Kondratieff Long Waves In Aggregate Output? An Econometric Test

NOT FOR QUOTATION WITHOUT PERMISSION OF THE AUTHOR

KONDRATIEFF LONG WAVES I N AGGREGATE OUTPUT?

An Econometric T e s t

Hans B i e s h a a r A l f r e d K l e i n k n e c h t

August 1984 CP-84-34

Paper p r e s e n t e d a t t h e Meeting on Long Waves, Depression a n d I n n o v a t i o n , S i e n n a / F l o r e n c e , I t a l y , 26-29 October, 1983.

~ o r t h c o m i n g i n K o n j u n k t u r p o l i t i k , No. 5 , Vol. 30, O c t o b e r , 1984.

C o Z Z a b o r a t i v e Papers r e p o r t work w h i c h h a s n o t b e e n p e r f o r m e d s o l e l y a t t h e I n t e r n a t i o n a l I n s t i t u t e f o r A p p l i e d S y s t e m s A n a l y s i s a n d w h i c h h a s r e c e i v e d o n l y l i m i t e d r e v i e w . V i e w s o r o p i n i o n s e x p r e s s e d h e r e i n d o n o t n e c e s s a r i l y r e p r e s e n t t h o s e o f t h e I n s t i t u t e , i t s N a t i o n a l Member O r g a n i z a t i o n s , o r o t h e r o r g a n i - z a t i o n s s u p p o r t i n g t h e work.

INTERNATIONAL INSTITUTE FOR APPLIED SYSTEMS ANALYSIS A-2361 L a x e n b u r g , A u s t r i a

ACKNOWLEDGEMENTS

The research underlying this paper has been subsidized by the Dutch Ministry of Science Policy (Wetenschapsbeleid). The authors would like to thank J . B . D . Derksen, P. Nijkamp, F.C. Palm, A. van Ravestein and J.

Reijnders for reading and commenting on the first draft of the manuscript.

The responsibility for the final version of the text is exclusively that of the authors.

FOREWORD

From t h e very b e g i n n i n g . o f t h e long-wave d e b a t e ( i n t e r r u p t e d s e v e r a l t i m e s i n t h e p a s t ) , a t t h e f o r e f r o n t of i n t e r e s t has been t h e q u e s t i o n of r e l i a b l e proof of t h e e x i s t e n c e of long waves a s r e f l e c t e d i n r e a l economic d a t a s e r i e s . Once proved it would be e a s i e r t o c o r r e l a t e them w i t h o t h e r important economic v a r i a b l e s and look f o r p o s s i b l e c a u s a l r e l a t i o n s .

However simple t h i s may seem i n p r i n c i p l e , t h e paper by D r s . B i e s h a a r and Kleinknecht shows how d i f f i c u l t t h i s problem i s i n p r a c t i c e . Even i f no one q u e s t i o n s t h e f l u c t u a t i o n s of economic d a t a , t h e problem of f i n d i n g i n them a c o h e r e n t p a t t e r n i s complicated. The novel method d e s c r i b e d h e r e seems t o be w e l l s u i t e d f o r d e p i c t i n g t r e n d s i n "long economic movements"

--

an e x p r e s s i o n t h a t draws l e s s o p p o s i t i o n t h a n t h e simple i d e a of p e r i o d i c c y c l e s . Important i n s i g h t i s shown i n t h e a u t h o r s ' a n a l y s i s of t h e d a t a o f many c o u n t r i e s .

T h i s paper i s a s i g n i f i c a n t s t e p i n p u r s u i t of t h e most important i s s u e i n t h e long-wave d e b a t e

--

t o produce r e l i a b l e d a t a and methods t h a t w i l l shed t h e n e c e s s a r y l i g h t on t h e q u e s t i o n o f t h e e x i s t e n c e of l o n g waves.

Tibor Vasko Leader

Clearinghouse A c t i v i t i e s

CONTENTS

INTRODUCTL ON OUR MODEL

DIFFERENCES BETWEEN OUR TEST AND TESTS BY OTHER AUTHORS THE PERIODIZATION OF LONG WAVES

REMARKS ON THE INTERPRETATION OF THE TABLES INTERPRETATION OF TABLE 3

CONCLUDING COMMENTS

APPENDIX: IMPUMENTING THE GLS ESTIMATE REFERENCES

The performance of most Western economies during the last decade has promoted renewed interest in research on the so-called Kondratieff long waves with a supposed wave length of some 45 to 60 years. According to t h e time schedule of the-Kondratieff wave, the period from t h e 1890s up to about World War I, a s well as t h a t from the late 1940s to the early 1970s would have to be considered as prosperous phases of the long wave, whereas the crisis phenomena of the last decade would be consistent with the Western economies having entered a new downturn of the long wave, comparable with the down- t u r n of the inter-war period. If we extrapolated that scheme in quite a simplistic and mechanistic way, it would be tempting to conclude t h a t a new revival of the world economy is to be expected somewhere between t h e late 1980s and t h e middle 1990s. However, i t is n o t our intention to further advance or substantiate such speculations. Neither is i t t h e task of this paper to given a n account of the large variety of hypotheses concerning the existence and possible causes of long waves. Nonetheless it has to be men- tioned t h a t the concept of long waves is subject to considerable discussion and research effort.* The range of opinions reaches from more or less full accep- tance of the hypothesis (van Duijn: 1979. 1983; Glismann e t al: 1978, 1981;

Mandel: 1973, 1960) through cautiously critical statements, (Kuczynsk: 1976, 1980; Metz: 1983; Kleinknecht: 1981; Spree: 1978; Rosenberg: 1983) up to outright rejection (Weinstock 1964, 1976; Milward: 1981; van Ewijk: 1981,

1982; van der Zwan: 1980).

As in the 1920s. there is again a concentration of long wave research in t h e Netherlands (Broersma: 1978; van Duijn: 1979, 1983; van Ewijk: 1981,

*See. for example, the discussion between Weinstock, Mensch and Nullau in Wirtschaitsdienst 58, April 1976, or more recently the contributions in: Schrbder/Spree (ed.) (1881), Petzina/Van Roon ( e d ) (1981), Futures (1881) or in Freeman (ed.) (1883).

1982; Kleinknecht: 1981a. 1984; van Paridon: 1979; Namenwirth: 1973;

Rijnders: 1983; van der Zwan: 1980),* who deserve to be mentioned (Coombs:

1983; Forrester: 1977; Freeman e t al: 1982; Graham/Senge: 1980; Ray: 1980;

Roztow: 1978; Rostow e t al: 1979; Wallerstein: 1979).

. Basically, the discussion centers around the question of whether t h e alleged long waves do exist, not only in monetary and price series but also in 'rea1"variables such as industrial output, GNP, etc. Whereas long waves in t h e former are not seriously questioned, several authors have expressed consider- able doubts about long waves in the latter.* Moreover, among those who t e n d to be convinced t h a t a Kondratieff-like pattern of fluctuations does exist, i t is still debatable whether t o conceive t h e m as being driven by exogenous or by endogenous forces. Assuming exogenous factors behind t h e long wave is con- sistent with the waves being historically unique events t h a t a r e not neces- sarily t o be repeated in t h e future; an endogenous explanation would imply a regular recurrence of the wave and some prognostic importance of t h e long wave hypothesis. Only in the latter case can we speak of t r u e cycles.

It rnight be argued t h a t debating the above points does not make much sense as long as t h e r e a r e serious doubts about whether long waves do exist a t all. There is t h e n some need to test the Kondratieff hypothesis m o r e rigorously.

The present paper will be restricted t o this task We shall present a new method for testing whether t h e r e a r e fluctuations over time t h a t fit into t h e time schedule of Kondratieff long waves, and whether the amplitudes of such

*It might be doubted whether Schurnpeter did justice to the early Dutch contributors an long waves (van Gelderen: 1813; de Wolff: 1824, 1929) when introducing the term 'Kondratieff long waves'. Given the quality and ti- of the Dutch publications we could equally speak of a van Gel- deren or a de WoVi cycle. However, these authors remained less well-known, since they mainly published in Dutch language.

*See, for example, van der Zwan (1880) or van Ewijk (1881, 1882) for the earlier discussion, see Gamy's critique of Kondratieff (Garvy, 1943).

fluctuations a r e strong enough to be considered significant. Our testing method will be applied to series on aggregate industrial production and GNP of several major industrial countries. Not to bother the reader with a lot of details about time series construction, we shall use time series t h a t have already been compiled by others (see Table 1). The quality of these series is beyond our judgment.

Table 1: Time Series to be Used for Testing

OUR

MODEL

Research experience until now h a s shown t h a t spectral analysis is not a very promising method for t h e analysis of long waves. In general, t h e avail- able time series as compared with the length of t h e cycle we a r e looking for are m u c h too sort.* Furthermore, the outcomes of spectral analysis are quite sensitive to t h e method of t r e n d elimination. The latter point also applies t o 'classical' methods of separating time series into components as Glismann e t al (1978). have done.

Therefore, we decided t o choose a completely different method. We con- ceive of long waves as a succession of longer periods of accelerated versus decelerated growth. To be more exact, we ought t o speak of 'trend periods' or 'rnouvements de fonds' (Dupriez), or in Spiethoff s terminology of 'Wechsel- lagen', instead of using t h e t e r m 'wave'. In the following, for pure conveni- ence, we shall use the t e r m 'A periods' for periods of accelerated growth, and

*See, for example, the experience of Kuczynsld (1978).

*It is possible, however, that a new method of determining trends in time series which has been a p plied most recently by our German colleague, Rainer Metz (1983), will bring a solution to that prob lem w i t h i n reach; cf. also the papers by Metz, Metz/Spree, Stier and Schulte in: D. Petzina/G, van Roon (ed.) (1981).

Table I . Time Series to be Used for Testing

Country United Kingdom

France

Germany Belgium

U.S.X.

Italy Sweden World ( 1 )

World (2)

Time Coverage 1801-1938 1946-1981 1830- 1979

1815-1913, 1919- 1938, 1947-1981 1900-1913

1920- 19 79

1850-1913, 1925- 1941, 1948-1979 1831-19 13

1920- 13 39 1946- 198 1 1889-1979

1861-1979 1561-1979 1780-1979

1850-1976 Variable

Industrial Product ion Gross Domestic Product

Industrial Production Net Domestic Product Net National Product

Industrial Product ion Gross National Product

Gross Domestic Product

Gross Domestic Product

Industrial Production

(excl. Mining) Total Industrial Product ion

(incl

.

^Mining)

Source

!4itcheLl 1981/OECD 1983 Glismann et al. 1981

Mitchell 1981lOECD 1983 Glismann et al. 1981 Clismann e c al. 1981 Gadisscur 1979

Hitchell 1981lOECD 1983 Clismann 1981

Glismann 1981 Glismann 1981 Kuczynski 19801 Haustein et al. 1982 Kuczynski 1980

periods of decelerated growth will be called

'B

periods'. If t h e Kondratieff long wave hypothesis is relevant, it should be possible to demonstrate t h a t t h e alleged A periods of t h e long wave have average growth rates t h a t a r e signifi- cantly higher than t h e average growth rates of t h e preceding a n d following

B

periods and vice versa. The average growth rates will be computed from t h e time series cited in Table 1.

There a r e two commonly used methods of establishing average growth rates: we can take either the logarithms of t h e geometric means or the slopes of t h e log-linear trend curves. Although the geometric means can be com- puted more easily, they have t h e disadvantage t h a t t h e average growth r a t e s depend only on t h e values of t h e beginning and end years of the periods.

Therefore, we decided to use t h e slopes of the log-linear t r e n d curves. With this method, the values of each year of the series a r e used, a n d the estimation is therefore less sensitive t o disturbances in t h e series.

However we decided to impose the following restrictions on t h e t r e n d esti- mates: i n t h e transition years ('peak' and 'through' years) t h e estimated values of t h e trends for t h e preceding and t h e following periods have t o equal each other. This is consistent with the assumption t h a t t h e transition from A t o

B

perios and vice versa is not subject t o erratic jumps in t h e absolute level of our variable.

To summarize t h e model verbally: we estimate log-linear trends for t h e different A a n d B periods, whereby the restrictions imposed guarantee a con- tinuous 'zig-zag' pattern. The below defined

Y,

a r e the estimated values in t h e transition years. Starting from t h e values in t h e transition years, we can reconstruct t h e complete 'zig-zag' line.

Mathematically our model can be written as follows:

To is the first year of the series,

T, is the last year of the series,

TI,

...,

Tm,I a r e the transition years ('I

-

^-h' and 'troughs' of t h e long waves)

In yt

=

ai

+

b i t is t h e log-linear trend formula for the i-th period consisting of the years: Ti t h e restrictions for the t r e n d estimates are:

9

+

^biTi

=

%+1

+

bi+lTi for i

=

1,2,

...,

m-1 defining

Yo

=

a l

+

b l T o and

Y, = ^q +

^{bi Ti for i}

=

1,

...,

m

the model can be re-wiitten without restrictions as:

Y.

-

In y t - - Yi,l + (t'

-

_{Ti-l) .(T. L}¹

-

^{'i-I T ~ - , 1 with t =} Ti,l,...,T i

or,

i.e., I n yt is nothing but t h e weighted s u m of t h e value of t h e beginning and end years of t h e period considered. The restriction discussed above requires that d l the Y, be estimated simultaneously.

To provide for a t e s t of wkether t h e growth r a t e s of two successive periods are consistent with t h e long wave hypothesis, t h e following rest statistic has been defined:

4

is nothing bu t h e difference in the growth r a t e s of two successive periods.

Assuming t h a t the residues will be normally distributed, the Yi and t h e

4

cah also be considered t o be normally distributed. Therefore, a one-sided t-test can be applied. We will test whether:

i f t h e pears T i ,

... ,

ii d e t e r n i n e a B-perioc

>'I i f t h e years f

,

7 . d e t e r n i c e an A-period i-1' " * 1

(for further details see Schmidt, 1976, p.18).

We need to add a disturbance t e r m E~ to the model. However, t h e existence of the medium-term 'classical' business cycle, among other reasons, suggests t h a t t h e E~ a r e autocorrelation, the estimates of the Yi would be unbiased, but t h e i r variances a r e likely to be biased; consequently, the signifi- cance levels of our t e s t may be biased. Therefore, we apply t h e following ten- tative solution t o t h e autocorrelation problem: we s t a r t with a n OLS estima- tion of t h e model to obtain t h e residuals. Then we estimate the autocorrela- tion pattern in t h e residuals using the following formula:

c _t = ₁₌₁ .I n p i ct-i + u _t w i t h : u _t

-

^{N(0, u2)}

(with n indicating the degree of autocorrelation)

Knowing t h e autocorrelation pattern, we re-estimate the with GLS (for the mathematical description of t h a t method, see t h e appendix).

Eventually we compare t h e autocorrelation pattern of the residuals of t h e GLS estimate with t h e previously obtained autocorrelation pattern. If both patterns match, we stop iterating; if they do not, we have t o continue t h e iterating process taking t h e last obtained autocorrelation pattern and repeat- ing t h e GLS estimate, and so on. Thus we actually obtain maximum-likelihood estimates.

DFFEEUZNCES BETWEEN OUR

TEST AND

TESI'S BY OTHER AUTHOFZS The advantage of our approach can be summarized as follows:

-

Unlike attempts a t applying spectral analysis (cf. Kuczynski'l978, van Ewijk 1982) t h e reliability of our test outcomes is not crucially dependent on the mere length of the available time series.

For our test we use time series from a larger range of countries than was done by van Ewijk (1981, 1982) or by van der Zwan (1980).

Whereas most of van der Zwan's series end during t h e 1930s. our data also cover t h e more recent period, for which t h e long wave hypothesis appears to be most relevant.

The study by Glismann e t a1 (1978, 1981) has t h e advantage of also using a wider range of data. However, it shares with t h e van Ewijk (1981) study t h e weakness t h a t the results are crucially dependent on the use of moving average methods, t h e effects of which are hard to control. Although we also included a nine year moving average in our graphs for illustrative purposes, t h e t e s t results on which we concentrate our interpretation do not depend on that method.

--

In contrast with the methods of Kuczynski (1980) and van der Zwan (1980). our estimates of growth rates explicitly take into account t h e existence of autocorrelation. Furthermore, our estimates a r e some- what more 'stable* as we apply t h e restriction t h a t t h e values of t h e estimated trends have to be equal in the transition years for t h e period preceding and following the transition year. As a conse- quence, our test is more robust against minor changes in t h e period- ization of long waves.

-

It is one of the admittedly weak points in our test that we have no method to determine the years of transition from one long wave period to t h e next one. The transition years are assumed to be known a priori from the literature. This point deserves some more discussion.

THE PERIODIZATION OF LONG WAVES

Table 2 offers a survey of long wave chronologies as given by van Duijn (1983) to which we added the chronologies by Bouvier (1974). Amin (1975), and Kuczynski (1980). Given the variety of indicators and methods used by the dif- ferent authors, i t is astonishing that most of the chronologies nonetheless remain within the time schedule given by Kondratieff.

Other than the position taken by Rostow for the most recent period, which is based on a different approach,' important deviations from Kondratieff's chronology occur only in the chronology of van Duijn and Clark, taking 1929 as the upper turning point of the third Kondratieff. Since we wanted to restrict the bulk of statistical documentation in this paper to a minimum, we did not test all the chronologies in Table 2.'

Instead we made a selection. In principle, there are six chronologies in Table 2 t h a t a r e suitable for testing since they are carried up t o the present.

Among the latter, we decided to choose the one given by Mandel. The main reasons for this choice a r e t h e following. First, Mandel's chronology is closest .See Rostow (1978), for a clarification see Wallerstein (1979).

'Anyone who would like to test a wider range of chronologies or other +teresting time series may request the complete computer program (FORTRAN) from the authors.

1 T a b l e 2 : Long wave c h r o n o l o g i e s a c c o r d i n g t o v a r i o u s a u t h o r s

Kondratieff ( !926)

V..n Ci riacy- Wan trup

(1936) Schumpe ter

( 1939) Clark

( 1944)

Kos tow (1978)

Van Duijn _- ( 1983)

- - - - -

Bouvier

Kuczyns ki (198a)

1st Kondratieff 1 owe r upper ca. 1790 I810117

2nd Kondratieff lower upper

3rd Kondratieff lower upper

4th Kondratieff lower upper

to t h e dating of long waves as suggested by Kondratieff, i.e., it is the most 'orthodox'. Secondly, Mandel conceives his chronology as being valid for t h e Kondratieff wave as a world market phenomenon. So i t can be applied to data on various countries without taking too much notice of natonal peculiarities.

Such a time scheme can be regarded as a n example of quite a rigid conception of long waves which claims a strong synchronization of t h e long wave process between countries in a world market context, besides implying a relatively strict regularity of t h e long waves.

Compared with t h e Mandelian standard, the chronologies by the other five modern authors are certainly not less sophisticated Actually they a r e some- what 'softer', trying to adapt themselves better to t h e national characteristics of individual countries. Their main differences with Mandel a r e certainly related to t h e question of how to treat t h e two World Wars in a long wave con- text. In some countries we miss u p to eleven year's data around World Wars I

and 11. In some other countries, the statistical series were continued throughout t h e war, but we do not h o w to what extent the data a r e influenced by pre-war armament booms, by the war economy, or by post-war reconstruc- tion booms. In t h e case of Germany, it could. for example, be argued that dur- ing t h e first half of the 20th Century the data a r e biased against as well as in favor of the long wave hypothesis: the reconstruction effect after World War I (the 'golden twenties') as well as Hitler's armament boom caused an 'exag- geration' of growth rates during the interwar B period, whereas the pre-World War I armament race a s well a s the reconstruction effect of t h e 1940s and

1950s yield a higher level of growth rates in the A periods of the third and fourth Kondratieff. Under such circumstances, along with missing observa- tions. a somewhat precise demarcation of long wave periods is extremely diffi- cult.

In that situation an optical inspection of the 11 series from Table 2 may be of some help. All t h e 11 series to be tested are documented in graphs A1 to A l l of the Appendix. For illustrative purposes, the series have been detrended with a log-linear trend, and a nine-year moving average on the residues has been included. It is especially interesting to look a t the Swedish series (Graph A7), since Sweden did not participate in either of the two World Wars. The Swedish series suggests that the year 1913, as given by Mandel. seems indeed to be the appropriate transition year from the A to t h e B period of the third Kondratieff, and that the transition to the A perod of the fourth Kondratieff should be dated quite closely around World War 11. The year 1951 as suggested by Kuczynski is obviously too late. The impression from graphs A 1 to A l l in the Appendix for the different series and countries is consistent with inter- preting the 'golden twenties' primarily in terms of a reconstruction boom, since the peak of 1929 is much stronger in countries that were directly involved in warfare as compared with such countries as Sweden. Conse- quently, taking 1929 and/or 1951 as transition years would clearly bias our test against the long wave hypothesis.

A first test on the Mandelian scheme quickly revealed that 1966 and 1987 are obviously no adequate transition years to the present B period. It should be mentioned. that Mandel's chronology was already developed during the early 1970s, and that today, with roughly a decade more of data. we can judge this point in a more reliable way. Therefore we changed t h e original Man- delian scheme, and took 1974 instead of 1966.'

*Other authors might have plausible reasons for talang earlier years such as 1973, the year af the oil crisis. We nonetheless took 1874, since this choice is consistent with Mandel's criterion of tak- in# as an end point of a Kondratieff period the trough year of the last short-term business cycle b e longing t o the A or B period considered. The first year after that trough year is the starting year of a new A or B period. According to the formal reqkements of our test, we only took the trough year as a demarcation point between two periods.

Furthermore, in contrast to Mandel's rigid time scheme, we used in several cases a "softer" chronology. The latter was derived from inspection of graphs A1 through A l l (Appendix). The turning points in the smoothed series that were closest to Mandel's transition years were taken as alternative transi- tion years. In general. the "soft" s c h e m e appears to be better adapted to the peculiarities of each series. Therefore, it should yield somewhat better signifi- cance levels than the hard scheme by Mandel. The test on both, the hard and the soft scheme should a t the same time give some illustration, to what extent the test is sensitive to smaller changes in the demarcation of A and B periods.

R E U R B ON

THE

INTERPREXATION

OF THE

TABLES

Before studying t h e results, four remarks have t o be made.

First: For the period from 1974 onwards, all the estimates documented in different tables of this paper have tremendously high standard errors due to the low number of observations. This might explain that, in spite of remark- ably declining growth r a t e s in most series after 1974, significance levels remain poor. However given the actual economic development, i t is certainly realistic to expect t h a t significance levels will become increasingly better if in future years we can include more and more data, from the 1980s.

Secondly: A similar problem applies to the beginning periods of the Itqlian and the Swedish series which s t a r t only in 1861 (instead of 1847) or for the NDP series of France, starting in 1900 (instead of 1893). The first estimate for the USA, covers only 4 years (1889-93) and should better not be intepreted.

Thirdly: All the test results documented in this paper a r e based on t h e assumption'that a second degree of autocorrelation exists in the residues of

the series. Given the relatively strong evidence of the 'classical' short-term business cycle from t h e 1820s-30s onwards, taking no account of autocorrela- ton is likely to bias our test seriously. In view of the allegedly sinus-shaped pattern of the short-term business cycle, the assumption of a second degree of autocorrelation seems t o be most appropriate. To be quite safe, we repeated all .the tests, assuming also a first, a third, and a fourth degree of autocorrela- tion. The results did not substantially differ from those obtained &th a second degree of autocorrelation, i.e., the significance levels changed only slightly so ,that our conclusions would have been the same using a different degree of autocorrelation.

Fourth: There is one point in Mandel's chronology which is not clearly determined: he gives 1939 as well as 1948 as possible transition years to the A period of t h e fourth Kondratieff. Therefore, we tested all our series with Mandel's chronology, taking both 1939 a n d 1948. In interpreting the results, one property of our estimates of growth rates has to be kept in mind: We imposed a restriction on the estimation of trends such that t h e t r e n d values of two subsequent periods a r e equal in the transition year, i.e., two subsequent trend periods intercept i n their common transition year. This creates a kind of 'harmonicae effect: If one transition year is changed, this will influence t h e t r e n d estimates for all the other A and

B

periods in t h e series, with t h e har- monica effect fading the further we move away from the altered transition year. Therefore, taking 1948 instead of 1939 may bring about some change in t h e outcomes for the entire series. Tentative testing with slightly changed demarcation years showed, however, that, in general, t h e changes due t o t h e 'harmonicaf effect a r e not dramatic. Only in t h r e e out of our eleven series did the substitution of 1948 for 1939 bring notable changes in the significance lev- els:

--

in the series for France, we got contradictory results: depending on whether we look a t the GNP or a t the industrial output series, or whether we take 1939 or 1948, we get significance levels respectively below and above the 95% level, and vice versa. Due to the unknown influence of World War 11, i t is hard to say which of the two transition years is more adequate.

--

in the USA, World War I1 brought a strong boom; t a k n g 1948 instead of 1939 would imply that we group this war-boom by the B period.

This would obviously be a problematic decision t h a t would bring down one significance level from 99% to 90%, and another from 99.8% to 95.8%.

-

in the Swedish series, substituting 1948 for 1939 would have an enor- mously negative impact for several significance levels. However, from looking a t graph A7 we can be safe in saying that 1948 would be much too late as a demarcation year.

Since, in general, 1939 appears to be the more realistic demarcation point, the test results based on Mandel's chronology with 1939 are docu- mented in Table 3.

A

comparable table based on the Mandelian scheme taking the year 1948 can be found in the Appendix (Table Al). To allow for an illustra- tive check of the Mandelian periodization, we included in Graphs A1 to All of the Appendix the trend lines estimated with his time scheme (i.e., the trend estimates underlying Table 3). It can be seen from these graphs, t h a t in some cases the trend lines could be fitted a bit more perfecfly, if we modified t h e Mandelian chronology so a s to move either transition year a bit forward or backward in the series. As mentiond above, we have tried out some dating alternatives using the optical impression from the nine-year moving averages in the graphs of the Appendix. The outcomes from testing this 'softer' scheme

x', a a u

h h h h h h

N - N 9 N U N N N u N N 9 N N - N N "'4 o. ^In? o. ^{9 U . QI,} Q I Q ‘ " o

3' 2 _{4 ,}

,

^{4 9 N .}

. Z ?

' O a ) . o m - 0 - - c u

f 0 - 9 0 - QI N - QI 0 - gr u w 9 o w

are documented in Table A2 of the Appendix. I t becomes obvious from Table A2 that our testing method is relatively robust against deviations from the 'hard' scheme.

Only in t h e case of Sweden do these changes lead t o a remarkable increase in one significance level (from 85.5% to 96.1%). In all other cases, significance levels a r e only slightly changed; in most cases this change is in the positive direction. In t h e following, we will therefore concentrate our interpretation on the results obtained from testing t h e 'rigid' Kondratieff chronology of Mandel. These results a r e given in Table 3.

-ATION OF TABLE 3

The results from testing Mandel's 'rigid' chronology can be summarized as follows:

-

In Kuczynski's two series on world industrial production, as well as in t h e series for France, Germany and t h e USA, significance levels vary between fairly good and excellent from t h e 1890s u p to the present (with t h e exception of the most recent period for which we lack suffi- cient d a t a for reliable testing). During the pre-1893 periods, t h e r e a r e no significant differences in average growth r a t e s for the alleged A a n d

B

periods, a n d in several cases the variation of growth rates is even inverse t o the one we would expect from a long wave view.

-

_As opposed to t h e dichotomy between the pre-1890s and post-1890s pattern in the above-mentioned series, the Belgian industrial produc- tion series of Gadisseur reveals a highly significant long wave pattern from t h e 1830s up t o the present.

-

The outcomes of the GDP series for Italy and Sweden show a result similar t o t h a t of the Belgian data; i.e.. from 1861 onwards growth rates vary in a way consistent with the long wave hypothesis. Only for t h e 1861 to 1873 period a r e significance levels below 95%, due t o t h e high standard error of t h e estimate (incomplete coverage of t h e

1848 t o 1873 period).

-

Very weak evidence for t h e existence of long waves comes from t h e two British series. As can be seen from a look a t Graphs A10 and A l l of the Appendix. t h e British series are dominated by a kind of very long-term cycle of rising (1820s-1870s) and declining (from t h e 1870s

I

onwards) worid market hegemony of British industry. This pattern can also be discerned from the growth r a t e s in t h e above table. The 'hegemonial' life cycle may have obliterated t h e Kondratieff long wave. Only f r o m t h e inter-war period onwards is t h e British growth pattern consistent with t h e Kondratieff long wave hypothesis.

CONCLUDING COl!uamTs

A comparison of t h e above results with those from previous studies clearly indicates t h e importance of testing the long wave hypothesis with time series from a larger range of countries. Kuczynski (1978, 1980) tested t h e hypothesis exclusively with his world series. van Ewijk (1981, 1982) and van

der Zwan (1980) concentrated heavily on British, US, French and German data (with van der Zwan not even covering t h e post-World War I1 period). In our test, all these series proved indeed to have no long wave pattern in t h e pre-1890 period, and, in the British case, this holds even for t h e entire pre-World War I period. Consequently, t h e negative conclusions in t h e above-cited studies a r e not surprising.

On t h e other hand, although our outcomes a r e much more in favor of t h e long wave hypothesis, they do not allow us to share the full optimism of t h e study by Glismann e t a1 (1978). One of us has previously expressed some s c e p ticism about t h e method of discerning iong waves by Glismann e t a1 (1978) (see K l e i n h e c h t , 1981; for a reply see Glismann e t al., 1981). From t h e viewpoint of o u r above results, this scepticism is only partially confirmed.

Wlth t h e exception of t h e British series, we can say that, according to our test, and for roughly the last hundred years, all t h e series show a pattern con- sistent with the long wave hypothesis. However, as opposed to t h e study by Glismann e t al., our results remain ambiguous for t h e pre-1890 period. On t h e one hand, important series such as those on world production, or t h e data for Great Britain and France, give no support for long-term fluctuations of t h e Kondratieff type during the pre-1890 period; on t h e other hand, the Belgian data show a highly significant long wave pattern from the 1830s onwards. Bel- gium is a small and open economy. As opposed to countries such a s t h e USA with large domestic market, t h e Belgian data may much more reflect develop ments on t h e world market. So far the strong evidence for long waves in t h e Belgian series is quite remarkable. Furthermore, evidence for long waves dur- ing t h e pre-1890 period comes from the Italian and Swedish data, although for shorter periods (from 1861 onwards).

There a r e several possibilities of dealing with the above ambiguity.

Adherents of the long wave might argue that, in general, the further we go back in history, t h e less reliable our data will become. Here, an important argument could be derived from t h e Schumpeterian tradition, arguing with t h e role of young, innovative growth industries as a driving force behind the A periods. This Schumpeterian element of growth may be somewhat underes- timated insofar as young industries often only draw t h e attention of statisti- cians once they have reached a certain minimum size. Naturally, if such as 'anti-Schumpeterian' bias should exist, i t would be relevant r a t h e r for t h e 19th than for the 20th Century. Still another argument could refer to the fact t h a t only highly aggregated data have been used for the above tests. A r a t h e r smooth pattern i n aggregate data could still be consistent with the Kondrateiff long wave having a 'primary impact on price, wage, and interest r a t e trends.

on t h e sectoral composition ( r a t h e r t h a n volume) of investment, and on regional a n d international income distribution', as has been emphasized most recently by Rostow (1982, p.02). However, this possibility, too, can only be mentioned without being investigated in this paper.

Summarizing t h e above points, t h r e e positions appear t o be reasonable.

One of t b e m could be t h a t the Konratieff cycle is indeed relevant even before the 1890s, but it does not show up due to biased data. or due to high levels of aggregation. &d so on.

A different position could be t h a t i t is not only bad data, but also t h e existence of movements temporarily stronger than the Kondratieff wave, t h a t makes evidence in favor of the l a t t e r r a t h e r weak. Such an argument could refer t o t h e already mentioned 'hegemonial' life cycle of Great Britain, t h e shorter-term Kuznets cycle, or t h e fact t h a t countries entered t h e i r rapid growth 'take-off phase a t different times, some of them during Kondratieff B

periods.

Still a different possibility could be that the mechanism bringing about Kondrateiff long waves is indeed not relevant for the infant phase of capital- ism. and that the system had to reach a certain level of consolidation before it could produce such waves; i.e., the Kondratieff long wave would be primaily important for the e r a of 'Hochkapitalismus' and 'Spgtkapitalismus'. The Kon- dratieff pattern from the 1830s onwards in the Belgian series does not strongly contradict this argument, since Belgium has been ,one of the forerunners in the industrialization process of continental Europe.

Principally, the outcomes of this paper are consistent with each of the three above propositions, and it is up to more detailed historical research to decide which is more realistic.

Finally, an important limitation of this paper has to be kept in mind: no evidence has been given for t h e existence of Kondratieff long waves as h e c y c l e s . The above test does give evidence that in several major industrial countries there are

-

a t least since the 1890s

-

differences in average growth rates for A and B periods which excellently fit into the time schedule of Kon- dratieff long waves; and these differences are statistically significant. How- ever, as already mentioned in the introduction of this paper, it can still be argued that these fluctuations are due to historically unique causes, and need not necessarily be repeated in the future. This argument is supported by the fact that, up to now, such a low number of A and

B

periods can be observed that merely quantitative proof of long cycles is just not possible for the time being. Therefore, we fully agree with the point made by Spree (1978) or Rosen- berg (1983), t h a t . a concept of long cycles can only attain credibility if long cycle theorists develop theoretically convincing endogenous, models of the long cycle; i.e., it has to be demonstrated that A periods necessarily develop

into B periods, a n d vice versa.

A s can be s e e n from t h e references i n t h e above introduction. discussion a r o u n d this topic h a s b e e n quite vivid recently. Our above r e s u l t s should be sufficiently encouraging t o continue t h a t type of r e s e a r c h w o r k

APPENDIX: WP-G

THE'

GLS ESI'IMATE Knowing the autocorrelation pattern:

it is possible to calculate t h e covariance matrix-C and subsequently apply

GLS.

This is, however a time-consuming and computationally inefficient method. I t is known that there exists a triangular matrix V such t h a t

V'V = f-I

Therefore, V describes a transformation, which, if applied to the residuals, gives u s identical normally distributed noncorrelated variables. We have now, in fact, shifted the problem of generating C to that of generating the triangu- lar matrix V, describing t h e necessary transformation. The larger part of this transformation, bowever, follows directly from the rewritten autocorre~ation pattern:

the right side of which consists of noncorrelated disturbances, while the left side describes a row of the needed matrix V

I t can easily be seen that we always need the n values preceding the values to be transformed; this implies a loss of observations a t the beginning of the time series and after possible interruptions (World Wars). It is certainly possi- ble to avoid the loss of observations caused by the interruptions, but this requires a substitution process based on the assumption that the autocorrela- tion pattern remains unchanged during the interrupted periods. Given the dis- turbances of the economies by World Wars, this does not appear to be a very realistic assumption. Therefore, we preferred to describe the disturbances before and after the interruptions separately; this implies that we treat the time series as if, after the interruptions, the stochastic process had started anew. Therefore, in some cases, we would lose three times the n starting obsemations.

To avoid this loss we also need to find the n rows describing the transfor- mation for the first n observations.

Clearly, this has to be done in a different manner. From the knowledge of the autocorrelation pattern we can conclude that the autocorrelation matrix

C is symmetrical in both its diagonals. Therefore, its inverse must be symrnetrica1,in both its diagonals as well. From the part of V we already know, and the fact that

V

is triangular, we conclude that

V

is a band matrix. But if V is a band matrix so is C1. With the part of

V

we already know we can calculate a part of 1-l. The other parts of 1-l are easily constructed using the sym- :metry and its band form. Once we have found 2.r1 we can easily complete V using the method of Choleski. After using V to transform the observations we can apply

OLS

on the transformed variables.

N m N N h N n&- N N - m - N N b - N NL- N N G

g-?

". ",V]

g ?

"\.

" "

^m

-

^'9

^g-•

^{m. m m} a , . ? , . Q m '0 r- '0 u - 0 m . O In .O o\ .O

* . -

m u . In m u h - u m o w r*. - w a m u Q o w

I n . . m . . r r . . N . . a . ^{. h ( .} ' 0 m - 0 0 - 0 m . O m . O In . m I I I I I I e 4 - ,

-

m N U u m u m ^{- u} m m u gr - u

e4 ucu W,. u c m u c - Y c- u u c r ; u c .

Q

-

^{O 2 0 Q 0 O}

^z

^O

^z

^O

z

^O

z

^{0 .}

T a b l e A2: Average Growth R a t e s f o r A and B p e r i o d s of t h e Long Waves, T h e i r S t a n d a r d E r r o r s , and t h e S i g n i f i c a n c e of D i f f e r e n c e s

i n Average Growth R a t e s , According t o Our ' S o f t ' Chronology

1) t h e growth r a t e f o r t h e 1740-1792 p e r i o d is: 5.26 (0.86).

I t a l y (GDP)

- - - - - -

1861-1873 0.74%

(0.71) 51.9%

1873-1898 0.70%

(0.28) 99.9%

1898-1913 3.16%

(0.43) 99.9%

191 3-1946 0.89%

(0.18) 99.92

1946-1977 5.13%

(0.22) 89.7%

1977-1980 -0.33%

(4.10)' Country and Belgium

V a r i a b l e : ( I n d . Pro- d u c t i o n

1

U.S.A.

(GNP)

- - - - -

- - -

-

1889-1893 3.43%

(2.85) 64.9%

1893-1909 4.67%

(0.61) 99.9%

1909-1936 2.03%

(0.28) 99.9%

1936-1969 3.85%

(0.24) 85.1%

1969-1980 2.622 (1.02) World Ind.

P r o d u c t i o n ( e x c 1.

mining)

1792- I 825':

2.63%

(0.24) 1 .OX 1825-1847 3.87%

(0.34) 43.0%

1847-1871 3.76%

(0.35) 79.5%

1871-1883 2.98%

(0.68) 82.8%

1883-1'910 3.82%

(0.28) 99.9%

19 10-1950 A: growth r a t e :

s t a n d . e r r o r : s i g n . of d i f f . :

8: growth r a t e : s t a n d . e r r o r : sign. of d i f f . :

A: growth r a t e : s t a n d . e r r o r :

- -

-

1831-1847 1.84%

(0.46) 9.9%

1847-1873 3.92%

(0.24)

Germany NNP

- -

-

- -

-

1850-1874 2.95%

(0.57) 83.0%

1874-1882 1.24%

(1.39) 86.9%

1882-1913 3.09%

(0.39) 99.82

1913-1948

Sweden (CDP)

- - - - -

-

1861-1874 3.11%

(0.42) 96.0%

1874-1891 2.02%

(0.26) 99.9%

1891-1912 3.41%

(0.20) 99.9%

1912-1935 s i g n . of d i f f . :

B: growth r a t e : s t a n d . e r r o r : s i g n . of d i f f . :

A: growth r a t e : s t a n d . e r r o r : s i g n . of d i f f . :

8: growth r a t e : s t a n d . e r r o r : s i g n . of d i f f . :

2.24%

(0.16) 99.92

1935-1971 4.46%

(0.11) 99.92

1971-1980 1.38%

(0.66) 99.9%

1873-1889 1.15%

(0.36) 99.9%

1889-1913 3.222

(0.25) 99.92

1913-1946 0.23%

(0.17) 99.9%

1946-1975

2.54%

(0.17) 99.9%

1950-1974 5.51%

(0.35) 88.72

1974-1980 2.44%

(2.30) A: growth r a t e s t a n d . e r r o r

. -1

:, ^3.93% (0.22)

s i g n . of d i f f .

:!

^96.5%

I

1

^1975-1982

B: growth r a t e

:I

^1.07%

s t a n d . e r r o r

:I

^{(I -42)}

I

1.18%

(0.31) 99.9%

1948-1974 5.65%

(0.47)

.

^95.9%

1974-1980 1.33%

(2.18)

I

I

$ 1

0:

0 1 a,

Yi

73

a cam.

C Q ) . J I C 0 .J > I

a

D L O I L a, a,

x f e .

1 V) a : 0 1

2 L I 0 0 0 ' 4 .

c

a,; 0

-J - 1 E

1-2

0

m;LI

I

I

-J 1 1 4 ,

1 I a 1

I

m i

tl ^m

Yi

w

00 ClW*

c m

2 1

c m - J > l a m c

O ' C

I

m m x ! ~ . A m

2 C I

m

-J I 1 4 ,

0

miw

I

'

^I

llil

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