A Simple Basic Causal Macro Impact Model

 

George E. P. Box (1919-2013) was a statistician at the University of Wisconsin--Madison.

Economists are having trouble with macroeconomic models (I posted about the topic here). Macroeconomic modeling got off track by requiring that models have micro-foundations based on expectations, meaning that macro-societal economic forces had to be derived from the individual decisions of economic agents, for example, you and me buying groceries. Unfortunately, there are lots of different ways expectations can be formed (rational expectations, model-consistent expectations, adaptive expectations, etc.)  From the perspective of macro Systems Theory, micro-foundations make a logical category error. "Expectations" are not an attribute of macro-systems but of economic agents. The decision has led to a dead end in macro-economic modeling.

Having a solid basis for macro-modeling makes all sorts of sense. You would like the causal foundations of your theories to be true by definition.* Actually, there are three causal models that macro-economics could be based upon, that is, used to derive other, more complicated models.  They are the Kaya Identity, the Solow-Swan Model of economic growth**, and the AD-AS (Aggregate Demand-Aggregate Supply) Market Model.

NOTES

* In logic, a statement that is true by definition is a tautology.

** Actually, the Solo-Swan model can be derived from the Kaya Identity, so we really only need two models.

Code

If you would like to run the R program in your web browser, cut and paste the following code into the editor window at https://rdrr.io/snippets/.

Kaya <- function (time=100,N=100,n=1.4,L=50,Q=100,q=1.04,CO2=1,
Temp=1,l=.5,e=.75,c=.0002,t=.0001,limit=1) UseMethod ("Kaya")
Kaya.default <- function (time=100,N=100,n=1.4,L=50,Q=100,q=1.04,CO2=1,
Temp=1,l=.5,e=.75,c=.02,t=.01,limit=1) {

TEMP <- matrix(0,time,1)
TIME <- matrix(0,time,1)
for (i in 1:time) {
N <- N * n;

L <- N * l;
Q <- Q * q + L * e;
CO2 <- Q * c;
Temp <- CO2 * t;
TEMP[i,1] <- Temp;
TIME[i,1] <- i;
if (i > time/2) {c <- c * limit}
}
plot(TIME,TEMP)
}
par(mfrow=c(2,2))
# Sample Function Calls
Kaya(n=1.03,q=1.04)
title(main="Exponential")
Kaya(n=.9,q=1)
title(main="Asymptote")
# De-Growth
Kaya(n=.9,q=.9)
title(main="Degrowth")
# Decline
Kaya(n=.6,q=.6)
title(main="Decline")
Kaya(n=1.03,q=1.04,limit=0.95)
title(main="IPCC Slow")
Kaya(n=.9,q=1,limit=0.95)
title(main="IPCC Fast")