Jones model

The Jones model is a growth model developed in 1995 by the economist Charles I. Jones .

The model is essentially identical to the Romer model (1990), in particular it generalizes or modifies the description of how new technologies, ideas or construction instructions arise. This should take into account the criticism made against the Romer model that there the long-term growth rate depends positively on the population size ( scale effect ). This is problematic in several ways: First, larger countries do not necessarily grow faster. On the other hand, an increasing population or intensified research work did not increase the average growth rate. Furthermore, the extent of the influence of the current state of knowledge on new inventions ( standing on shoulders effect ) should be relativized.

Model structure

For a single company , the following modeling applies to the development of new ideas or construction instructions: ${\displaystyle i}$

${\displaystyle {\dot {A}}_{i}=\delta \cdot A(t)^{\phi }\cdot L_{A}(t)^{\lambda -1}\cdot L_{A_{i}}(t)}$

With

${\displaystyle L_{A}}$: Number of employees in the research sector

${\displaystyle A}$: Technology level

${\displaystyle {\dot {A}}}$denotes the derivative of the variable with respect to time, i.e. ${\displaystyle A}$ ${\displaystyle {\dot {A}}={\frac {\partial A(t)}{\partial t}}}$

the parameters the following values: . The Romer model ( ) results for parameter values ​​of . After aggregation across all companies results: ${\displaystyle 0<\lambda <1;\phi <1}$ ${\displaystyle \lambda =\phi =1}$ ${\displaystyle {\dot {A}}=\delta \cdot A\cdot L_{A}}$

${\displaystyle {\dot {A}}=\delta \cdot A(t)^{\phi }\cdot L_{A}(t)^{\lambda }}$.

The parameters here have the following meaning:

• ${\displaystyle \lambda }$limits the effect of additional labor in the research sector. More researchers produce absolutely more ideas , but each additional researcher contributes less and less. This relationship is also called the standing-on-shoes effect (stepping on your feet, see also Income Law ). This parameter reflects a possible negative externality of the duplication. For a single company, however, this problem does not exist because all researchers within a research department know about the work of their colleagues.
• ${\displaystyle \phi <0}$: A negative value aims to ensure that there can only be a finite number of potential new ideas for a given point in time. This case is also referred to as the fishing-out effect: in the course of time, the relatively "simple" inventions are first made; today it is becoming increasingly difficult to develop a new drug, for example.
• ${\displaystyle \phi =0}$: Here productivity in the research sector would be independent of the existing level of knowledge. For example, a physicist should be able to come up with the same new ideas whether he lives today or 100 years ago (an unrealistic case).
• ${\displaystyle \phi >0}$: Describes in principle a positive externality and the case to be found in reality. The current state of the art is to a certain extent included in the research. The standing on shoulders effect is only weakened compared to the Romer model.

Growth rate

In the Jones model, the steady state growth is given by:

${\displaystyle {\frac {\dot {\hat {A(t)}}}{\hat {A(t)}}}=0\quad \Leftrightarrow \quad {\hat {A(t)}}={\frac {\lambda \cdot n}{1-\phi }}}$

where stands for the growth rate of people working in the research sector. ${\displaystyle n}$

Individual evidence

1. ^ Acemoglu, Daron. Introduction to modern economic growth. Princeton University Press, 2008. pp. 488/489.

literature

• Charles I. Jones: R&D-based models of economic growth. In: Journal of Political Economy. 1995, pp. 759-784.

Web links

• Jones model - article in the Gabler Wirtschaftslexikon