The productivity puzzle and the Kaldor-Verdoorn law: the case ...the case of Central and Eastern...

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); [email protected]

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


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.


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).


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).


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


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.


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


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.


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


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.


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.



Figure 1: Growth trends in GDP, autonomous demand and labour productivity

Sources: Author s calculations and drawings.


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



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


is not redundant.









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)



4.5 Causality tests






of this study.








is not redundant.









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)



4.5 Causality tests






of this study.








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.










Dependent variable


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






shown.










Dependent variable


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






shown.


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


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***




a Adjusted R











regressions.











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 ---


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***




a Adjusted R











regressions.











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 ---


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***


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


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



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.


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 --- ---


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




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


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 --- ---


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 --- ---


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***



4.85 4.85 3.39 3.39 4.35 4.01



b -(Y(-1))/(-Q(-1) or (YA(-1))/-Q(-1).


d Adj. R

2 refer









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


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 --- ---


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 --- ---


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***



4.85 4.85 3.39 3.39 4.35 4.01



b -(Y(-1))/(-Q(-1) or (YA(-1))/-Q(-1).


d Adj. R

2 refer








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


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.


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.


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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.


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:


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.


Productivity

Q

Calculated as value added in volumes (2010 prices) in millions of euros

label VALK per hour worked.


Gross

domestic

product GDP

Y

GDP at market prices, volumes (2010 prices), and millions of euros.

Source: Eurostat.


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:


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.


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

).


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

.


Annexes

Table A 4: Constant terms and cross-section effects of regressions

OLS model 1 - 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


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


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


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


Figure A1: Stability of ARDL models - inverse Roots of ARMA Polynomial(s)

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