WORKING PAPER 17/2007
Growth Accounting for Visegrad
States: Dual Approach
Miroslav Hloušek
August 2007
Working Papers of the Research Centre for Competitiveness of Czech
Economy are issued with support of MŠMT project Rresearch centres
1M0524.
ISSN 1801-4496
Head: prof. Ing. Antonín Slaný, CSc., Lipová 41a, 602 00 Brno,
e-mail: slany@econ.muni.cz, tel.: +420 549491111
GROWTH ACCOUNTING FOR VISEGRAD
STATES: DUAL APPROACH
Abstract:
The main goal of this paper is to calculate TFP growth for Visegrad
states by the use of dual approach to growth accounting and
comparison of results. The dual approach is based on factor prices
rather than quantities and hence the result should be more reliable.
Another advantage is that data about prices are better available. Even
if Visegrad states seem to be very similar, results from growth
accounting show that economic growth has different sources. TFP and
technologies are the main cause of growth in the Czech Republic+ on
the other hand, the factor of accumulation plays a very important role
in Poland and Slovakia. Hungary is a country where the sources of
growth are divided evenly.
Abstrakt:
Cílem příspěvku je spočítat růst SPF (souhrnné produktivity faktorů)
pomocí duálního přístupu k růstovému účetnictví pro státy Visegrádu a
porovnat výsledky. Duální přístup není založen na množství, ale na
cenách výrobních faktorů a tudíž by výsledky měly být spolehlivější.
Další výhodou je, že data ohledně cen jsou lépe dostupná. I když se
státy Visegrádu zdají být velmi podobné, výsledky růstového účetnictví
ukazují, že ekonomický růst pramení z různých zdrojů. SPF
a technologie jsou hlavní příčinou růstu v České republice, naopak
v Polsku a Slovensku hraje důležitou roli akumulace výrobních faktorů.
Maďarsko pak je zemí, ve které jsou zdroje růstu rozděleny
rovnoměrně.
Recenzoval:
Ing. Petr Harasimovič, M.A.
1. INTRODUCTION
Growth accounting is a decomposition of the growth rate of output into
contributions of individual factors of production. The main point is to
find out if it is the factor of accumulation or "something else" that plays
the crucial role. This "something else" is usually called Total Factor
Productivity (TFP) or Solow residual and measures technology
progress.
The first exercise of growth accounting was presented by Solow (1957)
and was based on subtracting of weighted growth rates of capital and
labor from the growth rate of output. The remaining (residual) part was
ascribed to growth of technology. This is primal approach to growth
accounting.
The main problem of primal approach is that it relies on measuring
inputs such as capital or labor which can be sometimes unreliable. On
the other hand, dual approach is based on factor prices rather than
quantities, which are usually easier to measure. Another advantage of
price-based estimates is that the prices are formed at the markets and
agents have an incentive to get the right price. A firm that pays to
factor more than its marginal product is wasting money. The other
advantage is that data about prices are measured more frequently and
are available more easily, especially for cross-country comparison.
This paper takes advantage of the dual approach and calculates TFP
growth and its contribution to output growth for Visegrad states. The
main goal is to determine sources of economic growth in these
countries. The paper is organized as follows: the theoretical derivation
of TFP growth rate from factor prices is presented in Section 2. Section
3 briefly describes data and their transformation. Section 4 interprets
and discusses results and finally, Section 5 makes summary and
concludes with prospects for further research. The Appendix provides
more details about the data used for analysis.
4
2. DUAL APPROACH TO GROWTH
ACCOUNTING
The first exposition of equivalence of primal and dual approach was
presented by Jorgenson and Griliches (1967). Here, however, we
follow a more transparent explanation provided by Hsieh (2002).
He starts with national income accounting identity that output is equal
to factor incomes
wLrKY += (1)
where Y is output, K is capital, is labor andL r and w is the rental
price of capital and the real wage, respectively.
Differentiation of (1) with the respect to time and dividing by Y gives






++





+=
L
L
w
w
s
K
K
r
r
s
Y
Y
LK
&&&&&
(2)
where YrKsK = and YwLsL = are the factor-income shares.1
Rewriting the same in a more convenient way where variables with
"hat" denote growth rates gives
)^^()^^(^ LwsKrsY LK +-+= (3)
Placing terms of the growth rates of production factors on left-hand
side of the equation, we obtain
wsrsLsKsY LKLK ^^^^^ +=-- (4)
The left-hand side of equation (4) is the primal estimate of Solow
residual or Total Factor Productivity growth. Share-weighted growth
rates in factor quantities are subtracted from the growth rate of output
LsKsYTFP LKPRIMAL
^^^ --= (5)
The right-hand side of equation (4) is a dual measure of TFP that is
obtained as share-weighted growth in factor prices
wsrsTFP LKDUAL ^^ += (6)
The primal and dual measures of TFP growth rate should be the same
with the only condition that output equals factor incomes.2
No other
assumptions about the form of the production function, bias of
technological change or relationship between factor prices and their
1
In this setting, the sum of factor-shares is equal to unit, .1=+ LK ss
2
Equation (1).
5
social marginal products need to be made.3
The two measures will
differ only if national accounts are inconsistent with the data on factor
prices. Hloušek (2007) showed that primal and dual approaches give
approximately the same results for the case of the Czech Republic.
That means that national accounts provided by statistical office are
consistent with factor prices.
The initial goal of this paper was a comparison of primal and dual
approach for Visegrad countries but it is quite difficult to obtain
consistent data of quantities of factor inputs, especially the data of
capital for all countries. Therefore we use only the dual approach
which uses factor prices and applies them in the calculation of TFP
growth in Visegrad states (namely Czech Republic, Hungary, Poland
and Slovakia).
3
If factor prices deviate from social marginal products, the estimated value of
TFP would deviate from the "true" value. However, the error from dual
approach will be the same as that resulting in the primal approach.
6
3. DATA
The growth accounting exercise can be extended to allow for different
types of capital and labor. However, this paper deals only with
aggregate measures of factor prices.
To assure complete consistency of data, one would like to have time
series from one source. However, not all data were possible to find in
the only database, thus the hypothesis of consistency is slightly
violated. The data are obtained from three sources: EUROSTAT,
OECD and IMF databases. Frequency of the data is quarterly, sample
period is from 1996Q1 to 2006Q4.4
Specifically, the real interest rate that measures the rental price of
capital is represented by three-month nominal interbank rate deflated
by CPI inflation (ex post approach).5
The real wage is calculated as a
ratio of nominal wage rate and consumer price index. The aggregate
output is represented by gross domestic product.
To calculate the TFP growth, we also need factor-income shares. The
labor-income share, which corresponds to YwLsL = , is calculated
as a ratio of total labor cost to gross value added (all in current prices).
Subsequently, the capital-income share is computed as a
complement to unit: . These shares are allowed to change
over time but the time subscript is omitted for the sake of transparency.
The average shares of labor to income, , for all countries are shown
in Table 1.
Ls
LK ss -=1
Ls
Table 1: Labor shares for period 1996Q1­2006Q4
Country Labor share in %
Czech Republic 57.8
Hungary 56.7
Poland 61.1
Slovakia 51.5
Note: Low quality of estimate for Hungary, see Appendix for details.
Source: Data OECD, own calculations
It must be mentioned that data of total labor cost were not available for
Hungary and some approximation was needed.6
Therefore estimations
4
More information about raw data can be found in Appendix.
5
Actually, the rental price of capital is the real interest rate plus depreciation
rate. But assuming constant depreciation rate during the time, the growth rate
of the rental price will be the same as the growth rate of the real interest rate.
6
See Appendix for more details.
7
of labor-income share are not completely reliable, which should be
kept in mind for further evaluation of results.
The highest share of labor has Poland where agriculture is the main
sector of national economy. Agriculture is labor intensive and thus this
result corresponds to our view. Slovakia stands on the other side with
the lowest labor share from all Visegrad countries. This result is quite
surprising and may arise some suspicion about quality of data.
Generally, the labor share of Visegrad countries is quite low compared
to e.g. United States, where estimates of this number reach value of
66 %. If it is common feature of transforming countries or the data bear
the blame, is open question.
8
4. RESULTS
After transformation of the data, a calculation of the factor prices
growth rates and TFP using equation (6) is an easy task. Graphical
results (growth rates of the output, factor prices and TFP) for all
countries are presented in Figures 2 ­ 4 in Appendix B, numerical
results can be seen in Tables 2 ­ 5. As quarterly data were used, the
growth rates are expressed in both quarterly and annualized
expression. The last row shows annualized weighted growth rates of
factor prices (using factor-income shares).
Table 2: Growth rates ­ Czech Republic
Rental price of capital Real wage TFP Output
Quarterly -0.04 0.91 0.51 0.69
Annual -0.16 3.65 2.06 2.76
Annual weighted -0.07 2.11 2.06 2.76
Source: own calculations
Table 3: Growth rates ­ Hungary
Rental price of capital Real wage TFP Output
Quarterly -0.20 1.07 0.52 1.07
Annual -0.80 4.28 2.07 4.30
Annual weighted -0.34 2.42 2.07 4.30
Source: own calculations
Table 4: Growth rates ­ Poland
Rental price of capital Real wage TFP Output
Quarterly -0.03 0.51 0.30 1.05
Annual -0.14 2.04 1.21 4.20
Annual weighted -0.05 1.25 1.21 4.20
Source: own calculations
Table 5: Growth rates ­ Slovakia
Rental price of capital Real wage TFP Output
Quarterly -0.04 0.48 0.21 1.08
Annual -0.15 1.91 0.85 4.31
Annual weighted -0.07 0.99 0.85 4.31
Source: own calculations
All the countries experienced decrease of rental price of capital which
should correspond to increase of capital stock. It is obvious that these
countries were undercapitalized in the past and were subject to large
investment inflows during the transition. Assuming decreasing marginal
product to capital, the rental price had to decrease.
On the other hand, there was excessive employment in these
countries. As the economies were being restructuralized and people
were being dismissed from their jobs, labor productivity and the real
9
wages, too, increased. This is evident from the growth rates of the real
wages for all countries.
The remaining part of output growth that is not ascribed to changes in
factor inputs is the total factor productivity (here calculated as weighted
sum of growth of factor prices). It is that "something else," simply
something that is not explained; John Vaizey denotes it as "a measure
of our ignorance."7
TFP usually represents technological progress, but
it is a residual term and it can also cover qualitative increase of the
inputs or some other unidentified factors.
Hungary had the highest average growth rate of TFP (2.07 % per
year), and was tightly followed by the Czech Republic (2.06 %). TFP
growth in Poland and Slovakia was 1.21 % and 0.85 %, respectively.
As shown in Table 6, growth of TFP in respect to growth of output are
relatively more important measures. In the case of the Czech Republic,
TFP constitutes nearly 75 % of output growth. Growth of output in
Hungary can be divided approximately half to half between factor
accumulation and TFP. More precisely, TFP can account for 48.2 % of
output growth. TFP in Poland and Slovakia is less important. Poland
output growth can be explained by TFP from 29 %, in the case of
Slovakia only from 21 %.
Table 6: TFP to output
Country Share of TFP to output (in %)
Czech Republic 74.1
Hungary 48.2
Poland 29.0
Slovakia 21.2
Source: own calculations
These results are quite interesting. Visegrad countries have very
similar features and can be treated as a homogenous group. However,
economic growth has different sources. If we believe that all the
assumptions about shape of production function and remuneration to
factor inputs are valid for all countries and TFP growth is mainly
represented by technological progress, we can infer following
conclusions.
It the case of the Czech Republic, the technological progress plays the
most important role. Even if the average growth rate of output was
smallest from all Visegrad states, Czech economy can be considered
to be quite competitive. The economic growth is not based on
extensive type of growth (factor accumulation) but on improvements of
technology.
7
J. Vaizey, The Residual Factor and Economic Growth, 1964.
10
Slovakia stays on the other side with the highest average growth rate
of output but technological progress can account only for 21 % of this
growth. Does it imply that technology is unimportant in the case of
Slovakia? Not necessarily. Barro and Sala-i-Martin (2004) show8
that
small numbers of TFP (as percentage of growth of GDP) does not
mean that technology is not important source of growth. Technology as
an ultimate source of growth can explain large portion of economic
growth, because it triggers factor accumulation that would never
happen without it.
Poland has also very high growth that was mainly driven by factor
accumulation. As noted earlier, data about factor-income shares for
Hungary are not so reliable and neither are thus conclusions. Without
regard to this fact, Hungary had very rapid average growth of output
(same as Slovakia), reasons of which seem to be evenly divided
between factor accumulation and technology improvement.
From the point of view of economic theory, these differences can be
partly explained by the neoclassical growth model, specifically by the
Solow (1956) model with exogenous technological progress.
Explanation is based on hypothesis of absolute convergence and
different initial quantity of capital per person (k). One can see these
countries as converging to the steady-state during transition period as
it is illustrated in Figure 1.
The Czech Republic has the lowest growth rate of output that is mainly
driven by technological progress. This country is nearest to the steadystate
(k*). On the other hand, Poland and Slovakia are farther from the
steady-state, with lower level of capital but high rate of its accumulation
and thus higher growth rate of output. Hungary is an exception. Very
high output growth ranks this country to the latter group yet technology
growth is quite important and suggests a position closer to the steadystate.
Reasoning can be that Hungary has different steady-state and
concept of conditional convergence should be applied.
8
Section 10.5.
11
Figure 1: Convergence
Growth rate
n +  + x
s f(k)/k
k*CZPOSK k
12
5. CONCLUSION
This paper examined sources of economic growth in Visegrad states
using dual approach to growth accounting. TFP growth was calculated
as a weighted sum of growth of factor prices. Shares of TFP to output
growth indicate what the main determinants of economic growth are.
Contrary to some similarities of Visegrad states, different sources stay
behind the economic growth during the transition process.
Technological progress is the main cause of growth in the Czech
Republic while factor accumulation plays the most important role in
Poland and Slovakia. Hungary is a country where the sources of
growth are divided evenly.
However, this paper made only first step of the analysis ­ it showed
which main determinants of economic growth are important for every
country. Further research should be aimed onto two directions.
One part can be focused on a more detailed analysis of growth
accounting. Factors of production (and their remunerations) can be
disaggregated with respect to their quality which primarily relates to
labor. Next, dual approach can be connected to primal approach in
order to find out the exact contribution of individual factors. Due to bad
availability of data of capital, its contribution to growth can be
calculated as a residual using equation (4) where the only unknown is
the growth rate of capital K^ .
Second and more important part of further research should be aimed
at identification of fundamental determinants of economic growth such
as government policies, household preferences, natural resources,
initial level of physical and human capital etc. Growth accounting is
only mechanical decomposition and it does not constitute a theory of
growth.
13
6. REFERENCES
ADDERLEY, C. (1958): Somethin' Else, Blue Note.
BARRO, R. J. ­ SALA-i-MARTIN X. (2004): Economic Growth,
Cambridge, MA: MIT Press, second edition.
EASTERLY, W. ­ LEVINE, R. (2001): Iťs Not Factor Accumulation:
Stylized Facts and Growth Models World Bank Economic Review, Vol.
15, No. 2, pp. 177-219.
HÁJEK, M. (2005): Economic growth and total factor productivity in the
Czech Republic from 1992 to 2004, Working Paper CES VŠEM No. 5.
HLOUŠEK, M. (2007): Dual approach to growth accounting ­
Application for the Czech Republic, In Mathematical Methods in
Economics 2007, Ostrava: Faculty of Economics, VŠB ­ Technical
University of Ostrava, pp. 185-190.
HSIEH, C. T. (1999): Productivity Growth and Factor Prices in East
Asia, American Economic Review, Vol. 89, No. 2, May, pp. 133-138.
JORGENSON D. W. ­ GRILICHES Z. (1967): The Explanation of
Productivity Change, The Review of Economic Studies, Vol. 34, No. 3,
July, pp. 249-283.
SOLOW, R.M. (1956): A Contribution to the Theory of Economic
Growth, The Quarterly Journal of Economics, Vol. 70, No. 1, February,
pp. 65-94.
SOLOW, R.M. (1957): Technical Change and the Aggregate
Production Function, The Review of Economics and Statistics, Vol. 39,
No. 3, August, pp. 312-320.
14
APPENDIX A ­ DATA DESCRIBTION
The dataset is available on request. The data were obtained from
databases of EUROSTAT, OECD and IMF. Frequency of data is
quarterly, spanning the period from 1996Q1 to 2006Q4. The series that
were not seasonally adjusted from the source were adjusted (when
needed) by Kalman filter smoother.
The following raw series from the following databases were used:
EUROSTAT
* Gross domestic product at market prices / unit: Millions of Euro (at
1995 prices and exchange rates) / Seasonally adjusted and
adjusted data by working days / Constant prices / All countries
* 3-month interbank rate / per cent p.a. / Cnt: Czech Republic,
Poland, Slovakia
* Yield 90-day treasury bills, / per cent p.a. / Cnt: Hungary
IMF
* Consumer Price Index / Index Number / Base year: 2000 /
averages / All countries
* Average Monthly Wages / Index Number / Averages / All countries
OECD
* Benchmarked total labor costs ­ Total / Millions of local currency /
Cnt: Czech Republic, Poland, Slovakia
* Benchmarked total labor costs ­ Industry and Construction /
Millions of HUF / Cnt: Hungary
* Total gross total value added at basic prices / Current prices,
quarterly levels, S.A. / Millions of local currency / Cnt: Czech
Republic, Poland, Slovakia
Total labor costs for all sectors were not available for Hungary. I used
labor cost for industry and construction, spanned in the period 2000--
2006. These sectors comprise about one third of GDP9. The total
labor costs were then approximately completed using these fractions
and share to gross value added was calculated. The average labor
share from this shorter period was used as extrapolation for years
1996--1999.
9
Exact numbers were obtained from Statistical reports of Hungarian Central
Statistical Office.
15
APPENDIX B ­ GROWTH RATES
Figure 2: Growth rates ­ Czech Republic
1996 1998 2000 2002 2004 2006
-0.5
0
0.5
1
1.5
time
%
Output
1996 1998 2000 2002 2004 2006
-1
0
1
2
time
%
Real wage
1996 1998 2000 2002 2004 2006
-4
-2
0
2
4
time
%
Real interest rate
1996 1998 2000 2002 2004 2006
-2
-1
0
1
2
time
%
TFP
Figure 3: Growth rates ­ Hungary
1996 1998 2000 2002 2004 2006
0.5
1
1.5
time
%
Output
1996 1998 2000 2002 2004 2006
-1
0
1
2
3
time
%
Real wage
1996 1998 2000 2002 2004 2006
-4
-2
0
2
4
time
%
Real interest rate
1996 1998 2000 2002 2004 2006
-1
0
1
2
time
%
TFP
16
Figure 4: Growth rates ­ Poland
1996 1998 2000 2002 2004 2006
-2
0
2
4
6
time
%
Output
1996 1998 2000 2002 2004 2006
-0.5
0
0.5
1
1.5
time
%
Real wage
1996 1998 2000 2002 2004 2006
-4
-2
0
2
4
time
%
Real interest rate
1996 1998 2000 2002 2004 2006
-2
-1
0
1
2
time
%
TFP
Figure 5: Growth rates ­ Slovakia
1996 1998 2000 2002 2004 2006
-2
0
2
time
%
Output
1996 1998 2000 2002 2004 2006
-2
0
2
time
%
Real wage
1996 1998 2000 2002 2004 2006
-5
0
5
time
%
Real interest rate
1996 1998 2000 2002 2004 2006
-4
-2
0
2
time
%
TFP
17
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Martina Vašendová: Pohyb zahraničního kapitálu v průběhu
transformace a jeho vliv na konkurenční schopnost slovenské
ekonomiky
WP č. 4/2007
Jitka Doležalová: Vliv politiky na konkurenceschopnost Slovenské
republiky
WP č. 5/2007
Daniel Němec: Komparace demografického vývoje Maďarska a Polska
v období transformace
WP č. 6/2007
Veronika Bachanová: Regulace a deregulace v Maďarsku v období
1990­2006
WP č. 7/2007
Martina Vašendová: Pohyb zahraničního kapitálu v průběhu
transformace a jeho vliv na konkurenční schopnost polské ekonomiky
WP č. 8/2007
Tomáš Otáhal: Vývoj korupce v SR v období transformace
WP č. 9/2007
Jitka Doležalová: Rozvoj demokracie v Polsku a jeho vliv na výkonnost
hospodářství
WP č. 10/2007
Monika Jandová: Zahraniční obchod Slovenské republiky 1993­2006
WP č. 11/2007
Milan Viturka: Inovační profily regionů
WP č. 12/2007
Veronika Bachanová: Regulace a deregulace v Polsku a ve Slovenské
republikce v období 1990­2006
WP č. 13/2007
Jitka Doležalová: Demokracie a její vliv na výkonnost maďarského
hospodářství
WP č. 14/2007
Tomáš Paleta: Strukturální politika Slovenské republiky 1990­2005
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WP č. 15/2007
Naďa Voráčová: Hospodářský růst na Slovensku a v Polsku: jaký vliv
měla fiskální politika?
WP č. 16/2007
Monika Jandová: Komparace zahraničního obchodu Maďarska a
Polska (1990-2006)
WP č. 17/2007
Miroslav Hloušek: Growth Accounting for Visegrad States: Dual
Approach
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