Multiple Identities Can Deceive Even More

Consider a closed economy (no international transactions) so that \begin{equation} Y=C+I+G \end{equation} Savings is defined as unconsumed income, so national savings ($S$)-- which counts both private and government consumption-- is given by \begin{equation} S=Y-\left(C+G\right)=I \end{equation} Thus, the mystical “savings-investment identity” is born. In a closed economy, savings must equal investment. You like investment, don’t you? You believe that increasing the capital stock makes us more productive, right? So we should strive to increase national savings, don’t you think? And since we only can consume or save our income, we ought to consume less.

Not necessarily. It depends on the model. Suppose I gotta install microwave ovens. Custom kitchen deliveries!¹ If you unexpectedly fail to buy a new oven then very likely I am stuck with a larger inventory and the immediate effect is to increase $I$ by the same amount as the fall in $C$, leaving $Y$ unchanged. Or maybe I will then fail to buy from the manufacturer who then slows production, lowering both $C$ and $Y$. These are not the only possible results, but the point is it matters because equation (2) says that lowering your consumption increased savings only in the former case.

And even then the increased investment came as an inventory increase-- which is nice because it allows for additional future consumption, but it doesn't actually increase productivity.

The bottom line is that while it is tempting to argue from an accounting identity, it is the story that matters. The identity just helps keep the story straight.

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1 Back in 1984, someone totally could have kept his issues to himself instead of calling a guitarist on your MTV a “f****t”.^↩