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\author{Wolfgang Keller\thanks{
1180 Observatory Drive, Madison, WI 53706; email: wkeller@ssc.wisc.edu.
Thanks are due to Gerwin Bell, Buz Brock, Willem Buiter, Paul Cashin, John
McDermott, Xavier Sala-i-Martin, and in particular T.N. Srinivasan for
useful comments on an earlier draft.} \\
%EndAName
University of Wisconsin and NBER}
\date{May 1997}
\title{From Socialist Showcase to Mezzogiorno?\\
Lessons on the Role of Technical Change from East Germany's Post-World War
II Growth Performance\thanks{
Parts of this paper circulated earlier under the title: ''On the Relevance
of Conditional Convergence Under Diverging Growth Paths: The Case of East
and West German Regions, 1955-88''.}}
\maketitle

\begin{abstract}
\noindent In this paper we emphasize the contribution of technical change,
broadly defined, towards productivity growth in explaining the relative East
Germany-West Germany performance during the post-world war II era. It is
argued that previous work was excessively focused on physical capital
investments determining productivity differentials, which consequently led
to an overestimation of the East German performance during the Socialist
era, and an overly pessimistic assessment of the East German prospects of
catching up with West Germany during the post-reunification era. We show,
first, that the rates of technical change in the manufacturing industries of
East German states were significantly below those in Western states, helping
to account for the fact that East Germany was not the socialist showcase for
which it was frequently taken before German reunification. Second, we
demonstrate that the rates of technical change in the East German states
have been considerably higher than those in the West since German
reunification. This suggests that the Mezzogiorno prediction for East
Germany--that it will stay persistently behind West Germany as does Italy's
South relative to its North--, based on an analysis of the need for physical
capital accumulation alone, will prove too pessimistic.
\end{abstract}

\newpage 
\setcounter{page}{1}

\section{Introduction}

How long will it take until East European economies will be similarly rich
as the countries in the West of Europe? Barro (1991a) argued that, based on
his own estimates from US states, it would take about 70 years until
three-quarters of the per capita income gap in the specific case of East and
West Germany would be eliminated\footnote{%
In Barro and Sala-i-Martin (1991), the authors predict that it will take 35
years until half of the initial income per capita difference between East
and West Germany will have disappeared, p.154; these two estimates are
equivalent. They are based on equation (\ref{elev}) and an estimate of $%
\lambda $ of 2\%. Barro did not stand alone with his pessimism;
Hughes-Hallett and Ma (1993), e.g., estimate 30-40 years to full
convergence. See also Sinn and Sinn (1992) for a review of other predictions.%
} this would mean that East Germany would become a German Mezzogiorno,
similar to Italy's South which persistently stays behind its North.

How well was East Germany doing during its socialist period before German
reunification? In 1987, two years before the Berlin Wall came down, the
Deutsche Institut fuer Wirtschaftsforschung (DIW) in Berlin-West, which has
been most consistent in tracking the East German productivity performance,
estimated that the ratio of East German to West German labor productivity in
the industrial sector was ca. 50\% (Report 1987, p.390), which, compared to
other socialist countries, would have made East Germany the socialist
showcase economy.

It is, with the benefit of hindsight, easy to see that both of these
estimates were way off: Right before German reunification, the relative
labor productivity of East Germany's manufacturing sector was not 50\%, but
ca. 25\% of the West German level.\footnote{%
A level of productivity of 25\% for 1989 seems plausible, see the references
in Hughes-Hallett and Ma (1993), and Sinn and Sinn (1992), Ch.2. Akerlof et
al. (1991) even assume a productivity level of less than one sixth for GDR
manufacturing in 1989. The estimates are usually projections based on
officially published data for the second half of 1990 or 1991. According to
Arbeitskreis (1995), the average manufacturing labor productivity of East
German states relative to West German states was 28.6\% in 1991 (average
Eastern relative GDP per capita was 31.23\% [ibid]).} At the same time, the
developments of East German GDP per capita between 1991 and 1995 suggest
that it will take East German states on average not 70, but 20 years or less
until it has reached three-quarters of the per capita GDP of West Germany.
For labor productivity in the manufacturing sector, we estimate only about
ten years until East Germany has reached three-quarters of the West Germany
level.\footnote{%
These estimates are obtained by calculating the speed of catch-up between
the average East and West German state between 1991-95 (see section 4.2
below), and extrapolating it into the future.} Why is it that the East
German productivity levels even at the end of the socialist era in Germany
were overestimated by 100\%? And why did Barro apparently overestimate the
time to converge for East Germany by a factor of three? In this paper, we
argue that ignoring differences in the rate of technical change--in the
sense of Solow (1957)--as a factor determining productivity growth is at the
heart of why these estimates are off by a factor of two and three,
respectively.

This is because Barro's post-reunification prediction is based on a model of
physical capital accumulation where all economies experience the same
exogenous rate of technical change. But East Germany's rate of technical
change can be much higher than West Germany's while new production and
management techniques are adopted, and even more generally, because the
economic agents now face the different incentive structures of a market
economy. Further, technical change is at least to a certain degree not
embodied in capital goods, which implies that it is not enough to compare
rates of physical capital investments of East and West Germany to estimate
how large the difference in the rates of technical change are. In this
paper, therefore, we propose a Solow-Swan model of growth with differential
rates of technical change; in this model, the rates of physical capital
accumulation and technical change are independent from each other, and can
also take on different values for different economies.

We will estimate the model using data on East and West German regions (%
\textit{Laender} for the West, \textit{Bezirke} in the East) during East
Germany's socialist era (1949-89). First of all, there are practical reasons
for that, as a formal statistical analysis is hard to conduct with only five
years of post-reunification data. Second, a comparative analysis of East and
West during that period might be of interest in its own right. Ultimately,
however, an analysis of East and West German regions during that era is the
appropriate way of estimating the model because both today's overly
pessimistic assessment of East Germany's growth prospects ('Mezzogiorno'),
and the excessively optimistic estimates of East Germany's growth
performance during its socialist era ('Showcase') can be attributed to
ignoring the consequences of differences in the rates of technical change
between economies. We show below that East German rates of technical change
were below those in the West, which, if ignored,\footnote{%
For evidence on this, see Report (1987) and the studies cited therein.}
explains why East Germany's achievements during its socialist era had been
overestimated. In a nutshell, placing less emphasis on physical capital
accumulation by accounting for differences in the rate of technical change
can both explain the apparent East German 'Showcase' phenomenon before
re-unification and suggest why a 'Mezzogiorno' scenario for East Germany in
the post-reunification era is extremely unlikely.

This paper is related to work on income convergence across countries or
regions using the framework of the Solow-Swan model of growth, including
Barro (1991b) and Mankiw, Romer, Weil (1992) who consider cross-sections, as
well as De Gregorio (1991) and Islam (1995) who use panel data analysis. The
estimation here is more general in the sense that we allow, corresponding to
the argument above, for differences in the rates of technical change across
economies. Our analysis for the post-reunification era builds on the
literature on the measurement of TFP growth, going back to Solow (1957).

The paper is also related to recent work specifically on East Germany,
including Boltho et al. (1996), Burda and Funke (1993), and Hughes-Hallett
and Ma (1993).\footnote{%
See also the work by Akerlof et al. (1991), Ritschl (1996), and the overview
in Sinn and Sinn (1992).} Boltho et al. attempt to answer the question of
whether East Germany will remain Germany's Mezzogiorno by studying the
circumstances which led to the Mezzogiorno problem proper, in Italy's South
versus its North, before making comparisons with East Germany. Although
criticizing the work by Barro and Sala-i-Martin (1991) in several respects,
Boltho et al. conclude within that framework that Italy's South did not
converge with its North between 1928 and 1991. Based on a variety of factors
such as innovative policy design, a history of entrepreneurship, and
wholesale administrative reform, Boltho et al. are cautiously optimistic
that East Germany will not be a Mezzogiorno case.\footnote{%
While it is clear from this that Boltho et al.'s analysis of East Germany
incorporates more elements than what is captured in the framework analyzed
to study Italy's South, we note that Boltho et al. do not consider their
convergence regressions as estimating a particular model either, p.4. This
is due to Boltho et al.'s objections to the Barro and Sala-i-Martin (1991)
approach.}

Both Hughes-Hallett and Ma and Burda and Funke are studies of the prospects
of East Germany in the post-reunification period which are explicitly tied
to a specific formal framework. The former base their predictions on
simulations with the IMF's MULTIMOD model, stressing almost exclusively
physical capital investments as the way to close the productivity gap
between East and West. Therefore, Hughes-Hallett and Ma reach qualitatively
similar conclusions as Barro (1991a) on the East-West catch-up time. In
contrast, and similar to the views proposed here, Burda and Funke find the
prediction that it will take 70 years until East Germany has caught up (to
75\%) with West Germany to be overly pessimistic. Burda and Funke's model
emphasizes the high mobility of human capital within Germany after
reunification, and show evidence on the convergence of productivity between
East and West. Burda and Funke, however, do not estimate their growth model
with high capital mobility with both East and West German data.\footnote{%
Moreover, while human capital mobility might be relevant to some extent, it
cannot be the full story, because evidence in Sinn and Sinn (1992) and
Ritschl (1996) shows that East Germany was relatively well endowed with
skilled labor at the time of German reunification.}

Taken together, there are few studies which estimates East Germany's
relative economic performance along the lines of a formal growth model;%
\footnote{%
At the same time, to conduct this analysis in a formal growth model implies
that we will abstract particular elements in the current East German
economic situation. The applicability of this approach in the face of some
particular aspects of the East German situation is discussed in section 5
below.} even fewer authors have integrated the analyses of Germany's pre-
and post-reunification era, and no study isolates the effect of differences
in the rate of technical change\footnote{%
Among the work which mentions this issue are Sinn and Sinn (1992), Boltho et
al. (1996), and much of the work cited there. However, much of that work is
not based on a structural model of economic growth, which makes it difficult
to both isolate the exact mechanisms at work as well as to empirically
verify them.} as a critical factor, together with physical capital
investment, in making long-term predictions on East Germany's economic
prospects.

The remainder of the paper is as follows. Section 2 presents the Solow-Swan
model with differences in the rate of technical change, and derives the
estimating equation. In section 3, we give some background on the two parts
of Germany which existed separately between 1949 and 1989, and discuss the
data used in this paper. Estimation results are presented in the central
section 4 of the paper; we first estimate and discuss results for the period
until 1989, prior to German re-unification, before turning to evidence on
the developments since 1989. Section 5 concludes.

\section{The Model}

\subsection{Developing an Estimation Equation in the Augmented Solow-Swan
Model}

We employ a standard Solow-Swan model of growth where the exogenous rate of
productivity growth is allowed to vary between economies. Let output be
produced according to $Q(t)=K(t)^\alpha (A(t)L(t))^{1-\alpha }\,,$ $0<\alpha
<1,$ then it is well-known that, in the neighborhood of the steady-state,
output per worker $q(t)$ follows (see the appendix) 
\begin{equation}
\ln \left[ \frac{q\left( t_2\right) }{q(t_1)}\right] =(1-e^{-\lambda
\,\Delta })\left\{ \frac \alpha {1-\alpha }\ln \left[ \frac s{n+g+\delta
}\right] +\ln \,A(0)-\ln q(t_1)\right\} +g(t_2-t_1\,e^{-\lambda \,\Delta })
\label{sev}
\end{equation}
Here, $s$ is the savings rate, $n$ the growth rate of the labor force; $g$
is the rate of technical change, $A(t)$ is a productivity parameter
capturing the level of technology, $\delta $ is the rate of depreciation, $%
\Delta \equiv t_2-t_1$, and the parameter $\lambda \equiv (1-\alpha
)(n+g+\delta )$ has been termed the speed of convergence. The term $\left\{
\frac \alpha {1-\alpha }\ln \left[ \frac s{n+g+\delta }\right] \right\} $ is
the log of steady-state output per efficiency unit of labor. Early work
based on equation (\ref{sev}) regressed per capita income growth of a
cross-section of countries on a constant and initial per-capita income. A
negative coefficient on $\ln q(t_1)$ was then interpreted as evidence for
convergence in the sense that, ceteris paribus, initially poorer economies
grow faster. However, not all sets of countries generated a negative
coefficient on $\ln q(t_1)$. Barro (1991b) and Mankiw, Romer, Weil (1992)
then coined the concept of 'conditional convergence': by controlling for
differences in savings and labor force growth rates ($s$ and $n$), these
authors restored the earlier finding that initially poorer countries grow
faster than initially richer countries.\footnote{%
Note that allowing for differences in $n$ or $s$ across economies implies
that $\lambda ,$ given its definition, is economy-specific as well, and
hence, so is $\beta ,$ the regression coefficient on initial income.
Nevertheless, the convergence literature has usually constrained the
coefficient $\beta $ to be the same for all economies; to ensure
comparability with earlier results, we will do the same.}

By construction, these studies can capture only the effect that output per
worker goes up as the capital-labor ratio rises; this is called the
''capital-deepening effect''. It is a maintained assumption in these studies
that $g$, the rate of technical change, is identical across all economies.
This is problematic for two reasons: If the rate of technical change is
economy-specific and not orthogonal to the other regressors, this will bias
the estimated coefficients. The bias is the standard omission-of-variable
bias. More importantly, the assumption of identical rates of technical
change effectively shuts off the mechanism that differences in the rates of
technical change are driving differences in per capita growth rates. Even in
and of itself, therefore, it is interesting to see both the
capital-deepening as well as the technical change at work in one model,
because only that will allow to estimate their relative importance.

In this paper we argue that ignoring differential rates of technical change
is the fundamental reason why the East German productivity gap relative to
West Germany was underestimated during the socialist era. At the same time
this is the reason why the prospects of East Germany after re-unification
are underestimated. Therefore, we extend the specification (\ref{sev}) so as
to allow for regional-specific rates of technical change.

\subsection{Identifying Assumptions}

In equation (\ref{sev}), we specify 
\[
(1-e^{-\lambda \,\Delta })\left\{ \frac \alpha {1-\alpha }\ln \,(s)+\ln
A(0)\right\} =c_1+\varepsilon _{it},\,\,\,\forall
i,t;\,\,i=1,...,I;\,\,\,t=1,...,T, 
\]
where $i$ indexes a region, and $t$ indexes time. The term $c_1$ is a
constant, and $\varepsilon _{i\,t}$ is an i.i.d. disturbance with $%
E[\varepsilon _{i\,t}]=0$ and $Var[\varepsilon _{i\,t}]=\sigma _\varepsilon
^2$, reflecting random shocks which are uncorrelated across individual
regions and across time, like the local weather conditions in a region.

Two assumptions are being made. First, we posit that all German regions
shared an identical initial technology level $A(0)$ at the beginning of the
period of observation. This is justifiable, see UN (1949), Stolper (1960),
and Boltho et al. (1996). Second, we postulate that the savings (and
investment)\footnote{%
The German regions were open relative to each other (at least within West
and within East), not closed, as the basic Solow-Swan model assumes. It is
well-known that, with perfect capital mobility between economies, the
Solow-Swan model predicts instantaneous convergence of per capita GDP; but
Barro, Mankiw, and Sala-i-Martin (1995) show that the qualitative
convergence properties carry over to a world in which capital mobility is
only partial.} rates of all regions were identical and time-invariant. This
assumption is simply necessary to do this analysis; there is no investment
data at a regional level for East Germany during the pre-reunification era.%
\footnote{%
Keller (1997) presents relevant data on this and other assumptions made
below: there was little variation among West German regional investment
rates at a given point in time, and that they were in general falling before
1989. The national East German investment rates, as published in the
official statistics, were usually as high as, or even higher than, West
German investment rates. The efficiency of East German investment was likely
to be lower, though, especially for the 1970s and 1980s. Keller (1997) shows
that the main estimation results for the pre-reunification era hold even if
it were true that the effective East German investment rates were falling
behind the West German ones during the the 1970s and 1980s.}

Further, we assume that, in (\ref{sev}), 
\begin{equation}
g(t_2-t_1\,e^{-\lambda \,\Delta })-(1-e^{-\lambda \,\Delta })\frac \alpha
{1-\alpha }\ln \,(n+g+\delta )=g_i\,\pi _{i\,t}-\omega _i\ln \,(n+g_i+\delta
),  \label{eig}
\end{equation}
with $\pi _{it}=(t_2-t_1\,e^{-\lambda \,\Delta })$ and $\omega
_i=(1-e^{-\lambda \,\Delta })\frac \alpha {1-\alpha }.$

Although the labor force growth rates $n$ were clearly not time-invariant
and identical across individual regions, the assumption appears to be valid
if East and West are compared as blocks over the entire period.\footnote{%
On the one hand, labor force growth between 1955-1961--the Berlin Wall was
built in 1961--was, due to outmigration, lower in the East. On the other
hand, hours worked came down much slower in East Germany. In addition,
women's labor force participation rose much faster in the East. In
combination, these two effects suggest that there was no big East-West
difference of labor force growth rates as a whole; see Keller (1997).}
Allowing the rate of labor-augmenting technical progress to be
region-specific, $g_i,$ in equation (\ref{eig}) is the main emphasis of this
paper.\footnote{%
The factors $\pi _{it}$ and $\omega _i$ are indexed by region $i$ because if
the rate of technical change $g_i$ is region-specific, then $\lambda
=\lambda _i$ from the expression for $\lambda $ above. The expression holds
as long as $\Delta $, the length of a subperiod, is constant. For values of $%
n$, $\delta $, $\pi _{it}$, $\Delta $, and $\omega _i$ in the relevant
range, the expression in (\ref{eig}) is increasing in $g_i$.} The estimation
will rely on a linear approximation of (\ref{eig}), with 
\begin{equation}
g_i\,\pi _{i\,t}-\omega _i\ln \,(n+g_i+\delta )=c_2+\upsilon _t+\mu _i\,\,,
\label{10p}
\end{equation}
where $c_2$ is a constant.\footnote{%
To obtain this linear approximation, we assume that $g_i=g+o_i,\,\,\pi
_{it}=\pi _i+\rho _t\,,$ and Corr($o_i,\rho _t$) = 0. For a time-varying
subperiod length $\Delta ,\,\Delta _t$ as will be the case in the estimation
below, we hypothesize in addition that $\omega _{it}=\omega _i+\xi _t\,,$
with Corr($o_i,\xi _t$) = 0.} The term $\upsilon _t$ captures influences on
the development of output per worker which are common to all regions in
Germany. The last term, $\mu _i$, is region-specific and time-invariant. It
measures the rate of regional technical change above or below the mean in
the sample. Therefore, solving the left hand side of (\ref{sev}) for $\ln
q(t_2)$, the estimating equation is given by 
\begin{equation}
\ln q(t_2)=\chi +\mu _i+\upsilon _t+\beta \,\ln q(t_1)+\varepsilon _{i,t},
\label{elev}
\end{equation}
with $\chi =c_1+c_2,$ $\upsilon _t=h(\pi _{it})$, $\beta =e^{-\lambda \Delta
},$ and $\mu _i=f(g_i)$, where $f\,^{\prime }(.)>0.$

Equation (\ref{elev}) is a dynamic panel model where the group fixed effects 
$\mu _i$ identify differences in the rate of technical change across
economies. Equation (\ref{elev}) contains therefore two independent effects
of why economies might grow at different rates: first, there is the
well-known capital-deepening effect, related to the convergence of the
economies to their steady-state. In the estimation, this is captured by the $%
\beta $ parameter. For $\beta <1,$ growth of economies with higher values of 
$q(t)$ will be lower than for those with lower values of $q(t)$, which is
the conditional convergence prediction emphasized by Barro and Mankiw,
Romer, Weil. Figure 1 shows the case where all economies display the same
rate of technical change. Under these circumstances, all economies (two are
shown) converge to a path which has the same slope (same $g_i$). Second, in
the model of equation (\ref{elev}), economies can also exhibit steady-state
growth (which is solely technical change) at different rates; this
corresponds to the $\mu _i$ being different across economies. This is shown
in Figure 2, where different slopes in the steady-state growth paths
indicate different rates of technical change, related to $\mu _i.$ In that
case, it is possible that although the economies, call them A and B,
converge to their respective growth paths, and therefore undergo
capital-deepening in the conditional convergence sense, the two economies
can converge to steady-state growth paths which have different slope. Hence,
it is possible to have conditional convergence and absolute divergence at
the same time.\footnote{%
Of course, we could redefine the concept of conditional convergence so that
it encompasses differences in the rate of technical change. In this case,
however, it would be possible to question the overall significance of the
concept of conditional convergence--if what we are primarily interested in
is the relative growth performance of econmies.}

\section{Data}

The study is based on German regional data from the post World War II era.
Between 1949 and 1989, there existed both the Federal Republic of Germany
(West Germany) and the German Democratic Republic (East Germany). With
German reunification in 1989, the German Democratic Republic ceased to
exist. West Germany consists of eleven states (\textit{Laender}),\footnote{%
The Laender are Schleswig-Holstein, Niedersachsen, Nordrhein-Westfalen,
Hessen, Rheinland-Pfalz, Saarland, Baden-Wuerttemberg and Bayern. In
addition, there are three city states: Hamburg, Bremen, and Berlin-West.}
whereas the latter was arranged into fifteen regions called \textit{Bezirke}.%
\footnote{%
These were Berlin-East, Cottbus, Dresden, Erfurt, Frankfurt (on the river
Oder), Gera, Halle, Karl-Marx-Stadt (now renamed Chemnitz), Leipzig,
Magdeburg, Neubrandenburg, Potsdam, Rostock, Schwerin, and Suhl.} The total
area of West Germany is ca. 248,000 square kilometers, whereas East Germany
had an area of ca. 108,000 square kilometers. See Figures 3 and 4 for the
location of the regions in the pre-reunification era. After 1989, the
administrative structure of East Germany reverted back to the five states
which had existed until 1945.\footnote{%
These states are Brandenburg, Mecklenburg-Vorpommern, Sachsen,
Sachsen-Anhalt, and Thueringen.} Because the former fifteen Bezirke are,
with small exceptions (see the dotted lines in Figure 4), uniquely
attributable to one of the five East German states (and East Berlin was
merged with West Berlin), the continuity of this analysis of regional
productivity dynamics over the point of German reunification is guaranteed.

\subsection{Pre-reunification Data}

The data sources for West German regions during the pre-reunification period
is Statistisches Bundesamt (1990), with the series \textit{%
Bevoelkerungsstruktur und Wirtschaftskraft der Bundeslaender}. For East
German regions, it is less clear which data source to use. This is primarily
because the East German statistical office overstated, either directly or
indirectly--by direct falsification, or by labeling economic quantities with
Western names although Eastern methodology did actually differ from the one
applied in the West--the East German economic achievements. Consequently,
one might consider relying on Western estimates of the East German economic
performance. There are a number of reasons, however, why this is both futile
as well as unnecessary.

First of all, Western estimates of East Germany output per capita at any
given point during the communist era were varying considerably, even when
largely similar methods were applied. A study by Wharton Associates (1986),
for instance, estimated for 1980 a GDP per capita of 45\% of the West German
level. But for a World Bank publication, Collier (1985) estimated that East
German GNP\ per capita in 1980 was 70\% of the West German level; this is no
less than 77.7\% higher than the Wharton estimate (never mind the GDP-GNP
difference). Second, Western estimates, even if they came from the same
source, have been revised frequently (usually downwards), showing the degree
of uncertainty involved. Consider the estimates by researchers at the DIW in
Berlin-West: Wilkens estimated in 1976 (see Wilkens 1981) that in 1970, East
Germany's GNP per worker in the industrial sector was ca. 70\% of West
Germany's. This contrasts with the DIW\ study for Report (1987), which gives
48\% as the relative productivity level for 1970--a downward revision of
more than twenty percentage points. From this and other examples which could
be cited, it appears that Western estimates of East Germany's economic
performance are very uncertain with respect to the time at which the
estimates were made. In addition, the raw data for Western estimate of East
German economic performance was the official East German statistics: no
independent data collection to speak of was permitted.

If East German official data is deemed to be unreliable, however, another
possibility would be to wait until recalculated figures of historical East
German productivity according to Western methods are becoming available. The
German Federal Statistical Office has investigated whether it is possible to
revise the results of the GDR statistics according to West German concepts
(Statistisches Bundesamt 1991, 1993). According to Statistisches Bundesamt
(1991), there is no possibility that East German relevant data were directly
falsified by the reporting enterprises, or by the ministries and statistical
offices in the process of aggregating the data. Of course, this does not
imply that official East German statistics are as such comparable to West
German figures. However, if, as these studies indicate, official East German
statistics can be used for a historical recalculation, this would imply that
the statistics could not have been forged by very complex or arbitrary
techniques. At the same time, given that the recalculation project has not
been completed yet (and will not, for the foreseeable future), in the
following we will propose independent estimates of East German statistics
during its socialist era.

The output data we are using is the gross industrial product per worker
(GIPW), taken from Statistisches Amt/DDR (1990). The reason why we compare
the dynamics of GIPW, as opposed to GDP per worker, is that services data on
a regional level cannot be obtained for East Germany. However, we will be
able to incorporate growth through structural shifts in the composition of
output by conditioning on the share of employment in the agricultural
sector, also from Statistisches Amt/GDR (1990).

For a comparison of industrial product dynamics between East and West German
regions, two problems must be addressed: (1) Relative to Western figures,
East German GIP figures are inflated through double counting at each
intermediate step of production (e.g., Stolper 1960). (2) In East German
statistics, the main mechanism of overstating real economic growth was to
understate inflation. This was done for ideological reasons--inflation is
not supposed to exist in a system where prices are nominally frozen. For
several reasons (see the discussion in Budde et al. 1991), however, had
inflation been calculated in the East in the same way as this was done in
the West, it would have been much higher in East Germany than officially
reported.\footnote{%
One mechanism has recently been exemplified by Hoelder, the director of the
German Federal Statistical Office: He reports that the index of retail
prices rose, according to East German statistics, over the years 1980-89 by
only 0.1\% annually. While this number is calculated correctly, and
consistent with the prices of the products quoted in East German statistics,
it encompasses only the change in prices for ''comparable goods'', but not
so-called ''new'' goods. When the increase in the price index was
recalculated according to West German methods--which adjust for changes in
the basket of goods over time--annual inflation was on average 12.3\%.
(Quoted in Budde et al. 1991, pp.91ff.).}

Point (1) implies that in Eastern statistics, GIP is not equivalent to value
added, but conceptually the same as Western turnover (''Umsatz'').
Therefore, we use West German turnover and East German GIP data in this
study.\footnote{%
Thanks are due to T.N. Srinivasan for suggesting this approach.} Point (2)
requires to make an assumption of what the East German real rate of growth
was had inflation been computed for 1955-89 as it had for West Germany.
Equivalently, we can ask by how much the real rate of growth was overstated
in the East.

Because we want to prevent an understatement of the growth achievements in
Eastern regions, we adjust the rate of growth of real GIPW in the East
downward by 25\%, uniformly across all regions and over all years. We
consider this as the upper bound of any estimate of East German industrial
product growth which is consistent with the post-reunification evidence on
the East-West productivity gap in 1989, as discussed above. Depending on
whose productivity gap estimates for 1989 one accepts, the adjustment of
real growth in East Germany should be even larger than 25\%.\footnote{%
Winiecki's (1986) pre-reunification analysis, which turned out to be
consistent with most estimates of the ex-post productivity gap in 1989,
suggests that between 1951-73, the actual growth of the East German net
national product was only 55\% of the official figures; hence, a 45\%
downward adjustment, as opposed to the 25\% which we propose here. Another
way of looking at the proposed adjustment is to compute what the equivalent
rate of inflation to a 25\% downward adjustment of growth is. Making this
calculation, we find that it implies an equivalent rate of inflation of
1.17\% per year; with the official rate of inflation equal to zero, the rate
of 1.17\% is much lower than the average rate of inflation in West German
regions over this period, with 2.74\%.}

Although an across-the-board downward revision of official East German
figures is common practice for studies on the East German economy during
this era,\footnote{%
Melzer (1980), p.76, e.g., reports that the DIW estimates of the GDR
performance in the late 1970s relied on an adjustment of official East
German annual growth figures by two percentage points.} it is to some degree
arbitrary even ex-post, because the 1989 estimates on the productivity gap
between East and West varied substantially (see above). The sensitivity
analysis in Keller (1997), therefore, allows for alternative adjustments of
East German real growth to assess whether the particular adjustment used
here is driving qualitative results, and finds that this possibility can be
excluded. Lastly, because East and West German GIPW levels in 1955 were not
comparable--West German levels were higher, but we do not know exactly by
how much--there is no loss in placing the average East German region at par
with the average West German region. Summary statistics of the data we use
are shown in Table 1.

The pre-reunification period is divided into six subperiods with a length of
five years each, and the subperiod of 1985-88, with three years.\footnote{%
We exclude data for the year 1989 from the sample because of internal
consistency reasons: By 1989, the former East German statistical office was
strongly under the influence of West German concepts and politicians,
causing a break with the pre-reunification tradition of data collection.}%
{\normalsize \ }We believe that working with five-year long subperiods of
smoothed time series is a compromise between a subperiod long enough so that
transitional growth effects can be identified, and at the same time not too
short so that cyclical or outlier effects might have no strong impact on the
estimation results. In addition to that, we have smoothed the data by
employing three-year moving averages in order to reduce the distorting
effects of outliers and short-run movements.

The first eleven regions in Table 1 are Western \textit{Laender}, the last
fifteen were the Eastern \textit{Bezirke} until German reunification. The
first column shows the gross industrial product per worker (GIPW) in 1955.
The second column shows the GIPW in 1985, the initial year of the last
subperiod. The last column in Table 1 shows the share of the labor force
working in the agricultural sector by industry, averaged over the whole
pre-reunification period. From that it is clear that, on average, the
structural change away from agriculture was faster in the West than in the
East.

\subsection{Post-reunification Data}

To preserve the continuity of the analysis, we analyze also after German
re-unification gross industrial production (not GDP).{\normalsize \ }We
calculate TFP growth series for both Eastern and Western states from data in
Statistisches Bundesamt (1996) and Arbeitskreis (1995,1996) for the years
1991-1995; for 1990, the German statistical office did not publish official
data for Eastern regions. In Arbeitskreis (1995, 1996), there are figures on
the number of manufacturing workers for 1991-95, as well as on current price
and constant price manufacturing value added, which we utilize as the output
measure. This latter fact allows to compute state-specific deflators for the
manufacturing industry. In Statistisches Bundesamt (1996), one finds current
price gross investment in manufacturing (and mining) for the years
1991/2-1993/4. After computing constant price investment series using the
output deflators, we use the value added and number of workers data to
predict constant price gross investment for the year 1994/5.\footnote{%
This is done in separate regressions for East and West German states; the
main results of this section do not depend on that.} We finally estimate
capital stocks for the states between 1991 and 1995 using the perpetual
inventory method.\footnote{%
The benchmark capital stock for 1991, $k_{1991}$ is estimated in a standard
way: $k_{1991}=\frac{inv_{1991}}{(g_{9194}+\delta )},$ where $inv_{1991}$ is
real gross investment in 1991, $g_{9194}$ is the rate of growth of real
investment between 1991 and 1994, and $\delta $, the rate of depreciation,
is set at $0.1$. For the years $t=1992-1995$, $k_t=(1-\delta )k_{t-1}+inv_t.$
The main results do not depend on the particular choice of $\delta .$}

\section{Estimation Results}

\subsection{Pre-reunification Period: Dynamic Panel Estimation}

We will present estimates based on two different techniques: a linear
least-squares dummy variable (LSDV) estimation, and the minimum distance
(MD) estimation proposed by Chamberlain (1982). The LSDV procedure amounts
to estimating a dummy for each economy and subperiod, as well as the slope
coefficient $\beta $, by ordinary least squares (OLS). The estimation
equation is (\ref{elev}) from above 
\[
\ln q(t_2)=\chi +\mu _i+\upsilon _t+\beta \,\ln q(t_1)+\varepsilon _{i,t}, 
\]
where, for instance, for the 1955-60 subperiod, $q(t_2)$ is equal to the
1960 per worker output, and $q(t_1)$ is equal to the 1955 level. Hence,
there is the complication that the right-hand side includes the lagged
dependent variable. It is well known that this implies that OLS estimates of 
$\beta $ and $\mu _i$ are inconsistent for any number of subperiods $%
T<\infty $ (see, e.g., Amemiya 1985, Hsiao 1986). Because in this study, $T$
is only equal to 7, the OLS\ estimates of (\ref{elev}) are likely to be
severely biased. However, Monte-Carlo methods can be used to assess the
direction and the size of the bias (as a function of any 'true' $\beta $ and 
$T$). With eleven states in West Germany and fifteen regions in the East, $%
N= $ 26, and the number of subperiods $T=$ 7. The results can be seen in
Table 2a. Asymptotic standard errors are given in parentheses.{\normalsize \ 
}

The LSDV estimation gives a coefficient $\beta ^b$ of $0.716$, which is
significant at a standard 5\% level of significance. Because this estimate
is biased, we use Monte Carlo experiments and response surface techniques to
estimate the direction and extent of the bias.\footnote{%
These methods are described in detail in the appendix.} Briefly, a limited
number of Monte Carlo experiments for different values of 'true' $\beta $'s
and number of subperiods, $T,$ result in different biases as a function of $%
\beta $ and $T.$ The response surface technique then allows the bias of the
coefficient $\beta $ in (\ref{elev}) to be estimated for any combination of $%
\left( \beta ,T\right) $. With this bias function, we can infer the unbiased
estimate of $\beta $ in (\ref{elev}) from the estimated coefficient $0.716$
in Table 2a. We find the unbiased estimate of $\beta $ to be equal to $\beta
^{bc}=0.973$, given in the last line of Table 2a.

The LSDV estimation together with bias correction might appear as not the
preferred estimation technique, as it is indirect. Therefore, we also
present an estimate of $\beta $ from a MD estimation as proposed in
Chamberlain (1982). This estimation technique is equivalent to limited
information maximum likelihood, hence efficient relative to the class of
estimators that do not impose a priori restrictions on the
variance-covariance matrix of the errors. Therefore, the MD estimator can
accommodate arbitrary patterns of serial correlation and unspecified
heteroskedasticity. Its disadvantages are that it is computationally less
robust, and it relies on the presence of a strictly exogenous variable.%
\footnote{%
The MD estimation procedure is laid out in the appendix.} In our context, we
employ the share of employment in agriculture in the initial year of the
subperiod as this exogenous variable. The results are shown in Table 2b.

As one sees from Table 2b, the $\beta $ from the MD-estimation is
significantly different from zero at any standard level of significance. The
point estimate of $0.942$ is close to the bias-corrected LSDV estimate of $%
0.973$. The parameter $\lambda $--which governs the speed of convergence
towards the steady-state growth path--implied by the estimate of $0.942$ is
equal to 1.27\%. This is lower than the estimate by Barro and Sala-i-Martin
(1992) of 2\%., and, correspondingly, it would lead to an even longer
estimated time until East Germany had caught up in the post-reunification
era were we to use this estimated value of $\lambda $ to make this
prediction.

However, we have neglected so far the growth effects due to differences in
the rate of technical change across regions, as captured by the $\mu _i$'s.
In Figure 5 the twenty-six regional fixed effects for 1955-88 are shown,
based on the bias-corrected LSDV slope estimate of $0.973$.\footnote{%
The fixed effects calculated from the MD slope estimate of $0.942$ are very
similar to what is shown in Figure 5.} By construction, these twenty-six
values sum to zero. In the left part of Figure 5, we see the estimated $\mu
_i$ for the West German regions; in the right part of the figure are the
East German fixed effects. Note that only one $\mu _i$ is estimated to be
negative in the West (or, in 9\% of all cases), whereas for East Germany, we
find nine out of fifteen (60\%) to be negative. On average, a West German
region has a $\mu _i$ of 0.02, whereas for the East, the average is equal to
-0.015. This means for the specific case of East and West Berlin, for
instance, that if East and West Berlin would start out at the same GIPW
level, after five years the GIPW level in West Berlin would be about 4.5\%
higher than in East Berlin due to differences in the rate of technical
change alone.

From these results, we reject the model given in Figure 1 where all
economies converge to the same steady-state growth path, corresponding to
the same rate of technical change across these economies. Instead, our
estimation provides evidence in favor of the augmented Solow-Swan model of
Figure 2. Suppose we abstract from differences in the rates of technical
change \textit{within} the East and the West of Germany during the period of
1955-88. Then the economy converging to the steeper steady-state growth path
captures West Germany during the period of 1955-88, whereas the East German
economy has been converging to the steady-state growth path with the lower
slope. It is clear from the figure that conditional convergence in the sense
of capital-deepening was present in Germany between 1955-88 at the same time
where the output per worker difference between East and West region was
increasing.

Moreover, the finding of different rates of technical change in East and
West Germany between 1955 and 1988 suggests that perhaps also in the
post-reunification era, this effect is important in determining the dynamics
of relative (East-West) output per worker. Specifically, we conjecture that
technical change could well be faster in the East than in the West for a
while, due to the adoption of new management techniques, a change in
incentive structures, and disembodied technological change in general. This
would lead to faster catch-up of the East as would be implied by the
capital-deepening model with identical rates of technical change. To
investigate this possibility, we estimate TFP growth in East and West German
regions for the years 1991-95.

\subsection{Post-Reunification Period: Growth Accounting Analysis}

As before, our focus is on differences of the rates of technical change
across economies. However, we cannot estimate these effects in the same way
as for the pre-reunification era, because the identifying assumptions we
have employed above no longer hold.\footnote{%
Both the initial level of technology $A\left( 0\right) ,$ for time $0=1989$
(the year of re-unification) in Eastern regions was lower than in Western
regions (see again Figure 4), and the rates of physical capital investments
have been considerably higher in the East than in the West.} But because we
have comparable data on capital and labor inputs in the production of all
regions, we can estimate whether there have been differences in the rate of
technical change across East and West German regions directly, following
Solow's (1957) growth accounting method.\footnote{%
Our framework is still the Solow-Swan model with exogenous differences in
the rates of technical change (with the minor caveat that above, technical
change was assumed to be Harrod-neutral, whereas now, we assume it to be
Hicks-neutral). What is different is the method we use to estimate
differences in the rate of technical change.}

Consider a constant returns to scale Cobb-Douglas production function for
gross industrial product with exogenous technical change, 
\begin{equation}
Q^{\prime }(t)=A(t)K(t)^\alpha L(t)^{1-\alpha },\,0<\alpha <1.  \label{hicks}
\end{equation}
From equation (\ref{hicks}), the standard growth accounting formula can be
derived through taking log-differences; we define $\Delta x(t)=\ln X(t)-\ln
X(t-1)$, then 
\begin{equation}
\Delta a(t)=\Delta q^{\prime }(t)-\alpha \Delta k(t)-\left( 1-\alpha \right)
\Delta l(t),  \label{tfp}
\end{equation}
and $\Delta a(t)$ is the rate of TFP growth between period $t$ and $t-1$,
which captures in this context the rate of technical change$.$ Assuming a
value for $\alpha =2/3$,\footnote{%
The qualitative results are identical if other plausible values for $\alpha $%
, such as 0.6 or 0.7, are chosen.} we have computed the rate of TFP growth
for the eleven states which constituted West Germany before reunification in
1989, and for five states which were formerly East Germany, plus East
Berlin. The results of this for the years 1991-1995 can be seen in Figure 6.

The five East German states, plus East Berlin, are on the right in Figure 6.
It is clear from the graph that the TFP growth rates of these regions have
been considerably faster than in the West, in particular during the early
years after reunification. Table 3 gives average rates of TFP growth over
1991-95. As the last column in Table 3 indicates, the estimated rate of TFP
growth of the average East German region was 10.3 percentage points higher
than for the average West German region. This clearly supports our
conjecture that the rate of technical change in East Germany has been
considerably above that of West Germany after 1989. It is also consistent
with the model we estimated for the pre-reunification period above. Further,
the development of TFP growth rates between 1991 and 95 also suggests that
the difference in the rates of technical change between East and West German
regions was highest in the year of 1990, when the Federal Statistical Office
did not publish data for Eastern regions. Moreover, we can show that the
rate of technical change in the East was not just higher because investment
rates in physical capital were higher, which rejects the notion of technical
change embodied in capital goods at least in its extreme form.\footnote{%
Consider a linear regression of TFP growth on capital stock growth and a
constant, with annual data for the six East German states for 1991-95 (24
observations). We find a slope coefficient of $-0.48$ with a standard error
of $0.319$, and, hence, no statistically significant correlation.}

\section{Conclusions}

In this paper, we have shown that the contribution of technical change in
the overall growth performance of East Germany since World War II has been
underemphasized by previous research, and argue that this has important
implications for assessing East Germany's growth prospects today. Using
estimation techniques and assumptions which build on the particular,
laboratory-type nature of the East and West German economic development
after 1945, we show that the rate of technical change has on average been
faster in West, relative to East German regions, in Germany's the
pre-reunification period. We claim that this is the reason why analyses
which solely relied on the effects of physical capital accumulation have
generally failed to account for the extent to which East Germany had fallen
behind West Germany's productivity level by 1989.

At the same time, employing growth accounting techniques, we demonstrate
that the rates of technical change in the post-reunification period have
been considerably higher in East than in the West between 1991 and 1995. We
therefore argue that any analysis which does not allow for the possibility
of technical change at differential speeds in East and West Germany will be
mistaken in assessing future economic growth in East Germany, in the same
way as the earlier estimates for the pre-unification era were wrong.
According to our estimates, East Germany will not remain the German
Mezzogiorno for 70 or 100 years (or forever). Instead, the performance of
the East German economy suggests a period of 20 years or less until
seventy-five percent of the West German output per capita level will be
reached.

It is important to note that this analysis has its own limitations. After
all, it is cast in a growth model which does not account for wage setting
above labor's marginal productivity in East Germany. Neither does it capture
the significant West German transfer payments and, in general, an activist
government policy influencing economic outcomes. We agree with those who
believe that this means that our time to catch-up forecast is associated
with a high degree of uncertainty. However, we do not believe that it
invalidate our central point that the dynamics of technical change will have
to be analyzed independently from capital investment rates in order to make
accurate predictions on East Germany's growth prospects.

In fact, taking into account the West German transfers to East Germany into
account suggests further research should focus even more, not less, on
technical change as opposed to physical capital investment, for the
following reasons. Figure 7 shows the growth rates of capital stock and TFP
for East and West German states between 1991-95. On the one hand, from the
capital stock growth rates, it appears that the high annual transfers from
West to East were at least in part coming at the expense of physical
investment in West German regions. On the other hand, turning to the TFP
growth rates, although these are much lower in the West than in the East,
they are positive in all West German states. In addition, they are not far
from the average TFP growth rates in West Germany in the decade before
reunification. The difference between these two developments is at least in
part due to the fact that physical capital investments are rival, whereas
disembodied technical change is, to some degree, non-rival.

Lastly, although this paper focuses only on East and West German regions,
differences in the rates of technical change are likely to be important in
determining overall performance in other economies as well. Future research
need answer the question of how to identify, measure, and estimate the
contribution of technical change as an independent source of economic growth
in a more general context.\newpage 

\pagestyle{empty}\appendix

\section{Derivation of the empirical implications of the Solow-Swan model}

We start out with 
\begin{equation}
Q\,(t)=K\,(t)^\alpha \,(A(t)\,L(t))^{1-\alpha }\,\,\,,\text{\thinspace }%
0<\alpha <1,  \label{1}
\end{equation}
where $Q$ is output, $K$ physical capital, $L$ labor, and $A$ the level of
technology, all functions of time, $t$. $L$ and $A$ are growing at the
exogenously given rates $n$ and $g$: $L(t)=L(0)e^{nt}$ and $A(t)=A(0)e^{gt}$%
. The model assumes that the savings rate $s$ is constant. Defining $%
k_e\equiv K/(AL)$ and $q_e\equiv Q/(AL)$ as capital and output,
respectively, per efficiency unit of labor, then $k_e$ changes over time as 
\begin{equation}
\dot k_e=s\,k_e^\alpha -(n+g+\delta )\,k_e.  \label{3}
\end{equation}
Here, $\delta $ is the rate of depreciation. This has the solution $%
[k_e\left( t\right) ]^{1-\alpha }=(1-e^{-\lambda t})[k_e^{*}]^{1-\alpha
}+e^{-\lambda \,t}[k_e(0)]^{1-\alpha },$ with the definitions of $%
k_e^{*}=[s/(n+g+\delta )]^{(1-\alpha )^{-1}}$ and $\lambda =(n+g+\delta
)(1-\alpha ),$ where $k_e^{*}$ denotes the steady-state value of $k_e$. The
steady-state value of $q_e$, denoted by $q_e^{*}$, is given by $%
q_e^{*}=[s/(n+g+\delta )]^{\alpha /(1-\alpha )}.$ To obtain an expression
which is linear in $k_e$ (resp. $q_e$)$,$ perform a Taylor expansion of
equation (\ref{3}) which results in 
\begin{equation}
\frac{d\,\ln q_e(t)}{d\,t}=\lambda \,[\ln q_e^{*}-\ln q_e(t)]\,\,.  \label{5}
\end{equation}
The solution of equation (\ref{5}) implies, after rearranging, that for some 
$\Delta =$ $t_2-t_1$, 
\begin{equation}
\ln q_e(t_2)-\ln q_e(t_1)=(1-e^{-\lambda \,\Delta })\,\ln
q_e^{*}-(1-e^{-\lambda \,\Delta })\ln q_e(t_1)  \label{6}
\end{equation}
Substituting in for $q_e^{*}$ and rewriting the equation in terms of output
per capita $q\equiv Q/L$ gives equation (\ref{sev}) in the text.

\section{Bias-Correction for the LSDV Model}

\subsection{The Monte Carlo Experiments}

For a given region $i$,\footnote{%
See Davidson and McKinnon (1993).} 
\[
\begin{array}{c}
y_t=\beta _j\,y_{t-1}+u_t.
\end{array}
\,\,\,\, 
\]
Here, $\,u_t\sim N(0,\sigma ^2),$ $\beta _j$ = 0.5, 0.6, 0.7, 0.8, 0.9, and
we consider four different numbers of subperiods $T_k$, namely $T_k$ = 6,
20, 50, and 150. We conduct 1000 experiments for each combination ($\beta _j$%
, $T_k$). The results are given in Table A, where the $\hat \beta _j$ column
gives the average estimates from applying equation (\ref{elev}) above for a
combination of 'true' parameter and number of subperiods $\left( \beta
_j,T_k\right) $. Control variates, denoted $\tau ,$ are used to improve the
accuracy of the simulations 
\[
\tau =T^{\,-\frac 12}\sum_{t=1}^T\,u_t\,y_{t-1} 
\]
Intuitively, the ''naive'' simulated LSDV estimator uses only the
information that $E\left[ u_t\right] =0$, for all $t$, whereas the control
variate-simulated LSDV estimator uses the specific value of $u_t$. This
reduces the standard error of the point estimate, which can be thought of as
increasing the number of simulations (to more than 12-fold, see the last
column in Table A).

\subsection{The Bias Function (Response Surface)}

The Monte-Carlo results show that the bias of the LSDV estimator is a
function $\Psi $ which depends on $\beta _j$, and $T_k$. The specific form
of is unknown; we model $\Psi (\beta _j,T_k)$ as a function of a parameter
vector $\mathbf{\eta }$ which will be estimated. The $i$th experiment
generates an estimated bias $\psi _i^e$, $i$ = 1,..., 20. A good
approximation for $\Psi $(.), with all variables standardized by the
standard error of experiment ($j$,$k$), is (see Davidson and McKinnon 1993): 
\begin{equation}
\psi _i^e=\eta _1\left( \frac{\beta _j^0}{T_k}\right) +\eta _2\left[ \left( 
\frac{\beta _j^0}{T_k}\right) \left( 1-(\beta _j^0)^2\right) ^{-\frac
12}\right] +\varsigma _i  \label{a3}
\end{equation}
where $\varsigma _i$ is an error term. This regression produces the
following results: $\eta _1(s.e.):-3.51$ $(0.1),$ $\eta _2(s.e.)=0.383$ $%
(0.059),$ a F-statistic of $3388,$ and an adjusted $R^2$ of $0.997.$ From
this, and the estimates of $\eta _1$ and $\eta _2$, we can solve for the
''true'' $\beta ^0$.

\section{The Minimum Distance Estimator}

Chamberlain's (1982) MD estimator has, in the present context, the following
form: 
\[
y_{i,t}=\beta \,y_{i,t-1}+\gamma \,x_{i,t\,}+\mu _i+\varepsilon
_{i,t\,\,\,\,}\,\,, 
\]
where $x_{i,t}$ is an exogenous variable. The data has been transformed
through the inclusion of time-fixed effects. In addition, it is assumed that 
\begin{equation}
\begin{array}{ccc}
\mu _i & = & \kappa _1x_{i1}+\kappa _2x_{i2}\,+\ldots +\,\kappa
_Tx_{iT}+\zeta _i \\ 
y_{i0} & = & \theta _1x_{i1}+\theta _2x_{i2}\,+\ldots +\,\theta
_Tx_{iT}+\tau _i
\end{array}
\label{14}
\end{equation}
where $E[\zeta _i\mid x_{i1},..,x_{iT}]=0$, $E[\tau _i\mid
x_{i1},..,x_{iT}]=0$. The first step is to express $y_{i,t}$, $t=1,..,7$,
only in terms of $y_{i0}$ and $\mu _i$. Then $y_{i0}$ and $\mu _i$ are also
substituted for by the exogenous variables. This results in 
\begin{equation}
\mathbf{Y=\pi \,X+u}  \label{15}
\end{equation}
where $\mathbf{u}$ is the composite error term consisting of $\varepsilon
_{i,t}$ only if we substitute from (\ref{14}) the conditional expectations
of $y_{i0}$ and $\mu _i$. Here, $\mathbf{Y=\,}(y_{i1},y_{i2},..,y_{i7})^{%
\prime }$, $\mathbf{X}=(x_{i1},x_{i2},..x_{i7})^{\prime }$, and $\mathbf{\pi
}$ equals $\pi _1+\pi _2+\pi _3,$ with
\[
\pi _1=\left[
\begin{array}{ccccccc}
\gamma & 0 & 0 & 0 & 0 & 0 & 0 \\ 
\beta \gamma & \gamma & 0 & 0 & 0 & 0 & 0 \\ 
\beta ^2\gamma & \beta \gamma & \gamma & 0 & 0 & 0 & 0 \\ 
\beta ^3\gamma & \beta ^2\gamma & \beta \gamma & \gamma & 0 & 0 & 0 \\ 
\beta ^4\gamma & \beta ^3\gamma & \beta ^2\gamma & \beta \gamma & \gamma & 0
& 0 \\ 
\beta ^5\gamma & \beta ^4\gamma & \beta ^3\gamma & \beta ^2\gamma & \beta
\gamma & \gamma & 0 \\ 
\beta ^6\gamma & \beta ^5\gamma & \beta ^4\gamma & \beta ^3\gamma & \beta
^2\gamma & \beta \gamma & \gamma
\end{array}
\right] 
\]
and $\pi _2$ and $\pi _3$ given by
\[
\pi _2=\left[
\begin{array}{c}
\beta \\ 
\beta ^2 \\ 
\beta ^3 \\ 
\beta ^4 \\ 
\beta ^5 \\ 
\beta ^6 \\ 
\beta ^7
\end{array}
\right] \,\,\theta ^{\prime }\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\pi
_3=\left[ 
\begin{array}{c}
1 \\ 
1+\beta \\ 
1+\beta +\beta ^2 \\ 
1+\beta +\beta ^2+\beta ^3 \\ 
1+\beta +\beta ^2+\beta ^3+\beta ^4 \\ 
1+\beta +\beta ^2+\beta ^3+\beta ^4+\beta ^5 \\ 
1+\beta +\beta ^2+\beta ^3+\beta ^4+\beta ^5+\beta ^6
\end{array}
\right] \,\,\kappa ^{\prime }\,\,\,, 
\]
where $\,\theta ^{\prime }=(\theta _1,..,\theta _7)$, and $\kappa ^{\prime
}=(\kappa _1,..,\kappa _7)$. If the $x_{i,t\text{ }}$are strictly exogenous,
one can estimate (\ref{15}) by OLS. The matrix $\mathbf{\pi }$ has 49
elements which are nonlinear functions of the underlying 16 coefficients $%
\beta ,\,\gamma ,\,\,\theta ^{\prime }$, and $\kappa ^{\prime }.$ We denote
these by $\phi $. MD estimation then amounts to finding the optimal $\phi $
by imposing the restrictions in $\mathbf{\pi }$ and minimizing
\[
\hat \phi =\arg \min (vec\,\pi -g(\phi ))^{\prime }A_N^{-1}(vec\,\pi -g(\phi
))\,\,\,\,\,, 
\]
where $g(\phi )$ is the vector valued function mapping the elements of $\phi 
$ into vec $\pi $, and $A_N^{-1}$ is the optimal $\overline{}$weighing
matrix as proposed by Chamberlain. The estimation relies on its consistent
sample analog, which is the inverse of 
\[
\begin{array}{c}
\hat \Omega =\frac 1N\sum_i^N\left[ (y_i-\hat \pi \,x_i)\,\,(y_i-\hat \pi
\,\,x_i)^{\prime }\,\otimes \,S_x^{-1}(\,x_i\,x_i^{\prime
}\,)\,S_x^{-1}\right] \,\,, \\ 
\\ 
\text{where}\,\,\,S_x=\frac 1N\sum_{i=1}^Nx_i\,x_i^{\prime }\,\,\,.
\end{array}
\]
{\footnotesize \ \newpage}{\normalsize \ }

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\newpage\ {\small 
\[
\fbox{%
\begin{tabular}{l|l|l|l}
\multicolumn{4}{l}{TABLE\ 1: Summary Statistics by Region} \\ \hline\hline
\multicolumn{1}{l|}{Region} & \multicolumn{1}{l|}{$
\begin{array}{c}
\text{GIPW in 1955} \\ 
\text{in 1000 DM} \\ 
\text{(1980 West)}
\end{array}
$} & \multicolumn{1}{l|}{$
\begin{array}{c}
\text{GIPW in 1985} \\ 
\text{in 1000 DM} \\ 
\text{(1980 West)}
\end{array}
$} & \multicolumn{1}{l}{$
\begin{array}{c}
\emptyset \text{ Share of} \\ 
\text{Agriculture} \\ 
\text{in the Labor} \\ 
\text{Force (per cent)}
\end{array}
$} \\ \hline
\multicolumn{1}{l|}{Schleswig-Holstein} & \multicolumn{1}{|c}{60.92} & 
\multicolumn{1}{|c}{187.66} & \multicolumn{1}{|c}{10.25} \\ \hline
\multicolumn{1}{l|}{Niedersachsen} & \multicolumn{1}{|c}{59.36} & 
\multicolumn{1}{|c}{202.53} & \multicolumn{1}{|c}{12.9} \\ \hline
\multicolumn{1}{l|}{Nordrhein-Westf.} & \multicolumn{1}{|c}{53.79} & 
\multicolumn{1}{|c}{181.06} & \multicolumn{1}{|c}{4.34} \\ \hline
\multicolumn{1}{l|}{Hessen} & \multicolumn{1}{|c}{48.22} & 
\multicolumn{1}{|c}{151.95} & \multicolumn{1}{|c}{7.25} \\ \hline
\multicolumn{1}{l|}{Rheinland-Pfalz} & \multicolumn{1}{|c}{51.34} & 
\multicolumn{1}{|c}{190.63} & \multicolumn{1}{|c}{12.71} \\ \hline
\multicolumn{1}{l|}{Baden-Wuerttbg.} & \multicolumn{1}{|c}{46.61} & 
\multicolumn{1}{|c}{156.04} & \multicolumn{1}{|c}{9.3} \\ \hline
\multicolumn{1}{l|}{Bayern} & \multicolumn{1}{|c}{45.07} & 
\multicolumn{1}{|c}{153.35} & \multicolumn{1}{|c}{15.08} \\ \hline
\multicolumn{1}{l|}{Saarland} & \multicolumn{1}{|c}{33.29} & 
\multicolumn{1}{|c}{157.35} & \multicolumn{1}{|c}{3.39} \\ \hline
\multicolumn{1}{l|}{Hamburg} & \multicolumn{1}{|c}{87.7} & 
\multicolumn{1}{|c}{496.29} & \multicolumn{1}{|c}{1.3} \\ \hline
\multicolumn{1}{l|}{Bremen} & \multicolumn{1}{|c}{73.28} & 
\multicolumn{1}{|c}{243.97} & \multicolumn{1}{|c}{1.21} \\ \hline
\multicolumn{1}{l|}{Berlin-West} & \multicolumn{1}{|c}{44.48} & 
\multicolumn{1}{|c}{239.15} & \multicolumn{1}{|c}{0.35} \\ \hline\hline
\multicolumn{1}{l|}{Berlin-East} & \multicolumn{1}{|c}{55.97} & 
\multicolumn{1}{|c}{189.28} & \multicolumn{1}{|c}{1.25} \\ \hline
\multicolumn{1}{l|}{Cottbus} & \multicolumn{1}{|c}{43.57} & 
\multicolumn{1}{|c}{119.63} & \multicolumn{1}{|c}{15.98} \\ \hline
\multicolumn{1}{l|}{Dresden} & \multicolumn{1}{|c}{48.82} & 
\multicolumn{1}{|c}{158.29} & \multicolumn{1}{|c}{10.03} \\ \hline
\multicolumn{1}{l|}{Erfurt} & \multicolumn{1}{|c}{44.36} & 
\multicolumn{1}{|c}{152.71} & \multicolumn{1}{|c}{16.03} \\ \hline
\multicolumn{1}{l|}{Frankfurt/Oder} & \multicolumn{1}{|c}{72.11} & 
\multicolumn{1}{|c}{253.9} & \multicolumn{1}{|c}{21.9} \\ \hline
\multicolumn{1}{l|}{Gera} & \multicolumn{1}{|c}{48.29} & \multicolumn{1}{|c}{
191.97} & \multicolumn{1}{|c}{12.63} \\ \hline
\multicolumn{1}{l|}{Halle} & \multicolumn{1}{|c}{63.38} & 
\multicolumn{1}{|c}{174.5} & \multicolumn{1}{|c}{12.59} \\ \hline
\multicolumn{1}{l|}{Karl-Marx Stadt} & \multicolumn{1}{|c}{41.7} & 
\multicolumn{1}{|c}{148.69} & \multicolumn{1}{|c}{7.22} \\ \hline
\multicolumn{1}{l|}{Leipzig} & \multicolumn{1}{|c}{51.27} & 
\multicolumn{1}{|c}{147.61} & \multicolumn{1}{|c}{10.28} \\ \hline
\multicolumn{1}{l|}{Magdeburg} & \multicolumn{1}{|c}{59.73} & 
\multicolumn{1}{|c}{173.11} & \multicolumn{1}{|c}{20.15} \\ \hline
\multicolumn{1}{l|}{Neubrandenburg} & \multicolumn{1}{|c}{60.18} & 
\multicolumn{1}{|c}{119.45} & \multicolumn{1}{|c}{35.62} \\ \hline
\multicolumn{1}{l|}{Potsdam} & \multicolumn{1}{|c}{63.87} & 
\multicolumn{1}{|c}{180.71} & \multicolumn{1}{|c}{20.86} \\ \hline
\multicolumn{1}{l|}{Rostock} & \multicolumn{1}{|c}{59.34} & 
\multicolumn{1}{|c}{154.51} & \multicolumn{1}{|c}{19.68} \\ \hline
\multicolumn{1}{l|}{Schwerin} & \multicolumn{1}{|c}{71.09} & 
\multicolumn{1}{|c}{141.15} & \multicolumn{1}{|c}{28.91} \\ \hline
\multicolumn{1}{l|}{Suhl} & \multicolumn{1}{|c}{40.08} & \multicolumn{1}{|c}{
127.25} & \multicolumn{1}{|c}{11.64}
\end{tabular}
}
\]
}\newpage\ 
\end{thebibliography}

{\normalsize {\small 
\[
\fbox{$
\begin{tabular}{ll|c}
\multicolumn{3}{l}{Table 2a: Results for Transitional Growth Effects with
LSDV Estimation} \\ \hline\hline
&  &  \\ 
$%
\begin{array}{c}
\beta ^b:\ln q(t_1) \\ 
(s.e.)
\end{array}
$ & $%
\begin{array}{c}
\text{biased} \\ 
\text{estimate}
\end{array}
$ & $%
\begin{array}{c}
0.716 \\ 
(0.061)
\end{array}
$ \\ 
&  &  \\ 
R$^2$ &  & 0.961 \\ 
&  &  \\ 
No. of observations &  & 182 \\ 
&  &  \\ 
$%
\begin{array}{c}
\beta ^{bc}:\ln q(t_1) \\ 
(s.e.)
\end{array}
$ & $%
\begin{array}{c}
\text{estimate after} \\ 
\text{bias correction}
\end{array}
$ & $0.973$
\end{tabular}
$}
\]
}}\newpage\ 

{\small 
\[
\fbox{%
\begin{tabular}{l|c}
\multicolumn{2}{l}{$
\begin{array}{cc}
\text{TABLE 2b:} & \text{Results for Transitional Growth} \\ 
& \text{Effects with MD Estimation}
\end{array}
$} \\ \hline\hline
&  \\ 
$
\begin{array}{c}
\beta :\ln q(t_1) \\ 
(s.e.)
\end{array}
$ & $
\begin{array}{c}
0.942 \\ 
(0.26)
\end{array}
$ \\ 
&  \\ 
$
\begin{array}{c}
\gamma :\text{ coefficient on} \\ 
\text{exog. variable} \\ 
(s.e.)
\end{array}
$ & $
\begin{array}{c}
-0.834 \\ 
(0.04)
\end{array}
$ \\ 
&  \\ 
No. of observations & 182
\end{tabular}
}
\]
}\newpage\ 

{\small 
\[
\fbox{%
\begin{tabular}{l|c|c|c|c|c}
\multicolumn{6}{l}{TABLE 3: Post-Reunification TFP Growth Rates} \\ 
\hline\hline
\multicolumn{1}{l|}{} &  &  &  &  &  \\ 
\multicolumn{1}{l|}{} & 1991/2 & 1992/3 & 1993/4 & 1994/5 & $\emptyset $
1991-95 \\ \hline
\multicolumn{1}{l|}{} &  &  &  &  &  \\ 
\multicolumn{1}{l|}{Eastern Regions} & 0.254 & 0.077 & 0.104 & 0.052 & 0.122
\\ 
\multicolumn{1}{l|}{} &  &  &  &  &  \\ 
\multicolumn{1}{l|}{Western Regions} & -0.005 & -0.021 & 0.07 & 0.032 & 0.019
\\ 
\multicolumn{1}{l|}{} &  &  &  &  &  \\ 
\multicolumn{1}{l|}{Difference (East-West)} & 0.259 & 0.098 & 0.034 & 0.02 & 
0.103
\end{tabular}
} 
\]
}{\footnotesize 
\[
\fbox{%
\begin{tabular}{llcc}
\multicolumn{4}{l}{TABLE\ A} \\ \hline\hline
\multicolumn{1}{l|}{$\beta _j$} & \multicolumn{1}{l|}{T$_k$} & 
\multicolumn{1}{c|}{$\hat \beta _j$ / (s.e.)} & $
\begin{array}{c}
\text{Equivalent No. of Simulations} \\ 
\text{using control variates}
\end{array}
$ \\ \hline
\multicolumn{1}{l|}{0.5} & \multicolumn{1}{l|}{6} & \multicolumn{1}{c|}{$%
0.225$ / (0.0026)} & 1382 \\ \hline
\multicolumn{1}{l|}{0.5} & \multicolumn{1}{l|}{20} & \multicolumn{1}{c|}{$%
0.422$ / (0.0013)} & 3151 \\ \hline
\multicolumn{1}{l|}{0.5} & \multicolumn{1}{l|}{50} & \multicolumn{1}{c|}{$%
0.467$ / (0.8 $\times 10^{-3}$)} & 6766 \\ \hline
\multicolumn{1}{l|}{0.5} & \multicolumn{1}{l|}{150} & \multicolumn{1}{c|}{$%
0.49$ / (0.5$\times 10^{-3})$} & 12685 \\ \hline
\multicolumn{1}{l|}{0.6} & \multicolumn{1}{l|}{6} & \multicolumn{1}{c|}{$%
0.293$ / (0.0027)} & 1208 \\ \hline
\multicolumn{1}{l|}{0.6} & \multicolumn{1}{l|}{20} & \multicolumn{1}{c|}{$%
0.511$ / (0.0013)} & 2762 \\ \hline
\multicolumn{1}{l|}{0.6} & \multicolumn{1}{l|}{50} & \multicolumn{1}{c|}{$%
0.567$ / (0.8$\times 10^{-3})$} & 5353 \\ \hline
\multicolumn{1}{l|}{0.6} & \multicolumn{1}{l|}{150} & \multicolumn{1}{c|}{$%
0.59$ / (0.4$\times 10^{-3})$} & 10140 \\ \hline
\multicolumn{1}{l|}{0.7} & \multicolumn{1}{l|}{6} & \multicolumn{1}{c|}{$%
0.363$ / (0.0027)} & 1082 \\ \hline
\multicolumn{1}{l|}{0.7} & \multicolumn{1}{l|}{20} & \multicolumn{1}{c|}{$%
0.604$/ (0.001)} & 2095 \\ \hline
\multicolumn{1}{l|}{0.7} & \multicolumn{1}{l|}{50} & \multicolumn{1}{c|}{
0.663 / (0.7$\times 10^{-3})$} & 4347 \\ \hline
\multicolumn{1}{l|}{0.7} & \multicolumn{1}{l|}{150} & \multicolumn{1}{c|}{
0.688 / (0.4$\times 10^{-3}$)} & 9578 \\ \hline
\multicolumn{1}{l|}{0.8} & \multicolumn{1}{l|}{6} & \multicolumn{1}{c|}{
0.428 / (0.0029)} & 1066 \\ \hline
\multicolumn{1}{l|}{0.8} & \multicolumn{1}{l|}{20} & \multicolumn{1}{c|}{
0.694 / (0.0011)} & 1642 \\ \hline
\multicolumn{1}{l|}{0.8} & \multicolumn{1}{l|}{50} & \multicolumn{1}{c|}{
0.76 / (0.6$\times 10^{-3})$} & 2783 \\ \hline
\multicolumn{1}{l|}{0.8} & \multicolumn{1}{l|}{150} & \multicolumn{1}{c|}{
0.787 / (0.3$\times 10^{-3})$} & 6175 \\ \hline
\multicolumn{1}{l|}{0.9} & \multicolumn{1}{l|}{6} & \multicolumn{1}{c|}{0.5
/ (0.0027)} & 1009 \\ \hline
\multicolumn{1}{l|}{0.9} & \multicolumn{1}{l|}{20} & \multicolumn{1}{c|}{
0.776 / (0.001)} & 1177 \\ \hline
\multicolumn{1}{l|}{0.9} & \multicolumn{1}{l|}{50} & \multicolumn{1}{c|}{
0.855 / (0.5$\times 10^{-3})$} & 1752 \\ \hline
\multicolumn{1}{l|}{0.9} & \multicolumn{1}{l|}{150} & \multicolumn{1}{c|}{
0.886 / (0.3$\times 10^{-3})$} & 3889
\end{tabular}
} 
\]
}

\end{document}