Vector autoregression, cointegration and causality: testing for causes ...

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Edinburgh, Scotland .... in the 18th century as British trade shifts from Europe to the West Indies and ... by investment in education and even physical capital in.
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