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This blog documents an approach to Technological Change that is consistent with General Systems Theory, which contains models that cover Neoclassical Growth Technology, Learning-by-Doing Technology, World-systems Theory and Classical models of Technology to include Schumpeter's Creative Destruction. None of these models are consistent over time within a single country and across countries. Partly, the changing approaches to Technology are historically determined and partly they are due to data limitations that prevent consistent testing over all time periods and countries. 

Therefore, there is no general conclusion about technology accept that it may follow one of the time patterns above (unlimited exponential growth, growth and decline or decline). Moreover, Technological change is not always the best model to describe growth across time and countries. Different models may dominate during particular periods and in particular countries.

Solow-Swan Technology

In the Solow-Swan long-run growth model, Technology (TECH) is an exogenous input variable along with Population (N). Labor (L), Production (Q) and Capital Stock (K) are all endogenous variables. Technology can be defined as an exponential time trend or as the residual from a log-linear production function.

Learning-by-Doing can be added to the model with a self-loop in Q, that is, a lagged value for Q(t-1).

Kaya Technological Efficiency

The Kaya Identity Model, used by the IPCC, assumes that in the short-run, the important socio-economic variables are related linearly: More population (N) leads to more employment (L), more employment leads to more production (Q), more production leads to more capital accumulation (K), more capital accumulation (machines and buildings) leads to more energy use (E), more energy use creates more CO2 emissions and more CO2 Emissions increase Global Temperature (T).

The Kaya Identity Model can be made dynamic by adding self-loops on N, Q, E, CO2 and T. Capital can be reduced out of the Directed Graph using Loop-Reduction Theorems (see below).

Technology in the Kaya Identity Model is measured by the Intensive Coefficients: c=CO2/E, e=E/Q, t=T/CO2, l=L/N. A PCA index of the Intensive Coefficients provides a multidimensional measure of Technical Efficiency TECHE=[c,e,q,l].

Data on Capital Stock (K) is not available for most countries and time points in the World-System. Luckily, K can be reduced out of the model.

By simplifying the Kaya Identity Model (first directed graph above) and using Loop-Reduction Theorems, the Capital Investment loop can be reduced out of the model (second directed graph) making a somewhat more complicated equation for Labor Productivity Q = q/(1-ik) L. The result does not mean that Capital is unimportant. For the system to be stable and produce positive Labor Productivity, q, then  i x k must be less than 1.0 in value. In other words, Investment (i) and Capital Productivity (k) are essential to stabilizing the system.

Techical Productivity

A general model of Technical Productivity can be derived with a slightly different Directed Graph (above) if we define general productivity as output per person..

Learning By Doing