Let’s Assume Full Employment: Implications for the Development of Classical Growth Theory

By

Norman Sedgley Assistant Professor of Economics

Loyola College in Maryland 410-617-2848

nsedgley@loyola.edu

and

Bruce Elmslie Associate Professor of Economics

University of New Hampshire 603-862-3347

bte@hopper.unh.edu

September 9, 2001 The authors thank Taras Smetaniouk for providing research assistance. The usual caveats apply.

Rough Draft: Please do not cite or quote without authors' permission

1

Abstract:

Traditionally, classical theorists assume an elastic labor supply at a constant conventional share of wages in gross output. This assumption together with a fixed proportion production technology creates endogenous growth via an "AK" style model. Policy has permanent implications for the long run growth rate. Luigi Pasinetti explored this model when the wage is allowed to adjust so full employment is reached in each period, as in the neoclassical model of economic growth. Even though important differences in interpretation between the full employment classical model and neoclassical model continue to exist, the extension shows that the rate of growth becomes exogenous in the classical full employment model as it does in the neoclassical model. Furthermore, policy implications in the full employment classical model become similar to the neoclassical model in the sense that policy has an impact on variables in levels, but has no impact on growth rates. It is fair to say that most classical economists find the full employment assumption untenable, and continue to utilize the assumption of a constant conventional wage share. New growth theory is viewed as being more closely allied with neoclassical theory since both are based on a full employment specification of the labor market. From a neoclassical point of view this is necessary because the full employment assumption makes growth exogenous in the neoclassical framework. If the full employment assumption can be shown to apply, then it is important for classical growth theorists to pay more attention to new growth theory as well, and incorporate these same advances into classical growth models. Our research uses the modern time series econometric techniques of cointegration and Penn World Table data to explore the empirical validity of the full employment assumption. The full employment specification suggests productivity growth and per capita growth should be cointegrated. Without full employment no such relationship exists because per capita growth is driven entirely by the rate of growth of the capital stock while labor productivity is allowed to follow its own path of advance. This suggests an easy method of testing the full employment assumption. This assumption has important consequences for future development of the classical approach to economic growth.

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I. Introduction

In economics, as in the world of fashion, what was once popular, but is

now passe, comes back into style eventually. Like wide ties and bell-bottom

jeans, the inquiry into causes of economic growth is in vogue once again. The

pages of economics journals are full of formulations of ideas on productivity

growth.

The resurgence in interest in economic growth is not a surprise. What is

surprising, however, is that the “new growth” theory has largely been allied with

neoclassical theory (Verspagen, 1992). This is surprising because the ideas

encapsulated in the "new" theories are related to technological change, increasing

returns to scale, and the role of research and development. These ideas are found

in the writings of early classical economists. Smith and Marx certainly

appreciated the importance of technological advance in explaining economic

growth and development.

This paper is written on the premise that the frontier of "new growth"

theory can be advanced by research steeped in the classical tradition, and that this

can be accomplished within the realm of formal theorizing. We realize that some

economists in both camps will object, hoping that their own research program will

be adopted in entirety and "as is", leaving the other tradition to fade into the pages

of the history of thought journals and texts. Scientific progress rarely proceeds

along these lines and a further discussion of these issues is best left to economic

methodology.

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Why, then, has new growth theory developed mostly along neoclassical

lines? Opinions abound, but we believe there are two aspects of neoclassical

theory that are now firmly routed in new growth theory that promote the close

relationship. First is the assumption that factor substitutability exists in

production. Early attempts at creating endogenous growth concentrated on

eliminating diminishing “marginal returns to capital.” Many classical economists

do not recognize such substitutability or the possibility of measuring a “marginal

product of capital.” Second, these new growth models share with neoclassical

economics the assumption that the wage rate adjusts to bring about full

employment of the labor force, save for some natural rate of unemployment

associated with employment search costs. Classical economists would look to

institutions and relative bargaining power to explain the prevailing level of wages

and a conventional share of wages in gross output. It is the joint assumptions of

factor substitutability and wage adjustment, in synergy, that eliminates a role for

political economy in the neoclassical growth tradition, old and new.

This paper asks a simple question. Is it the classical conventional wage

share or the adjustment to full employment that provides the more empirically

justified specification of the labor market? The answer to this question has

important implications for the direction of the future development of classical

growth theory and its relationship with new growth theory.

The remainder of the paper is organized as follows. Section two reviews

the theory needed to develop an empirical test aimed at answering our simple

question. Section three discusses the data, econometric methodology, and the

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empirical results. Section four investigates some implications of the results

reported in section three for the future development of the classical approach to

understanding economic development and growth.

II. Theoretical Models

Our basic aim, at this stage, is to briefly review some well-known results

in the classical tradition of modeling economic growth and lay out variable

definitions. We model growth along the lines of Johansen (1967) and, more

recently Foley and Michl (1999). Table 1 provides variable definitions. Begin by

defining the distribution of income, the employment rate, and output per capita as:

pY

wL=µ , and (1)

N

Lv = (2)

NY /=χ (3)

where µ is labors’ share of national income, Y . The money wage is w , the

price level is p , Labor employed is L, and the available supply of workers

(assumed to be equal to the population) is N. v is, therefore, the employment rate

and χ is per capita income. For now assume a fixed proportion production

technology, exogenous labor augmenting technological change, and an exogenous

population growth rate,

•

=N

Nn . These assumption lead to the following

mathematical relationships:

5

],min[ ALKY ρ= , (4)

teAA γ)0(= and (5)

nteNN )0(= (6)

where ρ is capital productivity, A is labor productivity, and γ is the rate of

technological change. This simple model is completed by assuming

ANK <ρ , (7)

and accumulation follows the rule:

δρ −=

•

sk

k, (8)

where s is the rate of savings out of income and δ is the rate of depreciation. The

model is classical in nature due to equation (4) and equation (7). The wage share

in equation (1) is assumed constant and determined via wage negotiation,

economic customs and institutions. This implies the real wage grows at the rate

γ .

Equations (1) through (8) imply that per capita growth and labor

productivity growth are given by the following equations:

ns −−=

•

δρχχ

(9)

γ=•

A

A (10)

and there is no reason, at this point, to expect equations (9) and (10) to be equal to

each other.

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Another method of determining the model above is to assume wages

adjust such that all resources in the economy are fully employed (Pasinetti, 1974).

It is explicitly assumed that:

),( vNA

Kw −=• ρ

φ ∞→φ (11)

therefore,

NvA

K =ρ, (12)

where the bar over v reminds us that the employment ratio is now exogenous.

The natural rate of unemployment is )1( vuN −= and is seen as a function of such

factors as the level of unemployment benefits, job search and matching costs (see

Katz and Meyer 1988). Log differentiation of equation (12) with respect to time

together with equation (8) shows that the growth of capital per worker is equal to

the rate of productivity growth. Therefore

γχχ

==

••

A

A. (13)

Under conditions of full employment labor productivity grows at the same rate as

per capita output. In other words labor productivity and per capita output move

together under the full employment specification of the classical model while they

follow independent time paths under the conventional wage share model.

This suggests an easy test of the full employment assumption using the

modern tools of time series analysis and cointegration. If the evidence suggests

cointegration between productivity and output per capita then the variables move

together through time in the manner suggested by the full employment labor

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market specification. If we cannot find evidence of cointegration the specification

outlined in equations (1) through (8) may be more appropriate. It is worth

suggesting the possibility of fixing up the conventional wage share model to be

consistent with evidence of cointegration. Such a formulation will require

population growth to depend on wages and the functional distribution of income

so that population grows with employment. This formulation has problems of its

own and, rather that getting too far ahead of ourselves, we save a discussion of

this extension for section IV.

III. Data and Empirical Results

The data used in this study is from the Penn World Tables Mark 5.6a.

This data set allows the collection of time series data from 1950 through 1992.

Output, population, and employment statistics are used to calculate per capita

output and labor productivity for 41 countries with data for the full 42 year

period.

The first step in investigating the cointegrating relationships involves pre

testing the variables for stationarity. Table 2 presents the results of tests for unit

roots in the variables. The first five columns are statistics of interest for the

variable A and columns six through ten show information for the variable χ .

Notation ττ and τZ represent alternative tests for the null hypothesis of a unit

root and nonstationarity in a specification of the augmented Dickey Fuller

equation that includes a drift and a deterministic time trend. ττ is more commonly

reported, but the Z test provides more power in distinguishing between a unit root

and a time trend. τφ provides a test of the joint hypothesis that there is a unit root

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but no time trend. The µτ and µZ provide a test of the unit root in a Dickey Fuller

equation without the time trend. The conclusion, pretty much across the board, is

that the variables contain unit roots.

Given the nonstationarity of the variables traditional statistical techniques

cannot be applied to investigate the relationship between productivity growth and

per capita growth. Cointegration analysis simply investigates whether there is a

linear combination of A and χ that is stationary in the long run. If such a

cointegrating vector exists then the two variables do not drift aimlessly toward or

away from each other over time. In other words cointegration suggests A and

χ drift together over time as suggested by our classical growth model with full

employment of all resources. A lack of cointegration is not consistent with this

specification of the model.

We estimate a Vector Auto Regression in A and χ for each country with

various lag structures, ρ . A VAR( ρ ) is defined as:

∑−

=−− +Π+∆Π=∆

1

1

ρ

ρ εi

ttitit yyy (14)

where

ΠΠ

ΠΠ=Π

20

10

2212

1211

a

a,

=

χ

Ay

and ∆ signifies the first difference.

The Johansen technique of testing for cointegration consists of testing the

rank of the matrix Π . If the rank, r, is zero the variables are not cointegrated, if

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r=1 they are cointegrated. If the matrix is of full rank the variables are stationary

(Enders, 1995).

The choice of lag can be critical (though in most cases this is not true with

our data) and lag choice for each country is based on the diagnostic statistics

tabulated in Table 3. Careful consideration of the multivariate Schwarz Baysian

criterion (SBC), Hannan Quinn criterion (HQC), the LM test for autocorrelation,

and a test for normality of the errors is undertaken in determining the lag reported

in Table 4. (See table footnote for details.) The lag actually chosen is indicated

in parenthesis after the country name in Table 4.

Johansen and Juleius (1990) suggest likelihood ratio tests known as the

max−λ and trace statistics. These statistics along with the associated null

hypothesis, alternative hypothesis, and critical values are reported in Table 5. The

results indicate that, for most nations, there exists one cointegrating vector

between A and χ . Of 41 nations the null hypothesis of no cointegration can be

rejected in 33 cases. Of these, 8 can be found to have 2 cointegrating vectors at

the 95% confidence level. The second cointegrating vector is rejected at the 99%

confidence level. Given the strong evidence of nonstationarity reported in Table

2 it is best concluded that these 8, too, have one cointegrating vector. Of the 41

countries only 8 lack evidence of cointegration. These include the Phillipines,

Spain, Turkey, Uganda, Mauritius, Kenya, India, and Honduras. The trace and

max−λ tests provide conflicting evidence for Columbia, West Germany,

Greece, and Sri Lanka. For each of these cases, however, we can conclude there

is one cointegrating vector if the 90% confidence level is used.

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The evidence, therefore, is in overwhelming support of the full

employment model rather than the classical conventional wage share. This

evidence has important implications for the future development of classical

growth theory and the relationship between new growth theory and classical

growth theory.

IV. Some Implications

There are various ways of correcting the classical model presented in

equations (1) through (8) so it is consistent with the empirical facts. The most

obvious solution at this point is to accept the full employment specification.

Before making this appeal we review several implications of abandoning the

conventional wage share model of wage determination. These include tractability

and ease of exposition, the link between the conventional wage share model and

the classical school’s over emphasis of the reswitching question, and finally the

opportunities for classical economists to add a new and fundamentally important

dimension to current debates in the new growth literature.

The relative merits of fixing up the conventional wage model versus

adopting a full employment approach should be assessed. Velupillai (1993) has

demonstrated how the model represented by equation (1) through equation (8) can

be made consistent with a constant natural rate of unemployment. The model is

updated with Mathusian population growth. Velupillai augments equations (1)

through (8) with the following three equations:

0'),( >=•

gvgw

w (15)

11

),()),((),( µµµ vfvgfw

wf

N

N===

••

(16)

0>vf , 0>µf

),()),((),( µµµ vhvghw

wh

p

p===

••

(17)

0>vh , 0>µh

Equation (15) is a wage bargaining equation. Equation (16) relates population

growth to the functional distribution of income and wage growth. Equation (17)

is a function showing how a firm’s mark-up depends on wage growth and labor’s

share.

Equations (2), (3), (5), (8), and (16) are combined to form:

),( µγδρ vfsv

v−−−=

•

(18)

equations (1), (15), (17), (4), (5), (8) give:

),()( µγµµ

vhvg −−=

•

(19)

Equations (18) and (19) are two equations of motion in two state variables v and

µ . The signs of the derivatives in equations (16) and (17) indicate (18) and (19)

as two stable loci. Regardless of where the economy starts in v and µ space it

will end up at a steady state with a constant v and µ . The growing employment,

that caused a decrease in the rate of unemployment in the simpler formulation of

the conventional wage share model, is now offset by population growth creating a

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constant employment ratio and a constant natural or long run rate of

unemployment. It is easy to see that γχχ

==

••

A

A.

This formulation does lead to a steady state, but the sign of the derivative

of equation (16) with respect to the employment ratio is problematic. It is well

known that the Malthusian idea that population growth rates rise with the wage is

false. A large literature in the new growth tradition deals with the demographic

transition or the fact that fertility and population growth rates fall with

development (Barro and Lee, 1994). This sign reversal makes the employment

ratio locus unstable. The model becomes saddle path stable but equations (1)

through (8) and (15) through (17) do not provide the boundary conditions

necessary to insure that the economy stays on the saddle path and moves to an

equilibrium. The employment ratio can be taken as historically given. Once the

employment ratio is established, the wage share can take only one value if the

economy is to reside on the path towards the desired equilibrium, and the model

provides no guarantee that this wage share prevails.

The foundations necessary to show that the only intertemporal path the

economy can take without violating optimizing conditions leads to a steady state

can, perhaps, be added to the model. Of course the other option is simply to

continue to add ad hoc equations and assumptions concerning the magnitudes of

partial derivatives until the desired result is achieved. This approach should

probably be avoided. Even if it where successful the model outlined above would

be a difficult one to push a great deal further. As Velupillai states:

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It is reasonably easy to go part of the way towards generalizing the production function with which we have worked, whilst retaining the simplicity of two dimensional dynamics. One way would be to use a variant of Kaldor’s technical progress function in its more recent versions-as used in modern growth theory. All other generalizations put us in the technically complicated domain of three – and higher –dimensions, where simple results are at a premium (Velupillai, 1993:159).

What can we gain by embracing the full employment classical growth model

instead? For starters one state variable is eliminated, since, according to equation (12)

the employment ratio becomes exogenous. Okun's razor suggests the full employment

assumption. The full employment model is simple, consistent with the data, and draws

classical research into some of the sticky but interesting issues new growth researchers

have been struggling with in recent years.

Another convenience of the full employment assumption is that it eliminates

reswitching when multiple techniques are allowed. Reswitching is the adoption of

previously used, labor intensive techniques of production as the wage rises and the rate of

profit falls. This counterintuitive possibility exists if we use a multi-sector model and

measure the stock of capital as a value aggregate. The assumption of full employment is

enough to eliminate reswitching and dispense with this counterintuitive nuisance which

has occupied too much of classical economists’ time (see Sedgley and Elmlsie 2001 for a

more detailed discussion). A switch to a more labor intensive production technique under

full employment requires either idle capital or a move in wages that violates equation

(11). As Champernowne (1953) argues:

With all labor employed it is interesting to conceive what would happen next when a further rise in real wages and a fall in the rate of interest would make competitive only equipment with lower productivity and employing more men per unit quantity, and thus requiring negative net

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investment. Presumably, the only way investment could remain positive without a prolonged interval of disinvestment would be for food wages to leap up and the rate of interest to leap down to the levels where capital equipment even more productive than that in existence became competitive (Champernowne, 1953: 118).

This argument was expressed less clearly in Robinson’s (1953) article that started

the reswitching debate. In fact she states that neoclassical economics is based on the

“postulate that, in the long run, the rate of real wages tends to be such that all available

labor is employed” (Robinson, 1953:96). Given that this is an axiom of the neoclassical

school it is surprising that the capital controversies ever made it as far as they did.

Neoclassicals have moved on in extremely interesting directions, the evidence provided

in this paper suggests that they were correct in doing so.

What, in particular, does the adoption of the full employment assumption mean

for classical growth theory beyond tractability and a potential resolution to the

reswitching debate that has occupied much of the classical research agenda for at least

two decades? Only time and careful investigation will tell, but it clearly requires

classical economists to get involved in difficult debates currently being discussed in the

“New Growth” literature. Consider, as an example, the issue of scale effects. The

conventional wage share model is itself an endogenous growth model of the "AK" variety

(Kurz, 1997). Once full employment is specified growth becomes exogenous as it is in

the neoclassical model. Thus, policies which impact the savings rate no longer have a

permanent effect on the rate of growth. This policy effectiveness debate is a central

theme in new growth theory, and has been a driving force in the development of

endogenous innovation models.

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Scale effects are a central issue in new growth economics. The early new growth

theories often predict a scale effect, or that larger economies with more resources (labor)

to devote to R&D grow faster (Agion and Howitt, 1992 ; Grossman and Helpman, 1994).

Empirical evidence of scale effects has been elusive and endogenous innovation

researchers, lead by Jones (1995), are developing of nonscale endogenous growth models

(Segerstrom, 1998). These models delve into interesting issues of returns to scale in the

production function for new ideas and the economics of information and technology.

The classical model with a conventional wage share is free of a scale aspect, since

it is capital rather than labor that limits growth. To see this result follow Arrow (1962)

and allow labor augmenting technology to grow with spillovers associated with capital

investment and learning by doing:

λKA = (20)

With the classical conventional wage share the model is already an “AK” growth model

and increases in capital now has an offsetting negative impact on employment.

Otherwise the model remains the same. Note that neither population levels nor growth

rates enhance growth in equations (9) or (10), thus the model is free of scale effects. The

assumption of full employment changes this conclusion within the classical model. With

full employment NKK λρ = . Log differentiation of this identity and (20) shows that the

growth rate is:

)1( λ

λχχ

−==

••

n

A

A (21)

Scale effects in levels appear in the model if 1=λ and N=ρ since the model becomes

an “AK” model with A=N. The growth rate, then, becomes:

16

)( δχχ

+−=

•

nsN (22)

Such a formulation restores the savings rate and policy effectiveness to the growth

equation. Thus the vast literature on scale effects should be of great interest to classical

economists since the full employment classical model must grapple with the same scale

issues and policy effectiveness issues as neoclassical “new growth” models.

V. Conclusion

The classical conventional wage share model has long formed basis of classical

growth theory. This paper provides empirical evidence that this model must be modified.

We argue that the conventional wage share model should be replaced with a full

employment classical model. The conventional wage share model can only be rescued at

the cost of extreme comp lication, making further development very difficult. The

conventional wage share model has caused an unwarranted focus on the question of

reswitching. Neoclassical growth theory has moved on from the reswitching debate,

leaving classical growth theory on the sidelines. The adoption of a full employment

assumption opens up classical growth theory to some of the interesting questions now

being debated in the new growth area.

Taking the approach suggested in this paper does not eliminate the unique

contributions classical growth models can potentially make to contemporary growth

theory. Nelson (1997) has argued that a deep understanding of institutions is lacking in

the neoclassical growth paradigm. This cannot be denied. This lack of institutional focus

is a result of full employment assumptions in combination with perfect factor

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substitutability in production. Burmeister (1984) shows, using a Sraffian commodities

model, how a model with full employment but limited factor substitutability defines

bounds within which there is room for wage bargaining, the specification of power

relationships, and institutions not typically considered by neoclassical economic growth

theory.1 This suggests an opportunity for classical growth economists and political

economy to make important contributions to what is currently known regarding the

determinants of economic growth.

1 Given the critique of Kurz and Salvadori (1987), the term “Sraffian commodities” may be misleading. However, the model remains a powerful example of the importance of institutions in the distributional solution to a classical model with full employment.

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Bibliography

Aghion, P. and P. Howitt (1992), “A Model of Growth through Creative Destruction,” Econometrica, 60, 2, 323-351. Arrow, Kenneth (1962), “The Economic Implications of Learning by Doing,” Review of Economic Studies, 29, 155-173. Barro, R. and G. Becker (1989),”Fertility Choice in a Model of Economic Growth,” Econometrica, 57, 2, 481-501. Bunmeister, E. (1984),”Sraffa, Labor Theories of Value, and the Economics of Real Wage Determination,” The Journal of Political Economy , 92, 3, 508-526. Champernowne, D.G. (1953), “The Production Function and the Theory of Capital: A Comment,” The Review of Economic Studies, 21, 2, 112-135. Doornik, J. and H. Hansen (1994),"An Omnibus Test for Univariate and Multivariate Normality,” Working Paper, Nuffeild College, Oxford. Enders, W. (1995), Applied Econometric Time Series, Wiley Press, New York Foley, D. and T. Michl (1999), Growth and Distribution, Harvard University Press, Cambridge Massachusetts. Grossman, G., and E. Helpman (1994), “Endogenous Innovation in the Theory of Growth,” Journal of Economic Perspectives, 8, 23-44. Johansen, L. (1967), “A Classical Model of Economic Growth,” C.H. Feinstein, ed., Socialism, Capitalism, and Economic Growth, Cambridge University Press, Cambridge. Johansen, S. and K. Julieus (1990), “Maximum Liklihood Estimation and Inferences on Cointegration-with Application to the Demand for Money,” Oxford Bulletin of Economics and Statistics, May, 169-210. Jones, C. (1995), “R&D Based Models of Economic Growth,” Journal of Political Economy, 103, 759-784. Katz, L. and B. Meyer (1988), “The Impact of the Potential Duration of Unemployment Benefits on the Duration of Unemployment,” Unpublished Manuscript, Harvard University. Kurz, H. (1997), "What Could the 'New' Growth Theory Teach Smith or Ricardo?" Economic Issues, 2, 2, 1-20.

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Kurz, H. and N. Salvadori (1987), “Burmeister on Sraffa and the Labor Theory of Value: A Comment,” Journal of Political Economy ,95, 4, 870-81. Nelson, R. (1997), “How New is New Growth Theory,” Challenge, 40, 5, 29-58. Pasinetti, L. (1974), Growth and Income Distribution: Essays in Economic Theory, Cambridge University Press, Cambridge. Robinson, Joan (1953), “The Production Function and the Theory of Capital,” The Review of Economic Studies, 21, 2, 81-106. Sedgley, N and B. Elmslie (2001), “Reswitching in a Growth Framework,” unpublished manuscript. Segerstrom, P. (1998), “Endogenous Growth Without Scale Effects,” American Economic Review, 88, 5, 1290-1310. Velupillai, K. (1993), “On Leif Johansen’s Classical Model of Growth,” Journal of Economic Behavior and Organization, 22, 153-159. Verspagen, B. (1992), “Endogenous Innovation in Neo-Classical Growth Models: A Survey,” Journal of Macroeconomics, Vol 14, No. 4, pp. 631-62.

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Table 1. Variable Definitions

w : Money wages p : Price level

L: Labor employed N: Population Y: Gross Output µ : Wage share v : Employment rate (L/N) ρ : Capital productivity A : Labor productivity γ : Rate of labor augmenting technological change s : Savings rate δ : Rate of capital depreciation

n : Population growth rate (•

N

N )

χ :Output per capita (Y/N)

nu :Natural rate of unemployment

21

Table 2: Tests for Unit Roots Country

A,ττ A,τφ AZ ,τ A,µτ AZ ,µ x,ττ x,τφ xZ ,τ x,µτ xZ ,µ

USA -1.98 2.31 -6.80 -1.34 -1.35 -2.31 2.67 -10.22 -0.43 -0.32 UK -2.50 3.14 -13.66 -0.50 -0.35 -3.13 4.91 -23.08** -0.09 -0.05 ARGENTINA -0.44 1.38 -1.79 -1.66 -2.85 -0.40 1.38 -1.51 -1.56 -3.38 AUSTRALIA -1.95 2.09 -8.56 -1.01 -1.05 -2.50 3.14 -12.28 -0.56 -0.47 AUSTRIA -0.39 8.42** -0.52 -4.07* -1.41 -0.94 4.68 -1.80 -3.07** -1.10 BELGIUM -0.91 1.24 -2.25 -1.65 -0.71 -1.03 0.64 -2.64 -0.62 -0.25 BOLIVIA -0.57 0.48 -1.42 -0.99 -1.20 -0.81 0.48 -2.10 -0.93 -1.37 BRAZIL -0.19 1.80 -0.52 -1.90 -1.27 -0.20 1.10 -0.56 -1.49 -0.94 CANADA -2.41 3.08 -10.67 -0.94 -0.73 -2.03 2.08 -7.35 -0.08 -0.04 COLOMBIA -1.31 1.48 -4.71 -1.33 -0.84 -2.08 2.29 -10.17 -0.09 -0.06 CYPRUS -2.85 4.07 -14.56 -0.49 -0.58 -2.93 4.33 -15.41 -0.26 -0.28 DENMARK -0.86 1.48 -2.03 -1.70 -1.20 -1.16 0.88 -3.57 -0.86 -0.52 DOMINICAN REP. -1.09 2.32 -4.41 -2.12 -2.63 -2.12 2.78 -11.16 -1.48 -1.98 EL SALVADOR -0.97 4.08 -1.96 -2.73 -3.36 -0.87 2.73 -1.94 -2.27 -3.04 FINLAND -2.30 4.25 -7.79 -2.06 -1.16 -2.33 3.26 -10.10 -1.26 -0.68 FRANCE -0.12 9.96* -0.15 -4.37* -1.24 -0.10 4.81 -0.14 -3.09** -0.86 GERMANY, WEST -1.74 16.70* -2.28 -5.85* -2.14 -3.00 16.15* -4.54 -5.26* -1.92 GREECE 0.16 2.25 0.33 -2.33 -0.92 0.26 3.00 0.48 -2.32 -0.94 GUATEMALA 0.26 1.19 0.51 -1.59 -1.30 -0.06 1.04 -0.12 -1.29 -1.30 GUYANA -0.90 1.41 -2.98 -0.43 -1.38 -1.27 1.17 -4.88 -1.21 -4.64 HONDURAS -0.23 1.27 -0.68 -1.57 -1.67 -1.09 0.97 -3.91 -1.20 -1.53 ICELAND -2.21 3.09 -10.68 -1.44 -1.23 -2.45 3.05 -12.56 -0.60 -0.42 INDIA -2.05 2.17 -9.18 -0.15 -0.19 -1.37 1.23 -5.41 0.16 0.25 KENYA -2.41 3.10 -12.61 -1.60 -3.99 -3.17 5.02 -17.09 -1.51 -4.53 LUXEMBOURG -2.43 2.96 -11.09 -0.44 -0.46 -2.80 4.34 -14.60 0.32 0.35 MAURITIUS -1.49 2.06 -5.40 -0.28 -0.83 -1.41 2.61 -4.36 0.24 0.56 MOROCCO -1.34 1.09 -4.65 -0.99 -1.03 -2.04 2.08 -8.02 -0.45 -0.44 NETHERLANDS -0.65 3.48 -1.13 -2.66 -1.53 -0.81 1.03 -1.96 -1.35 -0.74 NEW ZELAND -1.20 1.26 -4.15 -1.48 -2.24 -1.84 1.82 -8.01 -0.94 -1.11 NICARAGUA -0.67 5.47 -1.51 -1.80 -3.98 -0.83 4.66 -2.03 -1.67 -4.09 NIGERIA -0.30 1.12 -0.79 -1.39 -2.01 -0.86 0.83 -2.32 -1.30 -1.97 PARAGUAY -1.91 1.84 -6.69 -0.54 -0.74 -2.04 2.22 -6.54 -0.37 0.53 PERU 0.06 5.00 0.14 -2.35 -3.60 -0.14 3.66 -0.42 -2.26 -3.88 PHILIPPINES -1.34 7.16** -2.41 -3.83 -2.56 -1.32 4.13 -2.95 -2.89 -2.30 SPAIN -0.99 3.89 -1.75 -2.82 -1.39 -1.38 3.60 -2.64 -2.61 -1.35 SRI LANKA -1.71 1.64 -6.21 -0.05 -0.07 -1.44 1.58 -4.34 0.30 0.40 SWEDEN -0.94 3.96 -1.59 -2.84 -1.27 -0.66 2.32 -1.30 -2.16 -0.78 SWITZERLAND -1.60 2.64 -4.14 -2.07 -1.69 -1.67 2.66 -4.39 -1.98 -1.45 TRINIDAD & TOBAGO -0.38 5.32 -0.89 -2.95** -3.56 -0.41 3.58 -1.14 -2.59 -3.00 TURKEY -2.94 5.78 -10.59 -2.15 -1.74 -3.51** 6.83** -15.31 -1.69 -1.77 UGANDA -2.89 4.37 -15.28 -2.97** -14.63** -3.08 4.87 -16.49 -3.16** -16.56** URUGUAY -2.85 4.21 -13.24 -2.31 -7.57 -2.78 3.96 -12.85 -2.47 -9.23

*=significant at 1%, **=significant at 5%. Unit root tests with time trend included based on

Unit root tests with time trend not included based on εδδµ +++= ∑=

−−

k

iititt DyyDy

11

t

k

iititt

TD yyD y εαδδµ ++++= ∑=

−−1

1

22

Table 3: Determination of the Optimal Lag in the VAR Model Country Lag LM(4) Norm(4) SBC HQC USA 1 0.09 0.30 -17.77 -17.96 2 0.80 0.44 -18.76 -19.09 3 0.19 0.80 -18.61 -19.10 4 0.44 0.76 -18.09 -18.79 UK 1 0.95 0.85 -19.96 -20.15 2 0.93 0.08 -20.75 -21.08 3 0.08 0.32 -20.28 -20.77 4 0.21 0.57 -19.78 -20.48 ARGENTINA 1 0.70 0.50 -18.80 -18.99 2 0.85 0.08 -18.96 -19.30 3 0.66 0.09 -18.73 -19.22 4 0.93 0.07 -18.15 -18.85 AUSTRALIA 1 0.17 0.60 -20.15 -20.34 2 0.82 0.47 -21.22 -21.55 3 0.62 0.54 -21.06 -21.56 4 0.65 0.62 -20.68 -21.38 AUSTRIA 1 0.39 0.37 -18.38 -18.57 2 0.11 0.18 -18.58 -18.92 3 0.23 0.59 -18.19 -18.69 4 0.60 0.79 -17.94 -18.63 BELGIUM 1 0.18 0.22 -19.35 -19.54 2 0.09 0.05 -19.67 -20.00 3 0.27 0.04 -19.23 -19.72 4 0.53 0.27 -18.55 -19.25 BOLIVIA 1 0.49 0.59 -20.60 -20.79 2 0.56 0.12 -20.61 -20.94 3 0.67 0.13 -20.26 -20.75 4 0.87 0.08 -20.17 -20.87 BRAZIL 1 0.71 0.68 -18.11 -18.30 2 0.71 0.01 -18.04 -18.37 3 0.64 0.18 -17.97 -18.46 4 0.80 0.40 -17.55 -18.25 CANADA 1 0.01 0.31 -16.88 -17.07 2 0.74 0.01 -17.91 -18.24 3 0.45 0.71 -17.62 -18.11 4 0.74 0.64 -17.13 -17.83 COLOMBIA 1 0.37 0.60 -20.15 -20.34 2 0.35 0.52 -20.00 -20.33 3 0.32 0.93 -20.04 -20.53 4 0.62 0.99 -20.27 -20.97 DENMARK 1 0.36 0.79 -19.86 -20.05 2 0.58 0.12 -20.58 -20.91 3 0.56 0.09 -20.47 -20.96 4 0.59 0.02 -20.16 -20.86 DOMINICAN REP. 1 0.58 0.69 -16.81 -17.00 2 0.32 0.00 -16.93 -17.26 3 0.12 0.02 -16.71 -17.21 4 0.39 0.69 -16.00 -16.70 EL SALVADOR 1 0.50 0.18 -20.44 -20.64 2 0.54 0.80 -21.15 -21.48 3 0.85 0.64 -21.39 -21.88

23

4 0.80 0.73 -20.69 -21.39 FINLAND 1 0.80 0.39 -21.44 -21.63 2 0.70 0.07 -21.78 -21.11 3 0.28 0.11 -21.36 -21.85 4 0.37 0.13 -21.16 -21.86 FRANCE 1 0.54 0.17 -21.34 -21.53 2 0.32 0.02 -21.47 -21.80 3 0.57 0.02 -20.92 -21.42 4 0.60 0.46 -20.34 -21.05 GERMANY, WEST 1 0.30 0.06 -16.18 -16.36 2 0.46 0.14 -15.69 -16.01 3 0.51 0.10 -15.49 -15.97 4 0.38 0.23 -15.42 -16.08 GREECE 1 0.48 0.33 -20.18 -20.37 2 0.31 0.28 -20.55 -20.88 3 0.22 0.26 -19.96 -20.45 4 0.12 0.66 -19.41 -20.11 GUATEMALA 1 0.49 0.14 -20.29 -20.48 2 0.42 0.03 -20.56 -20.89 3 0.64 0.05 -19.94 -20.44 4 0.79 0.12 -19.53 -20.23 GUYANA 1 0.29 0.39 -14.23 -14.42 2 0.35 0.01 -14.66 -14.99 3 0.50 0.03 -14.19 -14.68 4 0.43 0.27 -13.62 -14.32 HONDURAS 1 0.07 0.65 -18.20 -18.39 2 0.61 0.51 -18.82 -19.16 3 0.84 0.66 -18.37 -18.86 4 0.92 0.24 -17.72 -18.42 ICELAND 1 0.03 0.49 -16.62 -16.81 2 0.95 0.00 -17.98 -18.31 3 0.91 0.06 -17.28 -17.78 4 0.11 0.32 -17.43 -18.13 INDIA 1 0.24 0.06 -18.52 -18.71 2 0.47 0.08 -18.25 -18.58 3 0.44 0.11 -18.25 -18.75 4 0.33 0.11 -18.38 -19.08 KENYA 1 0.85 0.58 -12.74 -12.93 2 0.67 0.00 -13.60 -13.93 3 0.58 0.00 -12.99 -13.48 4 0.69 0.00 -12.15 -12.85 LUXEMBOURG 1 0.28 0.02 -16.55 -16.74 2 0.04 0.01 -17.01 -17.35 3 0.46 0.10 -16.92 -17.41 4 0.25 0.40 -17.41 -18.11 MAURITIUS 1 0.16 0.85 -15.73 -15.93 2 0.73 0.12 -16.61 -16.94 3 0.67 0.19 -16.18 -16.67 4 0.96 0.01 -16.26 -16.96 MOROCCO 1 0.15 0.30 -15.13 -15.32 2 0.14 0.19 -14.90 -15.23 3 0.16 0.25 -14.76 -15.25 4 0.55 0.68 -14.46 -15.16

24

NETHERLANDS 1 0.32 0.94 -20.68 -20.87 2 0.85 0.21 -20.93 -21.26 3 0.70 0.26 -20.57 -21.06 4 0.83 0.53 -20.02 -20.72 NEW ZELAND 1 0.09 0.93 -20.01 -20.20 2 0.12 0.02 -20.28 -20.61 3 0.21 0.14 -19.62 -20.11 4 0.39 0.57 -19.96 -20.67 NICARAGUA 1 0.23 0.00 -16.82 -17.01 2 0.19 0.00 -18.02 -18.35 3 0.60 0.02 -17.52 -18.02 4 0.91 0.19 -16.99 -17.69 NIGERIA 1 0.55 0.28 -11.51 -11.70 2 0.82 0.01 -12.36 -12.70 3 0.88 0.08 -11.66 -12.16 4 0.61 0.51 -11.73 -12.43 PARAGUAY 1 0.40 0.22 -18.81 -19.00 2 0.74 0.05 -19.06 -19.39 3 0.44 0.08 -18.41 -18.90 4 0.47 0.47 -17.94 -18.64 PERU 1 0.31 0.28 -15.92 -16.11 2 0.98 0.01 -16.87 -17.20 3 0.89 0.02 -16.55 -17.04 4 0.97 0.04 -16.20 -16.91 PHILIPPINES 1 0.07 0.27 -19.18 -19.37 2 0.96 0.29 -20.19 -20.52 3 0.76 0.28 -19.84 -20.33 4 0.79 0.20 -19.33 -20.03 SPAIN 1 0.59 0.69 -18.61 -18.80 2 0.69 0.01 -19.39 -19.72 3 0.72 0.05 -18.80 -19.30 4 0.92 0.21 -18.10 -18.81 SRI LANKA 1 0.04 0.68 -16.76 -16.95 2 0.40 0.34 -18.12 -18.45 3 0.18 0.03 -18.76 -19.26 4 0.01 0.53 -18.31 -19.01 SWEDEN 1 0.07 0.48 -20.91 -21.10 2 0.29 0.00 -21.42 -21.75 3 0.16 0.23 -21.31 -21.80 4 0.26 0.50 -20.74 -21.44 SWI TZERLAND 1 0.41 0.01 -20.22 -20.41 2 0.82 0.00 -20.53 -20.86 3 0.85 0.01 -19.82 -20.31 4 0.96 0.10 -19.45 -20.15 TRINIDAD & TOBAGO

1 0.54 0.25 -16.57 -16.76

2 0.97 0.00 -16.96 -17.29 3 0.94 0.02 -16.43 -16.92 4 0.91 0.08 -16.35 -17.05 TURKEY 1 0.04 0.17 -17.88 -18.07 2 0.68 0.32 -18.36 -18.69 3 0.19 0.35 -18.11 -18.60 4 0.68 0.46 -17.62 -18.32 UGANDA 1 0.06 0.01 -13.28 -13.47

25

2 0.55 0.00 -13.69 -14.02 3 0.27 0.08 -14.04 -14.53 4 0.24 0.56 -13.62 -14.32 URUGUAY 1 0.01 0.71 -20.75 -20.94 2 0.05 0.21 -21.03 -21.37 3 0.16 0.26 -20.97 -21.47 4 0.34 0.30 -20.82 -21.52

All statistics are 2χ . LM is the Breusch-Godfrey Lagrange multiplier test for autocorrelation at a lag of 4. The test for normanlity is a multivariate version of Shenton and Bowmantest proposed by Doornik and Hansen [1994]. P-values are reported. SBC and HQC are multivariate Schwarz Bayesian criterion and the multivariate Hannan and Quinn criterion.

Table 4: Testing Cointegratin for χ and A Using Johansen's Maximum Liklihood Procedure

Country (lag) Eigenvalue Null Hypothesis

Alternative Hypothesis

95% 99%

26

Hypothesis Hypothesis

USA (3) Trace Test: 0.4743 r = 0 r > 0 22.79 17.95 23.52 Lambda Max: 0.4743 r = 0 r = 1 16.08 14.90 19.19 0.2356 r = 1 r = 2 6.72 8.18 11.65 Trace Test: UK (1) 0.7836 r = 0 r > 0 54.33 17.95 23.52 Lambda Max: 0.7836 r = 0 r = 1 45.92 14.90 19.19 0.2445 r = 1 r = 2 8.41 8.18 11.65 ARGENTINA (2) Trace Test: 0.3568 r = 0 r > 0 19.86 17.95 23.52 Lambda Max: 0.3568 r = 0 r = 1 12.35 14.90 19.19 0.2350 r = 1 r = 2 7.50 8.18 11.65 AUSTRALIA (2) Trace Test: 0.3147 r = 0 r > 0 17.78 17.95 23.52 Lambda Max: 0.3147 r = 0 r = 1 10.58 14.90 19.19 0.2268 r = 1 r = 2 7.20 8.18 11.65 AUSTRIA (4) Trace Test: 0.4561 r = 0 r > 0 22.21 17.95 23.52 Lambda Max: 0.4561 r = 0 r = 1 12.79 14.90 19.19 0.3615 r = 1 r = 2 9.42 8.18 11.65 BELGIUM (4) Trace Test: 0.5414 r = 0 r > 0 22.23 17.95 23.52 Lambda Max: 0.5414 r = 0 r = 1 16.37 14.90 19.19 0.2434 r = 1 r = 2 5.86 8.18 11.65 BOLIVIA (2) Trace Test: 0.6060 r = 0 r > 0 35.13 17.95 23.52 Lambda Max: 0.6060 r = 0 r = 1 26.08 14.90 19.19 0.2762 r = 1 r = 2 9.05 8.18 11.65 BRAZIL (1) Trace Test: 0.8621 r = 0 r > 0 64.02 17.95 23.52 Lambda Max: 0.8621 r = 0 r = 1 59.43 14.90 19.19 0.1419 r = 1 r = 2 4.59 8.18 11.65 CANADA (3) Trace Test: 0.3851 r = 0 r > 0 19.52 17.95 23.52 Lambda Max: 0.3851 r = 0 r = 1 12.16 14.90 19.19 0.2552 r = 1 r = 2 7.37 8.18 11.65 COLOMBIA (4) Trace Test: 0.4533 r = 0 r > 0 18.98 17.95 23.52 Lambda Max: 0.4533 r = 0 r = 1 12.68 14.90 19.19 0.2593 r = 1 r = 2 6.30 8.18 11.65 DENMARK (1) Trace Test: 0.9567 r = 0 r > 0 103.12 17.95 23.52

27

Lambda Max: 0.9567 r = 0 r = 1 94.21 14.90 19.19 0.2569 r = 1 r = 2 8.91 8.18 11.65 DOMINICAN REP. (1) Trace Test: 0.9020 r = 0 r > 0 74.52 17.95 23.52 Lambda Max: 0.9020 r = 0 r = 1 69.69 14.90 19.19 0.1487 r = 1 r = 2 4.83 8.18 11.65 EL SALVADOR (3) Trace Test: 0.4931 r = 0 r > 0 18.44 17.95 23.52 Lambda Max: 0.4931 r = 0 r = 1 16.99 14.90 19.19 0.0565 r = 1 r = 2 1.45 8.18 11.65 FINLAND (1) Trace Test: 0.9798 r = 0 r > 0 121.30 17.95 23.52 Lambda Max: 0.9798 r = 0 r = 1 117.00 14.90 19.19 0.1338 r = 1 r = 2 4.31 8.18 11.65

FRANCE (4) Trace Test: 0.5206 r = 0 r > 0 20.32 17.95 23.52 Lambda Max: 0.5206 r = 0 r = 1 15.44 14.90 19.19 0.2073 r = 1 r = 2 4.88 8.18 11.65 GERMANY, WEST (2) Trace Test: 0.3258 r = 0 r > 0 19.78 17.95 23.52 Lambda Max: 0.3258 r = 0 r = 1 11.83 14.90 19.19 0.2329 r = 1 r = 2 7.95 8.18 11.65 GREECE (2) Trace Test: 0.3819 r = 0 r > 0 18.21 17.95 23.52 Lambda Max: 0.3819 r = 0 r = 1 13.47 14.90 19.19 0.1558 r = 1 r = 2 4.74 8.18 11.65 GUATEMALA (1) Trace Test: 0.9264 r = 0 r > 0 83.34 17.95 23.52 Lambda Max: 0.9264 r = 0 r = 1 78.27 14.90 19.19 0.1553 r = 1 r = 2 5.06 8.18 11.65 GUYANA (1) Trace Test: 0.7961 r = 0 r > 0 50.07 17.95 23.52 Lambda Max: 0.7961 r = 0 r = 1 47.70 14.90 19.19 0.0758 r = 1 r = 2 2.36 8.18 11.65 HONDURAS (3) Trace Test: 0.3065 r = 0 r > 0 14.12 17.95 23.52 Lambda Max: 0.3065 r = 0 r = 1 9.15 14.90 19.19 0.1801 r = 1 r = 2 4.97 8.18 11.65 ICELAND (4) Trace Test: 0.5493 r = 0 r > 0 24.84 17.95 23.52 Lambda Max: 0.5493 r = 0 r = 1 16.74 14.90 19.19 0.3202 r = 1 r = 2 8.11 8.18 11.65

28

INDIA (3) Trace Test: 0.3474 r = 0 r > 0 17.89 17.95 23.52 Lambda Max: 0.3474 r = 0 r = 1 10.67 14.90 19.19 0.2507 r = 1 r = 2 7.22 8.18 11.65 KENYA (1) Trace Test: 0.2230 r = 0 r > 0 8.53 17.95 23.52 Lambda Max: 0.2230 r = 0 r = 1 7.57 14.90 19.19 0.0316 r = 1 r = 2 0.96 8.18 11.65 LUXEMBOURG (4) Trace Test: 0.6622 r = 0 r > 0 30.44 17.95 23.52 Lambda Max: 0.6622 r = 0 r = 1 22.79 14.90 19.19 0.3054 r = 1 r = 2 7.65 8.18 11.65 MAURITIUS (3) Trace Test: 0.3125 r = 0 r > 0 13.74 17.95 23.52 Lambda Max: 0.3125 r = 0 r = 1 9.37 14.90 19.19 0.1606 r = 1 r = 2 4.38 8.18 11.65 MOROCCO (4) Trace Test: 0.5941 r = 0 r > 0 23.61 17.95 23.52 Lambda Max: 0.5941 r = 0 r = 1 18.94 14.90 19.19 0.1995 r = 1 r = 2 4.67 8.18 11.65 NETHERLANDS (2) Trace Test: 0.4167 r = 0 r > 0 23.04 17.95 23.52 Lambda Max: 0.4167 r = 0 r = 1 15.09 14.90 19.19 0.2471 r = 1 r = 2 7.95 8.18 11.65 NEW ZELAND (4) Trace Test: 0.7244 r = 0 r > 0 32.27 17.95 23.52 Lambda Max: 0.7244 r = 0 r = 1 27.07 14.90 19.19 0.2196 r = 1 r = 2 5.21 8.18 11.65 NICARAGUA (4) Trace Test: 0.4729 r = 0 r > 0 20.52 17.95 23.52 Lambda Max: 0.4729 r = 0 r = 1 13.45 14.90 19.19 0.2860 r = 1 r = 2 7.07 8.18 11.65 NIGERIA (4) Trace Test: 0.4928 r = 0 r > 0 23.33 17.95 23.52 Lambda Max: 0.4928 r = 0 r = 1 14.26 14.90 19.19 0.3510 r = 1 r = 2 9.08 8.18 11.65 NORWAY (1) Trace Test: 0.8511 r = 0 r > 0 67.64 17.95 23.52 Lambda Max: 0.8511 r = 0 r = 1 57.14 14.90 19.19 0.2953 r = 1 r = 2 10.50 8.18 11.65 PAKISTAN (4) Trace Test: 0.7466 r = 0 r > 0 39.51 17.95 23.52 Lambda Max:

29

0.7466 r = 0 r = 1 28.83 14.90 19.19 0.3985 r = 1 r = 2 10.68 8.18 11.65 PARAGUAY (1) Trace Test: 0.5741 r = 0 r > 0 30.12 17.95 23.52 Lambda Max: 0.5741 r = 0 r = 1 25.60 14.90 19.19 0.1398 r = 1 r = 2 4.52 8.18 11.65 PERU (1) Trace Test: 0.5857 r = 0 r > 0 28.31 17.95 23.52 Lambda Max: 0.5857 r = 0 r = 1 26.43 14.90 19.19 0.0606 r = 1 r = 2 1.88 8.18 11.65 PHILIPPINES (2) Trace Test: 0.3638 r = 0 r > 0 17.77 17.95 23.52 Lambda Max: 0.3638 r = 0 r = 1 12.66 14.90 19.19 0.1666 r = 1 r = 2 5.10 8.18 11.65 SPAIN (4) Trace Test: 0.2575 r = 0 r > 0 10.23 17.95 23.52 Lambda Max: 0.2575 r = 0 r = 1 6.25 14.90 19.19 0.1727 r = 1 r = 2 3.98 8.18 11.65 SRI LANKA (2) Trace Test: 0.4114 r = 0 r > 0 17.90 17.95 23.52 Lambda Max: 0.4114 r = 0 r = 1 14.84 14.90 19.19 0.1037 r = 1 r = 2 3.06 8.18 11.65 SWEDEN (3) Trace Test: 0.5404 r = 0 r > 0 26.98 17.95 23.52 Lambda Max: 0.5404 r = 0 r = 1 19.44 14.90 19.19 0.2605 r = 1 r = 2 7.54 8.18 11.65 SWITZERLAND (4) Trace Test: 0.5998 r = 0 r > 0 22.00 17.95 23.52 Lambda Max: 0.5998 r = 0 r = 1 19.23 14.90 19.19 0.1236 r = 1 r = 2 2.77 8.18 11.65 TRINIDAD & TOBAGO (1) Trace Test: 0.8603 r = 0 r > 0 63.51 17.95 23.52 Lambda Max: 0.8603 r = 0 r = 1 59.05 14.90 19.19 0.1383 r = 1 r = 2 4.46 8.18 11.65 TURKEY (2) Trace Test: 0.2911 r = 0 r > 0 15.04 17.95 23.52 Lambda Max: 0.2911 r = 0 r = 1 9.63 14.90 19.19 0.1755 r = 1 r = 2 5.40 8.18 11.65 UGANDA (4) Trace Test: 0.3117 r = 0 r > 0 12.08 17.95 23.52 Lambda Max: 0.3117 r = 0 r = 1 7.84 14.90 19.19 0.1827 r = 1 r = 2 4.24 8.18 11.65 URUGUAY (4) Trace Test:

30

0.6500 r = 0 r > 0 25.22 17.95 23.52 Lambda Max: 0.6500 r = 0 r = 1 22.05 14.90 19.19 0.1404 r = 1 r = 2 3.18 8.18 11.65

Lambda Max is a maximum eigen value test for at most r cointegrating vectors against an alternative of r+1 cointegrating vectors. Trace is a stochastic matrix trace test for at most r cointegrating vectors.