The Adam Smith Model

In this post, I am not going to start by reading Adam Smith's work and looking for general variables and interconnections (Hage, 1972). I'll do that in some future post. Instead, I will implement Saeed's (2008) Smithian System Dynamics model (see the Notes below) as a causal directed graph and then as a State Space Model (see the Boiler Pate). 

I find that the Smith Model of Saeed (2008), when given a Systems Analysis, is essentially a Small Open Economy (Small Country) model with no state variables, equivalent to a Random Walk (RW).

Starting from the Kaya Identity (see the Boiler Pate),  Saeed (2008) can be seen to have focused on four variables: Labor (L), Capital (K), Production (Q) and Technology (T). Translating Saeed's (2005) model to a directed graph yields the causal diagram above (Saeed's System Dynamics model is a little more complicated, see the Notes below, but I have reduced it above to the basic linkages).

From the standpoint of Systems Theory, the model's one obvious limitation is that there are no input variables.  Saeed (2008) resolves the problem by adding Population growth (N) as an input and concludes that "Population is the Limit-to-Growth" in the Smith model. Before exploring Saeed's conclusion, let's explore the basic Smith model further because there are other conclusions that can be drawn.

First, we can add initial conditions as exogenous variables and, second, we can add coefficients to the directed graph (above).

Then, with Directed Graph Reduction Theorems (see the Notes), we can reduce out all endogenous variables or any endogenous variables that we choose. For example, we can (1) add coefficients (as above) and (2) reduce out Capital and Technology and get the digram below:

where:

A = l/(1-e) * i/(1-k) * t/(1-d)

This result is the causal interpretation of the Labor Theory of Value which has plagued Marxists analysis since it was borrowed from David Ricardo (see Schumpeter, 1944). Given an initial condition for Labor (L0), the model makes an equilibrium prediction for the ultimate value of production (Q). Also notice that the coefficient e, k and d must all be less than one for the model to predict a positive value for Q.

To analyze the stability of the model we can make it dynamic by adding self-loops to the directed graph (above). For stability, the coefficients (b-d), t, Q, and d (capital stock depreciation) must all be less than 1.0 in value.

Returning to Saeed's model, simulated time paths for the model are provided in  Saeed (2008). We can use that data to estimate a state space model. The Sytem matrix for the estimated model is presented above.** Notice that all the coefficients, except for the constants [0.51, 0.52 and 0.53], are all zero (the constants are the initial conditions of the model). The model can be recognized as the Small Open Economy (Small Country) model with no state variables, meaning that the economy is entirely at the mercy of exogenous World-System forces. 

You can run the Smith Small Country model here. It is essentially no different from a Random Walk (RW) which is also run in the code. In future posts, I will provide examples of countries in the World-System where the Small Country model is the best descriptor.

Notes

** Notice that I have reduced Technology (T) out of the model. It is never really defined adequately by the Classics so there is really no possibility of estimating undefined variables. The Capital Stock (K) can also be reduced out of the model since there is no long-term Capital Stock data for any country in the World-System.

Speed's System Dynamics Model

Saeed (2008) summarizes Adam Smith's Wealth of Nations with the following paragraph:

If you have read the Wealth of Nations, the summary will be entirely inadequate. However, Saeed's goal is to formulate the basic model as a System Dynamics model (below) and then develop other Classical models (Ricardo, Marx, Schumpeter, etc.) and explore how Limits to Growth enters all the Classical models. He started from Benjamin Higgins (1968: 57) Classical model.

To construct my causal diagram of Saeed's System Dynamics model (at the beginning of this post), I trace all the linkages between the "level" variables (L, K, T and Q) and connected them as nodes in a directed graph (digraph).

The benefit of what Saeed has accomplished will become clearer as we move on to the other Classical Economists in future posts.

References

• Saeed Limits to Growth in Classical Economics
• Adam Smith Wealth of Nations
• Schumpeter Capitalism, Socialism and Democracy
• Huggins and Entwisle Introduction to Systems and Design
• Higgins Economic Development