Jones model

The Jones model is a growth model developed in 1995 by 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 design instructions arise. This should take into account the criticism made of the Romer model that the long-term growth rate depends positively on the size of the population (economies of scale). This is problematic in several respects: on the one hand larger countries do not necessarily grow faster. On the other hand, an increasing population or intensified research work did not increase the growth rate on average.[1] Furthermore, the extent of influence from the current state of knowledge on new inventions (standing on shoulders effect).

Model Structure

For a single company i According to the following modeling applies to the emergence of new ideas or design instructions:

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

With

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

${\displaystyle A}$: Technology level

${\displaystyle {\dot {A}}}$ refers to the derivation of the variables ${\displaystyle A}$ A after the time, so ${\displaystyle {\dot {A}}={\frac {\partial A(t)}{\partial t}}}$

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

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

Here the parameters have the following meaning:

• ${\displaystyle \lambda }$ lambda restricts the effect of additional labor input in the research sector. Although more researchers are producing more ideas , each researcher is contributing less and less. This relationship is also called standing-on-shoes effect (step on your feet, see also yield law ). This parameter reflects a possible negative externality of the duplication. For a single company, however, this problem does not exist because within a research department, all researchers know about the work of their colleagues.
• ${\displaystyle \phi <0}$: A negative value aims at giving only finitely many potential new ideas for a given time. This case is also referred to as a fishing-out effect: over time, the relatively "simple" inventions are made first; Today, it is becoming increasingly difficult to develop a new drug.
• ${\displaystyle \phi =0}$: Here, productivity in the research sector would be independent of existing knowledge. For example, a physicist should be able to develop 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 encountered in reality. The current state of the art is to a certain extent involved in research. The standing-on-shoulders effect is only weakened compared to the Romer model.

Growth rate

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

${\displaystyle {\frac {\dot {\hat {A(t)}}}{\hat {A(t)}}}=0\quad \Leftrightarrow \quad {\hat {A(t)}}={\frac {\lambda \cdot n}{1-\phi }}}$ n for the growth rate of persons working in the research sector.

Further reading

• Daron Acemoglu (2008). Introduction to modern economic growth. Princeton: Princeton University Press. pp. 488/489.CS1 maint: ref=harv (link)

References

1. Charles I. Jones (1995). "R&D-based models of economic growth". Journal of Political Economy. 103 (4): 759–784. doi:10.1086/262002. JSTOR 2138581.CS1 maint: ref=harv (link)

Links

• Jones model - Article in the Gabler Wirtschaftslexikon.