R&D – Based Models of Economic Growth

R&D based models

• Virtually all R&D based models share a prediction of ”scale effects”

• This prediction is not supported by empirics

• This article comes up with suggestions for an alternative R&D based model

Setting up the normal model

(1)

(2)

Arguments against this model

• The size of labour force has grown dramatically over the last 25-100 years, but average growth rate has been relative constant!

Arguments against this model

• Another way to introduce R&D in the model so that it doesn’t impose scale effects could be:

• But this is not consistent with the micrfoundations for R&D models developed by Romer et al.

• Also it imposes that an economy with one unit of labour can produce as much TFP-growth as 1 million units of labour.

(3)

Arguments against this model

• Also empirics doesn’t support eq. (3)

R&D based models are still very appealing

• R&D based models presented in the literature can are all easely rejected as mentioned above.

• However they share an intuitive appeal:– Growth arises as a result of intentional innovation by

rational, profit-maximizing agents and the models have strong microfoundations.

• We therefore would like to maintain the basic structure, while eliminating the “scale effect.”

Introducing a new model

• Simplest way that innivations evolve:

• We can then put restrictions on the arrival rate of new ideas:

• And finally that overlap of research reduce the total number of innovations so that rather than belongs in the R&D equation. Inserting this and (4) and (5) gives:

(4)

(5)

(6)

The decentralized economy

• Three sectors:1. A final goods sector that uses labour and

producer durables

2. An intermediate-goods sector of monopolists transforming capital into producer durables using designs discovered by the third sector.

3. The R&D sector.

The decentralized economy

Growth in the stock og knowledge:

Differentiating both sides of (7) we can solve explicitly for the balanced growth path:

The growth now depends on the population growth rate and not on the population stock.

(7)

(8)

The decentralized economy

• The share of labour in the decentralized economy:

The social planner

The social planner

• Setting up the usual Hamiltonian ans solving this program reveal that the growth in steady state is given once again by:

• And the amount of labour devoted to the R&D is:

Transition effects in the model

Where and

Transition effects in the model

• (19) and (20) are nonlinear, but linearizing around its steady state yields:

Transition effects in the model

• The article then argues that even though the impact from changes in R&D doesn’t last forever, they can still be of great importance in the transition period.

• It is of importance, both in the case of over- versus underinvestment to obtain empirically plausible parameter values of λ and .

• Several other articles conclude that it is difficult to separately identify the effects from λ and .

Conclusion

• The paper starts with a strong prediction of R&D based models, which exhibits intertemporal scale effects.

• The “semi-endogenous” R&D based model proposed by the paper is more consistent with empirical findings. – It does (unlike the AK-style and the R&D based models

mentioned) predict that the growth rate is determined by parameters that are typically invariant to policy manipulation.

– As in the Solow model, subsidies to R&D and to capital-accumulation have no long run effects, but only affect the transition path.

– But unlike the Solow-model, this model is endogenous in the sense that it derives from the pursuit of new technologies by rational, profit-maximizing agents.

– The model provides a well defined answer to the question, Why do economies exhibit sustained per capita income growth?