long-run sectoral development: time-series evidence for the german economy

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Structural Change and Economic Dynamics 21 (2010) 111–122

Contents lists available at ScienceDirect

Structural Change and Economic Dynamics

journa l homepage: www.e lsev ier .com/ locate /sced

ong-run sectoral developmentime-series evidence for the German economy

ndreas Dietrich ∗, Jens J. Krügerarmstadt University of Technology, Department of Law and Economics, Residenzschloss, Marktplatz 15, D-64283 Darmstadt, Germany

r t i c l e i n f o

rticle history:eceived February 2008eceived in revised form August 2009ccepted November 2009vailable online 6 December 2009

EL classification:

a b s t r a c t

In economic development, long-run structural change among the three main sectors of aneconomy follows a typical pattern with the primary sector (agriculture, mining) first dom-inating, followed by the secondary sector (manufacturing) and finally by the tertiary sector(services) in terms of employment and value added. We reconsider the verbal theoreticalwork of Fourastié and build a simple model encompassing its main features, most notablythe macroeconomic influences on the sectoral development. Estimation and analysis withGerman data for the period 1850–2001 show that this model is quite capable of replicating

161441

eywords:tructural change

the empirical facts.© 2009 Elsevier B.V. All rights reserved.

the tertiary sector will never be saturated. Accordingly,

ndustrializationertiarization

. Introduction

The analysis of long-run structural change is concernedith the differential development of the three main sectors

f the private economy. This research intends to explainhe successive dominance of the so-called primary (agri-ulture, mining), secondary (manufacturing, construction),nd tertiary (services) sectors in terms of employment andalue added of an economy. In the literature there are sev-ral early accounts and explanations for this pattern ofectoral development, given by Fisher (1939, 1952), Clark1957) and Wolfe (1955), as well as more recent approacheso integrate the sectoral development into formal growth
heory; see inter alia Echevarria (1997), Kongsamut et al.2001) and Ngai and Pissarides (2007).
A frequently neglected but particularly appealing expla-ation for long-run sectoral development of the three

∗ Corresponding author. Tel.: +49 6151 163192; fax: +49 6151 163897.E-mail address: [email protected] (A. Dietrich).

954-349X/$ – see front matter © 2009 Elsevier B.V. All rights reserved.oi:10.1016/j.strueco.2009.11.009

sectors is given by Fourastié (1949/1969).1 In his book,Fourastié verbally develops a broad theory of economicdevelopment involving psychological and sociological ele-ments supplementing the economic considerations. On thesupply side, the final effect of technological process is toincrease aggregate income. On the demand side, a hierar-chy of needs is associated with different saturation levelsfor the goods of the three sectors. In the course of increas-ing income, the demand for goods of the primary sectoris first saturated. Further increases of income lead to asaturation of the demand for goods of the secondary sec-tor. According to Fourastié, only the demand for goods of

the demand side determines the direction of structuralchange.

1 Note that the year 1949 refers to the original first edition published inFrench language and the year 1969 refers to the second edition in Germanlanguage available to us.

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dx.doi.org/10.1016/j.strueco.2009.11.009

ge and E

Substituting for � ln Yit

from Eq. (4) gives

� ln Ldit = �−1

i(�iˇi� ln Yt−1 + (1 − �i)� ln Yit−1

− � ln A ) (7)

112 A. Dietrich, J.J. Krüger / Structural Chan

In this paper, we reconsider the Fourastiéian perspec-tive of long-run structural development. Therefore, wecompress this wealth of insights into a simple theoreti-cal framework, emphasizing the interaction of supply anddemand side forces for shaping the characteristic pattern ofstructural change among the primary, secondary and ter-tiary sector. To perform the empirical analysis a dataset hasbeen assembled for the German economy that spans therelevant time period starting from 1850 to the present. Inconstructing the dataset, substantial effort has been under-taken to obtain consistent annual time series. Structure isrepresented by the division of total employment and valueadded among the primary, secondary and tertiary sector.

The empirical results show that the very simple theo-retical model is quite able of replicating the characteristicpattern of sectoral development. This comprises not onlythe monotonically declining share of the primary sectorand the monotonically rising share of the tertiary sector,but also the inverse U-shaped trajectory of the secondarysector. By that the model covers the period of industrial-ization as well as the subsequent period of tertiarization. Inthe case of employment, a major role in achieving this fit isplayed by the growth rate of aggregate income representedby GDP. For value added the results are less conclusive.Taken together, however, the results reported in this papershow that the consideration of macroeconomic growth inexplaining long-run sectoral development improves thestatistical account of sectoral dynamics substantially. Weinterpret this as evidence in favor of the theory of Fourastié,at least in the simplified version we employ here.

The plan of the paper is as follows: The following Sec-tion 2 outlines a simple theoretical reasoning to motivatethe empirical analysis. Section 3 explains the estimationand model evaluation strategy as well as the dataset. Thissection also summarizes the results of an extensive testingfor unit roots (the detailed results of which are relegated toAppendix B). The empirical results for structural change interms of employment and value added are then discussedin Sections 4 and 5, respectively. Section 6 concludes witha summary of the main results and points to some waysfor extending the analysis that we plan to pursue in futurework.

2. Theoretical motivation

To motivate the empirical analyses in the subsequentsection we develop here a stylized log–linear formulationof structural change with both demand and supply sideconsiderations. On the demand side, consumer preferencesdetermine a saturation level for the consumption in sectori, with i ∈ {1, 2, 3} denoting either the primary, secondaryor tertiary sector, towards which the consumers plan toadjust their consumption levels. This planned growth ofconsumption is directly associated with a certain growthrate of labor requirements. On the supply side, labor isthe single production factor and changes of wage differ-
entials induce labor flows between the sectors. Demandand supply side changes are assumed to be coordinated bymarkets in a way that the realized changes in labor inputand produced output are somewhere in between the plansof consumers and producers. This is not necessarily associ-
conomic Dynamics 21 (2010) 111–122

ated with an equilibrium situation in which both plans areequalized.

Starting on the demand side and considering a particularsector i, i ∈ {1, 2, 3}, we assume that the planned growthrate of demand in sector i at time t, ln Yd

it− ln Yit−1, depends

on the deviation of the realized demand in the previousperiod Yit−1 from its saturation (target) level Yit . This leadsto a formulation of the partial-adjustment model in logs

ln Ydit − ln Yit−1 = �i(ln Yit − ln Yit−1) (1)

with �i ∈ (0, 1) denoting the adjustment speed2.We further assume that the target levels of the sector

depends on the aggregate level of economic activity, rep-resented by the lagged level of GDP, Yt−1, via ln Yit = ˛i +ˇi ln Yt−1. Here, ˛i and ˇi are sector-specific parametersthat can be interpreted as reflecting consumer preferencesfor the goods of the sector. Given that, the partial adjust-ment Eq. (1) can be reformulated leading to

ln Ydit − ln Yit−1 = �i(˛i + ˇi ln Yt−1 − ln Yit−1) (2)

and therefore

ln Ydit = �i˛i + �iˇi ln Yt−1 + (1 − �i) ln Yit−1. (3)

Taking first differences gives

� ln Ydit = �iˇi� ln Yt−1 + (1 − �i)� ln Yit−1. (4)

where � denotes the usual first-difference operatordefined by �xt = xt − xt−1.

The supply side is represented by the production func-tions

ln Yit = ln Ait + �i ln Lit, (5)

where Lit denotes labor input of sector i in period t, �i >0 is an elasticity parameter governing returns to scaleand Ait represents the sector-specific technology level.In general, it is to be expected that returns to scale aremore pronounced in the secondary and tertiary sectorssince externalities originating from capital accumulation asemphasized in growth theory (Romer, 1986; Lucas, 1988)or from the agglomeration of those activities in cities (Lucasand Rossi-Hansberg, 2002; Eeckhout, 2004) naturally playa much larger role in these sectors compared to the primarysector.

To satisfy the planned demand growth, output in eachsector needs to be increased by a certain rate which can beachieved if there is sufficient technological progress lead-ing to � ln Ait > 0 and/or labor input in the sector increasesat a sufficiently high rate

� ln Ldit = �−1

i(� ln Yd

it − � ln Ait). (6)

d

it

2 Note that the demand of period t is a planned magnitude (indicated bythe superscript d) whereas the demand of the previous period is of coursea realized magnitude.

ge and E

ab

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A. Dietrich, J.J. Krüger / Structural Chan

nd substituting for the lagged growth rate of sector outputy the production function in Eq. (5) leads to

ln Ldit = �−1

i(�iˇi� ln Yt−1

+ (1 − �i)(� ln Ait−1 + �i� ln Lit−1) − � ln Ait).

(8)

Assuming a constant but sector-specific technologicalrogress rate gi = � ln Ait = � ln Ait−1 we obtain

ln Ldit = −�−1

i�igi + (1 − �i)� ln Lit−1

+ �−1i

�iˇi� ln Yt−1. (9)

Labor input either grows because the population growsr as a result of reallocation of workers between sectors.he growth rate of labor supply in sector i, as plannedn the supply side, is therefore affected by the rate ofopulation growth and growth differentials of wages. Pop-lation grows at the rate � ln Lt . The wage differential is

nduced by initial period differences in sectoral labor pro-uctivity (ln Yit−1 − ln Lit−1 = ln Ait−1 + (�i − 1) ln Lit−1) toconomy-wide labor productivity ln Yt−1 − ln Lt−1. Thisives rise to the growth differential of labor productiv-ty � ln Ait−1 + (�i − 1)� ln Lit−1 − (� ln Yt−1 − � ln Lt−1).herefore, the planned growth of labor supply in sector i is

ln Lsit = � ln Lt−1 + �i(gi + (�i − 1)� ln Lit−1

− (� ln Yt−1 − � ln Lt−1)), (10)

here �i > 0 is an adjustment speed parameter.The third element is to assume that markets are suffi-

iently working to coordinate the plans from the demandide and the supply side. A very weak implication of thiss that the resulting labor input in sector i lies some-

here in between the plans from the demand (Eq. (9))nd supply sides (Eq. (10)). Formally this can be statedy letting the realized labor input (which is observable

n the data) in sector i be a convex combination of ln Ldit

nd ln Lsit

, i.e. ln Lit = � ln Ldit

+ (1 − �) ln Lsit

with � ∈ [0, 1].ince this does not necessarily imply the equalization ofemand and supply it is perfectly compatible with dise-uilibrium situations without excluding the possibility ofquilibrium.

Expressed again in growth rates, these considerationsead us to

� ln Lit = �� ln Ldit

+ (1 − �)� ln Lsit

= �[−�−1

i�igi + (1 − �i)� ln Lit−1 + �−1

i�iˇi� ln Yt−1

]+ (1 − �

= (�i − �(�i + �−1i

�i))gi + (�(1 − �i) + (1 − �)�i(�i − 1))� ln Lit

= � + � � ln L + � � ln Y + � � ln L

� ln Yit = (1 − �)(1 + �i)gi + (�(1 − �i) + (1 − �)�i(�i − 1))� ln Y

= �i1 + �i2� ln Yit−1 + �i3� ln Yt−1 + �i4� ln Lt−1

i1 i2 it−1 i3 t−1 i4 t−1

ith obvious definitions of the parameters �i1 to �i4. Thisquation represents an autoregressive process in logs forhe growth rate of labor input in sector i with the laggedrowth rates of aggregate GDP and population as additional

conomic Dynamics 21 (2010) 111–122 113

t−1 + �i(gi + (�i − 1)� ln Lit−1 − (� ln Yt−1 − � ln Lt−1))]

�−1i

�iˇi + �i) − �i)� ln Yt−1 + (1 − �)(1 + �i)� ln Lt−1

(11)

explanatory variables. The parameters �i1 to �i4 depend onthe structural model parameters in a very complex wayso that the structural parameters unfortunately cannot berecovered from estimates of �i1 to �i4.

The corresponding change of sectoral out-put can be found by substituting � ln Lit =�−1

i(� ln Yit − gi) into Eq. (11) and rearranging, resulting

in

(�iˇi + �i�i) − �i�i)� ln Yt−1 + �i(1 − �)(1 + �i)� ln Lt−1 (12)

with the parameters �i1 to �i4 to be estimated. This outputvariable resembles a value-added measure for which dataare available.

As mentioned in Section 1, the model comprises cen-tral elements of Fourastié’s theory of structural changeamong the three main sectors of the economy (Fourastié,1949/1969). According to Fourastié, technological progressleads to increases in labor productivity which affect thethree sectors differentially. In our model this is reflectedin the sector-specific values of gi and �i. These differentialincreases of labor productivity are associated with decreas-ing product prices and simultaneously contribute to theincrease of overall income. The rising overall income, whichis represented by GDP growth, allows the consumers to buynew products that tend to be produced in other sectors(meaning products of the secondary sector instead of theprimary sector or products of the tertiary sector insteadof the secondary sector). By that, all three sectors suc-cessively reach their saturation levels, the primary sectorfirst, followed by the secondary sector. Fourastié assumesthat demand for the products of the tertiary sector neverbecomes saturated. In our model this saturation is capturedby the partial-adjustment formulation for product demand.The change of the demand structure needs to be accommo-dated by the change of the production structure and this isinevitably associated with labor reallocation between thesectors which is a further central element of our model. Insum, the dynamics in the model work in a way that tech-nological progress raises aggregate income and this leadsto changes of the production and employment structure asa cause of changes in the structure of consumption.

3. Estimation strategy and data

The equations for both employment growth and value-added growth for the three sectors, each together withthe restriction that the sector values add up to the total,constitute a system. Subsequently, the model equationsfor employment (and likewise for value added) are esti-mated as a two-equation system of seemingly unrelatedregression equations (SURE; Zellner, 1962) with updating

coefficients and the weighting matrix simultaneously ateach iteration. The system is specified by two equations

114 A. Dietrich, J.J. Krüger / Structural Change and Economic Dynamics 21 (2010) 111–122

Table 1Results for employment.

Specification A1 B1 C1

Dep.Var./sector �ln L1t primary �ln L2t secondary �ln L1t primary �ln L2t secondary �ln L1t primary �ln L2t secondary

Intercept 0.004 (0.563) 0.012 (2.582) −0.005 (−0.315) 0.003 (0.315) −0.011 (−0.357) 0.017 (0.912)�ln Lit−1 0.201 (2.274) 0.381 (4.758) 0.122 (1.336) 0.191 (2.074) 0.072 (0.798) 0.158 (1.685)�ln Yt−1 0.204 (1.072) 0.474 (3.919) 0.486 (2.157) 0.553 (3.785)�ln Lt−1 0.349 (0.261) −0.012 (−0.015) 1.240 (0.878) 0.474 (0.531)Post1950 −0.030 (−3.066) −0.010 (−1.715) −0.032 (−2.104) −0.017 (−1.911) −0.184 (−2.421) −0.062 (−1.361)Time 0.000 (−0.408) 0.000 (−1.087)Time × post1950 0.001 (1.499) 0.001 (1.181)

N 86 86 86 86 86 86R2 0.097 0.134 0.121 0.268 0.160 0.266Q(1) 5.486 (0.019) 0.855 (0.355) 2.040 (0.153) 0.008 (0.929) 1.501 (0.221) 0.015 (0.904)Q(4) 7.961 (0.093) 1.293 (0.863) 4.231 (0.376) 0.578 (0.966) 5.113 (0.276) 1.038 (0.904)

76 (0.40

sectorsBox–Lj

the world economic crisis 1929–1933 (the German expres-sion for the Great Depression in the US).

Since the validity of our statistical estimates depends onthe order of time-series integration of the data series used

SB 1.139 (0.289) 0.403 (0.527) 0.9

Note: Estimated as SURE system with the additional restriction that thesample size, R2 is reported in the corrected version, Q(1) and Q(4) are thefor our test of a structural break (p-values are reported in parentheses).

for the primary and the secondary sector with the addi-tional restriction that all three sectors add up to the total.From a statistical point of view, a very fortunate featureof the model is that all variables in the system are read-ily expressed in growth rates, thereby avoiding spuriousregressions (Phillips, 1986). This will become clear shortlywhen we discuss the results of our unit-root and station-arity analysis. Moreover, all explanatory variables appearwith a lag and are thus less prone to endogeneity.3

To judge the appropriateness of the model to replicatethe typical pattern of long-run structural change among thethree sectors, it is not sufficient to have just estimates fora model in growth rates. Therefore, our strategy to evalu-ate the explanatory power of the model is first to estimatethe SURE system and then to solve it numerically for thedevelopment of the sector shares of either total employ-ment or total value added in a second step. We use theGauss–Seidel algorithm (see Judd, 1998, p. 72) for comput-ing the dynamic solution of the model which actually isa multi-step forecast where the forecasted values of theendogenous variables itself are used for their lags in laterperiods. The final judgement of the goodness-of-fit of themodel relies on comparing the solution trajectories to theactual development.

Our database is compiled from various sources. Sec-toral employment is measured by the number of employedpersons (including paid employees, self-employed personsand unpaid family workers). The value-added series actu-ally represent real net value added at factor cost. For theperiod before 1950 our primary data source is Hoffmann(1965). Employment data in the period since 1950 are takenfrom the 10-Sectoral Database (1950–1991) and the 60-Industry Database (1992–2001) of the Groningen Growthand Development Centre (GGDC; see O’Mahony and van
Ark, 2003; van Ark, 1996). Value-added data since 1950are taken from the national accounts provided by the Ger-man federal statistical office (Statistisches Bundesamt). Forthe calculation of the value-added series three different
3 The model equations are related to a first-order vector autoregressionand indeed the estimation of such a system leads to similar results.

8) 1.822 (0.150) 2.186 (0.097) 1.993 (0.122)

add up to the total; t-statistics are reported in parentheses; N denotesung statistics for one and four lags, respectively, and SB is the F-statistic

variants have been implemented. The details of these vari-ants and of the various operations undertaken to reach thefinal set of sectoral data are described in Appendix A. Themacroeconomic time series for real GDP and population aretaken from Angus Maddison’s web page (Maddison, 2007).

The data for employment span the period 1878–2001,whereas the data for value-added span the period1850–2001. By that our sample period starts in the midof the 19th century, when the industrial revolution inGermany started (see e.g. Galor, 2005; Maddison, 1991).4

Unfortunately, for both variables and all three sectors twosubstantial data gaps exit around the two world wars, sothat data are missing for the years 1914–1924 for both vari-ables and 1945–1949 (1939–1949) for employment (valueadded). To deal with this problem we opted for omitting theentire period 1914–1949 and taking account for this by per-mitting a structural break in the estimates. This is done byallowing for a break in the mean growth rates and later onan additional break in the deterministic trend in the growthrates (i.e. by defining a dummy variable post1950 equal tounity for all years since 1950 and zero otherwise). By thatpossible biases from the necessary currency conversion tothe Deutsche Mark are also alleviated.

The application of interpolation and imputation meth-ods appears to be dangerous in this case because two 11year blocks of data are missing and moreover the availabledata for the period 1925–1938 are suspect of being partic-ularly unreliable because of the very turbulent political andeconomic environment during these years, including majorcrises such as the German hyperinflation 1922–1923 and

4 As an example, in 1835 the first German railway train went from Nürn-berg to Fürth. Economically important was the railroad between Leipzigand Dresden opened in 1837. Along with the railroadization the demandfor metal and steel products increased and could be satisfied by the risingindustrial sector which was increasingly equipped with steam engines. InGermany, the industrial sector was quantitatively dominating until 1960(see Bairoch, 1982, Table 4 on p. 281).

ge and E

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cieivuttp

sBBtpSgftr1

tvsolttb

sbosPtsa

omvt


e have extensively tested for unit roots and stationarity.etailed tables of the results are shown in Appendix B andre just summarized here for brevity. Nearly all of the unit-oot tests are not able to reject their null hypothesis for thelogged) level series whereas the stationarity tests vividlyeject their reverse null hypothesis. Thus, all variables usedor the estimates, the sectoral growth rates of employmentnd value added as well as the growth rates of economy-ide GDP and population are treated as stationary. This

utcome also holds when structural breaks in various formsre permitted in the tests.

. Results for employment

The results of three model specifications for structuralhange in terms of employment are shown in Table 1. Spec-fication A1 is a first-order autoregressive process for themployment growth rates augmented by a structural breakn the intercept. In specification B1, the macroeconomicariables, the lagged growth rates of real GDP and pop-lation, are included. This specification is closest to theheoretically motivated equation derived above. Specifica-ion C1 further includes a linear deterministic trend whichermits for the possibility of a structural break.

In the table the coefficient estimates with their t-tatistics in parentheses are reported above the dashed line.elow the dashed line the corrected version of R2 and theox–Ljung portmanteau statistics testing for autocorrela-ion at one and four lags, Q(1) and Q(4), together with their-values in parentheses are presented. In the line labeledB the F-statistics of a test for a structural break in 1950 areiven (again with p-values in parentheses). This test checksor a structural break in the regression parameters excepthe intercept and the time trend. It is based on the artificialegression described by Davidson and MacKinnon (2004, p.45).

The results for specification A1 show significantly posi-ive estimates for the parameters of the lagged dependentariables. They reveal autoregressive dependence in bothectors, a bit stronger in the secondary sector. The impactf the structural break in the intercept is significant on a 5%evel only in the primary sector.5 As can be inferred fromhe row SB the other parameters are not affected by a struc-ural break. However, residual autocorrelation appears toe a problem in the equation for the primary sector.

Once the macroeconomic variables are introduced inpecification B1, the degree of autoregressive dependenceecomes weaker and remains significant only in the casef the secondary sector. GDP growth acts positively in both
ectors, but is significant only in the secondary sector.opulation growth, by contrast, is never significant. Never-heless, the introduction of the macroeconomic variables isuited to increase the explanatory power of both equationsnd furthermore removes residual autocorrelation.
5 This dummy variable also accounts for territorial changes as a causef the two world wars. The further territorial change following the Ger-an reunification in 1990 can be accounted for by an additional dummy

ariable (results not shown) with the result of a slightly improved fit ofhe regressions but no substantive modifications of our conclusions.


As already mentioned above, specification B1 is closestto our theoretical considerations leading to Eq. (11). There-fore we now have a closer look at the numerical values ofthe parameter estimates. Starting with the coefficient per-taining to � ln Lt−1 we observe insignificant values for boththe primary and the secondary sector. This coefficient isequal to (1 − �)(1 + �i) and becomes close to zero only if �is close to its upper bound of unity. This implies that it isthe demand side that dominates labor force reallocationsbetween the sectors as postulated by Fourastié. This findinghas implications for the other parameter estimates. With �close to unity the coefficient pertaining to � ln Lit−1 is closeto 1 − �i which should be between zero and unity and thecoefficient pertaining to � ln Yt−1 is close to �−1

i�iˇi which

should be positive. The corresponding parameter estimatesare indeed in these ranges, although they are significantonly in the case of the secondary sector, thus supportingthis interpretation.

In specification C1 a deterministic trend with a possiblestructural break is added, leading to a further weaken-ing of the autoregressive dependence. Now, GDP growthhas a significantly positive effect in both sectors, whereaspopulation growth remains insignificant. Residual autocor-relation is also not a problem in this specification. As before,no structural break of the other parameters can be foundin this specification.

Common in all three specifications A1, B1 and C1 is thatautoregressive dependence appears to be stronger in thesecondary sector. In B1 and C1 the positive effect of GDPgrowth is also stronger in the secondary sector, whereasthe effect of population growth is stronger in the primarysector (although not statistically significant). The structuralbreak between 1913 and 1950 is associated with a shift ofthe intercept but not with a change of a deterministic trend.The latter fact is consistent with all variables appearingstationary.

Additional results, not reported in this paper, supportthese general findings and can be briefly summarized asfollows: First, the introduction of the broken determinis-tic trend in the otherwise pure autoregressive specificationwithout the macro-variables is associated with a weak-ening of the autoregressive dependence without beingsuited to remove residual autocorrelation. Second, in caseswhere either GDP growth or population growth is con-sidered in isolation (without a deterministic trend) onlyGDP growth appears significant. This variable increasesexplanatory power recognizably and also removes residualautocorrelation. Third, in contrast to the dummy variablepost1950, introducing a blip dummy (equal to unity for thefirst year after the break and zero otherwise) was not suitedto account for the possible structural break sufficiently.It was never significant and did not improve explanatorypower.

To judge the ability of the estimates in Table 1 to repli-cate the typical development of the sector shares in totalemployment, the following Figs. 1–3 plot the realized time
paths of the shares of the primary, secondary and tertiarysectors (from left to right) as the solid lines, together withthe solution paths (numerically computed by Gauss–Seidelas remarked above) as the dashed lines. Starting with spec-ification A1, Fig. 1 shows that the specification is quite

116 A. Dietrich, J.J. Krüger / Structural Change and Economic Dynamics 21 (2010) 111–122

Fig. 1. Employment shares with solution from specification A1.

with sol
Fig. 2. Employment shares
good in explaining the monotonically declining employ-ment share of the primary sector, but has considerabledifficulty with explaining the developments of the sec-ondary and tertiary sectors after World War Two. This isalso reflected in the goodness-of-fit measures of 0.996,0.779 and 0.910 for the primary, secondary and tertiarysectors, respectively, computed as the squared correlationcoefficients of the realized share path and the associatednumerical solution.

Introducing the macro-variables as suggested by thetheoretical model improves the fit of the numerical solu-tion substantially as Fig. 2 shows for specification B1. Thisholds especially for the secondary sector, where the inverseU-shaped form of the time path is now tracked quite closelyby the numerical solution, except for the period from themid of the 1970s to the start of the 1990s. Goodness-of-fitis here 0.996, 0.925 and 0.902 for the primary, secondaryand tertiary sectors, respectively.

A rather surprising feature of this solution is thatalthough we have only included growth rates into the spec-
ification, the numerical solution is indeed not only able toreplicate the monotonically decreasing or increasing pathsof the primary and tertiary sectors, but is also suited toreplicate the more challenging path of the secondary sectorwith its inflecion point.
Fig. 3. Employment shares with sol

ution from specification B1.

In specification C1 a deterministic trend with a breakis added and leads to the solution paths depicted inFig. 3 as the dashed lines. The figure reveals that intro-ducing a deterministic trend component is associatedwith a further improvement of fit. This is also reflectedin the goodness-of-fit measures of 0.996, 0.933 and0.950 for the primary, secondary and tertiary sectors,respectively.

Taken together, the results show that whereas theautoregressive specification in A1 has some difficultiesin replicating the sector shares, the explanatory powerimproves considerably once the macroeconomic vari-ables are introduced in specification B1, as suggested byFourastié and by the theoretical model. In further analyses,not reported here, we introduced the growth rates of themacroeconomic variables after eliminating the short-runcomponent of GDP and population by the Hodrick–Prescottfilter (Hodrick and Prescott, 1997). This modification wasassociated with an even better fit but the filtering operationmay induce an endogeneity problem so that we decided

ution from specification C1.

not to report the details. The introduction of a deter-ministic trend component in specification C1 improvesthe fit only slightly, which is not overly surprising in thelight of the small and insignificant coefficients of theseregressors.

A. Dietrich, J.J. Krüger / Structural Change and Economic Dynamics 21 (2010) 111–122 117

Table 2Results for value added.

Specification A2 B2 C2

Dep.Var./sector �ln Y1t primary �ln Y2t secondary �ln Y1t primary �ln Y2t secondary �ln Y1t primary �ln Y2t secondary

Intercept 0.021 (3.510) 0.028 (4.583) 0.020 (1.447) 0.023 (1.849) 0.030 (2.039) 0.038 (3.045)�ln Yit−1 −0.190 (−2.257) 0.250 (3.081) −0.265 (−2.527) 0.150 (1.296) −0.255 (−2.446) 0.057 (0.510)�ln Yt−1 0.297 (1.397) 0.292 (1.359) 0.052 (0.226) 0.043 (0.210)�ln Lt−1 −0.458 (−0.381) 0.157 (0.144) −1.404 (−0.996) −1.350 (−1.117)Post1950 0.008 (0.917) 0.018 (2.120) 0.003 (0.234) 0.019 (1.626) 0.177 (2.585) 0.297 (4.910)Time 0.000 (0.480) 0.000 (0.975)Time × post1950 −0.002 (−2.180) −0.002 (−4.055)

N 112 112 112 112 112 112R2 0.025 0.147 0.025 0.140 0.066 0.265Q(1) 0.589 (0.443) 0.139 (0.710) 1.044 (0.307) 0.093 (0.760) 0.876 (0.349) 0.103 (0.749)Q(4) 1.959 (0.743) 1.396 (0.845) 2.238 (0.692) 1.031 (0.905) 3.373 (0.497) 3.143 (0.534)SB 1.013 (0.316) 1.898 (0.171) 1.228 (0.304) 1.269 (0.289) 0.428 (0.733) 0.773 (0.512)

Note: Estimated as SURE system with the additional restriction that the sectors add up to the total; t-statistics are reported in parentheses; N denotessample size, R2 is reported in the corrected version, Q(1) and Q(4) are the Box–Ljung statistics for one and four lags, respectively, and SB is the F-statisticfor our test of a structural break (p-values are reported in parentheses).

Fig. 4. Value-added shares with solution from specification A2.

Fig. 5. Value-added shares with solution from specification B2.

ith sol

5

vst

Fig. 6. Value-added shares w

. Results for value added

In this section we report the corresponding results foralue added in Table 2. The specifications are autoregres-ive processes for the value-added growth rate analogouslyo those of the previous section. In contrast to the results

ution from specification C2.

for employment, the estimates of specification A2 show
a significantly negative coefficient for the lagged depen-dent variable in the case of the primary sector. A significantstructural break in the intercept is present only in the sec-ondary sector. With the inclusion of the macroeconomicvariables in specification B2 the autoregressive depen-

ge and E

not as well here.Moreover, due to the simplicity of our model several


dence weakens and looses significance in the secondarysector. The macroeconomic variables are, however, not sig-nificant in any case here. In specification C2 the linear trendwith a possible break is added. This lets the dummy vari-able post1950 for a structural break in the intercept besignificant. In addition, there appears to be a structuralbreak in the trend. The macroeconomic variables are hereagain insignificant. This appears to be a major differenceto employment where GDP growth is significant and thestructural break is less important. Concerning the explana-tory power, the values of R2 here begin to rise not until thedeterministic trend is introduced in specification C2. TheQ(1) and Q(4) statistics show that residual autocorrelationis absent in all specifications. Likewise, the tests for a struc-tural break in the other parameters never reject their nullhypothesis.

As for the employment shares, the following Figs. 4–6plot the realized time paths of the value-added shares asthe solid and the paths of the numerical solution as thedashed lines. Comparing the development of the employ-ment and the value-added shares it becomes apparentthat the general pattern is rather similar. Also in termsof value added the share of the primary sector declines,the share of the tertiary sector rises and the share of thesecondary sector is inverse U-shaped. In parallel to spec-ification A1 the fit of specification A2 is very good forthe primary but considerable weaker for the other sectors(Fig. 4). The corresponding squared correlation coefficientsare 0.994 for the primary, 0.089 for the secondary and0.854 for the tertiary sector.6 Thus, the fit for the sec-ondary sector is much lower in the case of the value-addedshares.

Here, the inclusion of the macro-variables improvesthe fit of the numerical solution to the realized devel-opment only slightly in the case of the secondary sector(Fig. 5). The goodness-of-fit measures are here 0.995,0.303 and 0.891 for the primary, secondary and ter-tiary sectors, respectively. Accordingly, fit remains muchlower for the secondary sector compared to the othersectors.

This pattern changes once the deterministic trend witha possible structural break is included in specification C2(Fig. 6). Now the solution tracks the realized develop-ment quite well for all three sectors and is also able tofit the inverse U-shaped form of the time path of the sec-ondary sector. Goodness-of-fit is here 0.994, 0.944 and0.955 for the primary, secondary and tertiary sectors,respectively.

In sum, the results show that analogous to the results
for employment the pure autoregressive specification hassome difficulties in replicating the sector shares. In con-trast to employment the impact of the macroeconomicvariables is only of minor importance whereas the inclu-sion of the deterministic trend with a break is suitable
6 The difference in the squared correlation coefficients of the secondaryand the tertiary sector appears a little bit puzzling at first, but becomesmuch more reasonable once a scatter plot of the realized and the fittedvalues is considered.


to bring the numerical solution close to the realizeddevelopment.7

6. Conclusion

The main result of this paper is that a simple modelbased on Fourastiéian ideas is quite capable of explain-ing the long-run decline of the primary, the long-runrise of the tertiary and the inverse U-shaped develop-ment of the secondary sectors for the German economyduring the period 1850–2001. This model features twocentral ideas of Fourastié (1949/1969), namely sectorallydiffering rates of demand growth as a consequence ofthe convergence towards sector-specific saturation levelswith rising economy-wide income and employment flowsacross sectors due to productivity differences inducingwage dispersion. The model is expressed in terms of growthrates of sectoral as well as economy-wide employment andvalue added. It is estimated as an equation system andevaluated by the fit of the numerically calculated shares ofeither employment or value added to their realized coun-terparts. Apart from the reasonable fit in general, the modelappears to be better suited for the case of the employmentshares than for the case of the value-added shares. In thelatter case the fit is primarily due to the introduction of atrend with a structural break instead of the macro-variablessuggested by theory.

Admittedly, the development described by Fourastiéis not universal and many time and country specific fac-tors affect structural change beyond those included in ouranalysis.8 In our analysis we have tested some of thesefactors by adding dummy variables to the specificationwithout finding substantive changes. What makes the find-ings reported in this paper so interesting in our view,however, is that structural change follows a specific pat-tern in the long run which can be explained reasonablywell by a small number of variables. Due to our treatmentof the data gap several exceptional periods are excludedfrom the analysis anyway. Similar data gaps exist for otherdeveloped countries such as France, the Netherlands or theUK. In the US consistent data at an annual frequency areonly available after most of the industrialization alreadyhad taken place. One exceptional example of a country withcomplete consistent sectoral time-series data starting fromthe 19th century up to our days is Sweden.9 Repeating ouranalysis for the Swedish case shows the same basic patternof sectoral development but also reveals that our model fits

forces that lead to productivity improvements in the sec-tors are not explicitly considered. In addition, the current

7 We also repeated the analysis of this section for the two alternativeways to construct the value-added series explained in Appendix A whichoverall confirmed the reported findings.

8 A similar point is made by Kaelble (1997) who argues that whereasthe three-sector development proceeds in a rather similar fashion acrossEuropean countries it appears to be much more diverse in the rest of theworld.

9 The Swedish data are very thoroughly described in Edvinsson (2005)and can be downloaded from http://www.historicalstatistics.org.

http://www.historicalstatistics.org/

ge and E

vitIpehegTtow

A

sEeFwfiRod

A

A

patew

1

1

1

1

A

tivfwmd

the ISIC (international standard industrial classification).Possible inconsistencies should be of minor importanceat this high level of aggregation. Because of the dataavailability we were forced to accept the political bor-


ersion of the model does not account for direct sectoralnterdependencies and feedback effects from the change ofhe sectoral composition to the macroeconomic outcomes.n future work we plan to improve the theoretical under-innings to address these weaknesses by searching for anxplicit integration of the mechanism for structural changeighlighted here into a multi-sectoral model of endogenousconomic growth. On the empirical side a more disaggre-ate cross-country analysis for the period after World Warwo seems to be promising. This analysis aims at iden-ifying those sectors or industries that shape the processf deindustrialization towards tertiarization in a particularay.

cknowledgements

Financial support by the Deutsche Forschungsgemein-chaft (DFG) from the research training group 1411 “Theconomics of Innovative Change” is gratefully acknowl-dged. We are also grateful to Stephan Hitzschke andabian Kleine for excellent research assistance. Finallye want to thank the participants of the EMAEE con-

erence in Manchester (May 2007), the EEFS conferencen Prague (May 2008) and the EAEPE conference inome (November 2008) for their suggestions with-ut denying our sole responsibility for all remainingeficiencies.

ppendix A. Sectoral data

.1. Employment

Employment is measured as the number of employedersons, including paid employees, self-employed personsnd unpaid family workers. We have complete annualime series for 1878–1913 and 1950–2003. Incomplete dataxist from 1850 until 1878 and between the two worldars. Our data sources are:

850–1939: Hoffmann (1965), Table 19 (pp. 203f.) andTable 20 (pp. 204f.)

939–1944: Wagenführ (1963), Table 2 (p.139) and Table3a (pp. 104ff.)

950–1991: Groningen Growth and Development Centre(GGDC), 10-Sectoral Database, van Ark (1996)

992–2003: Groningen Growth and Development Centre(GGDC), 60-Industry Database, O’Mahony andvan Ark (2003)

.2. Net value added

Value added is defined as real net value added at fac-or costs (gross value added minus depreciation minusndirect taxes plus subsidies). Complete time series for
alue added are available from 1850 to 1939 exceptor the period 1914 to 1924. For the period since 1950e use data from the national accounts of the Ger-an federal statistical office (Statistisches Bundesamt). In
etail:


1850–1939: Hoffmann (1965), Table 100 (p. 450) and Table103 (pp. 454f.)

1950–1957: Statistisches Bundesamt (1960): StatistischesJahrbuch 1960, Table 3 (pp. 543f.)


1960–1966: Statistisches Bundesamt (1971): StatistischesJahrbuch 1971, Table 4 (pp. 505f.), with 1962from Statistisches Bundesamt (1967):Statistisches Jahrbuch 1967, Table 4 (pp. 521f.)


1970–2003: StatisBund Online(http://www.destatis.de/genesis), corrected forpublic services with data from StatistischesBundesamt, Fachserie 18, Reihe 1.4, Tables3.2.1 and 3.4.3.1

Concerning net value added, mining and energy genera-tion are treated as a single industry in the official statisticsduring 1950–1969. To allocate mining to the primary andenergy generation to the secondary sector we assigneddepreciation, indirect taxes and subsidies to mining andenergy generation according to their shares in gross valueadded. The accuracy of this operation depends on the rela-tion of net and gross value added in both sectors. Requiredadditional data on gross value added are taken from:

1950–1957: Statistisches Bundesamt (1960): StatistischesJahrbuch 1960, Table 4 (p. 545)




1965: Statistisches Bundesamt (1972): StatistischesJahrbuch 1972, Table 5 (p. 517)

1966–1969: Statistisches Bundesamt (1973): StatistischesJahrbuch 1973, Table 5 (p. 524).

This construction of the value-added series, however,relies on having available real net value added before 1950from the Hoffmann source, but using net value added atcurrent factor costs after 1950. To assess the possible errorcommitted with that choice we also computed the resultsfor two alternative constructions of value added. The firstalternative is to use the real gross value-added data fromthe 10-Sectoral Database of the GGDC in prices of 1985 forthe years 1950–1991 and extend these data to the period1992–2001 by suitably summarized and deflated data fromthe 60-Industry Database of the GGDC.10 The second alter-native is to take net value added of the year 1995 fromthe German federal statistical office and extend this to thewhole period 1950–2001 by growth rates based on the realgross value-added data from the 10-Sectoral Database andthe 60-Industry Database of the GGDC.

We did our best to harmonize the varying industry clas-sifications used in these different data sources oriented at

10 For the industries 30 (office machinery) and 321 (electronic valuesand tubes) the harmonized US deflators instead of the national deflatorsare used.

http://www.destatis.de/genesis

ge and E
ders for the respective time periods. For the period before1871 the censuses of enterprises in 1846 and 1861 aretaken as representative for the German Empire withoutAlsace–Lorraine. For the period 1918–1944 the Germanterritory is assumed to exclude Austria and Sudeten-land, but comprising Saarland since 1934. For the timeperiod after World War Two, Germany is defined as West-Germany excluding Saarland and West-Berlin until 1959,as West-Germany including Saarland and West-Berlin from1960-1991 and as reunified Germany afterwards.

Appendix B. Unit-root and stationarity test results

This appendix reports the results of our unit-root andstationarity tests for the variables used in the body of thepaper. The specific tests applied are:

• the ERS point optimal test of the unit-root null hypothesis(Elliott et al., 1996)

• the KPSS test of the reverse stationary null hypothe-sis (Kwiatkowski et al., 1992) with critical values fromSephton (1995)

• the Perron test of the unit-root null hypothesis (Perron,1989) with an a priori assumed structural break betweenthe years 1913 and 1950 and critical values calcu-lated by implementing the response-surface estimates ofSilvestre et al. (1999)

• the Kurozumi test of the stationary null hypothesis
(Kurozumi, 2002) also with an a priori structural breakfixed between the years 1913 and 1950
• the Zivot–Andrews test of the unit-root null hypothesis(Zivot and Andrews, 1992) with an endogenously deter-mined break date

Table B.1Unit-root and stationarity tests for (log) employment.

ERS KPSS Pe

Intercept:P 0 1.470 8.473*** −2P 1 1.300 4.292*** −2P 2 1.144 2.891*** −2P 3 1.027 2.190*** −1S 0 0.036 6.514*** −1S 1 −0.050 3.342*** −1S 2 −0.096 2.274*** −2S 3 −0.084 1.740*** −2T 0 2.895 8.105*** −2T 1 2.432 4.152*** −1T 2 2.129 2.822*** −1T 3 1.988 2.156*** −2

Intercept and trend:P 0 −1.385 1.250*** −5P 1 −1.371 0.652*** −3P 2 −1.363 0.449*** −2P 3 −1.337 0.348*** −2S 0 −0.853 1.750*** −4S 1 −0.982 0.912*** −2S 2 −1.031 0.629*** −2S 3 −0.982 0.487*** −3T 0 −1.664 0.706*** −2T 1 −1.814 0.377*** −1T 2 −1.919 0.266*** −1T 3 −1.916 0.211** −2

Note: P, S and T in the first column indicate the primary, secondary and tertiary seused in the test regression or the window width; rejections on 1%, 5% and 10% lev


In the tables the results of these five tests are reportedfor employment and value added of each of the three sec-tors (primary, secondary and tertiary), respectively, as wellas the macroeconomic variables GDP, population and GDPper capita. Throughout, all variables are expressed in nat-ural logarithms. Autocorrelation is controlled for up to alag of three years in the test regressions and for the win-dow widths. To show the robustness of the findings, thisis preferred to the determination of an optimal lag lengthby t-tests or information criteria. For all tests the variantswith an intercept only and with both intercept and trendare computed.

The test outcomes for employment in Table B.1 givea clear indication of the existence of a unit root in allthree sectors irrespective of the lag length chosen. Theunit-root tests are not able to reject their unit-root nullhypothesis, whereas the stationarity tests vividly rejecttheir stationary null hypothesis. This holds for the ERS andKPSS tests without the permission of a structural breakas well as for the Perron and Kurozumi tests with an apriori fixed break between 1913 and 1950 (the data gapdiscussed in the main text). Somewhat conflicting resultscome from the Zivot–Andrews test with an endogenouslydetermined break date. From this test we have a rejec-tion of the unit-root null hypothesis for the tertiary sectorwhen the deterministic component consists of an inter-cept only and for the primary sector in the case of bothintercept and trend. In sum we interpret the whole set of
results as evidence in favor of a unit root in sectoral employ-ment and therefore use first differences of the loggedvariables in our regressions. This decision is also made inthe light of the dangers of the spurious correlation problemin time-series regression (Phillips, 1986) which is deemed
rron Kurozumi Zivot–Andrews

.451 2.817*** −3.694

.316 1.498*** −3.709

.052 1.031*** −3.722

.962 0.793*** −3.715

.920 1.292*** −2.835

.911 0.678*** −2.907

.234 0.476*** −2.975

.199 0.376*** −3.015

.890 2.351*** −5.618***

.831 1.227*** −5.685***

.868 0.853*** −5.711***

.051 0.667*** −5.638***

.448*** 0.310*** −7.838***

.613 0.212*** −7.565***

.931 0.166*** −7.274***

.577 0.139*** −6.933***

.192* 0.259*** −3.138

.587 0.141*** −3.334

.745 0.102*** −3.450

.178 0.083** −3.422

.807 0.389*** −4.917*

.900 0.215*** −4.784

.972 0.153*** −4.600

.134 0.122*** −4.296

ctor, respectively, with the number behind indicating the number of lagsel are indicated by ***, ** and *, respectively.

A. Dietrich, J.J. Krüger / Structural Change and Economic Dynamics 21 (2010) 111–122 121

Table B.2Unit-root and stationarity tests for (log) value added.

ERS KPSS Perron Kurozumi Zivot–Andrews

Intercept:P 0 2.524 11.529*** −3.890** 2.853*** −4.896**P 1 2.979 5.827*** −2.461 1.487*** −4.302P 2 2.624 3.919*** −2.360 1.026*** −4.161P 3 2.072 2.963*** −2.261 0.795*** −4.020S 0 5.519 11.483*** −2.454 2.742*** −8.258***S 1 2.437 5.797*** −2.732 1.448*** −7.494***S 2 1.885 3.895*** −2.036 1.004*** −7.998***S 3 1.241 2.943*** −2.077 0.780*** −8.111***T 0 6.159 11.162*** −1.621 2.474*** −5.820***T 1 3.427 5.639*** −1.734 1.304*** −5.973***T 2 2.214 3.791*** −1.190 0.900*** −6.028***T 3 1.883 2.866*** −1.268 0.697*** −6.697***

Intercept and trend:P 0 −2.098 1.807*** −4.285** 0.228*** −4.893*P 1 −1.547 0.960*** −2.620 0.137*** −3.597P 2 −1.431 0.662*** −2.581 0.103*** −3.082P 3 −1.423 0.510*** −2.603 0.086** −2.807S 0 −0.777 2.059*** −2.404 0.440*** −5.233**S 1 −1.062 1.043*** −2.749 0.252*** −5.174**S 2 −1.087 0.704*** −1.974 0.182*** −5.122**S 3 −1.191 0.534*** −2.009 0.146*** −5.068*T 0 −0.385 2.676*** −4.362** 0.402*** −6.760***T 1 −0.560 1.355*** −3.108 0.258*** −6.649***

N rtiary seu 10% lev

to(ws

TU

Nt

T 2 −0.744 0.913***T 3 −0.767 0.692***

ote: P, S and T in the first column indicate the primary, secondary and tesed in the test regression or the window width; rejections on 1%, 5% and

o be much more serious than the reverse problem ofverdifferencing when residual autocorrelation is absentPlosser and Schwert, 1977). The results for employmentithout application of the logarithm appear to be quite

imilar.

able B.3nit-root and stationarity tests for (log) macro-variables.

ERS KPSS

Intercept:GDP 0 6.444 11.633***GDP 1 2.520 5.874***GDP 2 1.731 3.947***GDP 3 1.007 2.983***POP 0 5.031 11.486***POP 1 1.260 5.799***POP 2 0.658 3.896***POP 3 0.149 2.943***GDPPC 0 5.790 11.427***GDPPC 1 2.734 5.770***GDPPC 2 2.026 3.878***GDPPC 3 1.307 2.930***

Intercept and trend:GDP 0 −0.717 1.642***GDP 1 −0.913 0.833***GDP 2 −1.017 0.562***GDP 3 −1.192 0.426***POP 0 1.101 2.240***POP 1 −0.071 1.135***POP 2 −0.452 0.765***POP 3 −0.855 0.581***GDPPC 0 −0.705 2.119***GDPPC 1 −0.882 1.072***GDPPC 2 −0.968 0.722***GDPPC 3 −1.122 0.547***

ote: GDP, POP and GDPPC in the first column indicate the GDP, population size anhe number of lags used in the test regression or the window width; rejections on

−2.645 0.194*** −6.515***−2.420 0.159*** −6.163***

ctor, respectively, with the number behind indicating the number of lagsel are indicated by ***, ** and *, respectively.

For the case of value added Table B.2 the pic-ture is rather similar. The only rejections from thePerron test are for cases without control for auto-correlation and are therefore somewhat suspect. TheZivot–Andrews test leads here to a more consistent rejec-

Perron Kurozumi Zivot–Andrews

−2.985 2.947*** −6.972***−3.493* 1.555*** −6.062***−2.849 1.081*** −5.985***−2.683 0.842*** −5.674***−0.785 3.499*** −2.372

0.365 1.812*** −2.1110.572 1.240*** −2.0640.285 0.953*** −2.113

−2.647 2.627*** −6.783***−2.485 1.390*** −6.058***−2.250 0.969*** −6.295***−1.970 0.757*** −6.091***

−2.653 0.512*** −4.499−3.381 0.285*** −4.433−2.559 0.205*** −4.600−2.497 0.164*** −4.578−2.747 0.686*** −3.652−2.909 0.368*** −3.706−2.832 0.257*** −3.795−3.017 0.202*** −3.770−2.674 0.461*** −3.953−3.244 0.255*** −3.882−2.629 0.183*** −3.934−2.349 0.147*** −3.941

d GDP per capita series, respectively, with the number behind indicating1%, 5% and 10% level are indicated by ***, ** and *, respectively.

ge and E
tion of the unit root for the secondary and the tertiarysector.

In the case of the GDP and population series we havea clear-cut confirmation of a unit root in the case of thepopulation time series as can be inferred from Table B.3.The rejections of the Zivot–Andrews test for GDP and GDPper capita are not very plausible in light of the trendingbehavior of both series. This becomes evident once a lineartrend with a possible break in that trend is considered. Nowthe Zivot–Andrews test is no longer able to reject the unit-root hypothesis, completely in line with the other four tests.

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