Proceedings of 13th Asian Business Research Conference
26 - 27 December, 2015, BIAM Foundation, Dhaka, Bangladesh,
ISBN: 978-1-922069-93-1
Level Accounting And Convergence For Six SAARC
Countries: What Does The Data Show?
Monika Islam Khan*
This papers aims to extrapolate the degree of contribution of total
factor productivity and inputs used for production in total output per
worker during 1980-2011 for six South Asian countries: India,
Pakistan, Bangladesh, Maldives, Nepal and Sri Lanka. The agenda
is to attribute variations in output per worker to characteristics
explaining those differences. The proceedings begin with a CobbDouglas aggregate production function as used by the augmented
Solow model. When output is defined in terms of output per worker,
it is decomposed into capital intensity, labor-augmenting total factor
productivity and human capital. The decomposed equation is then
rearranged to calculate total factor productivity as the Solow
Residual. The measured productivity and data on the decomposed
elements are tabulated to observe the extent of their contribution to
output per worker. This paper also aims to reveal whether there is
any tendency of convergence in output and total factor productivity
within these countries. Sigma and beta convergence models have
been used to ascertain convergence in output and the Solow
Residual. On an accounting basis, the analysis shows that physical
capital and human capital in terms of educational attainment only
partially accounts for the variation in output per worker amongst the
six countries; a large portion of the difference can be expounded by
variation in labor-augmenting total factor productivity in terms of the
Solow Residual. Sigma and beta tests reveal no convergence in both
output per worker and total factor productivity within the six SAARC
nations.
Field of Research: Economics, Economic Development
JEL classification: E22, E23, O15 and O47
Keywords: capital output ratio, Cobb Douglas, convergence, technological change,
productivity
1. Introduction
In the year 2010, the PPP-adjusted output per worker of Maldives was approximately
9.6 times that of Bangladesh. So, in other words, in 2010 the average Maldivian worker
had produced as much as the average Bangladeshi worker would have produced in
almost ten years. Explaining such monumental differences in output per worker are
important contributions to the region’s growth literature. What is facilitating the high
output per worker in Maldives? This seemingly simple question has important
implications for the individual economies as a whole. Could the level of output per
worker for Bangladesh have been faster?
___________________________________________________________________
*Miss Monika Islam Khan, Masters’ student, Department of Economics, School of Business and
Economics, North South University, Mail: 72/C-7, Naval Headquarters, Dhaka, BD, Email:
monikaislamkhan@gmail.com, Tel: +88028871446, Cell: +8801715050295, Economics
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Proceedings of 13th Asian Business Research Conference
26 - 27 December, 2015, BIAM Foundation, Dhaka, Bangladesh,
ISBN: 978-1-922069-93-1
Research and literature on growth and level accountings is ubiquitous. Considerable
studies have been conducted on South Asian countries particularly those belonging to
the South Asian Association for Regional Cooperation (SAARC). There is no doubt
that all the SAARC countries have been growing economically over the past few
decades with high growth rates of real GDP. However, this paper does not focus on
whether their real GDP is growing; it discusses each country’s level of output per
worker. How productive are the six countries in utilizing their available resources to
produce their prevailing output per worker? This study is to ascertain the factors
contributing to output per worker within the SAARC region apart from the more
traditional capital and labor.
Economic growth literature suggest that such differences in output per worker in a
country over time can be attributed to over-time differences in number of employed
persons, physical capital, human capital and total factor productivity 1. A standard
Cobb-Douglas production function reveals capital and labor as primary variables
determining the level of output that an economy can produce, but development in
growth literature brought forth the distinction between physical and human capitals.
Hypothetically speaking, the total factor productivity in a developing country should be
increasing due to globalization, knowledge transfer and spillovers, but has it truly been
the case for these six nations would be interesting to see. However, the most
fascinating thing to observe would be the variation in total factor productivity between
these countries and the extent to which variations determine differences in output per
worker.
The concept of convergence is often described as forces accelerating the growth of
nations with a tendency of converging towards the same level of output per worker.
Globalization, technology and knowledge transfer are considered forces driving this
process between the poorer and richer countries by enlarging the size of their markets.
Economic theory suggests that poor countries over time “catch up” to richer countries
in terms per worker output. The SAARC was established to increase regional
cooperation between the countries so as reap the benefits of economies of scale
enjoyed by countries within regional blocs such as the European Union and ASEAN;
there was much discussion on whether the countries within the SAARC are indeed
experiencing convergence. Hence, an investigation into the current convergence
scenario and its importance seems imperative.
Section 2 discuss the degree to which literature supports our methodology of using
level accounting rather than growth accounting, and the extent to which past studies
have concluded on the convergence hypothesis regarding the SAARC nations. Our
methodology of decomposing output per worker into capital intensity, human capital
1
Total factor productivity can be simply defined as the portion of surplus output that cannot be
explained by the amount of inputs used in production. It is generally explained by level of
technological progress or knowledge transfer and spillovers in an economy.
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Proceedings of 13th Asian Business Research Conference
26 - 27 December, 2015, BIAM Foundation, Dhaka, Bangladesh,
ISBN: 978-1-922069-93-1
and total factor productivity, and techniques used in predicting convergence,
divergence or neither have been discussed in Sections 3.1 and 3.2 respectively.
Section 4 and its sub-sections present the empirical results based on the methodology
and modeling espoused for this paper. Section 5 prepares to terminate the paper by
offering some personal thoughts on the analysis of convergence and decomposition
of output per worker that may aid researchers who would further dwell on this issue in
the future. Finally, the paper finishes with remarks on the study itself, results obtained
and conclusions drawn.
2. Literature Review
This research has been greatly inspired by earlier contributions to this line of study;
the two professors in their paper (Hall & Jones, 1999), aimed to check for degree of
contribution of the traditional factors of production to output per worker for 127
countries. The empirical growth literature associated with the likes of (Hall & Jones,
1999) and (Barro, 1991) shares common features in terms of explaining the reasons
for differences in total factor productivity. However, empirically, the two researches
differ significantly. While (Barro, 1991) focuses on growth rates, the empirical
framework of (Hall & Jones, 1999) differs fundamentally in its focus on levels rather
than rates of growth. They elaborate on why a focus on levels is necessary to realize
the true nature of variations in output per worker and differences in long-run economic
performance that are most likely relevant to welfare.
Several other contributions point toward a focus on levels as well instead of growth
rates. Research provides evidence on the relatively low correlation of rates of growth
across several decades, suggesting that differences in growth rates are rather
transient (Easterly, et al., 1993). Hence, it was argued the empirical relevance of
endogenous growth and in the paper presented a model in which differences in
technological change and economic performance is associated with differences in
levels, not rates of growth (Jones, 1995). A number of other papers with models of
knowledge flows across countries like (Parente & Prescott, 1994), (Eaton & Kortum,
1995) and(Barro & Sala-i-Martin, 1992) also advocate for level accounting instead of
growth accounting. They imply that technological transfer between countries
precludes them from drifting apart from each indefinitely and in the long run all
countries are likely to grow at a common rate. The role of technological progress has
been emphasized to explain international output per worker output differences
(Parente & Prescott, 2004), (Easterly, 2001) and (Hall & Jones, 1999).
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Proceedings of 13th Asian Business Research Conference
26 - 27 December, 2015, BIAM Foundation, Dhaka, Bangladesh,
ISBN: 978-1-922069-93-1
Empirical analysis suggests that smaller samples of countries somewhat show a
stronger tendency for convergence specially those at similar income levels. Papers
focused on convergence like (Ben-David, 1998) and (Chatterji, 1992) find strong
empirical evidence within the richer countries and within the poorer countries, although
they failed to do so for the middle income countries. Some studies like (Quah, 1997)
and (Galor, 1996) provide theoretical justifications for the convergence club
hypothesis, according to which convergence will occur amongst smaller group of
countries or subsets rather than broader samples of countries.
Growth literature suggests two basic techniques of predicting convergence: sigmaconvergence and beta-convergence. Some studies found no convergence in per
capita income across the seven SAARC countries during 1960-2000 following
absolute and conditional beta convergence tests(Chowdhury, 2003). While (Solarin,
et al., 2014) following a series of unit root and conditional beta convergence tests
found no empirical evidence of convergence in real income across the SAARC
countries covering the period (1970-2009). Finally, econometric analysis by
(Jayanthakumaran & Lee, 2008) showed that pertaining to the oil crisis in the 1980s
and the engagement of more bilateral Regional Trade Agreements (RTAs) outside of
the SAARC, income divergence increased amongst the member countries. They
concluded that India entered several bilateral RTAs that coincided with the income
divergence, which is contradictory to the original objective of SAARC.
3. Methodology and modeling
3.1 Level Accounting and Output per Worker
Economic success can be defined by higher output i.e. GDP, per capita income or
output per worker. Output per worker is evidently better able to capture the economic
performance of an economy as opposed to the other two; while output does not take
into account the labor required to produce it, per capita income either overestimates
or underestimates economic performance disregarding the fact that not every person
in the population is productive. Hence, economic advancement can be explained by
decomposing output per worker into inputs and total factor productivity which,
subsequently, aids in describing the causes of higher output per worker in each of the
six SAARC nations.
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Proceedings of 13th Asian Business Research Conference
26 - 27 December, 2015, BIAM Foundation, Dhaka, Bangladesh,
ISBN: 978-1-922069-93-1
There are three important approaches to the decomposition of output per worker into
inputs and productivity in literature. The first was developed by (Christensen, et al.,
1981) and involves the comparison of each country to a reference point by the
arithmetic average of the particular country’s factor share and the reference factor
share and repeating the process for each country. Second is a method directly based
on (Solow, 1957) that gives results similar to that of the first and second approaches
with standard elasticities elaborated below.
Assuming output Yit for country i at time t, this simple Cobb-Douglas function can be
used to define the production framework:
(1)
Yit = Kitα [Ait Hit]1-α
where Kit denotes the physical stock of capital, Ait the labor-augmenting measure of
total factor productivity and Hit amount of human capital augmented labor required to
produce Yit. α is the output elasticity of capital and thus, the model assumes constant
returns to scale by imposing the output elasticity of labor as one minus the output
elasticity of capital (1-α). The model assumes that labor is homogenous across each
country and each unit of labor has been trained with equal years of schooling
(educational attainment). Hence, the human capital-augmented labor is given by
(2)
Hit = hit Eit
where hit is the human capital index per person and E it is the number of employed
persons engaged in production.
It would make more sense to rewrite the production function as output per worker as
previously explained in this section. Dividing both sides of the output equation by labor
Eit yields the output per worker
(3)
K
yit = Ait  it
 Yit

 1
 hit, where yit = Yit/Eit and hit = Hit/Eit

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Proceedings of 13th Asian Business Research Conference
26 - 27 December, 2015, BIAM Foundation, Dhaka, Bangladesh,
ISBN: 978-1-922069-93-1
This equation allows us to decompose differences in output per worker into specific
differences in total factor productivity, capital intensity, and human capital per person.
This is a similar approach used by (David, 1977), (Mankiw, et al., 1992), (Klenow &
Rodriguez-Clare, 1997) and (Hall & Jones, 1999) in which the decomposition results
in a capital-output ratio rather than the capital-labor ratio for two reasons. First, the
capital-output ratio is proportional to the investment rate; hence, this decomposition
has a natural explanation. Second, (Hall & Jones, 1999) consider an economy that
experiences an exogenous increase in productivity, holding investment rate constant.
Over time the country’s capital-labor ratio will rise due to the increase in total factor
productivity. Thus, in a capital-labor framework, some of the increase in output that is
fundamentally due to productivity would be imputed to capital accumulation.
Now taking log on both sides of the output per worker equation (3) and rearranging
yields the log of total factor productivity,
(4)
ln yit = ln Ait +
K 

ln  it  + ln hit
1    Yit 
ln Ait = ln yit -
K 

ln  it  - ln hit
1
 Yit 
Taking exponent on both sides gives us the level of total factor productivity in terms of
the Solow Residual.
3.2 Convergence Hypothesis
The concept of convergence can be defined in several ways. According to (Sala-iMartin, 2006) "there is β-convergence if poor economies tend to grow faster than rich
ones, and a group of economies are converging in the sense of σ if dispersion of their
real per capita GDP levels tends to decrease over time”. According to the Solow’s
convergence hypothesis, poor countries tend to experience faster growth which
facilitates the per capita income to converge. The Solow model also implies that
returns to capital is lower in countries with higher capital per worker, hence, capital
flows from rich to poorer countries will gradually lead to convergence. Differences in
output per worker also arise if there are lags in diffusion of knowledge. Once the poorer
countries gain access to the cutting edge technology, the differences in total factor
productivity and hence output per worker will tend to disappear over time.
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Proceedings of 13th Asian Business Research Conference
26 - 27 December, 2015, BIAM Foundation, Dhaka, Bangladesh,
ISBN: 978-1-922069-93-1
Sigma-convergence tests the dispersion of data over time and economies tend to
converge when dispersion decreases over time. Absolute sigma convergence can be
tested by estimating the following model:
(5)
σt = α + βt + νt
Where σt is the standard deviation of our variable concerned in time period t. α and
coefficient β are parameters and νt is the stochastic error term. For convergence to
take place, our value of β must be negative and statistically significant. A more generic
model for sigma-convergence has been shown in equation (5) which will be used to
estimate regress dispersion over time for output per worker and total factor
productivity.
Beta-convergence tests the “catching up” process within countries and can be
estimated using the following model:
(6)
(xit – xi,t-1) = λ + γxi,t-1 + εt
Where at time t xit is the log value of the concerned variable for country i and xi,t-1 is
the log value of the variable at time t-1. λ and coefficient γ are parameters, and εt is
the stochastic error term. For convergence to take place, our γ must be negative and
statistically significant.
All the data used in this paper has been extracted from Penn World Tables (PWT) 8.1
(Feenstra, et al., 2015). For output, capital stock, total number of employed persons
and human capital, data on output-side real GDP at current PPPs (in mil. 2005US$),
capital stock at current PPPs (in mil. 2005US$), number of persons engaged (in
millions) and index of human capital per person, based on years of schooling
(Barro/Lee, 2012) and returns to education (Psacharopoulos, 1994) have been used
respectively. Since labor shares in output is not available for all the six countries, we
assume output elasticity of labor (1-α) to be 0.70 and equal across all countries.
4.1 Empirical Results: Level Accounting
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Proceedings of 13th Asian Business Research Conference
26 - 27 December, 2015, BIAM Foundation, Dhaka, Bangladesh,
ISBN: 978-1-922069-93-1
A depiction of how the output per worker differs and behaves over time somewhat
hints the overall trend of economic performance. Figure (1) shows that output per
worker for Bangladesh, Pakistan and Nepal have been increasing very mildly over the
years while Maldives, Sri Lanka and India have experienced rapid increase in per
worker output.
7
8
9
10
11
Figure 1: Output per worker (1980-2011)
1980
1990
2000
2010
Year
country = Bangladesh
country = Maldives
country = Pakistan
country = India
country = Nepal
country = Sri Lanka
All values of output per worker are in logs.
Data on output, number of persons engaged, physical and human capitals is
incorporated into equation (4) to calculate total factor productivity in logs.
Table 1 depicts the decomposition of output per worker into the three multiplicative
terms shown in equation (3): the contributions of capital intensity, human capital per
person and total factor productivity. To make comparisons easier, values are
expressed in ratios of Indian values. For example, according to this table the output
per worker of Nepal is approximately 38% that of India. Using this simple analogy,
Table 1 allows us to ascertain the reasons contributing to the high or low levels of
output per worker (our primary measure of productivity and economic performance for
this paper) in each country.
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Proceedings of 13th Asian Business Research Conference
26 - 27 December, 2015, BIAM Foundation, Dhaka, Bangladesh,
ISBN: 978-1-922069-93-1
Table 1: Productivity Calculations (2010) - Ratios to Indian Values
Country
India
Pakistan
Bangladesh
Maldives
Nepal
Sri Lanka
Standard
Deviation
Y
L
1
1.010204
0.551125
5.264308
0.380068
1.861339
1.830592

 K  1
 Y 
1
1.055394
1.163908
1.043064
1.213704
1.045592
0.082682
h
1
1.033355
1.073708
1.086392
0.88738
1.63842
0.263837
A
1
0.989109
0.508414
5.48298
0.27788
2.916677
2.003519
4.1.1 India and Pakistan
One would predict India to have a much higher output per worker between the two.
However, data suggests otherwise. Table (1) reveals that, in terms of economic
performance, the discrepancy is minimal. Output per worker and capital intensity are
1% and 5.5% higher in Pakistan than in India respectively. Despite a higher capital
intensity and human capital (3.3% higher), output per worker is only slightly higher in
Pakistan owing to the low level of labor-augmenting technical progress or knowledge
pointing towards the importance of total factor productivity in production.
4.1.2 India and Bangladesh
Engulfed in poverty and famine till the end of the last century, Bangladesh has only
recently been able to achieve food security and relief from hardcore poverty. With a
satisfactory GDP growth of approximately 6% per annum, the country has made
serious efforts in achieving its millennium goals. However, productivity is a different
affair altogether. With only 55% of the output per worker compared to India,
Bangladesh still remains one of the less productive nations within the SAARC, despite
its significantly higher levels of capital intensity and human capital at 116% and 107%
respectively to that of India. The data depicts that this anomaly is primarily due to lower
levels of technical progress or knowledge spillover that Bangladesh faces exhibited in
the total factor productivity ratio, A, in Table (1) which is only almost 51% that of India.
This suggests a general inability to use the available resources in the most productive
manner.
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Proceedings of 13th Asian Business Research Conference
26 - 27 December, 2015, BIAM Foundation, Dhaka, Bangladesh,
ISBN: 978-1-922069-93-1
4.1.3 India and Maldives
Maldives, one of the world’s most geographically dispersed countries is economically
driven by tourism and fishing with minuscule reliance on manufacturing and agriculture
as compared to India. Despite the lack of dependency on the traditional drivers of an
economy, Maldives has been able to grow at a rate of 7.5% per annum primarily due
to tourism. As per Table 1, the Maldivian output per worker is more than five times or
a tremendous 508% that of India despite having a little higher capital intensity and
human capital (approximately 4.3% and 8.6% respectively more than India). The total
factor productivity measure again becomes important in explaining the monumental
discrepancy between the output per worker measures of the Maldives and the five
other nations which is approximately 5.5 times that of India.
4.1.4 India and Nepal
An economy inflicted by political uncertainty and poverty, Nepal has still been able to
maintain a satisfactory growth rate. However, in terms of productivity they seem to be
well lagging behind. With the highest capital intensity amongst the six countries and
approximately 21% higher than that of India, Nepal has an output per worker only 38%
of India as per Table 1. The low level of output per worker is attributable to human
capital (88% that of India) and total factor productivity (only 27.8% of India) which is
the lowest amongst all six countries. The importance of the contribution of total factor
productivity is nowhere more prominent than for Nepal. The ratios shown in Table 1
clearly point out that the low levels of total factor productivity have acted as an
impediment to increase in output per worker.
4.1.5 India and Sri Lanka
Recovering from a civil war that continued to the early 2000s, Sri Lanka has been
touted for attaining a commendable literacy rate of 98% of its population. As per Table
1, with a high level of human capital (approximately 63% higher than that of India), Sri
Lanka seems to be the star performer amongst the lot. It has achieved an output per
worker almost twice that of India even with capital intensity only analogous to and at
times lower than that of the other five countries which is attributable to a high level of
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Proceedings of 13th Asian Business Research Conference
26 - 27 December, 2015, BIAM Foundation, Dhaka, Bangladesh,
ISBN: 978-1-922069-93-1
knowledge spillover in terms of total factor productivity (almost 2.92 times that of
India). Hence, for Sri Lanka, high human capital and total factor productivity appear to
be significantly acting as drivers towards the high levels of output per worker.
After careful analysis of Table 1, it can be extrapolated from the data that capital
intensity in an economy and human capital per person may only partially be able to
explain the differences in output per worker and total factor productivity to a large
extent is able to discern the discrepancy in output per worker between the six SAARC
nations.
4.2 Empirical results: Convergence
Using the traditional models of estimating convergence shown in equations (5) and
(6), we construct Tables 2 and 3.
A careful look at Table 2 reveals that it shows no evidence of convergence. None of
the coefficients have a negative value that depicts convergence; the statistically
significant p-values (less than 0.05) for most statistics points towards income and total
factor productivity divergence. The only statistically insignificant p-value of 0.982
signifies neither convergence nor divergence.
Table 2: Sigma-convergence
time period
1980-1996
1996-2011
1980-2011
Output per Worker
coefficient
p-value
.0056587
0.028
.0143012
0.000
.0069231
0.000
Total Factor Productivity
coefficient
p-value
.0000561
0.982
.012584
0.000
.0055804
0.000
Looking at Table 3, the weight of evidence is towards divergence or no convergence.
Only one of the coefficients has a negative value but it is statistically insignificant. Rest
of the values signifies neither convergence nor divergence.
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Proceedings of 13th Asian Business Research Conference
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ISBN: 978-1-922069-93-1
Table 3: Beta-convergence
Output per Worker
Total Factor Productivity
time period
coefficient
p-value
coefficient
p-value
1980-1996
.0013363
0.894
-.0077262
0.473
1996-2011
.0119841
0.181
.0080481
0.405
1980-2011
.0068921
0.296
.0000227
0.998
Divesting from the traditional models of testing convergence, we could look at level
accounting to determine convergence between the six countries. Extending the last
row of Table 1 for a decade-wise table would serve to compare the level of dispersion
between the nations every ten years shown in Table 4.
Table 4: Decade-wise Standard Deviation
Year
Y
L

1990
2.405597
 K  1
 Y 
0.132637
2000
1.807592
1.830592
0.105512
0.082682
2010
h
A
0.312469
3.582323
0.319227
0.263837
2.136096
2.003519
According to Table 4, the standard deviations for capital intensity and human capital
declined rather slowly; however, there was a steeper fall in standard deviation of total
factor productivity over the decades coupled with a fall in dispersion of output per
worker within the countries. This is indeed a necessary condition for convergence to
occur, however, not the essential condition. Table 4 is not enough to comment
anything definitively on the degree of convergence. Therefore, the no-convergence
situation still exists within the six SAARC countries.
6. Recommendation and Conclusion
Countries produce high levels of per worker output in the long run because they invest
magnanimously on physical and human capital coupled with high levels of total factor
productivity. Empirical analysis reveals that capital intensity and human capital may
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Proceedings of 13th Asian Business Research Conference
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ISBN: 978-1-922069-93-1
only be partially attributable to high levels of output per worker between India,
Pakistan, Bangladesh, Maldives, Nepal and Sri Lanka; a large portion of the
differences in per worker output in these economies may be due to differences in
productivity in terms of knowledge or technology.
The basic definition of convergence constitutes a flow of capital, technology or
knowledge from the richer countries to the poorer ones, thereby, causing a
convergence of per capita output or per worker output. So if convergence is basically
a transfer between the rich and the poor, then there will be very little to transfer if the
countries have similar levels of capital, technology or knowledge. The countries in the
SAARC are basically very similar to each other in terms of the four factors in the
previous statement; so convergence between these nations seems highly unlikely as
per the current situation. Furthermore, a couple of these countries may be engaging
in RTAs with countries outside the SAARC leading to non-existent convergence in per
worker output within the countries as depicted by the sigma and beta convergence
tests.
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Proceedings of 13th Asian Business Research Conference
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Proceedings of 13th Asian Business Research Conference
26 - 27 December, 2015, BIAM Foundation, Dhaka, Bangladesh,
ISBN: 978-1-922069-93-1
15