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The evolution of models of economic growth: which generations of models can be recognized starting from the seminal Solow model? Be able to explain the improvements brought by more recent models.

Neoclassical Model – Mankiw (Based on Solow Model)

The basic version of neoclassical model of economic growth was developed by Robert Solow (1956). In this model, the production function of an economy is the center piece, it defines relationship  between production factors and output.

In neoclassical models, the main production factors are capital and labour, the level of technology is considered as an exogenous factor that increases efficiency. Thus, the production function takes the form of Y = F(K,A*L), in which A is the level of technology and A*L is an ‘efficiency unit’ of labour.  If the production function is assumed to have constant returns to scale, then the output per efficiency unit (y = Y/A*L) is only dependent on the amount of capital per efficiency unit. Economic growth arises from the accumulation of capital. In the Solow model, the amount of capital per efficiency unit (k = K/A*L) is governed by two opposing forces: investment and depreciation. As long as the production function is ‘well behaved’ the economy over time approaches a steady state, in which income per efficiency unit constant.

In the Solow model an economy reaches a ‘steady state’, which is independent of the initial conditions of an economy.  In this steady state, the level of income depends on the rate of savings and population growth; the growth of the level of income only depends on technological growth; therefore, sustained growth requires technological growth.

Herman Daly, one of the founders of the field of ecological economics and a leading critic of neoclassical economics,[1] defines a steady state economy as

…an economy with constant stocks of people and artifacts, maintained at some desired, sufficient levels by low rates of maintenance “throughput”, that is, by the lowest feasible flows of matter and energy from the first stage of production to the last stage of consumption.”[2]

A steady state economy, therefore, aims for stable or mildly fluctuating levels in population and consumption of energy and materials. Birth rates equal death rates, and saving/investment equals depreciation.

Theoretical objection to Solow Model:

-          Solow model in the end could not explain all factors included. For instance, saving rate is taken as exogenous parameter, while saving decisions involve complex behaviour (which is should be endogenous)

-          Technological growth which is treated as exogenous parameter become the only one that matters for determining growth once the steady state has been reached.

Some of these restriction are overcome in the growth accounting methodology, in which a production function of Y=A*F(K,L) is assumed; the A parameter of efficiency is now regarded as the measure of ‘Total Factor Productivity’ (TFP), which incorporates all causes of growth. In growth accounting, growth is explained by deducting various causes from the TFP, minimizing the residual. However this methodology too is not free of problems: it fails to explain the role of institutions and technology, and Abramovits has called the residual as ‘measure of our ignorance’

Model objection to Solow Model:

-          Prediction about effect of population growth were not consistent with reality

-          Model predicts higher rate of convergence between countries (and independence of initial conditions) than is observed.

-          It does not explain fact that there is less capital flow than expected to developing countries. (For example accounting in human capital of developing countries, they need human capital, but lending money to train/educate people is difficult, as human capital does not serve well as a collateral)

-          The magnitude of international differences. The model underestimates income  inequality  in the world. Makwin shortly describes that it could be that an other production function and therefore a lack of imitating western technology, is the cause, but assumes this cannot be taken for granted without further research.

-          The rate of convergence: the phenomenon that poor countries tend to grow faster than rich countries. The rate of conditional convergence is not predicted by the model, only the quality of conditional convergence is explained. Initial conditions of an economy are underestimated in time:  initial conditions play longer a role. This will be discussed more broadly in seminar 12.

-          Rates of return. The difference in rate of return between countries is predicted much higher than in the real world is the case. These different rate of returns makes it now western markets are or soon will become saturated more attractive for companies to invest in emerging markets in thrird world countries. This topic is also discussed in courses like Development theory, strategy and policy and Technology and Globalization. This could be also linked to Commercial expansion, a gain of trade due to more trade and therefore better division of labour, also known as smithian growth, described by Mokyr (Mokyr, 1990).

All three problems are related to the capital share and therefore the shape of the production function.

Endogenous Model – Mankiw (Development from Neo-classical Solow Model)

From Solow Model, it is clear that a model of economic growth should at least incorporate an explanation from technological growth: simply including it as a factor is not enough. An attempt at incorporating the role of technological growth is the endogenous growth model (EGM).

EGM model also stems from the accumulation of capital. EGM assumes Y = A*K as the production function; this implies output is doubled when capital is doubled. An implication is that there is no such thing as a steady state: as long as sA > d (rate of saving * TFP larger than depreciation rate), income grows, even without the assumption of exogenous technological growth.  While savings increase growth only temporarily in the neo-classical model, they increase growth forever in the EGM.  Therefore, differences in savings across countries lead to larger differences over time than the neo-classical model.

One group holds that changes in TFP measure the rate of technical change. (Law,

Statscan, Krugman, Young.) We refer to this as the “conventional view”.

The second group holds that TFP measures only the free lunches of technical

change, which are mainly associated with externalities and scale effects.

(Jorgenson, and Griliches (6)) We refer to their position as the “J&G view”.

The third group is sceptical that TFP measures anything useful. (Metcalf, and

Griliches (8))

a b Y = AL K , a + b= 1

Total aggregate output is measured as Y. L is an index of aggregate labour inputs. K is an index of aggregate capital. Typically Y, L and K are independently measured while A, a and b are statistical estimations. A is an index of the aggregate state of technology called total factor productivity. Since A is not a pure number, it carries no interesting information in itself. But changes in the number indicate shifts in the relation between measured aggregate inputs and outputs and in this aggregate model these changes are assumed to be caused by changes in technology (or changes in efficiency and/or in the scale of operations of firms).

In EGM, knowledge is added to the model as a type of capital (albeit capital that is “less likely to exhibit diminishing returns” and “might even exhibit increasing returns”). An example of a model that incorporates knowledge which distinguishes between manufacturers that produce goods and universities that knowledge. The model also shows that there is a clear role for policy for defining and influencing ‘university-labour’ ratio. However the model does not account for research done within firms (and the necessary incentives, such as a patent system to stimulate it); endogenous growth models assume that knowledge eventually ‘spill over’ from a firm to the whole market.

It is important to note that human capital is a different thing than knowledge. As Mankiw et al put it, “knowledge is the quality of society’s textbooks; human capital is the amount of time spent reading them.”  What this refers to is the difference between embodied and disembodied technological progress. In the Solow model, only embodied technological progress is considered, which is progress that is embedded in tangible assets (i.e machine) and/or increases the efficiency of labour.  Disembodied technological progress, in contrast, is technological progress that allows more output using the already given inputs.

Evolutionary Model – Verspagen & Silverberg

Three pillars of any evolutionary theory are variation, selection, and inheritance. In the evolutionary models Verspagen describes the unit of analysis are firms, who use a particular technology; in biological terms the technology is the genotype, while the firm is the phenotype.  Variation is caused by the fact that individuals operate under bounded rationality, which means that individuals or firms simply cannot see ‘the best’ or even all possible opportunities, and therefore act according to ‘rules of thumbs’ and routines.  This is in contrast with neoclassical theories, who typically assume a ‘birds-eye’ view over the economy. The selection environment is the market: successful firms grow, while others disappear.  Although Verspagen does not go into very much detail, imitation between firms can be seen as a kind of inheritance.

The first evolutionary growth model is introduced by the work of Nelson and Winter in 1982. From the course evolutionary foundations it is already learned that an evolutionary approach is applicable to economics, due to the resemblance in both areas of competition, innovation, variation and selection. Furthermore Verspagen and Silverberg argue that economic evolution is part of a larger evolutionary process and not something developed by accident.

The aim of the evolutionary growth model is to formulate a population dynamics if the multilevel evolutionary process.  Another aim is to show that the precision in results of neoclassical models are illusionary.

All the evolutionary growth models talked about in the article focus on technical change.

They are microeconomic based and mostly analyzed by computer simulations.

An other group of evolutionary growth models is not microeconomic based and not analyzed by computers. Characteristics that they do have in common are:

-           Heterogeneity of the population (firms, countries, techniques)

-          The  generation of novelty in the population (mutation by example innovations)

-          Selection (largely driven by rate of returns)

-          Economic outcomes of the analysis

The neoclassical model of Solow and the evolutionary model by Nelson and Winter seem to explain the same empirical trends, the underlying mechanisms are different:

-          In evolutionary growth models there is no production function.

-          Evolutionary growth models growth is driven by selection.

-          Innovations are generated endogenously, rather than exogenously

-          Evolutionary models are only applied in certain time spaces.

-          Evolutionary models do not give a result which indicate precisely which factors play which role explaining growth, whereas neoclassical theory comes with precise results

-          Evolutionary models work in circumstances where heterogeneous firms, disequilibrium and bounded rationality are present

-          Most evolutionary models have the driving force stochastic technical change for economic growth.

Silverberg and Verspagen argue that the evolutionary approach should be extended with the ‘chance and necessity’ debate which includes that some events are more likely to occur in history than others. There is much uncertainty about exact outcomes, but there is a limit to this randomness.

Evolutionary and neo-classical models differ along many key dimensions: be able to list and discuss the key differences and why they are important for what the models are able to do and what not.

Neoclassical + Endogenous	Evolutionary
-          Unit of analysis: macro level Aggregate production function	-          Unit of analysis micro level (firm, sector) Firm or sector use particular type of technology
-          Deterministic, newtonian view of time Future time of the system can be predicted with full accuracy if only enough information about the present state is known.	-          Non deterministic view of time A mixture of change and necessities. Cannot go back and go forth. Impact of particular policy change cannot be predicted exactly, since such change has its effect on a ‘complex range of interrelated factors’
-          Simplifying assumption Example: knowledge is public good available freely Perfect competition	More realistic assumption -          Knowledge’s restricted -          Possibility of market failure
-          Weak Uncertainty Top down view of economy, if information assume available enough, uncertainty then assumed weak.	Bounded rationality and strong uncertainty
Formal quantitative model	Appreciative qualitative model
Mockyr growth theory: Solovian growth: the growth of capital stock is the main pilar, investment is possible when money is saved. In Solow model does not elaborate on how this saving decision is made (given/exogenous) Smithian growth: Growth through commercial expansion, caused by increasing trade. Policies like intellectual property does not cover. Related to this growth is growth through scale and size effects, this incorporated in production function, solow model does incorporate quite explicitely is the population growth, but this is about the cange of income per capita than economic growth. Schumpetarian growth Growth caused by increase in the stock of human knowledge, in the form of technological change and innovations. In neoclassical model Schumpetarian growth is included only as a single ‘g’ parameter, and knowledge stock concept is not used. Endogenous treat knowledge as special type of capital.	Mockyr growth theory: Solovian growth: Decision of saving could be incorporated as a gene for a firm, firm’s fitness can be influenced by its decision to save or not. Smithian growth: Not explaination for intellectual property Use technological change and entrepreneurial activity as the starting point, firms are units of analysis and their performance is defined by the fitness of their technology.