For Germany, the fall of the Berlin wall meant the reunification of the country after 45 years of separation. There should be no doubt that the recent improvement in living standards in the former Eastern Bloc countries is one of the most important economic success stories in modern times. However, despite the fact that the former DDR is now much wealthier and better place to live in than 25 years ago, many Germans are quite critical about the economic reconstruction of East Germany. More specifically, many Germans are bitterly disappointed about the development of East Germany since 1989. Gross domestic product per inhabitant was only at about 67% of that of West Germany in 2013 despite the fact that total federal transfers from the Western States to the Eastern States have amounted to about 2 trillion Euros from 1990 to 2014. Only a fraction of the money was spent on infrastructure (around 300 billion Euros) while most of the transfers involved social benefit programs such as unemployment benefits, pension payments, etc. All of the money originated from taxpayers in West Germany who, for the most part, think that they got little bang for the buck.

However, in what follows I will use the Solow growth model to show that it was utopic to think that equalization of income per capita would take place within a short period of time. The process of economic convergence is, in general, very lengthy and can take up to several decades, depending on the size of the initial income gap.

The Solow model was developed in the 1950s by Nobel laureate Robert Solow and was one of the first growth models and is as such very simplistic in contrast to more recently developed growth models. Despite its simplicity, however, the Solow model can teach us a quite a bit about the fundamental process of economic growth.

The starting point of the model is the Cobb-Douglas production function:

The model makes a number of assumptions about various parameters. Population growth n, the savings rate s, the depreciation rate d and productivity growth g are all assumed to be constant. This is, of course, quite restrictive and somewhat unrealistic.

The process of capital accumulation is described by a dynamic equation. It is not that difficult to solve the model mathematically, which I will not do here. Instead, I will focus on the general results of the model.

**The general results of the Solow model:**

*1.*

*Factor accumulation can only lead to transitional growth.*

Capital accumulation can lead to growth in per capita income in the short- to medium run, especially if the initial stock of capital is very low. However, the accumulation of capital runs into diminishing returns, which means that growth will eventually fall to 0

*without productivity gains (i.e. technological progress).*

*2.*

*Countries with the same production function (i.e. similar quality of institutions, infrastructure, education and same level of technology) and the same underlying parameters (i.e. the same savings rate, depreciation, population growth, productivity gains) will converge to the same level of income per capita in the long-run.*

This means that countries with a lower initial income per capita will grow faster than countries with higher initial income per capita that have the same steady state (long-run equilibrium). The process of catch-up growth one can observe in the low-income countries occurs because capital accumulation yields high returns if the initial stock of capital is very low, thus creating the possibility for very high (transitional) growth rates.

The prime examples of catch-up growth are Germany and Japan after World War II, for example, which eventually converged to a similar level of per capita income as the U.S.

China of today also experienced rapid catch-up growth thanks to capital accumulation with an average growth rate of almost 10% over the last two decades. The Solow model predicts that the country will not be able to sustain such high growth rates for much longer. Indeed, it is very likely that the recent economic slowdown in China (to growth rates of about 7%) is secular.

3.

*Long-run growth can only result from productivity gains.*

While factor accumulation can potentially lead to high growth rates in the short-run, these effects will not be long-lasting because of diminishing returns. Economic growth can only be sustained in the long-run if there are productivity gains in the economy. Breakthroughs in science and technology are the source of higher living standards and long-run growth would not be possible without innovation and technological progress.

*4.*

*The Solow model omits how innovation occurs.*

The ultimate source of growth, the rate of innovation, is not modeled in the Solow model, but is taken as given. This is obviously an abstraction from reality. The world technological frontier advances at the rate of innovation. A slowdown in technological progress would lead to a slower economic growth in the U.S. and other developed economies that are at the technological frontier. Developing countries, on the other hand, might initially be not affected by such a slowdown since they could still experience high catch-up growth thanks to factor accumulation.

More recently, more complicated so-called endogenous growth models have tried to explain how, why and at what speed innovation occurs.

*5.*

*Convergence is an economic process that can last for decades.*

As previously mentioned, a low-income country grow faster than a high-income countries with the same steady state, which means that both countries will eventually reach the same level of GDP per capita. This process, called conditional convergence, is very long-lasting. The Solow model predicts that the speed of convergence is equal to the following:

This value of 4% implies that Germany’s income gap to the U.S., for example, would halve in about 18 years if the two countries shared the same steady state. If Germany has an income per capita of 80% relative to the U.S., then it would have per capita income of 90% and 95% relative to the U.S. in 18 and 36 years, respectively (since the income gap of 20% halves in 9 years and the remaining income gap of 5% then halves again).

However, it turns out that the Solow model largely overestimates the speed of convergence by a factor of roughly 2. In their famous paper “A contribution to the empirics of economic growth”, the economists Mankiw, Romer and Weil have estimated that the speed of convergence is typically much closer to 2%. For OECD countries between 1960 and 1985, they find a value of 2,06 with a 95% confidence interval of [1.66, 2.46].

**The augmented Solow model:**

As we have seen above, most of the basic predictions of the Solow model seem to be confirmed by what one can observe from time series data on long-run economic growth. While the magnitude of some effects is misspecified in the Solow model, the sign of the effects seem to be right, in general. The overestimation of the convergence parameter thus does not represent a rejection of the model, which can be easily adapted. For instance, Mankiw, Romer and Weil simply add another factor of production, namely human capital H, to the model, which largely improves its predictive power:

Assuming that human capital ‘depreciates’ at the same rate as physical capital, a somewhat dubious assumption, then the convergence speed predicted by the model is now:

In what follows, I will look at the convergence between Eastern and Western Germany since the fall of the Berlin wall. I will take the year 1991 as the starting point. GDP per capita in Eastern Germany in 1991 was only at about 33% of that in the West, implying an income gap of 67%. Within 22 years, per capita income rose to 67% in 2013, meaning that the income gap between the East and the West was reduced to 33%. Assuming that East and West Germany share the same steady state, it is relatively easy to calculate the speed of convergence:

67% * (1-x)^22 = 33%

--> x = 3.16%

The calculated convergence speed for East Germany x is thus equal to about 3.2%, which is more than 50% higher than the empirical estimate of Mankiw, Romer and Weil. The difference is also highly statistically significant (at the 1% level). Nevertheless, even such a value implies that the income gap between the East and the West would halve only roughly every 24 years.

**Fast convergence in East Germany**

We have seen above that the actual convergence speed of East Germany is significantly higher than what international data suggests. Of course, there are several reasons why one would expect East Germany to converge faster.

1. East Germany has received enormous federal transfers from West Germany over the last 25 years, amounting to about 2 trillion Euros as of 2014.

2. Intra-German labor mobility sped up the process of wage equalization. Since 1989, East Germany lost 2 million inhabitants (13.5% of the population), most of it as a result of migration to the West. This, of course, has put some downward pressure on wages in West Germany (as supply of labor increases) while increasing wages in the East. Labor mobility thus accelerated the process of wage equalization. As of 2013, East to West migration seems to have come to a halt (http://www.telegraph.co.uk/news/worldnews/europe/germany/10466089/East-to-west-German-migration-trickles-to-a-halt-23-years-after-reunification.html).

With the exception of the EU, labor mobility is usually severely restricted across international borders. This and the absence of federal transfers mean that convergence within country should happen more rapidly than convergence across countries. The experience of Eastern Germany seems to confirm this hypothesis.

Of course, there are several reasons why one could expect Eastern Germany to converge at a much slower pace as of 1990. The inheritances from the socialist regime, bad infrastructure, a lower level of human capital per worker and institutions incompatible with a capitalist economy, would imply a much lower steady state, meaning that convergence could not happen at all.

As of 2014, institutions, infrastructure and the level of human capital per worker are roughly comparable between East and West Germany. In all likelihood, economic convergence will thus continue and the East will slowly catch up over time. But as we have seen above, this process is very slow and it will take up several decades until ‘full’ convergence is achieved.

By the way, the following is a link to a great interview in which Nobel laureate Robert Solow talks economic growth at the age of 90!!! Quite amazing and highly interesting!!!

http://www.econtalk.org/archives/2014/10/robert_solow_on.html