American Economic Association
Factor Reallocation in Eastern Germany after Reunification
Author(s): Michael C. Burda
Reviewed work(s):
Source: The American Economic Review, Vol. 96, No. 2 (May, 2006), pp. 368-374
Published by: American Economic Association
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GERMANREUNIFICATION:
LESSONSAND LEGACYt
FactorReallocationin EasternGermanyafterReunification
By MICHAELC. BURDA*
Fifteen years afterreunification,the economy
of the former East Germany is on the mend.
Industrial production excluding construction
has expanded by more than 60 percent since
1995 and by 28 percent since 2000, compared
with only about4 percentin West Germany,for
the latterperiod. Real GDP has grown 3.5 percent per year since 1991 and 8.2 percent annually in the manufacturingindustryalone. More
thanhalf of the measuredlaborproductivitygap
and more than a thirdof the GDP per capitagap
between East and West have been closed, in
considerably less time than predicted by
Robert J. Barro (1991). As Table 1 shows,
convergence has been impressive on a wide
array of indicators, although it has slowed in
recent years and remains most difficult in the
labor market.
Despite this positive news, net migrationcontinues from East to West-about 70,000, or 0.5
percent of the population, per annum since
2000, especially concentratedamong 18- to 25year-olds. At the same time, new physical capital continues to flow into the East--80 to 90
billion euros, or about 20 percent of GDP each
year. The reallocation of productionfactors is
one of the most impressive aspects of German
unification. Since 1991, more than 1.2 trillion
euros of new investment (in 1995 prices) was
Discussants: Hans-WernerSinn, CES-ifo and University of Munich; Nicola Fuchs-Schiindeln,HarvardUniversity; Claudia Buch, University of Tiibingen.
*
Faculty of Business and Economics, HumboldtUniversitaitzu Berlin, SpandauerStrasse 1, D-10178 Berlin,
Germanyand Centrefor Economic Policy Research(e-mail:
burdamic@cms.hu-berlin.de).This researchwas supported
by the Deutsche ForschungsgemeinschaftResearch Center
649 (SFB 649). I thank Olivier Blanchard,Maike Burda,
and KurtHelmes for very useful discussions;ClaudiaBuch,
Irwin Collier, and Nicola Fuchs-Schiindelnfor their comments; and Dirk Bethmann, Sebastian Braun, and Katrin
Rusch for research assistance.
368
spent in the East, yet the workforce of East
Germany shrankby roughly 1.2 million, or 15
percent,over the same period;employmentrose
in the West by 4.1 percent. As Figure 1 shows,
the intensity of factor movement was not constant, but ratherhigh at first, and declining into
the 1990s. Migration was greatest in the early
1990s, falling until mid-decade, rising again
until 2001, and declining since. In addition, a
large fraction (two-thirds)of the cumulatedinvestment flow in Eastern Germany was dedicated to residential and business structures,
compared with about one-third in business
equipment. The large runup in investment
spending on structuresis often blamed on distorted investment incentives, with possible
longer-run consequences for the structure of
output and factor demands (Hans-WernerSinn
and Gerlinde Sinn, 1992).
This intensive movement of productionfactors in opposite directionsis difficult to explain
as a reaction to disturbances in technology,
preferences,or demand.To use Horst Siebert's
(1992) terminology,Germanywas hit by a massive integration shock.1 I offer the following
definitionof economic integration:the achievement of the efficient productionpatternby two
or more geographic regions made possible by
their union, measuredat world marketprices.2
The German integration episode presents a
unique opportunity to study this form of economic integration and the roles of the relative
importance of adjustment costs in determin1 Several mechanisms are associated with economic integration:internalaccumulationof productionfactors in the
poorer region, labor mobility from the capital-poorto the
capital-richregion, capital mobility to the capital-poorregion, Heckscher-Ohlintradebetween incompletely specialized regions, and technology transfer.In the following, I
focus exclusively on factor mobility.
2
See Barry Eichengreen(1990).
VOL.96 NO. 2
GERMANREUNIFICATION:LESSONSAND LEGACY
369
TABLE 1-EAST GERMANCONVERGENCE,
1991-2004
(% of West German value)
Year
Consumption
Nominal
wages
Labor
productivity
GDP per
capita
Unemployment
rate
Nonemployment
rate
Participation
rate
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
74
74
76
78
81
83
82
82
83
83
83
82
83
83
50
65
71
72
74
72
76
76
76
73
74
74
75
75
44
57
67
70
71
72
72
70
71
72
72
73
73
N/A
49
53
60
64
66
67
67
66
66
66
65
66
67
67
170
261
240
224
206
198
206
207
211
233
248
243
236
231
103
112
111
108
106
106
106
107
107
109
110
110
110
109
137
121
111
108
108
106
107
107
106
104
102
102
101
100
Sources: Federal StatisticalOffice, Federal EmploymentOffice, author's calculations.
ing the speed of efficient economic integration, as well as the interpretationof regional
factor price differentials in the process of
dynamic adjustment to a new steady state.
The episode can serve as a foil for other
integration episodes, such as the European
Monetary Union or the recent wave of European Union accessions.
Eastand
awdVest
kIresmtein
Gqermay
35.0
30.0
25.0
20.0
15.0
10.0
5.0
0.0
GDP
%of
I. Elementsof a FormalModelof Factor
Mobilityand RegionalIntegration
19f911.9
19
19
193 1l6 1997 199 1999 2100 21
20e2
Year
Equipment-West
Equipment-East
Structures-West
Structures-East
Fraction
ofGerman
andPopulation
inEast
Employment
23,0
22,0
21,0
total
20,0
%of19.0
18,0
17.0
1991199219931994199519961997 1998199920002001200220032004
Year
Fraction
of employmentin East
Fractionof populationin East
A. Model Setup
Two regions, East (E) and West (W), produce
outputYtat time t, employingthe same neoclassical constant returnsproductionfunction, Yt =
F(K,, G,, L,), with standardproperties.3Factor
inputs consist of two types of capital-equipment (K) employed in productionand structures
(G), both used to shelter enterprisesand households-and labor (L). Both types of capital are
internationallymobile and depreciateat rates 6K
and SG,respectively, with SK> 6G. The world
rate of interest is exogenously given at r. In
contrast, labor mobility is possible only between the two regions, and with total supply
normalizedto 1. The populationof the East is
denoted by LE, so under full employment
FIGURE 1. INVESTMENT AND EMPLOYMENT IN GERMANY,
1991-2004
Sources: Federal Statistical Office, author's calculations.
3Thatis, FK> 0, FG> O,FL> 0, FKK < , FGG <, F,
0, and det(D2F)= 0. I also assumethatFi > 0 Vi * j.
<
370
AEA PAPERSAND PROCEEDINGS
assumptionsLw = 1 - LE.4 The model is deterministic,and economic growthis suppressed.
Let f(k, g) = F(K, G, L)/L be the intensive
form of F with per capita inputs k KIL and
=
g = GIL. With identical technologies in both
regions, static efficiency in regional factor endowmentsis achievedalongthe granddiagonalof
a three-dimensionalEdgeworthbox, with dimensions 1, k*, g*, where (k*, g*) is the solutionto
fk(k,g) = RK r + 6K andfg(k,g) = RG r +
8G. All points on thatdiagonalare efficientin the
sense that the marginalproductof capitalequals
the worldinterestrateplus depreciation;the common real wage can be read off the factor price
frontier(theresidualoutputaftercapitalis paidits
gross marginalproductin competitivefactormarkets). The multiplicityof these allocationshints
that an output-or welfare-maximizingtrajectory
for the economy will be determinedby factor
adjustmentcosts requiredto reachthe steadystate.
Capitaladjustmentcosts for both types of capital
are assumedto be externaland convex in the net
changeof the capitalstock.I also assumeconvex
costs of migration. In particular,these costs
are borne fully by migrants (there are no
externalities).Quadraticforms are chosen for
tractability.5
B. Social Planner's Problem
Because the economy I consider fulfills the
conditionsfor the first and second welfare theorems,a decentralized,competitivemarketequilibrium can replicatethe migrationand investment
policies in the East and West chosen by a hypotheticalsocial plannerwho maximizesthe present
discountedvalue of nationaloutput(net of migration and investmentcosts).6 I seek functionsof
time, t E [0, oo),governinginvestmentin equipment (Ihwand If) and in structures(Jtwand JE)in
the West and East, respectively,as well as net
to make
migrationfrom West to East
(Xt)
4I assume full employment throughout.Adding labor
supply, search,and unemploymentadd little to the aspects I
focus on in this paper.
5 See Andrew B. Abel and Olivier J. Blanchard(1983)
and Abel (2001).
6 As
long as production and consumption decisions are
separableandthe world interestrateis given, there is no loss
of generalityin focusing on the productionside.
(1)
MAY2006
Lw)GW,
IW
fe-"F(KW,
+ F(KE,GE,LE)_E _JE _
(E _ K)2
J(J _ 6GG)2
22Xdt
G
2
_
as large as possible, subjectto initial conditions
(at t = 0) on factor supplies in both regions.
Gross and net migration flows are thus equal;
negative values of X imply net migration from
West to East. The positive parametersti1, tfj,
and 0 capturethe intensity of adjustmentcosts.
Labor and capital stocks obey the following
equations of motion:
(2)
kI = I - SK' for i = E, W
(3)
G =J' - SG' for i=E,W
(4)
LE= -Lw = X,.
By assuming that adjustmentof Westerncapital
stocks is costless, I shift emphasis to relative
adjustmentcosts in the East. These reflect bureaucracyand regulation,conflict over property
rights, and the qualityof business-relatedpublic
infrastructure.
C. Planner's Optimumas MarketEquilibrium
Define qE, E, and p as the costate variables
corresponding to the constraints (2), (3), and
(4). To simplify notation, superscriptsare used
to denote regions when argumentsof functions
are suppressed;time subscripts are suppressed
whenever obvious. Necessary conditions characterizingthe optimal policy are, for all t 0:
IE = (qE + K8KE
(5)
1)/It,
_
jE
= (pE 1)/q + 6GGE
(6)
(7)
(8)
X=
[ll
qW= 1
VOL.96 NO. 2
GERMANREUNIFICATION:LESSONSAND LEGACY
(9)
FW = r + SK = RK
(10)
F
(11)
4E+ F/
(12)
pE +
= r+ G = RG
+
K IKE
(r +
K)qE
+
G)pE
F + 8JGE=(r
(13)
. + (FEc- Fw) = r/,
as well as the equationsof motion(2), (3), and(4).
Equations(5), (6), and (7) relate optimalinvestment in the East and migrationto the East as
positive and linear functions of their respective
shadow prices, which are sufficientstatisticsfor
determiningthese activities.The greaterthe associated adjustmentcosts, the lower the respective
investmentrates, ceteris paribus. Equations(8)
and (9) representoutcomesin the absenceof adjustmentcosts. In the West, the static efficiency
conditionobtainscontinuouslywith constantcapital-laborratio k* and structures-laborratio g*
defined above. Migrants from the East are
equippedupon arrivalwith the same level of capital used by otherWesternresidents,and earnthe
Westernwage w = Fw.
By assumption, the three-state variables in
the model KE, GE, and LE cannot be changed
instantaneously;the costate variables q, p, and
t representthe marginalgain of moving them
371
to the East, given the economy is on the optimal
adjustmentpath. Equations(11), (12), and (13)
are arbitragerelations governing these shadow
values. When integrated forward from initial
values at t, with appropriatetransversalityconditions, qEand pEreflect the presentdiscounted
value of presentand futuremarginalproductsof
an additionalunit of capitalinstalledin the East.
Similarly, the shadow value of a worker in the
East, [k, represents the present value of the
difference in future marginalproductsof labor
between the East and West. Given the initial
conditions kw > kEand g' > gE, pt is negative.
The model implies a persistent wage gap between East and West which disappearsasymptotically as capital accumulatesin the East and
labor migrates to the West.
III. SteadyState and Dynamics
A. Steady State
The economy's steady state is given by constancy of KE, GE, and LE, so qE = 9E = 1, FE
= RK,F = iG, and i = 00< F = FW = w.
The dynamic propertiesof the linearizedmodel
are encoded in the eigenvalues
{ ,-... , A6) of
the 6 x 6 matrixrelatingchanges in the endogenous variables (qEE,
p , , KE, GE, LE) to deviations from steady-statevalues:
, r+ r2+2(A+
A2-4B)
- r2 +2(A2(A + JWA--4B)
61r - Vr2+ --1
. .
, 1-r
0, r,tr+
r
r2+2(A-
I
A2-4B) ,
AZ-4B)]
where A = -(lLFEK
0 and
B
=
FjO-(E
+
+I-j1FGG
+
--1FE)
FE - (Fi)2
+ Iq(F
KFG - (F~)2
1
FK(FF - (FKL)2> 0.
+
>
For A2 - 4B 2 0, the model has meaningful
solutions. By inspection, all eigenvalues are
real-valued; three (A2, A3, A4) are always
greater than zero, while two (As, A6)are negative. This correspondsto a typical perfect foresight model with saddle-pathstability, plus the
importantnovelty of a zero root, implying hysteresis (path dependence). Initial conditions of
Easternfactor supplies KE, GE,and LE,as well
as the constellation of adjustment costs and
other parameters,determinethe system's steady
state. In a stochastic version of this model,
372
AEA PAPERSAND PROCEEDINGS
temporarydisturbancesto initial factor allocations, such as migration or privatizationpolicies, could have permanent effects on the
region's steady-statesize.7
B. The Central Role of AdjustmentCosts
The results of the last section establish that
adjustmentcosts are a key determinantof the
resting point of the economy, since the path
taken by the Eastern capital and labor stocks
depends on correctly anticipatedfuturepaths of
their shadow prices relative to their costs of
adjustment.Inspection reveals that the two stable (negative) roots are increasingin the adjustment cost parameters qif, fj,, and <p,so the
adjustmentspeed or persistence of the model is
determinedby the largest negative eigenvalue,
which is increasing in adjustmentcosts. In addition, adjustment costs enter multiplicatively
and, thus, amplify each other's effect on persistence. Local concavity of the productionfunction, in contrast, accelerates adjustment.
C. Implicationsfor Factor Prices and
AdjustmentCosts
Adjustmentcosts also have implications for
the behavior of observed wages and the rate of
return on capital in the integration process.
Since factor supplies cannot move instantaneously, the capital-laborratios in the East, kE
and gE, will remain below Western levels for
some time. Throughoutthis period, wages will
be lower and return on capital will be higher.
Persistent factor price differentials are consistent with finite factor flows over time, disappearing only in the long run. With competitive
factor remuneration,(11), (12), and (13) can be
rewrittenas
E-
(14)
(15)
Eq
RE= RK+ 85K
qE
RE== RG++5
G
(E
E
1
(16)
wE
MAY2006
+ r
- i.
Since p < 0 and 1> 0, wage differentialsare
consistent with a persistent wage gap across
regions over time (wE < i). Similarly, qE > 1,
cf < 0, andpE> 1; PE < 0 alongthe adjustment
path,so RK> RKandRE > RG. These theoretical
results can thus reconcile finite rates of factor
movements with persistentlylower wages and
higherratesof returnin EasternGermany.
The model lends itself to back-of-theenvelope calculations of adjustment costs as
well as shadow values consistent with recent
historical experience. Suppose, for example,
that r = 0.03 and the average rate of wage
convergenceis A over some time period;the historicalrecordof EasternGermanysince 1991 suggests A = 0.07.8 Measuringthe Easternwage in
units of the Westernequivalent, 1991 = 0.50. It
follows that /-1991 = -5, i.e., the implied value
of moving a worker from the East to the West
was 500 percentof the annualWestern wage in
1991. According to the GermanFederal Statistical Office, net migrationto Eastern Germany
was -165,000 in 1991.9 Using (7) plus the
observed net East-West migrationin that year,
I can compute the value of 0 consistent with
that migrationflow, 5/165,000, or 0.00303 percent of the annual Western wage per person
squared. Put in perspective, by 2004, wE =
0.75, so the wage gap had declined to 0.25,
implying a shadow value of the marginal migrant of 2.5, or 250 percent, of the Western
wage. Using this estimate of 0, the model predicts annual migration of 2.5/(0.0000303) =
82,500, compared with the average of 72,000
over the period 2000-2004 (in fact, net migration in 2004 had declined to -52,000). Net
migrationcumulatesto about 1.7 million, or 10
+ q)E
qE
+
+E
p
7 Blanchardand Lawrence F. Katz (1991) obtain a similar result in a model of regional unemploymentin which
mobile labor is the sole productionfactor.
8 With initial condition and
steady state wo and w-respectively, this approximation implies wE = woe-as + ii
0. The
)e-As for s
(1 - e-AS), or w - W =
model's true adjustmentspeed
will vary over time,
(wEo
- since
both stable eigenvalues jointly determine persistence. For
more precise details on calibrationsand implied dynamics,
see my working paper (Burda, 2006).
9 Source: Statistisches Bundesamt, "Abwanderungvon
Ostnach Westdeutschlandschwdichtsich weiter ab," press
release, September28, 2005.
VOL.96 NO. 2
GERMANREUNIFICATION:LESSONSAND LEGACY
percent, of the initial Eastern Germanpopulation. In a more pessimistic scenario with A =
0.02, the region would lose roughly 3.5 million
inhabitants.
IV. Conclusion
One of the distinctiveaspects of the reunification episode has been a significantreallocationof
factorsof production.Germaneconomic integration has been a puzzle, with productionfactors
moving in opposite directions,even as outputis
rising. Real regional integrationis a macroeconomic process,which may be sufficientlyunique
to merit special attention.I characterizeregional
integrationas a mobilityrace between factorsof
production,which is decidedby costs of moving
them, even if these costs are not relevantin the
long run.1' Steady-stateproductionhas constant
returnsto scale, and agglomerationeffects are
excluded a priori.Centralto the analysis are adjustment costs. While much attentionhas been
paid to agglomerationeffects, adjustmentcosts
associated with moving factors of production
acrossspace have generallybeen neglectedin the
formal study of economic integration."If at all
relevant,these costs must be importantfor the
massive redeploymentof labor and capitalassoof Germany.Unlike
ciatedwith the reconstruction
the economic integrationof the United States,
Canada,andMexico,or the EuropeanUnion,German reunificationalso involves significantlabor
mobility in addition to capital mobility and internationaltrade. Barriersrelated to language,
institutions,and culturein unified Germanyare
negligible; convergence of behavior in the past
15 years has been so significant that one can
really speak of a common representative
agent.12Yet even under these ideal conditions,
factor price convergence has been incomplete.
10 Thereis no role for
policy underconditionsconsidered
here. If externalities arise from migration not reflected in
market incentives, there might be a role for subsidizing
capital formationin the East (or bribing workers to stay in
the East).
11See Peter J. Neary (2001).
12 Recent research
by MiriamBeblo et al. (2000), Burda
and Jennifer Hunt (2001), and Nicola Fuchs-Schtindeln
(2004) suggests convergence in the behaviorof Easternand
Western Germansover time.
373
Clearly, there is much more to the reunification episode than factor mobility. The assumption of perfectly competitive factor markets is
grossly violated. Table 1 suggests a convergence of labor supply behavior, with East German labor force participation falling from
nearly 90 percent in the early 1990s and the
West Germanrate rising from under 50 percent
to converge to an almost identical value of 60
percent in the early 2000s. The fact that unemployment is higher in the East, despite almost
identical participationrates with the West, suggests that labor markets are not functioning
properly-not enoughjobs have been createdat
current wages, wages are not set at marketclearing levels, or labor and product market
rigidities prevent adjustment.Yet one can concede the importance of all these aspects, and
still learn a great deal by abstracting from
them-especially when what is left is sufficiently interesting.
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