1

Unified Growth Theory Contradicted by the

Hyperbolic Economic Growth Ron W Nielsen

1

Environmental Futures Research Institute, Gold Coast Campus, Griffith University, Qld,

4222, Australia

November, 2015

Data describing historical economic growth are analysed. Included in the analysis

is the world and regional economic growth. Two samples of national economic

growth, in Australia and Japan, are also analysed. Historical economic growth was

hyperbolic, which immediately questions the applicability of the Unified Growth

Theory. This theory is repeatedly contradicted by the same data, which were used

in its formulation. The paradox becomes clear if we notice that these excellent

data were never scientifically analysed. Their analysis reveals that the Unified

Growth Theory explains phenomena that did not exist and consequently that it

does not explain the mechanism of the historical economic growth. The correct

understanding of the properties of hyperbolic distributions is indispensable in the

economic growth research.

Introduction

The discussion presented here is the extension to the earlier study of the historical economic

growth (Nielsen, 2015a). The primary objective of the earlier analysis was to find the

simplest mathematical representations of the historical economic growth data. We have

demonstrated that the natural tendency for the historical economic growth was to increase

hyperbolically. We shall now use the results of this earlier work to discuss the reliability of

the Unified Growth Theory (Galor, 2005, 2011), which is supposed to be explaining the

historical economic growth.

Galor appears to have experienced a problem with the mathematical analysis of data. He used

Maddison’s data describing historical economic growth (Maddison, 2001) but he has never

analysed them properly. His analysis consisted in plotting the data, often by selecting just a

few strategically-located points, and then using straight lines to join the plotted points. Based

on such representations of data and supported by earlier publications he formulated three

fundamental postulates of the economic growth.

1. Economic growth can be divided into three distinctly different regimes of growth

governed by distinctly different mechanisms of growth. These alleged regimes were:

a. Regime of Malthusian stagnation (or epoch of Malthusian stagnation), which

allegedly lasted for thousands of years and was characterised by random

fluctuations and oscillations around a stable Malthusian equilibrium.

Economic growth data (Maddison, 2001) extend only down to AD 1, but

1AKA Jan Nurzynski, r.nielsen@griffith.edu.au; ronwnielsen@gmail.com;

http://home.iprimus.com.au/nielsens/ronnielsen.html

All diagrams are presented in the Supplement (Unified Growth Theory Contradicted by the Historical Economic

Growth: Supplement).

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Galor claims that the epoch of Malthusian stagnation commenced in 100,000

BC (Galor 2008, 2012).

b. The post-Malthusian regime.

c. The sustained-growth regime.

2. Transition from the alleged stagnation to growth is described as a takeoff or as an

escape from Malthusian trap. The state of Malthusian equilibrium “persisted until the

end of the 18th century” (Galor, 2005, p. 180). The usual interpretation is that the

takeoff from stagnation to growth occurred around the time of the Industrial

Revolution, but it allegedly occurred at different times for different regions. This

alleged phenomenon is called the differential takeoffs. Galor claims that Malthusian

regime ended in AD 1750 for developed countries and in 1900 for less-developed

countries (Galor, 2008, 2012). To complete this list of precise timing we have to add

that the post-Malthusian regime was supposed to have been between 1750 and 1870

for developed countries and from 1900 for less-developed countries (Galor, 2008,

2012). We shall see that the economic growth data give no support for all these

claims, simply because they give no convincing evidence that there was ever any

takeoff from stagnation to growth. They also show that three regimes of growth

simply did not exist.

3. The natural extension of these two postulated (the existence of the three regimes of

growth and the existence of the differential takeoffs) is the postulate of the existence

of the great divergence, based on the claim that the alleged transitions from stagnation

to growth propelled economic growth along distinctly different trajectories for

different regions.

This is the backbone of the Unified Growth Theory. Galor then describes when, how and why

all these events happened. His explanations are aimed at explaining the mechanism of the

historical economic growth.

We are going to use exactly the same data as used by Galor but we are going to use the newer

source of these data (Maddison, 2010). In this updated compilation, historical data are the

same as used by Galor but the difference is only in the data extended to 2008.

In contrast with the approach used by Galor, we are going to analyse the data. We are going

to show that the three regimes of growth did not exist and that there were no takeoffs from

stagnation to growth because there was no stagnation. We are going to show that the Unified

Growth Theory is contradicted by the data used by Galor. We are going to demonstrate that

Galor describes and explains non-existing phenomena and consequently that his theory does

not explain the economic growth.

Our earlier analysis (Nielsen, 2015a) was based on using the method of reciprocal values

(Nielsen, 2014). This method is in turn based on the observation (von Foerster, Mora &

Amiot, 1960) that the growth of human population during the AD era was increasing

hyperbolically. Recent but limited analysis (Nielsen, 2014) indicated that historical economic

growth was also increasing hyperbolically.

Hyperbolic distributions appear to be creating serious problem with their interpretation.

Consequently, to link the present discussion to the previous work we shall show again how

hyperbolic growth is reflected in the historical economic growth. This is essential for

demonstrating how the Unified Growth Theory is demonstrably contradicted by data.

Hyperbolic distribution describing growth is represented by a reciprocal of a linear function:

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1( ) ( )S t a kt , (1)

where ( )S t is the size of the growing entity, while a and k are positive constants.

The reciprocal of such hyperbolic growth,1/ ( )S t , is represented by a decreasing linear

function:

1

( )a kt

S t. (2)

Hyperbolic distributions should not be confused with hyperbolic functions (sinh( )t ,

cosh( )t , etc). Furthermore, reciprocal functions should not be confused with inverse

functions. Thus, for instance, for the expression given by the eqn (1) the objective of finding

the inverse function would be to calculate time t for a given size ( )S t . The roles of the

dependent and independent variables are reversed. For the reciprocal function, the objective

is to convert eqn (1) into eqn (2). The roles of dependent and independent variables are not

changed.

Reciprocal values help in an easy and generally unique identification of hyperbolic growth

because in this representation hyperbolic growth is given by a decreasing straight line. Apart

from serving as an alternative way to analyse data, reciprocal values allow also for the

investigation of even small deviations from hyperbolic distributions because deviations from

a straight line can be easily noticed.

Reciprocal values allow also for an easy identification of different components of growth.

This property can be used, in the investigation of the validity of the Unified Growth Theory

(Galor, 2005, 2011), to see whether the past economic growth can be divided into three,

distinctly-different regions and whether there is a convincing evidence for the claimed

takeoffs from stagnation to growth.

When comparing mathematically-calculated distributions with the reciprocal values of data,

we have to remember that the sensitivity of the reciprocal values to small deviations increases

with the decreasing size S of the growing entity.

Suppose we have two values of S at a given time: 1( )S t and 2 ( )S t , representing, for instance,

the empirical and the calculated values. It is clear that

1

2

1 2

S SS

S S S, (3)

where S is either 1S or 2S . For a given S , 1S increases rapidly with the decreasing S.

The separation of small values of data from calculated distributions are magnified.

It should be also noted that the decreasing reciprocal values describe growth, while a

deviation to larger reciprocal values describes decline. Consequently, a diversion to a faster

trajectory will be indicated by a downward bending of a trajectory of the reciprocal values,

away from an earlier observed trajectory, while the diversion to a slower trajectory will be

indicated by an upward bending.

The data describing the historical economic growth (Maddison, 2001, 2010) do not allow for

a detailed analysis below AD 1500 because there are two large gaps in the data: between AD

1 and 1000 and between AD 1000 and 1500. The best sets of data are from AD 1500.

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However, the compilation prepared by Magnuson appears to be the best, if not the only,

source of the historical economic growth data.

Throughout the analysis presented here, the values of the Gross Domestic Product (GDP) will

be expressed in billions of the 1990 International Geary-Khamis dollars. Furthermore, in

order to examine the quality of fitted distributions to the small values of data, we shall

display the GDP values and their corresponding calculated curves using semilogarithmic

scales of reference. All diagrams are presented in a self-contained Supplement. The captions

to each diagram contain enough information to help to understand them without necessarily

reading the main text.

World economic growth

Results of mathematical analysis of the world economic growth are presented in Figures 1-3.

Reciprocal values of historical data can be fitted using straight line (representing hyperbolic

growth) between AD 1000 and 1955. From around 1955, the world economic growth started

to be diverted to a slower trajectory as indicated by the upward bending of the reciprocal

values. This section is magnified in Figure 2. Global economic growth is now approximately

exponential (Nielsen, 2014, 2015b).

Hyperbolic fit to the world GDP data (Maddison, 2010) is shown in Figure 3. The fit is

remarkably good. The point at AD 1 is only 77% away from the fitted curve. We would need

more data between AD 1 and 1000 to decide whether such a difference is of any significance.

Hyperbolic economic growth of the historical GDP has been uniquely identified by the

straight-line fitting the reciprocal values of data.

Parameters describing hyperbolic trajectory fitting the data between AD 1000 and 1955 are: 21.684 10a and 68.539 10k . The point of singularity is at 1972t . However, from

around 1955, the world economic growth started to be diverted to a slower trajectory

bypassing the singularity by 17 years (see Table 1).

The data and their analysis contradict the first and fundamental postulate of the Unified

Growth Theory (Galor, 2005, 2011), which claims the existence of the three regimes of

growth (the epoch of Malthusian stagnation, the post-Malthusian regime and the sustained

growth regime). What is remarkable about this contradiction is that the same source of data

was used during the development of the Unified Growth Theory. However, the data were

never scientifically analysed. Their interpretation was based on impressions.

The contrast between the Unified Growth Theory (Galor, 2005, 2011) and the data is clearly

demonstrated in Figure 1, presenting the time-dependence of the reciprocal values of data. In

this representation, the hyperbolic economic growth between AD 1000 and 1955 is uniquely

identified by a decreasing straight line and it would be unreasonable to divide such a straight

line into two or three arbitrarily-selected sections and claim different mechanisms of growth

for each section. Which point on a straight line should be selected to mark the boundary

between different patterns of growth? How can we claim different patterns of growth on a

straight line if the straight line shows clearly only one pattern?

Even a monotonically-changing curve fitting data would be sufficient to demonstrate the non-

existence of different stages of growth. To claim such stages we would have to show

convincingly that different mathematical distributions have to be used for different sections

of data. If the data are fitted well using a single mathematical distribution, it would be

unreasonable to insist that they are not fitted by a single distribution. However, the

demonstration of a single pattern of growth, and consequently the demonstration of a single

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mechanism of growth reflected in such a single pattern, is much easier if the data follow a

straight line.

We can also see that Industrial Revolution, 1760-1840 (Floud & McCloskey, 1994), had

absolutely no impact on the economic growth trajectory. The straight-line representing the

reciprocal values of the GDP data shown in Figure 1 did not change until 1955. There was no

boosting in the economic growth, no unusual acceleration at any time between AD 1000 and

1955, and no escape from Malthusian trap simply because there was no trap. Economic

growth was steadily and freely increasing without any constrains or signs of impedance or

retardation. The concept of Malthusian trap is not supported by data. Concepts promoted by

the United Growth Theory are contradicted by data.

The world economic growth was increasing steadily before and after the Industrial

Revolution as shown by either a steadily increasing hyperbolic distribution in Figure 3 or by

the steadily-decreasing straight line shown in Figure 1. There was no takeoff in the world

economic growth at any time, let alone around the time of the Industrial Revolution. This

concept, promoted in the Unified Growth Theory, is clearly contradicted by the data

describing the world economic growth.

Economic growth may have been slow over a long time but there is no convincing evidence

that it was ever stagnant. On the contrary, there is convincing evidence that it was hyperbolic,

and the characteristic feature of hyperbolic growth is a slow growth over a long time and a

fast growth over a short time. Hyperbolic growth increases monotonically and it is impossible

to locate a place marking a transition from a slow to fast growth because such a transitions

does not exist.

The postulate of the existence of the epoch of Malthusian stagnation is demonstrably

contradicted by the world economic growth data. This postulate is based on the incorrect

interpretation of data, which were never properly analysed. Their small values over a long

time are incorrectly interpreted as stagnation while failing to notice that they were increasing

hyperbolically.

The concept of takeoffs, promoted in the Unified Growth Theory, is also contradicted by the

world economic growth data. In science, single contradicting evidence in data is sufficient to

reject a theory promoting contradicted concepts or at least to show that the theory has to be

revised to reconcile it with the empirical evidence. However, we are going to demonstrate,

that the Unified Growth Theory is contradicted not only by the data describing the world

economic growth but also by the data describing regional economic growth, and even by the

data describing national economic growth.

It obviously makes no sense to explain why the economic growth was stagnant if it was not

stagnant. It obviously makes no sense to explain why there was a transition from stagnation

to growth if there was no transition. It obviously makes no sense to describe various socio-

economic conditions and use them to explain the mechanism of economic growth if there is

no convincing evidence that the discussed conditions were shaping the economic growth.

Such discussions of socio-economic conditions might be interesting for another reason but

not to explain the mechanism of economic growth.

Unified Growth Theory explains phenomena that did not exist. (Non-existing phenomena

can be not only described but also convincingly explained.) Consequently, this theory does

not explain the mechanism of the economic growth.

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Western Europe

The growth of the GDP in Western Europe is shown in Figures 4-6. It is the growth for the

total of 30 countries: Austria, Belgium, Denmark, Finland, France, Germany, Italy, The

Netherlands, Norway, Sweden, Switzerland, United Kingdom, Greece, Portugal, Spain and

for 14 small, but unspecified countries. Ireland is missing in this list because it was included

only from 1921.

The best hyperbolic fit is between AD 1500 and 1900. Parameters for this distribution are 29.859 10a and 55.112 10k . The point of singularity is at 1929t . Between 1900

and 1910, economic growth started to be diverted to a slower, but still fast-increasing,

trajectory bypassing the singularity by 29 years (see Table 1).

The most complete set of data for Western Europe is for Denmark, France, the Netherlands

and Sweden. They are analysed separately and results are presented in Figures 7 and 8.

Parameters describing the historical hyperbolic growth of the GDP in these four countries

are: 13.821 10a and 41.986 10k . The point of singularity is at 1923t . From around

1875 economic growth in Denmark, France, the Netherlands and Sweden was diverted to a

slower trajectory, bypassing the singularity by 48 years.

The quality of the hyperbolic fit to the data is virtually the same as for the total of the 30

countries but now the fitted curve passes also through the AD 1 point. However, it still does

not reproduce the point at AD 1000. This point is only 41% below the fitted hyperbolic

distribution.

The historical growth of the GDP in Western Europe was definitely hyperbolic from AD

1500 to 1900 but there is also a good indication that it was hyperbolic from AD 1 (Figure 6).

There was no stagnation and no takeoff from stagnation to growth at any time.

The data for Western Europe contradict the Unified Growth Theory (Galor, 2005, 2011). The

four regimes of growth postulated and explained by Galor did not exist. The Industrial

Revolutions had absolutely no impact on the growth trajectory of the GDP in Western

Europe, the cradle of this revolution, where its effects should have been stronger than

anywhere else. Explanations of the economic growth offered by Galor are not only irrelevant

but also strongly misleading because they do not explain the historical economic growth but

only the images of growth created by the mistaken interpretations of hyperbolic distributions.

Unified Growth Theory explains phenomena that did not exist and consequently it does not

explain the mechanism of the economic growth.

Eastern Europe

Systematic data for Eastern Europe are available only for seven countries: Albania, Bulgaria,

Czechoslovakia, Hungry, Poland, Rumania and Yugoslavia. For other countries there are no

data until 1990. The analysis of the historical data for Eastern Europe is summarised in

Figures 9-11.

The best hyperbolic fit to the data is between AD 1000 and 1890. Hyperbolic parameters are: 17.749 10a and 44.048 10k . The point of singularity is at 1915t . From around

1890, the economic growth in Eastern Europe was diverted to a slower trajectory, bypassing

the singularity by 25 years.

There was no stagnation and no takeoff at any time. Industrial Revolution had absolutely no

impact on changing the economic growth trajectory in the countries of Eastern Europe.

Unified Growth Theory (Galor, 2005, 2011) is contradicted by the economic growth data for

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Eastern Europe. This theory explains phenomena that did not exist and consequently it does

not explain the mechanism of the economic growth.

Former USSR

The analysis of the data for countries of former USSR is presented in Figures 12-14. The best

hyperbolic fit is between AD 1 and 1870. Parameters fitting the data are: 16.547 10a and 43.452 10k . The point of singularity is at 1897t . From around 1870, or maybe even a

little earlier, the economic growth in the Former USSR was diverted to a slower trajectory,

bypassing the singularity by at least 27 years.

There was no stagnation and no takeoff at any time. Industrial Revolution had absolutely no

impact on changing the economic growth trajectory in the countries of former USSR. Unified

Growth Theory is contradicted by the economic growth data for countries of former USSR.

This theory explains phenomena that did not exist and consequently it does not explain the

mechanism of the economic growth.

Asia

Analysis of the historical economic growth in Asia is summarised in Figures 15-17. The best

hyperbolic fit is between AD 1000 and 1950. Parameters fitting the data are: 22.303 10a

and 51.129 10k . The point of singularity is at 2040t .

The data and their analysis indicate that the economic growth was diverted to a faster, but

non-hyperbolic, trajectory from around 1950. This boosting can be seen clearly in Figures 16

and 17 and it occurred well after the Industrial Revolution. The data demonstrate that there

was no stagnation in the economic growth between AD 1000 and 1950, and possibly even

earlier, and no takeoff from stagnation to growth as claimed by the Unified Growth Theory

(Galor, 2005, 2011). In particular, there was no takeoff that could be associated with the

Industrial Revolution.

The data displayed in Figure 17 show that the current economic growth in Asia approaches

its historical hyperbolic trajectory. However, the reciprocal values of the data suggest that the

economic growth will continue along it distinctly different trajectory.

Reciprocal values of the data presented in Figure 16 show that the economic growth became

slower at the time overlapping the time of the Industrial Revolution, 1760-1840 (Floud &

McCloskey, 1994), because while the point for 1820 is still located on the straight line,

representing hyperbolic growth, the point for 1870 is above this line. The deceleration in the

economic growth occurred sometime between 1820 and 1870. So, we could conclude that the

Industrial Revolution slowed down the economic growth in Asia but obviously such a

conclusion would have been unjustified without further examination of other related data.

The two events are most likely unrelated, which serves as a warning sign that coincidences

could be random. Just because the time of the Industrial Revolution coincides with a change

in the economic growth trajectory it does not mean that it caused this change. However, if at

the time of the Industrial Revolution there is obviously no change in the economic growth

trajectory then it would be incorrect to insist that the Industrial Revolution had strong

influence on the economic growth.

The brief deceleration in the economic growth between 1820 and 1870 was followed a

transient growth between 1870 and 1940. The data show also a brief economic decline

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between 1940 and 1950 before the economic growth settled along a new and still-continuing

trajectory.

Similar transient stage can be observed also in Japan between 1870 and 1944 (see Figure 18).

In this case the trend is clearer because there are more data during that time.

The data between AD 1 and 1700 were fitted using hyperbolic distribution. The parameters

are: 16.672 10a and 43.546 10k . The point of singularity is at 1882t . The delay in

the economic growth, which occurred around 1870, shifted the economic growth to a new

trajectory bypassing the singularity by 182 years representing the largest and the safest

bypass of this potentially catastrophic event.

The data for Japan show clearly that the Industrial Revolution did not boost economic growth

in this country. On the contrary, at the time coinciding with the Industrial Revolution (1760-

1840) economic growth slowed down considerably, as indicated by the significant shift in the

display of the GDP data shown in the top section of Figure 18 as well as by the points

representing the reciprocal values of the GDP in 1820, 1850 and 1870, which are located well

above the earlier straight-line trajectory. The deceleration in the economic growth occurred

between AD 1700 and 1820, i.e. during the time of the Industrial Revolution.

So, again, hasty interpretation of such a correlation might lead to conclusion that the

Industrial Revolution slowed down economic growth in Japan. However, the more plausible

conclusion is that the two events were unrelated, which is again a warning sign against

claiming that Industrial Revolution had impact on the economic growth even if we can

observe a correlation between the timing of the Industrial Revolution and the timing of

changes in the economic growth trajectory. However, so far, we have seen that even such

correlations are missing in the data.

The slowed-down growth in Japan continued until 1870, when it started to follow a fast,

transient trajectory until 1944. Between 1944 and 1945 the GDP value clearly decreased but

from 1945, economic growth settled along a new and still-continuing, non-hyperbolic

trajectory.

Economic growth in Japan increased hyperbolically between AD 1 and 1700. There was no

stagnation and no takeoff from stagnation to growth. In the place of the postulated takeoff

there was a significant delay in the economic growth. Unified Growth Theory is contradicted

by the economic growth data for Japan. This theory is also contradicted by the economic

growth data for Asia. Unified Growth Theory describes and explains phenomena that did not

exist. It is an irrelevant and misleading theory that does not explain the mechanism of the

historical economic growth.

Africa

Results of analysis of economic growth in the 57 African countries are presented in Figures

19-21. Reciprocal values of the GDP data, presented in Figures 19 and 20, show clearly that

the economic growth was following two hyperbolic distributions. At first it was a slow

hyperbolic growth between AD 1 and 1820 characterised by parameters 11.244 10a and 55.030 10k and by the singularity at 2473t . Then, around 1820, this slow hyperbolic

growth was replaced by a significantly faster hyperbolic growth characterised by parameters 14.192 10a and 42.126 10k and by the singularity at 1972t . Defined by the

parameter k, this new growth was 4.2 times faster than the earlier hyperbolic growth. From

around 1950, this fast hyperbolic growth was diverted to a slower, non-hyperbolic trajectory,

bypassing singularity by 22 years.

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There was a clear and well-defined takeoff in the economic growth in Africa. Furthermore,

this takeoff is well-correlated with the Industrial Revolution.

However, the takeoff in Africa was not from stagnation to growth, as required for the takeoffs

discussed and explained by Galor (2005, 2011), but from growth to growth. To be more

precise, it was a takeoff from a sustained hyperbolic growth to another sustained hyperbolic

growth, but faster. Furthermore, this takeoff cannot be associated with the usually claimed

improved living conditions and with the alleged general benefits of the Industrial Revolution

but with the ruthless exploitation of African resources at the expense of the native population

(Duignan & Gunn, 1973; McKay, Hill, Buckler, Ebrey, Beck, Crowston, & Wiesner-Hanks,

2012; Pakenham, 1992).

Even if the existence of a takeoff can be demonstrated, as in the case of Africa, and even if it

can be correlated with the Industrial Revolution, it does not necessarily mean that it was a

manifestation of the beneficial effects of this revolution such as the improved living

conditions of the population, reflected in the improved health care, improved housing,

improved education and with the improved income, but maybe only with the improved living

conditions of a certain, relatively small, group of people and at the expense of even greater

misery of the population living in a given country or region, at the expense of the ruthless and

wasteful exploitation of natural resources, when a new land was made suddenly available to

make the already rich countries even richer while making the native population even poorer

than before.

Industrial Revolution may have made the invasion of new lands easier and their mindless

exploitation more efficient but, such an intensified exploitation of other lands does not

necessarily represent a transition from stagnation to growth but from growth to growth and

most likely from a previously slow and sustained growth to a new, fast and unsustainable

growth, from a hyperbolic growth characterised by a singularity in a distant future to a

dangerously fast hyperbolic growth with the singularity much closer in time. In Africa the

transition was from the hyperbolic growth characterised by the singularity in 2473 to the

hyperbolic growth characterised by the singularity in 1972. There is no need to convince

anyone, which of these two trajectories should be regarded as safer and more sustainable. We

shall soon see that the respective singularities were 2113 and 1910 in Latin America, 7994

and 1853 in Australia and 2498 and 1828 in Western Offshoots. Fast economic growth is not

necessarily a safe or desirable economic growth.

If Africa continued along its fast hyperbolic trajectory, which commenced around the time of

the Industrial Revolution, it would have experienced economic collapse in the late 1900s.

Fortunately, this gloriously fast economic growth was spontaneously terminated and diverted

in 1950 to a slower, but still not necessarily sustainable, trajectory.

In Galor’s interpretation of economic growth, with his erroneous concept of the three stages

of growth, the crowning glory of economic development is the so called “Sustained Growth

Regime” (Galor, 2005, p. 195 on). Such an interpretation of economic growth is not only

incorrect but also dangerously misleading. It claims that after ages-long stagnation we have

now entered the golden age of sustained economic growth.

It is premature to celebrate the so-called sustained growth regime. If we accept Galor’s theory

we might imagine that now at last we can relax and enjoy the benefits of sustained growth

regime. This would have been not only an incorrect but also dangerous conclusion. As far as

we can tell after examining the economic growth data (Maddison, 2001, 2010), economic

growth was always sustained. The vital question is whether this sustained economic growth is

still sustainable (Nielsen, 2015b).

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Data for Africa (Maddison, 2001, 2010) demonstrate a steadily-increasing economic growth

from AD 1. People lived there for countless generations and they were using their natural

resources to support their population and to improve their living conditions. They may have

not been as greedy as people living in Europe but they were using their natural wealth to

support their life. Their economic growth was slow but steady, and by being slow it was safe.

The same might apply to other parts of the world, which were at a certain time conquered and

subdued by foreign forces, places such as Latin America, North America and Australia.

People living in these places were living from the land and they were using their natural

resources to support their life. It can be easily expected that they must have had some kind of

economic growth. It may not have been as fast as after the foreign invasion but it would be

incorrect to assume that it was stagnant.

It is a mistake to interpret fast economic growth as a desired process. Quite the opposite is

true. Prudent use of natural resources associated with a moderate economic growth is far

better than headless drive to produce more and more and to use more and more. It is because

of such increasing individual demands combined with the still-increasing global population

that our global economic growth faces now the insecure future (Nielsen, 2015b). The same

problem can be identified not only globally but also in individual countries and regions. The

recent economic crisis in Greece can be easily repeated in other countries not only because

there is a limit to natural resources and to how fast they can be renewed but also a limit to

how high wealth can be annually generated.

Latin America

Results of analysis of the economic growth in Latin America are presented in Figures 22 –

24. Data for Latin America are difficult to analyse because there was a significant decline in

the economic growth between AD 1500 and 1600 but they also appear to follow also two

distinctly different hyperbolic trajectories. However, the identification of the first trajectory is

not as clear as for Africa. The identification of the second hyperbolic trajectory is more

convincing. Tentative conclusion is that the economic growth in Latin America was

following a slow hyperbolic distribution between AD 1 and 1500 and a fast distribution

between AD 1600 and around 1870.

The tentatively assigned slow hyperbolic growth between AD 1 and 1500 is characterised by

parameters 24.421 10a and 52.093 10k . Its singularity is at 2113t . The better

determined fast hyperbolic growth between AD 1600 and 1870 is characterised by parameters 11.570 10a and 58.224 10k . Its singularity is at 1910t . Defined by the parameter k,

this growth was 3.9 times faster than the earlier hyperbolic growth. From around 1870, this

fast hyperbolic growth was diverted to a slower trajectory bypassing the singularity by 40

years.

The data for Latin America are in clear contradiction of the Unified Growth Theory (Galor,

2005, 2011). First, there is no compelling evidence that the economic growth was ever

stagnant. On the contrary, there is sufficiently convincing evidence that the economic growth

was not stagnant and that it was always steadily increasing. Second, there was no takeoff

from stagnation to growth. Third, Industrial Revolution had absolutely no impact on changing

the economic growth trajectory in Latin America. Fourth, the fast economic growth

commenced in AD 1600, well before the time of the Industrial Revolution (1760-1840). The

often-claimed causative correlation between technological development (usually associated

with the Industrial Revolution) and economic growth appears to be questioned by the

economic growth data for Latin America. Fifth, the economic growth in Latin America was

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diverted to a slower trajectory starting from around 1870, i.e. shortly after the Industrial

Revolution. Delayed boosting in Latin America by the Industrial Revolution in Europe could

have been easily explained, but the data show the entirely different pattern, which suggests

that technological progress and Industrial Revolution had no impact on shaping the economic

growth in Latin America.

Economic growth data for Latin America show that the three regimes of growth postulated by

Galor (2005, 2011) did not exist. In particular, the postulated takeoff from stagnation never

happened. Unified Growth Theory describes and explains phenomena that did not exist and

consequently it does not explain the mechanism of economic growth.

Australia

Australia is one of the four countries belonging to Western Offshoots. The other three are

Canada, New Zealand and the USA. The data for this group are difficult to analyse because

many essential historical data are missing. Fortunately, Australia has excellent set of data

containing the annual list of the GDP values between 1820 and 2008. We shall, therefore,

analyse first the data for Australian because this analysis will help to understand the data for

the whole group.

Results of analysis of the economic growth in Australia are presented in Figures 25 – 27. The

reciprocal values of the data between AD 1 and 1700 can be fitted by a straight line

suggesting a hyperbolic distribution. Parameters describing this distribution are 06.986 10a and 48.739 10k . It’s singularity is at 7994t .

Between AD 1700 and 1820, well within the range of the influence of the Industrial

Revolution (1760-1840), economic growth decreased from $180 million to $173 million but

then started to follow an exceptionally fast hyperbolic trajectory described by parameters 23.215 10a and 11.736 10k . Its singularity was at 1853t . From around 1848, or

shortly after the Industrial Revolution, the economic growth in Australia started to be

diverted to a slower trajectory, bypassing the singularity by only 5 years.

As in the case of the economic growth in Latin America, delayed effects of the Industrial

Revolution in Europe on the economic growth in Australia could have been easily explained.

However, the quick termination of the fast economic growth so close after the Industrial

Revolution is hard to explain by linking it with this event.

Economic growth was extremely slow over a long time but there is no convincing evidence

that it was ever stagnant. There is no evidence of random fluctuations and Malthusian

oscillations. On the contrary, there is sufficiently strong evidence that the growth was

hyperbolic, even though it was very slow.

The data for Australia give no support to the concept of the existence of the three regimes of

growth postulated by Galor (2005, 2011). The three regimes suggested by data are similar to

the three regimes in Africa: (1) slow hyperbolic growth, (2) fast hyperbolic growth, and (3)

slower, non-hyperbolic growth. There is no evidence of stagnation, post-Malthusian regime

and sustained growth regime. Economic growth in Australia gives no support to the Unified

Growth Theory.

Western Offshoots

As mentioned earlier, Western Offshoots include Australia, Canada, New Zealand and the

USA. Reciprocal values of the combined GDP for these four countries are presented in

12

Figure 28. There are no data between AD 1700 and 1820. However, the overall pattern of

growth appears to be similar as in Africa, Latin America and Australia. We can, therefore,

assume that the growth during that time was hyperbolic. The growth between AD 1 and 1500

also appears to have been hyperbolic.

The tentatively assigned hyperbolic distributions are presented in Figures 28-30. There

appears to have been a slow hyperbolic growth between AD 1 and 1500 and a fast hyperbolic

growth between AD 1700 and 1820. The economic growth decreased between AD 1500 and

1700, reflecting the pattern for Latin America.

Under these tentative assumptions we interpret the historical economic growth in Western

Offshoots as being represented by two hyperbolic distributions separated by a brief decline.

Parameters for the tentatively assigned slow hyperbolical trajectory between AD 1 and 1500

are 02.232 10a and 48.938 10k . It’s singularity is at 2498t . For the tentatively

assigned fast trajectory, between 1700 and 1820, the parameters are: 11.716 10a and 39.387 10k . It’s singularity is at 1828t . From around 1820 the data follow a well-

defined but non-hyperbolic trend (see Figure 29).

The data for Western Offshoots display a pattern resembling the economic growth in Africa,

Latin America and Australia. There appears to have been a slow hyperbolic growth, followed

by a faster hyperbolic growth, and followed again by a diversion to a slower, non-hyperbolic

trajectory. There is no convincing evidence of the existence of stagnation characterised by

random fluctuations and Malthusian oscillations. There is no evidence of the existence of the

three regimes of growth proposed by Galor (2005, 2011). Economic growth in Western

Offshoots gives no clear support for the Unified Growth Theory. On the contrary, it suggests

that the theory describes and explains phenomena that did not exist and consequently that it

does not explain economic growth

Summary and conclusions

Results of mathematical analysis of the historical economic growth are presented in Table 1.

The listed parameters are for the fitted hyperbolic distributions. The last column in this table

shows the results of the confrontation of the Unified Growth Theory with the data.

This analysis demonstrates that the natural tendency for the historical economic growth was

to increase hyperbolically. In general, there is a remarkably good agreement between the data

and the calculated hyperbolic distributions.

Data used in our study are the same as used by Galor in the formulation of his Unified

Growth Theory. However, it appears that he had a problem with their analysis, which is not

too surprising because hyperbolic distributions are hard to understand and Galor is certainly

not the first to make a mistake with their interpretation. He followed in the footsteps of many

of his predecessors.

Those who are familiar with hyperbolic distributions experience no problem with their

interpretation. They can immediately recognise their characteristic features. For them, these

features are plain and clear and they can immediately see that the distribution is hyperbolic.

However, those who are less familiar with mathematical distributions become easily

confused. It is hard for them to see that these distributions are not made of different

components. It is hard to see that they do not represent different stages of growth. It is hard to

see and to accept that they represent just one stage. It is hard to see that they represent a

single, monotonically-increasing growth, which is impossible to divide into different stages

of growth.

13

Table 1 Summary of the mathematical analysis or the historical economic growth

Region/Countries a k Hyperbolic

Range

Singularity Proximity UGT

World 21.684 10 68.539 10 1000 – 1955 1972 17 X

Western Europe 29.859 10 55.112 10 1500 – 1900 1929 29 X

Western Europe (4) 13.821 10 41.986 10 1 – 1875 1923 48 X

Eastern Europe 17.749 10 44.048 10 1000 – 1890 1915 25 X

Former USSR 16.547 10 43.452 10 1 – 1870 1897 27 X

Asia 22.303 10 51.129 10 1000 – 1950 2040 90 X

Africa

11.244 10

14.192 10

55.030 10

42.126 10

1 – 1820

1820 – 1950

2473

1972

22

X

Japan 16.672 10 43.546 10 1 – 1700 1882 182 X

Latin America

24.421 10

11.570 10

52.093 10

58.224 10

1 – 1500

1600 – 1870

2113

1910

40

X

Australia

06.986 10

23.215 10

48.739 10

11.736 10

1 – 1700

1820 - 1848

7994

1853

5

X?

Western Offshoots

02.232 10

11.716 10

48.938 10

39.387 10

1 – 1500

1700 – 1820

2498

1828

8

X?

a and k – Hyperbolic growth parameters [see the eqn (1)].

Hyperbolic Range – The range of time when the hyperbolic growth is confirmed by data.

Singularity – The time of escape to infinity for a given hyperbolic distribution.

Proximity – Proximity (in years) of the singularity at the time when the economic growth departed from the

hyperbolic growth leading to the corresponding singularity.

UGT – Unified Growth Theory (Galor, 2005, 2011).

Western Europe (4) – Four countries of Western Europe: Denmark, France, the Netherlands and Sweden

X – Unified Growth Theory is contradicted by the same source of data, which was used during the formulation

of this theory.

X? – Unified Growth Theory is contradicted or at least strongly questioned by data.

Unlike the more familiar exponential distributions, which are easier to understand because

they show more readily a gradually increasing growth, hyperbolic distributions appear, so

convincingly, to be made of two or maybe even three components: a slow component, a fast

component and perhaps even a transition component located between the apparent slow and

fast components.

Here we immediately have the source of the repeated misinterpretations of such distributions

and we can now understand why Galor, and many people before him, imagined a prolonged

epoch of stagnation represented by the apparent slow component, the explosion or the

sustained growth regime, represented by the apparent fast-increasing component and a post-

Malthusian stage represented by the apparent transition between the slow and the fast

14

components. However, the existence of these components is just an illusion, which readily

disappears if we use the reciprocal values of data (Nielsen, 2014). The difficult analysis of

hyperbolic distributions becomes trivial because the confusing hyperbolic distributions are

then represented by straight lines, which are easy to understand.

Had Galor used this method of analysis he would have saved a lot of time and he would have

never developed his Unified Growth Theory. In fact he would have quickly discovered that

the numerous and accepted interpretations of the historical economic growth are incorrect. He

would have made an important, breakthrough discovery and he would have used his skills to

formulate a correct theory of economic growth.

As shown in the last column of Table 1, the data used by Galor contradict repeatedly and

consistently the Unified Growth Theory. The evidence is overwhelming and undeniable. In

science, just one contradicting and convincing example in data is sufficient to reject

contradicted theory but in this case the evidence is overwhelming. There is not even one,

convincing evidence supporting this theory. There is not a single convincing evidence of the

existence of the three regimes of growth (Malthusian stagnation, post-Malthusian regime and

sustained growth regime). On the contrary, the data show that the three regimes of growth did

not exist. There is also not a single convincing evidence of takeoffs from stagnation to

growth. Results of this analysis show that Unified Growth Theory describes and explain

phenomena that did not exist. Consequently, this theory does not explain the historical

economic growth.

Data for Africa show a clear takeoff around the time of the Industrial Revolution but it was

not a takeoff from stagnation to growth but from a hyperbolic growth to another hyperbolic

growth. This takeoff coincides with the colonisation Africa and with its intensified

exploitation.

A similar takeoff from a slow to a fast hyperbolic growth appears to have taken place in Latin

America but the transition to a faster economic growth occurred around AD 1600, well

before the time of the Industrial Revolution.

The data for Australia might appear to support the Unified Growth Theory because the

economic growth was very slow before the transition to a fast hyperbolic trajectory.

However, there is no positive proof that the growth before the takeoff was stagnant because

there are not enough data to demonstrate the tell-telling signs of random fluctuations and

Malthusian oscillations. The past growth is definitely consistent with the hyperbolic growth.

The overall pattern of growth in Australia is similar to the pattern in Africa. In both cases

there was a slow hyperbolic growth followed by a fast hyperbolic growth, and the transition

between these two components coincided with the Industrial Revolution.

However, it would be impossible to claim that this fast economic growth in Africa and

Australia was associated with the usually claimed benefits of Industrial Revolution, definitely

not for the native populations in these two geographical locations. In addition, data for Latin

America suggest that such coincidences could be random because the transition from slow to

fast hyperbolic growth in Latin America occurred around 160 years before the

commencement of the Industrial Revolution in Europe.

Data for Western Offshoots are incomplete but the general pattern is similar as in Africa,

Latin America and Australia. They also suggest the existence of two hyperbolic distributions,

slow hyperbolic growth over a long time followed by a fast hyperbolic growth over a short

time. They also show that a transition to a slower, non-hyperbolic component might have

occurred during the Industrial Revolution, which appears to contradict the usually-claimed

effects of the Industrial Revolution.

15

Historical data describing economic growth are in clear contradiction of the two fundamental

postulates of the Unified Growth Theory: (1) the postulate of the existence of the three,

distinctly different regimes of growth (Malthusian stagnation, post-Malthusian regime and

sustained-growth regime) and (2) the postulate of the differential takeoffs from stagnation to

growth. This second postulate is obviously contradicted by the data because takeoffs from

stagnation to growth did not exist.

By extension, economic growth data and their mathematical analysis contradict also the third

fundamental postulate of the Unified Growth Theory: the existence of the great divergence.

This postulate is firmly based on the existence of the epoch of stagnation and the existence of

takeoffs from stagnation to growth. However, this issue will be discussed in a separate

publication. It will be shown that the great divergence, postulated and explained by Galor

(2005, 2011) did not exist.

Hyperbolic growth was slow over a long time but not stagnant. The postulate of the

existence of the three regimes of growth and, in particular, the postulate of the existence of

the epoch of Malthusian stagnation, is based on impressions but impressions can be strongly

misleading and in the case of hyperbolic growth they are strongly misleading. It is easy to

make a mistake with their interpretation. However, science is full of examples of mistaken

interpretations. The real mistake is not in making a mistake but in refusing to correct it. The

progress in the economic research can be made only by accepting that the past numerous

interpretations of the mechanism of the historical economic growth based on the conjured

images of Malthusian stagnation and on the imagined transition to a new distinctly different

epoch of growth are incorrect. Refusing to accept such a conclusion creates stagnation in the

economic growth research.

There appears to be no problem with accepting exponential growth. Indeed, exponential

growth is so popular and so generally accepted that it is often used even to describe the non-

exponential types of growth. However, exponential growth is not the only type of growth,

which can be used to interpret data, and the historical economic growth data clearly

demonstrate that they followed hyperbolic distribution. If the data clearly demonstrate that

they follow hyperbolic distribution we have no choice but to accept it. The next logical step is

then to try to explain why the historical economic growth was hyperbolic. This would be the

natural step forward in the economic growth research. The backward step, creating the state

of stagnation in this field, is to refuse to accept the hyperbolic growth and to continue

accepting the concepts of stagnation and of a transition to a fast economic growth at a certain

time.

To prove the existence of Malthusian stagnation we would have to demonstrate convincingly

random economic growth characterised by random fluctuations or oscillation, often described

as Malthusian oscillation. No-one has ever presented such a proof and yet these concepts of

stagnation and of a transition to a new regime of growth are the fundamental postulates of the

economic growth research, and numerous mechanisms are proposed to explain these

imagined features.

Hyperbolic growth is generally uniquely identified by the straight line fitting the reciprocal

values of data. It would take a great effort to falsify data in order to create such a growth, and

we would have to accuse Maddison of deliberately working on the falsification of data aimed

at contradicting the traditional interpretations of the historical economic growth and in

particular aimed at contradicting the Unified Growth Theory, which was not yet formulated

when Maddison published his data.

16

The only way to accept the Unified Growth Theory and other traditional interpretations of the

historical economic growth is to reject the data published by Maddison but such a decision

would have been not only unscientific and but also inconsistent because his data were used

(without the proper mathematical analysis) in the formulation of this theory. Such a practice

would be similar to the practice used by certain religious organisations who work hard to find

any scraps of data to support their preconceived ideas and to reject contradicting data or to

misinterpret them in order to claim support for the incorrect concepts. In such fields, where

doctrines and interpretations are accepted by faith, contradicting data are rejected. In science,

it is other way round: contradicting interpretations are rejected, because science is interested

in finding the truth. Even the most cherished theories and interpretations are rejected or

appropriately modified if they are contradicted by data. This is the only way progress in

science can be made and is made. In other fields, where doctrines and interpretations are

accepted by faith, all possible ways are used to reject contradicting data. It would be a

mistake to adopt the same process in science because such a practice would be scientifically

unjustified. Any science adopting this type of practice is no longer science.

References

Duignan, P., & Gunn, L. H. (Eds.) (1973). Colonialism in Africa 1870 – 1960: A

Bibliographic Guide to Colonialism in Sub-Saharan Africa. Cambridge, UK:

Cambridge University Press.

Floud, D. & McCloskey, D.N. (1994). The Economic History of Britain since 1700.

Cambridge: Cambridge University Press.

Galor, O. (2005). From stagnation to growth: Unified Growth Theory. In P. Aghion & S.

Durlauf (Eds.), Handbook of Economic Growth (pp. 171-293). Amsterdam: Elsevier.

Galor, O. (2008). Comparative Economic Development: Insight from Unified Growth

Theory. http://www.econ.brown.edu/faculty/Oded_Galor/pdf/Klien%20lecture.pdf

Galor, O. (2011). Unified Growth Theory. Princeton, New Jersey: Princeton University Press.

Galor, O. (2012). Unified Growth Theory and Comparative Economic Development.

http://www.biu.ac.il/soc/ec/students/mini_courses/6_12/data/UGT-Luxembourg.pdf

Maddison, A. (2001). The World Economy: A Millennial Perspective. Paris: OECD.

Maddison, A. (2010). Historical Statistics of the World Economy: 1-2008 AD.

http://www.ggdc.net/maddison/Historical Statistics/horizontal-file_02-2010.xls.

McKay, J. P., Hill, B. D., Buckler, J., Ebrey, P. B., Beck, R. B., Crowston, C. H., & Wiesner-

Hanks, M. E. (2012). A History of World Societies: From 1775 to Present. Volume C –

From 1775 to the Present. Ninth edition. Boston, MA: Bedford Books.

Nielsen, R. W. (2014). Changing the Paradigm. Applied Mathematics, 5, 1950-1963.

http://dx.doi.org/10.4236/am.2014.513188

Nielsen, R. W. (2015a). Mathematical Analysis of the Historical Economic Growth.

http://arxiv.org/ftp/arxiv/papers/1509/1509.06612.pdf

Nielsen, R. W. (2015b). The Insecure Future of the World Economic Growth.

http://arxiv.org/ftp/arxiv/papers/1510/1510.07928.pdf

Pakenham, T. (1992). The Scramble for Africa: White Man’s Conquest of the Dark Continent

from 1876-1912. New York: Avon Books.

17

von Foerster, H., Mora, P., & Amiot, L. (1960). Doomsday: Friday, 13 November, A.D.

2026. Science, 132, 1291-1295.

18

Unified Growth Theory Contradicted by the

Hyperbolic Economic Growth: Supplement

Ron W Nielsen

Environmental Futures Research Institute, Gold Coast Campus, Griffith University, Qld,

4222, Australia

November, 2015

19

World Economic Growth

Figure 1. Reciprocal values of the GDP data (Maddison, 2010) are fitted using straight line

between AD 1000 and 1955 representing hyperbolic growth. There was no stagnation and no

takeoff from stagnation to growth, as claimed by the Unified Growth Theory (Galor, 2005,

2011). The three regimes of growth, postulated and explained by Galor (2005, 2011), did not

exist. Industrial Revolution had absolutely no impact on changing the economic growth

trajectory. From around 1955, the economic growth started to be diverted to a slower

trajectory.

20

Figure 2. Reciprocal values of the GDP (Maddison, 2010) showing diversion of the economic

growth to a slower trajectory from the earlier hyperbolic trajectory. The current global

economic growth is approximately exponential (Nielsen, 2014, 2015b).

Figure 3. World GDP data (Maddison, 2010) fitted using hyperbolic distribution. The point at

AD 1 is 77% higher than the calculated distribution. There was also no stagnation and no

takeoff from stagnation to growth, as claimed by the Unified Growth Theory (Galor, 2005,

2011). The three regimes of growth postulated and explained by Galor (2005, 2011) did not

exist. Industrial Revolution had absolutely no impact on changing the economic growth

trajectory. From around 1955, the world economic growth started to be diverted to a slower

but still fast-increasing trajectory, which is now approximately exponential (Nielsen, 2014,

2015b).

21

Western Europe

The total of 30 countries

Figure 4. Reciprocal values of the GDP data (Maddison, 2010) for Western Europe are

compared with the hyperbolic distribution represented by the decreasing straight line. There is

no convincing evidence of stagnation. There was definitely no stagnation from AD 1500 and

no takeoff to a faster growth at any time. Industrial Revolution had absolutely no effect on

changing the economic growth trajectory in Western Europe, the centre of this revolution. On

the contrary, from around 1900, shortly after the Industrial Revolution, the economic growth

in Western Europe started to be diverted to a slower trajectory. Unified Growth Theory

(Galor, 2005, 2011) is contradicted by the economic growth data, used in this theory but never

properly analysed. This theory describes and explains phenomena, which did not exist and

thus it does not explain the mechanism of the historical economic growth.

Figure 5. Reciprocal values of the GDP (Maddison, 2010) for Western Europe between AD

1500 and 2008 showing a diversion to a slower trajectory between around 1900 and 1910.

There was no stagnation and no takeoff to a faster growth. Industrial Revolution had

absolutely no impact on changing the economic growth trajectory in Western Europe.

22

Figure 6. Economic growth in Western Europe. The GDP data (Maddison, 2010) are

compared with the first-order hyperbolic distribution [labelled as Hyperbolic Distribution

(1500 – 1900)]. The point at AD 1 is 42% higher than for the calculated distribution and 48%

lower at AD 1000. There was no stagnation and no takeoff to a faster growth. Industrial

Revolution had absolutely no effect on changing the economic growth trajectory in Western

Europe, the centre of this revolution. On the contrary, from around 1900, shortly after this

revolution, the economic growth in Western Europe started to be diverted to a slower

trajectory. Unified Growth Theory (Galor, 2005, 2011) is contradicted by the data used in the

formulation of this theory. It describes and explains phenomena that did not exist and thus it

does not explain the mechanism of the economic growth.

Denmark, France, Netherlands and Sweden

Figure 7. Reciprocal values of the GDP (Maddison, 2010) for four countries (Denmark,

France, Netherlands and Sweden) compared with the straight line representing hyperbolic

growth fitting the data between AD 1 and 1875. From around 1875, or shortly after the

Industrial Revolution, economic growth in these four countries started to be diverted to a

slower trajectory. Industrial Revolution did not boost economic growth in these four

countries.

23

Figure 8. Economic growth in Denmark, France, Netherlands and Sweden. The data

(Maddison, 2010) are compared with the best hyperbolic fit. The point at AD 1000 is 41%

lower than for the calculated distribution. From around 1875, the economic growth started to

be diverted to a slower trajectory. There was no stagnation and no takeoff from stagnation to

growth. Unified Growth Theory (Galor, 2005, 2011) is contradicted by the economic growth

data for these four countries of Western Europe.

Eastern Europe

Figure 9. Reciprocal values of the GDP data (Maddison, 2010) for Eastern Europe are

compared with the hyperbolic distribution represented by the decreasing straight line.

Economic growth was hyperbolic from at least AD 1000. Industrial Revolution did not boost

the economic growth in Eastern Europe. There was no takeoff from stagnation to growth

because there was no stagnation but a continuing hyperbolic growth from at least AD 1000.

Unified Growth Theory (Galor, 2005, 2011) is contradicted by the economic growth data for

Eastern Europe. This theory describes and explains phenomena that did not exist and

consequently it does not explain the mechanism of the economic growth.

24

Figure 10. Reciprocal values of the GDP data (Maddison, 2010) for Eastern Europe showing

that from around 1890, shortly after the Industrial Revolution, the economic growth started to

be diverted to a slower trajectory. Industrial Revolution did not boost the economic growth in

Eastern Europe. There was no takeoff from stagnation to growth because there was no

stagnation.

Figure 11. Economic growth in Eastern Europe. GDP data (Maddison, 2010) are compared

with the best hyperbolic fit. The point at AD 1 is 51% higher than for the calculated

distribution. From around 1890, economic growth started to be diverted to a slower trajectory.

Industrial Revolution did not boost the economic growth in Eastern Europe. There was no

takeoff from stagnation to growth because there was no stagnation. Unified Growth Theory

(Galor, 2005, 2011) is contradicted by the economic growth data. This theory describes and

explains phenomena that did not exist and consequently it does not explain the mechanism of

the economic growth.

25

Former USSR

Figure 12. Reciprocal values of the GDP data (Maddison, 2010) for the former USSR

compared with the hyperbolic distribution represented by the decreasing straight line. Data

indicate that the economic growth was hyperbolic from AD 1 to 1870. Industrial Revolution

did not boost the economic growth. There was no stagnation and no takeoff from stagnation to

growth. Shortly after the Industrial Revolution, the economic growth in Eastern Europe

started to be diverted to a slower trajectory. Unified Growth Theory (Galor, 2005, 2011) is

contradicted by the economic growth data. This theory describes and explains phenomena that

did not exist and consequently it does not explain the mechanism of the economic growth.

Figure 13. Reciprocal values of the GDP data (Maddison, 2010) for the former USSR

showing that from around 1870, shortly after the Industrial Revolution, economic growth

started to be diverted to a slower trajectory.

26

Figure 14. Economic growth in the former USSR. GDP data (Maddison, 2010) are compared

with the best hyperbolic fit. The growth was hyperbolic from AD 1 to 1870. From around

1870, shortly after the Industrial Revolution, economic growth started to be diverted to a

slower trajectory. Epoch of stagnation did not exist. Industrial Revolution did not boost the

economic growth. There was no takeoff from stagnation to growth because there was no

stagnation but a steadily-increasing growth. Unified Growth Theory (Galor, 2005, 2011) is

contradicted by the economic growth data. This theory describes and explains phenomena that

did not exist and consequently it does not explain the mechanism of the economic growth.

Asia

Figure 15. Reciprocal values of the GDP (Maddison, 2010) for Asia compared with the

hyperbolic distribution represented by the decreasing straight line. From at least AD 1000,

economic growth was hyperbolic. Industrial Revolution did not boost the economic growth.

There was no takeoff from stagnation to growth because there was no stagnation. The three

regimes of growth postulated and explained in the Unified Growth Theory (Galor, 2005,

2011) did not exist. Unified Growth Theory is contradicted by data. This theory describes and

explains phenomena that did not exist and consequently it does not explain the mechanism of

the economic growth.

27

Figure 16. Reciprocal values of the GDP (Maddison, 2010) for Asia. Industrial Revolution did

not boost the economic growth in Asia. During the time still coinciding with the Industrial

Revolution, economic growth started to slow down but between 1870 and 1940 it was

increasing along a transient. It slowed down again between 1940 and 1950 but then started to

increase along a new and still-continuing, non-hyperbolic trajectory. There was no takeoff

from stagnation to growth because there was no stagnation. The three regimes of growth

postulated and explained in the Unified Growth Theory (Galor, 2005, 2011) did not exist.

Unified Growth Theory is contradicted by data. This theory describes and explains

phenomena that did not exist and consequently it does not explain the mechanism of the

economic growth.

Figure 17. Economic growth in Asia. The data (Maddison, 2010) are compared with the best

hyperbolic fit. The point at AD 1 is 76% higher than for the calculated distribution. From

around 1950, economic growth accelerated but by 2008 it was close to the earlier hyperbolic

trajectory. There was no stagnation in the economic growth. Industrial Revolution did not

boost economic growth. There was no takeoff from stagnation to growth because there was no

stagnation. The three regimes of growth postulated and explained in the Unified Growth

Theory (Galor, 2005, 2011) did not exist. Unified Growth Theory is contradicted by data.

This theory describes and explains phenomena that did not exist and consequently it does not

explain the mechanism of the economic growth.

28

Figure 18. Economic growth in Japan. Unified Growth Theory (Galor, 2005, 2011) is

contradicted by the data. The three regimes of growth postulated and explained by this theory

did not exist. There was no takeoff from stagnation to growth because there was no

stagnation. Industrial Revolution did not boost the economic growth. On the contrary,

Industrial Revolution coincides with the time when the economic growth changed from a fast

hyperbolic to a slow non-hyperbolic between AD 1700 and 1870. The lower part of this figure

shows also a transient stage of growth between 1870 and 1944, a sudden drop in the GDP

value between 1944 and 1945 and a new but non-hyperbolic trajectory from around 1945.

Unified Growth Theory describes and explains phenomena that did not exist and consequently

it does not explain the mechanism of the economic growth.

29

Africa

Figure 19. Reciprocal values of the GDP data (Maddison, 2010) for Africa compared with

hyperbolic distributions represented by the decreasing straight lines. There was no stagnation

in the economic growth. Economic growth was increasing hyperbolically between AD 1 and

around 1820 and again from 1820 to around 1950. Economic growth was boosted around the

time of the Industrial Revolution but it was not a transition from stagnation to growth but

from a hyperbolic growth to another hyperbolic growth. The three regimes of growth

postulated in the Unified Growth Theory did not exist. There was also no takeoff from

stagnation to growth at any time because there was no stagnation. Unified Growth Theory

describes and explains phenomena that did not exist and consequently it does not explain the

mechanism of the economic growth.

Figure 20. Reciprocal values of the GDP (Maddison, 2010) for Africa showing that from

around 1950 economic growth started to be diverted to a slower trajectory.

30

Figure 21. Economic growth in Africa. Data (Maddison, 2010) are compared with hyperbolic

distributions. From around 1950, economic growth started to be diverted to a slower

trajectory. The transition in the economic growth around the time of the Industrial Revolution

was a transition from a hyperbolic growth to another hyperbolic growth. The three regimes of

growth postulated in the Unified Growth Theory did not exist. There was also no takeoff from

stagnation to growth at any time because there was no stagnation. Unified Growth Theory

describes and explains phenomena that did not exist and consequently it does not explain the

mechanism of the economic growth.

Latin America

Figure 22. Reciprocal values of the GDP data (Maddison, 2010) for Latin America are

compared with hyperbolic distributions represented by the decreasing straight lines. There

was no stagnation in the economic growth. From AD 1, economic growth was hyperbolic.

The growth was not boosted by the Industrial Revolution. There was no takeoff associated

with this event. Economic growth was shifted to a faster hyperbolic trajectory between AD

1500 and 1600, well before the Industrial Revolution. The three regimes of growth postulated

in the Unified Growth Theory did not exist. The postulated takeoff from stagnation to growth

also did not exist. Unified Growth Theory is contradicted by data. This theory describes and

explains phenomena that did not exist and consequently it does not explain the mechanism of

the economic growth.

31

Figure 23. Reciprocal values of the GDP data (Maddison, 2010) for Latin America showing

that from around 1870 or 1900, shortly after the Industrial Revolution, the economic growth

started to be diverted to a slower trajectory.

Figure 24. Economic growth in Latin America. Economic growth data (Maddison, 2010) are

compared with hyperbolic distributions. Industrial Revolution did not boost the economic

growth. The transition from a slower hyperbolic trajectory to a faster hyperbolic trajectory

occurred between AD 1500 and 1600, well before the Industrial Revolution and was

accompanied by a brief decline in the economic growth. From around 1870 or 1900, shortly

after the Industrial Revolution, the economic growth started to be diverted to a slower

trajectory. The pattern of two hyperbolic growths (slow and fast) is similar to the pattern in

Africa. Unified Growth Theory is contradicted by economic growth data. The three regimes

of growth postulated in this theory did not exist. There was also no takeoff from stagnation to

growth because there was no stagnation. Unified Growth Theory describes and explains

phenomena that did not exist and consequently it does not explain the mechanism of the

economic growth.

32

Western Offshoots

Australia

Figure 25. Reciprocal values of the GDP (Maddison, 2010) for Australia compared with

hyperbolic distributions represented by the decreasing straight lines. The growth was slow

over a long time but there is no convincing evidence that it was ever stagnant. The pattern of

two hyperbolic growths is similar to the pattern for Africa and Latin America. Transition from

the tentatively-assigned slow hyperbolic trajectory to the undeniably clear fast hyperbolic

trajectory coincides with the Industrial Revolution but it was preceded by a brief economic

decline, resembling the pattern in Latin America. There is no positive proof of the existence

of the three regimes of growth. On the contrary, there is strong indication that the three

regimes did not exist. There is also no positive proof of a takeoff from stagnation to growth.

The Unified Growth Theory is contradicted, or at least questioned, by the data describing

economic growth in Australia.

Figure 26. Reciprocal values of the GDP data (Maddison, 2010) for Australia showing that

from around 1820 to 1848, the economic growth was following an exceptionally fast

hyperbolic distribution. From around 1848 or 1850, shortly after the Industrial Revolution,

economic growth started to be diverted to a slower trajectory.

33

Figure 27. Economic growth in Australia. The best fits to the data (Maddison, 2010) suggest a

slow hyperbolic growth between AD 1 and 1700 followed by a fast hyperbolic growth

between 1820 and 1848. From around 1848, economic growth started to be diverted to a

slower, but still increasing trajectory. Transition from a slow to fast growth coincides with the

Industrial Revolution but there is no positive proof that it was a transition from stagnation to

growth. It may have been a transition similar as in Africa.

Australia, Canada, New Zealand and the USA

Figure 28. Reciprocal values of the GDP data (Maddison, 2010) for Western Offshoots

(Australia, Canada, New Zealand and the USA) are compared with the tentatively assigned

hyperbolic distributions represented by the decreasing straight lines. The overall pattern of

growth appears to be similar to the pattern for Africa, Latin America and Australia. The

tentatively-assigned hyperbolic distributions suggest a transition to fast hyperbolic growth

accompanied by a brief economic decline between AD 1500 and 1700. There is no positive

proof of the existence of the three regimes of growth. On the contrary, there is strong

indication that the three regimes did not exist. There is also no positive proof of a takeoff

from stagnation to growth. The Unified Growth Theory is contradicted, or at least strongly

questioned, by the data describing economic growth in Western Offshoots.

34

Figure 29. Reciprocal values of the GDP data (Maddison, 2010) for Western Offshoots

(Australia, Canada, New Zealand and the USA) showing a clear, non-hyperbolic trajectory

commencing around 1820, well within the boundaries of the Industrial Revolution.

Figure 30. Economic growth for Western Offshoots (Australia, Canada, New Zealand and the

USA). Economic growth data (Maddison, 2010) are compared with the tentatively assigned

hyperbolic trajectories. After a brief decline between AD 1500 and 1700, the economic

growth was presumably following a fast-increasing hyperbolic trajectory, as positively

identified for Australia, but from around 1820 it started to be diverted to a slower, non-

hyperbolic trajectory. There is no positive proof of the existence of the three regimes of

growth. On the contrary, by comparing these data with the data for Africa, Latin America and

Australia, there is strong indication that the three regimes did not exist. There is also no

positive proof of a takeoff from stagnation to growth. The Unified Growth Theory is

contradicted, or at least strongly questioned, by the data describing economic growth in

Western Offshoots.

35

References

Galor, O. (2005). From stagnation to growth: Unified Growth Theory. In P. Aghion & S.

Durlauf (Eds.), Handbook of Economic Growth (pp. 171-293). Amsterdam: Elsevier.

Galor, O. (2011). Unified Growth Theory. Princeton, New Jersey: Princeton University Press.

Maddison, A. (2010). Historical Statistics of the World Economy: 1-2008 AD.

http://www.ggdc.net/maddison/Historical Statistics/horizontal-file_02-2010.xls.