L15 - Endogenous Growth Theory Flashcards
How is the endogenous growth model different from the exogenous growth model?
- technology is assumed to be a function of other variables.
- This will equate to technology being related to the production of ideas in the economy; it is the result of purposeful research and development (R&D) activity.
- Put another way, technology will no longer be assumed to grow according to the process At = A0egt (where g is the growth rate of technology, and t denotes the time period).
How did Solow (1956) and MRW (1992) deal with technology?
- Recall that in the exogenous growth models of Solow (1956) and Mankiw, Romer and Weil (1992), technology growth was assumed to follow this (exponential) process.
- Adding exogenous technical progress to a simple Solow model leads to the prediction that in the steady-state, output per worker (yt = Yt/Lt) will grow over time.
- This prediction is consistent with the empirical (i.e., real-world) observation that for most countries, GDP per capita has grown over time.
- What MRW found is that adding human capital to a Solow model with technology is very effective in accounting for cross-country differences in economic growth.
- This naturally raises the issue of what can be gained from introducing endogenous technological progress into a theoretical model.
- If models with exogenous technological progress can explain many of the stylised facts of long-run economic growth, what is the point, for instance, of endogenising technological progress?
How long has the idea of endogenous technological progress been around?
- The notion of endogenous technological progress has been around for some time. From a policymaking perspective, it is an appealing idea if one applies the following line of reasoning:
- if the growth rate of technological progress plays an important role in determining the growth rate of output per worker ( y(dot) /y ), and we can determine the economic factors that drive At,
- this will allow governments to enact policies that affect these economic factors, thereby increasing y(dot) /y.
- This ultimately holds the implication that our living standards will increase over time
What is the Arrow approach?
The Arrow approach, which we set out here, is a form of the AK model and is characterised by technological progress being a by-product of the production process.
it is clear to see that Y = AKL1-α (a production function with increasing returns to scale), which reduces to Y = AK when L is normalised to one. We are therefore back where we started out fromñthe basic AK model
How do you derive the AK model and what can we learn from it?
- Consider a special case of a production function Y = AKaL1-α .
- Setting the capital share parameter, α, equal to one implies that Y = AKaL1-α reduces to Y = AK, hence the name ‘AK model’.
- In this model, let’s assume no technological progress, such that the parameter A is a constant: it does not evolve over time, and measures the amount of output produced for each unit of capital.
- The marginal product of capital is dY /dK = A. In other words, is it constant, and not characterised by diminishing returns to scale as would be the case in the’standard’ setting where 0 < α < 1.
- Some economists argue that assuming constant returns here is realistic if one assumes that K encompasses knowledge in addition to just physical capital.
- Knowledge is an important input into production, and it seems plausible to assume that it is not subject to diminishing returns.
What are some further implications of the basic AK model?
We can answer this question by finding the growth rate of Y , through taking logs then derivatives of Y = AK with respect to time. This will imply that Y(dot) /Y = K(dot) /K: put another way, the growth rate of output will be equal to the growth rate of capital. Prima facie, this result seems pretty innocuous.
So what more can be said about K(dot)/K.
What do we assume the equation of motion is for the basic AK model?
K(dot)= sY - 𝛿K
- If all savings (s) are channelled to investment, and there is no population growth (let’s assume L = 1, which implies that there is no difference between output per se and output per worker)
- dividing by K yields K(dot)/k= sY/K - 𝛿
- Thus Y(dot)/Y = A - 𝛿: δ: ceteris paribus, an increase in the saving rate leads to a permanently higher growth rate. It turns out that if we allow for population growth too, the result does not change
- Output per worker will grow at the rate y(dot)/y= sA - (𝛿+n)
- , where n is the population growth rate. The significant point here, however, is that output per worker will grow endogenously, with no role for technological progress
- and will be driven by the equation of motion k(dot) = sAk - (𝛿+n)k, where k = K/L
What does the Solow diagram of the AK model look like?
Using the simple AK model, assuming s= 0.3 δ = 0.1, A = 1 and with an initial value of K =3
Y increases by successively greater increments. This process is driven by the equation of motion, ∆K = sAK-δK. The economy grows perpetually at rate sA-δ and never converges to a ‘steady-state’. This is due to the investment line in the associated Solow diagram being both straight and steeper than the break-even line (we assume s > δ): as shown overleaf, the two lines can never cross each other
How does the Arrow model build upon the AK model?
- So, how does the ‘learning by doing’ model of Arrow fit in here? The Arrow model is a special form of AK model which assumes that in the production function Y = BKαL1-α ,
- B is an endogenous parameter which determines the amount of output produced given the modelís inputs.
- If B is accumulated endogenously, it implies that overall, production is characterised by increasing returns to scale.
- The key assumption here is that B captures knowledge about the economy, which is generated as a result of capital accumulation by firms.
What does the relationship B=AKα say?
- B will grow as K gets larger, where the parameter A is a positive constant. Here, capital accumulation leads to new knowledge, which is an unintended consequence of the production process.
- This is because firms only accumulate capital because it is a useful production input. This process is called learning by doing
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What is the short-coming of Arrow’s model?
- knowledge is produced unintentionally, and in practice, the search for knowledge is due to purposeful efforts.
- This is acknowledged in the work of Paul Romer, who in the 1980s developed models of endogenous growth in which technological progress was driven by the (purposeful) production of ideas and innovation
What view does Charles Jones hold about R & D?
- Charles Jones holds the view that R&D is not merely an accidental spillover from the capital accumulation process (this explains why it is given such brief treatment in his textbook).
- He believes that it is more likely that ‘knowledge accumulation is…the desired outcome of entrepreneurial effort rather than an accidental by-product of some other activity’ (Jones, p.163).
- Saying this, it does not mean that the notion of externalities playing some role in the knowledge generation process is totally nonsensical (consider Isaac Newton’s remark about ‘standing on the shoulders of giants’).
- We therefore want to consider a model where R&D is a result of conscious e§ort to innovate by firms
What are ‘ideas’ in the context of this model?
- Romer emphasizes that ideas differ significantly from other goods, in drawing on the concepts of their rivalrous / non-rivalrous nature, and their excludability.
- Charles Jones, drawing on Romer (1993) notes that compact disc (CD) players or lawyer services are rivalrous: if one person uses a CD player, it excludes another person using it at the same time. This property extends to most goods.
- Ideas are non-rivalrous. Just because one student uses calculus to help work their way through the economic models in this set of slides, it does not prevent other students from doing so at the same time.
- However, this might not be the case for all ideas, which brings us to the notion of excludability.
- In much the same way that an individual can charge a fee to purchase a product-thereby making it excludable-so too can the creators of ideas
What does Jones highlight the role of copyright and patent systems?
- Here, Jones highlights the role of copyright and patent systems in granting inventors who receive copyrights or patents the right to charge for the use of their ideas.
- This issue raises another important point.
- Unless intellectual property rights are protected, the incentive to innovate may diminish.
- After all, what is the point of innovating if oneís blueprints for inventions and ideas can be copied by others? Intellectual property theft may also have other significant economic ramifications
What was one of the main drivers of the trade war between the US and China in 2018?
- One of the main drivers of the trade war beginning in 2018 between the US and China is the latterís alleged theft of US firm’s intellectual property on a massive scale.
- This type of behaviour would clearly provide competitor forms with an unfair advantage (e.g., such forms would not have to invest the vast sums required for R&D), and according to the Commission on the Theft of American Intellectual Property in 2018, cost the US economy $600 billion per year (this figure is at the higher end of estimated losses).
How are ideas tied to the presence on increasing returns to scale and imperfect competition?
- In the former case, this is attributable to a high fixed cost of developing the product, and a constant marginal cost of producing units of the product once it is fully developed.
- Consider the creation of software, and its subsequent production in the form of CDs given by the simple production function y = f (x) = 100* (x -F )
- where y is the number of copies of the software produced, F is the fixed cost of developing the software (measurable in hours), and x is the number of input hours required to produce the software.
- F < x implies that the number of outputs (CDs) produced will be negative. This is obviously impossible.
- To produce the first CD required a tremendous amount of input F (F + 1/100 units). After this, mass production may be cheap.
Example of increasing returns to scale?
f(x) = 100 * (x - F)
first CD –> (F + 1/100 units)
- Assuming that F = 10,000 hours
- The relation implies that one hour of labour will produce 100 CDs
- It has taken 10, 001 hours to produce 100 CDs, 10, 002 hours to produce 200 CDs and so on.
- There are clearly increasing returns to scale: doubling the input hours more than doubles output.
- For instance, we did not have to double the number of input hours (from 10, 001 to 20, 002) to double the number of CDs produced from 100 to 200.
- All we had to do was to add an additional hour of labour. More generally, labour productivity (calculated as y/x) is rising with the scale of production.
What happens to fixed costs at higher levels of production?
- The previous example is characterised by a constant marginal cost, but a falling average production cost
- In the presence of a fixed cost - or more generally increasing returns - setting the price of a good equal to its marginal cost will result in negative profits.
- At higher levels of production, the initial fixed cost is spread over more and more units, and thus falls: average cost declines as the scale of production rises.
- Now assume that price is set to marginal cost (as in a perfectly competitive market).
- Average cost would outweigh the marginal cost of production.
- Under increasing returns, the firm would not set price equal to marginal cost, as negative profits would be generated.
- Firms thus charge more than marginal costs to recover the fixed costs associated with product development.
- This explains why for instance, software costs so much
What has been the rate of Patent issuance in the US?
- Patent counts for the US are shown in Figure 5 for the period 1880-1999. Approximately 13,000 patents were issued in the US in 1880, a figure which increases to 150,000 in 1999. As can be seen, the sample period is characterised by an increase over time in the proportion of patents being issued which are not of US origin.
- The increase in US patents issued over time is modest and subject to some volatility, but this pattern might not be reáective of all new inventions and ideas. This is because not all ideas are patented. Consider the example of Coca-Cola, the formula for which was invented by a chemist called John Pemberton.
- Had he patented his formula after inventing it in 1886, anybody would now be free to copy it: patents do not last forever.
- The Coca-Cola Company is a leading global soft drink manufacturer over 120 years later, in part due to the decision to keep the formula for Coca-Cola a trade secret.
How has R&D developed over time?
- plots the number of scientists and researchers in R&D -who can be regarded as ‘inputs’ into the process of knowledge creationñin the G5 countries and the US between 1950-1993.
- Considering scientific and research activity in this way provides a candidate mechanism for the creation of ideas, and hence endogenous technological progress.
- Significantly, this intuitively appealing mechanism provides the basis for Romer’s theoretical approach
- Figure 6 shows that the number of scientists and researchers clearly increase during the sample period.
- Although not shown in the figure, the empirical evidence also indicates that the share of the labour force devoted to R&D activity has also increased over time in advanced industrialised countries, as well as in emerging economies.
- This is no accident: governments associate the benefits and spillovers from domestic R&D activity with increased economic competitiveness and economic strength.
- Such activity, therefore, constitutes an integral part of a nation’s industrial strategy.
- In case of the UK, the promotion of STEM subjects at schools and universities reflects the importance attached to R&D and innovation activity, and further, the need to equip people with the skills to work in technologically advanced economic sectors.
What is the production function of Romel’s Model?
- Technological progress is explicitly modelled: we are therefore introducing a theory of technological progress.
- The model can be viewed as building directly on Solowís contribution: the model becomes more technically di¢ cult to grapple with, yet is more intuitively appealing.
What is the Capital stock equation of Romel’s Model?
How is Technology Modelled?
How does the stock of new ideas influence 𝛿(bar)?
What is the equation for the stock of ideas?
What is the Division of Labour in Romer’s model?
How can technology be modelled with the labour that creates the ideas?
What is the steady-state growth rate of Romer’s model?
What is the equation for the growth rate of researchers, and thus the growth rate of technology?
What happens when we increase the share of people devoted to R & D?
How can the graph of an increasing share of R&D be interpreted?
Need figure 7 graph to answer this question
Need figure 7 graph to answer this question
How can the growth rate of technology be depicted if the proportion of researchers increased?
How can the number of researchers affect the level of technology?
- The impact of increasing the number of researchers is to permanently increase the level of A: a ‘level effect’ thus arises
- The level of technology rises sharply following the initial shock at time t, due to the jump in A(dot)/A
- A keeps on rising, but the rate at which it rises gradually falls back in the long run to rate
- This level effect is plotted using natural logs below
What is the steady-state growth per capita?
How can the steady-state growth per capita be interpreted?
