I'm doing a research on the application of machinery in area of agriculture in Sandzak from 1918 - 2008 and why I need advice on what is the best way to express the degree of industrialization
One can follow W. W. Rostow, “The Stages of Economic Growth,” Cambridge, 1960. On page 21 Rostow wrote that “the essence of the transition can be described legitimately as the rise in the rate of investment to a level which regularly, substantially and perceptibly outstrips population growth.”
You may want to look at Schumpeter’s theory of creative destruction from the investment and R&D sides.
The growth model of Adolph Lowe as tested by W.G. Hoffmann, The Growth of Industrial Economies, Manchester 1958, examined the industrial base. A group of industries—agriculture, textile etc seems to characterize the early stage.
Paul Streeten seems to look at four functions, 1. Balance of Payment surpluses, 2. Financial Institutions to convert those surpluses into loans and equities. 3. Technological capacity to produce capital/intermediate goods, and 4. Military and police power to enforce contracts and keep the peace. (P. Streeten, “Thinking about Development," Cambridge, 1995, pp. 85-143.
Look at the factors suggested by modern growth theories as well, in particular Human Capital.
I think you can also consider the trend in the elasticity of substitution adopting a production function VES (Variable Elasticity of Substitution) to the disposable time series data of agricultural production in Sandzak.
Perhaps you could use Chenery and Taylor's Development Patterns among Countries abd over Time, (RES, Nov.,1968) in which they show how the size of an economy determines the path and the type of industrialization; as well as another study by Leamer, Maul, Rodríguez and Schott; Does Natural Resource Abundance Increase Latin American Income Inequality?; (JDE, 1999) for a description of the path and degree of industrialization based on different resource endowments.