Applied Economics, 1998, 30, 1387± 1397
Vector autoregression, cointegration and
causality: testing for causes of the
British industrial revolution
L E S O X L EY and D A V I D G R E A S L E Y *
Department of Economics, University of W aikato, Private Bag, Hamilton, New Zealand
and *Department of Economic History, W illiam Robertson Buildings, George Square,
Edinburgh, Scotland
The existence, timing, and possible causes of the British industrial revolution are
considered by investigating the time series properties of industrial production and
various explanatory variables. Utilising two types of robust cointegration-based
causality tests we argue that domestic forces, notably technological progress, shaped
the industrial revolution, whereas overseas trade expansion was mainly a consequence
of industrial growth. Results from Granger-type VAR tests are contrasted with those
of Toda and Phillips (Working paper 91-07, University of Western Australia, 1991b),
where the latter manifest some of the potential problems raised by the authors when
applied to a data set of this type. An understanding of the possible causes of the ® rst
industrial revolution may shed more general light on the forces promoting industrialization and growth. To the extent that the ® rst industrial revolution o€ ers a template,
exports appear not to provide a simple pathway to industrialization.
I. INTRODUCTION
Considerable debate still surrounds the existence and possible causes of the British industrial revolution. Economic
historians disagree on the revolutionary nature of the period
see for example, Deane and Cole (1969), Coleman (1983),
Lee (1986), Komlos (1989), Berg and Hudson (1992), Crafts
and Harley (1992), Mokyr (1993), O’Brien (1993). Mokyr’s
(1993) survey illustrates the breadth of ideas used to explain
variants of the question why Britain experienced the ® rst
industrial revolution. Many of the problems raised in trying
to understand the industrial revolution lie in isolating the
chief in¯ uences and direction of causal links. Older interpretations of the industrial revolution, for example Berrill
(1960), highlight the role of overseas trade, but following
John (1961) a new orthodoxy was established by Deane and
Cole (1969), and McCloskey (1981) which emphasizes the
primacy of domestic in¯ uences. O’Brien and Engerman
(1991), and Zahediah (1994), attempt to re-establish the
export-led growth thesis, while Komlos (1990) and Simon
(1994), argue British population growth was the primary
stimulus to technological and industrial progress during
the industrial revolution. Almost without exception such
0003± 6846
Ó
1998 Routledge
debates centre around qualitative issues of measurement
and often a microeconomic explanation of cause.
Greasley and Oxley (1994a,1994b, 1996) utilize modern
time series analysis to discern discontinuity in the Crafts±
Harley industrial output series for the period 1780± 1851,
and argue the result favours the existence of a British industrial revolution. They argue that the decisive qualitative
characteristic of British industrial growth between 1780 and
1851 was that output innovations had permanent e€ ects,
re¯ ecting the frequency and persistence of technological
shocks. Their ® nding that industrial production appears
integrated of order one, I(1), between 1780 and 1851, but I(0)
during earlier and subsequent years, provides a de® ning
characteristic for the industrial revolution and opens a route
to investigating its causes by providing a foundation for two
variants of robust cointegration-based causality tests.
The recent renewed interest among econometricians in
the univariate properties of macroeconomic time series has
increased concern for investigating their long-run equilibrium behaviour. The notion that in the long-run variables
might have convergent values has received considerable
empirical testing following the work of Granger (1981), and
others ± see Hendry (1986), on cointegration. Engle and
1387
L . Oxley and D. Greasley
1388
Granger (1987) show that if two time series are cointegrated
there will be a causal relation in at least one direction.
Causality testing has been deployed by economic historians
interested in the industrial revolution, for example Hatton
and Lyons (1983) consider export-led growth, and
Tsoulouhas (1992) the link between technology and population. However without cointegration causality tests may
yield spurious results.
Interest in, and possible causes of, the First Industrial
Revolution may have wide utility. Many recent discussions
of the rapid growth of the newly industrialized economies
(NIE s), centre upon the export-led growth (ELG), paradigm
see for example, Ahmad and Kwan (1991), and Giles et al.
(1993). Their results, however, are rather mixed with Chow
(1987), ® nding evidence of ELG in only one of eight countries considered. Hsiao (1987) found reverse causality in the
case of Hong Kong. Ahmad and Khan (1991) found no
evidence of ELG in the 47 African countries studied with
some evidence of reverse causality. To Lucas (1993), however, the `making of a (growth) miracle’ revolves around
human capital accumulation.
This paper extends the earlier research of Greasley and
Oxley (1994a, 1994b, 1995, 1996) by utilizing two types of
causality tests to consider the possible causes of the British
industrial revolution. Here we investigate Granger-causality
between industrial production, and population, real wages,
overseas trade, and technological activity for Britain during
the period 1780± 1851, using both `traditional’ and Toda and
Phillips (1991b) tests, in an attempt to shed light on the
possible causes of the ® rst industrial revolution. This
quantitative analysis contributes to the on-going debates
surrounding the respective contributions of domestic and
overseas forces to the industrial revolution.
In Section II, a series of potential testable hypotheses are
formulated drawing upon the substance of the debates in the
literature. Section III considers the econometric methodology of the paper including a discussion of the work of Toda
and Phillips (1991a). The results are presented as Section IV
and Section V concludes.
II. CAUSES OF THE INDUSTRIAL
REVOLUTION ± SOME TESTA BLE
H Y P O T H E S ES
Considerable debate revolves around the possible causes of
the British industrial revolution. Greasley and Oxley
(1994a, 1994b, 1996), utilize time series methods to identify
the timing though not the causes of the ® rst industrial
revolution dating the period as 1780± 1851. However, several candidates for its cause exist including:
(i)
1
Export L ed Growth (EL G): export growth causes
growth in output. This view is supported by for
The data used are discussed in the Appendix.
(ii)
(iii)
(iv)
(v)
(vi)
example, O’Brien and Engerman (1991), and Hatton
and Lyons (1983), and will be tested utilizing data on
industrial production and exports.1
Technological factors: developments in technology
cause a change in the productive process and/or e ciency of production leading to a discernible change in
the pattern of output growth. This view is supported by
Tsoulouhas (1992), and will be tested utilizing data on
the number of patents registered and processes
stemming from such patents, as measured by Sullivan
(1989).
Population growth: here growth in the population in¯ uences output by both providing a growing pool of
workers and also a growing source of domestic demand. Supporters of this view include Komlos (1990)
and Simon (1994).
Domestic factors (general): other domestic factors including for example wages and the change in domestic
demand, are seen as contributing to a domestically
determined revolution. Clearly population growth could
be included in this category, although it is generally
assigned a separate potential route of in¯ uence. Supporters of the domestically determined growth include
Deane and Cole (1969) and McCloskey (1981). Such
authors’ views are often contrasted with supporters of
the ELG hypothesis, and (i) and (iv) could be regarded
as two of the main competing explanations of the industrial revolution. In testing (iv) data on real wages taken
from Crafts and Mills (1994) are utilized to test whether
real wage levels, or rates of growth, caused industrial
production or vice versa.
Subsidiary hypotheses ± imports cause exports: Deane
and Cole (1969), posit that imports lead exports
in the 18th century as British trade shifts from Europe
to the West Indies and North America. Colonial
economies, however, had limited spending power
and as such needed to export to Britain if they
were to buy imports from Britain. If this hypothesis were true and were coupled with the ELG hypothesis, the data may suggest that imports cause output growth.
Other possible candidate hypotheses: given the current
level of interest in endogenous growth models see Rebelo (1991), it may seem natural to test for the e€ ects of
for example, human capital on growth. However, for
the period of interest, 1780± 1851, the absence of annual
data precludes formal investigation of the roles played
by investment in education and even physical capital in
the industrial revolution.
As such there are ® ve feasible testable hypotheses, (i)± (v)
above. Tests of such hypotheses utilize the range of methods
discussed in the next section.
1389
Causes of British industrial revolution
III. ECONOMETRIC METHODOL OGY ±
C A U S A L I T Y T ES T S
Conventional Granger-type tests
Many tests of Granger-type causality have been derived and
implemented, including Granger (1969), Sims (1972), and
Geweke et al. (1983), to test the direction of causality, for
example Fisher (1992) investigates money and income, and
Giles et al. (1993) export-led growth. The tests are all based
upon the estimation of autoregressive or vector autoregressive (VAR), models involving (say), the variables X and Y ,
together with signi® cance tests for subsets of the variables.
Guilkey and Salemi (1982) have examined the ® nite sample
properties of these three common tests and suggest that the
Granger-type tests should be used in preference to the
others.
Although it is quite common to test for the direction of
causality, the conclusions drawn in some studies are fragile
for two important reasons. First, the choice of lag lengths in
the autoregressive or VAR models is often ad hoc, see for
example, Jung and Marshall (1985), Chow (1987), and Hsiao
(1987), although the length of lag chosen will critically a€ ect
results. Secondly, in the absence of evidence on cointegration, `spurious’ causality may be identi® ed. In this study we
will attempt to overcome both these shortcomings via the
adoption of a three stage procedure.
Engle and Granger (1987), show that if two series are
individually I(1), and cointegrated, a causal relationship will
exist in at least one direction. Furthermore, the Granger
Representation Theorem demonstrates how to model cointegrated I(1) series in the form of a VAR model. In particular, the VAR can be constructed either in terms of the levels
of the data, the I(1) variables; or in terms of their ® rstdi€ erences, the I(0) variables, with the addition of an errorcorrection term (ECM) to capture the short-run dynamics.
If the data are I(1) but not cointegrated, causality tests
cannot validly be derived unless the data are transformed to
induce stationarity which will typically involve tests of hypotheses relating to the growth of variables (if they are
de® ned in logarithms), and not their levels. To sum, causality tests can be constructed in three ways, two of which
require the presence of cointegration. The three di€ erent
approaches are de® ned below.
The ® rst stage involves testing for the order of integration,
with the data de® ned as the logarithm of the levels of the
variables, using the Augmented Dickey± Fuller (ADF) statistic. Conditional on the outcome of the tests, the second
stage involves investigating bivariate cointegration utilizing
the Johansen maximum likelihood approach. If bivariate
cointegration exists then either unidirectional or bidirectional Granger causality must also exist, although in ® nite
samples there is no guarantee that the tests will identify it.
On the basis of the bivariate cointegration results a multivariate model of cointegration may then be investigated to
examine interaction e€ ects, taking the error term from this
cointegrating regression as a measure of the ECM term to
capture the short run dynamics of the model. The third
stage (or second if bivariate cointegration is rejected), involves constructing standard Granger-type causality tests,
augmented where appropriate with a lagged error-correction term, see Giles et al. (1993).
The three-stage procedure leads to three alternative approaches for testing causality. In the case of cointegrated
data Granger causality tests may use the I(1) data because of
the superconsistency properties of estimation. With two
variables X and Y :
Xt
=
a
m
+ +
i= 1
Yt = a + +
b i Xt ±
q
i= 1
+ +
i
n
j= 1
r
bi Y t ±
i
+
j=1
g jY t±
cj X t ±
j
j
+ ut
(1)
+ vt
(2)
where ut and vt are zero-mean, serially uncorrelated, random
disturbances and the lag lengths m, n, q and r are assigned on
the basis of minimizing Akaike’s Final Prediction Error
(FPE) following Giles et al. (1993).
Secondly Granger causality tests with cointegrated variables may utilize the I(0) data, including an error-correction
mechanism term, i.e.,
Xt
D
D
=
a
+ +
m
i= 1
Yt = a + +
q
i= 1
b i D Xt ±
biD Y t ±
i
i
+ +
n
g jD Y t ±
j= 1
+ +
r
j= 1
j
+ d ECMt ±
1
+ ut
(19 )
cj D X t ±
j
+ dECMt ±
1
+ vt
(29 )
where the error-correction mechanism term is denoted
ECM.
Thirdly if the data are I(1) but not cointegrated valid
Granger-type tests require transformations to induce stationarity. In this case the tests deploy formulations like
Equations 19 and 29 above, but without the ECM term, i.e.,
Equations 19 9 and 29 9 below.
Xt
D
D
=
a
+ +
m
i= 1
Yt = a + +
q
i= 1
b i D Xt ±
biD Y t ±
i
i
+ +
n
g jD Y t±
j
+ ut
(19 9 )
cj D X t ±
j
+ vt
(29 9 )
j= 1
+ +
r
j=1
With optimal lag lengths determined by minimizing
Akaike’s Final Prediction Error (FPE), Granger causality
tests based upon Equations 1 and 2 involve the following:
Y Granger causes (GC), X if, H0 : g 1 = g 2 = g 3 = ¼
=
g n = 0 is rejected against the alternative H 1 : = at least one
g j ¹ 0, j = 1, ¼ , n.
X GC Y if, H0 : c1 = c2 = c3 ¼
= cr = 0 is rejected
against the alternative H1 : = at least one cj ¹ 0,
j = 1, ¼ , r.
L . Oxley and D. Greasley
1390
For Equations 19 and 29 Granger causality tests involve the
following:
Granger causes (GC), D X if, H 0 : g 1 = g 2 =
= ¼ = g n = 0 is rejected against the alternative,
H1 : = at least one g j ¹ 0, j = 1, ¼ , n, or d ¹ 0. (see Gran-
Y
g
D
3
ger, 1986).
X GC D Y if, H0 : c1 = c2 = c3 = ¼
= cr = 0 is rejected against the alternative H1 : = at least one cj ¹ 0,
j = 1, ¼ , r, or d ¹ 0, (see Granger, 1986).
D
Notice in this case however, with the possibility of causality
being inferred from the signi® cance of d or d alone that the
causal nexus is altered i.e., causality runs from the past level
to the current rate of change without any lagged change
e€ ects.
For noncointegrated data (X and Y , I(1)), Granger causality tests involve tests based upon Equations 19 9 and 29 9 , in
particular:
Y
g
D
3
=
Granger causes (GC), D X if, H 0 : g 1 = g 2 =
= g n = 0 is rejected against the alternative, H1 :
at least one g j ¹ 0, j = 1, ¼ ,n.
In Toda and Phillips (1991b) ± henceforth TP ± the
authors consider a di€ erent, single-stage estimation, but
(potentially), sequential testing, framework as well as a critical review of previous tests.
Consider the n-vector time series {yt} generated by the kth
order VAR:
yt
= J(L ) yt ±
1
+ ut
D
Under conditions of cointegration, the ECM based tests
discussed above involve some form of two-step process, i.e.,
test for cointegration and retain the residuals as the ECM
term and utilize this variable in the second stage either as
a direct test of causality following Granger (1986) and Engle
and Granger (1987), or as part of the modelling strategy
when testing the signi® cance of the VAR terms.
(3)
yt
= J* (L )D yt ±
1
+ G A9 yt ±
1
+ ut
(4)
where J* (L ) is de® ned analogous to the expression above.
Causality tests. Following Sims et al. (1990), consider a test
of whether the last n3 elements of yt cause the ® rst n1
elements of the vector where yt is partitioned as:
12
y1 t
yt
n1
= y2 t n2
y3 t
(5)
n3
(1) L evels V AR. The null hypothesis of noncausality based
upon Equation 3 would be:
H: J1 , 1 3
= ¼
= Jk , 1 3 = 0
(6)
±
and J1 3 = + ki= 1 Ji , 1 3 L i 1 is the n13 n3 upper-right submatrix of J(L ). Denoting A3 as the last n3 rows of the matrix
of cointegrating vectors A, if rank (A3) = n3, then via TP,
Corollary 1, under the null hypothesis from Equation 6:
d
F®
x 2n1 n 3 k. However, the rank condition on the submatrix
(A3), based upon OLS estimates, su€ ers from simultaneous
equation bias, such that there is no valid statistical basis for
determining whether the required su cient condition applies. When the condition fails, the limit distribution is more
complex than that shown above and involves a mixture of
a x 2 and a nonstandard distribution and generally involves
nuisance parameters.
(2) Johansen-type ECMs. Based now upon Equation 4, the
null hypothesis of non-causality becomes:
H*: J*
1,
Toda and Phillips (1991)-type tests
,T
where L is the lag operator de® ned as, J (L ) = +
and ut an n dimensional random vector. Making su cient
assumptions to ensure that yt is cointegrated, CI(1, 1) with
r cointegrating vectors (r > 1), see TP for details, rewrite
Equation 3 in the equivalent ECM form:
D
Given the inclusion of lagged dependent variables in Equations 1 and 2, 19 and 29 and 19 9 and 29 9 , tests of the hypotheses
utilizing OLS results require the Schmidt (1976) modi® ed
Wald statistics, nF1 and rF2 , distributed (asympotically) as
x 2 with n and r degrees of freedom, where F1 and F2 are the
`normal’ F statistics of the joint signi® cance of the g ’s and c’s
respectively. Furthermore, in the case of Equations 1 and
2 we invoke the results of Lutkepohl and Leimers (1992),
and Toda and Phillips (1991a), which show that in bivariate
nonstationary cointegrated models the Wald test will have
the usual asymptotic x 2 distribution.
In addition to the Wald test of zero restrictions, t tests on
d and d where appropriate, the FPE can be used as an
additional indication of causality, i.e. if FPE (m*, n*) <
FPE(m*), it implies Y Granger-causes X (or D Y Granger
causes D X where appropriate), likewise for r* and q*, see
Giles et al. (1993) for more details. All three criteria are used
in the empirical section of the paper.
= - k + 1, ¼
k
i± 1
i = 1 Ji L
= ¼
X GC D Y if, H0 : c1 = c2 = c3 = ¼
= cr = 0 is rejected against the alternative. H1 : = at least one cj ¹ 0,
j = 1, ¼ , r.
t
13
= ¼
= J*k ±
1, 13
= 0 and G 1 A93 = 0 (7)
and J1 3 = +
is the n13 n3 upper-right submatrix of J*(L ), and G 1 are the ® rst n1 rows of the loading
coe cient matrix G . If rank G 1 = n1 or rank (A3) = n3,
k
i± 1
i = 1 Ji , 1 3 L
d
2
then under the null hypothesis Equation 7 F*®
x n1 n3 k .
Again, if neither of these conditions are satis® ed causality tests
based upon x 2 will not in general be valid. However, unlike
the case above, tests of such conditions are relatively easy to
construct and constitute the sequential testing strategy of TP.
1391
Causes of British industrial revolution
Consider for the moment either n1 = 1 or n3 = 1, (or
n1 = 1 and n3 = 1), such that G 1 is a scalar denoted g 1 as is
A3 denoted a 3, then de® ne the following null hypotheses:
H* : J*
1,13
= ¼
= J*k ±
1,13
= 0 and
H*
1,13
­ : J*
= ¼
= J*k ±
1,13
= 0
H*
1 : g
1
= 0
H*
3: a
3
= 0
H*
1 3 : g 1 a 93
g 1 a 93
= 0
= 0
The TP sequential testing strategy involves:
(P1) Test H*
1:
{
(P2) Test H*
3:
and when n1
(P3) Test H*
­
{
{
= n3 = 1:
If H*1 is rejected test H*
Otherwise test H*­
If H*3 is rejected test H*
Otherwise test H*­
{
If H*
is rejected, reject the null
­
hypothesis of noncausality
Otherwise,
test H*
1 and H*
3
If both H*1 and H*
3
are rejected
test H*1 3 if rW > 1
or reject the null
if rW = 1
Otherwise, accept
the null
of noncausality
subtests (H*
1 , H*
3 ), then we would have approximately 5%
signi® cance level for the overall causality test ¼
but of
course we cannot do so without allowing large upward size
distortions in other cases ¼ ’ ± TP. More generally, under
many plausible cases it seems that the sequential procedures
involve the potential to introduce large size distortions for
relatively small deviations from assumed theoretical values,
i.e., lag length, coe cient values and properties of the error
term.
IV. EMPIR ICAL RESULT S
The ® rst stage of the causality testing procedure investigates
the order of integration of the data. Table 1 presents the
results of Augmented Dickey± Fuller tests for the log-levels
of the various variables for the period 1780± 1851. In all
cases the null hypothesis of nonstationarity is not rejected.
Similar tests on the ® rst di€ erence of the variables indicate
that the variables are all I(1). On this basis investigation
into the existence of possible cointegrating relationships can
be undertaken which represents stage 2.
Tables 2 and 3 report the results of bivariate and multivariate cointegration tests between industrial production
and the other variables of interest, namely, real wages;
exports; imports; patents; processes and population.
A single signi® cant bivariate cointegrating relationship was
found to exist between industrial production and the variable of interest in all cases but imports.
Table 1. T esting for unit roots, log-levels data, 1780± 1851
where rW is an estimate of r.
Having established this theoretical hierarchy of testin g,
based upon their Monte Carlo results, TP make the following observations/recommendations:
Variable
(1) (P1) generally performs better than (P2) and should be
preferred over (P2).
(2) When n1 = n3 = 1, (P1) and (P2) are less vulnerable to
size distortions than (P3) which should be avoided.
(3) None of the sequential procedures (or conventional
tests), performed well for sample sizes below 100, at least
with systems of three or more variables.
(4) The sequential tests outperform the conventional VAR
tests which su€ er considerable size distortions where
tests are not valid asymptotically x 2 .
Exports
- 2.617
Imports +
- 1.188
Patents
- 3.149
Processes
- 2.589
Population
- 2.848
Furthermore, consideration of their Monte Carlo results
reveals that for many cases considered, `our testing procedures do not have much power unless the lag length k is
speci® ed correctly. This is not surprising because if k > 1 the
coe cients of the lagged di€ erences of y3 are all zero.’ For
other cases, `If we choose 22% critical values for those
Ind. prodtn
Real wages
ADF(2)
- 1.16
(-
-
3.472)a
2.959
LM(1)
Q*
0.840
(0.359)
0.014
(0.905)
0.515E (0.982)
0.315
(0.575)
1.352
(0.245)
0.251
(0.616)
0.065
(0.799)
5.400
(0.403)
1.721
(0.943)
2.045
(0.915)
1.176
(0.978)
2.408
(0.879)
1.822
(0.935)
1.919
(0.927)
3
Note: aDenotes MacKinnon (1991), 5% critical values which are
the same for all the variables; ® gures in parentheses are probability
values except those in column two which are 5% critical values;
LM(1) is a Lagrange Multiplier version of a ® rst-order serial
correlation test; Q* denotes the Ljung± Box (1978) test based upon
6 lags; + denotes ADF(3) as the ADF(2) statistic exhibited positive serial correlation. The conclusions are not dependent on the
augmentation used, for valid, i.e., non-serially correlated ADF
regressions.
L . Oxley and D. Greasley
1392
Table 2. Testing for bivariate cointegration, Johansen method, industrial production, 1780± 1851
Variable
Real wages
Exports
Imports
Patents
Processes
Population
Maximum
eigenvalue
statistic
Trace
statistic
H0
23.53*
2.25
14.21*
0.38
11.13
0.54
22.35*
0.67
20.91*
0.47
47.75*
0.09
25.79*
2.25
14.59*
0.38
11.68
0.54
23.02*
0.67
21.39*
0.47
47.84*
0.09
r
r
r
r
r
r
r
r
r
r
r
r
= 0
<
=
<
=
<
=
<
=
<
<
=
b
VAR
3.44
2
0.700
1
Ð
1
0.747
1
0.688
1
2.14
1
H1
1
0
1
0
1
0
1
0
1
0
1
r
r
r
r
r
r
r
r
r
r
r
r
=
=
=
=
=
=
=
=
=
=
=
=
1
2
1
2
1
2
1
2
1
2
1
2
Note: *Denotes signi® cant at the 95% level. r = 0 represents no cointegrating vector, b are coe cient values from vector 1, normalized on industrial production; VAR de® nes the length of lag in the
Vector Autoregression chosen on the basis of economic interpretation and the properties of the
cointegrating vector residuals.
Table 3. Testing for cointegration, Johansen method, industrial production, 1780± 1851
Variable
Real wages
Exports
Processes
Population
Maximum
eigenvalue
statistic
Trace
statistic
H0
H1
38.25*
22.55
85.16*
46.63
r = 0
r< 1
r
r
b
= 1
= 2
VAR
2
0.619
0.177
0.120
0.840a
Note: aTests of the restriction that the coe cient on population = 1.0 were not rejected, i.e. the x 2 (1)
test = 0.194 with a p value of 0.659. *Denotes signi® cant at the 95% level; b are coe cient values
from vector 1, normalized on industrial production.
Utilizing these results a multivariate Johansen approach
was adopted including all variables except imports. The
version using processes rather than raw patents as a
measure of technological change is reported below although
the qualitative and quantitative di€ erences between the two
are small. On the basis of the results presented as Table
3 one cointegrating vector was identi® ed. A test of the
restriction that the coe cient on population equals unity
was not rejected implying that a proportionate relationship
between the level of population and the level of industrial
production cannot be rejected.
The results presented as Tables 2 and 3 demonstrate the
existence of both bivariate and multivariate cointegration
between the variables of interest. The only candidate variable for which cointegration was not identi® ed was imports.
This constrains tests of causality to the I(0) representation of
the import data, i.e. in this case, ® rst di€ erence or growth
rates, and does not rule-out the identi® cation of a spurious
relationship. The potential for cointegration between exports and imports is discussed later in this section.
Tables 4 and 5 report the results of bivariate causality
tests on the levels and growth (® rst-di€ erenced) data of the
cointegrated variables and a summary of the causality tests
based upon the FPE criteria, the x 2 distributed Wald test
and, where appropriate, t distributed tests on the ECMt ± 1
term.
Granger-type tests ± levels data
Based upon the results presented as Table 4, a mixture of
results emerge. First, unambiguous support for exports
leading output is not found with only the FPE criteria
® nding any support for export levels leading industrial production levels, but then only as a feedback relationship.
Interestingly, real wage levels appear to cause industrial
production levels on both criteria. For all other levels data
1
6
0.0129582
0.0106731
27.48
(0.000)
EXP
EXP
3
4
0.0017162
0.0017148
7.535
(0.110)
IPÛ
IPÞ
m*
n*
FPE m*
FPE m*n*
WALD
(prob)
FPE criteria
2
x criteria
RWÞ
RWÞ
3
2
0.0017162
0.0015936
9.025
(0.011)
RW
IP
IP
IP
3
1
0.00677066
0.00692054
0.400
(0.527)
IP
RW
IPÛ
IPÞ
3
1
0.0017162
0.0017029
2.398
(0.121)
PROC
IP
PROC
PROC
1
1
0.0505757
0.0470510
7.159
(0.007)
IP
PROC
IPÛ
IPÛ
3
1
0.0017162
0.0016591
4.203
(0.040)
PATS
IP
PATS
PATS**
2
1
0.0444707
0.0433997
3.595
(0.058)
IP
PATS
IPÛ
IPÛ
3
1
0.0017162
0.0015916
7.183
(0.007)
POP
IP
POP
POP
2
2
3.36206E-6
3.17631E-6
7.871
(0.020)
IP
POP
Note. **Denotes at the 7% level.
-
4
1
0.0146485
0.0137874
0.403
5.868
(0.015)
EXP
EXP
EXP
2
1
0.00160544
0.00162858
2.497
0.918
(0.338)
IPÞ
IPÞ
IPÛ
m*
n*
FPE m*
FPE m*n*
ECMt ± 1 ( t value )
WALD
(prob)
FPE criteria
2
x criteria
OV ERAL L
-
IP
EXP
Independent
EXP
IP
Dependent
-
2
1
0.00160544
0.00162471
2.859
1.075
(0.300)
IPÞ
IPÞ
IPÛ
RW
IP
2
2
0.00758688
0.00740165
1.498
5.432
(0.066)
RW
RW
RW
IP
RW
-
2
1
0.00160544
0.00162778
2.756
0.951
(0.330)
IPÛ /
IPÛ /
PROCÞ
PROC
IP
Table 5. T ests of bivariate causality± (Cointegrated) ® rst-di€ erence (Growth) data, 1780± 1851
3
1
0.0547522
0.0571084
0.901
0.098
(0.753)
PROC
PROC
IP
IP
PROC
-
2
1
0.00160544
0.00163439
2.704
0.684
(0.408)
IPÞ
IPÞ
IPÛ
PATS
IP
3
4
0.0506225
0.0496718
0.823
8.685
(0.069)
PATS
PATS**
PAT S
IP
PATS
-
2
1
0.00160544
0.00163935
2.646
0.485
(0.486)
IPÞ
IPÛ /
IPÛ
POP
IP
-
1
2
3.36934E-6
3.27118E-6
2.052
2.019
(0.364)
POP
POP
POP
IP
POP
Note. FPE criteria compares the FPE in the restricted (m*) and general (m*, n*) model; Wald is the Wald test of the zero restrictions implied by n*; x 2 criteria relates to the
Wald test conclusion. IP = Industrial Production; RW = Real Wages; EXP = Exports; PATS = Patents; PROC = Processes; POP = Population.
Þ denotes unidirectional causality in the direction shown; Û denotes bidirectional causality or `feedback’; Û / denotes no causal relationship was established.
** Denotes at the 6% level.
IP
EXP
Independent
EXP
IP
Dependent
Table 4. T ests of bivariate causality levels data, 1780± 1851 (cointegrated)
Causes of British industrial revolution
1393
L . Oxley and D. Greasley
1394
relationships and all criteria apart from x
processes, feedback is discerned.
2
for the e€ ect of
Granger-type tests ± ® rst di€ erence (growth rate) data
For most of the hypotheses, particularly ELG, technology
and population, however, the relevant hypotheses relate to
growth rates. Table 5 considers such results. In these cases
the relevant equations to test are Equations 19 and 29 which
introduce a one period lagged ECM term into the test
equation and additional causality consequences on the decision process, see Granger (1986). In particular, we have
3 possible `tests’ of causality: FPE criteria, Wald-type tests
and t distributed tests of the signi® cance of the lagged ECM
term. On the basis of the ® rst two of these criteria some
degree of consistency emerges. First, ELG is rejected in
favour of reverse causality. The real wage results in levels
are reversed when considering growth rates. Changes in
technology measured by the number of processes appears to
involve no causal relationship with industrial production,
although using patents as an alternative measure implies
reverse causality. On population growth, the FPE criteria
implies causality running from industrial production to
population although this is not supported by the Wald test
which implies no causal relationship. However, as shown by
Granger (1986), causality can be inferred either from the
( joint) signi® cance of lagged independent variables or of the
lagged ECM term. Taking this view, the overall result row
implies the following. All variables apart from processes
(measuring technological change), support the view that
feedback or bidirectional characterizes the data. For the
variable processes, however, the overall assessment is of
unidirectional causality from processes to output or that
technological change caused changes in industrial production
± the Industrial Revolution.
Toda and Philips-type tests
Results for levels VAR and Johansen-type ECM formulations are presented as Table 6 and are based upon k = 2
taken from the cointegration test results presented above.
On the basis of tests of the levels VAR, hypothesis H, the
null hypothesis of noncausality was not rejected for any
bivariate case. Notice, however, that with the exception of
real wages, the relative ranking of the p value magnitudes in
Table 6 and Table 4 suggest the possibility of major size
di€ erences. For example, the strongest rejection of noncausality in Table 4 is in relation to industrial production
causing exports2 with a p value of 0.000. This compares with
a p value of 0.283 in Table 6 which is the lowest value
reported for tests of H.
2
Turning to tests of the Johansen-type ECM model, with
n1 = n3 = 1 there is the option of testing for causality via
P1 and P2 or P3. However, following the recommendations
of TP and choosing P1, the relative rankings of p
values are the same as presented in Table 5, although
the di€ erences are larger. In the case where Granger-type
Wald tests do not reject either null, i.e., the Processes column, the TP p values are much the same. Tests involving P2
lead to a rejection of the null of noncausality in all cases.
However, note that with n1 = n3 = 1, we are concerned
with a joint test of P1 and P2. Testing these restrictions
jointly, P3, leads to nonrejection of the null in all cases with
a similar story on di€ erences in p value to that of P1, also to
be noted.
Overall, it appears that there are considerable di€ erences
in conclusions derived from the TP approach and the traditional Granger-type test criteria. TP note the problems of
test size which might occur with these traditional methods
when the underlying model is known, and in their own approach, when the underlying model is known. When the
underlying model has to be estimated, possibly with error,
possibly with incorrect lag length and assumptions about
error structure, it is di cult to favour one set of results over
another. However, with a sample size of 71 and ® ve variables the example used here satis® es none of the prerequisites of the TP requirements. The TP test procedure also
involves a joint test on a and g , whereas in e€ ect the Granger
approach considers the signi® cance of either or both. Finally, the TP approach imposes the same VAR structure on
each variable, whereas the approach adopted with traditional tests is to optimize the lag length for each bivariate
test combination.
Causality testin g with non-cointegrated data ± imports
Finally we consider the relationship between industrial production and imports where cointegration was not established. Table 7 reports the results of bivariate causality tests
and a summary of the causality results based upon the
noncointegrated data. Given the lack of cointegration, the
tests must be undertaken on I(0), i.e. ® rst-di€ erenced data
only.
The results presented as Table 7 suggest that industrial
production growth unidirectionally Granger-caused import
growth. The noncointegrated data causality tests do point
to the growth of industrial production leading the growth of
imports, o€ ering no support to the ® rst stage of Deane and
Cole’s (1969) interpretation of the connections between
overseas trade and the industrial revolution. Furthermore,
it seems unlikely that import growth causally led export
growth.
Note however, that the lag length here is 6. TP note that `One interesting observation on levels VARs which have been widely used in the
econometrics literature is that causality tests begin to deteriorate as k exceeds 6 even for the sample size equal to 200’.
1395
Causes of British industrial revolution
Table 6. T P tests of causality, (k
= 2), 1780± 1851
Dependent
IP
EXP
IP
RW
IP
PROC
IP
POP
Independent
EXP
IP
RW
IP
PROC
IP
POP
IP
LEVELS VAR
H
(prob)
TP criteria
0.112
(0.990)
IP
3.806
(0.283)
Û / EXP
0.778
(0.854)
IP
3.345
(0.341)
Û / RW
0.551
(0.907)
IP
3.037
(0.385)
Û / PROC
0.531
(0.912)
IP
3.426
(0.330)
Û / POP
JOHANSEN ECM
H*
(prob)
H*
1 (P1)
(prob)
H*
3 (P2)
(prob)
H*
­ (P3)
(prob)
13.81
(0.003)
0.148
(0.699)
11.97
(0.000)
0.024
(0.988)
0.069
(0.995)
0.784
(0.376)
434.9
(0.000)
0.839
(0.657)
2.786
(0.426)
0.148
(0.699)
221.9
(0.000)
0.220
(0.896)
0.097
(0.992)
0.463
(0.496)
434.9
(0.000)
0.727
(0.695)
1.888
(0.596)
0.148
(0.699)
75.43
(0.000)
0.552
(0.758)
0.668
(0.881)
0.159
(0.689)
434.9
(0.000)
1.008
(0.604)
2.181
(0.535)
0.148
(0.699)
807.0
(0.000)
0.083
(0.959)
0.772
(0.856)
0.957
(0.328)
434.9
(0.000)
0.541
(0.763)
IP
Û / EXP
IP
Û / RW
IP
Û / PROC
IP
Û / POP
TP criteria
Table 7. Tests of bivariate causality ® rst di€ erence (growth) data,
1780± 1851 (not cointegrated)
Table 9. T ests of bivariate causality, levels data, 1780± 1851
(cointegrated)
Dependent
IP
IMP
Dependent
EXP
IMP
Independent
IMP
IP
Independent
IMP
EXP
m*
n*
FPE m*
FPE m*n*
WALD
(prob)
FPE criteria
x 2 criteria
4
1
0.00169796
0.00169898
1.806
(0.179)
IPÞ
IPÞ
3
3
0.0111205
0.0106952
8.379
(0.039)
IMP
IMP
m*
n*
FPE m*
FPE m*n*
WALD
(prob)
FPE criteria
x 2 criteria
1
2
0.0129582
0.0129997
3.614
(0.164)
EXPÞ
EXP** Þ
3
1
0.0115091
0.0113102
3.864
(0.080)
IMP
IMP
Note: IMP = Imports.
Note: **Denotes at the 8% level.
Table 8 reports bivariate Johansen cointegration results
for exports and imports, normalizing the results on imports.
On the basis of Table 8 a unique cointegrating relationship
was identi® ed and the ECM from this vector was used in the
causality test results reported below as Table 9. On either
criteria the results for levels data imply unidirectional
causality from exports to imports.
The results on growth rates or ® rst-di€ erenced data presented as Table 10 are also unambiguous in their rejection
of any causal relationship between the variables. Most importantly none of the results point to unidirectional causation from imports to exports. These ® ndings o€ er support to
Hatton and Lyon’s (1983) view that export volumes were
not predicated on imports, but provide no basis for rehabilitating the export-led growth thesis.
Table 8. Testing for bivariate cointegration, Johansen Method, real imports, 1780± 1851
Variable
Real exports
Maximum
eigenvalue
statistic
Trace
statistic
H0
H1
20.64*
0.180
20.82*
0.180
r = 0
r< 1
r
r
= 1
= 2
b
VAR
0.666
1
Note: *Denotes signi® cant at the 95% level; b are coe cient values normalized on real imports.
L . Oxley and D. Greasley
1396
Table 10. T ests of bivariate causality, ® rst di€ erence, (growth)
data, 1780± 1851 (cointegrated)
Dependent
EXP
IMP
Independent
IMP
EXP
m*
n*
FPE m*
FPE m*n*
WALD
(prob)
ECMt ± 1 (t value)
FPE criteria
x 2 criteria
Overall
4
1
0.0147007
0.0149874
0.580
(0.446)
0.000
EXPÛ /
EXPÛ /
EXPÛ /
3
1
0.010841
0.011065
0.511
(0.474)
1.579
IMP
IMP
IMP
a€ ected by patent activity is used here as a proxy for
technological change. As such, it seems that technological
change was a crucial independent cause of industrial
change.
The use of Toda and Phillips (1991b) methods, although
potentially useful, failed to show any indication of causality
for any of the data. However, given the properties of the
data used (71 observations), the formulation of the estimated model (® ve variables), and the known limitations of
the Toda and Phillips approach, it is perhaps not surprising.
To sum, the origins of the British industrial revolution
seem to lay within the domestic market. What was distinctive about the British marketplace in the period 1780 to
1851 was a conjunction of critical real wage, population,
and technological creativity levels. To the extent that the
® rst industrial revolution o€ ers a template, exports appear
not to provide a simple pathway to industrialization.
V. CONCLUDING REMAR KS
Recent developments in the econometric analysis of macroeconomics time series o€ ers the promise of new perspectives
on frequently-asked questions surrounding the British industrial revolution. The Crafts± Harley (1992) industrial
production series appears to have alternating stochastic
properties which highlight the period 1780± 1851 as a distinctive macroeconomic epoch. We argue that the permanence of output innovations during these years, re¯ ecting
the on-going technological transformation of the economy,
was the de® ning characteristic of the industrial revolution.
Identifying the industrial revolution as a historical discontinuity via the time series properties of the industrial production estimates opens a route to considering possible
causes of Britain’s industrial revolution. Robust causality
tests require cointegration among the variables of interest.
Our ® ndings point to multivariate cointegration between
industrial production, population, real wages, exports, and
technological activity measured by industrial processes affected by patents, which o€ ers a foundation for investigating
the causal links between these variables.
Several types of causality tests are invoked to study the
existence of causal relationships during the industrial revolution. Traditional Granger-type tests emphasize that with
the levels data, domestic rather than overseas forces shaped
the British industrial revolution. Bidirectional causality appears to exist between the level of industrial production,
population, and industrial processes a€ ected by patents, but
the results do not indicate that export levels, or industrial
processes caused industrial production. Interestingly, it appears that the level of real wages caused industrial production, although this does not transpose into growth rate
implications. With the data presented as ® rst di€ erenced
logs, i.e., growth rates, bidirectional causality appears to
exist for all variables except processes which Grangercauses changes in industrial production where the Sullivan
(1989), measure of the number of industrial processes
AC K N O W L E D G E M EN T S
Earlier versions of this paper were presented at Curtin
University of Technology, Murdoch University, the University of Edinburgh, the University of Oxford, the University
of Warwick and the 1995 Monash Econometrics Conference. We would like to thank Clive Granger, Hiro Toda,
Junsoo Lee, and particularly Colin McKenzie, for comments, clari® cations and useful information. Part of this
work was completed whilst the ® rst author was visiting the
University of Western Australia.
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AP P EN D I X : D A T A
The industrial production data used here are the `best guess’
estimates from Crafts and Harley (1992). Raw numbers of
patents and the industrial processes they might a€ ect are
from Sullivan (1989). Real wages are measured by Crafts
and Mills (1994) cost of living real wage estimates. The
population data simply pertain to England. Annual UK
population estimates are not available for years before 1800,
whereas Wrigley and Scho® eld (1989) report earlier estimates for England. The data for imports and domestic
exports are o cial values for the UK for the years since
1801, and for Great Britain for earlier years, taken from
Mitchell and Deane (1962). Overseas trade data are missing
for 1813, and are estimated here by the geometric mean of
trade in 1812 and 1814.