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CESifo Area Conference on
Public Sector Economics
22 – 24 April 2005
CESifo Conference Centre, Munich
Debt sustainability in Germany
– A long run view
Frank Westermann
CESifo
Poschingerstr. 5, 81679 Munich, Germany
Phone: +49 (89) 9224-1410 - Fax: +49 (89) 9224-1409
E-mail: [email protected]
Internet: http://www.cesifo.de
Debt sustainability in Germany – A long run view
By Frank Westermann
Public Finance Group
University of Munich
Ludwigstr. 28 Vdg. III
80539 Munich, Germany
PRELIMINARY VERSION
1. Introduction (Abstract)
In this paper we construct a long run data set for public debt, deficit- and primary deficit-toGDP ratios in Germany. The sample ranges from 1850 to 2004. Using this data set we apply
recent time series tests for sustainability of public debt ratios. Although the previous results
on the post World-War-Two period are largely confirmed, both, a long run view and the very
recent experience are indicating that the public debt ratio’s in Germany are not following a
sustainable path. From a long run perspective, there is only little evidence that Germany is on
a path consistent with fulfilling the intertemporal budget constraint. From a short run
perspective, Germany’s fiscal policies in recent years, if continued, will accumulate the
largest steady state debt-to-GDP ratio within the Euro-area. While analysing the German data
set, we also critically review the concepts of testing for sustainability of public debt in a time
series framework.
2. The data - Public debt in Germany since 1850
The historical data used in this section have been collected by Walter G.Hoffmann, in his
book “Das Wachtum der deutschen Wirtschaft seit Mitte des 19. Jahrhunderts”. Using this
book as a basis, several estimations where needed to approximate the time path of German
deficits and debt, which are described in the detail in the appendix of the paper. This data set
covers the period from 1850 to 1959. The series thereafter have been updated, using data from
the German statistical office (Statistisches Bundesamt, Wiesbaden), the International
Financial Statistics (IMF) and the OECD Economic Compendium.
Figures 1 and 2 show the time path of German public debt in levels (on a logarithmic scale)
and as a ratio of Gross Domestic Product (GDP). The figures display the evolution of public
debt from 1850 until 2004. Several of the larger changes in these time series can be clearly
attributed to events in the economic history of Germany. The debt ratio’s started at a
relatively low level, when the German states where not yet united and there existed hardly any
debt at the national level. Further more, a large negative drop occurred in the early 1870ies,
when large transfer income due to reparation payments from France coincided with a boom
economy. In this period the debt-to-GDP fell from about 30% to a historically low level of
20%. Thereafter three major changes contributed to a dramatic increase in the debt to GDP
ratio: first, the build up and completion of the German railroad system. Although financed
with private equity until 1880, the government injected substantial amounts of public capital
thereafter in order to complete the project. Secondly, the introduction of the social security
systems by Bismarck in the late 1870ies to 1890ies were initially only partly covered by
social security contributions, and to a large extend financed through the overall budget.
Finally, these periods of extended public debt spending coincided with the so-called
“Gründerkrise”, the crisis of the founders, which Germany experienced for several years after
about 1974/5. During this period, the debt-ratio accumulated to a maximum of 67% in 1894
and a level of about 60% was kept until the 1st world war. As the figure shows, this debt level
was than almost entirely eroded by the period of hyperinflation in the aftermath of the war.
The in-between war-period was characterized by very distinct sub periods. While in the late
20ies, the public debt increased as a ratio of GDP, the government’s reaction to the great
depression that took place in Germany as well as in the United States was to consolidate the
budget and even run public primary surpluses. This pro-cyclical policy has been named
“Parallelpolitik” (parallel policy) and motivated the “Wachstumsgesetz” in 1967, a law that
gave the government to obligation to stabilize the economy in times of recession and provided
guidelines for the extend to which the public budget could be used for this purpose. The
Stability and Growth Pact of the European Monetary Union was largely modelled after this
example.
After the Second World War, again a currency reform was to a large extent responsible for a
relatively low public debt ratio in the early 1950ies, where the ratio once again fluctuated
around 20%. During the late 1970ies and the early 80ies, post-war Germany experienced it
first major increase in the public debt ratio due to the build up and extension of the German
welfare state (and thereby increased for exactly the same reason as almost exactly 100 years
earlier). While the booming late 1980ies reduced this trend for a few years, the German
unification was the second large influence that pushed the debt ratio to today level of about
60-65%.
The causes of these fluctuations will be important to keep in mind when discussing the
sustainability criteria and the results of the regression analysis below.
Figure 1: Public Debt and GDP since 1850
(Logarithmic scale)
5000
4000
3000
2000
Public debt
GDP
1000
1860 1880 1900 1920 1940 1960 1980 2000
Figure 2: Debt-to-GDP ratio
0.8
0.6
0.4
0.2
0.0
1860
1880
1900
1920
1940
1960
1980
2000
Figure 3: Deficit/GDP Ratios
0.15
0.10
0.05
0.00
-0.05
-0.10
Primary Deficit/GDP
Deficit/GDP
-0.15
1860 1880 1900 1920 1940 1960 1980 2000
3. Evidence on sustainability in Germany
Sustainability criteria, based on time series evidence have been developed by Trehan and
Walsh (1991) and Bohn (1998). In this section we apply these criteria to the German data set
and discuss the implication for the German fiscal policy.
Unit root tests
We start by conducting unit root test for the deficit- and debt-to-GDP ratios. The intuition for
the unit root tests in the deficit to GDP ratio is that a stationary path of the deficit ratio implies
at most a linear increase in the debt levels. As the present value of the expected debt in the
future is discounted with an exponential factor (1+r)t, the present value of the expected debt
will be zero, as t goes to infinity. A stationary debt-to-GDP ratio would be an implication of
these considerations.
As the connection of different data sources, as well as the interruption of the time series by
war periods it is likely to introduce structural breaks in the data, making it more difficult to
reject a unit root, we consider several sub periods of the total sample period as well. Fist the
period before the 1st world war 1850-1913, secondly the post World War II period and thirdly,
the post war period, excluding the period after German unification. The test results are
reported in table 1.
Table 1: Unit root tests
Phillips-Perron
Test Statistic
(Lag
truncation)
Augmented DickeyFuller Test
(Lags)
Primary deficit/GDP
1850-2004
1850-1913
1950-2004
1950-1989
-8.47**
-5.90**
-6.22**
-5.62**
4
3
3
3
-5.48**
-3.80**
-4.78**
-4.65**
4
2
1
1
Total deficit/GDP
1850-2004
1850-1913
1950-2004
1950-1989
-8.02**
-5.60**
-5.70**
-5.39**
4
3
3
3
-4.35**
-3.48*
-4.33**
-4.47**
4
2
1
1
Debt/GDP
1850-2004
1850-1913
1950-2004
1950-1989
-1.15
-0.93
0.61
-0.07
4
3
3
3
-0.80
-1.10
0.25
-0.52
4
2
1
1
We find that the evidence on sustainability is very similar across time periods, but do not
yield a clear cut result. While the tests for a unit root in the primary deficit as well as the total
headline deficit indicate stationarity by clearly rejecting the null hypothesis of a unit root, we
are not able to reject a unit root in the debt-to-GDP ratio. The later however would be an
implication of the first result. This result is corresponding to the findings in Bohn (1998), who
is facing the same puzzle in the US data. In his paper, he argues that slow mean revision and
the omission of relevant other explanatory variables are responsible for this apparent
contradiction. In US data, he shows, that conditional on other variables (the situation of the
business cycle and unexpected military spending), the debt –to-GDP ratio is indeed mean
reverting. Before implementing the conditional unit root test for Germany, we follow the
sequence of tests implemented in Bohn (1998) by first looking at the policy reactions of the
government to increases in the public debt to GDP ratios.
Test for policy reactions to high public debt
As unit root tests suffer from poor small-sample performance, and furthermore rests on
particular assumptions about the interest rate, Bohn (1998) develops an alternative testing
procedure that focuses on the policy reaction of the government. He shows that a permanent
reaction of the primary surplus to an increase in the debt ratio is a sufficient criterion for
fulfilling the intertemporal government budget constraint. In a general equilibrium model, he
shows that this criterion is consistent with an optimal consumption path of the households as
well as a general range of interest rates.
In table 2, we implement these tests, and – in contrast to previous findings on the US time
series, cannot confirm that a model based testing procedure is able to prove the sustainability
of the path of public debt. We estimate the same regression as in Bohn (1998 and 2004) for
the same time periods as for the unit root tests, but fail to find significance in any of the
specifications. In the first 4 columns, we regress the primary budget deficit-to GDP ratio on a
constant and the debt ratio only. In a second set of regression – column 5-8 of table 2 -, we
control furthermore for a possible impact of the cyclical situation (deviation of the output
series from a Hodrick-Prescott trend) as well as unexpected military expenditure. For the later
variable, we regress the military expenditures on a linear time trend and two autoregressive
lags, and compute the forecast errors from this regression as the unexpected component. This
component is particularly large in the build of the second world war (up to 6 percent of GDP),
somewhat more important in the 1850ies and 1860ies (up to 2 % of GDP), but relatively small
otherwise. We find that also in this conditional regression, the debt-t-GDP ratio is not
statistically significant in any of the sample intervals. Furthermore, also the point estimates
fluctuate very close to zero and are not of the same sign (a positive one would be expected for
sustainability) across time periods.
Table 2: Test of the structural model (specification of Bohn (1998))
Dependent variable: The primary deficit/GDP
Constant
Debt/GDP
1850-2004
1850-1913
1950-2004
1950-1989
1850-2004
1850-1913
1950-2004
1950-1989
-0.007
0.005
-0.004
0.012
0.001
0.010
-0.019
0.020
-0.011
0.007
0.013
0.022
-0.008
0.007
0.003
0.029
0.062
0.040
-0.015
0.014
-0.064
0.040
-0.324
0.339
-0.078*
0.043
-0.028
0.036
0.083**
0.040
-0.290
0.489
0.142**
0.056
0.006
0.025
-0.150**
0.054
2.857*
1.652
0.179**
0.054
-0.031
0.028
-0.177**
0.050
2.881*
1.660
-0.007
1.487
0.008
1.472
-0.011
1.782
-0.027
1.883
0.042
1.538
0.068
1.459
0.229
1.904
0.309
2.098
YVAR
GVAR
Adj. R-sq.
DW-Stat.
This result is in contrast to the previous findings of Grainer et. Al (1999 and 2004), who
report significant reactions of the primary surplus to the debt-to-GDP ratio at the least for the
post WWII period (after 1960). However, the regression equation in table 2 is not exactly the
same as theirs, as Grainer et. Al include the interest payment as a share of GDP as an
additional control variable, as also include the lagged debt-to-GDP ratio, rather than the
contemporaneous one. The first 4 columns of table 3 show the result for the historical data set,
when exactly following their specification. We find that the evidence indeed changes
considerably, as, when using the lagged values of the debt –to-GDP ratio, the coefficient
becomes statistically significant and has the expected positive sign in most of the time
intervals. Taking the full period from 1850-2004 as well as the pre-WWI sample, the
coefficient is significant at the 10 percent level and has a magnitude that is comparable to
those reported in Grainer et al (1999 and 2004) and Bohn (1998 and 2004). Taking both post
WWII periods, the coefficient on the debt-to-GDP ratio becomes significant at the 5% level
and has even larger coefficients between 0.106 and 0.237. This would imply a quite strong
reaction of the primary surplus to the debt-to-GDP ratio and thereby a sustainable debt path
that is consistent with the stationary of the deficit-to-GDP ratio’s reported above.
Table 3: Test of the structural model (specification of Grainer et. Al (2004))
Dependent variable: The primary deficit/GDP
Constant
Debt/GDP
(-1)
Debt/GDP
YVAR
IP_GDP
Adj. R-Sq.
DW-Stat.
1850-2004
1850-1913
1950-2004
1950-1989
1850-2004
1850-1913
1950-2004
1950-1989
0.048
0.044
0.027*
0.016
-0.082
0.051
0.155*
0.082
0.087
0.037
0.106**
0.033
-0.016
0.069
0.237**
0.121
0.059
0.044
-0.071**
0.039
0.130**
0.066
0.110**
0.043
-0.377
0.095
0.069
0.040
9.713**
2.288
0.011
0.055
-0.131**
0.063
-0.479
0.478
0.062**
0.022
-0.111**
0.042
-1.185**
0.380
0.260
1.307
-0.005
2.068
0.089
2.031
-0.056
0.044
-0.550
0.347
0.074
0.049
-4.109*
2.331
-0.090**
0.035
-1.712**
0.569
-0.004
0.060
-2.495**
1.201
-0.005
0.014
-0.063
0.044
-0.116
0.312
0.040
1.532
0.116
1.612
0.246
1.934
0.263
1.787
0.014
1.570
Columns 5-8 of table 3 however show that this result is only present on the post WWII period,
when including the contemporaneous debt-to-GDP ratios, rather than the lagged ones. This
finding clearly raises the issue of endogeneity among the two variables, which, if important,
would question the entire regression. If it is the case, that present deficit – and debt-to-GDP
ratios are endogenous, the appropriate model would be to use an instrumental variable
approach, rather than just lagging one of the independent variables. Table 4 therefore shows
the regression from Tables 2 and 4, using a two stage least squares procedure, where lagged
values of all right hand side variables are used as instruments.
Table 4: Instrumental variables regression (2SLS), with lagged values as instruments
Dependent variable: The primary deficit/GDP
Constant
Debt/GDP
YVAR
GVAR
1850-2004
1850-1913
1950-2004
1950-1989
1850-2004
1850-1913
1950-2004
1950-1989
0.132**
0.058
0.016
0.015
-0.146**
0.061
0.484
0.435
-0.145
0.120
0.042
0.038
0.116
0.107
0.861
0.697
0.339**
0.150
0.034
0.026
-0.356**
0.154
1.082
3.975
0.364**
0.175
-0.008
0.025
-0.370**
0.178
2.219
3.339
0.128**
0.053
0.004
0.013
-0.138**
0.053
-0.117
0.106
0.058
0.248
0.106
0.104
0.284**
0.117
0.056**
0.028
-0.292**
0.120
0.297**
0.149
0.044
0.116
-0.304**
0.149
0.038
0.323
-1.399
6.598
-0.753
0.580
-0.652
1.378
-0.061
1.595
-0.035
1.556
-0.062
2.007
-0.182
1.997
IP_GDP
Adj. R-Sq.
DW-Stat.
-0.179
1.426
-0.220
1.756
0.027
1.420
0.196
1.475
We find that in this regression, once again, only the post-war period, which includes the
interest payment to GDP ratio as additional regressor provides evidence of sustainability,
while all others do not.
Good policy reactions vs. bad policy reactions
The model based sustainability criteria investigate the policy response of the government to
high public debt, via budget surpluses. However, a potential shortcoming of this approach is
that there exist other policy options to get rid of the debt that are less benevolent. For instance
the government could opt for higher inflation or simply default. Does the probability of
default increase at higher debt levels? Does the inflation rate increase at high debt ratios? For
the strong conclusion of sustainability, these alternative policy reactions need to be ruled out.
We therefore estimate the same policy function as in the sustainability literature, with the
exception that we use it to explain inflation, rather than the budget surplus.
As table 5 shows, we do not find such systematic negative reactions to the public debt ratio. It
needs to be pointed out however, that both the hyperinflation in the 20ies as well as the
currency reform after the Second World War can be interpreted as such negative policy
reactions that a large public debt ratio can induce. Neither of the two events is part of our data
set.
Table 5: Other policy reactions to high debt ratios
Dependent variable: Inflation
Constant
Debt/GDP
1850-2004
1850-1913
1950-2004
1950-1989
0.027**
0.008
-0.033*
0.018
0.021
0.015
-0.024
0.030
0.037**
0.008
-0.031
0.021
0.035**
0.013
-0.026
0.047
0.018
1.103
-0.006
1.332
0.022
1.128
-0.018
1.123
YVAR
GVAR
Adj. R-Sq.
DW-Stat.
1850-2004
1850-1913
1950-2004
1950-1989
-0.162**
0.047
-0.025
0.018
0.186**
0.046
0.017
0.272
-0.232
0.097
0.023
0.038
0.229**
0.089
0.495
0.470
-0.110*
0.058
-0.035**
0.016
0.150**
0.058
1.979**
0.679
-0.151*
0.081
-0.007
0.035
0.185**
0.077
2.002**
0.736
0.131
0.932
0.066
1.272
0.256
0.766
0.241
0.629
Conditional mean revision in public debt ratios
We now return to the puzzle in table 1, where we found evidence of sustainability when
looking at the stationarity of the deficit ratios, but no such evidence when looking at the debtto-GDP ratios.
The same puzzle is resent in the US data analyzed by Bohn (1998), and he reconciles this
observation in the following way: As in the structural regression, he argues that it is necessary
to include the control variables in the regression. While this is rather unusual procedure, it
renders the debt-to-GDP ratios mean-reverting in the US data. Clearly, the interpretation
changes when modifying a unit root test in this way: When finding conditional mean revision
in the debt-to-GDP ratio, the message is, that that part of government spending, that is not
driven by cyclical fluctuations or unexpected war-time spending is sustainable. This is
different from the statement that the debt-to-GDP ratio is mean reverting, unconditionally.
The cyclical expenditures, and in particular, the unexpected war time spending may or may
not be sustainable. Eyeballing the US data, this appears to be the case, but there is not format
test for it. Furthermore, it is not clear if, given the evidence of conditional convergence, all
econometric problems of mixing I(1) and I(0) variables (in the structural regressions) have
been solved (If the regression is spurious, the parameter on the debt-to-GDP ratio cannot be
estimated in a consistent way).
Nevertheless, we follow the literature in estimating the ADF test regressions including the
explanatory variables from the previous regressions. We find that again the control variable of
the interest rate payments to GDP ratio is necessary to find evidence on convergence. Given
the discussion on the changing interpretation above, it seems questionable however to
interpret this result too strongly, as, unlike the war and cyclical expenditure, there is no
straightforward motivation why this systematic part of the public debt should be abstracted
from. (Only the period 1850-1913 is statistically significant at the 10% level.) (See table 6
Table 6: Conditional stationarity
Dependent variable: Debt/GDP-Debt/GDP(-1)
Constant
Debt/GDP
(-1)
YVAR
GVAR
1850-2004
1850-1913
1950-2004
1950-1989
1850-2004
1850-1913
1950-2004
1950-1989
0.083**
0.046
-0.025
0.018
-0.067
0.044
0.031
0.264
0.357**
0.074
-0.057*
0.030
-0.324**
0.070
-0.413
0.377
-0.109
0.087
0.018
0.025
0.111
0.085
-2.877**
1.014
-0.119
0.109
0.031
0.049
0.116
0.103
-2.912
0.974
0.075*
0.043
-0.062**
0.021
-0.069
0.041
0.186**
0.053
-0.615**
0.076
-0.175**
0.051
-0.049
0.081
-0.072**
0.035
0.037
0.080
0.079
0.093
-0.291**
0.073
-0.073
0.088
1.339**
0.440
15.886**
2.035
2.004**
0.604
3.954**
0.801
0.075
1.427
0.619
1.072
0.149
1.742
0.362
1.677
IP_GDP
Adj. R-Sq.
DW-Stat.
0.006
1.475
0.244
1.394
0.118
1.793
0.154
1.841
Near stationarity vs. near unit root
The danger not being able to reject a unit root in small samples is highlighted in many papers
on debt sustainability. The argument is that the null hypothesis is a unit root, and a short time
series may simply not have enough data to reject the null, although the time series is actually
stationary. This argument is correct and is called a near unit root problem in the time series
econometrics literature. When evaluating the evidence based on unit root tests, it needs to be
pointed out however, that the opposite problem also exists. Suppose that a time series has
indeed a unit root, but the persistence of a shock is rather low. For instance, a government,
that reacts to increases in the debt by repaying its debt, but always repays only say 95% of it.
In this case, the process is near stationary, although the process in the long run is clearly not
sustainable and the debt will go to infinity in the long run. It is therefore important to point
out that the potential mistake in unit tests is symmetric. In a simulation of near unit root and
near stationary processes one can easily confirm that both can be equally misleading.
4. The Domar rule and long run steady states
A common criticism of time series based test of debt sustainability is the focus on the
intertemporal budget constraint, thereby neglecting the actual levels of the debt-to GDP ratios.
For instance – as an extreme example- a country, who borrows 1000% of GDP every year,
would be considered sustainable, as long as it does so in continuous way. (i.e. not
exponentially increasing) In this case, the exponentially growing discount factor of the debt
would lead to the expected value of the debt to be zero as t goes to infinity. Based on this
problem the test of the IBC is often regarded as a test that is of purely academic interest. In
this section, we try to complement this time series test of the IBC, by looking at the mean of
the steady state debt-to-GDP ratio’s that would be obtained if current policies would be
pursued into the infinite future.
These long run steady states can be obtained from the well-know Domar Formula:
d& = α − Yˆ ⋅ d
Where d& is the change in the debt ratio, α is the deficit to GDP ratio, Ŷ is the nominal
growth rate of GDP and d is the debt-to-GDP ratio. Setting the change in the debt ratio to zero
as a condition for a steady state, and solving the equation for d, yields the long run steady
state growth rate, simply as the ratio of the deficit-to-GDP ratio and the growth rate of GDP.
Table 7 displays these steady states for the time intervals analysed before as well as for some
shorter, more recent intervals. We see that for most of the time intervals, we find reasonably
low values of the debt-to-GDP ratio. Only in the last 10 years, the path has been such that a
debt-to-GDP ratio of more than 100% would arise, if the policy would be carried on for ever
at the current GDP growth rates.
Steady state long run debt ratios:
1850-2004
1850-1913
1950-2004
1950-1989
1990-2004
1994-2004
Average of...
deficit/GDP GDP growth
0.023
0.052
0.021
0.036
0.027
0.072
0.024
0.081
0.035
0.047
0.031
0.025
Steady state
debt ratio
0.448
0.566
0.380
0.301
0.747
1.237
A 10-year window is rather small, of course, but we nevertheless feel that it is a window that
is relevant for economic policy. It is not an exaggeration of the problem, as the last 10 years
include both, the stagnation period after 2001, and the boom period of the late 1990ies. It is
therefore not just driven by a cyclical effect (which was also controlled for in the regressions).
Also, even when not counting the off-balance sheet debt items, that where attributed to the
German unification in the official statistics, this ratio would be nearly 110 %.
This is a very high number, both in a historical perspective as well as in comparison to other
European countries. Figure 4 shows a graph that was constructed by rolling a 10-year window
forward over the sample period that we have. Each point in this graph reflects the steady state
long run growth rates that would prevail of the policy of the past 10 years, as well as the
nominal GDP growth rates would be carried on for ever. We see that this number is below
100% in nearly all years, except for the period of the 1880ies, where the social security
systems in Germany where introduced. If this spending path would have continued for ever at
given GDP growth rates, the debt-to-GDP ratio would have converged to nearly 1000%.
Except for this time, the current values mark a record-high in German history.
Figure 4: Long run steady state based on 10-year windows
5
4
3
2
1
2001
1991
1981
1971
1961
1951
1941
1931
1921
1911
1901
1891
1881
1871
1861
1851
0
Figures 5a and 5b show the debt ratios in international comparison. While in the current
situation, Italy, Belgium and Greece have the largest debt-to-GDP ratios, Germany will have
the largest debt-to-GDP ratio in the Euro Area, it the current policies and GDP growth rates
are not changed.
Figure 5a: Present Debt/GDP ratios in the Euro Area
Italy
Greece
Belgium
Austria
Germany
France
Portugal
Spain
Netherlands
Finland
Ireland
Luxembourg
-40
-20
0
20
40
60
80
100
120
Figure 5b: Long run steady states for debt/GDP ratios in the Euro-Area, based on
deficits and nominal growth rates in the last 10-years
Germany
France
Italy
Austria
Belgium
Portugal
Spain
Netherlands
Greece
Ireland
Finland
Luxembourg
-40
-20
0
20
40
60
80
100
120
5. Conclusions
6. Data Appendix
7. References
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of Economics, pp. 949-963.
Bohn H. (2004), “The Sustainability of Fiscal Policy in the United States” ”, present at the
CESifo / LBI Conference on Sustainability of Public Debt 22 - 23 October 2004.
Greiner A. and W. Semmler (1999): “An inquiry into the sustainability of German
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Grainer A., U. Koeller and W. Semmler (2004): “Testing Sustainability of German Fiscal
Policy: Evidence for the Period 1960-2003”, present at the CESifo / LBI Conference on
Sustainability of Public Debt 22 - 23 October 2004.
Hoffmann, Walter G. “Das Wachstum der deutschen Wirtschaft seit Mitte des !9.
Jahrhunderts” Springer Verlag, Berlin 1965.
Trehan B. and C. Walsh (1991) “Testing intertemporal budget constraints: theory
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