Romer model

Paul Romer, 2005

The Romer model is a mathematical description (economic model) of the growth of an economy developed by Paul Romer in 1990 . It is an early and well-known proponent of the endogenous growth theory , which emerged from the 1980s as a criticism and response to the neoclassical models of growth.

The more recent growth theories have in common that the growth process can be derived from the preferences of the market participants (and their savings, consumption and investment behavior) and can thus be "endogenized". Technical progress is assumed to be the main driving force behind growth ( Economics of Ideas ). Research and development always result in completely new product variants (variety model), there are no plans to improve existing products or capital goods (quality model).

A generalization of Romer's work by Charles I. Jones in the Jones Model (1995) followed later .

The model

Model assumptions

In the Romer model, technical progress is the decisive factor behind economic growth. Technical progress is the result of deliberate actions by market participants who respond to incentives, i. i.e., it results from research by for-profit companies. In order to invest funds in technical progress, they forego consumption and save or invest what they save. The greater the consumption, the higher the funds used for research by the companies and the greater the number of new ideas. Refraining from consumption is therefore the actual basis of all technical progress.

The most important assumption of Romer is the characterization of the "ideas" in the sense of pure knowledge as a non-rival good (see degree of rivalry ). This means that once a discovery has been made and, for example, the construction instructions derived from it, any number of people can use it at the same time without hindering each other. Research thus serves as the basis for further research.

Some of the ideas that are decisive for growth can be excluded because they can be secured through patents and other property rights . They may only be used in the production of goods by the respective licensee or patent holder, which creates short-term market power (monopoly). This ensures that the (often high) fixed costs in the production of an idea are brought in again, but that there are positive external effects in the form of knowledge spillovers.

In fact, Romer does not classify ideas in his models as either a public good or a private good :

"Externalities suggest incomplete control or appropriateness, but they do not capture the absence of opportunity costs that is the key characteristic of an idea. The combination of some degree of private control and an absence of opportunity costs means that ideas are neither public goods nor private goods - nor a mixture of the two. "

- Paul M. Romer (1993)

Model structure

The structure of the Romer model.

The model distinguishes between three sectors: a research and development sector (which develops new ideas), an intermediate product sector and an end product sector which produces consumer goods.

Research sector

In the research sector , new designs ( blueprints ) for intermediate products are developed. An essential task is the production of new knowledge (and thus an increase in the current level of knowledge for the next period). Another is the sale of produced designs, which are secured by patents , for example . The exclusivity created by patents is necessary to cover the costs of knowledge production - which otherwise would not be possible under perfect competition (see also economic analysis of patents ). For the sake of simplifying the model, it is assumed that each unit of technical knowledge is reflected in exactly one unit of an intermediate good. Technical knowledge can therefore be described numerically by the number of patents.

In order to increase the stock of designs or knowledge, researchers or their work ( human capital ) with a certain productivity and the current state of technical knowledge ( state of the art ) are available to the research sector. This sector can be modeled using a knowledge production function as follows: ${\displaystyle H_{A}}$ ${\displaystyle \delta }$ ${\displaystyle A_{t}}$

${\displaystyle {\dot {A}}_{t}=\delta \cdot H_{A}\cdot A_{t}.}$

This modeling has two main consequences:

• Economies of scale : The rate at which new designs are developed increases with the use of human capital or the number of active researchers. This contradicts many observations in reality and was tried to avoid in many other growth models (e.g. the Jones model ).
• Gigantic effect : Productivity in the research sector (with constant staffing) increases permanently with every new invention. This tendency is also called the “shoulders on giants” effect (after the parable of the dwarfs on the shoulders of giants ). On the other hand, there is a tendency that future inventions are more and more difficult to make because the relatively simple ones were made first (“fishing out” problem). This effect is also modeled and relativized more precisely in the Jones model .

Intermediate product sector

The intermediate product sector requires a certain number of consumer goods for its production. For the production of intermediate goods, a certain number of end products are dispensed with. In addition, this sector (like the end-product sector) needs labor and human capital and additional patents from the research sector. The intermediate products can also be viewed as capital goods.

The companies here acquire the patents of infinitely long duration at the highest bidder at a price so that each capital good is only produced by one company (monopoly). ${\displaystyle p_{A}}$

Their production technology is very simple: A constant amount of raw capital becomes a unit of the capital good without further input of factors - sometimes it is simplified to the extent that exactly one unit of raw capital is converted into one unit of the capital good. This technology is the same for all varieties for the sake of simplicity. In addition, the capital goods are not subject to depreciation. ${\displaystyle \eta }$

The capital stock of the permanent capital goods produced here is calculated as follows:

${\displaystyle K_{t}=\eta \cdot \int _{0}^{\infty }x(i)\,\mathrm {d} i}$.

The positive parameter describes how many units of consumer goods you have to give up in order to produce a capital good. In this case , this means that by foregoing a unit of the consumer good, exactly one unit of a new machine is created, which becomes the capital stock. In this sense, capital accumulation takes place as a non-consumed portion of end products: ${\displaystyle \eta }$ ${\displaystyle \eta =1}$

${\displaystyle {\dot {K}}_{t}=Y_{t}-C_{t}.}$

More precisely, this means that this proportion of unused end products is not even produced. The resources that would have been needed to manufacture the portion of end products are instead used to produce capital goods.

End product sector

The end product sector consists of a large number of competitive companies ( perfect competition ), but all of which use identical production technology to produce homogeneous consumer goods (end products). Some of the consumer goods are consumed while the other is saved and leads to capital accumulation .

In this sector, (unskilled) labor , human capital (such as skilled labor) and intermediate products are required. The present technology has constant returns to scale (i.e., all exponents add to one). The end product sector can be modeled as follows: ${\displaystyle L}$ ${\displaystyle H_{Y}}$ ${\displaystyle x(i)}$

${\displaystyle Y=H_{Y}^{\alpha }\cdot L^{\beta }\cdot \int _{0}^{\infty }x(i)^{1-\alpha -\beta }\,\mathrm {d} i\quad \forall t}$,

where for a specific point in time t the upper integration limit can also assume a specific value . This is the finite number of intermediate products realized at a given point in time, which were developed according to the currently available construction plans (ideas), although these construction plans or ideas are potentially infinite. ${\displaystyle A_{t}}$

All previously existing intermediate products (raw capital) flow into production with a certain proportion, whereby these are not perfect substitutes , i.e. That is, two machines of different types produce more output than two machines of the same type. The result is increasing specialization.

Long term equilibrium and growth rate

A growth equilibrium is reached when the growth rate of production corresponds to that of consumption, i.e. supply and demand are in equilibrium and the factor markets are cleared. The intertemporal utility preferences are balanced by the interest.

In the Romer model, economic growth arises as follows:

1. Refraining from consumption leads to an increase in productivity and thus to growth via capital accumulation.
2. If consumption is foregone (i.e. if households have a low rate of time preference), part of the human capital can be used in research rather than in consumer goods. Current production will be lower, but instead new products will be developed and technology will improve. This creates growth and more opportunities for production and consumption in the future.
3. This effect is closely related to the externalities in the research area: The knowledge available to all other researchers is also increased and thus the productivity of all further research activities. So the growth process does not come to a standstill.

• Demand for capital goods
  The demand for capital goods (machines) in the end product sector results from the profit maximization of the manufacturers there. The profit function leads to the inverse demand function
  ${\displaystyle {\underset {x}{\operatorname {max} }}\int _{0}^{\infty }[H_{Y}^{\alpha }\cdot L^{\beta }\cdot x(i)^{1-\alpha -\beta }-p(i)x(i)]\,\mathrm {d} i}$
  
  ${\displaystyle p(i)=(1-\alpha -\beta )\cdot H_{Y}^{\alpha }\cdot L^{\beta }\cdot x(i)^{-\alpha -\beta }.}$
• Maximizing Profits in the Intermediate Product Sector
  Manufacturers in the intermediate product sector, which is subject to monopoly competition, maximize their profit taking into account this demand for their goods. Thus, their profit function looks like this: Here the rental income ( ) is set against the interest costs that are required to create the required capital goods. The profit-maximizing price results as follows: The numerator of the fraction contains the marginal costs ( ). Since the denominator is less than one, the total price is above these marginal costs, which is referred to as mark-up . The mark-up on marginal costs is also a result of the elasticity of demand ( Chamberlin's mark-up ).
  ${\displaystyle \pi ={\underset {x}{\operatorname {max} }}=p(x)\cdot x-r\cdot \eta \cdot x}$
  ${\displaystyle p(x)\cdot x}$
  ${\displaystyle {\overline {p}}={\frac {r\cdot \eta }{1-\alpha -\beta }}}$
  ${\displaystyle r\cdot \eta }$
• Profit maximization in the research
  sector Here there is perfect competition through the acceptance of free market entry. The value or price of a patent must correspond to the present value of the profits or the discounted future profits from the production of intermediate products: There is an intertemporal no-profit condition: the current profits of a capital goods manufacturer are just enough to cover the costs of the interest rate of the initial To cover investment in the patent. ${\displaystyle p_{A}}$
  ${\displaystyle p_{A}=\int _{t}^{\infty }\Pi _{x}\cdot e^{-r(\tau -t)}\,\mathrm {d} \tau ={\frac {\Pi _{x}}{r}}}$
  
• Consumption optimization of households
  In the economy there is a constant number of households. Households maximize their intertemporal utility function subject to the constraint: This eventually leads to the Keynes-Ramsey rule : .
  ${\displaystyle {\underset {C_{t}}{\operatorname {max} }}=\int _{0}^{\infty }{\frac {C_{t}^{1-\sigma }-1}{1-\sigma }}e^{-\rho t}\,\mathrm {d} t}$
  
  ${\displaystyle \int _{0}^{\infty }C_{t}e^{-R_{t}}\,\mathrm {d} t=A_{0}.}$
  
  ${\displaystyle {\frac {\dot {C}}{C}}={\frac {1}{\sigma }}(r_{t}-\rho )}$
• Equilibrium growth path Consumption, output and innovations must grow at the same and constant rate g
  along the balanced growth path , so that:
  ${\displaystyle {\frac {\dot {C}}{C}}={\frac {\dot {Y}}{Y}}={\frac {\dot {A}}{A}}=g}$
• Optimal growth rate
  Through further transformations the growth rate results as:
  ${\displaystyle g={\frac {\delta \cdot H-\Lambda \cdot \rho }{1+\Lambda \cdot \sigma }}\quad {\text{mit}}\quad \Lambda ={\frac {\alpha }{(\alpha +\beta )(1-\alpha -\beta )}}.}$

Welfare Maximization

The growth rate calculated to be optimal is not necessarily socially desirable. If one were to give a social planner full decision-making power over the economy and if he were to base his decision on the intertemporal utility function of the households, the socially optimal growth rate would result in :

${\displaystyle g_{w}={\frac {\delta \cdot H-{\frac {\alpha }{\alpha +\beta }}\cdot \rho }{{\frac {\beta }{\alpha +\beta }}+{\frac {\alpha }{\alpha +\beta }}\cdot \sigma }}.}$

Whereby applies. This is because research increases the productivity of researchers in the future, but this intertemporal externality is not reflected in the price of the patents, and the demand for machines is lower than with full competition because of the monopoly distortion. ${\displaystyle g_{w}>g}$

Implications

External effects

External effects exist in the equilibrium of the Romer model . Externalities appear in goods with a low level of excludability (applies to ideas ). Goods with positive (negative) externalities are regularly too little (too much) available on the market.

• Negative external effect : monopoly competition
  The intermediate product market (capital goods market) is characterized by monopoly competition, since the acquisition of a patent ensures that the owner has sole control over the corresponding design. A social planner would try to create more competition by lowering the price at marginal cost. The increasing demand would free up human capital in production. B. can be used in research.
• Positive external effect :
  the research sector is not rewarded for the increase in knowledge, but only for the patent sold. The knowledge produced is in turn available to everyone. Innovations therefore increase the current and future productivity of researchers (and thus future wages). However, this is not taken into account, but could be compensated for by higher wages.

Economies of scale

The criticism of the economies of scale initiated the development of a whole class of growth models that avoid this effect. Dinopoulos and Thompson (1999) provide a good overview of this literature.

Innovation process

Romer's modeling of the research sector neglects essential characteristics of the real economic innovation process.

• Variety model (exclusively horizontal innovation )
  On the one hand, the variety of products at Romer is constantly increasing, since all variants ever designed remain in the product range forever. But there is also the case of old products being displaced, an observation made by Joseph Schumpeter as early as 1942 (see Creative Destruction ). There are also a number of models that focus on the aspect of product quality, for example Grossman and Helpman (1991) or Aghion and Howitt (1992).
  Another mathematical disadvantage of the variety models is that the labor employed per product line decreases exponentially (since the population is assumed to be constant).
• Security of the research result
  On the other hand, there is absolute certainty about the research result in Romer's formulation. If you have a sufficient number of researchers with the appropriate productivity, they will always come up with new ideas. This neglects the fact that the research process is in principle insecure (stochastic). It is mostly unclear whether the expenditure on research actually leads to the invention of new, improved product variants (and how long this takes), whether the later, discounted income from the sale of the product variant exceeds the research costs incurred today , and how long the quality leadership after successful innovation in the respective industry persists.

reception

Romer's work on endogenous growth was widely received and taken up in the professional world. In the Research Papers in Economics database (RePEc), his article Endogenous Technological Change , published in 1990, was ranked 14th; the essay, Increasing Returns and Long-run Growth , published four years earlier, even took 9th place (as of November 2015).

Romer and his endogenous growth model were repeatedly discussed as candidates for the Alfred Nobel Memorial Prize in Economics in the 2010s . Romer was finally awarded this prize in 2018, together with William D. Nordhaus . The last growth theorist to win this prize before him was Robert Solow in 1987. In addition to Romer, Robert J. Barro is often mentioned as another growth theorist .

literature

Original literature

• Paul M. Romer : Endogenous Technological Change . In: Journal of Political Economy . tape 98 , no. 5 , 1990, pp. 71-102 , JSTOR : 2937632 .
• Paul M. Romer: Increasing Returns and Long-run Growth . In: Journal of Political Economy . tape 94 , no. 5 , 1986, pp. 1002-1037 , JSTOR : 1833190 .

Textbooks

• Charles I. Jones: Introduction to Economic Growth . 3rd edition. Norton, 2013, ISBN 978-0-393-92078-9 . Chapters 4 and 5.
• Xavier Sala-I Martin, Robert J. Barro: Economic Growth . Second edition. MIT Press, 2003, ISBN 978-0-262-02553-9 . Chapter 6.3.
• Lutz Arnold: Growth Theory. Vahlen, Munich 1997, ISBN 3-8006-2242-4 .
• Michael Frenkel, Hans-Rimbert Hemmer : Foundations of the growth theory. Vahlen, Munich 1999, ISBN 3-8006-2396-X .

Other secondary literature

• Thomas Trauth: Innovation and Foreign Trade. A contribution to the theory of endogenous growth in interdependent economies (= economic contributions. Volume 145). Physica-Verlag, Heidelberg 1997, ISBN 3-7908-1019-3 (also: Mainz, University, dissertation, 1996).
• Wolfgang Kornprobst: Innovation-based growth theory . Diss. 2008.

Web links

• Romer model. In: Gabler Wirtschaftslexikon

Individual evidence

1. ↑ Malcolm H. Dunn: Growth and endogenous technological change-A critique of the growth model by Paul Romer from the perspective of evolutionary economics . In: ORDO Yearbook for the Order of Economy and Society , Stuttgart, 51, 2000, pp. 282–283, here p. 282.
2. ↑ ^{a b c} Kornprobst (2008): Innovation-based growth theory .
3. ^ Paul M. Romer: Two Strategies for Economic Development: Using Ideas and Producing Ideas . In: Proceedings of the World Bank Annual Conference on Development Economics , 1992. World Bank, Washington DC 1993, pp. 63-91, here: p. 64.
4. ^ Alfred Maussner: Growth theory . Jumper; Edition: 1996 (October 4, 2013). ISBN 978-3-540-61501-9 . P. 256ff.
5. ↑ Malcolm H. Dunn: Growth and endogenous technological change-A critique of the growth model by Paul Romer from the perspective of evolutionary economics . In: ORDO Yearbook for the Order of Economy and Society , Stuttgart, 51, 2000, pp. 282–283, here p. 287.
6. ^ Jones: Introduction to Economic Growth . 2013
7. ^ ^{A b} Romer: Endogenous Technological Change . 1990
8. ↑ Elias Dinopoulos, Peter Thompson: Scale effects in Schumpeterian models of economic growth . In: Journal of Evolutionary Economics , 9 (2), 1999, pp. 157-185.
9. ↑ Fritz Söllner: The history of economic thinking . 3. Edition. Springer, 2012, ISBN 978-3-642-28177-8 . P. 205.
10. ↑ Top 1 ‰ Research Items by Number of Citations. ideas.repec.org ( Research Papers in Economics ), accessed on November 13, 2015 . 
11. ↑ Our favorites for the Nobel Prize in Economics . In: FAZ , October 14, 2012; Review article, accessed April 5, 2014.
12. ↑ Who will win the Nobel Prize in Economics? In: Handelsblatt , October 11, 2013; Retrieved April 5, 2014.