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## Über dieses Buch

The author shows that the enormous gap between theory and facts in modern macroeconomics can only be eliminated by nonlinear macroeconomic dynamics with the following special characteristics: First of all, only certain group-theoretical invariants generate the correct growth cycles with irregularly varying lengths, not any stochastic process as usually applied for this purpose. Furthermore, a special extended value function and generalized human capital are needed for a correct representation of scientific and technological innovation. Finally, the correct nonlinear macroeconomic dynamics are not reducible to microeconomics, for both of the above mentioned reasons.

## Inhaltsverzeichnis

### 1. The Macroeconomic Problem

Abstract
Does it apply to economics? In mathematical natural sciences, such as physics and chemistry, theoretical development has indeed been largely determined by observed facts. In economics the situation is a little different. Economics has become an influential practical science, like medicin and law. It is like medicin and law a profession, where professional solidarity plays an important role. Being a profession and a science simultaneously implies that theorizing in economics is partly determined by the general wisdom of the day, as accepted in the profession. Because of this important professional connection the basic theoretical assumptions at any given time tend to be widely accepted over most of the profession. It follows that new fundamental ideas have come slowly in economics, where theoretical foundations carry that professional responsability.
Arvid Aulin

### 2. Canonical Formalism: Basics

Abstract
The canonical formalism will be here revisited emphasizing the parametric conditions of the existence of solutions in economic applications.
Arvid Aulin

### 3. The Canonical Formalism of Macroeconomics

Abstract
Let the total human time in a country within a period of production, say a year t, be defined as the grand total N(t) of the living times of all working-age people in society during the year t:
$$N\left( t \right) = \begin{array}{*{20}{c}} {N*\left( t \right)} \\ {\sum {{N_i}\left( t \right).} } \\ {i = 1} \end{array}$$
Arvid Aulin

### 4. The Principle of Economy in Scientific Explanation

A Survey of Empirical Verifications
Abstract
There is a principle of economy of scientific explanation, in economics stressed especially by Milton Friedman, stating that observed facts should be explained by the least possible theoretical assumptions. Following this principle a minimal macroeconomic dynamics, with a generalized value function but without the two dogmas (cf. Section 1.2), was constructed in Chapter 3.
Arvid Aulin

### 5. Growth Paths Determined by Canonical Formalism

Abstract
This is the case where = 0 and = 0, so that the equations (3.39) are valid. Both pairs of the equations (3.29) and (3.34), and thus the first and second normal forms of cycle equations, are identical in this case.
Arvid Aulin

### 6. The Plosser Fact and Other Growth Effects of Savings Rate

The first decisive piece of evidence
Abstract
We shall study in this chapter how the generalized value function affects the growth of variables connected to the labour input E on the balanced-growth path. The Plosser fact 7 states the positive effect of savings rate on the growth of output per worker Y/E, while no similar effect exists in the case of output or employment. This will be theoretically reproduced, and the effects of savings rate on the growth of output and employment will be analysed. The Plosser effect, with a positive effect on Y/E and an absence of it for Y or E, is a puzzle in growth theories. The solution given here is based on the extraordinary connections, which in this theory exists between the net savings rate and the level of output per worker, output and employment.
Arvid Aulin

### 7. The Kydland Facts on Leads and Lags in Business Cycles

The second decisive piece of evidence
Abstract
The minimal macroeconomic dynamics constructed in Chapter 3 indeed suggests a solution to the problem of business cycles along those lines, emphasizing further the significance of the cycles in labor input and labor productivity. This concerns also the problem of leads and lags.
Arvid Aulin

### 8. Correlations and Variances over the Ordinary Business Cycles

Complementary Evidence
Abstract
The choice between the two normal forms of cycle equations is irrelevant in Chapter 8 (because of their symmetry) — we shall here use the first of them, (3.29), since it applies in Chapter 9 too. The Solution of the linear approximation (3.46)-(3.47) can be written in the form
$$s - {s^*}\mathop = \limits^{Lin} C{e^{ut}} + \overline C {e^{\overline u t}},C = \left( {\frac{1}{2} + \frac{{ia}}{{4\omega }}} \right)\left[ {s(0) - {s^*}} \right]$$
(8.1)
,
$$x - {b^*}\mathop = \limits^{Lin} D{e^{ut}} + \overline D {e^{\overline u t}},D = \left[ {\frac{{ia({\alpha ^2} + 4{\omega ^2})}}{{8(1 - {s^*})\omega }}} \right]\left[ {s(0) - {s^*}} \right]$$
(8.2)
.
Arvid Aulin

### 9. Correlations over Anomalous Business Cycles

Complementary Evidence
Abstract
In 1992 a group of economists published an interesting article1, in which they observed anomalous business cycles in the period 1914–50 in the U.S.A. and the U.K. Their results can be summarized as follows.
Arvid Aulin

### 10. The Role of Stochastic Shocks in the Business Cycle

Complementary Evidence
Abstract
It is an accomplished fact in current growth theories that stochastic shocks do not essentially affect the long-term economic development. But ever since the remarkable paper of the Russian mathematician Eugen Slutsky from the year 1927 was translated and published in English in a completed form (Slutsky, 1937), the economists have been fascinated by the idea that the business cycles may be produced in the way discussed by Slutsky in his analysis of the Gaussian distribution. He showed that random series are capable of forming cyclic phenomena. This follows already from the symmetry of the Gaussian curve around the mean of the series, but he also showed that the effect can be made more visible by summations over certain sequences in a random series. These discoveries became generally known much later.
Arvid Aulin

### Backmatter

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