EXPORTS AND PRODUCTIVITY IN A SMALL OPEN ECONOMY:
A Causal Analysis of Aggregate Norwegian Data
Erik Nesset*
Aalesund University College
October 2001
ABSTRACT
Keywords: Trade; Productivity; Causality; Cointegration
JEL classification: F12; F14; F43; C32; C51
*
Institute of International Business and Marketing, Aalesund University College, 6025 Aalesund, Norway.
Email:en@hials.no, tel: +4770161319; fax: +4770161300. I would like to thank Kjell Grønhaug for valuable comments on
earlier versions of the paper. Thanks also to Roger Hammersland and Gunnar Bårdsen for comments and stimulating
discussions. The estimation results are based on PcGive 9.0 and PcFiml 9.0.
1.
INTRODUCTION
If export growth causes productivity growth, an initial export stimulus may lead to a "virtuous
circle" in productivity growth through economies of scale and price competitiveness (Beckerman
(1965), Atesoglu (1994)). Given this dynamic externality, the policy recommendations would
then be some kind of strategic trade policy, e.g. an export subsidy. If, on the other hand, the
Ricardian model of international trade is valid, the causality is turned the other way around, and
an optimal growth policy would involve more direct productivity stimulus, e.g. R&D or
educational support. Despite an upsurge in research over the past decades, the frequently
observed co-movement of export volume and productivity still seems to be a caveat in the
economic literature of economic growth and international trade. To be able to give adequate trade
and industrial policy recommendations, the fundamental causal links between exports and
productivity must be uncovered, and this is mainly an empirical problem. The theoretical
considerations, however, play a vital role by imposing identifying structure on the empirical
model.
Previous causality analyses within this field were largely based on cross-country correlations
between productivity (or Gross Domestic Product) and exports.1 They often failed to identify the
empirical findings, and the results may simply reflect the fact that exports are a component of
Gross Domestic Product, and not a fundamental causal link. More recent analyses focus on
modern time-series techniques like Granger-causality and cointegration (Kunst and Marin
(1989), Marin (1992), Ghatak, Milner and Utkulu (1995)). But even with these approaches, lack
of structural identifying conditions may give rise to the classical identification problem. The
cointegration approach in Marin (1992) implicitly assumes the presence of one unique
cointegration relationship. With more than two variables in the information set this assumption
will hardly be statistically or theoretically acceptable: there probably will be more than one
See e.g. Marin (1992).
relationship governing the joint behaviour of the variables. In general, any linear combination of
cointegration vectors will form a new cointegration vector. The one that shows up when
assuming only one such relationship may therefore give parameters which are difficult to
interpret. Another shortcoming of previous studies is connected to the interpretation of the
causality-concept. By applying Granger-causality tests the previous exports-productivity analyses
cannot claim to have revealed fundamental causal links, as causality is closely related to
explanations and not mere predictions. To be able to recommend the proper policy for
productivity enhancement, we need a model with autonomous relations. It therefore seems to be a
gap between the theoretical claims and the empirical practice regarding analyses of causal
relationships within this field.
In order to deal with some of the shortcomings of the earlier analyses and partly fill the gap
between theory and empirical practice, I will focus on the identification of possible cointegrating
relationships within a more comprehensive information set, and test the exports-productivity
relationship for the degree of autonomy by applying different exogeneity tests. By exploiting the
techniques of multivariate cointegration (Johansen (1988, 1994) and Johansen and Juselius
(1994)) a statistical congruent vector autoregression (VAR) model will serve as a general point of
departure for structural testing and identification of fundamental causal links. Stability and
invariance of the parameters of interest will be a central part of the empirical analysis, and this is
approached by different exogeneity tests. What we are really interested in is the kind of policy
that will be relevant for improving the productivity performance of firms, and to be able to give
such advice the link(s) between exports and productivity must be reasonably stable with respect
to the recommended interventions. The novelty of this paper thus lies in assessing the exportsproductivity causality issue within this structural VAR-modelling approach, with strong
emphasis on parameter stability and invariance.
The rest of the paper is organized as follows: Section 2 contains the theoretical framework.
Section 3 briefly describes the data. In section 4 some methodological issues are discussed,
focusing on cointegration, invariance and exogeneity in particular. In section 5, cointegrating
vectors and exogeneity test results are reported. Section 6 summarizes and concludes.
2
A CONCEPTUAL FRAMEWORK
2.1
The export-led growth hypothesis
According to the traditional export-led growth hypothesis, export growth causes positive
productivity growth through various externalities (e.g. Beckerman (1965), Kaldor (1970)). For a
small open economy, the external demand enables a small economy to exploit economies of
scale, and makes the domestic firms internationally competitive. This will boost productivity
growth and cause a dampening on the wage cost inflation (given that wages are not 100 percent
productivity-indexed). Lower wage cost inflation will improve the price competitiveness, and
further increase the growth of exports. The initial export stimulus may, accordingly, induce a
"cumulative causation" mechanism in productivity growth, and export promotion policies will
have a significant effect on productivity. This is the essence of the Kaldorian export-led growth
model, originally outlined in Kaldor (1970) and further formalized in Dixon and Thirlwall (1975,
1979). A static version of the Dixon-Thirlwall model can be represented by the four equations:
(2.1)
ln(X) = ax + bxp {ln(PX) - ln(PF)} + bxy ln(YF),
(2.2)
ln(PX) = apx + bpwz {ln(WC) - ln(ZY)},
(2.3)
ln(ZY) = azy + bzy ln(Y) + bzTT,
bzy , bzT > 0
(2.4)
ln(Y) = ay + byx ln(X),
byx > 0

bxp < 0, bxy > 0
bpwz = 1
where X is real export volume, PX is the export deflator, PF is the external price expressed in
domestic currency, YF is world's real income, WC is domestic wage costs, ZY is labour
productivity, Y is real output and T is a linear trend. Equation (2.1) is an export demand
equation, similar to an ordinary Armington function (Armington (1968)). Equation (2.2) is an
export price relation, expressed as a constant mark-up on unit labour costs.2 This is also in
correspondence with the Armington monopolistic competition model, in which export prices are
determined under the assumptions of constant elasticity of demand and constant marginal costs.
This implies an export price equation conditioned on costs and technology, with a constant markup. Equation (2.3) is a static version of Verdoorn's law, which states that labour productivity
growth is determined by output growth and autonomous productivity growth. In Dixon-Thirlwall
(1975) the autonomous rate of labour productivity growth is determined by the autonomous rate
of disembodied technological progress, autonomous rate of capital growth per worker, and the
extent to which technical progress is embodied in capital accumulation. Assuming that these
autonomous growth rates are constant, this will be captured by a linear trend in the static version
of Verdoorn's law. Equation (2.4) reflects the Kaldorian view that output growth is determined
by demand, and, in particular, by exports. Substituting (2.4) into (2.3) gives:
(2.5)
ln(ZY) = (azy + ay ) + bzyx ln(X) + bzTT,
where bzyx = bzy · byx
Equations (2.1), (2.2) and (2.5) may now be regarded as a static version of the Dixon-Thirlwall
export-led growth model.
The advances in "new" endogenous growth theory, with contributions by e.g. Romer (1986,
1990), Lucas (1988), Rivera-Batiz and Romer (1991) and Young (1991), seem to support the
traditional export-led growth hypothesis. In Romer's (1986,1990) theory this is accomplished by
introducing non-convexity of the cost function, with semi-fixed inputs, including non-rival
2
Assuming that the growth rate of the mark-up on unit labour costs is zero, this is captured by a constant term in the static
equation.
factors. In line with the endogenous growth arguments, Grossman and Helpman (1990) lists four
features of a globalized economy: 1) comparative advantages determine the extent of
specialization in human capital intensive production of goods, 2) large scale of the world
economy induces an exploitation of new technologies, 3) ideas and information spread quickly
and creates spillover effects (positive externalities) and 4) better financial opportunities induces
ordinary investments in general and investments in research and developement in particular. The
export-led growth hypothesis thus seems to be consistent with the endogenous growth theory,
only shifting the externality focus from knowledge to exports. The causal implication seems
clear: export growth causes productivity growth through positive external effects.
2.2
Trade theory and causal ambiguity
In the Ricardian model of international trade, differences in labour requirements induces
comparative advantages between countries. Within this classical model increases in labour
productivity will cause export expansions. Vernon's (1966) "product cycle" theory, which is a
simplified description of the innovation and technology transfer processes in world trade, also
proposes a positive causality that runs from productivity to trade. New trade theory based on
imperfect competition is, however, fundamentally ambiguous with respect to both the sign and
the direction of the causality.
Assuming a representative monopolistic competitive firm facing a downward sloping demand
curve similar to equation 2.1, profit maximazation yields the familiar marginal costs mark-up
relationship where the mark-up consists of the elasticity of demand. With both constant elasticity
of demand and constant marginal costs, shifts in the demand curve via changes in foreign prices
and/or world trade volume will have no effect effect on export prices - i.e they are determined
solely by domestic costs and technology (like equation 2.2). Lack of foreign price impulses in
Norwegian export price equations are, however, contrasted by empirical evidence in e.g. Nesset
(1992) and Hammersland (1996). Allowing for non-constant marginal costs, export prices will
also be influenced by the demand side. This is also the case in an oligopoly setting where the
importance of the competitors' behaviour must be stressed. Although oligopoly theory does not
yield a well defined price equation, it is assumed that even though costs are important, firms are
constrained in their pricing behaviour by the threat of potential competition (Cuthbertson
(1985)). Compared to equation 2.2 in the export-led growth model outlined above, export prices
will now be determined by both domestic costs and foreign prices, and probably also by the level
of capacity utilization (cu):
(2.6)
ln(PX) = apx + bpw {ln(WC) - ln(ZY)} + (1-bpw ) ln(PF) + bpcu cu
Within the recent development of trade theories where imperfect competiton, economies of scale
and product differentiation are present, it is suggested that productivity will increase in response
to exploitation of the scale, and thereby causing intra-idustry trade. Trade may on the other hand
increase average productivity by shifting resources to industries with lower average costs, and
through concentration and - if increased competition induces exit - rationalization of the
production (see e.g. Helpman and Krugman (1985), Flam and Helpman (1987) and Krugman
(1994)). There may also be a link from terms of trade to both productivity and exports: A
deterioration in the terms of trade (or a more direct import protection) may allow domestic sales
to expand by exploiting the scale and thereby increasing the productivity, and more indirectly by
improving the strategic position of the domestic firms (if Cournot competition). Productivity may
thus be determined both by exports and terms of trade, as well as by supply-side factors
subsumed in the trend-variable T:
(2.7)
ln(ZY) = azy + bzx ln(X) + bzp {ln(PX) - ln(PF)} + bzyT T
The causal links between exports and productivity may accordingly be bi-directional,3 and this
calls for an empirical assessment.
3.
THE DATA
The data used in this analysis are all quarterly seasonally unadjusted series, covering the period
1966.4 - 1992.4. The variable X is an aggregate of Norwegian mainland export volume. ZY is
value-added labour productivity in manufacturing and construction. YF is an GDP based index of
world trade. These variables are all fixed to 1991 prices. The export price index, PX, is the
implicit deflator for the X-aggregate. PF is an index of foreign competing export weighted GDP
prices in Norwegian currency. WC is hourly wage costs in manufacturing and construction. U is
"total" unemployment rate, and is a proxy for capacity utilization (cu). The series for PX, PF and
WC are indices, with 1991 as the base year. Variable definitions and sources are listed in
appendix A. Throughout the paper, lower letters indicate that the series are transformed to
logaritmic scale.
10.4
3
log(X)
5.3
log(ZY)
The sign of the causal effects will, however, depend on the underlying domestic market structure. In an oligopolistic
5.2
10.2
setting
with quantity competition (Cournot competition) firms may precommit themselves to a high level of exports by
5.1
over-investing in technology, thereby increasing labour productivity.
If, on the other hand, prices are the strategic
10
5
parameters
(Bertrand competition), an export expansion will lead to
agressive competition because of excess profits and
therefore
under-investment in technology. This implies a negative4.9causal effect from trade to productivity. The results thus
9.8
hinges on whether more or less competition induces more or less 4.8R&D.
9.6
4.7
9.4
4.6
4.5
1965
1970
1975
1980
1985
1990
1965
1970
1975
1980
1985
1990
.35
log("real exchange rate")
log(ZY) x log(X)
5.3
.3
5.2
.25
5.1
.2
5
.15
.1
4.9
.05
4.8
0
4.7
-.05
4.6
-.1
1965
Figure 3.1
1970
1975
1980
1985
1990
4.5
9.2
9.3
9.4
9.5
9.6
9.7
9.8
9.9
10
10.1
10.2
10.3
10.4
10.5
Export volume (x), labour productivity (zy), real exchange rate (px-pf), and cross plot
export volume and labour productivity. All variables in log form.
From figure 3.1 we see that the level of export (upper left panel) and labour productivity (upper
right panel) both exhibit non-stationarity. There also seems to be a co-movement between the
two series (lower right panel). The lower left panel shows the real exchange rate variable (px-pf).
Univariate unit root tests indicate that all the variables (including the real exchange rate) are first
order integrated (non-stationary) processes (I(1)), except for the unemployment rate, which can
be interpreted as a stationary process (I(0))4 (see table B.1 in appendix B).
4
Naug and Nymoen (1994) also argue for the unemployment rate in Norway as a stationary variable.
4.
COINTEGRATION HYPOTHESES, EXOGENEITY AND CAUSALITY
4.1
Cointegration hypotheses
Nonstationary variables (i.e. variables with timedependent mean, variances and/or
autocovariances), make the use of conventional inference theory difficult. If the nonstationarity
can be approximated by stocastic trends, differencing makes the variables stationary, and the
variables are called integrated variables. A variable which is made stationary by differencing d
times is accordingly integrated of order d, denoted I(d). Most economic time series appear to be
I(1). Cointegration states that a linear combination of different I(1) variables is stationary (I(0)),
and implies an empirical long-run relationship between these variables. Error correction models
incorporate these aspects by mapping the I(1) variables into the I(0)-space (see e.g. Granger
(1983)). In this way it is possible to draw valid statistical inference and at the same time preserve
the theoretical interpretability (Hendry (1994b)).
By applying the Johansen-approach (Johansen (1988)), the null hypothesis of no cointegration
may be tested against different alternatives implying two or more cointegrating vectors. A
general VAR model with the six modelled variables: xt, pxt, zyt, wct, pft and yft, the assumed I(0)variable, ut, a constant term and centered dummies (sesonals and impulse dummies) represents
the starting point for testing the various alternative hypotheses. A general imperfect competition
model of international trade, which allows for demand influences in the price determination as
well as the possibility of bi-directional causality between exports and productivity, and terms of
trade, can be represented by the three cointegrating vectors in hypothesis H1A:
H1A:
4.1)
4.2)
4.3)
{x - yf yf - px (px - pf)}
{px - wc (wc - zy) - (1-wc) pf}
{zy - x x - T (px - pf)}
~
~
~
I(0)
I(0)
I(0)
The first vector is the export demand relation, the second vector is the export price relation and
the third vector is the productivity/exports/terms-of-trade relation. By not restricting the constant
term to enter only the cointegration term, we may allow for a linear trend in levels, and thus
taking account of possible supply-side effects.
The Kaldorian export-led growth model, H1B, may now (partly) be represented by imposing the
restrictions wc = 1 and T = 0 in H1A:
H1B:
4.4)
4.5)
4.6)
{x - yf yf - px (px - pf)}
{px - (wc - zy)}
{zy - x x }
~
~
~
I(0)
I(0)
I(0)
In addition, we have to be explicit about the causal direction: i.e. exports are a direct cause of
productivity in equation (4.6).
As an alternative to the price setter strategy embedded in H1A , we may also consider a situation
with elasticity influenced export determination and price taking, where the domestic factors in
the export price determination are absent. Price taking implies {px - pf} ~ I(0) and
{wc - zy - pf} ~ I(0). Then {x - x yf } must also be stationary in order to obtain a balanced
export volume equation. This leaves us with the four cointegrating vectors (hypothesis H2A ) :
H2A
4.7)
4.8)
4.9)
4.10)
{x - yf yf }
{px - pf }
{wc - zy - pf }
{zy - x x}
~ I(0)
~ I(0)
~ I(0)
~ I(0)
Both of the hypothesis, H1A and H2A, can be tested against the alternatives of no cointegration
between productivity and export volume, i.e. H1A1 (4.1-4.2) and H2A1 (4.4-4.6).
4.2
Exogeneity and causality
Cointegration already implies causality in at least one direction. For two or more variables to
have a sustainable long run equilibrium there must be some kind of causation between them to
give the necessary dynamics in order to reach or stay in the equilibrium state (Granger (1988)).
One of the most common definitions of causality in the econometric literature is put forth by
Granger (1969). This definition (somewhat loosely) states that x is a Granger-cause of zy if
present zy can be better (more accurate) predicted by using past values of x. Granger-causality is,
however, basically concerned with prediction and not causality in the strict philosophical sense.
Causality is, on the other hand, connected to explanations, which necessitates an understanding
of the underlying economic structure (i.e. “structural causality”). The economic structure must
also exhibit a certain degree of stability, or, as David Hendry states: "[a parameter] defines a
structure if it is invariant and directly characterizes the relations of the economy under analyses".5
Causality is thus closely related to the well known identification problem, which consists in
finding meaningful estimates of the structural parameters in a system of equations. In order to
identify what we are analyzing we need more a priori information (identifying restrictions). This
information must be determined outside the model, and in this way identification and causality
are closely connected to the exogeneity issue.
In order to grasp the meaning of structural causality it is necessary to distinguish three different
forms of exogeneity: 1) weak exogeneity, 2) strong exogeneity and 3) super exogeneity. The first
one is concerned with conditional inference (efficient estimation) for a given set of parameters of
interest without loss of information. The parameters of interest will thus be variation free with
respect to changes in the exogenous variables. The second one is fulfilled for a variable if it is
weakly exogenous for the parameters of interest and there is no Granger-causality from the
endogenous variable to the exogenous variable (i.e. lagged values of the endogenous variable do
not improve the prediction of the exogenous variable). The last form of exogeneity, super
5
Taken from Bårdsen and Fisher (1995) p. 6.
exogeneity, is considered to be a necessary condition for valid inference in a policy analysis
experiment. This is fulfilled for a variable when it is weakly exogenous for the parameters of
interest and, in addition, the parameters are invariant for changes in policy. Super exogeneity
may thus be considered as a necessary condition for inference of “structural causality”.
Weak exogeneity with respect to the long run parameters may be evaluated within the Johansenprocedure by testing restrictions on the feedback-matrix (the 's). This is assessed by maintaining
the -restrictions imposed by e.g. H1A, and testing the joint ( and ) restrictions by a LR-test.
Table 4.1 shows the correspondance between the feedback-coefficients of the cointegration
vectors CIi (i=1,2,3) and the equations.
Cointegration vectors
Table 4.1
Equations
CI1
CI2
CI3
x
px
zy
wc
pf
yf
0
3
6
9
12
15
1
4
7
10
13
16
2
5
8
11
14
17
A general feedback-matrix
Testing for weak exogeneity means testing for zero restrictions in this matrix. If e.g. 2=0, then
disequilibrium in CI3 does not adjust through the x equation, and x must be weakly exogenous
with respect to the parameters in CI3 . This test is, however, only applicable to the long run
parameters. Another test of weak exogeneity is to test for the independency between the residuals
of the conditional and the marginal models. This can be obtained by including the estimated
residuals from the marginal model(s) in the conditional regression equation, and test the
hypothesis of a zero-impact of these residuals. This is the so called Wu-Hausman test, which is
also a test for weak exogeneity with respect to short run parameters.
Super exogeneity may be tested according to a procedure proposed by Engle and Hendry (1993):
A simple marginal model for the supposed exogenous variable is estimated. If we need variables
(e.g. dummies) to stabilize this marginal model, then we can test for invariance of the parameters
in the conditional model by including these variables in the conditional model and test for their
significance. If these variables have no impact in the conditional model, and if the conditional
model is otherwise a stable relationship with weakly exogenous variables, then we interpret these
exogenous variable(s) also to be super exogenous with respect to the parameters of the
conditional model.
5.
EMPIRICAL RESULTS
5.1
Cointegration
System: xt, pxt, zyt, wct, pft, yft. Predetermined (I(0)): ut
Deterministic part: unrestricted const, centered seasonals and impulse dummies (OPEC2, DEVAL78,DEVAL86)
Estimation period: 1968 (1) – 1992 (4)
VAR order: 4
Eigenvalues: 1 = 0.35 2 = 0.21 3 = 0.17 4 = 0.14 5 = 0.11 6 = 0.08
max eigenvalue test
null
Alternative
r=0
r1
r2
r3
r4
r5
r=1
r=2
r=3
r=4
r=5
r=6
eigenvalue trace test
43.6 (39.4)
24.1 (33.5)
18.6 (27.1)
15.0 (21.0)
12.8 (14.1)
8.5 (3.8)
null
alternative
r=0
r1
r2
r3
r4
r5
r1
r2
r3
r4
r5
r=6
Values in brackets are the critical values at the 5%-level (Doornik and Hendry (1997)).
Table 5.1:
Johansen cointegration tests
122.0 (94.2)
78.4 (68.5)
54.3 (47.2)
35.7 (29.7)
20.7 (15.4)
8.5 (3.8)
Equation
xt
pxt
zyt
wct
pft
yft
AR 1-5 F[5,63]
0.50
0.92
2.94
2.01
0.77
0.48
Vector
(0.77)
(0.47)
(0.02)
(0.09)
(0.57)
(0.78)
2N [2]
ARCH 4 F[4, 60]
0.15
0.77
1.72
0.04
0.52
0.93
(0.96)
(0.54)
(0.16)
(0.99)
(0.72)
(0.45)
F[180,202]
1.04 (0.39)
0.64
5.51
0.11
5.97
2.46
1.18
(0.73)
(0.06)
(0.95)
(0.05)
(0.29)
(0.56)
2N [12]
15.17 (0.23)
Values in brackets are the significance levels (Doornik and Hendry (1997)).
Table 5.2:
Diagnostics for the unrestricted VAR
In table 5.2 AR 1-5 is the F-distributed Lagrange multiplier (LM)test for autocorrelated residuals
from lag one to five, ARCH 4 is the F-distributed LM-test for autocorrelated squared residuals
form lag one to four, and N2 is the 2-distributed Jarque-Bera (1980) test for normally
distributed residuals. The AR 1-5 and N2 tests are reported both as single equation diagnostics
and as system (vector) diagnostics. Table 5.1 shows the results from Johansen's maximum
likelihood estimation when the length of the VAR is set to 4. The evidence seems somewhat
mixed. Based on the eigenvalue trace test we cannot reject the possibility of six cointegrating
vectors, while there is some evidence of only one cointegrating vector based on the max
eigenvalue test. The diagnostics in table 5.2 indicate residual autocorrelation in the equation for
zy, but this is not evident at the 10% critical level. Reducing the order of the VAR to 1, seems
to support the existence of three cointegrating vectors both from the max eigenvalue and the trace
test, but at the same time indicating severe problems with autocorrelated and non-normal
residuals. Monte Carlo evidence in Eitrheim (1995), however, show that the maximum likelihood
cointegration method is reasonable robust against autocorrelation and non-normality in the
marginal error processes.
Figure 5.1
Resticted cointegration vectors for export volume, export price, and labour productivity
As noted by Johansen and Juselius (1992), the cointegration tests may have low power when the
cointegration relation is close to the non-stationary boundary. This can lead to ambiguity when
choosing the number of cointegrating vectors according to the lambda max and trace tests. It is
nor always theoretically reasonable to consider a null hypothesis of a unit root, a problem that is
often present when the speed of adjustment to the hypothetical equilibrium state is slow. This
may be a problem in our empirical model, as regulations and short run dynamics probably keep
the export prices and productivity processes off the equilibrium path for a considerably length of
time.6 In such cases Johansen and Juselius (1992) propose to base the final determination of the
number of cointegrating vectors on both formal testing, the interpretability of the coefficients and
inspections of the cointegration graphs (see figure 5.1). Based on the mixed statistical evidence,
economic theory and figure 5.1, we interpret the results in favour of three cointegrating vectors.
Next we try to identify the long run system by testing general restrictions on the cointegrating
coefficients (the 's). Hypothesis H1A is tested by imposing the following restrictions: In the first
cointegrating vector we normalize on x and restrict the -coefficients for zy, wc and u to zero,
and the 's for px and pf to have the same value but opposite signs (i.e. relative price). In the
second vector we normalize on px and restrict the 's for x and yf to zero, the 's for wc and zy to
have a value of 0.1 and -0.1 respectively (i.e. unit labour costs with an elasticity of 0.1), and the
 for pf to have a value of 0.9. This implies testing homogeneity of degree one in domestic costs
and foreign prices. The third vector is normalized on zy. We further restrict px and pf to have
same coefficient but with opposite signs, and all other variables to have zero -coefficients. The
restrictions are accepted by a likelihood ratio (LR) test statistic, approximated by a 2(7)
distribution, with a value of 5.62, implying a probability value of 0.58. Hypothesis H2A is on the
other hand rejected with a 2(10) test statistic of 33.54. We can also reject H2A1 (2(9)) = 36.26).
H1A1 , on the other hand, is not rejected (2(7) = 10.29), but the probability value (0.17) is much
smaller than for H1A. The hypothesis H1B is also rejected (2(9) = 24.61).
6
The 's corresponding to the second and the third eigenvector are relatively small.
The particular homogeneity restriction in the second vector in H1A needs an explanation. A
general homogeneity restriction in the second cointegration vector (normalized on export price)
gave long run parameters which were impossible to interpret. On the other hand, we rejected H2A
and H2A1 , excluding the possibility of price-taking. After some tentatively proceedings, we
ended up imposing the particular homogeneity restriction, implying a relatively low weight for
domestic costs in the export price determination.
Table 5.4 shows the LR test-statistics for different joint ( and ) restrictions.Together with the
maintained hypothesis H1A, we cannot reject the hypothesis of export volume being weakly
exogenous with respect to the parameters in the cointegration vector for productivity, and
productivity being weakly exogenous with respect to the parameters in the cointegration vectors
for export volume and export price.
Table 5.4
LR test statistic for joint restrictions
Joint hypothesis
H1A and 2=0
H1A and 5=0
H1A and 6=0
H1A and 7=0
H1A and 2=5=6=7=0
H1A and
2=5=6=7=11=14=17=0
LR test-statistic
Probability value
2 (8) = 6.51
2 (8) = 10.02
2 (8) = 8.63
2 (8) = 5.63
2 (11) = 15.17
2 (14) = 17.75
0.59
0.26
0.37
0.69
0.17
0.22
We can reject the hypothesis of wc being weakly exogenous with respect to the parameters of the
cointegrating relations for export volume and price, even though the corresponding -values are
small. This may, however, be due to a poorly specified equation for labour wage costs in the
VAR. In appendix C we present an estimated (latent) marginal model of labour wage costs. The
estimated residuals from this marginal wage cost-model do not enter with any significance in the
export volume and price system (t-value of 0.04 and 1.32, respectively). We therefore conclude
that the wage cost-model is indeed a marginal model, and that wage costs are weakly exogenous
with respect to the parameters of the export volume and price system. We have also conducted
this Wu-Hausman test for labour productivity (see table 5.6), and conclude likewise: Labour
productivity is weakly exogenous with respect to the parameters of the export volume and price
system (the residuals from the labour productivity equation enter the export volume and price
equation with t-values of 1.71 and 0.48, respectively).
The normalized restricted cointegrating vectors are (asymptotic st.dev. in parentheses):
1)
x
= - 0.61 (px - pf) + 1.30 yf
(0.088)
2)
(0.083)
px = 0.10 (wc - zy) + 0.90 pf - 0.25 u
(0.042)
3)
zy = 0.64 x - 0.04 (px - pf)
(0.065)
(0.145)
The corresponding normalized -coefficients are:
0 = -0.39 , 1= 0.16 , 2 = 0.00 ,
3 = 0.16 , 4 = -0.07 , 5 = 0.00 ,
6 = 0.00 , 7 = 0.00 , 8 = -0.13
Disequilibrium in the long run export volume relation adjusts both through price and volume
changes. If e.g. the realized level of export volume exceeds the equilibrium level, there will be a
direct negative effect on x (-0.39). But there will also be an indirect positive effect on px
(0.16), which in turn causes x to decrease towards its equilibrium level. Disequilibrium in the
long run export price relation will also adjust through price and volume changes. When the
realized export price exceeds its equilibrium level, there will be a direct negative effect on px (0.07), as well as an indirect positive effect on x (0.16) which also contribute to an export price
movement towards its equilibrium level.
5.2
Invariance and super exogeneity
The next step is to map the data in the system to I(0) by differencing and cointegrating
combinations, and test the modelled I(0) system with respect to invariance. We model quarterly
change in export volume and export price by including - in each of the two equations - three lags
of the six system variables in differences and the three cointegrating vectors.7 Both in the export
volume and the export price equation, CI3 seems irrelevant: Disequilibrium in the long run
solutions for export volume and export price does not adjust through the productivity equation,
confirming the results from the Johansen procedure (6 = 7 = 0). We may therefore exclude CI3
from both equations.
The conditional restricted model is estimated by Full Information Maximum Likelihood (FIML).
The results are shown in table 5.5, where CI1 and CI2 are the restricted cointegration vectors for
export volume and export price respectively, and S1, S2 and S3 are the quarterly seasonal
dummies.
7
Three lags of the differenced variables matches four lags of the levels in the Johansen estimation.
Table 5.5
Estimating the model by FIML
Sample period: 1968 (2) to 1992 (4)
Equation 1 for x
Variable
Coefficient
Std.Error
T-value
________________________________________________________________
const
5.74
0.88
6.54
px_1
0.57
0.14
3.87
px_2
-0.23
0.15
-1.54
pf_2
-0.41
0.15
-2.74
zy
0.55
0.19
2.77
zy_1
0.43
0.20
2.17
yf_2
-1.59
0.67
-2.37
u
0.04
0.01
2.16
CI1_1
-0.53
0.08
-6.41
CI2_1
0.22
0.04
5.10
S1
-0.07
0.01
-3.84
S2
-0.07
0.02
-2.97
S3
-0.16
0.02
-6.76
________________________________________________________________
 = 0.042
Equation for px
Variable
Coefficient
Std.Error
T-value
_________________________________________________________________
const
-2.93
0.44
-6.56
pf
0.20
0.08
2.57
pf_1
0.29
0.07
3.66
zy
-0.27
0.06
-4.15
zy_1
-0.16
0.06
-2.49
yf_2
0.88
0.37
2.38
yf_3
1.27
0.36
3.50
CI1_1
0.27
0.04
6.52
CI2_1
-0.13
0.02
-6.01
S1
-0.02
0.01
-2.66
________________________________________________________________
 = 0.023
Vector AR 1-5 F(20,154) = 1.10 (0.35) Vector normality 2(4) = 8.60 (0.07)
loglik = 710.34 T = 100
LR test of over-identifying restrictions: 2(35) = 24.52 (0.90)
The LR test of over-identifying restrictions tests whether the model is a valid reduction of the
unrestricted system (URF). The reduction is well accepted by this test, with a probability value of
0.90.
Figure 5.2 shows the FIML recursive 1-Step Residuals for the two equations (upper part), as well
as the 1-Step and break-point Chow F-statistics (lower part). None of the statistics indicate
unstability at the five percent level.
Figure 5.2
FIML recursive 1-Step residuals for export volume and price (upper part), and
1-Step Chow F-statistics (lower left) and break-point Chow F-statistics (lower right).
Next we check whether productivity can be regarded as super exogenous with respect to the
parameters in the export volume and price equations. This is verified if productivity is weakly
exogenous for the parameters of interest, and the parameters in the export volume and price
equations are invariant to changes in the distribution of the productivity variable. We use the
super exogeneity test of Engle and Hendry (1993). First we specify a simple marginal model for
productivity. We formulate an error correction model for productivity growth, where the long run
coefficients are estimated freely, based on equation 2.5. To account for cyclical movements in
productivity growth, changes in man-hours by wage-earners (tw) is included in the model. In this
way we can control for short-run fluctuations in productivity merely reflecting Okun's law. In
addition, a wider set of intervention dummies is needed in order to stabilize this simple marginal
model. The dummies i1985p1, i1988p3, i1990p4, i1991p3 and i1992p3 are designed to capture
the effects of productivity changes due to policy interventions during the 1980's and early
1990's.8 If this wider set of intervention dummies is insignificant in the export volume and price
model, then productivity is super exogenous, and export volume and export price may be
considered as an autonomous system with respect to the class of interventions that caused
productivity changes. The preferred augmented marginal model for productivity is shown in table
5.6.
Variable
8
Coefficient
Std.Error
T-value
The dummies have value 1 in the quarter (last number) and year (second and third number) indicated by the name of
the particular dummy, and 0 elsewhere. They all capture effects from policy interventions (in the financial or the exchange
rate market) except i1990p4, which takes account of effects due to the Kuwait crisis. See appendix A.
___________________________________________________________________
Const
0.415
0.224
1.852
Log(trend)
0.081
0.032
2.463
zy_1
-0.281
0.076
-3.690
zy_3
-0.529
0.046
-11.432
4tw
-0.130
0.041
-3.164
zy_1
-0.303
0.088
-3.443
x_1
0.076
0.021
3.496
(px-pf)_1
-0.036
0.013
-2.819
D1
0.064
0.006
10.199
D2
0.037
0.003
9.330
__________________________________________________________________
R2 = 0.932
 = 0.013
DW = 2.17
AR 1-5 F(5,86) = 1.334 (0.257)
Norm 2 (2)
= 2.195 (0.333)
XI2 F(17,73)
= 1.512 (0.114)
Table 5.6
ARCH 4 F(4,83) = 0.751 (0.560)
RESET F(1,90) = 0.534 (0.466)
Estimating the augmented marginal model for productivity (zy) by OLS
Sample period: 1967 (4) to 1992 (4)
In table 5.6 R2 is the multiple correlation coefficient, DW is the Durbin-Watson statistic for first
order autocorrelation, RESET is the F-distributed Ramsey (1969) regression specification test,
and XI2 is the F-distributed White (1980) test for heteroscedasticity. The estimation results show
that a 1% yearly reduction in man-hours leads to a 0.13% quarterly (short-run) increase in labour
productivity. The constant yearly increase in autonomous labour productivity is estimated to
0.64%. The intervention dummy-variables all have the expected signs and are significant at the
5% level. In table 5.6 the dummies (impulse and seasonals) are combined in D1 (S1-DEVAL86)
and D2 (S2+i1985p1-i1988p3-i1990p4-i1991p3-i1992p3) in order to facilitate recursive
estimation. Figure 5.3 and 5.4 show the break-point F-test for the simple and the augmented
marginal model respectively. Figure 5.3 show how parameter constancy is violated when the
intervention dummies are dropped from the equation.
Figure 5.3
Break-point Chow F-statistics for the simple marginal model of labour productivity.
Figure 5.4
Break-point Chow F-statistics for the augmented marginal model of labour productivity.
The intervention dummies are not significant when included in the conditioning restricted models
for export volume and export price. None of the dummies are significant in the export volume
equation and only one is significant in the export price equation (this is the dummy for the
Kuwait crisis). Significance of all the intervention dummies in the export volume and export
price equations is rejected by a 2 (2) = 0.169, with a probability value of 0.91.
6.
CONCLUSIONS
We are not able to reject the hypothesis that productivity is super exogenous with respect to the
parameters of the export volume and price equations. A certain set of intervention dummies
during the 1980's and early 1990's (policy) had great impact on the productivity performance, but
did not alter the stability of the export model. The export model seem to be autonomous with
respect to productivity policy, or to put it another way, export volume and prices are structurally
caused by productivity. The empirical evidence thus seem to corroborate the causal implications
of the Ricardian model and "new" trade theories: economic growth is "productivity-led" and not
"export-led".
The policy implications of these empirical findings are important. One should not promote
exports by e.g. subsidies or other strategic trade policies, but instead give more direct
productivity stimulus – e.g. R&D, infrastructure or general educational support.
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APPENDIX A
DATA DEFINITIONS
X
Total Norwegian mainland export volume less exports of ships and oil platforms,
foreign consumption in Norway, trading profit and some ordinary goods.
PX
Export-daflator (derived from the X aggregate). Index with 1991 as base year.
ZY
Value added labour productivity in manufacturing and construction.
WC
Wage costs per man-hour in manufacturing and construction.
U
Total rate of unemployment.
YF
Indicator of foreign real income. Weighted sum of gross domestic products of
nine of Norways main trading partners. Exports to the individual countries as a
share of total exports are used as weights (documented in Frøyland and Nymoen
(1993)). Index with 1991 as base year.
PF
World market price in Norwegian currency. PF=PFV*(0.63*USD+0.37*VAL),
where PFV is a weighted sum of GDP-price indices from nine of our main trading
partners (the weights are the same as for YF), USD is the exchange rate of US
dollar and VAL is a weighted sum of the exchange rate of nine of our main
trading partners, with weights as in YF. Index with 1991 as base year.
Si (i=1,2,3)
Seasonals.
T
Time trend.
OPEC2
Dummy for the oil price shock in 1979. 0.5 in 1979 (1), -0.5 in 1979 (2), 0 else.
DEVAL78
Dummy for devaluation of the Norwegian krone in 1978. 0.5 in 1978 (1),
-0.5 in 1978 (2), 0 else.
DEVAL86
Dummy for devaluation of the Norwegian krone in 1986. 0.5 in 1986 (2),
-0.5 in 1986 (3), 0 else.
The data series are all from Norges Bank.
“Intervention” dummies
i1985p1
Dummy for abolition of bond investment quota. 1 in 1985 (1), 0 else.
i1988p3
Dummy for abolition of direct loan controls and loan guarantee
limits. 1 in 1988 (3), 0 else
i1990p4
Dummy for the Kuwait crisis. 1 in 1990 (4), 0 else.
i1991p3
Dummy for interventions in the exchange market. 1 in 1991 (3), 0 else.
i1992p3
Dummy for the change to a floating exchange rate regime. 1 in 1992 (3), 0 else.
APPENDIX B
UNIT ROOT TESTS
Table B.1 Augmented Dickey-Fuller (ADF(4)) unit root tests1
Variables
Levels
First differences
___________________________________________________________
x
-2.74
(-0.23)
-5.40** (-1.70)
px
-0.64
(-0.01)
-4.63** (-0.79)
zy
-2.74
(-0.15)
-5.22** (-1.82)
pf
-1.94
(-0.05)
-4.97** (-0.99)
wc
0.63
( 0.01)
-3.81** (-0.77)
yf
-3.01
(-0.07)
-3.55** (-0.59)
u
-5.45** (-0.16)
-4.43** (-0.57)
px-pf
-1.69
(-0.05)
-5.00** (-0.96)
___________________________________________________________
1
The ADF(4) tests are based on the t-value of the lagged dependent variable. The equation includes four lags of
differenced variables, constant term, sesonal dummies and trend. Estimated coefficients in parantheses.
** indicates significance at the 1%-level.
APPENDIX C
Table C1
ADDITIONAL REGRESSION RESULTS
Marginal model of wage costs (wc)
Estimated by OLS
Sample period: 1967 (4) to 1992 (4)
Variable
Coefficient
Std. Error
T-value
____________________________________________________________________________
Const
-0.062
0.132
-4.691
u_3
-0.034
0.007
-4.984
cpi_1
0.157
0.082
1.920
pf_1
0.167
0.042
3.970
(wc_4 - cpi_4 - zy_2)
-0.105
0.025
-4.191
u_4
-0.016
0.002
-6.826
DW1
-0.044
0.005
-8.726
S1
-0.014
0.005
-2.855
S2
0.015
0.004
3.810
S3
-0.018
0.004
-4.760
____________________________________________________________________________
R2 = 0.749
 = 0.011
AR 1-5 F(5,86) = 0.361 (0.874)
Norm 2 (2)
= 4.497 (0.106)
XI2 F(15,75)
= 0.954 (0.511)
DW = 1.98
ARCH 4 F(4,83) = 1.064 (0.380)
RESET F(1,90) = 0.968 (0.378)
In table C1, cpi is the consumer price index and DW1 = u_1 + i1970p1 - i1976p2 - i1980p2 - i1989p2 -i1990p3.