## If Only Our Spacetime Was Five Dimensional, We Could Do Our IS-LM Diagrams Right...

Now one big thing wrong--or missing--with the IS-LM framework as Hicks set it out is his failure to specify what "the" interest rate that goes on the vertical axis is:

Is the interest rate the current instantaneous nominal safe Treasury bill rate? Then the LM curve is derived from the instantaneous demand for today's money stock--and everything else in the economy is loaded into the IS curve.

Is the interest rate something like the five-year nominal safe Treasury note rate? Then the LM curve is some average of current and expected monetary conditions over the next half decade--and everything else in the economy is loaded into the IS curve.

Is the interest rate something like the ten-year real risky interest rate for BAA corporate borrowers? Then the IS curve is derived from something like business demand for investment as a function of that interest rate and expectations as fed through the Keynesian cross--and everything else is loaded into the LM curve.

The fact is that if the LM curve comes from the money demand equation, then the interest rate on the IS-LM diagram is the short-term safe nominal interest rate. The fact is that if the IS curve comes from business demand for investment as a function of expectations and long-term borrowing costs as fed through the Keynesian cross, then the interest rate on the IS-LM diagram is the long-term real risky interest rate.

That means that everything that affects:

- the term premium between short-term and long-term rates.
- the risk premium between safe and risky rates.
- the expected inflation rate that drives a wedge between nominal and real interest rates

has to show up in the IS-LM diagram somewhere, but has no single and natural home. Each of these can be put into the LM curve. Each of these can be put into the IS curve. Or you could put both the short-term safe nominal LM interest rate and the long-term real risky IS interest rate on the vertical axis, and define a set of factors that are neither "IS" nor "LM" but rather "spread". (I prefer to do it that way.)

That way we have "fiscal policy" and related issues that affect the location of the IS curve (with the long-term real risky interest rate on the vertical axis); "monetary policy" that affects that the location of the LM curve (with the short-term safe nominal interest rate on the vertical axis); and the expected inflation rate and "banking policy" that affect the spread between the two interest rates.

In order to summarize all this in a readily comprehensible manner, we need to draw diagrams that have not two axes on a flat piece of paper but rather three axes in a cube--which we could do if we lived in a five-dimensional space-time universe with four spacelike dimensions.

But alas!...