World-System (1872-1908) A Classical Model of German Development

 

In a prior post (here), I discussed whether we should pay attention to the Classical Economists who wrote in the Nineteenth Century. They had brilliant insights but they lacked the statistical tools to test their ideas. But now that we have the tools and the historical data, there is no reason not to test and extend their ideas. One of the problems is figuring out what the Classics actually meant because their writing was verbose, obscure and difficult for modern readers to wade through.

Benjamin Higgins (1968) (here) has come to our rescue with a book (now out of print but still available used) that develops a generalized mathematical model of economic development based on the classics (see Chapter 3). He presents eight structural equations (p. 63) and a time plot of the relationship between N (Population) and Q (GDP), above. His Figure 2-3 (above) looks very similar to the time series plot for the German 19th Century model (DEL19) at the beginning of this post which was based on an estimated dynamic state space model. The DEL19 model used the same variables identified by Higgins but did not arrive at the time plot using Higgins classical structural equations. Understanding how the DEL19 model was constructed will help me explain how to approach the Classics with modern tools.

Higgins identifies the following variables as central to the general Classical model: Output(Q), Labor (L), Capital (K), Wages (W), Profits (R) and Investment (I). The Classics struggled with definitional issues. Did Capital include land, machines, buildings, knowledge, etc.? Were wages driven to subsistence in order to increase profits (R = Q - wL) where w is the subsistence wage. So many questions, so much speculation so little testing.

Systems Theory avoids these arguments by defining the System State, S = S(Q,L,K,W,R,I), as being a function of all the essential variables in a system. The problem then is to estimate a state variable index and other independent indexes that describe Error Correcting Controllers (ECCs) for the system, that is, describing growth and control as two separate issues that have to be estimated separately for the system allowing that the system might not be under adequate control.

The Measurement Matrix for the DEL19 state space model is presented above. The first state variable, Classic1, describes overall growth (it's time plot is displayed at the beginning of this post). The second state variable, Classic2 = (0.86 N - 0.48 I), involves monitoring population growth relative to investment. The third state variable, Classic3 = (0.73 I - 0.47 L), involves monitoring investment relative to employment. The first three state variables explain over 99% of the variation in the indicators. The remaining three indicators deal mostly with wage controllers and explain little variance.

There are a number of interesting points about the estimated Measurement Matrix (estimate with Principal Components Analysis), The classics were very interested in Wages and Investment. But, they were also interested in the Capital Stock, K, and it plays little role other than in system growth. in Germany (even though the Nineteenth and Twentieth Centuries are labeled as Capitalist). 

I can resolve this confusion with graph theory and a Kaya Identity (two more tools not available to the Classics).