## Wednesday, November 25, 2009

### Interest Rates and "Tight" Money

An excess demand for money exists when the quantity of money is less than the demand to hold money. That is how I would define "tight money."

Such a shortage of money results in people reducing expenditures out of income in order to increase money balances. One of the many things upon which people might reduce expenditures is bonds. Further, an alternative way of building up money balances is to sell nonmonetary assets. One such nonmonetary asset is bonds. People short of money can sell bonds.

If this occurs, and bond prices fall, then the yields on bonds increase. In other words, an excess demand for money can plausibly lead to an increase in "the" nominal interest rate.

Some monetary assets pay interest as well. Typically, currency pays no interest, but checkable deposits can pay interest. If the nominal interest rates on bonds rise, and the nominal interest rates on monetary assets are unchanged, then the opportunity cost of holding money is higher. Holding money is less attractive than holding other assets.

Suppose money demand takes the following form:

Md = P md(Rb-Rd, y, x)

Where:

P is the price level and md is the demand for real money balances. The demand for money is a demand for purchasing power, and so nominal money demand is proportional to the price level.

Rb is the interest rate on bonds and Rd is the interest rate on monetary assets, so Rb-Rd is the opportunity cost of holding money (or at least one of the opportunity costs.) The demand for real money balances is negatively related to the opportunity cost of holding money.

y is real income. The demand for real money balances is positively related to real income. In other words, money is a normal good.

And finally, x represents other things that could impact money demand.

If there is a shortage of money, so Ms is less than Md, then, other things being equal, and increase in Rb, the interest rate on nonmonetary assets, can result in Md falling to match the existing quantity of money. This is often called the "liquidity effect" and plays an important role in Keynesian monetary theory.

The above diagram shows the Keynesian money market. "The" nominal interest rate on nonmonetary assets changes so that quantity of money demanded adjusts to the existing quantity of money. This is given the price level, real income, and the interest rate paid on money. Changes in any of those things shifts this money demand curve to the right or left and so causes changes in the nominal interest rate.

Does this mean that nominal interest rates can adjust to clear up monetary disequilibrium? No. Interest rates have an important role in coordinating saving and investment.

Saving is that part of income not spent on consumer goods and services. Saving results in an increase in net worth and an ability to increase consumption in the future. A higher real interest rate provides a signal and creates an incentive to reduce current consumption, increase saving, add more to net worth, and expand future consumption expenditure.

Investment is expenditure on capital goods--machines, buildings and equipment. While producing additional capital goods now reduces resources available to produce consumer goods now, the additional capital goods raise labor productivity and increases the ability to produce consumer goods in the future. A higher real interest provides a signal and creates an incentive to reduce investment expenditure, produce fewer new capital goods, and add less to the ability to produce future consumer goods. However, by producing fewer capital goods now, resources are freed to produce consumer goods now.

If the real interest rate is at the right level--the natural interest rate--then saving and investment are coordinated. Firms produce the amount of consumer goods now that households want to purchase now. Firms purchase and produce capital goods, increasing the capital stock to match the increase in the households net worth. And the additional capital goods increase the firms' ability to produce consumer goods in the future, matching the increase in the households' ability to purchase consumer goods in the future. The diagram above illustrates the natural interest rate, the real interest rate that coordinates saving and investment.

Because changes in current income can also impact saving, the concept of the natural interest rate can be ambiguous. Keynes emphasized this point. In his view, income and saving adjust until saving equals investment at a given interest rate. Further, the conventions of national income accounting include unplanned inventory investment as one sort of investment, which makes saving and investment always equal by definition.

However, the traditional approach has been to identify the natural interest rate as the level of the interest rate that coordinates planned investment and saving with income at a level consistent with productive capacity.

Since investment and consumption both represent demands for current output, and are both negatively related to interest rates, ceteris paribus, there is a negative relationship between real expenditure and real interest rates. The level of "the" real interest rate that generates a level of real expenditure that matches potential income--the productive capacity of the economy--is the natural interest rate.

The diagram above shows an IS curve, which is traditionally the combinations of real income and interest rates consistent with saving and investment being equal. However, it is better interpreted as the negative relationship between real interest rates and real expenditure on final goods and services. The "y" along the horizontal axis is real expenditure on final goods and services rather than production. The vertical line represents the productive capacity of the economy. Then rn, the natural interest rate, is where total real expenditure is equal to the productive capacity of the economy.

If the level of the nominal interest rate that results in a demand for money that matches the quantity of money results in a real interest rate greater than the natural interest rate, then saving is greater than investment and real expenditure is less than the productive capacity of the economy.

The diagram above shows the interest rate where the quantity of money demanded has adjusted to the existing quantity of money as R*. The expected inflation rate is positive, and when subtracted from R* generates a real interest rate r*. The real interest rate is above the natural interest rate. Real expenditures given r* is less than the productive capacity of the economy.

Has the shortage of money been corrected by the increase in the nominal interest rate? I think not. The interest rate needs to coordinate saving and investment--the production of consumer goods and spending on consumer goods through time. The quantity of money demanded at a nominal interest rate equal to the natural interest rate plus the expected inflation rate is greater than the quantity of money. The impact of a shortage of money on the nominal interest rate is just part of a disequilibrium process.

An excess demand for money exists when the quantity of money is less that what the demand to hold money would be if nominal interest rates are where they should be.

And where should the nominal interest rate be? It should be equal to the sum the expected inflation rate and the natural interest rate--the level of the real interest rate that coordinates saving with investment and maintains a level of real expenditure equal to the productive capacity of the economy.

This discussion of the relationship between monetary disequilibrium and interest rates is only a first pass. Most obviously, the relationship between real and nominal interest rates depends on expected inflation. Expectations about the future quantity of money and the demand to hold it are going to feed back to current money demand.

Worse, if changes in real expenditure impact expected future real income and output, then saving, investment, and the natural interest rate can change. The notion that "tight" money must imply that interest rates are higher than usual is fraught with difficulty.

Further, the liquidity effect isn't the sole relationship between money and interest rates. Banks create a substantial part of the quantity of money, so an imbalance between the demand for money and the quantity of money has implications for both the nominal and the real quantity of credit. With a monetary authority organized as a central bank, many of its operations are also best understood as impacting the nominal and real supply of credit.

And there are other avenues by which a shortage of money can impact real expenditures than through a divergence between the market and natural interest rate. Those short on money might directly reduce expenditures on currently produced output. Reduced real expenditures and a reduced volume of sales will likely result in less production of goods and services and so, less real income. And that too will impact money demand.

More on the complicated relationship between "tight money" and interest rates later. However, a first passt at real real output and real income comes first.