential, so the business cycle consists of only two main phases: recession and prosperity (or expansion) Long-run growth is defined as the sustained rise in the quantity of goods and services that an economy produces

Economic growth depends on two processes: accumulating assets (such as capital, labor, and land) and investing in these assets more productively Savings and investment are central, but investment must be effective to boost growth Government policy, institutions, political and economic stability, geographic characteristics, natural resources, health and educational qualifications all play a certain role in influencing growth of the economy The question arises: what determines the long-term growth rate of an economy?

The economy achieves growth from two sources: first, by increasing the amount of its inputs as capital, labor and raw materials and second, by improving the efficient use of capital, labor and the materials By improving productivity, a country can achieve economic growth by converting the same amount of inputs into higher levels of total output Productivity (including total factor productivity TFP) increases can also stem from a higher quality of goods and services without increasing their costs respectively

This study uses the Cobb-Douglas production function with the assumption of the exponents of labor and capital unchanged and introduces dummy variables explaining Vietnam's economic development stages from 1970 to 2020 to identify factors influencing Vietnam's long-term economic growth

The conceptual origin of an aggregate production function is clearly identified

in the work of Paul H Douglas et al There should be a careful distinction between concepts of an aggregate production function and a Cobb-Douglas logarithmic or linear function that are more frequently quoted from Douglas's contribution The conceptual framework in the study of economic growth was further developed by Kendrick, Solow, and other pioneers (Dale 1988)

2 Production function and economic growth

Until recently the studies on sources of economic growth were based on the view of an aggregate production function This concept is one of the master simplifications that make it possible to summarize a mess of details into a simple aggregate framework It is also the concept that seems relevant to the interpretation of figures of output, input, and productivity compiled in the national production accounts But the concept of an aggregate production function is ambiguous, requiring very strict assumptions about the production model at the stages of each sector of the economy Intuitively speaking, the technologies for each industry must contain a simulation of

the aggregate production function At the aggregate level, output is represented by the amount of value added, expressed as a function of capital and labor inputs and

productivity levels This would be helpful to explain basic assumptions about the aggregate production function and its implications

In a production process, labor, capital and intermediate inputs are combined to produce one or more outputs For any kind of certain assets, there is an inflow of capital that flows into production from the accumulated stock of past investments This flow of capital into production is known as the capital service of the asset and is an appropriate measure of capital input for production and productivity analysis Since capital service flows are often not directly observable, they are approximated by assuming that the capital service flows are proportional to the stock of assets after each transformation converted into consumption standard efficiency units The reserves of capital so calculated are called the productive stock of a given type of asset Consequently, building the capital stock produced for each asset type is the first creation step towards measuring the amount of capital services Do this using the Perpetual Inventory Method (PIM) The general formula for calculating the capital stock for a given year is:

Where, K(t) is the total amount of capital in year t, I(t) is investment, also known as capital formation in year t, δ is the depreciation coefficient

Labor is also the most important input to production processes From a production analysis perspective, labor input is most appropriately measured as the total hours worked Because a labor's contribution to production includes raw labor (or physical presence) and the transformation from human capital of labor - an hour worked by one person is not necessarily generating the same amount of labor input as

an hour worked by someone else Labor input can also be measured by the number of jobs This measurement is simpler, but it does not reflect changes in average hours worked per worker nor changes in people doing multiple jobs and the roles of self-employed workers (or labor quality) (OECD 2001) Let L be the total supply of labor

In addition, there are other factors that determine growth, such as technology - including science, engineering, management techniques; natural resources - land, oil, minerals, environmental quality; institutions - property rights, execution contracts (legal system), patent and copyright law; and culture - social capital, entrepreneurship, work ethic and capitalism spirit (Max Weber)

Determining the factors affecting economic growth has long been done by a large number of domestic and foreign researchers Cobb and Douglas, two American mathematicians and economists, applied a production function growth model to study the effect of labor and capital factors on gross industrial products manufacturing in America In addition to the contribution of each factor of labor and capital, we also see a new value created by an intangible part This intangible part is the aggregate effect of inputs and is called A

Economists use the abstract concept of the aggregate production function:

The Cobb-Douglas production function is presented in an exponential form:

A is the technological level, also known as the total factor productivity TFP, the exponents α, β are the elasticity of capital and labor, β = 1 - α

Another useful approximation Suppose 𝑌𝑡 = (1 + 𝑔𝑡)𝑌𝑡−1, where gt is the rate

of growth that changes over time Then:

𝑙𝑜𝑔(𝑌𝑡) = 𝑙𝑜𝑔 ((1 + 𝑔𝑡)𝑌𝑡−1) = 𝑙𝑜𝑔(1 + 𝑔𝑡) + 𝑙𝑜𝑔 (𝑌𝑡−1) (4)

Take the logarithm of both sides of the production function (3):

𝑙𝑜𝑔(𝑌𝑡) = 𝑙𝑜𝑔(𝐴𝑡)+∝ 𝑙𝑜𝑔(𝐾𝑡) + (1−∝)𝑙𝑜𝑔 (𝐿𝑡) (6) 𝑙𝑜𝑔(𝑌𝑡−1) = 𝑙𝑜𝑔(𝐴𝑡−1)+∝ 𝑙𝑜𝑔(𝐾𝑡−1) + (1−∝)𝑙𝑜𝑔 (𝐿𝑡−1) (7) The 𝑙𝑜𝑔(𝑌𝑡)function states that with an increase of 1% of capital or 1% of labor, output will increase by an amount α% or (1 - α)% of output respectively

Subtract equation (6) from equation (7), we have:

𝑙𝑜𝑔(𝑌𝑡) − 𝑙𝑜𝑔(𝑌𝑡−1) = 𝑙𝑜𝑔(𝐴𝑡) − 𝑙𝑜𝑔(𝐴𝑡−1)+ ∝ (𝑙𝑜𝑔(𝐾𝑡) − 𝑙𝑜𝑔(𝐾𝑡−1) +

Or have the growth accounting equation:

The Cobb-Douglas production function model (9) shows that the main contributors to GDP growth are labor L growth, capital K growth, and the total factor productivity (TFP) growth

Rearrange (9) to get TFP growth rate:

Rearrange the growth accounting equation (9):

𝑔𝑡𝑌− 𝑔𝑡𝐿 is the growth rate of GDP per worker (Y/L), sometimes known as labor productivity

𝑔𝑡𝐾− 𝑔𝑡𝐿 is the growth rate of the capital-labor ratio (K/L) The increase in K/L

is called capital intensity: each worker has more capital to work with

Equation (11) states: at the aggregate-level labor productivity growth can be decomposed into the effects of increasing capital intensity and increasing TFP - these factors are keys in promoting labor productivity

3 Contribution of capital, labor and TFP to economic growth

Annually, the Vietnam General Statistics Office (GSO) publishes data on GDP and Gross Capital Formation, Fixed Capital Formation in the national account, but there is no data on the capital stock, so, to answer the important question: How do inputs of capital, labor, and technological progress contribute to economic growth in Vietnam? The paper uses the above economic growth model and the data source of the APO Productivity Database 2019 (APO 2019) Data on GDP, capital stock and labor (total employment) in the APO Productivity Database 2019 are updated to 2017,

so the author estimates more data of years 2018, 2019 and 2020 based on the latest published statistics of the GSO

Data on GDP at basic price, Capital stock at constant prices (in 2017 prices) and Number of persons/jobs (Total employment) from 1970 to 2020 is shown in Figure

1 From this data source, the paper calculates the growth rate of GDP, capital and labor from 1971 to 2020

Source: APO Productivity Database 2019 and author estimates

Figure 2 Growth chart shows that Vietnam's economy seems to have experienced a number of significant shocks and changes, most notably in 1975-80 (the first domestic economic crisis), 1985-86 (second domestic economic crisis), 1989-90 (collapse of the Soviet Union), 1998-99 (impact of 1997 Asian financial crisis), 1989-

2013 (when bold reform policies shifted to the factor-driven market economy), and after 2014 the economy entered a transition period into efficiency-driven (Pham Minh Ngoc 2008) In 2020, due to the Covid-19 pandemic, the growth rate of GDP, capital and labor all are decreased, but the growth rates of GDP and capital are positive thanks

to good disease control and a strong export sector in the face of this shock, labor growth is negative yet Clearly, the Covid-19 pandemic has deprived many workers of the opportunity to have formal jobs, making a part of them unable to find new jobs, others having to switch to informal unstable, unsustainable jobs

0 10000 20000 30000 40000 50000 60000

0 2000000 4000000 6000000 8000000 10000000 12000000

1970 1973 1976 1979 1982 1985 1988 1991 1994 1997 2000 2003 2006 2009 2012 2015 2018

Figure 1 GDP, Capital stock and Total employment 1970-2020

GDP Capital stock Total employment

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1971 1973 1975 1977 1979 1981 1983 1985 1987 1989 1991 1993 1995 1997 1999 2001 2003 2005 2007 2009 2011 2013 2015 2017 2019 Figure 2 Growth of GDP, Capital and Employment 1971-2020

GDP growth Capital growth Employment growth

Table 1 shows the average annual growth rates of GDP, capital and labor per 5-year periods from 1971-2020

Table 1 Average annual growth rate of GDP, capital and labor in period

1971-2020

Running the model on gretl software, Cobb-Douglas Logarithmic regression has the following form:

^l_GDP = -2.31 + 0.820*l_K + 0.415*l_L

(0.576) (0.0401) (0.106)

T = 51, R-squared = 0.996

(Standard errors in parentheses)

Model 1: OLS, using observations 1970-2020 (T = 51)

Dependent variable: l_GDP HAC standard errors, bandwidth 2 (Bartlett kernel)

Coefficient Std Error t-ratio p-value

Log-likelihood for GDP = −637.68 that is the parameter value “most likely” to have produced the data

The square of the correlation coefficient measures the goodness-of-fit of the regression function R-squared = 0.996 means that the model is explained by a high degree (≈100%) of variability of the dependent variables The p-values < 0.01 in the regression indicates that the coefficients of the constant and the dependent variables are statistically significant

Test hypothesis α + β = 1:

Variables: l_K l_L

Sum of coefficients = 1.23494

Standard error = 0.0689354

t(48) = 17.9144 with p-value = 6.78039e-023

The p-value = 6.78039e-023 < 0.0001 means that the hypothesis that the capital and labor exponents sum to 1 cannot be rejected at a high degree of confidence in this regression Choose β = 0.414691, then α = 1 - 0.414691 = 0.585309

TFP growth rate is calculated by formula (10) and Table 1, here choose α = 0.585309 Figure 3 shows that GDP growth is mainly due to the contribution of capital and technology, the share of the labor contribution tends to be decreased gradually over time Note that labor input is measured here by total employment; if labor input

is measured by total number of hours worked, the share of labor's contribution to growth may be higher Moreover, the tendency of the share of labor contribution to growth decreased suggests a problem of low quality of labor: the quality of human resources in Vietnam is still challenging, even though the labor force is young and plentiful, but their skill level and technical expertise are low, not meeting the country's development orientation and international integration

The average annual GDP growth rate for the whole period 1971-2020 was 5.5%, the average annual growth rate of capital was 5.59%, contributing 3.27 point (or 59.52%) to economic growth, the growth rate of labor was 2.41%, contributing 1.0 point (or 18.2%) to growth, TFP growth rate was 1.23%, contributing 22.29% to economic growth for the whole period 1971-2020 Capital is still the main contributor

to GDP growth during the period 1971-2020 Advances in technology result in increased levels of output with the same input, and help improve productivity

GDP growth since the early 2000s has been achieved by factors compensating for weakness and decline in productivity growth, but now these factors have reached their natural limit threshold Labor productivity growth, which is inherently low and declining throughout the economy, is compensated by a rapidly growing workforce;

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Figure 3 Contribution of capital, labor and TFP in GDP growth

1971-2020

Capital contribution Labor contribution TFP growth

while low total factor productivity TFP is replaced by an increase in capital accumulation In the next stage of development, it is forecast that the effect on overall economic growth of each of the above factors will be decreased more strongly than the effect on productivity trends In addition, the world economic context will be much less favorable than the period before the global financial crisis

More than that, the epidemic of respiratory infections caused by a new strain of the Coronavirus (Covid-19) has exploded and spread globally, and has severely affected the world economy by 2020 In Vietnam, although it is heavily affected by the Covid-19 pandemic, thanks to proactive and creative countermeasures at all levels, and decisive policies to prevent the economic slowdown, Vietnam's economy has resilient and recovered significantly, gradually resuming operations in new normal conditions and should rebound in 2021

Capital productivity is an indicator used in determining the value generated from a unit of capital used - a criterion to evaluate the efficiency of capital use Through capital productivity, we can know how capital is used and how it contributes

to production and business results In general, the total capital productivity did not change significantly over the years from 1971 to 2020, but fluctuated between 0.5 and 0.6 VND/VND, meaning that 1 VND of capital creates 0.5 to 0.6 VND of added value The average annual capital productivity of the whole period 1971-2020 was 0.55 VND/VND (Figure 4) This shows that the efficiency of capital use has not been significantly increased In addition to the ineffective use of capital due to waste, a portion of the real capital put into production is eroded (overhead), with a ratio of σ,

so real capital actually put into production is only (1- σ) * K

Labor productivity reflects the efficiency of using labor Labor productivity was low in the years 1971-1986 and almost did not increase, fluctuating between 18 and 20 million VND, and after 1986 the labor productivity increased from 20.15 to 99.47 million VND in 2020 The average labor productivity per year for the whole period 1971-2020 was 39.75 million VND, which means that the average of 1 year per employee created 39.75 million VND of added value (Figure 4) Vietnam's labor productivity (in terms of purchasing power equivalent) is low and still far from the labor productivity of many ASEAN countries (APO 2019)

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1970 1972 1974 1976 1978 1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 2012 2014 2016 2018 2020 Figure 4 Productivity of capital and labor 1971-2020

GDP/L GDP/K

The main driver of economic growth (GDP growth) is increasing labor productivity Under limited (labor and capital) input conditions, increasing productivity is the only path to long-term sustainable economic growth At the aggregate-level, labor productivity growth can be decomposed into the effects of capital intensity (measured in capital input per worker), which reflect capital-labor substitution and TFP In other words, these factors are keys in boosting labor productivity

The growth rate of labor productivity and capital intensity are calculated from formula (11) Figure 5 shows the contribution of increasing capital intensity and increasing TFP to increasing labor productivity The increasing level of technology (TFP increase) from 2006 up to now shows that the contribution of technology to productivity growth increases The average annual growth rate of labor productivity

in the period 1971-2020 was 3.08%, the capital intensity growth rate was 1.86%, contributing 60.29% to the growth rate of labor productivity, the TFP growth rate was 1.23%, contributing 39.71% to the increased labor productivity Labor productivity increase is still due to increasing capital intensity To increase labor productivity requires more efficient use of existing resources including capital and human labor, which means increasing capital equipment per employee, while enhancing new scientific and technological advances, changing the way of working, creating newer products with higher quality and value, that means creating a greater rate of increase

in labor productivity

For a low middle-income country, to ensure more inclusive and sustainable growth, the challenge facing Vietnam is the transition to a new growth model based

on rapid productivity growth, innovation, high value added and promoting international competitiveness to bring more jobs to the majority of Vietnamese people Aware of this challenge, the Socio-Economic Development Strategy 2010-2020 and Vietnam's 5-year Socio-Economic Development Plan, specifically the plans for the period 2010-2015 and 2016-2020 highlight the importance of industrialization as well

as increasing national productivity and competitiveness Among the nine economic indicators of the Socio-Economic Development Plan for the period 2016-2020, there are two indicators: increase the contribution of total factor productivity (TFP) to

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Figure 5 Contribution of growth of capital intensity and TFP in

growth of labor productivity 1971-2020

TFP growth capital intensity growth Labor productivity growth

overall growth and reach the average annual labor productivity growth of 5% These two targets have been achieved

4 The impact of institutions on economic growth

History shows that the world economy has only really grown rapidly with the industrial and technological revolutions over the past two centuries During the 19th and 20th centuries, the world population increased five times, but the total real output increased by 40 times, making real output per capita increase eight times However, there is considerable difference in growth rate and development level between countries in many periods Even in the second half of the 20th century, some countries

"caught up" with the developed countries, while many countries still have not yet eradicated poverty and many countries lost their development momentum, even fell into economic crisis and social breakdown

Solow's theory (1956) of economic growth in relation to (capital, labor, technology) factors and with investment-saving is still considered "most useful" because it is not based on relatively realistic assumptions, but also with important policy implications such as: (i) while the role of savings and investment in economic growth is emphasized, investment only makes increasing per capita income in the transition period due to decreasing marginal productivity of capital; (ii) poor countries have faster economic growth and will eventually "catch up" with developed countries The reason is that poor countries have low capital-to-labor ratios, so the efficiency of capital is used higher, leading to faster growth in the transitional period However, this

"catch-up" process is conditional A number of economies have failed to keep pace with richer countries’ ones, and have even fallen into low growth and poverty; and (iii) the only factor to maintain sustainable growth is technological progress However, Solow has not yet shown how technological progress is happening and is influenced

by policy (Solow 1956)

Vietnam's economy has undergone different stages of development: before

1986 it was a centrally planned economy, after 1986 Vietnam turned to a market-oriented economy, the first stage of development mainly based on the resource factors, just since 2014, Vietnam has started to transition to an efficient investment stage (Klaus Schwab 2018)

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Figure 6 Contribution of growth of capital intensity and TFP in growth of labor productivity in development stages

TFP growth capital intensity growth Labor productivity growth