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Some Issues on the Vietnam Economic Growth

Phuong Le1, Cuong Le Van2, Anh Ngoc Nguyen3, Ngoc Minh Nguyen4, Phu

Nguyen-Van5, and Dinh-Tri Vo6

1Paris-Sud/Paris Saclay University (France) & Banking University Ho Chi Minh City

(Vietnam)

2IPAG Business School, PSE, CNRS (France) & TIMAS (Vietnam)

3DEPOCEN (Vietnam)

4University of Nantes (France) & DEPOCEN (Vietnam)

5BETA, CNRS, INRA & University of Strasbourg (France) and TIMAS (Vietnam)

6IPAG Business School (France) & University of Economics Hochiminh City (Vietnam)

February 2020

Abstract

We first consider the question of the productivity of the economy of Vietnam at the

macro level. With theoretical models and empirical data, we find out the Leontief production

function, and its associated TFP (Total Factor Productivity). We show that the TFP is one

of the main engines of Vietnam economic growth.

However when we move to the micro level with the capital productivity of 2,835 State Owned

Enterprises (SOEs), we discover there exists an over utilization of the physical capital and

more importantly, diversion of the capital stock. This diversion may be due to a waste of

capital stocks or to a special form of bribery we call "hidden overhead".

To summarize, economic growth in Vietnam my be enhanced by investing in the founding

components of TFP such as new technology, Human Capital, better organisational system,

but also by fighting the bribery and the over utilization of the physical capital

Keywords: Productivity; Production Function; TFP; Hidden Overhead

JEL: E60, O11, 053, P21

1

1 Introduction

When the Vietnam War ended in April 1975, Vietnam was one of the poorest country in the

world. By the mid-1980s, Vietnam GDP per capita was stuck between 200 USD and 300 USD.

In recent years, Vietnam is one of the important emerging economies with growth of 6-7% and

a GDP per capita around 2,000 USD in 2017. The volume of goods trade is around 200% of

the GDP. This shows Vietnam economy is very open. The important question is how Vietnam

economy can go further.

Understanding the growth engines is therefore vital for policy makers, economists, and

investors. Recently, there are discussions and concerns about the productivity of the economy

of Vietnam, regarding TFP and labour productivity. Many papers and policy makers claim that

labour productivity is crucial for Vietnam economic growth. We prove that the productivity of

labour is not always an engine for growth. For sure , it is not when the production technology

is of Constant Returns to Scale.

Before studying the growth mechanisms, one must find out the economic structure on which

Vietnam economy relies. We show that the production function of Vietnam’s economy actually

is Leontief and the TFP has an important role .

As in Nguyen Duc Thanh & Ohno Kenichi (2018) we first consider the question of the

productivity of the economy of Vietnam at the macro level. We make a comparison with China

and Laos.

Macro level is not the only basis to study Vietnam economy. We hence move to the micro level

and consider the capital productivity of the State Owned Enterprises (SOEs). The period under

consideration is 2005 −2017.

The main findings of our paper are

•We have detected the production function of Vietnam is Leontieff.

•The TFP growth has a strong impact (42%) on the GDP growth of the three recent years.

•The TFP depends, with lag, on the GDP which is used as proxy of the expenditures for

human capital, R&D, new technology.

•If the production function is Cobb-Douglas with constant returns to scale, then contrarily

to the usual intuition, the rate of growth of labour productivity is negatively related to

the GDP rate of growth. The reason is that the capital productivity and the labour

productivity are substitutes.

2

•The labour productivities of Laos and Vietnam in the three recent years (2015-2017) are

quite comparable. However; for the same years, the average rate of growth of Vietnam

labour productivity is higher than the one of Laos.

•Vietnam labour productivity and its growth rate are lower than the ones of China.

•We found that the production function of China is Cobb-Douglas with constant returns to

scale, while the one of Laos is of increasing returns. For us, in view of the big differences

of their economic structure, comparison of labour productivities of these three countries

does not make sense.

•Using a census conducted by GSO in 2014, 2015 for 2,835 State Owned Enterprises (SOEs),

we found that some of Vietnamese SOEs are very capital intensive.

•1,832 SOEs make profit, the average profit rate is around 35.6%. They use 36.8% of the

total capital of 2835 SOEs, their revenues represent 84.9% of the total revenue.

•It is interesting to discover that 545 SOES, the revenue of which representing only 15.1%

of the total revenue, use 63.2% of the total capital. They make losses, the average rate of

their deficits is 29%

•We know consider the issue of "hidden overhead". It is well known that when a Vietnamese

SOE asks for say 1 billion of VND for its purchase of capital, it will receive (1-σ) billion.

But it has to declare receiving 1 billion, σbillion have been diverted. The number σis

called by us "hidden overhead". We found that the average distribution of σis 50%.

If we consider the 1,862 SOEs (65.7% of the SOEs) which make profits, the value of σis

very small, around 0.4%. For the 545 SOEs who make losses, some of them have σ= 60.%

It is astonishing to see that a minority of SOEs is so capital wasteful.

The missing point in this paper is that we do not consider the private sector, in particular, the

foreign firms. This point is explained by the fact we did not find time series about the capitals,

revenues, employment, wages of this sector.

The rest of the paper is organized as follows. Section 2presents some background informa-

tion about production functions and productivity. Section 3discusses the issues on Vietnam

Economic Growth at the macro level. We attempt to build a series of capital stocks of the

Vietnam economy and then run regressions in order to find out the production function with its

associated TFP (Total Factor Productivity). Subsection 3.4 of this section exhibits the produc-

tion functions of China and Laos and then compare the labour productivity of China, Laos and

3

Vietnam. Section 4move to the micro level by focusing on the 2,835 State Owned Enterprises

and show there exists an over utilization of the physical capital. We also question the issue of

diversion of the capital in these SOEs. This diversion may be due to a waste of capital stocks

or to a special form of bribery we call "hidden overhead". Section 5concludes the papers with

several remarks.

2 Literature

There are substantial numbers of papers discussing the production functions and productivity

to explain the growth of different economies around the world. Solow (1957) established the

steppingstone. He used a Cobb-Douglas production function with two basic inputs in produc-

tion, labor and capital, and a multiplier that represents the change of the production function

over time, which is called "technical progress". In the production process, the manager uses

labor and capital, with the help of technical progress (denoted later by TFP), to produce the

final product. Part of the finished product serves consumption and the rest is used for capital

accumulation purposes. For an economy where every factor of labor and TFP steadily increases,

using the Solow model can prove that the economy can grow indefinitely but the rate of growth

is exogenous. Using US data from 1909-1949, Solow discovered TFP contributed 87.5% to US

economic growth.

The model of Solow-Swan still had certain limitations, especially in the hypothesis of the

exogenous nature of total factor productivity (TFP), leading to restrictions in policy orienta-

tion. Endogenous growth theory is then introduced in order to give the founding components

of TFP. We will focus on the contributions of Romer (1986) and Lucas (1988).

Romer (1986)’s approach has the same starting point as Solow’s, with a significant improvement

in integrating "Knowledge" into capital. He argued that when economic entities accumulate

knowledge, promote creativity, innovation, then positive externalities will be created, helping

to increase capital productivity for the economy as a whole. Accordingly, TFP and capital

productivity will not be limited and can always increase with new innovative technology ideas.

Romer’s model can be used to describe the impact of technology on growth.

The model of Lucas Jr (1988) shows that investment in education and training may be another

founding element of growth engine through the rise of labor productivity.

Thus, endogenous growth theory not only transcends previous models in the ability to explain

factors related to TFP, capital productivity and labor productivity, but also has clear policy

implications. In particular, these models encourage the use of new technology, human capital

4

accumulation, and technological advances to promote growth.

While numerous research about production function and productivity has been carried out

in developed countries, there is only small amount of research focusing on emerging markets,

especially in Vietnam. Khương (2016) investigated the Vietnam labor productivity based on

an application of growth accounting method (Jorgenson et al.,2005) in which GDP growth of

an economy during the period can be divided into: the growth of capital, labor, and TFP. This

research assumed the production function of Vietnam was of Constant return to scale. Nguyen

Duc Thanh & Ohno Kenichi (2018) also assumed that the production function of Vietnam is

Cobb-Douglas with the elasticity of the capital equals 0.35. The value of the elasticity was in-

spired by Collins et al. (1996). Therefore, most of these research were based on the assumptions

about production function of Vietnam economy such as: Cobb-Douglas with Constant return

to scale. In our paper, through regression equations, we first find out the economic structure

on which Vietnam economy relies on, and then investigate the productivity at both macro and

micro levels.

Van Thang and Freeman (2009) show there is a negative correlation between SOE growth

and private sector growth. There is an evidence that SOEs are ’crowding-out’ the private sector

in Vietnam. Similarly, Nguyen and Van Dijk (2012) find that corruption hampers the growth

of Vietnam’s private sector but is not detrimental for growth in the state sector. For Takeyama

(2018), if the Vietnamese government has made efforts for several years to promote the reform

of SOEs, this process cannot be completed since will be required the introduction of regulations

and systems to correct opaque financial situation and management techniques of SOEs.

We are not aware of papers which quantify the degree of capital waste and bribery in Vietnamese

SOEs. This issue is studied in Section 5 of our paper.

3 Part 1: Issues on Vietnam Economic Growth at the macro level

3.1 Production Function and Total Factor Productivity

3.1.1 Capital stocks

In subsection 3.1.2 we will determine the production function for Vietnam economy, during the

period 2005-2017. The first step is to build the series for Capital Stocks.

Our methodology is as follows. We use the formula

Kt+1 =Kt(1 −δ) + It(1)

5

We have the data for the investments in constant price It. The depreciation rate δis supposed

equal to 0.05. We want to compute Ktfor t= 2005 to t= 2017. We denote by t= 0 the year

2005. If we know K0we can generate the series {Kt}, t = 1,...,12. To have K0we suppose

K0=v0Y0where Y0is the GDP at t= 0 and v0is the capital coefficient at date 0. Let ICOR0

defined by

ICOR0=I0

Y0−Y−1

Suppose K−1=v−1Y−1. This formula is immediate

I0=v0Y0−(1 −δ)v−1Y−1

We suppose v0=v−1=v. We then get

ICOR0=v1 + δ

g0

where g0=Y0

Y−1

−1

We obtain v= 2.886. In the table 1, we present below the series of capital stocks generated by

(1).

Table 1: The capital stocks of Vietnam from 2005 to 2017, (USD in millions)

Year 2005 2006 2007 2008 2009 2010 2011

K 246325.30 262821.25 281215.09 305856.77 328281.49 352350.79 376113.92

Year 2012 2013 2014 2015 2016 2017

K 393951.42 409568.74 425545.07 443131.31 463589.77 484026.07

Source: Authors’ calculations with World Bank data

For robustness check, we used also the Perpetual Inventory Method (PIM) which is usually

employed by the OECD and other international institutions to generate the capital series (see,

e.g., Kamps, 2006). The PIM consists of the capital accumulation equation above and the

initial capital stock defined as K0=I0/(gI+δ)where gIis the average annual growth rate

of investment over the period of study. So, by using the series on investment flows, we can

calculate gIas gI=Pn

t=1(It−It−1)/n.1

1There is a close relationship between our method based on ICOR and PIM method. Indeed, if we denote by

sthe rate of investment, then from PIM we get K0=sY0

gI+δ. Our capital coefficient vequals s

gI+δ. The difference

is: for PIM method investment and physical capital have the same rate of growth, while for our method assumes

the capital coefficient is unchanged for the two beginning periods. If we use the Harrod model for the periods

before the one taken as beginning period, the two methods coincide.

6

There is a divergence between Kcalculated using ICOR and Kbased on the PIM. Please

refer to Figures 1and 2, with respectively δ= 0.05 and 0.07, for more details). However, when

δ= 0.07, the results obtained by the two calculations are very close.

Figure 1: Kbased on ICOR and Kbased on PIM, depreciation rate δ= 0.05.

3.1.2 Production Function

The authors in Nguyen Duc Thanh & Ohno Kenichi (2018) assume that the elasticity of the

capital in the production function equals 0.35. They use the value given in Collins et al. (1996).

This approach is questionable. First, Collins et al. (1996) actually refer to Kim and Lau (1994)

and Harrison (1994) who respectively α= 0.2and α= 0.4for Asia countries. The value 0.35 is

arbitrarily chosen in the interval [0.2,0.4].

Second, twenty years separate these papers and Vietnam in 2019.

Third, the value was obtained by cross-sectional regression with many countries.

Logically, once one has on hand, the data for capital stocks Kt, for labour Ntand GDP

Yt, one should run regressions to find out the elasticity of the capital stock, assuming the

7

Figure 2: Kbased on ICOR and Kbased on PIM, depreciation rate δ= 0.07.

production function is Cobb-Douglas with constant returns to scale

ln( Yt

Nt

) = A+αln(Kt

Nt

)

That is what we did. The results of the regression are in Table 2. In view of the standard errors

of the parameter αwe assume that α= 1. The production function is in fact

Yt=AtKt(2)

We then generate the series of TFP, A

At=Yt

Kt

Having computed the series Atwe run the following regression

Yt

At

=bNt

8

Table 2: The regression for Vietnam’s Production Function (1)

Dependent Variable: Ln(Y/N)

Method: Least Squares

Date: 04/13/19 Time: 12:37

Sample: 2005 2017

Included observations: 13

Variable Coefficient Std. Error t-Statistic Prob.

C -1.4453 0.57801 -2.5001 0.0295

Ln(K/N) 1.0415 0.0650 16.0281 0.0000

R-squared 0.9589 Mean dependent var 7.8193

Adjusted R-squared 0.9552 S.D. dependent var 0.1532

S.E. of regression 0.0324 Akaike info criterion -3.8789

Sum squared resid 0.0116 Schwarz criterion -3.7919

Log likelihood 27.2126 Hannan-Quinn criter. -3.8967

F-statistic 256.9006 Durbin-Watson stat 0.2769

Prob(F-statistic) 0.0000

We obtain (see below, Table 3)

Yt=At×bNt

with b= 7506. The production function of Vietnam, during the period 2005-2017, is Leontief

Yt=Atmin{Kt, bNt}2

For robustness of the results, we used also the series of capital stocks which are computed by

the Perpetual Inventory Method. With δ= 0.05, the regression results are not reasonable due

to the negative elasticity for N. While with δ= 0.07, the results are very consistent with the

findings using the ICOR method. We report in Appendix 2, the results of regressions obtained

with PIM. In both cases, we can conclude that the production function for the Vietnam economy

is a Leontief function.

Remark (1) In this remark we present another way to test whether the production function is

Cobb-Douglas or Leontief

Let us consider a more general function, i.e. CES function,

Y=A[aKα+ (1 −a)Nα]1/α (3)

where s≡1/(1 −α)is (constant) elasticity of substitution between capital and labor.

Now, suppose that the Vietnam economy satisfies the profit maximization program maxK,N Y−

2Actually during this period we have Yt=AtKt=At×bNt. Implicitly, we suppose that all the representative

firm of Vietnam maximizes the profit and hence AtKt=At×bNt.

9

rK −wN ). First-order conditions with respect to capital and labor lead to the following well-

known equality:

w

r=1−a

aK

N1−α

,(4)

which states that real wage (LHS) is proportional to the capital-labor ratio. Real wage also

depends on the relative share between capital and labor (i.e. (1 −a)/a) and the inverse of

elasticity of substitution (i.e. 1−α= 1/s).

In order to use data to investigate the form of production function, we apply the log trans-

formation and add an error term εto equation (4):

ln w

r=c+ (1 −α) ln K

N+ε, (5)

where c≡ln 1−a

acorresponds to the intercept. Estimation of equation (5) will provide the value

of α. Using the property of the CES function, we can predict the form of production function.

More precisely, it is a Cobb-Douglas if α= 0, a Leontief if α=−∞, a linear function if α= 1,

or none of these forms otherwise.

We must therefore have data on wage and interest rate in constant prices (the reference year

is 2010 as for investment and capital), capital stock (we can use either ICOR-based capital or

PIM-based capital series) and labor (can be proxied by population aged 15 and 60). However, we

have no data on Vietnam wages. We have data only for nominal incomes for every two years.

This approach is very interesting. But it hits, in the case of Vietnam, the problem of data. If we

have data for wages, but it is commonly known that the quasi totality of Vietnamese workers,

in particular in the administrations, cannot live with their salaries. Almost of them have extra

jobs. These incomes have been recorded. However, they are published once every two years. The

samples are very too short to have significant regressions results.

This method may be used in the future when the annual data of incomes will be available.

3.2 Total Factor Productivity

In this section, we use the regression results obtained with the capital stocks generated by the

method based on ICOR

The labour productivity of Vietnam is therefore expressed as

Yt

Nt

=A(t)Kt

Nt

We can conclude that the Vietnam labour productivity is low (high) if the economy is less

10

(more) intensive in capital than in labor or/and if the TFP is low (high).

We plot the graphs of Atand of ∆A

A

Figure 3: Total-Factor Productivity of Vietnam

Table 3: The regression for Vietnam’s Production Function (2)

Dependent Variable: Y/A

Method: Least Squares

Date: 04/17/19 Time: 17:18

Sample: 2005 2017

Included observations: 13

Variable Coefficient Std. Error t-Statistic Prob.

N 7506.7760 282.5649 26.5666 0.0000

R-squared 0.58252 Mean dependent var 3.67E+11

Adjusted R-squared 0.58252 S.D. dependent var 7.80E+10

S.E. of regression 5.04E+10 Akaike info criterion 52.1993

Sum squared resid 3.05E+22 Schwarz criterion 52.2428

Log likelihood -338.2957 Hannan-Quinn criter. 52.1904

Durbin-Watson stat 0.07021

We go back to (2). Let vdenote the capital coefficient, gdenote the annual GDP growth rate,

sdenote the Vietnam national investment rate. From Le Van and Dana (2003), Section 1.2 on

the Harrod Model, we have the relation

g+δ=s

v(6)

11

Given the production function we found (2), (6) becomes

g+δ=sA (7)

where Ais the TFP. Suppose the target for gis 0.07 then, with δ= 0.05, we must have

sA = 0.12

This relation points out the importance of the investment rate and of the TFP as well.

For 2018, the Vietnam General Statistics Office (GSO) announces 7.1% for GDP growth, 33.5%

for investment rate and the contribution of the TFP is 43%.3. We use (7) to compute the TFP

for 2018 with g= 0.071 and s= 0.335. We get

A=0.121

0.335 = 0.361

in accordance with the range of the values of TFP given above.

Another interesting thing when we want to find out the contribution of Agrowth to the

GDP growth. For that, consider again (2). By differentiation we get

∆Y

Y=∆A

A+∆K

K

This implies

1 = ∆A/A

∆Y/Y +∆K/K

∆Y/Y

If we look at the graph of ∆A/A in Figure 1, we may expect that its value will be around

0.03 for 2018. Since the rate of GDP growth in 2018 is 0.071 if we follow GSO, the contribution

of Agrowth to GDP growth is

0.03

0.071 = 0.422

i.e. 42.2% in accordance with the results given by GSO.

For 2019, suppose the target for gis 7%. If s= 30% then, from (6),we obtain A= 0.4.

Since in 2017, the true value is A= 0.36, not very far from 0.4. We think that the target for g

can be reached for 2019.

We will now attempt to explain the TFP. For that, we refer to Romer (1990) and Lucas Jr

(1988). We introduce the concepts of effective capital ˜

Kand effective labour Ldefined as

3See the link https://www.gso.gov.vn/default.aspx?tabid=382&idmid=2&ItemID=19041

12

follows.

˜

K=φ(New technology, Innovation, Knowledge)×K

L=ψ(education, training, working time)×N

The production function will now be

Yt=A0˜

KαLβ

where A0is a scaling constant. This production function can be rewritten as

Yt=hA0(φ(Technology, Innovation, Knowledge))α×(ψ(education, training, working time))βiKαNβ

The TFP Ais therefore

A=hA0(φ(Technology, Innovation, Knowledge))α×(ψ(education, training, working time))βi

The functions φ, ψ are non decreasing in their variables.

The TFP Adepends on the New Technology, the innovation, knowledge, Human capital and

working time. The working time is exogenous. It is commonly accepted that Innovation, New

Technology, Knowledge, Education, Human capital depend on the percentages over GDP of

the expenditures devoted to these factors. Since we have no data for these expenditures, we

assume that the percentage of the expenditures is constant over time and use GDP Yas a proxy

of the percentage over GDP of the expenditure for Innovation, New Technology, Knowledge,

Education, Human capital. If our intuition is correct, the GDP Ywill impact the rate of

growth of the TFP. Moreover, we think the impacts are observed with some delay. We will run

regression

∆At

At

=a+bYt−2

Y2010

(8)

We assume the lag is of two years4. The results are given below in Table 4. The coefficient bis

positive and confirms our intuition.

This result suggests that the TFP is high or low according to amount we devote to invest in it.

We design in Appendix 1 a simple two-period model of investment in TFP.

4As the value of Y is too much higher than the value of ∆At

At, we divided the Yt−2by Y2010. The regression

result would be the same, but the coefficient bwould be easier to observe.

13

Table 4: The impact of Innovation, New Technology, Knowledge, Education, Human capital on

TFP

Dependent Variable: ∆(At) /At

Method: Least Squares

Date: 04/13/19 Time: 23:39

Sample (adjusted): 2007 2017

Included observations: 11

Variable Coefficient Std. Error t-Statistic Prob.

C -0.0724 0.0170 -4.2691 0.0021

Y(t−2)/Y2010 0.0753 0.0165 4.5746 0.0013

R-squared 0.6992 Mean dependent var 0.0039

Adjusted R-squared 0.6659 S.D. dependent var 0.0175

S.E. of regression 0.0101 Akaike info criterion -6.1919

Sum squared resid 0.0009 Schwarz criterion -6.1195

Log likelihood 36.0553 Hannan-Quinn criter. -6.2375

F-statistic 20.9273 Durbin-Watson stat 1.6002

Prob(F-statistic) 0.0013

3.3 Labour productivity and GDP growth

3.3.1 Is the rate of growth of labour productivity the root of the GDP growth?

In Nguyen Duc Thanh & Ohno Kenichi (2018), at page 117, the authors claim that " the de-

crease of the labour productivity is the cause of the decrease of Vietnam GDP growth during

the period 2005-2013"

Let us check this assertion from the theoretical point of view. We follow the authors by assuming

that the production function of Vietnam economy is Cobb-Douglas of constant returns to scale.

We denote by Ythe GDP, by K, N respectively the capital and the number of workers. We have

Y=AKαN1−α, α ∈(0,1) (9)

Log-linearizing this relation, we easily get

α∆Y

Y=∆A

A+α∆K

K−(1 −α)∆Y

Y−∆N

N(10)

In other words

α×Rate of growth of GDP= rate of growth of TFP + α×rate of growth of the capital -

14

(1 −α)×rate of growth of labour productivity

Relation (9) can be rewritten as

1 = AK

YαN

Y1−α

or 1 = 1

AY

KαY

N1−α

(11)

In (10), we see that labour productivity growth negatively impacts GDP growth. To understand

this result which seems counter intuitive look at relation (11). This one shows that actually the

labour productivity and capital productivity are substitutes. If labour productivity decreases

then capital productivity must increase. If the capital Kand the TFP Aare kept constant,

then a diminution of labour productivity will imply an augmentation of the GDP. Both (11)

and (10 ) show that our theoretical results contradict the claim of the authors.

Moreover, both Vietnam GDP growth rate and Vietnam labour productivity growth rates are

positive during 2005-2013 (Table 5and 6).

(10) points out the importance the sum :

rate of growth of TFP + α×rate of growth of the capital

for the positiveness of GDP growth when labour productivity growth is negative (under the

assumption of Cobb-Douglas constant returns to scale production function).

Table 5: The growth rates of Vietnam Gross Domestic Product, 2005-2017

Year 2005 2006 2007 2008 2009 2010 2011

7.55% 6.98% 7.13% 5.66% 5.40% 6.42% 6.24%

Year 2012 2013 2014 2015 2016 2017

5.25% 5.42% 5.98% 6.68% 6.21% 6.81%

Source: Authors’ calculations with World Bank data

Table 6: The growth rates of Vietnam Labour Productivity, 2005-2017

Year 2005 2006 2007 2008 2009 2010 2011

4.59% 4.05% 4.22% 2.81% 2.57% 3.59% 3.49%

Year 2012 2013 2014 2015 2016 2017

3.06% 3.84% 4.99% 6.40% 5.29% 6.02%

Source: Authors’ calculations with World Bank data

15

3.3.2 Comparison of the labour productivity between two countries

Let us consider two countries, say 1,2with production functions

y1=Ak1αN11−α

y2=Ak2βN21−β

with α∈(0,1), β ∈(0,1). The capital stocks are respectively k1, k2while the number of

workers are N1, N2. The labour productivity of the two countries will be

y1

N1=Ak1

N1α

y2

N2=Ak2

N2β

Suppose the ratios k1

N1and k2

N2are equal and greater than 1. If α > β then the labour

productivity in country 1is higher than the one of country 2. We obtain the opposite conclusion

if α < β. We see that the comparison of the labour productivity of these two countries does not

make sense if we do not know their production functions. The exercise will be harder when one

country has a production function with decreasing returns while the other one has increasing

returns.

In this simple example we assume both countries have the same TFP A, and their production

functions are Cobb-Douglas with constant returns to scale. We worry when people claim that

the labour productivity in Vietnam is lower than the one in Laos without showing the produc-

tion functions of these two countries. Maybe, their TFP are not the same and we are not sure

that their technologies are Cobb-Douglas of constant returns to scale. Claiming that the labour

productivity of Vietnam is lower of the one in Laos is not very useful if we have no information

about the structure of the economy through the aggregate production functions.

Indeed, it is written in a report of the World Bank:

http://www.worldbank.org/en/country/lao/publication/lao-pdr-development-report-2014

"Lao PDR’s economy is growing fast but growth is mainly driven by the hydro and mining sec-

tors where very few jobs are created: only 22,000 people work in these sectors and this number

is unlikely to increase much, given how capital intensive those sectors are."

Clearly, Lao economy is capital intensive and it may explain why the Lao labour productivity

is higher than Vietnam labour productivity.

16

3.4 Production Functions of China and Laos Economies

In this section, first we will find the production functions of China and Laos. Second we try to

compare the labour productivites of China, Laos and Vietnam.

We apply the same methodology as in 3.1.2 to generate the capital stocks of China and Laos

from 2005 to 2017. We got the data of China, Laos, Vietnam about GDP, Investment from the

"World Development Indicators" dataset of World Bank. Employment data of Vietnam and

China come from the ADB (Asia Development Bank) dataset. For Laos employment, the data

from the datasets of World Bank and ADB were mismatched. So, in our study, the employment

of Laos is computed by using the data about total labor force and unemployment rate in the

World Bank dataset. We will now give the production functions of China and Laos.

Table 7: The regression for China’s Production Function

Dependent Variable: Ln(Y/N)

Method: Least Squares

Date: 04/15/19 Time: 23:09

Sample (adjusted): 2005 2017

Included observations: 13

Variable Coefficient Std. Error t-Statistic Prob.

C 0.8217 0.2681 3.0654 0.0107

Ln(K/N) 0.8129 0.0265 30.6557 0.0000

R-squared 0.9884 Mean dependent var 9.0335

Adjusted R-squared 0.9874 S.D. dependent var 0.3220

S.E. of regression 0.0362 Akaike info criterion -3.6603

Sum squared resid 0.0144 Schwarz criterion -3.5734

Log likelihood 25.7921 Hannan-Quinn criter. -3.6782

F-statistic 939.7743 Durbin-Watson stat 0.4076

Prob(F-statistic) 0

The production function of China is of constant returns to scale (Table 7). The elasticity

of the capital is 0.81, the one of labour is 0.19.

From Table 8, the production function of Laos is of increasing returns.

Y=e−13.5K0.74N1.24

The labour productivity in Laos depends not only on the ratio K/N but also on N.

To understand why this productivity is of increasing returns, we run the following regression

ln(Y/N) = a+bln(K/N) + cln(N)

17

Table 8: The regression for Lao’s Production Function (1)

Dependent Variable: LnY

Method: Least Squares

Date: 04/16/19 Time: 22:31

Sample (adjusted): 2005 2017

Included observations: 13

Variable Coefficient Std. Error t-Statistic Prob.

C -13.4913 1.338438 -10.0799 0

LnK 0.7421 0.092947 7.9845 0

LnN 1.2448 0.234771 5.3021 0.0003

R-squared 0.9993 Mean dependent var 22.7598

Adjusted R-squared 0.9992 S.D. dependent var 0.2928

S.E. of regression 0.0084 Akaike info criterion -6.5133

Sum squared resid 0.0007 Schwarz criterion -6.3829

Log likelihood 45.3365 Hannan-Quinn criter. -6.5401

F-statistic 7220.6860 Durbin-Watson stat 0.7156

Prob(F-statistic) 0

Table 9: The regression for Lao’s Production Function (2)

Dependent Variable: Ln(Y/N)

Method: Least Squares

Date: 04/16/19 Time: 23:30

Sample (adjusted): 2005 2017

Included observations: 13

Variable Coefficient Std. Error t-Statistic Prob.

C -13.4913 1.3384 -10.0799 0.0000

Ln(K/N) 0.7421 0.0929 7.9845 0.0000

Ln(N) 0.9869 0.1428 6.9131 0.0000

R-squared 0.9985 Mean dependent var 7.8042

Adjusted R-squared 0.9982 S.D. dependent var 0.1991

S.E. of regression 0.0084 Akaike info criterion -6.5133

Sum squared resid 0.0007 Schwarz criterion -6.3829

Log likelihood 45.3365 Hannan-Quinn criter. -6.5401

F-statistic 3338.7460 Durbin-Watson stat 0.71556

Prob(F-statistic) 0.0000

The results are in Table 9:

ln(Y/N) = −13.49 + 0.742 ln(K/N)+0.987 ln(N)

This relation can be written as

Y=e−13.49N0.987K0.742N0.258

18

or

Y=A(N)K0.742N0.258

with A(N) = e−13.49N0.987 .

The production function of Laos has a TFP which depends positively on N. An explanation of

this positive dependence on Nis given in Appendix 3.

We mentioned above in Subsubsections 3.3.2 that comparing the labour productivities of

these countries with very different economic structures does not really make sense.

4 Part 2: Issues on Vietnam Economic Growth at the micro level

4.1 Vietnam SOEs capital uses

To study the use of capital in the SOEs in Vietnam, we use a Census conducted in 2014 by the

General Statistics Office (GSO) of Vietnam (2014, 2015). In this census we have the data of

2,835 SOEs concerning the values of their outputs, their capital stocks and the labor costs.

The average value of the ratios [Value of the capital stock/Labor cost] is 29.6The Vietnam real

interest rate in 2014 is 4.84%

See the link

https://www.statista.com/statistics/794619/vietnam-real-interest-rates/

Take the capital depreciation rate equal to 0.05. The average value of the ratios

[Investment cost/labor cost]

is therefore

(0.048 + 0.05) ×29.6=2.95

However, there are 1,862 SOEs those revenue represents 84.9% of the total revenue of 2,835

SOEs, using 36.8% of the total capital, for which the ratio [Investment cost/labor cost]equals

1.8. Their capital coefficient is 0.6which is very correct. The remaining firms represent 15.1%

of the total revenue, but use 63.2% of the total capital. Their ratio [Investment cost/labor cost]

is vertiginous: it equals 6.9and their capital coefficient is impressive 9.7. This shows that the

Vietnamese SOEs are very capital intensive. Some of them are extremely capital intensive. In

developed countries, the ratio [Investment cost/labor cost]is 0.5. Maybe there is a waste of

physical capital?

5Let qK be the value of the capital, and wN the value of total wages. q, w are respectively the price of the

capital and labour wages. If ris the real interest rate and δis the capital depreciation rate, then the ratio

[Investment cost/labor cost] is (r+δ)qK

wN

19

We now consider the profit rates of these SOEs. The profit rate r(π)is defined by

r(π) = value of the revenue - investment cost - labour cost

value of the revenue

For the 1,862 SOEs which have a relative low ratio [Investment cost/labor cost]correspond to

those with a capital coefficient lower than 2(we consider the norm for the capital coefficient

is to be lower than 2). Then there rate of profit is positive and equals 35.6%. For the SOEs

with a capital coefficient greater than 4(their number is 545), their profit rate is negative and

equals −29%.

4.2 Capital diversion

We now check the diversion issue. Let λidenote the rate of waste, or of bribery of the physical

capital of firm i. We call it also "hidden overhead". Why? It is well known that when a

Vietnamese SOE asks for say 1billion of VND for its purchase of capital, it will receive (1 −λi)

billion. But it has to declare receiving 1billion. So, λibillion have been diverted. The effective

production function of firm iis actually

Yi=A[(1 −λi)Ki]αNβ

ieεi(12)

which includes a white noise disturbance (εi).

We found that the average distribution of λ(for inefficient firms) is higher than 60%.

If we consider the 1,862 SOEs (65.7% of the SOEs) with [Investment cost/labor cost]equal to

1.8, the value of λis very small, around 0.4%. For the other SOEs, some of them have λ= 60.%

It is astonishing to see that a minority of SOEs is so capital wasteful.

Taking the logarithm of equation (12) gives

ln Yi=α0+αKln Ki+αNln Ni+εi−[−αKln(1 −λi)]

| {z }

ui

,(13)

where α0≡ln A. The new residual term corresponds to εi−ui. Remark that ui≥0because

0≤λi≤1.

Following the literature on stochastic frontier production (e.g. Kumbhakar and Lovell,

2003), uicorresponds to the well-known stochastic technical inefficiency. Besides the normal

distribution assumption for εi, we need an additional assumption about the distribution of ui

in order to calculate the maximum likelihood estimator of the model. For instance, we assume

20

that uifollows a half-normal distribution N+(0, σ2

u). Hence, the technical inefficiency uican be

estimated by (see for example Jondrow et al., 1982):

ˆui=E(ui|εi−ui) = ˜µi+ ˜σφ(−˜µi/˜σ)

Φ(−˜µi/˜σ),(14)

where ˜µi=−(εi−ui)σ2

u/σ2

s,˜σ=σεσu/σs,σs= (σ2

ε+σ2

u)1/2. Note that φ(.)and Φ(.)

are respectively the density and the cumulative distribution function of the standard normal

distribution.

When an estimation of technical inefficiency (ui) and output elasticity of capital (αK) are

available, one can recover an estimate for the hidden overhead (λi):

ˆ

λi= 1 −exp −ˆui

ˆαK.(15)

In the following, we only discuss the Cobb-Douglas case. Remark 2 below presents difficulties

to use the translog production function instead of Cobb-Douglas function.

We want to apply this modelling to the whole sample of Vietnamese SOEs. However, they

are very heterogeneous and using all of them can produce imprecise estimates. Table 10 reports

main descriptive statistics for firm production Y, capital stock K, labor L. We also calculate

the ratio of capital in production K/Y . Data on these variables are in values (i.e. in monetary

terms): we employ capital costs, labor costs, and revenue for K,Land Yrespectively. As a

result, the ratio K/Y represents the share of capital value in revenue.

We observe a very large heterogeneity in the sample as the ratio K/Y can vary from 0.026 to

62471. To limit the impact of this heterogeneity, we perform the analysis into two two separate

subsamples, one with K/Y <= 20 and another with K/Y > 20. The first subsample includes

2686 firms for which the range of K/Y is between 0.026 and 19.921 while the second subsample

only contains 149 firms with K/Y covering the interval from 20.359 to 62471 (see Table 11. We

add another feature to control for data heterogeneity consisting of the heteroskedastic dispersion

of firm’s inefficiency ui, i.e. σ2

u,i = exp(w0

iγ).

Table 15 reports estimation results of model (13) using maximum likelihood and bootstrap

standard errors. It is shown that output elasticities of capital and labor are respectively 0.680

and 0.346, which correspond to a constant returns to scale (CRS) production function (the chi

squared statistic for the null hypothesis of CRS is 1.17 with the p-value = 0.28). It is also

shown that variance of technical inefficiency (σ2

u) is heteroscedastic as it significantly depends

on several variables like export activity, sectoral dummies and firm size. We remark the negative

21

Table 10: Data on SOEs in 2014.

Variable Obs Mean Std. Dev. Min Max

K2,892 1291.834 9903.845 .0231 399530.8

L2,895 43.198 176.957 .002 6656.3

Y2,840 908.086 5269.548 .001 154775.3

K/Y 2,835 41.116 1199.921 .026 62471

Notes. Source: GSO Enterprise Census 2014.

Table 11: Data on SOEs in 2014, subsample with K/Y ≤20.

Variable Obs Mean Std. Dev. Min Max

K2,686 1226.485 9922.021 .023 399530.8

L2,686 45.354 182.997 .085 6656.3

Y2,686 958.308 5414.208 .035 154775.3

K/Y 2,686 2.212 2.984 .026 19.921

Notes. Source: GSO Enterprise Census 2014.

Table 12: Data on SOEs in 2014, subsample with K/Y > 20.

Variable Obs Mean Std. Dev. Min Max

K149 2530.804 10740.81 6.094 110069.5

L148 14.966 56.040 .056 652.8

Y149 24.707 76.036 .001 729

K/Y 149 742.429 5200.734 20.359 62471

Notes. Source: GSO Enterprise Census 2014.

Table 13: Distribution of firms over different sectors, subsample with K/Y < 20.

Sectoral dummies Sector Frequency Percentage

1 Agriculture, Forestry & Fishing (Reference group) 315 11.73

2 Manufacturing, Mining & Quarrying 638 23.75

3 Electricity, Gas, Water Supply 279 10.39

4 Construction 326 12.14

5 Wholesale & Retail Trade 394 14.67

6 Transportation & Storage 222 8.27

7 Others 512 19.06

Total 2,686 100.00

Table 14: Firm size, subsample with K/Y < 20.

Size dummies Size Frequency Percentage

Small Small and very small firms (Reference group) 1,123 41.81

Medium Medium firms 403 15.00

Large Large firms 1,160 43.19

Total 2,686 100.00

22

Table 15: Estimation results of the Cobb-Douglas production frontier

Variable Coefficient Std.Err.

Capital 0.680*** 0.018

Labor 0.346*** 0.032

Intercept 2.502*** 0.149

ln σ2

ε-0.218*** 0.032

ln σ2

u

Economic zone 0.060 0.219

Export -0.693*** 0.193

Sectoral dummies

2 -1.991*** 0.135

3 -0.872*** 0.079

4 -1.254*** 0.107

5 -36.175*** 1.292

6 -1.502*** 0.156

7 -1.185*** 0.112

Firm size dummies

Medium -0.357** 0.149

Large -0.134 0.137

Intercept 1.158*** 0.080

Notes. Number of observations: 2686 firms. Reference group for sectoral dummies is ‘Agriculture,

Forestry and Fishing’. Reference group for firm size is ‘Super Small Firms’. Significance levels: ***1%,

**5%, *10%.

impacts of sectoral dummies on σ2

uindicating that firms operated in all economic sectors are

more efficient than the reference group (Agriculture, Forestry and Fishing sector). Moreover,

large-size firms are not significantly different from small firms in terms of (in)efficiency while

medium-size firms are more efficient (its coefficient is significantly negative).

Figure 4presents the distribution of λifor the subsample with K/Y ≤20. There is an

important group of SOEs (exactly 394 firms) which have a λiclose to zero, meaning that they

employed capital efficiently. These firms correspond to those operating in Wholesale & Retail

Trade sector. The remaining 2292 firms in other sectors have the average λof 0.623, which is

considerably high.

Remark (2) Instead of the Cobb-Douglas function, we can use the translog production func-

tion. In this case, we have the following regression equation

ln Yi=β0+βKln Ki+βNln Ni+βKK (ln Ki)2+βN N (ln Ni)2+βKN ln Kiln Ni+εi

−n−(βK+ 2βKK ln Ki+βK N ln Ni) ln(1 −λi)−βKK [ln(1 −λi)]2o

|{z }

ui

,(16)

This part is too complicated to estimate because of endogeneity of Kiand Ni(because E(Kiui)6=

23

Figure 4: Distribution of ˆ

λi, firms with Ki/Yi<20.

0and E(Niui)6= 0).

24

5 Concluding remarks

1. As we mentioned above, the contribution of TFP growth to GDP growth is important. How

could we increase this impact of TFP on growth? From Romer (1990) and Lucas (1988) it

should depend on the expenditures for knowledge, education, health. In this respect, we ob-

serve that the Vietnam public expenditures are very small (6.5% of GDP). We can compare

them with those in China, or developed countries such as Germany or France. For China, one

finds 14%. For Germany and France, more than 20%). See the links

https://www.ceicdata.com/en/country/vietnam

https://www.ceicdata.com/en/country/germany

https://www.ceicdata.com/en/country/france

https://www.ceicdata.com/en/country/china

2. The calculations of the capital stock are not satisfactory. We use the amount of invest-

ments given by GSO. This includes also investments in construction, in health and education

infrastructure. GSO should decompose this amount in its components in order to obtain the

productive investment. However, the result we get for Vietnam production function seems to

show that Vietnam economy depends strongly on investments, maybe, in particular, invest-

ments in infrastructure, construction. In any case this point should be clarified if GSO gives

more information on the several investments. For sure Vietnam economy depends on FDI, but

from the production function it depends on the TFP A too. For the sustainability purpose,

Vietnam should rely less on FDI and more on TFP.

3. To study the TFP, we would like GSO publishes the expenditures for health, education

too. It is very important to have these information in order to study their impact on the TFP.

Relation (7) shows the importance of the TFP for the GDP growth rate.

4. Obviously, investing in New Technology, Innovation, Digital Economy 4.0, Education and

Health, Open Data uses,. . . is very important. We do not insist anymore on these recommen-

dations since there exists an abundant literature on these topics.

One can only worry about the number of researchers in Vietnam and the investment in R&D:

4.1. In Vietnam, there are 675 researchers by million of inhabitants, while in China, there are

1,113, in Korea, 6,899.

4.2. In 2013, Vietnam invested in R&D 0.37% GDP, while China 2.07% in 2015, Korea 4.23%

25

in 2015. 6. Vietnam should attract scientists of Vietnamese origin who are actually dispersed

over the world. 7

5. We can address critics to the current literature (including the present paper) on labour

productivity that it seems to focus only on macro data. We should go to the micro level.

5.1. For instance, Vietnam should conduct surveys on the number of calories the workers obtain

with the meals in the canteens of firms and also at home. If the number of calories is low, it will

not be a surprise that labour productivity is also low. Moreover, the food safety in Vietnam still

remain poor and the living conditions of workers need to be improved much (Research Center

for Employment Relations,2016).

5.2. Vietnam should also conduct surveys on the needs of types of labour of the firms in different

sectors and to see whether the skills of workers correspond to the needs of firms. These informa-

tion are important to implement appropriate teaching programs in the Colleges, Universities.

5.3. Everybody finds the life in big cities in Vietnam very stressing with the volumes of motor

bikes. This is probably harmful for health and hence for labour productivity. It might be inter-

esting to correlate labour productivity in big cities with the number of motor bikes by square

meters in these cities.

5.4. High blood pressure, diabetes, cardiovascular diseases are frequently mentioned in the

newspapers. We think that these diseases strongly impact the quality of labour.

5.5. Pollution in the big cities is very probably harmful for the workers. What should Vietnam

authority do? A big concern!

5.6. Young and less young male populations drink too much beer! This custom, for sure, will

not be benefit for health. Should the Vietnamese Health authority "educate" these populations?

5.7 The missing point in the present paper is the consideration of the private sector, in partic-

ular the foreign firms.

6. Finally, from our production function we see that TFP has a very important role for

Vietnam economy. We suggest Vietnam to implement policies to push up the TFP. The road-

map we suggest is as follows:

6.1. Invest in health, education, training. The priority is for low- income population and low

skilled workers.

6.2. In parallel, investigate the needs of firms in labor and technology in order to renovate the

6Sources: World Development Indicators, World Bank

7Recently, an interesting forum in Paris, jointly organized by Association of Vietnamese Scientists and Experts

and the State Committee for Overseas Vietnamese gathered around 200 scientists, experts, entrepreneurs of

Vietnamese origin around the world

26

contents of teaching in the high schools, colleges and universities.

6.3. Invest in research on numerical economy, innovation, new technology, economics, organi-

zational management.

6.4. Improve the functioning in the administrations with open data uses. But the most difficult

point is to increase the income of the employees of these administrations including high schools,

colleges and universities too. With higher incomes, they will be more motivated and hence more

efficient. This point should be deepened by the Vietnamese authority and is beyond the scope

of our paper.

6.5. It would be important to know exactly the expenditures devoted for health, education,

training. If the percentage over GDP of these spending is low, the quality of health care and

education suffer of this weakness. A low number of public expenditures may be explained by

the fact that the collected taxes are very little. If the incomes become higher and transparent

we should collect, in principle, more tax.

7. We have to point out the weakness of this paper. It relies on the short length of the data:

2005 −2017,13 years. We are not able to check whether some of the time-series we use are

stationary or not. The test requires at least 20 years. In this case, we meet the difficulty that

from 1996 to 2004, it is hard to claim that the Vietnam economy during this period was really

a market economy as the one after 2005.

6 Appendix 1: A simple two-period model of investment in TFP

Consider the model with a social planner who wants to maximizes the intertemporal utility of

a representative agent. This utility is ln(c0) + βln(c1), β ∈(0,1). The constraints are

c0+k1= (1 −θ)Ak0

c1=Aζ(θAk0)k1

with k0>0.

The consumptions per head are c0for period 0,c1for period 1. In period 0, the agent buys

k1capital stock per head which will be used in period 1to produce consumption good. The

production functions are linear (as for Vietnam). Here θ∈[0,1] is the part of the output Ak0

of the first period t= 0 devoted for improving the TFP Ain the second period (t= 1). The

function ζis strictly increasing and satisfies ζ(0) = 1. Hence if θ > 0the TFP in period 1

becomes Aζ(θAk0)> A.

27

The optimal value for the capital stock per head k∗

1is

k∗

1=β

1 + β(1 −θ)Ak0

The rate of growth of output at period 1is

g=Aζ(θAk0)(1 −θ)Ak0β/(1 + β)

(1 −θ)Ak0

−1 = Aζ(θAk0)β

1 + β−1

Assume Aβ < (1 + β)and Aζ (Ak0)β > (1 + β). Then there exists θ∈(0,1) for which g > 0.

Suppose the government fix a target g∗. If g∗satisfies

(1 + g∗)≤ζ(Ak0)A×β

1 + β(17)

then the part devoted to investment in TFP is given by

g∗=Aζ(θ∗Ak0)β

1 + β−1

The value θ∗satisfies θ∗∈(0,1). The condition (17) on g∗means that the government should

not be too ambitious and fixes a too high target for the rate of GDP growth g∗.

7 Appendix 2: Regression results with PIM

Table 16: The regression for Vietnam’s Production Function with PIM, δ= 0.05

Dependent Variable: Ln(Y/N)

Method: Least Squares

Date: 07/31/19 Time: 23:49

Sample: 2005 2017

Included observations: 13

Variable Coefficient Std. Error t-Statistic Prob.

C -6.573999 0.633661 -10.37463 0.0000

Ln(K1/N) 1.595797 0.070251 22.71573 0.0000

R-squared 0.979127 Mean dependent var 7.819346

Adjusted R-squared 0.977230 S.D. dependent var 0.153227

S.E. of regression 0.023122 Akaike info criterion -4.555452

Sum squared resid 0.005881 Schwarz criterion -4.468536

Log likelihood 31.61044 Hannan-Quinn criter. -4.573317

F-statistic 516.0046 Durbin-Watson stat 0.411381

Prob(F-statistic) 0.000000

Note: K1is the series of capital stocks which are computed by the Perpetual Inventory

Method with δ= 0.05

In table 16, we see that the elasticity of labour is negative (−0.405). We reject this regression

28

result.

Table 17: The regression for Vietnam’s Production Function with PIM, δ= 0.07 (1)

Dependent Variable: Ln(Y/N)

Method: Least Squares

Date: 07/31/19 Time: 23:43

Sample: 2005 2017

Included observations: 13

Variable Coefficient Std. Error t-Statistic Prob.

C -1.872534 0.586587 -3.192253 0.0086

Ln(K2/N) 1.087842 0.065833 16.52433 0.0000

R-squared 0.961275 Mean dependent var 7.819346

Adjusted R-squared 0.957754 S.D. dependent var 0.153227

S.E. of regression 0.031494 Akaike info criterion -3.937404

Sum squared resid 0.010911 Schwarz criterion -3.850489

Log likelihood 27.59313 Hannan-Quinn criter. -3.955269

F-statistic 273.0534 Durbin-Watson stat 0.282489

Prob(F-statistic) 0.000000

Note: K2is the series of capital stocks which are computed by the Perpetual Inventory

Method with δ= 0.07

Table 18: The regression for Vietnam’s Production Function with PIM, δ= 0.07 (2)

Dependent Variable: Y/A2

Method: Least Squares

Date: 07/31/19 Time: 23:47

Sample: 2005 2017

Included observations: 13

Variable Coefficient Std. Error t-Statistic Prob.

N 7602.865 275.2466 27.62201 0.0000

R-squared 0.593926 Mean dependent var 3.72E+11

Adjusted R-squared 0.593926 S.D. dependent var 7.71E+10

S.E. of regression 4.91E+10 Akaike info criterion 52.14685

Sum squared resid 2.90E+22 Schwarz criterion 52.19031

Log likelihood -337.9545 Hannan-Quinn criter. 52.13792

Durbin-Watson stat 0.070569

Note: The series of TFP A2is generated by A2=Y

K2.K2is the series of capital stocks

which are computed by the Perpetual Inventory Method with δ= 0.07

8 Appendix 3

To explain the dependence of the TFP of Lao economy, on the number of workers , we suppose,

for simplicity, that Lao economy is composed by two firms which have as production functions

Y1=AF 1(K1, N 1), Y 2=AF 2(K2, N 2)

29

They have the same TFP Awhich depends posivitely on the total employment N=N1+

N2. The functions F1, F 2are increasing, concave with decreasing returns to scales. When N

increases (respectively decreases), communication, deliveries, . . . between the two firms become

faster (respect. slower) hence more (resp. less) efficient. The aggregate production function is

F(K, N ) = max

N1+N2=N,K1+K2=KA(N1+N2)F1(K1, N 1) + F2(K1, N2)

=A(N) max

K1+K2=KF1(K1, N 1) + F2(K1, N2)

=A(N)G(K, N )

One can check that the function Gis increasing, concave with decreasing returns to scales.

Assume A(N)>1when N > ˜

N, A(˜

N) = 1. Let ˜

Y=G(K, ˜

Y). When the functions F1, F 2

have no TFP, say A(x)=1,∀xthen given K, Y the quantity of labor Nnecessary to produce

is dertermined by the equation

G(K, N ) = Y

We will prove if Y > ˜

Ythen when F1, F 2have a TFP which depends positively on N, the

number of workers N0which satisfy

A(N0)G(K, N 0) = Y

will verify N0< N. The labour productivity is better with TFP than without TFP.

First we prove that N0>˜

N. If not we will have

Y=A(N0)G(K, N 0)≤A(˜

N)G(K, ˜

N) = G(k, ˜

N)< G(k, N ) = Y

and that is a contradiction. Second we prove that N0< N. Indeed, we have

G(K, N 0) = A(˜

N)G(K, N 0)< A(N0)G(K, N0) = Y=G(K, N )

This implies N0< N.

We now prove that when Y < ˜

Ythen N0> N. Since G(K, N ) = Ywe have N < ˜

N. Assume

the contrary. Then N0≤N < ˜

N. We have a contradiction

Y=A(N0)G(K, N 0)< A(˜

N)G(k, N 0) = G(K, N0)≤G(K, N ) = Y

30

The labour productivity is lower with TFP than without TFP.

To summarize, when Y > ˜

Y, the labour productivity of Laos is high in the sense it is higher

than the one obtained with a production technology without TFP. And when Y < ˜

Y, the labour

productivity of Laos will be low, in the sense it is lower than the one we get with a technology

without TFP.

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