Abstract
We address two interrelated issues: structured technology and non-stationary equilibrium growth. We do this by modelling multiple, co-existing, non-identical general purpose technologies (GPTs). Three sectors producing pure and applied research and consumption goods, employ different, evolving, technologies. Agents within each sector operate under conditions of Knightian uncertainty and path dependence, employing technologies that differ in specific parameter values. This behaviour produces a non-stationary (non-ergodic) growth process. Important characteristics of structured technology, previously only described historically, are successfully modelled, including co-existing GPTs some of which compete with each other while others complement each other in varying degrees. Because changes in technology are partial causes of, but not contemporaneous with, GDP changes, their separate evolutions can be studied.
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Notes
Davidson (2002) provides a statement of the difference between the ergodic axiom that is central to the stationary equilibrium concept of New Classical and Neoclassical economics and the non-ergodic equilibrium concepts employed in Keynesian and evolutionary economics. We employ the latter here. Lipsey et al. (2005: Chapters 16 and 17) make the distinction critical for the development of what they call technology enhancement policy. Lipsey (2007) uses the same distinction extensively in his reconsideration of second best theory.
For examples in economic history see Crafts (2003), Greasley and Oxley (1997), Jovanovic and Rousseau (2005), Mokyr (2006), and Ruttan (2005); in applied microeconomics see Hornstein et al. (2005), Lindmark (2005), and Sapio and Thoma (2006); in assessments of policy see Forman et al. (2003), Safarian and Dobson (2002), van Zon and Kronenberg (2007), and Wehrli and Saxby (2006); in practical policy strategies that directly employ the concept, see New Zealand’s development of two entire policy frameworks in The Growth and Innovation Framework (GIF) and the Digital Strategy. (see, http://www.digitalstrategy.govt.nz/) as well as the Australian Research Council (2006).
All of these sources of uncertainty combined with the endogenous behaviour of agents and the path dependant evolutions of each major new technology result in a non-stationary (non-ergodic) time series process.
The two main empirically established sources of improvement after a major technology is introduced are ‘learning by doing’ and ‘learning by using.’ The former refers to improvements into the production technique of the GPT itself and the later to improvements in its design and application as experience with its use accumulates and is fed back to manufacturers and designers. On the former, see Arrow (1962) and on the later Rosenberg (1982: Chapter 6).
H&Ta and b deal with only one GPT while A&H deal with a succession of them but each new arrival displaces the incumbent in all sectors before yet another GPT arrives.
Davidson argues (e.g., Davidson 1993, 2002, 2009.) that this stationary equilibrium concept is founded on what he calls the ergodic axiom whose introduction into mainstream neoclassical economics he largely attributes to Samuelson. The axiom allows for statistical inference from cross sectional and time series samples using standard empirical techniques and is the rational for employing stationary equilibria in economic modelling.
The dates in the study paper versions of C&L show that it was written before LCB, although published after.
Although these two concepts are often treated as identical, a TEP includes one or more GPTs and their supporting technologies and economic structure. The distinction between the two is discussed in detail in LCB, pp 372–77.
See LCB (2005: 482–88) “A Simple Model of Facilitating Structure and GPTs.”
Cohen and Levinthal (1990) call this knowledge producing activity the building of “absorptive capacity”.
See, for example, Rosenberg (1982: Chapter 7).
More sophisticated representations of the model would include explicit and formal embodiment processes. But at the current level of abstraction and aggregation these are unnecessary complications for our modelling exercise. When computing the total capital stock for this model as is done, for example, in Carlaw and Lipsey (2010) we value the stock of pure knowledge at its resource cost, as is usually done for R&D in official statistics.
LCB (451–54) studied the effects of five different adoption criteria, any of which could be used here.
As a check, if a third version of GPT class 2 is invented and adopted by R&D facility 1, the first column in the operative matrix alters to read: \(\nu _{1,2}^{3_1 } ;\nu _{1,2}^{3_2 } ;\nu _{1,2}^{1_3 } \).
Presented with an either-or choice between private and public financing of pure research, we think the better choice to reflect historical reality is public. It would be relatively easy to add some private behaviour allocating resources to the activity of creating pure knowledge and ultimately to the creation of GPTs. However, this is one of the many complications that we do not think would add as much to insight as it would to complexity so we have held with our either-or choice. Most major technologies developed in the twentieth century had significant amounts of public support at their early stages. (See, e.g. Ruttan (2001) As we go back in time before the twentieth century we do meet cases where private support is more important than public. But we also note that the historical case is mixed. For example, although it had rudimentary commercial beginnings in the West, writing was fully developed there by the state itself—in this case the Sumerian priests and their scribes (see Dudley 1991). Bronze and Iron seem to have enjoyed significant state support at least for key military applications, which may, as with so many twentieth century GPTs, have developed the production processes sufficiently for their uses to be extended fully to the civilian sector. Navigation that supported the invention and development of the three masted sailing ship certainly enjoyed state support, particularly in Portugal. Although British Red Brick universities were set up around 1900, US land grant colleges are 50 years earlier. Further back in time, much education was funded by the church (which we regard as part of the public sector) and by secular governments (both city states and more aggregated entities) in institutions that have existed in Europe since at least the thirteenth century. Many of the great inventions generated by China were entirely state financed, and so on.
This assumption greatly simplifies the calculations and is adequate for present purposes. In some specific applications, we need to make each consumption industry use more than one type of applied knowledge. At the extreme, if each uses all types, their production functions become: \(c_t^i =\left[ {\prod\limits_{y=1}^Y {\left( {\mu A_{t-1}^y } \right)^{\alpha _y }} } \right]^{\frac{1}{Y}}\left( {r_t^i } \right)^{\alpha _{_{Y+1} } }\), \(\alpha _y \in \left( {\mbox{0,1}} \right]\mbox{ }\forall y\in Y\mbox{, }\alpha _{Y+1} \in \left( {0,1} \right)\).
We maintain the assumption made by C&L and discussed in Section I above, that applied knowledge is divided into a proportion, μ, that is useful in the consumption industries and a proportion, (1 − μ), that is useful in pure knowledge production. LCB relax this assumption in their one at time GPT model and let the full stock of applied knowledge be useful in both the pure knowledge and consumption sectors. Doing so generates a knowledge spillover of the sort found in Lucas (1988) and Romer (1986) which could easily be incorporated into applications of the model developed here.
If the \(\bar {\nu }\mbox{s}\) attached to the other GPTs operating in applied R&D facility, y, were also expected to diverge from those in the appropriate column of the operative matrix, we would have to calculate the complete value of the \(a_t^y \)term from Eq. 2 as it would be under the existing GPTs and the operative set of νs and then compare it with what that a term would be given the new column vector of expected \(\bar {\nu }\)s.
Agents in our model do not know the parameter values of the logistic function and these can be either fixed or determined randomly in the model each time a new GPT arrives. When determined randomly, they model uncertainty source 8(v).
This comparison must be made in every time period, for every applied R&D facility that has not yet adopted the latest version of every class of GPT in existence. It must also be made for all of the GPTs of any given class that are more recent than the one currently being used by a given facility.
Because the pure knowledge sector only periodically produces a useful GPT, we adopt the standard national accounting convention of valuing the output of that sector at its input costs in each period.
For specific applications where the private/public investment mix in pure knowledge R&D is under investigation it is possible to accommodate a mix of private and government agents allocating resources to pure R&D. To do so requires that private agents maximize their expected current-period profits as is done in the consumption and applied R&D sectors of the current model. This in turn requires that we have an expected price associated with the output of the pure knowledge sector that is transacted when a GPT is invented and taken up by at least one applied R&D facility. The formation of expectations about these prices can be as simple or complex as the application requires.
Agents’ lack of foresight has some implications for the allocation of resources in the model. We have run a number of simulations where agents have one or two periods of foresightedness in the sense that they are aware of the impact of more than one period’s allocation decisions on the marginal product of resources in applied R&D. For the simulations run so far we find that with foresight agents allocate slightly more resources to applied R&D because they are aware of its future effects in raising consumption output but that this has a negligible impact on output over time. Depending on the relative allocations of resources to applied versus pure research and on the arrival rates of GPTs, the foresightedness that we allow sometimes causes the output growth to increase and at other times causes it to decrease relative to the simulation with no foresight. But in all cases, the overall impact is negligible. We do not allow agents to have infinite foresight because such an assumption would be meaningless in our model which incorporates Knightian uncertainty and because, even without uncertainty, having full foresight over the lifetime of a GPT that often extends for more than a century is quite impossible.
The initial value of \(t_{n_x} = 2\) is chosen because we have lagged variables indexed on it and MatLab does not allow zero as an index value.
We choose this range based on Angus Madison’s historical data set (see Madison’s web pages http://www.ggdc.net/maddison/ for the complete data set). We calculate the average annual growth rate of GDP per person from 1870 to 2003 for the USA to be 1.86% and for Canada to be 1.96%.
μ can alter shares because it alters the marginal product of labour in consumption, and labour is paid the same wage everywhere.
We choose 3.78% because the United States allocates about 2.63% of total GDP to R&D and 2.3% of GDP to post-secondary education and research making 4.93% in total. We choose the figure 3.78% because we make the crude assumption that half of post-secondary expenditure goes into R&D activities. But since this ignores the significant fraction of total government expenditure that goes to R&D, particularly from the Department of Defense, this number would need to be significantly increased for practical applications. The upper limit would be the total public expenditure (not including transfers) which is 19.1% of GDP.
In our model, private agents allocate resources to applied R&D based on the effect of such research on the near-future productivity of the consumption goods industries. If private sector agents looked further into the future, there would be an incentive to allocate more to current R&D. However as long as they only look a few periods ahead when calculating their expected returns (as is often alleged) the public return from such R&D will exceed the private return, providing a case for some diversion of public funds to encourage private R&D (as governments do in many countries by policies such as tax relief or direct subsidies for R&D).
The negative shock followed by a productivity gain is similar to what we seen in the 1970s–1990s with the ICT revolution.
This concept is defined and its significance discussed in LCB 55–63.
LCB make a start at modelling the interaction between a GPT and the facilitating structure in their one-GPT model on pp 482–496.
These results were presented in Carlaw and Lipsey (2010) at the 2010 International Schumpeter Society meetings on Innovation, Organization, Sustainability and Crisis in Aalborg Denmark.
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Carlaw, K.I., Lipsey, R.G. Sustained endogenous growth driven by structured and evolving general purpose technologies. J Evol Econ 21, 563–593 (2011). https://doi.org/10.1007/s00191-010-0212-2
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DOI: https://doi.org/10.1007/s00191-010-0212-2
Keywords
- Structured technology
- General purpose technologies
- Non-stationary growth
- Technological evolution
- Non-ergodic equilibria