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CENTRE FOR APPLIED MACROECONOMIC ANALYSIS

The Australian National University

_________________________________________________________

CAMA Working Paper Series August, 2012

__________________________________________________________

THE LEVEL AND GROWTH EFFECTS IN EMPIRICAL GROWTH MODELS FOR THE

NORDIC COUNTRIES: A KNOWLEDGE ECONOMY APPROACH

Arusha Cooray

School of Economics, University of Wollongong

Centre for Applied Macroeconomic Analysis, ANU

Antonio Paradiso

Italian National Institute for Statistics (ISTAT), Italy

________________________________________________________

CAMA Working Paper 36/2012

http://cama.anu.edu.au

1

The level and growth effects in empirical growth models for the Nordic

countries: A knowledge economy approach

Antonio Paradiso*

anto_paradiso@hotmail.com

Italian National Institute for Statistics (ISTAT), Rome (Italy)

Arusha Cooray

arusha.@uow.edu.au

School of Economics University of Wollongong, Wollongong (Australia)

Centre for Applied Macroeconomic Analysis, Australian National University (Australia)

Abstract

We estimate the steady state growth rate for the Nordic countries using a “knowledge economy”

approach. An endogenous growth framework is employed, in which total factor productivity is a

function of human capital (measured by average years of education), trade openness, research and

development, and investment ratio. We attempt to identify the variables which have significant

level and growth effects within this framework. We find that education plays an important role in

determining the long-run growth rates of Sweden, Norway, and Denmark; and trade openness has

growth effects in Sweden, Finland, and Iceland. The investment ratio plays an important role for

growth in Finland. In addition to growth effects, education also has level effects in Sweden,

Finland, and Iceland. Research and development, has no level or growth effects in any of the Nordic

countries. This may be attributable to the fact that research and development are driven by openness

and education. Policy measures are identified to improve the long-run growth rates for these

countries.

Keywords: Endogenous growth models, Trade openness, human capital, investment ratio, Steady

state growth rate, Nordic countries

JEL Classification: C22, O52, O40

*The views expressed in the article are those of the author and do not involve the responsibility of the Institute.

Acknowledgements: We wish to thank Jakob Madsen for supplying the R&D data, and Mauro Costantini , Steinar

Holden, Jakob Madsen, Amnon Levy and Peter Sorensen for valuable comments. We thank Bill B. Rao for his

invaluable contribution in a preliminary stage of this paper.

2

1. Introduction

During the second half of the 1990s the Nordic countries (Sweden, Finland, Norway, Denmark, and

Iceland) were among the most successful economies in the OECD. These countries, with the

exclusion of Denmark, exhibited above average GDP growth rates from 1995 to 2010 (Norway

2.5%, Sweden 2.6%, Finland 2.9%, Denmark 1.5%, and Iceland 2.9%), in comparison to an average

growth rate of 1.8% for the 15 European Union countries. The Nordic countries additionally, are

among the top performers in the Knowledge Economic Index (KEI) constructed by the World Bank.

The KEI is based on an average of four sub-indexes the four pillars of the knowldege economy: (1)

economic incentive and institutional regime, (2) innovation and technological adoption, (3)

education and training, and (4) information and communication technologies (ICTs). The Nordic

countries are exemplified by their strong performance in these four pillars. Denmark, Sweden,

Finland and Norway rank within the top 5 in the KEI (see Table 1). Although Iceland comes lower

down the KEI, it has seen the fastest improvement in rankings among the top 20 countries rising 8

spots to 13th place in 2009 from 1995 (World Bank 2012).

Compared to other regions, the Nordic countries are relatively homogenous with respect to human

resources. This is due to the emphasis placed on free public education by the Nordic welfare state.

Education is a vital component of a knowledge based economy as it influences both the demand for,

and supply of innovation. A well educated labour force is a pre-requisite for the adoption of

innovation and investment in Research and Development (R&D). Investment in R&D and

diversification through trade have been equally important for restructuring the Nordic economies

towards knowledge based economies. The performance of these economies in terms of the KEI

suggests that education, investment and trade have played an important role in the emergence of

new knowledge based industries and knowledge spillovers promoting long-term growth in the

Nordic countries.

Many studies have shown evidence of R&D knowledge spillovers through trade as a channel of

total factor productivity (TFP) growth, for example, Coe and Helpman (1995), Engelbrecht (1997),

Lumenga-Neso et al. (2001), Madsen (2007b), Lichtenberg et al. (1998). Increased openness, raises

the intensity of competition through the transfer of technology embodied in traded products, lowers

barriers to trade, reduces the monopoly power of domestic firms, and could facilitate R&D, through

the dynamic competition of firms in a Schumpeterian sense. Studies by Coe and Helpman (1995)

and Nadiri and Kim (1996) have highlighted the role of technological spillovers through trade

3

liberalization, for improving the efficiency of the domestic R&D sector. Similarly, Griffith et al.

(2003) show that R&D promotes innovation, the transfer of technology and R&D supported

absorptive capacity. However, it is also possible that there is an interaction of an economy’s R&D

activity with its stock of human capital, due to the fact that the major input into the R&D process is

highly skilled labour. This is evidenced by the studies of Blackburn et al. (2000) and Bravo-Ortega

and Lederman (2010) who show that economic growth is independent of research activity which is

driven by human capital accumulation1. Similarly, Bils and Klenow (2000) argue that human capital

could accelerate the adoption of technology and is necessary for technology use. The studies of

Welch (1970), Bartel and Lichtenberg (1987) and Foster and Rosenzweig (1996) support the

argument that human capital is important for the adoption of technology while the studies of Doms

et al. (1997), Autor et al. (1998), Berman et al. (1998) support the argument that human capital is

important for technology use.

Hence, given the importance of knowledge spillovers as a channel of Total Factor Productivity

(TFP) growth, we use an endogenous growth framework, in which total factor productivity is

assumed to be a function of human capital (measured by average years of education), trade

openness, investment ratio, and R&D. Within this framework we try to distinguish between

variables which have significant level effects and growth effects in the Nordic countries over the

1960 to 2010 period. This is the first study to our knowledge, which examines level and growth

effects from a knowledge economy perspective for the Nordic countries. Country-specific time

series data technique is used to conduct this study2. Our approach broadly follows the specification

and methodology in Rao (2010), Balassone et al. (2011), Paradiso and Rao (2011), and Casadio et

al. (2012).

1 Reis and Sequeira (2007) examine the interaction between the technological change and human capital accumulation

and its implications for investment in R&D from a theoretical perspective.

2Country-specific time series studies are important because it is hard to justify the basic assumptions of cross-section

and panel data studies that the forces of economic growth and underlying structural parameters are the same for all

countries and at all times, even if the countries belong to the same region or area. Furthermore, while cross-section and

panel data studies may give some insights into growth enhancing policies, they are not useful to estimate country-

specific steady state growth rates (SSGRs) and identify the effects of policies to improve SSGRs. See Greiner, et al.

(2005) on this point.

4

Our empirical results are consistent with the views of Blackburn et al. (2000) and Bravo-Ortega and

Lederman (2010) in that R&D is not statistically significant as a shift variable (both level and

growth effects) for any of the Nordic countries. This is probably because openness and HKI interact

with R&D, as mentioned above, so that R&D does not provide any additional information already

embodied in trade openness and human capital.

The paper is organized as follows. In Section 2 we illustrate the characteristics of the Scandinavian

model in the light of the knowledge economy framework. Section 3 presents the specification of the

model and implications for the estimates of the long run growth rate, which is the same as the

steady state growth rate (SSGR) in the Solow growth model. Section 4 presents our empirical

results and Section 5 concludes.

2. Scandinavian Countries as Knowledge Economies

In the past few decades where countries have experienced the effects of globalization and technical

innovation, knowledge has become the key driver of competitiveness and economic growth.

Dahlman and Anderson (2000) define a knowledge economy as “one that encourages its

organization and people to acquire, create, disseminate and use (codified and tacit) knowledge more

effectively for greater economic and social development”. Derek et al. (2004) postulated that the

knowledge economy is based on four pillars: (1) educated and skilled workers; (2) effective

innovation system of firms, research centers, universities, and other organizations; (3) modern and

adequate information of infrastructure to facilitate information dissemination; (4) economic and

institutional regimes to provide incentives for the efficient use of knowledge. In essence, these

authors postulate that the amount of knowledge is used as a key determinant of total factor

productivity (TFP). Strengthening the above four pillars will lead to an increase in the pool of

knowledge available for economic production.

The five Nordic countries can be defined as knowledge economies according to these

characteristics. Based on the work of Derek et al. (2004), the World Bank has developed an index

called the Knowledge Economy Index (KEI). The KEI is an economic indicator that measures a

country’s ability to generate, adopt and diffuse knowledge. The KEI summarizes each country’s

performance on 12 variables corresponding to the four knowledge economy pillars introduced

above. Variables are normalized on a scale of 0 (worst) to 10 (best) and the KEI is constructed as

5

the simple average of the normalized values of these indicators. For an overview of the

methodology and the construction of the index see World Bank (2008). In Figure 1, we make an

over-time comparison of the KEI of some countries in terms of their relative performance for two

points in time viz., 1995 and 2009. Countries above the diagonal line have made an improvement

in the KEI in 2009 compared to 1995, whereas countries below the line experienced a decline. As

we can see, Denmark, Finland, Sweden, and Norway rank very high in terms of the KEI, although

Denmark and Finland’s KEI in 2009 is a slightly smaller compared to 1995. Iceland has a KEI

index in line with other Western European countries but higher than some technological countries

such as Japan. Table 1 presents the KEI and its four components for 2009 for the best 5 countries

and Iceland, out of a total of 146 countries. Denmark ranks highest, followed by Finland, and

Sweden; Norway is in fifth position, whereas Iceland is placed 13th. It is interesting to note that

Iceland is penalized for not having a very high innovation system, whereas it is in line with the top

countries for education and economic incentive regimes.

The indicators used in the empirical analysis for estimation of the four components are the

following - Economic and institutional regime: To proxy for the innovation system, we use trade

openness as an indicator of the level of economic and institutional regime operating in the country3.

An open country is a country with (a) low tariff and non-tariff barriers on trade, (b) low barriers to

technology transfers and (c) low power of national monopolies in areas such as

telecommunications, air transport, finance and insurance industries (Houghton and Sheehan 2000)).

Innovation system: We use trade openness and R&D as proxies for innovation in a country. Trade

openness is perceived by many authors to have a positive impact on efficiency and innovation in the

economy. The idea is that international trade leads to faster diffusion of technology, and hence

higher productivity growth. In addition, there are also spillover effects due to “learning by doing”

gains and better management practices triggered by new technology leading firms to the best

practice technology (Krugman 1987)4. R&D is associated with the development of new ideas, new

products, product improvements and new technologies leading to innovation in a system. This is

supported by Griffith et al. (2003) who show that R&D promotes innovation, the transfer of

technology and R&D supported absorptive capacity. Human capital and education: One commonly

3 See for example Jenkins (1995), Baldwin and Gu (2004), Greenway and Kneller (2004), Coe and Helpman (1995),

Engelbrecht (1997), Madsen (2007b), Lumenga-Neso et al. (2001) and Lichtenberg et al. (1998).

4The studies of Jenkins (1995), Baldwin and Gu (2004), Madsen (2007b), Greenway and Kneller (2004), Coe and

Helpman (1995), Engelbrecht (1997), Lumenga-Neso et al. (2001) and Lichtenberg et al. (1998) support the argument

of R&D spillovers through trade as a channel of TFP.

6

used measure of human capital is the average years of schooling of the adult population5. Average

years of schooling is clearly a stock measure and reflects the accumulated educational investment

embodied in the current labour force6. Information infrastructure: Empirical assessments of the

effects of ICTs on aggregate output and economic growth typically entail the use of ICT

investment. However, due to the non availability of this series for a long time span and the

importance of non-ICT investments as well in economic growth, we use the aggregate series of

investment (as a ratio of GDP) in our estimations7.

Figure 1

Knowledge Economic Index by Countries:

1995 versus 2009

SE

NO FI

G7

US

AU

JP

DE

WE

SG

DN

CA

UKNL

ITA

ES

IS

7.5

8

8.5

9

9.5

10

7.588.599.510

2

0

0

9

1995

Source: World Bank-Knowledge Assessment Methodology (KAM), www.worldbank.org/kam. Notes: Countries above

the diagonal line have made an improvement in the KEI compared to 1995, whereas countries below the line

experienced a regression. Legend: DN = Denmark; SE = Sweden; FI = Finland; NL = Netherland; US = U.S.A.; NO =

Norway; IS = Iceland; UK = United Kingdom; CA = Canada; AU = Australia; DE = Germany; G7 = Group of seven

viz., France, Germany, Italy, Japan, United Kingdom, U.S.A., Canada; WE = Western Europe; JP = Japan; SG =

Singapore.

5 The average years of schooling are used by Hanushek and Woessmann (2008) and Krueger and Lindhal (2001) for

example. We use the data constructed by Barro and Lee (2010). This data are available only at five years intervals since

1950. We linearly interpolate the data between the five years. Another frequently used measure in empirical research is

enrollment rates. According to Bergheim (2008) the enrollment rate is not a useful measure of human capital because it

does not include information on years of education. Other measures available are cognitive skills indicators (IQ test and

standardized tests on reading, science, and mathematics) but these measures are not available over a long time span; for

example the OCED Program for International Student Assessment (PISA) has data starting only from 2000.

6Engelbrecht (1997) acknowledges the role of human capital in domestic innovation and knowledge spillovers.

7De Long and Summers (1991) for example, show that equipment investment has a significant effect on economic

growth. Further, Levine and Renelt (1992) and Sala-i-Martin (1997) have shown that the investment share is a robust

variable in explaining economic growth.

7

[Table 1, about here]

3. Specification of the Model

The steady state solution for the level of output in the Solow (1956) growth model is:

1

*

s

y

A

gn

(1)

where *(/)yYL is the steady state level of income per worker, s = the ratio of investment to

income,

= depreciation rate of capital, g = the rate of technical progress, n = the rate of growth of

labour,

A

the stock of knowledge and

the exponent of capital in the Cobb-Douglas production

function with constant returns (see below). This implies that the steady state rate of growth of per

worker output (SSGR), assuming that all other ratios and parameters are constant, is simply TFP

because:

*

ln lnySSGR ATFP (2)

However, the determinants of TFP are not known and are exogenous in the Solow (1956) growth

model. The new growth theories based on endogenous growth models (ENGM) use an optimization

framework and suggest several potential determinants of TFP. However, to the best of our

knowledge there is no ENGM which rationalizes that TFP depends on more than one or two

selected variables. We make TFP a function of a few of the determinants identified by the ENGMs.

For example, if the findings of Levine and Renelt (1992) are valid, then TFP depends only on the

investment ratio in spite of the findings by Durlauf et al. (2005) and Jones (1995).

Note that the SSGR can be estimated by estimating the production function. The production

function can also be extended by assuming that the stock of knowledge (

A

) depends on some

important variables identified by the ENGMs8. We start with the well-known Cobb-Douglas

production function with constant returns:

1,0 1

tttt

YAKL

(3)

8See Rao (2010), Paradiso and Rao (2011), Casadio et al. (2012).

8

where t

Y is aggregate output, t

A

the stock of knowledge , Kt the stock of physical capital, and Lt

the labour force in period t.

We assume the following general evolution for the stock of knowledge A, where 0

Ais the initial

stock of knowledge,

Z

is a vector which may consist of more than one variable9, whereas Sand

Ware assumed to consist of one variable each and T is time.

2

12 1

0tttt

Z

TS S W

t

AAe

(4)

Substituting (4) into (3) gives:

2

12 1 1

0tttt

ZT S S W

ttt

YAe KL

(5)

Dividing both sides of equation (5) by L yields:

2

12 1

0tttt

ZT S S W

tt

yAe k

(6)

where (/)yYLand (/)kKL.

Taking the natural logarithmic transformation of (6) gives,

2

0121

ln ln ln

tttttt

yAZTSSW k

(7)

Equation (7) captures the actual level of per capita output due to two types of variables viz., factor

accumulation and variables due to factors other than factor accumulation such as , and .

Z

SW

Specification of these other variables that may affect output is an empirical issue. Their effects may

be trended (

Z

), nonlinear (S) or simply linear (W). The variables that should be included in the

vector Z, and in S and W is also an empirical matter. We have experimented with various

alternatives but to conserve space report only the best and plausible results.

Taking first differences of (7) gives:

2

11 2 1

ln ln

tt t t t t t

y

ZT Z S S W k

(8)

9 For simplicity we ignore the i subscript.

9

Only trended variables (i.e.,

Z

variables entering the vector multiplied by trend) have a permanent

growth effect. For this reason, the variables in the Z vector are the sole determinants of the long-run

steady state growth rate. The other two variables S and W have only a level effect on output (i.e.,

they can raise the economy’s income level permanently but they have only transitory growth

effects), but with an important difference. S influences the level of output in a non-linear manner,

whereas W affects output in a linear manner.

For equation (8) to make sense 10

and 20

, so that the S variable has its maximum effect

when

12

0.5 /S

. This variable, prior to reaching its maximum effect, increases at a

decreasing rate. Each additional unit of S contributes less and less to the level of output. Examples

in the empirical growth literature of variables that may influence the output this way are trade

openness and education. Dollar and Kraay (2004) suggest that countries that had greater increases

in trade volumes saw greater increases in growth, but that countries with greater levels of trade

volumes saw lower levels of growth. This would seem to suggest that the effect of trade openness

on growth is such that it takes an inverted U-shaped pattern. In this case there might be an ‘optimal’

level of openness. A country possessing a trade regime more closed than its optimal level would

increase growth by liberalizing; a country possessing a more open trade regime than its optimal

level it would see lower levels of growth (Nye et al., 2002).

Concerning the education variable, several analyses show that the production of human capital

exhibits increasing returns to scale for low levels of education and decreasing returns to scale for

high levels of education. Krueger and Lindahl (2001), Paradiso et al. (2011), Casadio et al. (2012)

find that the best fit of the data is provided by a regression model that considers a quadratic form of

education. In particular, Krueger and Lindahl (2001) find that on average 7.5 average years of

schooling is the maximum level of the inverted U-shaped relation between schooling and output.

Above this level, marginal education has a negative effect, so incremental education is expected to

depress the growth rate. Several empirical studies have found a negative impact of schooling on

economic growth - see Pritchett (2001), Benhabib and Spiegel (1994), Spiegel (1994), Lau et al.

(1991), Jovanovic et al. (1992), Bils and Klenow (2000). Pritchett (2001) advanced three possible

reasons for this: 1) The institutional/governance environment could have been sufficiently perverse

so that the accumulation of educational capital lowered economic growth; 2) The marginal returns

to education could have fallen rapidly as the supply of educated labor expanded while demand

remained stagnant; 3) Educational quality could have been so low that years of schooling created no

10

human capital. The author sustains that the extent and mix of these three phenomena explains the

negative impact of education on growth. It is unlikely that these factors would cause schooling to

have a negative effect in the Nordic countries. In the case of the Nordic countries, the negative

effect of education above a certain level might be better explained by wage compression

(Fredriksson and Topel 2010), high tax rates (Fredriksson and Topel 2010), labour market

segregation (Nordic Co-operation on Gender Equality 2010). Wage compression occurs when wage

structures are not in proportion to professional maturity. This phenomenon has been historically

very high in the Nordic countries. There could be distortionary effects of higher education levels

associated with wage compression when schooling is over a certain level, for example, high skilled

workers have high expectations in terms of wages, and wage compression may discourage the

moral and the effort of high skilled workers pushing down productivity and therefore output.

Furthermore, Bils and Klenow (2000) show that countries with higher enrolment rates do not exhibit faster

human capital growth. This is because countries with high levels of human capital are maintaining these high

levels. Bils and Klenow find that as the years of enrolment increase, the returns to schooling falls.

In steady state, when ln 0k

and all differences go to zero, the Steady State Growth Rate

(SSGR) is equal to the growth rate of the stock of knowledge ( ln

A

)10 :

1t

SSGR Z

(9)

In what follows we try to understand the potential factors influencing the level effects and the

SSGR (i.e., the variables entering in the Z vector) and policy that can improve it.

4. Empirical Estimates

Data from 1960 to 2010 (with the exception of Iceland for which the data sample is from 1970-

2010) are used to estimate the SSGR, which is the long run growth rate. The long run relationship,

equation (2), is estimated using standard time series methods of cointegration. Our selected growth-

enhancing variables are: the ratio of trade openness (TRADE) to GDP, ratio of investment to GDP

(IRAT), ratio of R&D expenditure to GDP (R&D), and human capital (HKI) measured by years of

schooling. Definitions of variables and sources of data are provided in the Appendix. All variables

10The steady state is defined as a situation where all variables grow at a constant, possibly zero, rate (Sala-i-Martin,

1994).

11

are included in the estimation. Some of these variables may not be statistically significant due to

multicollinearity. In particular, we find no role for R&D as a shift variable (either as a level or

growth effect) for all Nordic countries11. This is probably because there is an interaction between

TRADE and HKI and R&D, as explained in Section 1. In the paper, we report only the estimations

showing economically and statistically plausible results.

Three estimations techniques are implemented viz., Fully Modified OLS (FMOLS), Canonical

Cointegrating Regression (CCR) and Dynamic OLS (DOLS). These estimators deal with the

problem of second-order asymptotic bias arising from serial correlation and endogeneity, and they

are asymptotically equivalent and efficient (see Saikkonen (1991) on this last point). The standard

least squares dummy variable estimator is consistent, but suffers from second-order asymptotic bias

that causes test statistics – such as the t-ratio – to diverge asymptotically (Phillips and Hansen,

1990). Therefore, in order to draw inferences, we use FMOLS, CCR, and DOLS estimation

techniques whose t-ratios are asymptotically standard normal12.

Our estimation strategy is as follows. We estimate the long-run relationship with the three methods

stated above (FMOLS, CCR, DOLS) and if all the results are similar and plausible, we verify the

existence of a cointegrating relationship under the Engle-Granger (EG) residual test. If the test

confirms the existence of a long-run relationship, we construct an Error Correction Model (ECM).

Then we study the factor loading and tests for correct specifications i.e., we test for normality,

absence of autocorrelation, and no heteroskedasticity in the residuals.

Dummy variables are added in the long-run estimations and are discussed in the Appendix. For

Finland and Denmark we consider two dummies for the 1960s taking into account important

changes in these two economies (see Appendix for explanation of these events), whereas we include

a dummy variable for the financial crisis for all countries. Two issues have to be discussed

regarding the use of these dummies. There is a debate in the literature on what critical values should

be used to judge the significance of the residual-based ADF test when dummy variables are

included in the cointegrating equations. Ireland and Wren-Lewis (1992) argue that since the dummy

variable is not stochastic, it could be interpreted simply as a modification to the intercept term. This

allows researchers not to regard the dummy variable as an extra variable and use the same critical

11 R&D is not statistically significant for Sweden, Norway, and Iceland. For Denmark and Finland R&D is statistically

significant but the residual EG test does not reject the null hypothesis of no cointegration.

12 Montalvo (1995) shows that the DOLS estimator has a smaller bias compared to the CCR and FMOLS.

12

values. This approach is followed for example by Bahmani-Oskooee (1995), and more recently in

the long-run growth literature by Rao (2010), Paradiso and Rao (2011), Casadio et al. (2012). The

second issue concerns the nature of the financial crisis dummy inserted in the long-run relation

estimated. This dummy covers the last three observations for Sweden, Finland, and Denmark (2008-

2010), the last four observations for Norway (2007-2010)13, and the last two for Iceland (2009-

2010). For this reason, the dummy could be interpreted such as a structural break occurring at the

end of the sample period. We do not have enough instruments (from an empirical and econometric

point of view) to detect the exact nature of this break, because the dataset stops in 2010 when the

crisis is still in action14. The econometric techniques available, Geregory and Hansen (1996)

cointegration test for example, are not able to detect the break occurring very close to the end of the

sample period. For this reason, we consider this dummy as a temporary and not a shift dummy.

Since the period under investigation is very long (over 40 years) and comprises important economic

changes, we investigate the stability of our estimated ECMs. In doing so, we subject the error

correction equation to the Quandt (1960) and Andrews (1993) structural breakpoint tests. Using

insights from Quandt (1960), Andrews (1993) modified the Chow test to allow for endogenous

breakpoints in the sample for an estimated model. This test is performed at every observation over

the interval [,(1 )]TT

and computes the supremum (Max) of the k

F statistics

([,(1)]

sup supkT Tk

FF

) where

is a trimming parameter. Andrews and Ploberger (1994)

developed two additional test statistics i.e. the average (ave F) and the exponential (exp F). The null

hypothesis of no break is rejected if these test statistics are large. Hansen (1997) derives an

algorithm to compute approximate asymptotic p-values of these tests.

4.1 Sweden

In the model for Sweden, trade openness and average years of schooling enter as long-run growth

determining variables. This is reasonable because Sweden ranks very high in terms of education

according to The Global Competitiveness Report (2011-2012) of the World Economic Forum and

the Barro and Lee (2010) education dataset. Sweden has also, historically supported trade

13 In Norway the financial crisis began in 2007, before the other Nordic countries, as reported by Grytten and Hunnes

(2010) .

14 Bagnai (2006) suggests the same reason for explaining that different studies have found a structural break in the US

twin deficit relation in the 1990s only because they do not have a large data sample, whereas ex-post this was only a

transitory phenomenon.

13

liberalization in the interest of its industrial firms (the access to foreign markets is required for

growth). According to equation (4) we have 12

,,

Z

HKI Z TRADE S HKI

and the equation

that is estimated is:

2

12 1 2

ln . ln

tttttt

y Interc k HKI HKI HKI T TRADE T

(10)

It is interesting to note that HKI enters as a variable having both a level (in a non-linear way) and

growth effect; openness enters as a shift variable having a growth effect. The results for equation

(10) are reported in Table 2. The estimates for equation (10) are satisfactory in that all of the

coefficients are correctly signed and statistically significant. The EG residual test shows that a

cointegration relationship exists at the 5% level of statistical significance. The ECM shows a

statistically significant factor loading (

) and has the expected negative sign. The diagnostic tests

show that the model is correctly specified. Table 3 (Quandt-Andrews test) shows that the ECM is

stable over the sample period under investigation.

[Tables 2-3, about here]

According to the results in Table 2, HKI as a level shift variable

(2

12 1t

HKI HKI HKI T

) has its maximum level effect when it equals a value of 7.9

(average years schooling)15. This implies that further increase in education will have negative

effects on growth. This is illustrated in Figure 2.

15 The HKI pattern for HKI Twas simulated assuming that an added one year of education is obtained after 10 years.

This assumption is in line with data on schooling for Sweden for the period 1960-2010.

14

Figure 2: Level effect of HKI in Sweden

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

1234567891011

HKI

By the end of the sample period in 2010, HKI reaches a value of 11.57 well above the optimal

value of 7.9. This effect is in line with the results of Krueger and Lindahl (2001). In long-run

steady-state, this level effect is intended to be superseded by a trended component of HKI (and the

other growth enhancing variables such as trade openness). But it is clear that there is a trade-off

between the short-run and long-run effect of HKI on output. A possible reason could be that high

wage compression and taxes in Sweden compared to international standards, may discourage the

productivity of skilled workers in the short-run, while in the long-run, these detrimental effects are

offset by positive effects of higher education linked to the introduction of new ideas and

technological improvements.

The SSGR ( 112 1tt

HKI TRADE

) for Sweden is illustrated in Figure 3. Trade openness and

HKI play an important and positive role in TFP growth. HKI contributes to 1.7% of income per

capita growth in the last 10 years, whereas TRADE yields a contribution of 1.3%. Finally, we plot

the per worker GDP growth (DLYL) against SSGR. The SSGR shows a smooth pattern with a

slight upward trend towards 3.3%.

15

Figure 3: SSGR for Sweden

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

1961

1963

1965

1967

1969

1971

1973

1975

1977

1979

1981

1983

1985

1987

1989

1991

1993

1995

1997

1999

2001

2003

2005

2007

2009

SSGR_HKI SSGR_TRADE SSGR

‐0.04

‐0.03

‐0.02

‐0.01

0

0.01

0.02

0.03

0.04

0.05

0.06

1961

1963

1965

1967

1969

1971

1973

1975

1977

1979

1981

1983

1985

1987

1989

1991

1993

1995

1997

1999

2001

2003

2005

2007

2009

DLYL SSGR

4.2 Finland

The model for Finland considers trade openness and investment ratio as long-run growth

determining variables. HKI enters only with a non-linear level effect. Investment and trade

openness enter multiplied by trend. That is, according to equation (4) we have

12

,,

Z

TRADE Z IRAT S HKI so that:

2

12 1 2

ln . ln

tttttt

y Interc k HKI HKI TRADE T IRAT T

(11)

The results for equation (11) are reported in Table 4. All the coefficients are statistically significant

and have the expected signs. The EG residual cointegration test confirms the existence of a long-run

relationship. The ECM shows a highly statistically significant factor loading and has the expected

negative sign. The residual diagnostic tests show that the model is correctly specified. Table 5

shows the Quandt-Andrews structural break tests for the ECM. The results are satisfactory because

the ECM does not show a break and it is stable over the period investigated.

[Tables 4-5, about here]

16

Figure 4: Non-linear level effect of HKI in Finland

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

1234567891011

HKI

Figure 4 shows the non-linear level effect of average years of schooling. The maximum level effect

is when average years of schooling is equal to 8.3 years. Thereafter the effect is negative. At the end

of the sample period (2010), schooling is 9.97, and additional investment in education may be

detrimental for income. This could also be due to the wage compression structure as in Sweden.

The SSGR ( 1121tt

TRADE IRAT

) is presented in Figure 5. TRADE and IRAT play a positive

and significant role in determining the SSGR. The average contributions of TRADE and IRAT to

SSGR are very similar: 0.5% and 0.6%, respectively.

Figure 5: SSGR for Finland

0

0.002

0.004

0.006

0.008

0.01

0.012

0.014

0.016

0.018

1961

1963

1965

1967

1969

1971

1973

1975

1977

1979

1981

1983

1985

1987

1989

1991

1993

1995

1997

1999

2001

2003

2005

2007

2009

SSGR_IRAT SSGR_TRADE SSGR

‐0.06

‐0.04

‐0.02

0

0.02

0.04

0.06

0.08

0.1

1961

1963

1965

1967

1969

1971

1973

1975

1977

1979

1981

1983

1985

1987

1989

1991

1993

1995

1997

1999

2001

2003

2005

2007

2009

DLYL SSGR

4.3 Norway

Norway has a historically higher number of years of education according to the Barro-Lee (2010)

dataset. According to the Global competitiveness report (2011-2012) Norway has evolved into a

very open economy, measured by the share of GDP and gross trade flows (exports and imports of

17

goods and services are higher than in most other countries). Norway’s long-run growth is

determined only by the average years of schooling. Trade openness enters as a variable having a

linear level effect only. Accordingly, we assume that, and ,

Z

HKI W TRADE

so that:

1

ln . ln

tttt

yInterc k HKIT TRADE

(12)

Estimates of this equation are reported in Table 6. All results appear satisfactory in terms of the

statistical significance of coefficients, the EG residual test, ECM, and residual diagnostic tests. The

Quandt Andrews test conducted in Table 7 shows that the estimated ECM is stable.

[Tables 6-7, about here]

In the case of Norway, 11t

SSGR HKI

and the contribution to SSGR is trivial (it only

determined by HKI). Figure 6 shows the pattern of SSGR together with the per capita output

growth dynamic (DLYL). SSGR shows a slight upward pattern toward 1% at the end of the sample.

Figure 6: SSGR and DLYL for Norway

‐0.03

‐0.02

‐0.01

0

0.01

0.02

0.03

0.04

0.05

0.06

1961

1963

1965

1967

1969

1971

1973

1975

1977

1979

1981

1983

1985

1987

1989

1991

1993

1995

1997

1999

2001

2003

2005

2007

2009

DLYL SSGR

4.4 Denmark

In the Denmark model, the average years of schooling is the sole variable explaining long-run

growth. This result is not unexpected. According to the education index16, published by the United

16 The education index is one of three indices - the other two are the income index and life expectancy index on which

the human development index is built. It is based on the adult literacy rate and the combined gross enrollment ratio for

primary, secondary and tertiary education.

18

Nations’ Human Development Index17 in 2009, based on data up to 2007, Denmark has an index of

0.993, amongst the highest in the world, in line with Australia, Finland and Belgium. Literacy in

Denmark is approximately 99% for both men and women. Accordingly, we assume that

Z

HKI,

so that:

1

ln . ln

ttt

yInterc k HKIT

(13)

The results appear satisfactory with regard to coefficient signs, the EG residual test, ECM, and

diagnostic tests on the ECM. These results are reported in Table 8 below. The stability test

conducted using the Quandt Andrews test (Table 9) shows that the ECM is stable over the period

1960-2010.

[Tables 8-9, about here]

The SSGR is small because the average years of schooling is the only variable entering long-run

growth. In this case 11t

SSGR HKI

is plotted in Figure 7 together with output growth

(DLYL). The SSGR shows a similar pattern to Norway’s SSGR, a slight upward trend but slightly

higher (1.2% at the end of the sample).

Figure 7: SSGR and DLYL for Denmark

‐0.08

‐0.06

‐0.04

‐0.02

0

0.02

0.04

0.06

0.08

0.1

1961

1963

1965

1967

1969

1971

1973

1975

1977

1979

1981

1983

1985

1987

1989

1991

1993

1995

1997

1999

2001

2003

2005

2007

2009

DLYL SSGR

17The Human Development Index (HDI) is a comparative measure of life expectancy, literacy, education, and standards

of living for countries worldwide published by United Nations. It is a standard means of measuring well-being. It is

used to distinguish whether the country is a developed, a developing or an under-developed country.

19

4.5 Iceland

For Iceland, the long-run growth model is determined by trade openness. Average years of

schooling enters as a level effect variable. The importance of openness for growth is not surprising

since the benefit of the trade openness, as maintained by Alesina et al. (2005), is larger for small

countries. In this case, we have ,

Z

TRADE S HKIand accordingly equation (7) becomes:

2

12 1

ln . ln

ttttt

y Interc k HKI HKI TRADE T

(14)

The results of the cointegrating estimations are reported in Table 10. The results appear satisfactory

in terms of coefficients signs, the residual cointegration test (EG test), ECM, and diagnostic tests on

ECM residuals. Table 11 reports the Quandt-Andrews test for stability of the ECM. The result show

that the ECM is stable over the period 1970-2010.

[Tables 10-11, about here]

In Figure 8 we report the nonlinear level effect of HKI. The maximum level effect is reached at 8.45

years of education.

Figure 8: Non-linear level effect of HKI in Iceland

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

2.2

1234567891011

HKI

In the case of Iceland the SSGR is trivial ( 11t

TRADE

). Figure 9 illustrates the SSGR against

per capita output growth (DLYL). The SSGR reaches a value of 2% toward the end of 2000.

20

Figure 9: SSGR and DLYL for Iceland

‐0.06

‐0.04

‐0.02

0

0.02

0.04

0.06

0.08

0.1

1970

1972

1974

1976

1978

1980

1982

1984

1986

1988

1990

1992

1994

1996

1998

2000

2002

2004

2006

2008

2010

DLYL SSGR

5. Conclusions

We use a knowledge economy approach to identify the variables which have level and growth

effects in the Nordic countries, where TFP is assumed to be a function of human capital, trade,

investment and R&D. Trade openness, human capital (proxied by years of education) and the ratio

of investment to GDP play key roles in determining their productivity and the long run growth rate

(SSGR). We show that education plays an important role in determining the long-run growth rates

of Sweden, Norway, and Denmark. Trade openness has growth effects in Sweden, Finland, and

Iceland. The investment ratio plays an important role in influencing the growth rate in Finland. In

addition to growth effects, education also has level effects in Sweden, Finland, and Iceland. Our

results show no role for R&D however, either as a level or growth enhancing variable. This result is

in line with studies maintaining that openness and education may influence R&D patterns (Coe and

Helpman (1995), Nadiri and Kim (1996), Blackburn et al. (2000), and Bravo-Ortega and Lederman

(2010)), so that incorporating R&D does not provide any additional information. Another argument

put forward by Moen (2001), are the high implementation costs of new innovations which he

attributes to the finding of a negative relationship between R&D expenditure and economic growth

for the Nordic countries.

A noteworthy feature of our estimates is the non-linear level effects of years of education (HKI) in

Sweden, Finland and Iceland. Evidence shows that wage compression and taxes have affected

decisions to work and invest in human capital in Sweden (Fredriksson and Topel (2010)). For

example, Fredriksson and Topel (2010) state that the combined effect of income, payroll and value

added taxes led to a fall in the take home wage to 21% of pre-tax wages in Sweden which adversely

21

affected capital formation and economic growth. Similarly, wage flexibility has been low in Finland

also due to centralized wage bargaining systems (OECD 2010).Therefore the same could be said to

apply to Finland which has similar labour market conditions to Sweden. Iceland however, has

relatively flexible labour market conditions compared to Sweden and Finland. Therefore, the non-

linear level effects of education here might be explained by labour market segregation (Barro 1998,

Kalaitzidakis et al. 2001). Evidence shows that higher educational levels have not been translated

into higher wage levels for females compared to males in Iceland (Nordic Co-operation on Gender

Equality 2010). This is partially due to preference of females for certain occupations leading to a

gender segregated labour market. In Denmark and Norway on the contrary, the results of the present

study show that human capital has linear level effects and is thus not constrained from contributing

to growth by assisting in the absorption of new technologies.

The challenge for Sweden and Finland are the strain of highly taxed labour in an environment of

global mobility in factors of production. Therefore the policy implications stemming from this

study are the need for greater labour market flexibility in the case of Sweden and Finland, and

greater labour market integration in the case of Iceland to further maximize the effects of human

capital on the absorption of new technologies to promote growth.

22

Appendix

Data Appendix

Y = Real GDP; L = Employment (Total economy); CAP = Real Capital Stock; HKI = Human

Capital measured as average years of education; IRAT = Ratio of investment to GDP; TRADE =

Ratio of imports plus exports to GDP; R&D = ratio of total research and development expenditure

to GDP. All data, excluding HKI, are taken and constructed from the AMECO-EUROSTAT

database with the exception of data for Iceland for which Y and IRAT are taken from the World

Bank, L from the OECD Statistics Portal, and TRADE from the Penn World Tables (PWT) 7.0

(Heston et al., 2011). HKI is taken from the Barro-Lee (2010) database for all countries. R&D are

from Madsen (2007a) who uses R&D data from the OECD, Main Science and Technology

Indicators; OECD, Paris, OECD Archive (OECD-DSTI/EAS); National Science Foundation,

Statistics Netherlands, and UN Statistical Yearbook.

The real capital stock for Iceland is constructed through the perpetual inventory method (PIM)

using the gross fixed capital formation available from World Bank database. The PIM formula is:

11

tt t

KK I

Where

= depreciation rate and I = is real investment. The PIM requires data on I, a value of

,

and a value of the initial capital stock 0

K.

The initial capital stock is chosen so the capital-output ratio in the initial period equals the average

capital-output ratio over the period 1960-1970:

1970

1960

1960

1960

1

11t

t

t

KK

YY

The depreciation rate is chosen such that the average ratio of depreciation to GDP using the

constructed capital stock series matches the average ratio of depreciation to GDP in the data over

the calibration period. The World Bank database reports depreciation as “consumption of fixed

capital”.

The choice of depreciation rate

matches the average ratio of depreciation to GDP in the data over

the calibration period 1970-2010:

23

2010

1970

10.13

36t

t

t

K

Y

The above three equations (PIM, capital-output ratio, and the depreciation-GDP ratio) form a

system used to solve for the initial capital stock 0

K, the depreciation rate

, and the capital stock

series t

K.

Dummy variables in the long-run relation

The dummy variables are inserted after an inspection conducted on the residuals of the

cointegrating regression. If we detect large departures in the mean-reverting behavior of the

cointegrating residuals in some periods, we insert dummy variables in the long-run relationship.

The departures correspond to important social and economic events described below for each

country.

Sweden. One dummy is added for the 2008-2010 financial crisis.

Finland. A first dummy for years 1966-1968 is added in the estimation. This period was

characterized by some important policy changes: income policies limiting wage increases to growth

in productivity, abolition of all index clauses, a market devaluation by 24% in 1967 (Kouri 1975). A

second dummy is inserted taking into account the 2008-2010 financial crisis.

Norway. Two dummy variables are added in the estimation. One dummy for the period 1989-1991.

(Nordic crises; see Honkapohja (2009)), and the other for the 2007-2010 financial crisis (see

Grytten and Hunnes (2010) for a chronology of financial crises in Norway).

Denmark. Two dummies are added in the estimated equations. One dummy for the years 1961-

1963 (evolution in the Danish industrial structure, see Marcussen (1997)), and the other for the

2007-2010 financial crisis.

Iceland. A dummy is added for the financial crisis 2009-2010.

24

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29

World Bank (2012) Knowledge Economy Index 2012 Rankings

http://siteresources.worldbank.org/INTUNIKAM/Resources/2012.pdf

World Economic Forum (2011) The Global competitiveness report 2010-2011, World Economic

Forum.

30

Table 1: KEI and its Four Component Values for the Best Countries (2009)

Rank Country KEI Economic Incentive

Regime

Innovation Education ICT

1 Denmark 9.52 9.61 9.49 9.78 9.21

2 Sweden 9.51 9.33 9.76 9.29 9.66

3 Finland 9.37 9.31 9.67 9.77 8.73

4 Netherlands 9.35 9.22 9.45 9.21 9.52

5 Norway 9.31 9.47 9.06 9.6 9.10

.

.

.

.

.

.

.

.

.

.

.

.

.

.

13 Iceland 8.95 9.54 8.07 9.41 8.80

Source: World Bank-Knowledge Assessment Methodology (KAM), www.worldbank.org/kam.

31

Table 2: Results for Sweden: 1960-2010

12 1 2

2

ln . ln

ttt ttt

y Interc k HKI HKI T TRADE THKI

FMOLS DOLS CCR

I

ntercept -2.862

(0.435)

[6.582]***

-3.283

(0.333)

[9.869]***

-2.868

(0.442)

[6.487]***

lnk 0.682

(0.085)

[8.027]***

0.532

(0.091)

[5.860]***

0.696

(0.082)

[8.472]***

TRADE T 0.015

(0.002)

[8.192]***

0.015

(0.002)

[7.827]***

0.015

(0.002)

[7.699]***

HKI T 0.001

(0.000)

[3.052]***

0.001

(0.001)

[1.350]

0.002

(0.000)

[3.237]***

HKI 0.543

(0.103)

[5.284]***

0.521

(0.188)

[2.771]***

0.553

(0.102)

[5.434]***

2

HKI -0.043

(0.007)

[6.031]***

-0.046

(0.015)

[3.081]***

-0.044

(0.007)

[6.392]***

-0.314

(0.098)

[3.222]***

EG residual test -5.221**

LM(1) test (p-value) 0.321

LM(2) test (p-value) 0.434

LM(4) test (p-value) 0.504

JB test (p-value) 0.484

BPG test (p-value) 0.776

Notes: Standard errors are reported in ( ) brackets, whereas t-statistics in [ ] brackets. *, **, *** denotes significance at

10%, 5%, and 1%, respectively. FMOLS = Fully Modified Ordinary Least Squares; DOLS = Dynamic Ordinary Least

Squares; CCR = Canonical Cointegrating Relationship. EG = Engle-Granger t-test for cointegration.

= factor loading

in the ECM; BPG = Breusch-Pagan-Godfrey heteroskedasticiy test; JB = Jarque-Bera normality test; LM = Bresuch-

Godfrey serial correlation LM test. FMOLS and CCR use Newey-West automatic bandwidth selection in computing the

long-run variance matrix. In the DOLS leads and lags are selected according to SIC criteria. The standard errors for the

DOLS estimation are calculated using the Newey-West correction. A dummy for 2008-2010 (financial crisis) and for

2004 (peak in the GDP growth (+4.2%)) are added in the ECM formulation.

32

Table 3: Quandt-Andrews structural break tests for Sweden ECM, 1960-2010

Statistics Value Break Probability

Max LR F-stat 2.245 1996 1.000

Max Wald F-stat 13.228 1996 0.373

Exp LR F-stat 0.720 - 1.000

Exp Wald F-stat 4.988 - 0.211

Ave LR F-stat 1.388 - 1.000

Ave Wald F-stat 8.326 - 0.145

Note: Probabilities calculated using Hansen's (1997) method.

33

Table 4: Results for Finland: 1960-2010

2

12 1 2

ln . ln

tttttt

y Interc k HKI HKI TRADE T IRAT T

FMOLS DOLS CCR

I

ntercept -3.382

(0.148)

[22.843]***

-3.032

(0.202)

[15.041]***

-3.372

(0.149)

[22.692]***

lnk 0.574

(0.015)

[38.879]***

0.606

(0.015)

[39.729]***

0.576

(0.016)

[36.614]***

IRAT T 0.028

(0.002)

[13.220]***

0.030

(0.004)

[7.559]***

0.028

(0.002)

[11.040]***

TRADE T 0.010

(0.000)

[25.367]***

0.009

(0.000)

[15.246]***

0.010

(0.000)

[20.440]***

HKI 0.260

(0.030)

[8.573]***

0.196

(0.040)

[4.934]***

0.259

(0.031)

[8.436]***

2

H

KI -0.016

(0.002)

[8.477]***

-0.012

(0.002)

[5.252]***

-0.016

(0.002)

[8.282]***

-0.529

(0.157)

[3.374]***

EG residual test -6.069***

LM(1) test (p-value) 0.669

LM(2) test (p-value) 0.908

LM(4) test (p-value) 0.989

JB test (p-value) 0.789

BPG test (p-value) 0.573

Notes: Standard errors are reported in ( ) brackets, whereas t-statistics in [ ] brackets. *, **, *** denotes significance at

10%, 5%, and 1%, respectively. FMOLS = Fully Modified Ordinary Least Squares; DOLS = Dynamic Ordinary Least

Squares; CCR = Canonical Cointegrating Relationship. EG = Engle-Granger t-test for cointegration.

= factor loading in

the ECM; BPG = Breusch-Pagan-Godfrey heteroskedasticiy test; JB = Jarque-Bera normality test; LM = Bresuch-Godfrey

serial correlation LM test. FMOLS and CCR use Newey-West automatic bandwidth selection in computing the long-run

variance matrix. In the DOLS leads and lags are selected according to SIC criteria. The standard errors for the DOLS

estimation are calculated using the Newey-West correction. A dummy for 2008-2009 financial crisis is added in the ECM

formulation.

34

Table 5: Quandt-Andrews structural break tests for Finland ECM (Model 1), 1960-2010

Statistics Value Break Probability

Max LR F-stat 2.915 1976 0.987

Max Wald F-stat 8.744 1976 0.319

Exp LR F-stat 0.596 - 0.974

Exp Wald F-stat 2.196 - 0.327

Ave LR F-stat 1.088 - 0.970

Ave Wald F-stat 3.264 - 0.343

Note: Probabilities calculated using Hansen's (1997) method.

35

Table 6: Results for Norway: 1960-2010

1

ln . ln

tttt

yInterc k HKIT TRADE

FMOLS DOLS CCR

I

ntercept -1.561

(0.031)

[49.806]***

-1.617

(0.045)

[2.623]***

-1.557

(0.031)

[49.402]***

lnk 0.586

(0.019)

[31.062]***

0.559

(0.015)

[36.806]***

0.591

(0.018)

[32.737]***

TRADE 0.644

(0.060)

[10.744]***

0.758

(0.075)

[10.149]***

0.639

(0.060)

[10.586]***

HKI T 0.001

(0.000)

[15.689]***

0.001

(0.000)

[7.456] ***

0.001

(0.000)

[16.032]***

-0.47

(0.156)

[2.236]**

EG residual test -6.337***

LM(1) test (p-value) 0.437

LM(2) test (p-value) 0.259

LM(4) test (p-value) 0.447

JB test (p-value) 0.856

BPG test (p-value) 0.220

Notes: Standard errors are reported in ( ) brackets, whereas t-statistics in [ ] brackets. *, **, *** denotes significance at

10%, 5%, and 1%, respectively. FMOLS = Fully Modified Ordinary Least Squares; DOLS = Dynamic Ordinary Least

Squares; CCR = Canonical Cointegrating Relationship. EG = Engle-Granger t-test for cointegration.

= factor loading

in the ECM; BPG = Breusch-Pagan-Godfrey heteroskedasticiy test; JB = Jarque-Bera normality test; LM = Bresuch-

Godfrey serial correlation LM test. FMOLS and CCR uses Newey-West automatic bandwidth selection in computing

the long-run variance matrix. In the DOLS leads and lags are selected according to SIC criteria. The standard errors for

the DOLS estimation are calculated using the Newey-West correction.

Table 7: Quandt-Andrews structural break tests for Norway ECM, 1960-2010

Statistics Value Break Probabilit

y

Max LR F-stat 2.616 2002 1.000

Max Wald F-stat 13.078 2002 0.252

Exp LR F-stat 0.873 - 1.000

Exp Wald F-stat 4.948 - 0.123

Ave LR F-stat 1.687 - 0.997

Ave Wald F-stat 8.433 - 0.068

Note: Probabilities calculated using Hansen's (1997) method.

36

Table 8: Results for Denmark: 1960-2010

1

ln . ln

ttt

yInterc k HKIT

FMOLS DOLS CCR

I

ntercept -0.301

(0.267)

[1.129]

-0.332

(0.337)

[0.987]

-0.356

(0.274)

[1.313]

lnk 0.449

(0.111)

[4.045]***

0.428

(0.142)

[3.022]**

0.424

(0.114)

[3.733]***

HKI T 0.001

(0.000)

[7.255]***

0.001

(0.000)

[6.376] ***

0.001

(0.000)

[7.209]***

-0.196

(0.088)

[2.216] **

EG residual test -6.172***

LM(1) test (p-value) 0.470

LM(2) test (p-value) 0.673

LM(4) test (p-value) 0.938

JB test (p-value) 0.748

BPG test (p-value) 0.720

Squares; CCR = Canonical Cointegrating Relationship. EG = Engle-Granger t-test for cointegration.

= factor loading

in the ECM; BPG = Breusch-Pagan-Godfrey heteroskedasticiy test; JB = Jarque-Bera normality test; LM = Bresuch-

Godfrey serial correlation LM test. FMOLS use Newey-West automatic bandwidth selection in computing the long-run

variance matrix. In the DOLS leads and lags are selected according to SIC criteria. The standard errors for the DOLS

estimation are calculated using the Newey-West correction. A spike dummy for 1964 (innovation in Danish pension

system with the introduction of earning-related pension supplement scheme) and one for the financial crisis (2008-

2010) are added in the ECM formulation.

Table 9: Quandt-Andrews structural break tests for Denmark ECM, 1960-2010

Statistics Value Break Probability

Max LR F-stat 1.749 2001 1.000

Max Wald F-stat 8.745 2001 0.688

Exp LR F-stat 0.544 - 1.000

Exp Wald F-stat 2.979 - 0.490

Ave LR F-sta

t

1.066 - 1.000

Ave Wald F-stat 5.332 - 0.367

Note: Probabilities calculated using Hansen's (1997) method.

37

Table 10: Results for Iceland: 1970-2010 2

12 1

ln . ln

ttttt

y Interc k HKI HKI TRADE T

FMOLS DOLS CCR

I

ntercept 9.523

(1.280)

[7.439]***

9.066

(1.903)

[4.763]***

9.351

(1.218)

[7.679]***

lnk 0.339

(0.067)

[5.049]***

0.343

(0.086)

[3.984]***

0.347

(0.069)

[5.049]***

HKI 0.449

(0.101)

[4.435]***

0.462

(0.162)

[2.844] ***

0.457

(0.111)

[4.112]***

2

HKI -0.030

(0.007)

[3.979]***

-0.027

(0.013)

[2.047]**

-0.030

(0.008)

[3.629]***

TRADE T 0.024

(0.005)

[4.557]***

0.027

(0.008)

[3.305]***

0.024

(0.006)

[4.155]***

-0.637

(0.175)

[3.643] ***

EG residual test -5.059**

LM(1) test (p-value) 0.756

LM(2) test (p-value) 0.942

LM(4) test (p-value) 0.954

JB test (p-value) 0.706

BPG test (p-value) 0.776

Squares; CCR = Canonical Cointegrating Relationship. EG = Engle-Granger t-test for cointegration.

= factor loading

Godfrey serial correlation LM test. FMOLS use Newey-West automatic bandwidth selection in computing the long-run

variance matrix. In the DOLS leads and lags are selected according to SIC criteria. The standard errors for the DOLS

estimation are calculated using the Newey-West correction.

Table 11: Quandt-Andrews structural break tests for Iceland ECM, 1970-2010

Statistics Value Break Probability

Max LR F-stat 2.714 2004 0.999

Max Wald F-stat 10.856 2004 0.298

Exp LR F-stat 0.611 - 1.000

Exp Wald F-stat 3.556 - 0.198

Ave LR F-stat 1.056 - 1.000

Ave Wald F-stat 4.223 - 0.369

Note: Probabilities calculated using Hansen's (1997) method.