German Regional GDP
Preliminary Land-Level Estimates, 1871-1907∗
Paul Caruana Galizia†
This draft version: October 10, 2011
(Please do not cite or circulate without explicit permission from the author.)
Abstract
This paper provides estimates of regional GDP for 23-Länder for
the benchmark years 1871, 1882, 1895, and 1907 in constant 1913
marks. The estimates are derived using a novel "top-down" structural
model, where GDP is specified as a function of shifts in employment
structure. Data are taken from census books. The model and its
results are tested for robustness.
∗
Prepared for the EH590 Workshop, LSE. This paper forms part of the author’s PhD on
European regional income differentials and their relation to market potential, supervised
by Max-Stephan Schulze.
†
[email protected] – London School of Economics and Political Science, Economic History Department, Houghton Street, WC2A 2AE, London, United Kingdom.
1
1
Introduction
Over the past five-years, there has been a flurry of research into European
regional income differentials. There now exist regional income estimates for
Austria-Hungary (Schulze, 2007b), Italy (Felice, 2009), Spain (Roses et al.,
2010), the UK (Crafts, 2005), France (Combes et al., 2011), Belgium (Buyst,
2009), and Sweden (Enflo et al., 2010). Although there has also been a
resurgence of interest in Germany’s regional development, a series of regional
income estimates for what was one of Europe’s most successful economies is
noticeably absent from this research. While Wolf (2010) is making much
progress in this regard, his estimates are mainly for the very late nineteenth
century and much of the twentieth century.
Debate on Germany’s internal development has been wide and heated. The
country went from a collection of some 300-principalities and other political
entities pre-unification, to a country of some 23-Länder in 1871. It has been
argued that the resulting complex political and geographical history is a
product of internal forces (religious, social, cultural, and linguistic) as well
as external forces. Germany was, after all, at the centre of a rapidly changing
continent (Wolf, 2010).
As Wolf points out, it has been difficult to conduct empirical research into
Germany’s history, as there have been no data that allow the analysis of
internal economic change. This paper provides such data. It is hoped that it
will provide historians with the basis for more empirical work on Germany,
and provide data that is comparable to regional income estimates for other
European countries. This paper in no way provides the final say on GDP estimates for the 23-Länder, but it does provide a series that allows researchers
an initial look into a country’s internal development. If this paper succeeds
in promoting such research, then hopefully the data presented here will be
scrutinised, revised, and made more robust.
2
Methodology
Higher income levels in one economy compared to another can indicate two
things. First, they can indicate higher labour productivity due to higher
capital and labour ratios or better technology. Second, they can indicate
a more efficient allocation of labour among economic activities. It is, we
maintain throughout this paper, the latter that really counts. European
2
economic history has shown that countries that remained heavily committed
to agriculture remained relatively poor, while those that reallocated labour
to the industrial and services sectors became relatively wealthy. In fact,
Broadberry et al. (Forthcoming) observes a negative relationship between the
level of per capita incomes and the share of the labour force in agriculture
for a sample of 14 European countries between 1870 and 1913.
Relationships between sectoral distributions of labour and incomes are hardly
news. Studies on the subject have a long history, going back to, for example
Fabricant (1942). More recently, in the economic history literature, the relationship has been exploited to derive income estimates for a number of European countries, starting with Geary and Stark (2002), which put forward a
short-cut method for estimating regional GDP based on sectoral employment
and wages. The method uses national GDP estimates, breaking them down
according to regional employment structure and corresponding regional, sectoral wages. However, as Wolf writes, such fine-scale data are hard to come
by for Germany. The approximations required (say, using national wages or
city wages to represent regions) to use this method for Germany, then, make
it not much more meticulous than the method presented here.
While there may be a number of more reliable ways to estimate Germany’s
regional GDP, most of them require a great deal of archival research. It
would make for highly useful research indeed, but until then, this paper aims
to provide an empirical strategy and its resulting estimates to fill the gap.
The strategy generates estimates of the probable per capita income levels of
23-Länder in constant 1913 marks.
2.1
Data
German census books provide sectoral employment by Land for each benchmark year (Cen, 1871, 1882, 1895, 1910, 1912). Frank (1994, p. XXX)
provides per capita income estimates in constant 1913 marks by district (subdivision of Länder ). These data allow the exploitation of the sectoral labour
share-income relationship.
The first step was defining a region or Land. The district marks per capita
series in Frank (1994) was first multiplied by population by district (taken
from the censuses), to produce total marks by district. These districts were
then aggregated into Länder according to what the Länder administrative
boundaries of the time were. His series misses a few free states and minor
principalities. These were either left as standalone untis, as with Brunswick
3
and Hamburg, or else put into the nearest Land, as with Lübeck in SchleswigHolstein. Some Land, and their districts, are altogether missing from his
series, like Alsace-Lorraine. These were included in the present series.1 Their
incomes, since Frank does not provide them, were scaled as a function of
population, according to the sample average. One might ask how reliable this
is. Scaling according to population data was deemed reliable as population
showed a consistent and strong positive correlation with income across all
benchmark years in all Länder. Furthermore, the sum of income of this new
Länder series was only around five per cent higher than Hoffman (1965)’s
widely used national level data for that year – actually, an average for 1913
to 1907 as Frank’s data series is such an average. Still, to ensure accuracy in
the modelling stage, this new series was scaled according to Hoffman’s data
average for 1913 back to 1907, yielding a Land cross-section of income for
1907.
Frank’s marks per capita series for the remaining years (1882, 1895) proved
to be too unreliable for use here.2 By his own admission, the estimates are
clearly too high3 . The income levels for these years were derived by keeping
wages constant at their 1913 level, and simply multiplying these wage levels
by their corresponding employment figures for those three years. Keeping
wages constant rather than deriving an elasiticty of sectoral productivity
is more likely to over-estimate income levels - as it has done. When we
multiplied Frank’s district marks per capita estimates by district population,
the resulting total income estimates summed to a figure far higher than
existing national income estimates (Hoffman, 1965; Maddison, 2007). This
can be seen in table 1, which compares Hoffman’s estimates for national
GDP, and national GDP estimates derived by multiplying Frank’s marks per
capita estimates by population, and then summing.
Table 1: Reliability of Frank’s income figures for years other than 1907.
Source: author’s own calculations, based on census books, Frank, and Hoffman.
Frank (derived)
Hoffman
Difference
1882
26,136,719,191
18,441,000,000
41.2%
1895
32,812,766,867
27,621,000,000
18.8%
The approach employed here describes the elasticity at which Land income
1
A list of all districts and their Länder is included in the Appendix.
Frank provides estimates for 1849 and 1939 as well, but besides also being unreliable,
these figures are beyond the period of this study. He provides no figures for 1871.
3
See Frank (1994, p. XXX).
2
4
responds to structural change, and so is dynamic: income levels vary with
employment levels. Frank’s method is not suitable for projecting through
time as it is not dynamic. The present model, although cross-sectional, takes
into account income level variation (from the 1907 cross-section) as well as
its associated employment variation, and then generates income estimates
based on the relationship, while controlling for population changes.
The next step was collecting and aggregating sectoral employment data for
the corresponding Länder. For the years 1907, 1895, and 1882 this was
simple. The census books list six-sectors: (1) agriculture (including fishing,
forestry and related industries), (2) industry (including manufacturing like
textiles and chemicals), (3) trade and commerce (including transport and
communication), (4) professional workers and the civil service, (5) army and
navy, and a (6) residuary category of “other occupations.” Coventionally,
sectors (3) to (6) were grouped, to produce a single services sector in the
contemporary sense (Broadberry et al., Forthcoming). The year 1871 proved
a little trickier. The book for this year listed seven-sectors: (1) agriculture,
(2) industry, (3) trade and commerce, (4) wage labourers (including workers
like farmhands), (4) army and navy, (5) professional workers and the civil
service, (6) the same residuary sector of “other occupations”, and (7) a sector
listing what can be translated as unemployed persons. Following Schulze
(2007a, p. 212), the first necessary adjustment was grouping (1) and (4).
The sum of persons in (1) made clear that census enumerators disaggregated
the agricultural labour force into permanent workers, and the daily wage
labourers listed in (4). Sector (7) was altogether dropped: there was no
comparable data of unemployed persons for the other years. The proportion
of unemployed as part of the national labour force was six per cent. The last
adjustment was grouping (3), (4), (5), and (6), to produce a service sector
comparable to the one found in later benchmark years.
These adjustments and groupings yield intuitive results, as table 2 shows.
Expectedly, agriculture shows a very large drop in its share of the labour
force, from 50 to 37 per cent, while industry and services are making rapid
gains. Services, in particular, grew by 40 percent.
2.2
Model Environment
Using this data, we can empirically deduce what the relationship between
sectoral labour shares and income was for at least one cross-sectional year,
then we can hypothesise how sectoral change affected income change for other
benchmark (census) years. Moving from the widely accepted and observed
5
Table 2: National sectoral shares in national labour force, 1871-1907. Source:
author’s own calculations, based on census books.
Year
1907
1895
1882
1871
Agriculture
37%
40%
47%
50%
Industry
42%
40%
36%
35%
Services
21%
20%
17%
15%
relationship outlined in Broadberry et al. (Forthcoming), that changing sectoral distributions of labour result in changing per capita income levels, the
cross-sectional ordinary least squares (OLS) empirical implementation that
follows from this is
I
S
A
)i,1907 + β2 ln( LF
)i,1907 + β3 ln( LF
)i,1907
ln GDP i,1907 =α + β1 ln( LF
+εi,1907
(1)
where subscript i indexes Länder, and subscript 1907 indexes the year of
the cross-section, α is a constant term, and ε is a random error term. The
dependent variable is Land GDP, and independent variables are agricultural
(A), industrial (I ), and services (S ) share of the labour force (LF) all at
the Länder -level. Taking logs on both sides, this model will produce the
elasticities at which GDP responds to structural shifts.
This specification presents three problems. First, the three sectoral shares,
which sum to the total labour force, are a linear combination. To get round
A
this multicolinearity, agriculture ( LF
) was dropped: a backward stepwise
regression procedure showed it to be statistically insignificant. Arguably,
any one of the sectoral terms could have been dropped, but such a stepwise
procedure was deemed to be the most objective way of handling the issue.
Second, using sectoral labour force shares alone does not capture Länder size
effects. Population (P) was included as an independent variable to control
for the varying sizes of Länder. Third, and perhaps most importantly, there
is the possibility that the market potential, a measure of economic centrality,
of each Land may be correlated with both GDP and one or more of the
independent variables - most likely, industry. This omitted variable bias
I
). The conventional
presents an upward bias of the the coefficient on ( LF
way of dealing with this is to construct a panel of at least two time periods
and implement a fixed-effects model. However, as we are dealing with a
cross-section, such an approach is impossible. Instead, we introduce market
potential as a control. It is constructed as
6
M Pd,1907 =
X GDPi,1907
i6=d
Disti,d
(2)
where the market potential (MP ) for Land d is the sum of the other departments’ (i 6= d) total GDP, weighted by the interdepartmental distance
Dist i,d . It is defined as the distance-weighted GDP of all surrounding Länder
- own GDP is left out to avoid endogeneity issues.
That market potential is strongly positively correlated (0.57) with industrial
I
labour force share ( LF
), and uncorrelated with the other variables, implies
I
that a regression model would have misattributed a greater effect to LF
in the absence of a locational control. The point here is to get a more
precise estimate of the sectoral elasticities. Market potential itself does not
enter the income estimation process. It is used to reduce the threat of an
omitted variable bias. In so doing, we are assuming that the locational
effects captured by market potential fixed, that is, time-invariant (as we
are projecting income backwards) and Land -specific. Unfortunately, we still
cannot totally rule out the possibility of time-variant Land -effects. Given
the current limitations, though, we feel that this is a reliable control.
The final specification is as follows
S
I
)i,1907 + β2 ln( LF
)i,1907 + β3 lnPi,1907
ln GDP i,1907 =α + β1 ln( LF
+ β4 lnM Pi,1907 +εi,1907
(3)
where all variables are previously defined.
2.3
Empirical Strategy
The elasticities produced by this model, which are shown in table 3, were
multiplied by structural change and population change (percentage change
from one benchmark year to the next) for each Land to project GDP going
back in time.
The sizes and significance of the elasticities are intuitive. Population was
growing fast during this period, and showed a strong positive correlation
with income, as in previous historical studies (Williamson, 1998). Population
growth can boost aggregate demand and allow for the division of labour. The
elasticities on industrial employment and commercial employment shares are
also positive. The industrial elasticity indicates a strong effect on income,
7
Table 3: Model results.
GDP
Population
Industry
Services
Market Potential
Constant
Elasticities
1.061
0.443
0.148
0.142
5.674
Standard errors
0.029
0.073
0.064
0.082
0.683
t-stat.
36.5
6.04
2.31
1.72
8.31
P>|t|
0.000
0.000
0.033
0.103
0.000
N
Residual DF
Prob>F
Root MSE
R-sq
Adj R-sq
23
18
0.000
0.0795
0.992
0.990
which is also expected during this time of rapid industrialisation. The size
of the services elasticity is much lower, at least in part, because the sector
includes unproductive sub-sectors such as the army and navy, and domestic
services. Market potential is positive and narrowly misses significance at the
ten percent level. This indicates that it is picking the Land -specific effects
on income that are not picked up by the sectoral shares or by population
growth.
Such a high coefficient of determination usually indicates multicolinearity,
but the correlation matrix displayed in table 4 shows that the only significantly correlated variables are the industrial labour force share and market
potential, as expected.
Table 4: Correlation matrix of independent variables. Significance levels of
correlation coefficients are in parentheses.
Population
Industry
Services
Market potential
Population
1
0.235 (0.281)
-0.335 (0.118)
-0.274 (0.206)
Industry
Services
Market potential
1
0.056 (0.818)
0.569 (0.005)
1
0.223 (0.307)
1
Using these elasticities to project backwards in time assumes that sectorspecific productivity remained constant, or changed insignificantly across
this paper’s 37-year period. Detailed data from Hoffman (1965) and also
presented in Wolf (2010) shows that this assumption is acceptable. For example, from 1895 to 1905, agriculture’s contribution to national GDP went
from 31 to 26 percent, industry went from 39 to 42 percent, and services
went from 30 to 32 percent (Wolf, 2010).
In detail, the steps followed were
IEx,i,t−1 = (1/βx ) × 100 ·
8
xi,t−1
xi,t
−
LFi,t−1 LFi,t
(4)
where the income effect IE of sector x in Land i in the preceding year (as we
are projecting backwards in time), is a function of that sector x ’s elasticity
(βx ) as estimated in model (3) multiplied by the shift in sector x ’s labour
force share from the current year to the preceding year - the year to be calculated. This exact same method was used to calculate the IE of population,
replacing all sectoral elements with population ones. That is, the elasticity
for population, multiplied as above by population change.
The IEs of both sectors (industry and services) and of population were
summed, yielding a total IE (TIE ) for each Land at each benchmark year
except, of course, the cross-section starting year 1907. The final step, then,
was to use these TIE values to project backward from the 1907 GDP crosssection, derived from Frank (1994). The next step is yet more straightforward:
GDPi,t−1
T IEi,t−1
= GDPi,t + GDPi,t ·
100
(5)
where, the actual (monetary) value of the TIE for Land i for the preceding
year (say, 1895) is calculated through multiplying it by current year GDP
(say, 1907) for Land i. This actual (monetary) value is then added to or
subtracted from current GDP to yield preceding year GDP. This step was
repeated for all Länder for all the benchmark years, again, except the starting
cross-section year of 1907.
3
Results
Table 5 shows the GDP estimates, where the national GDP per capita of
each benchmark year is set to 100. The estimates, and figure 1, make clear
that Länder in which most of the labour force worked in industry were the
richer Länder.
Comparing Ostpreussen (East Prussia), where even in 1907 61 percent of the
labour force was in agriculture, to the Kingdom of Saxony, where in 1907
some 64 percent of the labour force was in industry, we see stark differences
in per capita income levels. The per capita income of the latter was almost
double that of the former for each benchmark year. However, Ostpreussen’s
per capita income level was growing at practically the same (compound annual growth) rate as the Kingdom of Saxony’s. Not quite convergence, but
almost there.
9
Figure 1: Pooled relationship between GDP per capita and industry share,
1871-1907.
Differential growth rates come out most clearly between the early industrialisers and the later ones. Take, for example, Schleisen (Silesia) and the
Rhineland. The former, rich in natural resources like coal and metals, was already the richest province in Habsburg Austria by 1740, when is annexation
by Prussia began. With its manufacturing towns and productive agricultural sector, Silesia quickly became an integral part of Prussia, increasing
its wealth, area, and population. In 1871, its per capita income was some
100-marks higher than the Rhineland’s, but by 1907 it fell behind by some
160-marks. Across the period, the Rhineland’s compound annual growth rate
was 2.3 percent, while Silesia’s was just 0.93 percent.
What was the reason for this convergence? Like Silesia, the Rhineland was
also rich in natural resources. These mineral resources, in conjunction with
its favourable location and its advantageous waterway connections to western Europe (strong demands for its cloth and dyes came from London and
the Netherlands, brought about the concentration of industry, mainly around
Aix-la-Chapelle and Düsseldorf, which produced high value-added machinery, chemical goods, and cloths and dyes. Tipton (1976) notes that metal
products, a chief export of the region, were produced wherever iron ore joined
water transportation, along the southern bank of the Ruhr and in older areas
along the Rhine’s tributaries.
Hamburg stands out as relatively poor region, contrary what one might expect when it is now one of contemporary Germany’s wealthiest regions. There
are a number of reasons for this. The city-state of Hamburg was a predomi10
Table 5: Land -level GDP per capita, 1871-1907 in constant 1913 marks.
Deutschen Reichs=100.
nantly services-sector based region - only in 1871 did industrial employment
outnumber that of services, and by only 2 percent. As the model’s results
have made clear, the services sector was much less productive than the industrial sector. This is because, as it is defined here, it includes inefficient
sub-sectors such as the army or domestic services. Most workers in Hamburg,
according to Ferguson (1995), were employed in cleaning, clothing, furnituremaking, and power-generation. Moreover, some 43 percent of Hamburg’s
private sector employees worked in firms with less than 11-employees. Between 1877 and 1888, 843 of these firms went bankrupt, and 311 more went
bankrupt in 1913. The main industry was construction, but this depended
on Hamburg’s port and shipping industry, which in turn depended on ’the
vagaries of the trade cycle’ (Ferguson, 1995, p. 45). Ship building, low be11
tween 1880 and 1890, only really took off around 1895. According to our
data, income growth was fastest between 1882 and 1895. Why did Hamburg
miss out on early northern German industrialisation? The reason is simple: Hamburg (and Bremen) joined the Zollverein (Customs Union) last in 1888, that is, 17-years after German unification. Those Hamburg industrialists who went after the markets of other German regions, particularly
Prussia, located themselves outside the city-state’s formal border, in towns
like Pinneberg, Schleswig-Holstein (Ferguson, 1995). So while the owners
and workers of these factories were likely to be from Hamburg, for accounting and enumerating purposes, their output would have been recorded under
a different regional boundary. Our data shows that Hamburg’s per capita
income grew by a rapid annualised rate of 2.62 percent from 1882 to 1895,
seven-years after Hamburg joined the Customs Union.
4
Robustness
Estimates must always be put through robustness tests. The data and
method here are open to four main criticisms: 1) that we are venturing too
far out of the range of evidence and the actual estimates could be too high
or too low; 2) projections based on cross-sectional elasticities are unreliable;
and 3) the model and its results are unreliable or the sample on which it is
applied is too small to be reliable.
4.1
Checking income levels
That the specific income levels presented here are simply too high or low is
perhaps the most basic criticism that can be levelled. Besides going on intuition, and the estimates do work intuitively (generally, agricultural regions
have lower incomes and industrial regions have the highest incomes), the only
two possible checks are to see whether the sum of Länder incomes adds up
to a widely used and carefully calculated national income estimate and to
compare the evolution of Land -level income with that of regional income in
similar studies.
Table 6 shows sum of this paper’s Länder incomes and the corresponding
national estimates from Hoffman (1965). The reader is reminded that Hoffman’s figure for 1907 is actually an average for the years 1913 to 1907, as
Frank used such an average to construct his 1907 marks per capita by district
cross-section used for this paper’s estimates. Secondly, there is no difference
12
between the 1907 years because this paper’s 1907 cross-section was scaled
according to Hoffman’s figure for that year to ensure reliable projections.
Before scaling, the sum of Länder estimates was only five percent higher
than Hoffman’s figure.
Table 6: National GDP levels in marks, 1871-1907. Source: author’s own
calculations, based on census books and Hoffman (1965).
Hoffman
Own
Difference
1871
14,653,000,000
15,200,801,111
3.74%
1882
18,441,000,000
19,247,784,664
4.37%
1895
27,621,000,000
29,485,970,696
6.75%
1907
44,078,666,667
44,078,666,667
0%
It is clear that there is no substantial difference at the national level: the
biggest departure from Hoffman’s estimates is for 1895 at just 6.75 percent,
which is encouraging. In their seminal "short-cut" regional income estimations for the UK and Ireland, Geary and Stark report that their "best"
specification estimates deviate from official estimates by a maximum of 7.5
percent for one region. Of course, the distributions between regions could be
the issue. As these are the first estimates of their kind for Germany during
this period, we have no other data with which to draw comparisons. It is
possible, however, to compare growth trends and variation in regional income
data for other European countries. Table 7 presents the coefficient of variation, a measure of income inequality, and the compound annual growth rate
(CAGR) for a sample of European countries and for this paper’s data. The
years tabulated are general benchmarks as census years in different countries
did not always correspond.
Comparing per capita income variation across the sample, we see that income
variation between Germany’s Länder is very similar for each benchmark year
up until the final year when it is lower than all other countries. When considering the yet more concentrated patterns of industry in these other countries,
this is unsurprising. In the UK, for example, London’s per capita income
was 47 percent above the national average in 1871 and 66 percent above in
1911(Crafts, 2005). Averages of regional per capita income CAGRs are perhaps harder to compare. Germany’s is the highest (1.65 percent compared
to 1.63 percent at a national level in Maddison (2007)), followed closely by
Sweden, which went through a similar industrialisation path. Both Sweden
and Germany’s relatively high average CAGRs are the result of particularly
fast-growing big-city regions or regions endowed with natural resources. In
Sweden, Jönköpings län - where the populous city Jönköpings was home to
the country’s thriving matchstick industry - was growing at 1.98 percent.
13
Table 7: Regional GDP variation and average CAGR
across Europe, c. 1870-c. 1913. Source: author’s own
calculations, based on census books and Schulze (2007b),
Felice (2009), Roses et al. (2010), Crafts (2005), Enflo
et al. (2010).
Italy
Sweden
Spain
UK
Austria-Hungary
Germany
1870
0.16
0.25
0.30
0.18
0.35
0.21
1880
0.22
0.25
/
0.18
0.32
0.20
1890
0.24
0.26
/
0.22
0.31
0.19
1900
0.23
0.21
0.43
0.23
0.33
/
1913
0.25
0.26
0.38
0.26
0.31
0.18
CAGR
1.16%
1.42%
0.99%
0.77%
1.07%
1.65%
Precise years as follows. Sweden (1870, 1880, 1890,
1900, 1910), UK (1871, 1881, 1891, 1901, 1911), AustriaHunagry (1870, 1880, 1890, 1900, 1910), Spain (1860,
1900, 1910), Italy (1871, 1881, 1891, 1901, 1911), and
Germany (1871, 1882, 1895, 1907).
By far the fastest growing region, at 3.33 percent, was Kopparbergs län literally, "copper mountain county" (Enflo et al., 2010). One of Germany’s
best performers was the Kingdom of Saxony (2.32 percent), where by 1907
64 percent of the labour force worked in industry.
4.2
Checking projection
The elasticities produced by this paper’s model are a central part of this
study. Are elasticities derived from a cross-sectional model useful when it
comes to projecting backwards in time, as is done here? The assumption
here is that the elasticities will be the same, or very similar, in both the
cross-section and at different points in time. To test this assumption, the
elasticities are used to re-create the widely-used annual national GDP timeseries in Hoffman (1965). The same method of backward projection based
on structural sectoral shifts - sectoral labour force and population data is
also available in Hoffman (1965) - is employed. If this model’s elasticities are
reliable in the cross-section, they should also be reasonably reliable in a time
series. Figure 2 displays the results. The only caveat here is a gap between
1875 and 1871 in the series in Hoffman (1965). In projecting backwards, we
stopped at 1875 and set the start-year (1907) to 100. 4
4
Why not use a time-series model from Hoffman’s data and apply those coefficients to
the cross-section? Due to unsurprising problems of autocorrelation, the time-series model
14
Figure 2: Hoffman national annual GDP time-series and projected series,
1875-1907.Source: author’s own calculations based on Hoffman (1965).
The average deviation between the projected and Hoffman series is 1.1 percent. The maximum deviation is 5.72 percent in 1875, which stands out as
an exception. These results show that the elasticities used here are reliable
in capturing the time dimension, and so the cross-sectional model is useful
in projecting income estimates backwards in time.
4.3
Checking model and sample
A cross-section of 23-Länder makes for a inevitably small sample size. How
can we know that this sample size is reliable, that is, will the elasiticities be
stable across randomly drawn samples? To get at this concern, we performed
a simple Monte Carlo experiment.
The steps followed in this procedure were as follows. First, the observed elasticities and the observed independent variable vectors were used, along with
a randomised vector for the error term, to generate the dependent variable
vector, Land GDP. Second, this generated GDP vector and the observed independent variable vectors were used in a regression model of the same specification to obtain new elasticities. Third, this process was repeated a standard, 1,000-times, each time randomising the error term and re-generating
the dependent variable. If the model is robust, then the observed elasticities
should be very similar to the generated ones. The averaged generated results
are compared with the original in table 8.
was impossible to estimate. Even when correcting using the Cochrane-Orcutt procedure,
the model produced spurious, unreliable results that did not withstand robustness tests.
15
Table 8: Observed vs. averaged generated elasticites.
Generated elasticity
Observed elasticity
Constant
5.727
5.674
Population
1.058
1.062
Industry
0.438
0.443
Services
0.147
0.148
Market potential
0.147
0.142
The results bear a strong similarity to the observed elasticities. There is
no difference between the elasticities that would, in practice, alter the GDP
estimates in this paper. Indeed, figure 3 shows probability density plots of
the four model parameters, where each one is normally distributed.
Figure 3: Probability density plots of the generated model parameters after
1,000-resamples.
While there may be both over- and under-estmates, it is fair to say that all
the elasticities generated from resamples are clustered around the observed
values. The density plots show there are more good estimates than bad ones
- even after 1,000-resamples. These encouraging results tell us two important
things. First, the model is producing precise and robust estimates. Second,
it is doing this in spite of the small sample size.
16
5
Conclusion
Germany’s Länder showed variation in income levels during this period. This
was the product of variations in economic structure. Industrial Länder (e.g.
Rhineland) were characterised by higher incomes, and agricultural Länder
(e.g. Ostpreussen) were substantially poorer. The empirical strategy put
forward here exploits this relationship, modelling income levels as a function
of sectoral labour force shares. Though a short-cut strategy, robustness tests
have shown it to be reliable. Researchers who plan on using this paper’s
empirical strategy would do well to also go through these robustness tests.
The development of more robustness tests would make for useful research.
17
Bibliography
(1871): Statistik des Deutschen Reichs 1871, vol. A.F. 14/2, Berlin: Mitteilungen des statistischen Bureaus in Berlin.
(1882): Statistik Des Deutschen Reichs 1882, vol. N.F.111, Berlin: Mitteilungen des statistischen Bureaus in Berlin.
(1895): Statistik Des Deutschen Reichs 1895, vol. N.F.111, Berlin: Mitteilungen des statistischen Bureaus in Berlin.
(1910): Deutschen Reichs - Statistisches Jahrbuch - 1910, vol. 31, Berlin:
Mitteilungen des statistischen Bureaus in Berlin.
(1912): Deutschen Reichs - Statistisches Jahrbuch - 1912, vol. 33, Berlin:
Mitteilungen des statistischen Bureaus in Berlin.
Berghahn, V. (2005): Imperial Germany: Economy, society, culture, and
politics, 1871-1918, New York: Berghahn Books.
Broadberry, S., G. Federico, and A. Klein (Forthcoming): Unifying
the European Experience: An Economic History of Modern Europe,, London: Cambridge University Press, chap. An Economic History of Modern
Europe: Sectoral Developments, 1870-1914.
Buyst, E. (2009): “Reversal of Fortune in a Small, Open Economy: Regional GDP in Belgium, 1896-2000’,” VIVES Research Centre for Regional
Economics.
Caruana Galizia, P. (Forthcoming): “French Regional GDP: Preliminary
Department-Level Estimates, 1860-1911,” Mimeo.
Combes, P., M. Lafourcade, J. Thisse, and J. Toutain (2011): “The
rise and fall of spatial inequalities in France: A long-run perspective,”
Explorations in Economic History.
Crafts, N. (2005): “Regional GDP In Britain, 1871-1911: Some Estimates,”
Scottish Journal of Political Economy, 52, 54–64.
Enflo, K., M. Henning, and L. Schon (2010): “Swedish regional GDP
1855-2000: Estimations and general trends in the Swedish regional system,” Universidad Carlos III de Madrid Working Papers in Economic History.
18
Fabricant, S. (1942): Employment in Manufacturing, 1899-1939, New
York: National Bureau of Economic Research.
Felice, E. (2009): “Estimating regional GDP in Italy (1871-2001): sources,
methodology, and results’,” Universidad Carlos III de Madrid, Working
Papers in Economic History.
Ferguson, N. (1995): Paper and Iron: Hamburg Business and German Politics in the Era of Inflation, 1897-1927, Cambridge: Cambridge University
Press.
Frank, H. (1994): Regionale Entwicklungsdisparitäten im deutschen Industrialisierungsprozess 1849-1939: eine empirisch-analytische Untersuchung,
Hamburg.
Geary, F. and T. Stark (2002): “Examining Ireland’s Post-Famine Economic Growth Performance,” The Economic Journal, 112, 919–935.
Hoffman, W. (1965): Wachstum der Deutschen Wirtschaft seit der Mitte
des 19. Jahrhunderts., Berlin: Springer.
Lütge, F. K. (1963): Geschichte der deutschen agrarverfassung vom frühen
mittelalter bis zum 19. Jahrhundret, Stuttgart.
Maddison, A. (2007): Contours of the World Economy 1-2030 AD: Essays
in Macro-Economic History, Oxford: Oxford University Press.
Roses, J., J. M. Galarrga, and D. Tirado (2010): “The upswing of
regional income inequality in Spain (1860-1930,” Explorations in Economic
History, 47, 244–257.
Schulze, M.-S. (2007a): “Origins of catch-up failure: Comparative productivity growth in the Habsburg Empire, 1870-1910,” European Review of
Economic History, 11, 189–218.
——— (2007b): “Regional income dispersion and market potential in the late
nineteenth century Hapsburg Empire,” LSE Economic History Working
Papers 106/07.
Tipton, F. (1976): Regional Variations in the Economic Development of
Germany During the Nineteenth Century, Middletown, Connecticut: Wesleyan University Press.
Williamson, J. (1998): “Growth, Distribution and Demography: Some
Lessons from History,” Explorations in Economic History, 35, 241–271.
19
Wolf, N. (2010): “Regional GDP Across Germany: Some first estimates at
the level of NUTS-1, 1895-2000’,” Mimeo.
20
A
Districts and Länder, Eurostat data comparisons
21
Table 9: Districts were grouped under existing Länder administrative boundaries, while some free cities and minor principalities were grouped under their
nearest Länder as with Lübeck in Schleswig-Holstein.
22