## Savings = Investment

I was poking around on Nick Rowe’s blog, and came across this piece on Keynesian economics. If you recall in this post I recently pointed out a peculiar aspect of Keynesian economics:

[H]ow is it that if savings equals investment and savings equals income minus consumption, that when you lower interest rates investment increases but consumption stays the same?

When I was reading Nick’s post, I couldn’t help but think about this and think how ridiculous Keynesian economics would seem to people if they explained what they were really doing in the same way I think about it in my mind. So naturally I figured I should take a stab at this.

As Nick explains, the model begins with two identities (assuming a closed economy and no government for simplicity): Y=C+I and S=Y-C. This gives you S=I as an identity. In other words, given the way we have defined the variables, this must be true. This is different from an equilibrium condition such as quantity supplied = quantity demanded which is true only in an equilibrium. So at this point no economics has been done.

In order to do some economics, you must assume some values of variables and some causal relationships which determine the values of the other variables. The way Keynesians go about this is to assume the following equations from Nick’s post (to simplify even further I will assume that autonomous spending, which is “a” in his model, is equal to 0)

8. Cd = b*Y (where a>0 and 0<b<1)

9. Id = Ibar

Where Cd and Id are desired consumption and investment respectively. Then if you assume that in equilibrium C=Cd and I=Id, you have a model (6 equations and 6 unknowns). But here is what we have done in plain english:

1. We have assumed that investment is equal to a certain value no matter what. This value is not explained in any way in this model and nothing in the model can change it.

2. We have assumed that consumers spend a certain proportion (b) of their income on consumption. This proportion is not explained in any way by the model and nothing in the model can change it.

3. Based on our definition of savings, savings must be the amount of income not consumed, which *by assumption* is (1-b)Y.

4. Since, by definition, savings is always equal to investment, we know that the amount of savings must be equal to the value we *assumed* for investment. (Ibar=(1-b)Y)

5. The only thing we haven’t assumed yet is Y (output) so that must be whatever value makes the proportion we assumed would be saved equal to the value we assumed for investment.

To make this even simpler consider a numerical example. Assume the following:

1. People consume half of their income and save the rest.

2. Investment is $100.

3. Savings equals investment.

Now it follows logically that Income is $200. Why is that? Well it’s simple, since savings equals investment and investment is $100, then savings must be $100. And since people save half of their income and savings is $100, then their income must be 2×100=$200. This does nothing to explain where income actually comes from! Now if, for some reason, people decide to save only 1/4 of their income, then, by assumption, investment doesn’t change so the amount of savings must still be $100. But since people are saving more, their income must be higher in order to generate this arbitrary amount of savings. Therefore, income must increase to $400 to bring the model into equilibrium. This is essentially how Keynesians arrive at the “paradox of thrift,” by assuming that savings will have to be a fixed amount so if people insist on saving a smaller proportion of their income, then income will have to get larger to make that smaller proportion equal to the presumed constant level of savings.

This model works mathematically but it is a terrible way to do economics. Proper economics assumes some scarcity fixed by nature and some purposeful economic agents which choose between different ways of dealing with that scarcity. In other words, the degree of scarcity is constant and the model determines what people do in the face of it. On the other hand, this Keynesian approach takes human behavior for granted and assumes that the degree of scarcity in the system adjusts to make an equilibrium given this behavior. It’s an economic paradigm custom-made for people who think that human nature is the source of all the world’s problems and if only we could get better at social engineering, everything would be great. But this is a mistaken view of reality, and it leads to a mistaken view of economics. Perhaps more troubling, is that the converse is also true. Tread carefully, “practical men who believe themselves to be quite exempt from any intellectual influence, are usually the slaves of some defunct economist.”

*Note: If I were a Keynesian I would probably be fuming at this post and I would point out that the Keynesian cross is only *part* of the Keynesian model, and that it is misleading to present this part as a complete model. For instance, in the larger model, investment is not fixed, it is determined by interest rates. However, it still enters the Keynesian cross part of the model independently of the other variables in that part. It is my belief that the same general criticism is valid with regard to the larger IS/LM model but my goal here was to make the case as simply as possible and it would be much more complicated to analyze that entire model in the same way. So, I will leave it to the interested reader to look into it further, but this should get you started seeing it for what it is.*