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NBP Working Paper No. 318
The productivity puzzle and the Kaldor-Verdoorn law: the case of Central and Eastern EuropeHubert Gabrisch
Narodowy Bank PolskiWarsaw 2019
NBP Working Paper No. 318
The productivity puzzle and the Kaldor-Verdoorn law: the case of Central and Eastern EuropeHubert Gabrisch
Published by: Narodowy Bank Polski Education & Publishing Department ul. Świętokrzyska 11/21 00-919 Warszawa, Poland www.nbp.pl
ISSN 2084-624X
© Copyright Narodowy Bank Polski 2019
Hubert Gabrisch – Wiesbaden Institute for Law and Economics (WILE); h.gabrisch@wile-institute.eu
Acknowledgements:I express my thanks to Narodowy Bank Polski, where I presented first considerations about this topic at the 8th Annual Conference on the Future of the European Economy (CoFEE), Warsaw, 26 October 2018, on the ’Mystery of Low Productivity Growth in Europe’. Also, I am grateful to an anonymous reviewer for helpful suggestions on an earlier draft. All remaining errors are my own.
3NBP Working Paper No. 318
ContentsAbstract 4
1 Introduction 5
2 The productivity-output nexus in the literature 6
3 The analytical framework 10
4 Data and methodology 12
4.1 Variables and data 12
4.2 Use of panel techniques 13
4.3 Descriptive statistics and stylized facts 13
4.4 Unit root tests 16
4.5 Causality tests 17
5 Estimation results and discussion 19
5.1 The traditional KV law: growth rates 19
5.2 The bounds tested ARDL approach 21
6 Concluding remarks 27
Bibliography 28
Annexes 30
Narodowy Bank Polski4
Abstract
Abstract
This study attempts to identify the short- and long-run components of the Kaldor-Verdoorn
(KV) law in empirical economics. The law claims that demand dynamics drive productivity
dynamics. The law is tested with a panel of ten Central and Eastern-European countries,
where labour productivity and demand growth have been slowing since 2004/2006 and where
fears of an end of convergent growth are spreading. Meanwhile, the gradual slowing of
output and productivity growth applies not only to the region considered in this study, but it is
also a global phenomenon that is occurring despite remarkable technical progress and that is
referred to as the so-called productivity puzzle. However, this puzzle would be solved in light
of the KV law. To test for the short-term and long-term properties of this law, least squares
and autoregressive distributed lag (ARDL) models are applied. Our results confirm the law
for the region; slower productivity growth is not due to adverse technological progress but
to weakening external and domestic demand.
JEL codes: C23, E24, O47
Keywords: Productivity conundrum, Kaldor-Verdoorn law, panel autoregressive distributed
lag (ARDL) model, Eastern Europe
5NBP Working Paper No. 318
Chapter 1
1 Introduction
The productivity puzzle is a phenomenon widely discussed in empirical economics. It
describes the occurrence of a slowdown in productivity growth despite the presence of
impressive technical progress (automatization, digitalization, and robotization). This study is
distinct from the existing literature in two respects. First, it analyses productivity slowdown
from the perspective of the Kaldor-Verdoorn (KV) law. This law assumes a long-run
relationship between the growth rates of labour productivity and output/demand whereby
causality runs from the latter to the former. This is a widely neglected perspective in
conventional research that assumes productivity to be a major driver of output growth.
Second, distinct from the KV literature, the present study reveals short-run and true long-run
components of the relationship between productivity and output/demand. Methodologically,
this is done by applying a bounds tested autoregressive distributed lag (ARDL) model as a
cointegration technique. Empirically, a panel dataset of ten Central and East European (CEE)
countries is used. Since their transition from a socialist planned economy to a capitalist
market economy, CEE countries have entered a period of convergent economic growth
accompanied by strong progress in productivity. However, fears remain with respect to the
continuance of convergent growth.
The rest of the study is structured as follows. Section 2 provides an overview of the
productivity-output nexus described in the literature on CEE countries. Section 3 provides the
analytical framework on the short- and long-run relationships between productivity and
output/demand. Section 4 introduces relevant stylized facts for the CEE countries considered
and describes the data used for the empirical analysis. Section 5 applies a panel ARDL
cointegration model and compares its results with those of a traditional OLS approach.
Section 6 concludes. The study finds the short-run dynamics of productivity to be driven by
output/demand growth and a strong adjustment towards long-run equilibrium between level
variables, at which point the productivity puzzle vanishes.
Narodowy Bank Polski6
Chapter 2
2 The productivity-output nexus in the literature
Verdoorn (1949) observed a relationship between growth rates of labour productivity and
gross domestic product (GDP) with the equation
(1)
with q and y being the growth rates of labour productivity and GDP, respectively. Verdoorn
interpreted a positive as markets expand, hence broadly
defining this as a change in aggregate demand. He found a coefficient with a long-run value
of approximately 0.5.
With the rise of neoclassical growth theory, the original causality in equation (1) was
reversed: GDP growth became the dependent variable. Furthermore, the relationship changed
from a short- to long-run relationship. The starting point of endogenous growth theory is a
standard production function with output Y, capital K, employment N, and total-factor
productivity A, reflecting the state of technology broadly interpreted. When the production
function is differenced and when perfect competition and constant returns to scale are
assumed, causality runs from the rate of total factor productivity (TFP) to the long-run GDP
growth rate as -factor productivity rather
than labour productivity q in equation (1). However, the Cambridge capital theory
controversies have theoretically shown that aggregate production functions with a capital
factor likely do not exist. Nevertheless, a production function (and most conveniently, a
Cobb-Douglas function) dominates the empirical research on growth and convergence.
Researchers have tried to create unobservable variables (e.g., capital stock and total factor
productivity (TFP)) via the use of more or less complex calculations (growth accounting or
index construction). The growth rate of total factor productivity (TFP) is then endogenous to
various drivers such as research and development (R&D) expenditures, education,
institutional quality and others. Supply-side policy conclusions centre around the various
input factors involved. In empirical research, some researchers apply variables that are
thought to depict structural change, which is not irrelevant for countries having been in
transition to market economies. When aggregate demand comes into the play at all, it is
incidental to fundamentals and reduced to short-term shocks (OECD 2016: 65-70). Empirical
research is predominantly focused on the long-run trends reflected by fundamental factors,
and research designs sometimes completely disregard the demand side (e.g., see Ozanne,
2006 on high-performing Asian economies).
7NBP Working Paper No. 318
The productivity-output nexus in the literature
The neoclassical approach also dominates research on growth and convergence in CEE
economies. While in earlier research (Bah and Brady 2009; Burda and Severgnini 2009) one
finds explicit references to fundamental problems related to measuring capital stock (the
starting value is unobservable and depreciation rates are not stable), these problems vanish in
later research. Here, the main challenge is to find appropriate variables that reflect
technological progress in the broadest sense. With specific reference to information and
communication technologies (ICT) capital, Piatkowski (2003, 2004), Jorgenson and Vu
(2010), and Ahrendt (2015) use ICT data to apply growth accounting exercises to CEE
countries for various periods; they all find evidence of a positive impact of ICT capital on
labour productivity and TFP and then on GDP growth. Patent applications, expenditures on
research and development, various forms of education are other variables are often tested.
Ahrendt (2015) found differences in the impacts of ICTs between CEE countries and the US
and EU, which he among others attributes to capacity utilization, a short-term demand factor.
But, aggregate demand is not typically considered in such growth accounting exercises.
Levenko et al. (2018) present growth account models and include the degree of capital
utilization in their TFP simulation models and obtain results suggesting TFP to breathe in line
with boom and bust periods. For example, they found TFP growth to contribute
approximately half of the GDP growth occurring in the boom period of 2006-2007 while this
contribution has considerably declined since the financial crisis, which is seen as a kind of a
short-term demand shock. However, they confess that some assumptions regarding the
construction of the capital stock series are critical for the results (Levenko et al. 2018: p. 1).
A recent ECB study on CEE convergence conducted and Savelin (2018) does not
even consider a possible short-term role for demand among the various TFP drivers; output
growth and growth of the various TFP determinants are complementary drivers of income
convergence. The authors see output and TFP growth as complementary drivers of income
convergence in addition to other factors like structural change and trade openness.
Regressions with fixed effects and GMM allow drawing a picture of changing factor
compositions for income convergence over time.
Furthermore, most recently, Chiacchio et al. (2018) found that being integrated into global
value chains (GVCs) explains TFP growth in CEE countries and specifically its decline since
the global financial crisis. They shed light on a factor playing (similar to aggregate demand) a
minor role in the previous research: structural change (Ahrend, 2015 merely mentioned it).
Narodowy Bank Polski8
The authors suggest attributing the slowdown in TFP growth observed in CEE countries in the
post-crisis period (since 2008) mainly to a decline in host firms absorptive capacities for new
knowledge potentially caused by a drop in R&D investment and the slowdown in technology
creation among parent firms; whether this conclusion also holds for the previous boom period
remains undetermined. With the empirically tested correlation between output and TFP
growth at hand, this research can indeed explain why GDP growth is slowing down in many
regions of the global economy. However, the work is less successful in explaining why labour
and multi-factor productivity growth have slowed over the long-run (hence, independent of
cycles) despite technical progress. Even Chiacchio et al. (2018) fail to provide such an
explanation due to their focus on the post-crisis period. Thus, in CEE countries, fears of the
continuance of convergent growth seem to be spreading (see, e.g., Gomulka (2016)).
A potential explanation for the productivity puzzle concerns the potential size of markets.
Obviously, there has been inexhaustible progress in innovation, but companies are reluctant to
implement this innovation, as overall and specific demand is sluggish; the corresponding
return on investment seems not secured. This possibility has recently revived the KV research
agenda, according to which causality is assumed to run from output/demand growth to
productivity growth via increasing returns to scale. In addition to Verdoorn (1949), Kaldor
(1966, 1972) emphasized that sectors have different degrees of increasing returns, and thus
countries may grow at different rates due to differences in their sector structures of
production. Capital is a produced means of production, and investment responds to demand.
Also sceptical to the neoclassical production function approach, Kaldor proposed a technical
progress function that applies as arguments aggregate and sector demand. Krugman (1979)
attributed increasing returns to scale to intra-industry trade: trade integration expands the size
of the market. This enables firms to further exploit economies of scale and to lower prices,
and it also enables the introduction of additional product varieties that increase consumer
utility and demand. The automobile industry, a relevant specialization of many advanced
countries, may serve as the most striking example. Seen from this perspective, a strict
separation of structural and demand variables in empirical research does not appear to be
possible, as a country s integration into GVCs is a driver of structural change (Stöllinger
2016), intra-industry trade and allows for the expansion markets in related industries. Further,
with respect to the second crucial assumption of neoclassical growth theory, one may also
refer to Kalecki s attack on the assumption of perfect competition. In the 1930s, he observed
the degree of competition to fall in the downward business cycle period, as firms already in
9NBP Working Paper No. 318
The productivity-output nexus in the literature
the market are less inclined to implement new technologies or products, and they are more
inclined to form cartels to impede newcomers and their process and product innovations. We
would then expect to find less productivity enhancing investment in a stagnant economy.
Among empirical studies, Magacho and Combie (2017) test the two competing theoretical
approaches in their capacities to explain the productivity and output growth of manufacturing
industries of a sample of 70 countries with variables differing for supply- and demand-side
model specifications. Applying GMM techniques to rates of change, they find that demand-
side variables explain productivity growth better than supply-side variables. Podkaminer
(2017) applies Granger causality tests with OLS to a sample of 23 advanced market
economies while focusing on growth rates and levels. From tests of individual countries he
finds evidence that changes in per capita GDP cause changes in productivity in 16 countries
while causality runs in the opposite direction for 7 cases. Tests on the linkages between levels
of productivity and per capita GDP deliver evidence of causalities running in both directions
and further impair the general validity of the KV law. The author expands the analysis to the
ten CEE countries examined in the present study and obtains similar results.
Deleidi et al. (2018) investigate the validity of the KV law for nine major EU countries and
for four main sectors and find for each country significant KV coefficients at the aggregate
level; the situation is more mixed between sectors. The results are confirmed by a model
augmented with an investment variable following Kaldor s argument of technical progress
imbedded in investment. What differentiates their approach from the standard approach is an
attempt to find the long- and short-run elements of growth rates. The technique applied is
bounds tested ARDL cointegration. However, their results are difficult to assess, as all
variables used in the regressions are I(1) rather than mixed I(0)/I(1) characters typically used
in ARDL applications or I(0) only used in other cointegration models. Ozanne (2006) in her
TFP research on high-performing Asian countries was able to apply ARDL cointegration to
the levels of variables of the characteristic production function because she found
combinations of integration orders from unit root tests.
Narodowy Bank Polski10
Chapter 3
3 The analytical framework
The KV-law according to equation (1) above serves as the traditional baseline model for
empirical testing. However, the estimated coefficients are contingent on the actual state of the
output/demand cycle. A general model that identifies the irreversible (non-cyclical) and
reversible (cyclical) elements of increasing returns to scale is needed. If they exist,
irreversible elements could be found in the equilibrium between output/demand and
productivity levels and not in cycle deviations from the equilibrium. The literature has also
revealed that some elements of technical progress and changes in sector composition with
long-run traits may contribute to the irreversible output/demand-productivity relationship. A
general specification of a production function may serve as the theoretical background for
such a model with irreversibility traits where Yp is output and technology A and employment
N are the initial arguments:
Yp = Y(A N ) (2)
Technology is labour-augmenting, and hence Condition ensures increasing returns
to scale, as ( ). Distinct from the Solow and other neoclassical models, there is no
capital stock variable, preventing the emergence of valuation problems with respect to
physical capital and the usage of arbitrary variables. Productivity refers to labour productivity,
which is defined as:
(3)
Combie and Spreafico (2016) present a related approach using a technical progress function
that Kaldor developed as an alternative to the neoclassical production function. Changes in
technology and not in capital govern production over the long-run. Following Magacho and
McCombie (2017), part of the implemented technology is the result of exogenous factors such
as inventive genius, R&D expenditure, learning by doing, etc.. However, another part is
driven by demand, and hence expanding markets offer better opportunities for the
implementation of product and process innovation. Finally, increasing returns to scale at the
aggregate level not only result from diffusion mechanisms of technological progress
embedded in physical capital but also from specialization processes occurring between firms
and sectors following, for instance, intra-industry trade patterns. The distribution of resources
(here of labour) between sectors of differing levels of productivity affects productivity at the
11NBP Working Paper No. 318
The analytical framework
aggregate level.1 In a simplified manner, the state of technology A in equation (3) is
contingent on three factors:
A = A( , S, Y) (4)
where is exogeneous technology, S is the structural composition of production, and Y is
aggregate demand. The productivity function included in equation (3) takes the following
form:
with . (5)
Equation (5) is the characteristic function underlying the KV law on growth rates:
(6)
Equation (5) describes the long-run relationship between productivity, technology,
demand, and production structures, which governs the return of short-run dynamics
towards the equilibrium path; is the traditional KV coefficient. The empirical analysis
below is intended to reveal the long-run equilibrium relationship between output/demand
and productivity and short-run adjustment processes controlled by the insertion of
additional variables. ARDL modelling is used in this attempt.
Recent empirical work on the EU and UK (Hartwig 2011, Riley et al. 2018) has found negative effects of
shifts from fast- to slow-growing sectors in terms of productivity with the latter mainly involving the tertiary
sector via the so-called Baumol disease.
aggregate level.1 In a simplified manner, the state of technology A in equation (3) is
contingent on three factors:
A = A( , S, Y) (4)
where is exogeneous technology, S is the structural composition of production, and Y is
aggregate demand. The productivity function included in equation (3) takes the following
form:
with . (5)
Equation (5) is the characteristic function underlying the KV law on growth rates:
(6)
Equation (5) describes the long-run relationship between productivity, technology,
demand, and production structures, which governs the return of short-run dynamics
towards the equilibrium path; is the traditional KV coefficient. The empirical analysis
below is intended to reveal the long-run equilibrium relationship between output/demand
and productivity and short-run adjustment processes controlled by the insertion of
additional variables. ARDL modelling is used in this attempt.
Recent empirical work on the EU and UK (Hartwig 2011, Riley et al. 2018) has found negative effects of
shifts from fast- to slow-growing sectors in terms of productivity with the latter mainly involving the tertiary
sector via the so-called Baumol disease.
Narodowy Bank Polski12
Chapter 4
4 Data and methodology
4.1 Variables and data
The empirical section of this paper covers the ten CEE countries of Bulgaria, the Czech
Republic, Estonia, Hungary, Latvia, Lithuania, Poland, Romania, Slovakia, and Slovenia for
the period of 1995-2016. Reliable data for earlier years are not available. Missing values were
approximated. For an overview of sources used and calculations of variables, see the Annex.
The variables are entered into the models either as their logs, as first differences of their logs
(= their rates of change) or as first differences. Labour productivity Q is calculated as the
gross value added per hour worked. For aggregate demand, two alternatives are considered:
GDP Y and autonomous demand YA. 2
The latter is calculated from current disbursements of
the general government, government fixed capital formation and the export of goods and
services; Deleidi et al. (2018) propose the use of autonomous demand to reduce potential
sources of endogeneity between productivity and GDP. The KV law is confirmed when the
regression coefficients to aggregate demand are positive. The robustness of the estimates is
tested through the insertion of innovation and structural variables. The empirical literature
offers a multitude of variables, some of which are assumption-sensitive. Different from
public statistics with a long history, they may serve the specific cognitive interests of the
researcher. In the following tests, a first group of variables includes technology and
innovation variables: gross expenditures on research and development (GERD) per inhabitant
and the ICT capital share of consumption in GDP (ICT). ICT belongs to variables constructed
under specific assumptions and sources (see De Vries and Erumban 2017). Some authors also
use patent applications, but these are rather weak variables, as applications, implementation
and economic success are different issues.3 Other variables, such as educational ones, are
available for only short periods, and are not considered in regressions.
A second group of control variables consists of structural variables such as the employment
shares of industry (SIND) and the service sector (SSER). The latter not only covers traditional
services but also financial and other business-related services recently exhibiting strong
increases in productivity. A positive sign in regressions denotes shifts from less productive
13NBP Working Paper No. 318
Data and methodology
agriculture or construction to highly productive industries and services. Integration into a
GVC is at the borderline between structure and innovation. The variable used to control the
basic models QEURO9 is the productivity of the largest euro area countries assuming that a
GVC transmits productivity progress in this area to partner countries. The variable should
have a positive sign in regressions; its significance evidences the existence of a GVC. Finally,
trade openness (TO) is included as a control variable, as one can argue that the higher the
degree of trade openness, the higher the level of productivity. While one may also try to apply
credit data, the credit cycle is close to the demand cycle, and hence strong patterns of
collinearity may exist; therefore, credit is excluded from the list of variables.
4.2 Use of panel techniques
Because we dispose of only 21 observations for each country (1995-2016), a panel approach
is used to expand the sample to a maximum of 230 observations. The main advantage of the
use of panel data lies in the availability of a larger dataset and thus of additional information
and greater degrees of freedom. Further, a panel data approach can impose homogeneity
conditions upon parameters across countries. The approach also affords additional power and
may allow for the detection of common relationships not apparent in individual time series,
which often produce mixed results. With a panel model it is also possible to control for
country-specific, time-invariant characteristics through the use of country-specific intercepts
(fixed effects). The test procedures used in this study treat the panel data as one large stacked
set of data and are performed in the standard way with the exception of not allowing data
from one cross-section to enter the values of data from the next cross-section.
4.3 Descriptive statistics and stylized facts
A review of the stacked individual data series (Table 1) critically reveals high standard
deviations and remarkable differences between countries with respect to employment and
demand, calling for the inclusion of fixed cross-section effects in the regressions. Jarque-Bera
coefficients show a non-normal distribution due to high levels of leptokurtosis, denoting the
presence of high levels of instability after a shock, rendering forecasts impossible.
Narodowy Bank Polski14
Tab
le 1
: D
escr
ipti
ve
stat
isti
cs f
or
stac
ked
pan
el d
ata
Em
plo
ymen
t
mn
ho
urs
Y
mn
Eu
roa
YA
mn
Eu
roa
Pro
du
ctiv
ity
euro
per
hou
ra
GE
RD
euro
per
inha
bit
ant
ICT
per
cen
t o
f
GD
P
QE
UR
O9
eu
ro
per
hou
ra
SIN
D
sha
re i
n
emp
loym
ent
SS
ER
Sh
are
in
emp
loym
ent
TO
Ra
tio t
o G
DP
Mea
n
238
99
16
82
64
6
68
39
7
9.1
21
90
.475
3.1
97
34
.898
0.2
52
0.5
29
1.1
24
Med
ian
559
4
39
88
3
36
69
1
9.2
00
54
.850
3.2
00
35
.051
0.2
38
0.5
56
1.1
00
Max
imu
m
211
74
58
3
43
28
16
33
98
57
3
17
.700
45
4.1
00
11
.200
38
.237
0.5
92
0.6
79
1.9
00
Min
imu
m
102
8
79
33
38
25
2.3
00
4.9
00
0.4
00
30
.965
0.0
77
0.2
83
0.4
00
Std
. D
ev.
554
58
21
89
26
8
78
85
0
3.7
23
96
.548
1.2
65
2.1
89
0.0
98
0.1
08
0.3
47
Skew
nes
s 2
.33
2
2.0
06
2.0
99
0.1
65
1.8
23
2.5
32
-0.1
52
1.2
94
-1.0
47
0.1
21
Ku
rto
sis
7.0
54
6.9
14
7.5
84
2.1
61
6.1
24
15
.916
1.9
38
5.6
28
3.0
65
2.1
09
Jar
qu
e-B
era
334
.19
0
28
7.9
70
35
4.1
94
7
.07
2
22
0,9
05
18
44
.527
11
.189
12
4.7
24
40
.233
8.1
75
Pro
bab
ilit
y
0.0
000
0.0
00
0.0
00
0.0
29
0.0
00
0.0
00
0.0
04
0.0
00
0.0
00
0.0
17
Ob
serv
atio
ns
210
22
0
22
0
209
23
0
23
0
22
0
22
0
22
0
23
0
Vo
lum
es
(20
10
) p
rice
s.
Leg
en
d:
Q =
pro
duct
ivit
y;
Y =
Gro
ss D
om
esti
c P
rod
uct
; Y
A =
au
tono
mo
us
dem
and
; G
ER
D
= G
ross
E
xp
end
iture
on R
esea
rch
& D
evel
op
men
t p
er i
nhab
itant;
IC
T =
IC
T c
apit
al
shar
e co
nsu
mp
tio
n i
n G
DP
; Q
EU
RO
9 =
ag
gre
gat
ed l
abo
ur
pro
duct
ivit
y i
n 9
eu
ro c
ou
ntr
ies;
SIN
D =
em
plo
ym
ent
share
of
ind
ust
ry;
SS
ER
= e
mp
loym
ent
shar
e o
f th
e se
rvic
e
sect
or;
TO
= t
rad
e open
nes
s.
15NBP Working Paper No. 318
Data and methodology
Figure 1: Growth trends in GDP, autonomous demand and labour productivity
Sources: Author s calculations and drawings.
Narodowy Bank Polski16
Figure 1 shows trends4 in rates of change in GDP Y, in autonomous demand YA and in labour
productivity Q for the sample period of 2005 - 2016. The general impression is that there are secular
downward trends for GDP and productivity in most countries from roughly 2004-2006 except for
Bulgaria (Y) and Lithuania (YA from 2012) and for Estonia, Slovakia and Slovenia even
earlier on. In general, trend rates of change are higher for YA, which seems to be attributable
to the partly political nature (government demand) of the variable while Y and Q are more
market-endogenous. Trend growth in autonomous demand started falling shortly after 2004
when eight of the countries acceded the European Union and had to comply with the Union s
fiscal rules. The turning point for Y seems to have occurred around 2007/2008, when the
outbreak of the financial crisis began to affect these economies. Estonia and Lithuania show
extreme outliers at the start of the period, explaining the high standard deviation observed in
the descriptive statistics shown above. The figure illustrates the rationale behind the fears held
in the region of an end of convergent income growth.
4.4 Unit roots tests
The identification of data properties is an important step in the discussion and selection of an
econometric instrument. The most prominent issue concerns the presence of unit roots in the
data. When output/demand and productivity are both I(0) in their levels, one can simply apply
least square estimations with OLS to produce a long-run relationship. When both are only
I(1), two strategies can be applied:
- a simple OLS regression with growth rates; however, long-run information will be missing
(this was Verdoorn s best practice in 1949);
- a cointegrating approach when the respective tests reveal a cointegration relationship. In this
case, an error-correction (EC) model reporting (a) a long-run relationship, (b) short-run
dynamics, and (c) an adjustment parameter ( cointegration term ) can be applied.
In empirical research, variables often show a mix of I(0) and I(1) values or unit root tests do
not generate a stable result. In this case, the bounds-tested ARDL technique following
Pesaran et al. (2001) offers a means to combine stationary and non-stationary variables.
Clearly, a bounds test is meaningless when all variables are either I(0) or I(1). Some authors
argue that unlike other models, the ARDL cointegration method is advantageous in that it
does not involve conducting pre-tests for unit roots (Nkoro and Uko 2016: 64). However, the
Figure 1 shows trends4 in rates of change in GDP Y, in autonomous demand YA and in labour
productivity Q for the sample period of 2005 - 2016. The general impression is that there are secular
downward trends for GDP and productivity in most countries from roughly 2004-2006 except for
Bulgaria (Y) and Lithuania (YA from 2012) and for Estonia, Slovakia and Slovenia even
earlier on. In general, trend rates of change are higher for YA, which seems to be attributable
to the partly political nature (government demand) of the variable while Y and Q are more
market-endogenous. Trend growth in autonomous demand started falling shortly after 2004
when eight of the countries acceded the European Union and had to comply with the Union s
fiscal rules. The turning point for Y seems to have occurred around 2007/2008, when the
outbreak of the financial crisis began to affect these economies. Estonia and Lithuania show
extreme outliers at the start of the period, explaining the high standard deviation observed in
the descriptive statistics shown above. The figure illustrates the rationale behind the fears held
in the region of an end of convergent income growth.
4.4 Unit roots tests
The identification of data properties is an important step in the discussion and selection of an
econometric instrument. The most prominent issue concerns the presence of unit roots in the
data. When output/demand and productivity are both I(0) in their levels, one can simply apply
least square estimations with OLS to produce a long-run relationship. When both are only
I(1), two strategies can be applied:
- a simple OLS regression with growth rates; however, long-run information will be missing
(this was Verdoorn s best practice in 1949);
- a cointegrating approach when the respective tests reveal a cointegration relationship. In this
case, an error-correction (EC) model reporting (a) a long-run relationship, (b) short-run
dynamics, and (c) an adjustment parameter ( cointegration term ) can be applied.
In empirical research, variables often show a mix of I(0) and I(1) values or unit root tests do
not generate a stable result. In this case, the bounds-tested ARDL technique following
Pesaran et al. (2001) offers a means to combine stationary and non-stationary variables.
Clearly, a bounds test is meaningless when all variables are either I(0) or I(1). Some authors
argue that unlike other models, the ARDL cointegration method is advantageous in that it
does not involve conducting pre-tests for unit roots (Nkoro and Uko 2016: 64). However, the
17NBP Working Paper No. 318
Data and methodology
application of an ARDL model would fail when one variable is I(2) insofar as a unit root test
is not redundant.
Unfortunately, the results of unit root tests are sensitive to the test procedure applied, and the
outcome can include an uncertain combination of stationary and non-stationary variables such
as those reported in Table 2. This uncertainty provides an additional case for applying ARDL
co-integration methods at least in addition to and to draw comparisons with OLS models and
growth rates. Further, none of the series is defined as I(2), which is a relevant condition for
the application of an ARDL model.
Table 2: Panel unit root tests with individual intercept (all variables in their logs)
Levin, Lin, Chu ADF - Fisher Chi-
square
PP - Fisher Chi-
square
Im, Pesaran and
Shin W-stat
Q I(0) I(1) I(1) I(1)
Y I(1) I(1) I(1) I(1)
YA I(0) I(1) I(1) I(1)
GERD I(1) I(1) I(1) I(1)
ICT I(1) I(0) I(0) I(0)
SIND I(1) I(1) I(1) I(0)
SSER I(0) I(1) I(1) I(0)
QEURO9 I(0) I(1) I(1) I(0)
TO I(1) I(1) I(1) I(1)
Legend: see Table 1.
Sources: see Annex; author s calculations with Eviews 10.
4.5 Causality tests
Running a model according to equations (5) and (6) presupposes an appropriate causality of
productivity and demand in their levels and rates of change, and the sign of the independent
variable demand must be positive; a negative sign would be meaningless, since increasing
output would depress productivity. If there were no statistical evidence for positive causality
from output/demand to productivity, it would be difficult to argue in favour of the hypothesis
of this study.
Table 3 presents a summary of pairwise panel Granger causality tests conducted with the
variables in their log-levels; constant terms are not reported. The tests reveal that the null
hypothesis of GDP Y does not cause productivity can be rejected at the 5 per cent level of
significance within three lags. At lag two, the independent variable Y has the expected positive
sign and is significant at the 5 per cent level (column 1). The tests do not fail to reject the null
of reverse causality from Q to Y (column 3): an absence of significant Q-variables and Wald
application of an ARDL model would fail when one variable is I(2) insofar as a unit root test
is not redundant.
Unfortunately, the results of unit root tests are sensitive to the test procedure applied, and the
outcome can include an uncertain combination of stationary and non-stationary variables such
as those reported in Table 2. This uncertainty provides an additional case for applying ARDL
co-integration methods at least in addition to and to draw comparisons with OLS models and
growth rates. Further, none of the series is defined as I(2), which is a relevant condition for
the application of an ARDL model.
Table 2: Panel unit root tests with individual intercept (all variables in their logs)
Levin, Lin, Chu ADF - Fisher Chi-
square
PP - Fisher Chi-
square
Im, Pesaran and
Shin W-stat
Q I(0) I(1) I(1) I(1)
Y I(1) I(1) I(1) I(1)
YA I(0) I(1) I(1) I(1)
GERD I(1) I(1) I(1) I(1)
ICT I(1) I(0) I(0) I(0)
SIND I(1) I(1) I(1) I(0)
SSER I(0) I(1) I(1) I(0)
QEURO9 I(0) I(1) I(1) I(0)
TO I(1) I(1) I(1) I(1)
Legend: see Table 1.
Sources: see Annex; author s calculations with Eviews 10.
4.5 Causality tests
Running a model according to equations (5) and (6) presupposes an appropriate causality of
productivity and demand in their levels and rates of change, and the sign of the independent
variable demand must be positive; a negative sign would be meaningless, since increasing
output would depress productivity. If there were no statistical evidence for positive causality
from output/demand to productivity, it would be difficult to argue in favour of the hypothesis
of this study.
Table 3 presents a summary of pairwise panel Granger causality tests conducted with the
variables in their log-levels; constant terms are not reported. The tests reveal that the null
hypothesis of GDP Y does not cause productivity can be rejected at the 5 per cent level of
significance within three lags. At lag two, the independent variable Y has the expected positive
sign and is significant at the 5 per cent level (column 1). The tests do not fail to reject the null
of reverse causality from Q to Y (column 3): an absence of significant Q-variables and Wald
application of an ARDL model would fail when one variable is I(2) insofar as a unit root test
is not redundant.
Unfortunately, the results of unit root tests are sensitive to the test procedure applied, and the
outcome can include an uncertain combination of stationary and non-stationary variables such
as those reported in Table 2. This uncertainty provides an additional case for applying ARDL
co-integration methods at least in addition to and to draw comparisons with OLS models and
growth rates. Further, none of the series is defined as I(2), which is a relevant condition for
the application of an ARDL model.
Table 2: Panel unit root tests with individual intercept (all variables in their logs)
Levin, Lin, Chu ADF - Fisher Chi-
square
PP - Fisher Chi-
square
Im, Pesaran and
Shin W-stat
Q I(0) I(1) I(1) I(1)
Y I(1) I(1) I(1) I(1)
YA I(0) I(1) I(1) I(1)
GERD I(1) I(1) I(1) I(1)
ICT I(1) I(0) I(0) I(0)
SIND I(1) I(1) I(1) I(0)
SSER I(0) I(1) I(1) I(0)
QEURO9 I(0) I(1) I(1) I(0)
TO I(1) I(1) I(1) I(1)
Legend: see Table 1.
Sources: see Annex; author s calculations with Eviews 10.
4.5 Causality tests
Running a model according to equations (5) and (6) presupposes an appropriate causality of
productivity and demand in their levels and rates of change, and the sign of the independent
variable demand must be positive; a negative sign would be meaningless, since increasing
output would depress productivity. If there were no statistical evidence for positive causality
from output/demand to productivity, it would be difficult to argue in favour of the hypothesis
of this study.
Table 3 presents a summary of pairwise panel Granger causality tests conducted with the
variables in their log-levels; constant terms are not reported. The tests reveal that the null
hypothesis of GDP Y does not cause productivity can be rejected at the 5 per cent level of
significance within three lags. At lag two, the independent variable Y has the expected positive
sign and is significant at the 5 per cent level (column 1). The tests do not fail to reject the null
of reverse causality from Q to Y (column 3): an absence of significant Q-variables and Wald
Narodowy Bank Polski18
F-statistics. For autonomous demand YA, the null of lacking Granger causality running from YA
to Q can be rejected with one lag at the 5 per cent significance level (column 2). The reverse test
shows that Q does not Granger cause YA (column 4); the Wald F statistics is insignificant although
the one-lagged Q-variable is highly significant. Hence, we find more evidence of the fact that the
history of productivity levels observed in the panel countries can be better explained by the
two aggregate demand variables than vice versa. We may apply ARDL techniques where
levels are expected to play a leading role for the interpretation of the long-run relationship
between productivity and GDP.
Table 3: Summary of pairwise Granger causality test results (variables in log-levels)a,b
Dependent variable
Independent variable Q Y YA
1 2 3 4
Y(-1) -0.086 --- 1.241*** ---
Y (-2) 0.178** --- -0.294*** ---
Y(-3) -0.057** --- -0.020 ---
YA(-1) --- 0.042** --- 0.887***
Q(-1) 0.980*** 0.813*** 0.013 0.164***
Q(-2) 0.014 --- 0.018 ---
Q(-3) -0.093 --- 0.007 ---
Wald F stat. 2.841** 17.472*** 0.614 1.846
Observations 189 209 199 210
Significance levels: *** 1 per cent, ** 5 per cent.
Legend: see Table 1. The null hypothesis of the Granger causality test is that the lagged value(s) of the independent explanatory
variable do(es) not Granger cause the dependent variable, and is not rejected if p > 0.05.b Sample: 1995-2016;
fixed cross-section effects with cross-section weights. A constant term is included in all estimations but not
shown.
F-statistics. For autonomous demand YA, the null of lacking Granger causality running from YA
to Q can be rejected with one lag at the 5 per cent significance level (column 2). The reverse test
shows that Q does not Granger cause YA (column 4); the Wald F statistics is insignificant although
the one-lagged Q-variable is highly significant. Hence, we find more evidence of the fact that the
history of productivity levels observed in the panel countries can be better explained by the
two aggregate demand variables than vice versa. We may apply ARDL techniques where
levels are expected to play a leading role for the interpretation of the long-run relationship
between productivity and GDP.
Table 3: Summary of pairwise Granger causality test results (variables in log-levels)a,b
Dependent variable
Independent variable Q Y YA
1 2 3 4
Y(-1) -0.086 --- 1.241*** ---
Y (-2) 0.178** --- -0.294*** ---
Y(-3) -0.057** --- -0.020 ---
YA(-1) --- 0.042** --- 0.887***
Q(-1) 0.980*** 0.813*** 0.013 0.164***
Q(-2) 0.014 --- 0.018 ---
Q(-3) -0.093 --- 0.007 ---
Wald F stat. 2.841** 17.472*** 0.614 1.846
Observations 189 209 199 210
Significance levels: *** 1 per cent, ** 5 per cent.
Legend: see Table 1. The null hypothesis of the Granger causality test is that the lagged value(s) of the independent explanatory
variable do(es) not Granger cause the dependent variable, and is not rejected if p > 0.05.b Sample: 1995-2016;
fixed cross-section effects with cross-section weights. A constant term is included in all estimations but not
shown.
F-statistics. For autonomous demand YA, the null of lacking Granger causality running from YA
to Q can be rejected with one lag at the 5 per cent significance level (column 2). The reverse test
shows that Q does not Granger cause YA (column 4); the Wald F statistics is insignificant although
the one-lagged Q-variable is highly significant. Hence, we find more evidence of the fact that the
history of productivity levels observed in the panel countries can be better explained by the
two aggregate demand variables than vice versa. We may apply ARDL techniques where
levels are expected to play a leading role for the interpretation of the long-run relationship
between productivity and GDP.
Table 3: Summary of pairwise Granger causality test results (variables in log-levels)a,b
Dependent variable
Independent variable Q Y YA
1 2 3 4
Y(-1) -0.086 --- 1.241*** ---
Y (-2) 0.178** --- -0.294*** ---
Y(-3) -0.057** --- -0.020 ---
YA(-1) --- 0.042** --- 0.887***
Q(-1) 0.980*** 0.813*** 0.013 0.164***
Q(-2) 0.014 --- 0.018 ---
Q(-3) -0.093 --- 0.007 ---
Wald F stat. 2.841** 17.472*** 0.614 1.846
Observations 189 209 199 210
Significance levels: *** 1 per cent, ** 5 per cent.
Legend: see Table 1. The null hypothesis of the Granger causality test is that the lagged value(s) of the independent explanatory
variable do(es) not Granger cause the dependent variable, and is not rejected if p > 0.05.b Sample: 1995-2016;
fixed cross-section effects with cross-section weights. A constant term is included in all estimations but not
shown.
19NBP Working Paper No. 318
Chapter 5
5 Estimation results and discussion
5.1 The traditional KV law: growth rates
Because we do not have sufficient clarity on the stationarity of the tested variables, this
section starts with determine the traditional KV relationship to rates of change, as they are all
defined as I(1):
(7a)
and
(7b)
(7c)
where y and ya are the rates of change) of demand Y and YA, respectively, and q is that
of productivity Q. X is the matrix of control variables, and n denotes variations of equation
(7c). Since we use stacked data for i=10 countries, fixed cross-section effects ( i) can be
included by correcting for unobserved differences between some properties of countries (e.g.,
size). The regression technique involves the use of ordinary least squares (OLS). The
behaviour of the demand variables included in the two baseline models in equations (7a)
(Model 1) and (7b) (Model 2) is controlled by additional model specifications according to
equation (7c), of which the results of four are reported here. Ratios in variables (ICT, SIND,
SSER, and TO) enter regressions of their first differences, variables QEURO9 and GERD in
their log-differences (= rates of change). Models 3 and 4 test the behaviour of demand
variables under the impact of all control variables according to equation (7c= and provide
additional information about their significance. In contrast, Model 5 includes the control
variables only. Model 6 adds a test with the significant variables in Model 3 to check the
robustness of the latter s results. Table 4 presents results of least at the 5 per cent significance
level (constant terms are not shown here).
The general conclusion is that changes in aggregate demand either as Y or YA serve as a
robust explanation for progress in productivity. All estimations shown (and those not shown)
demonstrate that the traditional KV-coefficients are significant and positive for all five model
variations with demand aggregates; GDP Y is found to be stronger than autonomous demand
YA and correspondents to the traditional Kaldor-Verdoorn coefficient of 0.5. Model 3 includes
all control variables, the KV-coefficient is only slightly reduced, and the degree of
explanative power (adjusted R2) is somewhat higher. Among the control variables, only two
Narodowy Bank Polski20
Table 4 Results of OLS estimates with fixed effects
Dependent variable: productivity rates of change q (210 observations)
Significance levels: *** 1 per cent, ** 5 per cent. Legend: see Table 1.
a Adjusted R
2 refer to models with more than one independent variable.
are significant: the assumed introduction of progress in productivity from the euro area
( 9) likely via GVC integration and an increase in the employment share of the
service sector ( ). The relevance of productivity imports can be found in all of the other
models. With respect to positive structural change, or the reallocation of labour resources to
sectors with strong productivity increase: In most of the ten CEE countries, an increase in
labour productivity of the service sector was coupled with an increase of this sector s
employment shares, while despite high productivity increase in industry was accompanied by
a decrease in employment shares (see Annex Tables A2 and A3). This helps to explain why
the variable turned out to be insignificant, while is significant and positive in
regressions.
Model 5 excludes demand aggregates. The innovation variable GERD and QEURO9 are
significant with the predicted positive sign. Model 6 includes only and in
addition to the rate of change in Y. Again, we find evidence of the fact that the significance of
these two control variables does not change the significance or strength of the demand
variable. However, it is important to note that the strength of these two variables exceeds the
strength of the demand variables at least in the short-run. But, the general conclusion remains
valid: aggregate demand is important for productivity. We should also note that the
regressions do not confirm a significant role of ICT capital or trade openness (TO) in changes
in productivity in contrast to what is shown by other research and Savelin 2018). This
Model 1 Model 2 Model 3 Model 4 Model 5 Model 6
0.578*** --- 0.552*** --- --- 0.552***
--- 0.112*** --- 0.079** --- ---
--- 0.025 0.022 0.064*** ---
--- -0.006 -0.005 -0.005 ---
--- 1.264*** 1.461*** 1.675*** 1.048***
--- 0.001 0.016 -0.005 ---
--- 0.692** 0.313 0.261 0.791**
--- -0.063 -0.006 -0.032 ---
Diagnostic statistics
R2, Adj. R
2 a
0.311 0.171 0.317 0.175 0.152 0.310
1.895 1.923 1.934 1.914 1.923 1.930
2.004** 1.585 2.062** 1.828 2.043** 2.228**
51.808*** 51.857*** 42.051*** 75.972*** 61.900*** 39.785***
82.308*** 91.712*** 92.499*** 84.793*** 91.383*** 84.941***
Table 4 Results of OLS estimates with fixed effects
Dependent variable: productivity rates of change q (210 observations)
Significance levels: *** 1 per cent, ** 5 per cent. Legend: see Table 1.
a Adjusted R
2 refer to models with more than one independent variable.
are significant: the assumed introduction of progress in productivity from the euro area
( 9) likely via GVC integration and an increase in the employment share of the
service sector ( ). The relevance of productivity imports can be found in all of the other
models. With respect to positive structural change, or the reallocation of labour resources to
sectors with strong productivity increase: In most of the ten CEE countries, an increase in
labour productivity of the service sector was coupled with an increase of this sector s
employment shares, while despite high productivity increase in industry was accompanied by
a decrease in employment shares (see Annex Tables A2 and A3). This helps to explain why
the variable turned out to be insignificant, while is significant and positive in
regressions.
Model 5 excludes demand aggregates. The innovation variable GERD and QEURO9 are
significant with the predicted positive sign. Model 6 includes only and in
addition to the rate of change in Y. Again, we find evidence of the fact that the significance of
these two control variables does not change the significance or strength of the demand
variable. However, it is important to note that the strength of these two variables exceeds the
strength of the demand variables at least in the short-run. But, the general conclusion remains
valid: aggregate demand is important for productivity. We should also note that the
regressions do not confirm a significant role of ICT capital or trade openness (TO) in changes
in productivity in contrast to what is shown by other research and Savelin 2018). This
Model 1 Model 2 Model 3 Model 4 Model 5 Model 6
0.578*** --- 0.552*** --- --- 0.552***
--- 0.112*** --- 0.079** --- ---
--- 0.025 0.022 0.064*** ---
--- -0.006 -0.005 -0.005 ---
--- 1.264*** 1.461*** 1.675*** 1.048***
--- 0.001 0.016 -0.005 ---
--- 0.692** 0.313 0.261 0.791**
--- -0.063 -0.006 -0.032 ---
Diagnostic statistics
R2, Adj. R
2 a
0.311 0.171 0.317 0.175 0.152 0.310
1.895 1.923 1.934 1.914 1.923 1.930
2.004** 1.585 2.062** 1.828 2.043** 2.228**
51.808*** 51.857*** 42.051*** 75.972*** 61.900*** 39.785***
82.308*** 91.712*** 92.499*** 84.793*** 91.383*** 84.941***
Table 4 Results of OLS estimates with fixed effects
Dependent variable: productivity rates of change q (210 observations)
Significance levels: *** 1 per cent, ** 5 per cent. Legend: see Table 1.
a Adjusted R
2 refer to models with more than one independent variable.
are significant: the assumed introduction of progress in productivity from the euro area
( 9) likely via GVC integration and an increase in the employment share of the
service sector ( ). The relevance of productivity imports can be found in all of the other
models. With respect to positive structural change, or the reallocation of labour resources to
sectors with strong productivity increase: In most of the ten CEE countries, an increase in
labour productivity of the service sector was coupled with an increase of this sector s
employment shares, while despite high productivity increase in industry was accompanied by
a decrease in employment shares (see Annex Tables A2 and A3). This helps to explain why
the variable turned out to be insignificant, while is significant and positive in
regressions.
Model 5 excludes demand aggregates. The innovation variable GERD and QEURO9 are
significant with the predicted positive sign. Model 6 includes only and in
addition to the rate of change in Y. Again, we find evidence of the fact that the significance of
these two control variables does not change the significance or strength of the demand
variable. However, it is important to note that the strength of these two variables exceeds the
strength of the demand variables at least in the short-run. But, the general conclusion remains
valid: aggregate demand is important for productivity. We should also note that the
regressions do not confirm a significant role of ICT capital or trade openness (TO) in changes
in productivity in contrast to what is shown by other research and Savelin 2018). This
Model 1 Model 2 Model 3 Model 4 Model 5 Model 6
0.578*** --- 0.552*** --- --- 0.552***
--- 0.112*** --- 0.079** --- ---
--- 0.025 0.022 0.064*** ---
--- -0.006 -0.005 -0.005 ---
--- 1.264*** 1.461*** 1.675*** 1.048***
--- 0.001 0.016 -0.005 ---
--- 0.692** 0.313 0.261 0.791**
--- -0.063 -0.006 -0.032 ---
Diagnostic statistics
R2, Adj. R
2 a
0.311 0.171 0.317 0.175 0.152 0.310
1.895 1.923 1.934 1.914 1.923 1.930
2.004** 1.585 2.062** 1.828 2.043** 2.228**
51.808*** 51.857*** 42.051*** 75.972*** 61.900*** 39.785***
82.308*** 91.712*** 92.499*** 84.793*** 91.383*** 84.941***
21NBP Working Paper No. 318
Estimation results and discussion
finding underscores the argument that technical progress is available but may not
implemented at least due to the presence of a weak market environment.
The lower part of Table 4 reports the diagnostic statistics for each model. The DW statistics
show no strong presence of autocorrelation at lag 1 in the residuals. The cross-section F
statistics reveal that fixed effects are significant merely in regressions with Y. The distribution
of fixed effects suggests that the intercept (the constant term) at the productivity axis is
reduced for larger countries (Poland, Romania, and Bulgaria) and elevated for smaller
countries, e.g., the Baltics (see Table A4 of the Annex). Cross-section effects may correct for
size differences. Jarque-Bera coefficients exhibit a non-normal distribution in residuals due to
high levels of leptokurtosis. However, this is typical for panel regressions without cross-
section weights. When including cross-section weights (not shown in the table), Jarque-Bera
coefficients are reduced, and become even insignificant in some models. The cross-section
dependence test (Breusch-Pagan) does not reject the null of an absence of cross-section
dependence in both estimations.
5.2 The bounds tested ARDL approach
Although the previous section confirms the KV law in its traditional version, the models fail
to provide a long-run perspective. Yet we have no idea which forces shape short-term rates of
change or differences into a stable long-run relationship if there is any at all. In this study, it
is hypothesized that there must be a stable relationship between the levels of variables when a
stable relationship between the rates of variable change exist. If this is so, there must be a
process of adjustment at work, which, in the case of a disparity, pushes the system towards its
long-run equilibrium in each period. The bounds tested ARDL approach can provide
additional insights into the assumed dynamics. Basically, the ARDL instrument is an
unrestricted error-correction model (ECM) of the following form:
(8)
where Qit is (log) productivity and Yit is the (log) demand variable. Xit includes all or some of
the control variables when they enter the model. Zit includes all variables, including both
independent ones and the dependent variable Q. 0 is an intercept term representing the
structural similarities between countries, k = are vectors of slope coefficients,
which are assumed to be constant over cross-sections i denotes cross-section fixed
effects capturing structural dissimilarities between the countries and assumed to be constant
over time. 1 and 2 determine the long-run persistence of the level variables with ( 2/ 1) used
Narodowy Bank Polski22
as the GDP-multiplier or long-run KV coefficient; 4 determines the short-run adjustment
made to this equilibrium (in the present case rates of change), as all level variables are given
in their logs. Further, p is the specific lag-length of each differenced variable.
The bounds tested ARDL procedure follows Pesaran and Shin (1999). It allows the constant
term, error variances and short-run parameters to vary by country via fixed effects (Oshota
and Badejo 2015). The procedure begins with selecting the optimal lag-length p for each
variable in equation 8. Due to the short time span of time-series data available for each
country, the maximum lag-order is set to 4, and the Akaike Information Criterion (AIC) is
applied to find the optimal lag-structure. Once this is done, the ECM used in equation (8) is
reparametrized. The F-statistics (Wald test) is tested against Pesaran et al. s (2001) critical
value bounds. When the F-value exceeds the upper bound, there is evidence of cointegration
between the levels of the variables irrespective whether they are I(0) or I(1). When the value
falls below the lower bound, the variables are I(0), and cointegration is not possible. When the
F-statistic falls between the bounds, the test is inconclusive. When the test confirms the
presence of a long-run relationship, the residuals from this estimation will be tested against
the dynamic stability of the equilibrium, normal distribution, cross-section dependence, and
heteroskedasticity. Finally, the long-run relationship is estimated and analysed with respect to
the cointegration term. To this end, the short-run variables are set to zero, and equation (8)
reduces to:
(9)
The one-lag residuals t-1 replace the one-lag-level variables included in equation (8) and
change the unrestricted ECM into a restricted ECM, as the cointegration term corrects
potential disparities between the actual dependent variable and its equilibrium for each period:
(10)
The condition of cointegration and adjustment according to the long-run equilibrium is
fulfilled when the cointegration term t-1 is negative and significant at the 5 per cent level (p
< 0.05) at least. The regression equations are evaluated against a series of diagnostic tests:
The redundant fixed effects test confirms the significance of country specific fixed effects or
allegedly of the influence of large differences between the countries. The Jarque-Bera
coefficient captures distributional properties of the residuals; estimations with a non-normal
23NBP Working Paper No. 318
Estimation results and discussion
distribution would be less efficient. When the time-series dimension is larger in panels than
the cross-sectional dimension as is observed in the present case, cross-sectional dependence
may violate the conditions of homoskedasticity. Therefore, the Breusch-Pagan test is
performed. Finally, the EC equation is estimated with autoregressive terms that replace the
lagged dependent variables to test the dynamic stability of the computed long-run equilibrium
between productivity and GDP. The model is dynamically stable when inverse roots are
positioned within the unit circle.
The estimation results for six models (7-12) are presented in Table 5; the coefficients of the
lagged dependent variables and all other lagged independent variables are not shown when
they are not significant at p < 0.05 at least. The constant terms and the fixed effects are
reported in Table A4 in the Annex. These models are not precisely the same, but somewhat
similar to models 1-6 shown in Table 4. The second row shows the selected ARDL lag
structure for the Z-variables; the first figure denotes the number of lags of the differenced
dependent variable and the second of the differenced demand variable followed by the other
variables in the order that they appear in the table. All estimations account for cross-section
effects. Before discussing the estimation outcomes, we review the quality and efficiency of
the models:
- The cointegration terms are negative and significant in all of the estimations. This is what
one should expect when there is cointegration between variable levels notwithstanding the
presence of I(0) or I(1) values. The value of the adjustment parameter implies that roughly
0.22 to 0.28 per cent of any disequilibrium between the level time series is corrected
within one period (one year).
- The cross-section F statistics show that fixed cross-sectional effects (shown in Table A2
of the Annex) are significant. As was expected, fixed effects correct for size differences
between the countries.
- As observed in the previous estimations, the Jarque-Bera test reveals a non-normal
distribution of residuals due to high degrees of leptokurtosis. The Jarque-Bera coefficients
improve considerably when cross-section weights are applied to the panel options (results
are not shown here).
- The Breusch-Pagan test reveals no cross-sectional dependence in the models.
Narodowy Bank Polski24
Table 5: ARDL estimation results (unrestricted EC models)a
Dependent variable: q; 170 observations
Model 8 Model 9 Model 10 Model 11 Model 12
ARDL structure 4,1 4,2,1,1,1,1,2, 4,2,1,1,1,1,2, 4,1,2 4,1,1,1
Long-run equation
Q(-1) -0.236*** -0.234*** -0.194*** -0.272*** -0.261*** -0.235***
Y(-1) 0.177*** --- 0.152** --- 0.160*** 0.190***
YA(-1) --- 0.052*** --- 0.094*** --- ---
GERD(-1) --- --- 0.005 -0.048 --- -0.004
ICT(-1) --- --- -0.011 -0.017 --- ---
QEURO9(-1) --- -0.138 0.350 --- ---
SIND(-1) --- 0.067 0.193** --- 0.131
SSER(-1) --- 0.225*** 0.079 0.159** ---
TO(-1) --- -0.050 0.002 --- ---
Long-run KV termb
0.747 0.784 0.346 0.613 0.806
Short-run equation
Cointegration term -1) -0.255*** -0.273** -0.222*** -0.245*** -0.274*** -0.284***
0.528*** --- 0.378*** --- 0.552*** 0.454***
-1) -0.181** --- -0.056 --- -0.088 -0.297***
-2) --- --- 0.153 --- --- ---
--- 0.171*** --- 0.193*** --- ---
-1) --- -0.055** --- 0.050 --- ---
-2) --- --- --- -0.055 --- ---
Traditional KV termc
0.347 0.116 0.378 0.193 0.552 0.157
--- --- 0.003 -0.070** --- 0.023
-1) --- --- 0.051 0.106*** --- 0.031
--- --- 1.894*** 2.017*** --- ---
-1) --- --- -0.317 -1.257*** --- ---
-1) --- --- 0.238** 0.135 --- 0.077
-2) --- --- 0.198 0.079 0.244 ---
--- --- -0.136** -0.033 --- ---
Diagnostic statistics
R2, adj. R squared
d 0.438 0.434 0.455 0.532 0.394 0.446
Jarque Bera 46.852*** 24.181*** 24.074*** 6.474*** 51.416*** 64.628***
Breusch-Pagran 62.990*** 78.619*** 65.893** 60.023*** 64.900*** 70.565***
Cross-Section F 5.163*** 4.138*** 2.932*** 4.758*** 5.257*** 4.934***
Bounds test Wald F 25.374*** 24.914*** 6.609*** 8.989*** 14.188*** 11.491***
Upper critical valuee
4.85 4.85 3.39 3.39 4.35 4.01
Significance levels: *** p < 0.01; ** p < 0.05; Legend: see Table 1
a A all variables in their logs.
b -(Y(-1))/(-Q(-1) or (YA(-1))/-Q(-1).
c Only significant values.
d Adj. R
2 refer
to models with more than one independent variables. e Critical values at the 0.050 significance level (Pesaran et
al. 2001, Table CI(III), P. 300.
Sources: Author s calculations.
- F-statistics derived from the Wald-test clearly exceed Pesaran et al. s (2001) upper critical
value bound, which applies to (k+1 = 2) variables. Thus, the null hypothesis of the
Table 5: ARDL estimation results (unrestricted EC models)a
Dependent variable: q; 170 observations
Model 8 Model 9 Model 10 Model 11 Model 12
ARDL structure 4,1 4,2,1,1,1,1,2, 4,2,1,1,1,1,2, 4,1,2 4,1,1,1
Long-run equation
Q(-1) -0.236*** -0.234*** -0.194*** -0.272*** -0.261*** -0.235***
Y(-1) 0.177*** --- 0.152** --- 0.160*** 0.190***
YA(-1) --- 0.052*** --- 0.094*** --- ---
GERD(-1) --- --- 0.005 -0.048 --- -0.004
ICT(-1) --- --- -0.011 -0.017 --- ---
QEURO9(-1) --- -0.138 0.350 --- ---
SIND(-1) --- 0.067 0.193** --- 0.131
SSER(-1) --- 0.225*** 0.079 0.159** ---
TO(-1) --- -0.050 0.002 --- ---
Long-run KV termb
0.747 0.784 0.346 0.613 0.806
Short-run equation
Cointegration term -1) -0.255*** -0.273** -0.222*** -0.245*** -0.274*** -0.284***
0.528*** --- 0.378*** --- 0.552*** 0.454***
-1) -0.181** --- -0.056 --- -0.088 -0.297***
-2) --- --- 0.153 --- --- ---
--- 0.171*** --- 0.193*** --- ---
-1) --- -0.055** --- 0.050 --- ---
-2) --- --- --- -0.055 --- ---
Traditional KV termc
0.347 0.116 0.378 0.193 0.552 0.157
--- --- 0.003 -0.070** --- 0.023
-1) --- --- 0.051 0.106*** --- 0.031
--- --- 1.894*** 2.017*** --- ---
-1) --- --- -0.317 -1.257*** --- ---
-1) --- --- 0.238** 0.135 --- 0.077
-2) --- --- 0.198 0.079 0.244 ---
--- --- -0.136** -0.033 --- ---
Diagnostic statistics
R2, adj. R squared
d 0.438 0.434 0.455 0.532 0.394 0.446
Jarque Bera 46.852*** 24.181*** 24.074*** 6.474*** 51.416*** 64.628***
Breusch-Pagran 62.990*** 78.619*** 65.893** 60.023*** 64.900*** 70.565***
Cross-Section F 5.163*** 4.138*** 2.932*** 4.758*** 5.257*** 4.934***
Bounds test Wald F 25.374*** 24.914*** 6.609*** 8.989*** 14.188*** 11.491***
Upper critical valuee
4.85 4.85 3.39 3.39 4.35 4.01
Significance levels: *** p < 0.01; ** p < 0.05; Legend: see Table 1
a A all variables in their logs.
b -(Y(-1))/(-Q(-1) or (YA(-1))/-Q(-1).
c Only significant values.
d Adj. R
2 refer
to models with more than one independent variables. e Critical values at the 0.050 significance level (Pesaran et
al. 2001, Table CI(III), P. 300.
Sources: Author s calculations.
- F-statistics derived from the Wald-test clearly exceed Pesaran et al. s (2001) upper critical
value bound, which applies to (k+1 = 2) variables. Thus, the null hypothesis of the
Table 5: ARDL estimation results (unrestricted EC models)a
Dependent variable: q; 170 observations
Model 8 Model 9 Model 10 Model 11 Model 12
ARDL structure 4,1 4,2,1,1,1,1,2, 4,2,1,1,1,1,2, 4,1,2 4,1,1,1
Long-run equation
Q(-1) -0.236*** -0.234*** -0.194*** -0.272*** -0.261*** -0.235***
Y(-1) 0.177*** --- 0.152** --- 0.160*** 0.190***
YA(-1) --- 0.052*** --- 0.094*** --- ---
GERD(-1) --- --- 0.005 -0.048 --- -0.004
ICT(-1) --- --- -0.011 -0.017 --- ---
QEURO9(-1) --- -0.138 0.350 --- ---
SIND(-1) --- 0.067 0.193** --- 0.131
SSER(-1) --- 0.225*** 0.079 0.159** ---
TO(-1) --- -0.050 0.002 --- ---
Long-run KV termb
0.747 0.784 0.346 0.613 0.806
Short-run equation
Cointegration term -1) -0.255*** -0.273** -0.222*** -0.245*** -0.274*** -0.284***
0.528*** --- 0.378*** --- 0.552*** 0.454***
-1) -0.181** --- -0.056 --- -0.088 -0.297***
-2) --- --- 0.153 --- --- ---
--- 0.171*** --- 0.193*** --- ---
-1) --- -0.055** --- 0.050 --- ---
-2) --- --- --- -0.055 --- ---
Traditional KV termc
0.347 0.116 0.378 0.193 0.552 0.157
--- --- 0.003 -0.070** --- 0.023
-1) --- --- 0.051 0.106*** --- 0.031
--- --- 1.894*** 2.017*** --- ---
-1) --- --- -0.317 -1.257*** --- ---
-1) --- --- 0.238** 0.135 --- 0.077
-2) --- --- 0.198 0.079 0.244 ---
--- --- -0.136** -0.033 --- ---
Diagnostic statistics
R2, adj. R squared
d 0.438 0.434 0.455 0.532 0.394 0.446
Jarque Bera 46.852*** 24.181*** 24.074*** 6.474*** 51.416*** 64.628***
Breusch-Pagran 62.990*** 78.619*** 65.893** 60.023*** 64.900*** 70.565***
Cross-Section F 5.163*** 4.138*** 2.932*** 4.758*** 5.257*** 4.934***
Bounds test Wald F 25.374*** 24.914*** 6.609*** 8.989*** 14.188*** 11.491***
Upper critical valuee
4.85 4.85 3.39 3.39 4.35 4.01
Significance levels: *** p < 0.01; ** p < 0.05; Legend: see Table 1
a A all variables in their logs.
b -(Y(-1))/(-Q(-1) or (YA(-1))/-Q(-1).
c Only significant values.
d Adj. R
2 refer
to models with more than one independent variables. e Critical values at the 0.050 significance level (Pesaran et
al. 2001, Table CI(III), P. 300.
Sources: Author s calculations.
- F-statistics derived from the Wald-test clearly exceed Pesaran et al. s (2001) upper critical
value bound, which applies to (k+1 = 2) variables. Thus, the null hypothesis of the
25NBP Working Paper No. 318
Estimation results and discussion
presence of no level relationship in the productivity equation is rejected irrespective of
whether the variables are all I(0) or I(1) values or a mixture of both.
- AR (1, 2, 3, and 4) processes show that the inverse roots of the ARMA polynomials are
located strictly within the unit circle (Figure A1 of the Annex). Hence, the time-path of
productivity Q will eventually settle after a shock to the pre-shock level.
In summary, the models reported in Table 5 are of high quality and efficient; this
conclusion remains valid for additional estimations of different variable compositions,
which are not reported here.
We now discuss the results of the individual models.
The baseline models 7 and 8 confirm the existence of a characteristic equation for levels
underlying the KV law. The lagged levels of explanatory variables Y and YA are highly
significant and have a positive impact on the levels and the growth rate of productivity. Over
the long-run, a log unit of 1 in GDP Y is related to units in productivity (and
in 0.222 units in case of autonomous demand YA. The reader should note that the results are
in log values; converted into their default values, each million euro of GDP is linked with 2/3
(=0.666) euro per hour worked. This is the true long-run KV coefficient. Over the short-run,
a demand stimulus of 1 per cent is associated with a productivity growth rate of nearly 0.347
per cent for Y and of 0.116 per cent for YA. Presumably, a growth rate of Y should cause
productivity to grow less than observed in Model 1 above, echoing the coefficients that
Kaldor and Verdoorn found. Deleidi et al. (2018) found very different coefficients for more
recent periods ranging between 0.027 for the Netherlands and 0.640 for France. In contrast,
the short-term KV coefficient is higher in the ARDL estimates than in the OLS estimates (a
comparison of Models 7 and 2).
Models 9-12 control for the robustness of estimation results of the former models by
including various variables as discussed previously. Models 9 and 10 confirm that the
inclusion of all other non-demand variables does not impair the validity of the long-run KV
law. In model 9, the value of the Y-coefficient is only slightly reduced, and the long-run KV
term is even increased. As in model 3 above (Table 4), an increase in the employment share
of the service sector contributes significantly to an increase in productivity while the import
of productivity (QEURO9) appears to be insignificant over the long-run. In the estimate with
autonomous demand YA, an increase in the employment share of the industry but not of the
Narodowy Bank Polski26
service sector is significant a somewhat unexpected result. Again, all other control variables
are found to have no impact on long-run productivity; if at all, they are relevant for short-run
dynamics only. This is reason enough to test the robustness of previous estimations by only
including significant variable SSER (the service sector) from model 9 and variable SIND.
Indeed, Model 11 confirms the relevance of employment shifts from the other to the service
sector for aggregate productivity adding to demand; the traditional KV-term approaches the
values of short-term estimates included in Table 4. The same cannot be concluded for
industry (SIND), which is included in model 12 as the sole non-demand variable.
27NBP Working Paper No. 318
Chapter 6
6 Concluding remarks
Granger causality tests, estimations with least squares and the application of ARDL co-
integration techniques confirm the presence of the KV law for a panel of ten CEE countries.
We also find that progress in productivity is driven by a strong long-run equilibrium
relationship with output/demand. This stands in contrast to the majority literature, which
disregards the long-run impact of demand growth on productivity growth. Our results confirm
the law for the region; slower productivity growth is not due to adverse technological
progress but to weakening external and domestic demand. Without disregarding the role of
supply-side policies such as those facilitating innovation, structural change, trade openness
and inclusion in global value chains, changes in long-run productivity in the region is
substantially attributable to changes in aggregate demand. The recent (from the mid-2000s)
decline in productivity can thus safely be assumed to be mainly the outcome of weakening or
stagnant output/demand, complemented by employment shifts to high-productive service
sectors, at some cost even from high-productive industry. Cyclical effects, e.g. the crises after
2008, have rather strengthened these two long-run movements.
However, this conclusion should not be misread in favour of unthinking demand-side fiscal
policies. Demand-side factors include domestic and external market conditions, and in
countries with small domestic markets, such as the Baltic countries, Slovenia, and Slovakia,
with export shares of GDP of 80 per cent and more, the long-term stagnation in demand in
their (mainly EU) export markets matters, and national demand management has no relevant
influence. This is not so for economies with large domestic markets and their own currencies
such Poland s with an export share of 55 per cent (or Romania s with only 42 per cent). Here,
an active government may have an effective impact on the growth rates of GDP, productivity
and income convergence.
Narodowy Bank Polski28
Bibliography
Bibliography
Ahrend, 2015. The Digital Economy, ICT and Economic Growth in the CEE Countries . Olsztyn
Economic Journal, 10(3), 247-263.
Bah, E. M, and J. C. Brada. 2009. Total Factor Productivity Growth, Structural Change and
Convergence in the New Members of the European Union. Comparative Economic Studies,
vol. 51 (4), 421-447.
Burda, M. C. and B. Severgnini. 2009. TFP Growth in Old and New Europe. Comparative
Economic Studies, vol. 51 (4), 447-467.
Chiacchio, F., K. Gradeva, and P. Lopez-Garcia. 2018. The post-crisis TFP growth slowdown in CEE
countries: exploring the role of Global Value Chains. ECB Working Paper Series No. 2143
(April).
Deleidi, M., W. P. Meloni, and A. Stirati 2018. Structural change, labor productivity and the Kaldor-
Verdoorn law: Evidence from European countries , Universitá Degli Studi Roma Tre,
Dipartimento Di Economia, Working Paper 239.
De Vries, K. and A. A. Erumban. 2017. Total Economic Database. A detailed guide to its sources and
methods. Pdf-File via https://www.conference-
board.org/data/economydatabase/index.cfm?id=27762.
Gomulka, S. 2016. Poland's economic and social transformation 1989-2014 and contemporary
challenges . Central Bank of Turkey, Central Bank Review 16, 19-23.
Hartwig, J. 2011. Testing the Baumol Nordhaus model with EU Klems data . Review of Income and
Wealth. Series 57, Number 3, September 2011, 471-489.
Jorgenson, D. W. and K. Vu. 2010. Potential growth of the world economy . Journal of Policy
Modeling, 32(5): 615 631.
Kaldor, N. 1966. Causes of the Slow Rate of Economic Growth in the United Kingdom. Cambridge,
UK: Cambridge University Press.
Kaldor, N. 1972. The Irrelevance of Equilibrium Economics. Economic Journal, 82 (328), 1237
1255.
Krugman, P. 1979, Increasing Returns, Monopolistic Competition, and International Trade, Journal
of International Economics, 9(4), 469 479.
Levenko, N., K. Oja, K. Staehr. 2019. Total factor productivity growth in Central and Eastern Europe
before, during and after the global financial crisis. Post-Communist Economies, vol. 31(2) 1-
24.
Magacho, G. R., J. S. L. McCombie . 2017. Verdoorn s law and productivity dynamics: An empirical
investigation into the demand and supply approaches . Journal of Post-Keynesian Economics,
vol. 40, issue 4, 600-621
McCombie, J. S.L. and M. R. M. Spreafico. 2016. Kaldor s technical progress function and the
verdoorn law revisited . Cambridge Journal of Economics, vol. 40 (4), 1117-1136.
Bibliography
Ahrend, 2015. The Digital Economy, ICT and Economic Growth in the CEE Countries . Olsztyn
Economic Journal, 10(3), 247-263.
Bah, E. M, and J. C. Brada. 2009. Total Factor Productivity Growth, Structural Change and
Convergence in the New Members of the European Union. Comparative Economic Studies,
vol. 51 (4), 421-447.
Burda, M. C. and B. Severgnini. 2009. TFP Growth in Old and New Europe. Comparative
Economic Studies, vol. 51 (4), 447-467.
Chiacchio, F., K. Gradeva, and P. Lopez-Garcia. 2018. The post-crisis TFP growth slowdown in CEE
countries: exploring the role of Global Value Chains. ECB Working Paper Series No. 2143
(April).
Deleidi, M., W. P. Meloni, and A. Stirati 2018. Structural change, labor productivity and the Kaldor-
Verdoorn law: Evidence from European countries , Universitá Degli Studi Roma Tre,
Dipartimento Di Economia, Working Paper 239.
De Vries, K. and A. A. Erumban. 2017. Total Economic Database. A detailed guide to its sources and
methods. Pdf-File via https://www.conference-
board.org/data/economydatabase/index.cfm?id=27762.
Gomulka, S. 2016. Poland's economic and social transformation 1989-2014 and contemporary
challenges . Central Bank of Turkey, Central Bank Review 16, 19-23.
Hartwig, J. 2011. Testing the Baumol Nordhaus model with EU Klems data . Review of Income and
Wealth. Series 57, Number 3, September 2011, 471-489.
Jorgenson, D. W. and K. Vu. 2010. Potential growth of the world economy . Journal of Policy
Modeling, 32(5): 615 631.
Kaldor, N. 1966. Causes of the Slow Rate of Economic Growth in the United Kingdom. Cambridge,
UK: Cambridge University Press.
Kaldor, N. 1972. The Irrelevance of Equilibrium Economics. Economic Journal, 82 (328), 1237
1255.
Krugman, P. 1979, Increasing Returns, Monopolistic Competition, and International Trade, Journal
of International Economics, 9(4), 469 479.
Levenko, N., K. Oja, K. Staehr. 2019. Total factor productivity growth in Central and Eastern Europe
before, during and after the global financial crisis. Post-Communist Economies, vol. 31(2) 1-
24.
Magacho, G. R., J. S. L. McCombie . 2017. Verdoorn s law and productivity dynamics: An empirical
investigation into the demand and supply approaches . Journal of Post-Keynesian Economics,
vol. 40, issue 4, 600-621
McCombie, J. S.L. and M. R. M. Spreafico. 2016. Kaldor s technical progress function and the
verdoorn law revisited . Cambridge Journal of Economics, vol. 40 (4), 1117-1136.
Bibliography
Ahrend, 2015. The Digital Economy, ICT and Economic Growth in the CEE Countries . Olsztyn
Economic Journal, 10(3), 247-263.
Bah, E. M, and J. C. Brada. 2009. Total Factor Productivity Growth, Structural Change and
Convergence in the New Members of the European Union. Comparative Economic Studies,
vol. 51 (4), 421-447.
Burda, M. C. and B. Severgnini. 2009. TFP Growth in Old and New Europe. Comparative
Economic Studies, vol. 51 (4), 447-467.
Chiacchio, F., K. Gradeva, and P. Lopez-Garcia. 2018. The post-crisis TFP growth slowdown in CEE
countries: exploring the role of Global Value Chains. ECB Working Paper Series No. 2143
(April).
Deleidi, M., W. P. Meloni, and A. Stirati 2018. Structural change, labor productivity and the Kaldor-
Verdoorn law: Evidence from European countries , Universitá Degli Studi Roma Tre,
Dipartimento Di Economia, Working Paper 239.
De Vries, K. and A. A. Erumban. 2017. Total Economic Database. A detailed guide to its sources and
methods. Pdf-File via https://www.conference-
board.org/data/economydatabase/index.cfm?id=27762.
Gomulka, S. 2016. Poland's economic and social transformation 1989-2014 and contemporary
challenges . Central Bank of Turkey, Central Bank Review 16, 19-23.
Hartwig, J. 2011. Testing the Baumol Nordhaus model with EU Klems data . Review of Income and
Wealth. Series 57, Number 3, September 2011, 471-489.
Jorgenson, D. W. and K. Vu. 2010. Potential growth of the world economy . Journal of Policy
Modeling, 32(5): 615 631.
Kaldor, N. 1966. Causes of the Slow Rate of Economic Growth in the United Kingdom. Cambridge,
UK: Cambridge University Press.
Kaldor, N. 1972. The Irrelevance of Equilibrium Economics. Economic Journal, 82 (328), 1237
1255.
Krugman, P. 1979, Increasing Returns, Monopolistic Competition, and International Trade, Journal
of International Economics, 9(4), 469 479.
Levenko, N., K. Oja, K. Staehr. 2019. Total factor productivity growth in Central and Eastern Europe
before, during and after the global financial crisis. Post-Communist Economies, vol. 31(2) 1-
24.
Magacho, G. R., J. S. L. McCombie . 2017. Verdoorn s law and productivity dynamics: An empirical
investigation into the demand and supply approaches . Journal of Post-Keynesian Economics,
vol. 40, issue 4, 600-621
McCombie, J. S.L. and M. R. M. Spreafico. 2016. Kaldor s technical progress function and the
verdoorn law revisited . Cambridge Journal of Economics, vol. 40 (4), 1117-1136.
Bibliography
Ahrend, 2015. The Digital Economy, ICT and Economic Growth in the CEE Countries . Olsztyn
Economic Journal, 10(3), 247-263.
Bah, E. M, and J. C. Brada. 2009. Total Factor Productivity Growth, Structural Change and
Convergence in the New Members of the European Union. Comparative Economic Studies,
vol. 51 (4), 421-447.
Burda, M. C. and B. Severgnini. 2009. TFP Growth in Old and New Europe. Comparative
Economic Studies, vol. 51 (4), 447-467.
Chiacchio, F., K. Gradeva, and P. Lopez-Garcia. 2018. The post-crisis TFP growth slowdown in CEE
countries: exploring the role of Global Value Chains. ECB Working Paper Series No. 2143
(April).
Deleidi, M., W. P. Meloni, and A. Stirati 2018. Structural change, labor productivity and the Kaldor-
Verdoorn law: Evidence from European countries , Universitá Degli Studi Roma Tre,
Dipartimento Di Economia, Working Paper 239.
De Vries, K. and A. A. Erumban. 2017. Total Economic Database. A detailed guide to its sources and
methods. Pdf-File via https://www.conference-
board.org/data/economydatabase/index.cfm?id=27762.
Gomulka, S. 2016. Poland's economic and social transformation 1989-2014 and contemporary
challenges . Central Bank of Turkey, Central Bank Review 16, 19-23.
Hartwig, J. 2011. Testing the Baumol Nordhaus model with EU Klems data . Review of Income and
Wealth. Series 57, Number 3, September 2011, 471-489.
Jorgenson, D. W. and K. Vu. 2010. Potential growth of the world economy . Journal of Policy
Modeling, 32(5): 615 631.
Kaldor, N. 1966. Causes of the Slow Rate of Economic Growth in the United Kingdom. Cambridge,
UK: Cambridge University Press.
Kaldor, N. 1972. The Irrelevance of Equilibrium Economics. Economic Journal, 82 (328), 1237
1255.
Krugman, P. 1979, Increasing Returns, Monopolistic Competition, and International Trade, Journal
of International Economics, 9(4), 469 479.
Levenko, N., K. Oja, K. Staehr. 2019. Total factor productivity growth in Central and Eastern Europe
before, during and after the global financial crisis. Post-Communist Economies, vol. 31(2) 1-
24.
Magacho, G. R., J. S. L. McCombie . 2017. Verdoorn s law and productivity dynamics: An empirical
investigation into the demand and supply approaches . Journal of Post-Keynesian Economics,
vol. 40, issue 4, 600-621
McCombie, J. S.L. and M. R. M. Spreafico. 2016. Kaldor s technical progress function and the
verdoorn law revisited . Cambridge Journal of Economics, vol. 40 (4), 1117-1136.
https://www.conferenceboard.org/data/economydatabase/index.cfm?id=27762.
29NBP Working Paper No. 318
Bibliography
Nkoro, E. and A. K. Uko. 2016. Autoregressive Distributed Lag (ARDL) cointegration technique:
application and interpretation . Journal of Statistical and Econometric Methods, vol. 5, no.
4, 63-91.
OECD. 2016. Promoting Productivity and Equality: a twin challenge . OECD Economic Outlook,
Volume 2016 Issue 1: Chapter 2, 59-84, Paris.
Oshota, S. O., A. A. Badejo. 2015. What DrivesCurrent Account Balance in West Africa States:
Evidence from Panel ARDL . Journal of International and Global Economic Studies, vol.
8(2), 91-105.
Ozanne, A. G. 2006. A Bounds Test Approach to The Study of Level Relationships in a Panel of
High-Performing Asian Economies (HPAES) , Economics Discussion Papers Series No. 607).
University of Otago. https://ourarchive.otago.ac.nz/handle/10523/1045
Pesaran, M.H., and Y. Shin. 1999. An Autoregressive Distributed Lag Modeling Approach to
Cointegration Analysis . In: Strom, S., Holly, A., Diamond, P. (Eds.), Centennial Volume of
Rangar Frisch, Cambridge University Press, Cambridge.
Pesaran, M. H., Shin, Y. and Smith, R. J. 2001. Bounds testing approaches to the analysis of level
relationships . Journal of Applied Econometrics, 16, pp. 289 326.
Piatkowski, M. 2003. Does ICT Investment Matter for Output Growth and Labor Productivity in
Transition Economies? TIGER Working Paper Series, 47.
Piatkowski, M. 2004. The Impact of ICT on Growth in Transition Economies . MPRA Paper, 29399
(14).
Podkaminer, L. 2017: Labour productivity growth slowdown: an effect of economic stagnation rather
than ist cause? Acta Oeconomica, Vol. 67 (S), 67-77.
Riley, R., A. Rincon-Aznar and L. Samek. 2018. Below the Aggregate: A Sectoral Account of the
UK Productivity Puzzle . ESCoE Discussion Paper 2018-06, London U.K.
Stöllinger, R. 2016. Structural change and global value chains in the EU . Empirica, vol. 43, no. 4,
801-830.
Verdoorn, P. J. 1949. Fattori che Regolano lo Sviluppo della Produttivita del Lavoro. L Industria,
1, 3 10. English translation by A. P. Thirlwall, in J. S. L. McCombie, M. Pugno, and B. Soro
(eds.), Productivity Growth and Economic Performance: Essays in Verdoorn s Law.
Basingstoke: Palgrave MacMillan, 2002, 28-36.
2018. Real Convergence in Central, Eastern and South-Eastern Europe . ECB
Occasional Paper No. 212.
Nkoro, E. and A. K. Uko. 2016. Autoregressive Distributed Lag (ARDL) cointegration technique:
application and interpretation . Journal of Statistical and Econometric Methods, vol. 5, no.
4, 63-91.
OECD. 2016. Promoting Productivity and Equality: a twin challenge . OECD Economic Outlook,
Volume 2016 Issue 1: Chapter 2, 59-84, Paris.
Oshota, S. O., A. A. Badejo. 2015. What DrivesCurrent Account Balance in West Africa States:
Evidence from Panel ARDL . Journal of International and Global Economic Studies, vol.
8(2), 91-105.
Ozanne, A. G. 2006. A Bounds Test Approach to The Study of Level Relationships in a Panel of
High-Performing Asian Economies (HPAES) , Economics Discussion Papers Series No. 607).
University of Otago. https://ourarchive.otago.ac.nz/handle/10523/1045
Pesaran, M.H., and Y. Shin. 1999. An Autoregressive Distributed Lag Modeling Approach to
Cointegration Analysis . In: Strom, S., Holly, A., Diamond, P. (Eds.), Centennial Volume of
Rangar Frisch, Cambridge University Press, Cambridge.
Pesaran, M. H., Shin, Y. and Smith, R. J. 2001. Bounds testing approaches to the analysis of level
relationships . Journal of Applied Econometrics, 16, pp. 289 326.
Piatkowski, M. 2003. Does ICT Investment Matter for Output Growth and Labor Productivity in
Transition Economies? TIGER Working Paper Series, 47.
Piatkowski, M. 2004. The Impact of ICT on Growth in Transition Economies . MPRA Paper, 29399
(14).
Podkaminer, L. 2017: Labour productivity growth slowdown: an effect of economic stagnation rather
than ist cause? Acta Oeconomica, Vol. 67 (S), 67-77.
Riley, R., A. Rincon-Aznar and L. Samek. 2018. Below the Aggregate: A Sectoral Account of the
UK Productivity Puzzle . ESCoE Discussion Paper 2018-06, London U.K.
Stöllinger, R. 2016. Structural change and global value chains in the EU . Empirica, vol. 43, no. 4,
801-830.
Verdoorn, P. J. 1949. Fattori che Regolano lo Sviluppo della Produttivita del Lavoro. L Industria,
1, 3 10. English translation by A. P. Thirlwall, in J. S. L. McCombie, M. Pugno, and B. Soro
(eds.), Productivity Growth and Economic Performance: Essays in Verdoorn s Law.
Basingstoke: Palgrave MacMillan, 2002, 28-36.
2018. Real Convergence in Central, Eastern and South-Eastern Europe . ECB
Occasional Paper No. 212.
Nkoro, E. and A. K. Uko. 2016. Autoregressive Distributed Lag (ARDL) cointegration technique:
application and interpretation . Journal of Statistical and Econometric Methods, vol. 5, no.
4, 63-91.
OECD. 2016. Promoting Productivity and Equality: a twin challenge . OECD Economic Outlook,
Volume 2016 Issue 1: Chapter 2, 59-84, Paris.
Oshota, S. O., A. A. Badejo. 2015. What DrivesCurrent Account Balance in West Africa States:
Evidence from Panel ARDL . Journal of International and Global Economic Studies, vol.
8(2), 91-105.
Ozanne, A. G. 2006. A Bounds Test Approach to The Study of Level Relationships in a Panel of
High-Performing Asian Economies (HPAES) , Economics Discussion Papers Series No. 607).
University of Otago. https://ourarchive.otago.ac.nz/handle/10523/1045
Pesaran, M.H., and Y. Shin. 1999. An Autoregressive Distributed Lag Modeling Approach to
Cointegration Analysis . In: Strom, S., Holly, A., Diamond, P. (Eds.), Centennial Volume of
Rangar Frisch, Cambridge University Press, Cambridge.
Pesaran, M. H., Shin, Y. and Smith, R. J. 2001. Bounds testing approaches to the analysis of level
relationships . Journal of Applied Econometrics, 16, pp. 289 326.
Piatkowski, M. 2003. Does ICT Investment Matter for Output Growth and Labor Productivity in
Transition Economies? TIGER Working Paper Series, 47.
Piatkowski, M. 2004. The Impact of ICT on Growth in Transition Economies . MPRA Paper, 29399
(14).
Podkaminer, L. 2017: Labour productivity growth slowdown: an effect of economic stagnation rather
than ist cause? Acta Oeconomica, Vol. 67 (S), 67-77.
Riley, R., A. Rincon-Aznar and L. Samek. 2018. Below the Aggregate: A Sectoral Account of the
UK Productivity Puzzle . ESCoE Discussion Paper 2018-06, London U.K.
Stöllinger, R. 2016. Structural change and global value chains in the EU . Empirica, vol. 43, no. 4,
801-830.
Verdoorn, P. J. 1949. Fattori che Regolano lo Sviluppo della Produttivita del Lavoro. L Industria,
1, 3 10. English translation by A. P. Thirlwall, in J. S. L. McCombie, M. Pugno, and B. Soro
(eds.), Productivity Growth and Economic Performance: Essays in Verdoorn s Law.
Basingstoke: Palgrave MacMillan, 2002, 28-36.
2018. Real Convergence in Central, Eastern and South-Eastern Europe . ECB
Occasional Paper No. 212.
https://ourarchive.otago.ac.nz/handle/10523/1045
Narodowy Bank Polski30
Annexes
ANNEXES
Table A1: Descriptions of variables
Employment
N
Total and sector employment are determined based on the number of millions
of hours worked, total engaged. STAN Database for Structural Analysis (ISIC
Rev. 4) label HRSN. For Estonia and Poland, missing values for 1995
1999 were approximated by applying individual rates of employment change
label EMPN. These rates reflect the HRSN rate for the period from 1999.
Source: https://stats.oecd.org/Index.aspx?DataSetCode=STANi4#.
Productivity
Q
Calculated as value added in volumes (2010 prices) in millions of euros
label VALK per hour worked.
Source: https://stats.oecd.org/Index.aspx?DataSetCode=STANi4#.
Gross
domestic
product GDP
Y
GDP at market prices, volumes (2010 prices), and millions of euros.
Source: Eurostat.
http://appsso.eurostat.ec.europa.eu/nui/show.do?dataset=nama_10_GDP&lan
g=en. Label: nama_10_gdp.
Autonomous
demand
YA
Government demand plus exports of goods and services.
Government: Subsidies + net property income + social benefits and other
social transfers + other current transfers + capital transfers + investment
grants + government gross fixed capital formation + final consumption
expenditures in millions of euro, current prices, corrected through the
application of the implicit GDP deflator (2010 = 100)
GDP and main components; labels (COFOG) [gov_10a_exp] and
[nama_10_GDP].
Exports of goods and services: millions of euros, volumes (2010 prices).
Source:
http://appsso.eurostat.ec.europa.eu/nui/show.do?dataset=nama_10_GDP&lan
g=en
GERD Gross expenditures for research and development per inhabitant; GERD series
are taken from Eurostat (label: rd_e_gerdtot).
ICT
The share of ICT capital compensation in GDP is taken from the Total
2019. https://conference-
board.org/data/economydatabase/index.cfm?id=27762, accessed: 24/07/2019
QEURO9
QEURO9 is the productivity level of nine euro area countries calculated from
the sum of value added (VALK) divided by the sum of hours worked
(HRSN); data are taken from the STAN database at:
https://stats.oecd.org/Index.aspx?DataSetCode=STANi4#
TO
Trade openness calculated as the ratio of exports and imports to GDP (in
millions of euros at current prices). TO is calculated from Eurostat data
(nama_10_gdp).
SIND and
SSER
SIND and SSER were calculated from shares of industry (Stan code: D05T39)
and total services (Stan code: D45T99) of total employment (measured in
hours engaged); see the entry for Employment above.
ANNEXES
Table A1: Descriptions of variables
Employment
N
Total and sector employment are determined based on the number of millions
of hours worked, total engaged. STAN Database for Structural Analysis (ISIC
Rev. 4) label HRSN. For Estonia and Poland, missing values for 1995
1999 were approximated by applying individual rates of employment change
label EMPN. These rates reflect the HRSN rate for the period from 1999.
Source: https://stats.oecd.org/Index.aspx?DataSetCode=STANi4#.
Productivity
Q
Calculated as value added in volumes (2010 prices) in millions of euros
label VALK per hour worked.
Source: https://stats.oecd.org/Index.aspx?DataSetCode=STANi4#.
Gross
domestic
product GDP
Y
GDP at market prices, volumes (2010 prices), and millions of euros.
Source: Eurostat.
http://appsso.eurostat.ec.europa.eu/nui/show.do?dataset=nama_10_GDP&lan
g=en. Label: nama_10_gdp.
Autonomous
demand
YA
Government demand plus exports of goods and services.
Government: Subsidies + net property income + social benefits and other
social transfers + other current transfers + capital transfers + investment
grants + government gross fixed capital formation + final consumption
expenditures in millions of euro, current prices, corrected through the
application of the implicit GDP deflator (2010 = 100)
GDP and main components; labels (COFOG) [gov_10a_exp] and
[nama_10_GDP].
Exports of goods and services: millions of euros, volumes (2010 prices).
Source:
http://appsso.eurostat.ec.europa.eu/nui/show.do?dataset=nama_10_GDP&lan
g=en
GERD Gross expenditures for research and development per inhabitant; GERD series
are taken from Eurostat (label: rd_e_gerdtot).
ICT
The share of ICT capital compensation in GDP is taken from the Total
2019. https://conference-
board.org/data/economydatabase/index.cfm?id=27762, accessed: 24/07/2019
QEURO9
QEURO9 is the productivity level of nine euro area countries calculated from
the sum of value added (VALK) divided by the sum of hours worked
(HRSN); data are taken from the STAN database at:
https://stats.oecd.org/Index.aspx?DataSetCode=STANi4#
TO
Trade openness calculated as the ratio of exports and imports to GDP (in
millions of euros at current prices). TO is calculated from Eurostat data
(nama_10_gdp).
SIND and
SSER
SIND and SSER were calculated from shares of industry (Stan code: D05T39)
and total services (Stan code: D45T99) of total employment (measured in
hours engaged); see the entry for Employment above.
http://appsso.eurostat.ec.europa.eu/nui/show.do?dataset=nama_10_GDP&lang=en.Label: nama_10_gdp.
31NBP Working Paper No. 318
Annexes
Tab
le A
2:
Em
plo
ym
ent
shar
es a
nd l
abo
ur
pro
du
ctiv
ity i
n i
nd
ust
ry (
incl
ud
ing e
ner
gy)
SIN
D:
shar
e o
f in
dust
ry i
n t
ota
l em
plo
ym
ent
(to
tal
ho
urs
wo
rked
); Q
: la
bo
ur
pro
duct
ivit
y i
n i
nd
ust
ry (
gro
ss v
alue
add
ed p
er h
our
wo
rked
).
Tab
le A
2:
Em
plo
ym
ent
shar
es a
nd l
abo
ur
pro
du
ctiv
ity i
n i
nd
ust
ry (
incl
ud
ing e
ner
gy)
SIN
D:
shar
e o
f in
dust
ry i
n t
ota
l em
plo
ym
ent
(to
tal
ho
urs
wo
rked
); Q
: la
bo
ur
pro
duct
ivit
y i
n i
nd
ust
ry (
gro
ss v
alue
add
ed p
er h
our
wo
rked
).
Tab
le A
2:
Em
plo
ym
ent
shar
es a
nd l
abour
pro
du
ctiv
ity i
n i
ndust
ry (
incl
udin
g e
ner
gy)
SIN
D:
shar
e o
f in
dust
ry i
n t
ota
l em
plo
ym
ent
(to
tal
ho
urs
wo
rked
); Q
: la
bo
ur
pro
duct
ivit
y i
n i
nd
ust
ry (
gro
ss v
alue
add
ed p
er h
our
wo
rked
).
Narodowy Bank Polski32
Tab
le A
3:
Em
plo
ym
ent
shar
es a
nd l
abour
pro
du
ctiv
ity i
n t
he
serv
ice
sect
or
(tota
l se
rvic
es)
SS
ER
: sh
are
of
the
serv
ice
secto
r in
to
tal
em
plo
ym
ent
(to
tal
ho
urs
wo
rked
); Q
: la
bo
ur
pro
duct
ivit
y i
n s
ervic
es
(gro
ss v
alu
e ad
ded
per
ho
ur
wo
rked
.
Tab
le A
3:
Em
plo
ym
ent
shar
es a
nd l
abour
pro
du
ctiv
ity i
n t
he
serv
ice
sect
or
(tota
l se
rvic
es)
SS
ER
: sh
are
of
the
serv
ice
secto
r in
to
tal
em
plo
ym
ent
(to
tal
ho
urs
wo
rked
); Q
: la
bo
ur
pro
duct
ivit
y i
n s
ervic
es
(gro
ss v
alu
e ad
ded
per
ho
ur
wo
rked
.
Tab
le A
3:
Em
plo
ym
ent
shar
es a
nd l
abour
pro
du
ctiv
ity i
n t
he
serv
ice
sect
or
(tota
l se
rvic
es)
SS
ER
: sh
are
of
the
serv
ice
secto
r in
to
tal
em
plo
ym
ent
(to
tal
ho
urs
wo
rked
); Q
: la
bo
ur
pro
duct
ivit
y i
n s
ervic
es
(gro
ss v
alu
e ad
ded
per
ho
ur
wo
rked
.
33NBP Working Paper No. 318
Annexes
Table A 4: Constant terms and cross-section effects of regressions
OLS model 1 - 6
Model 1 Model 2 Model 3 Model 4 Model 5 Model 6
Constant term 0.012*** 0.018*** -0.004 0.003 0.007 -0.002
Fixed cross
section effects
Bulgaria -0.002 -0.006 -0.002 -0.007 -0.008 -0.001
Czech Republic 0.009 0.007 0.011 0.007 0.006 0.011
Estonia 0.010 0.010 0.011 0.012 0.012 0.013
Hungary -0.031 -0.033 -0.031 -0.035 -0.036 -0.032
Latvia 0.008 0.010 0.009 0.011 0.012 0.010
Lithuania 0.006 0.007 0.006 0.008 0.009 0.006
Poland -0.016 -0.009 -0.015 -0.009 -0.011 -0.015
Slovakia 0.001 0.004 0.001 0.004 0.006 0.001
Slovenia 0.001 0.004 -0.001 0.001 0.002 -0.002
Romania 0.014 0.008 0.010 0.008 0.012 0.010
ARDL models 7 - 12
Model 7 Model 8 Model 9 Model 10 Model 11 Model 12
Constant term -1.385*** -0.211 -0.050 -1.456 -1.053** -1.365**
Fixed cross
section effects
Bulgaria -0.051 -0.101 -0.035 -0.138 -0.074 -0.033
Czech Republic -0.072 0.044 -0.091 0.021 -0.058 -0.116
Estonia 0.284 0.124 0.212 0.205 0.243 0.296
Hungary -0.076 -0.019 -0.094 -0.045 -0.086 -0.087
Latvia 0.040 -0.100 0.218 0.119 0.086 0.183
Lithuania 0.149 0.062 0.115 0.114 0.178 0.180
Poland -0.031 -0.095 -0.300 -0.193 -0.286 -0.339
Slovakia 0.092 0.103 0.049 0.087 0.080 0.080
Slovenia 0.154 0.082 0.110 0.155 0.143 0.146
Romania -0.206 -0.100 -0.186 -0.323 -0.166 -0.310
Table A 4: Constant terms and cross-section effects of regressions
OLS model 1 - 6
Model 1 Model 2 Model 3 Model 4 Model 5 Model 6
Constant term 0.012*** 0.018*** -0.004 0.003 0.007 -0.002
Fixed cross
section effects
Bulgaria -0.002 -0.006 -0.002 -0.007 -0.008 -0.001
Czech Republic 0.009 0.007 0.011 0.007 0.006 0.011
Estonia 0.010 0.010 0.011 0.012 0.012 0.013
Hungary -0.031 -0.033 -0.031 -0.035 -0.036 -0.032
Latvia 0.008 0.010 0.009 0.011 0.012 0.010
Lithuania 0.006 0.007 0.006 0.008 0.009 0.006
Poland -0.016 -0.009 -0.015 -0.009 -0.011 -0.015
Slovakia 0.001 0.004 0.001 0.004 0.006 0.001
Slovenia 0.001 0.004 -0.001 0.001 0.002 -0.002
Romania 0.014 0.008 0.010 0.008 0.012 0.010
ARDL models 7 - 12
Model 7 Model 8 Model 9 Model 10 Model 11 Model 12
Constant term -1.385*** -0.211 -0.050 -1.456 -1.053** -1.365**
Fixed cross
section effects
Bulgaria -0.051 -0.101 -0.035 -0.138 -0.074 -0.033
Czech Republic -0.072 0.044 -0.091 0.021 -0.058 -0.116
Estonia 0.284 0.124 0.212 0.205 0.243 0.296
Hungary -0.076 -0.019 -0.094 -0.045 -0.086 -0.087
Latvia 0.040 -0.100 0.218 0.119 0.086 0.183
Lithuania 0.149 0.062 0.115 0.114 0.178 0.180
Poland -0.031 -0.095 -0.300 -0.193 -0.286 -0.339
Slovakia 0.092 0.103 0.049 0.087 0.080 0.080
Slovenia 0.154 0.082 0.110 0.155 0.143 0.146
Romania -0.206 -0.100 -0.186 -0.323 -0.166 -0.310
Narodowy Bank Polski34
Figure A1: Stability of ARDL models - inverse Roots of ARMA Polynomial(s)
www.nbp.pl