The Real Interest Rate as an Endogenous Variable
Up until this point, we have been saying the real interest rate, r, is determined by monetary policy. However, that is a simplification, on at least two dimensions.
monetary policy only affects the nominal interest rate, i, which is not adjusted for inflation. The real interest rate is the difference between the nominal interest rate and expected inflation, p*. We use p to denote the rate of inflation, and we use p* to denote the expected rate of inflation. That is the * means "expected" as opposed to actual.
The real interest rate is higher when i=3 and p* = 0 than when i = 8 and p* = 6. The real interest rate is what determines the demand for investment. If you remember the equation for profitability of investment--profitability equals rental rate plus appreciation minus interest cost, you can see that if a capital good is appreciating at the rate of expected inflation, then higher expected inflation reduces the cost of capital (holding the nominal interest rate constant).
Monetary policy only affects the short-term interest rate. Investment is determined by the long-term interest rate. The difference between long-term and short-term rates is called the "yield curve." When bond market investors have a different view of the economy from that of the monetary authority (which in the United States is the Federal Reserve), the yield curve may change in ways that offset changes in short-term interest rates.
The important point to remember is that there is sometimes slack in the connection between the interest rate that monetary policy can affect and the interest rate that matters for investment. The short-term nominal interest rate can change without affecting the real long-term interest rate. The latter is what is likely to affect investment and the trade balance (through the effect on the relative price of foreign goods).
Why Call it Monetary Policy?
Since we are talking about policies that affect interest rates, why do we call it monetary policy? Because the way that the monetary authority affects interest rates leads to changes in the quantity of money outstanding.
When the Federal Reserve wants to reduce interest rates, it makes short-term loans to banks in what is known as the Federal Funds market. The banks turn around and lend money to private investors, at a profit. The lending process has the effect of increasing the amount of money that is in circulation.
Why do banks not lend an infinite amount of funds, creating an infinite amount of money? Because they are constrained by reserve requirements. They are required to have a certain percentage of total deposits in the form of either currency or reserves that are the liabilities of the Federal Reserve, and hence fully guaranteed.
The total amount of currency plus non-currency reserves is called the monetary base. It is one of many possible measures of the supply of money. Another measure is M1, which is the sum of currency plus all money in bank checking accounts. Another measure is M2, which adds the sum of all money in bank savings accounts to M1. There are many measures of the money supply, and for a given period of history, at least one measure can be shown to track other economic variables really well. However, for forecasting purposes, you would have to pick a measure ahead of time, and that does not seem to be as easy to do.