31. Define the Nominal Interest Rate and the Real Interest Rate
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12. Real Macroeconomics
Questions:
30. Define and then discuss the relationship between the natural unemployment rate and potential income
31. Define the nominal interest rate and the real interest rate.
32. What is the natural interest rate? Illustrate with a diagram. Relate to the real market interest rate.
The Long Run
In the long run, money supply and demand has only a minor effect on real income, the unemployment rate, and real interest rates. Instead, money mostly influences the price level, nominal income, and nominal interest rates.
Output and Income
Nominal income is the aggregate of all individual incomes. Real income is nominal income corrected for any changes in the price level. Given real income, a higher price level implies higher nominal income and a lower price level implies lower nominal income.
The basic identity of macroeconomics is that income is equal to output. Real income is always equal to the real production of final goods and services.
Potential Income
In the long run, real income is equal to potential income.
yt = ypt
Potential income is the total production of goods and services possible if resources are fully employed. It depends on the quantity and quality of labor that workers are willing to supply, the existing stock of capital goods, and the technology for producing goods and services.
Potential income grows over time. It grows because of growing population, improving education, increasing amounts of capital goods, and improving technology. The average growth rate in the USA has been 3%.
Natural Rate of Unemployment
Full employment of resources does not imply a 100% utilization rate for capital or a zero percent unemployment rate for labor. Resources are considered fully employed if the unemployment rate for labor is equal to the natural unemployment rate. If the actual unemployment rate is equal to the natural unemployment rate, then real income is equal to potential income.
If u = un , then y = yp
The natural rate of unemployment is made up of frictional, structural, technological, and institutional unemployment. It includes all unemployment not associated with recession.
Most of the natural unemployment rate involves changing patterns of employment because of needed changes in the allocation of labor between firms and industries. Changes in demand for different products, improved technology for producing some goods, new and improved products replacing
inferior products, competition from imported goods, and competition for export markets can all contribute to the natural rate of unemployment.
Workers are laid off in shrinking industries. And it takes time for them to find new jobs in growing industries. Between the time they are laid off and the time they find a new job, they are unemployed. Most economists estimate the natural rate of unemployment to be between 5% and 6%.
The Real Interest Rate
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The nominal interest rate is the amount a debtor must pay a creditor for a loan, divided by the amount the loan. Nominal interest rates are observed in the economy.
The real interest rate is the nominal interest rate corrected for the expected inflation rate. It is equal to the nominal interest rate minus the expected inflation rate. Alternatively, the nominal market interest rate is equal to the real market interest rate plus the expected inflation rate. The expected inflation rate is the expected value of the natural log of the price level at time t + 1 minus the natural log of the price level at time t.
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Rt = rt + Pte
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Pte = E(lnPt+1 - lnPt)
So the real interest rate is the real amount of purchasing power that the debtor expects to pay the creditor. Given the real interest rate, a higher expected inflation rate implies a higher nominal interest rate. And a lower expected inflation rate implies a lower inflation rate.
If expectations about inflation are correct, then the real interest rate is the amount of purchasing power debtors must pay creditors. In the long run, assume expectations are correct.
The Real Interest Rate and Investment
In economics, investment spending is purchases of new capital goods. It includes purchases of machines, buildings, and equipment. But it does not include purchases of stocks, bonds, real estate, or even used capital goods.
Investment spending is negatively related to the real interest rate. A firm will a purchase capital good if it adds to its value. Additional capital goods imply additional future output and additional future revenues. The expected future revenues are discounted to find the present value. If the present value is greater than the price of the capital good, purchasing the capital good adds to the firm's value.
A lower real interest rate increases the present value of the revenues a firm expects to earn from purchasing any capital good. Typically, this will cause the present value to rise above the price of at least a few capital goods for at least some firms. At least some firms purchase more capital goods. Similarly, when the interest rate increases, at least some firms purchase fewer capital goods.
The argument holds whether firms are financing the purchase from borrowing, from accumulated "cash", or from current earnings. If firms use borrowing, an increase in the interest rate also increases the interest expense of purchasing the capital goods. If firms use accumulated "cash", an increase in the interest rate is also an increase in the earnings on bank deposits and security holdings. This makes firms less likely to sell these assets to purchase capital goods. And if firms use current earnings, an increase in the interest rate makes it more attractive to accumulate bank deposits and securities rather than purchase capital goods.
An increase in investment expenditures causes firms in capital goods industries to produce more capital goods. Because of scarcity, this leaves fewer resources for firms in consumer good industries. Fewer consumer goods can be produced now, but the additional capital goods will allow firms to increase the production of consumer goods in the future.
The Real Interest and Saving
In economics, saving is disposable income minus consumption. After taxes, any income not spent on consumer goods is saved.
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Saving implies an increase in net worth. Net worth is assets minus liabilities. If income is "not spent", the accumulated money holdings is saving, because it is an increase in an asset. If income is spent on stocks, bonds, or real estate, this is also saving, because it is an increase in an asset. If income is spent to repay debts, this is saving, because it is a decrease in liabilities. Selling off previously accumulated assets or borrowing to finance consumption is dissaving (negative saving).
Saving is positively related to the real interest rate. A higher real interest rate implies a household can earn more on any new assets purchased, providing an incentive to accumulate more. A higher real interest rate also implies a decrease in the value of the assets a household already holds (especially stocks or real estate). A household might try to regain the lost net worth by accumulating more assets and it is less able to finance consumption by selling assets. A higher real interest rate also makes borrowing to finance consumption more expensive. Similarly, a lower interest rate causes a decrease in saving.
If households save, they decrease their consumption now. But they add to their net worth, which increases their ability to consume in the future.
The Natural Interest Rate
The interest rate determined by the supply and demand for credit (or loanable funds) is the market interest rate. Nominal market interest rates are actually observable. When corrected for expected inflation, the observed interest rate is the real market interest rate. The real market interest rate is influenced by excess reserves or reserve deficiencies in the banking system. So it is influenced by the Fed's discount policy or open market operations.
The level of the real market interest rate at which savings and investment are equal is the natural interest rate. While the market interest rate might not be equal to the natural interest rate, the natural interest rate is important for three reasons.
First, it is the level of the real market interest rate that signals firms and households to coordinate production and consumption through time. Firms produce consumer goods now consistent with the amount households consume now. And firms invest to produce capital goods that increase their ability to produce consumer goods in the future consistent with the amount households save to increase net worth that increases their ability to consume in the future.
Second, it is the level of the real market interest rate that keeps total real expenditures equal to potential income. Someone is willing to buy the total amount of goods and services that can be produced if resources are fully employed. This is because the amount firms spend on new capital goods is just equal to the amount households don't spend on consumer goods.
Third, market forces cause the level of the real market interest rate to change until it is equal to the natural interest rate. While the adjustment process is very gradual, in the long run, the real market interest rate is equal to the natural interest rate.
IS Relationship
An increase in income causes an increase in savings. The interest rate at which saving and investment are equal is lower. This relationship is represented by the IS curve.
I stands for investment. S stands for saving. The IS curve shows combinations of income and interest rates consistent with saving and investment being equal.
An alternative approach looks at the relationship between the real interest rate and total real expenditure--consumption plus investment plus government spending. A lower real interest rate tends to stimulate consumption and investment spending. The increase in total spending, tends to cause firms to sell more. Assuming they expand their production, output and income rise.
A log linear function representing the is function would be:
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lnyt = co - c1tt - c2r bt +c3 lngt+ c4 lnxt - c5 lnnt + t
where: co, c1, c2, c3, c4, c5 are positive coefficients, and γt is a real expenditure shocks. t is the tax rate, rbt is the real interest rate on bonds, x is exports and n is imports. Permanent changes in consumption or investment would be represented by a change in c0 in the same direction. Temporary increases in investment and consumption or decreases in saving are positive real expenditure shocks. Temporary decreases in investment or consumption or increases in saving are negative real expenditure shocks.
The IS curve is the graph of this relationship.
The IS curve shows the long run relationship between potential income and the natural interest rate.
Changes in the Natural Interest Rate
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The natural interest rate can change. Changes in saving habits by households or optimism or pessimism about future profits by firms influence the natural interest rate. Further, the government's budget deficit is considered dissaving. And the foreign "investment" that matches any trade deficit is considered an addition to savings. So the budget deficit and trade deficit both influence the natural interest rate.
Changes in Real Expenditure: shifts of the IS curve
Given potential income, the shifts in the IS curve show how various factors cause changes in the natural interest rate. The natural interest rate changes in the same direction as the IS curve.
An increase in the IS curve is a shift to the right. A decrease in the IS curve is a shift to the left. (To remember the relationships, note that increases in spending tend to increase production and income in the short run. More consumption, more production, IS curve shifts right.)
Factor Relationship to IS
Consumption (c0) Positive
Saving (negative c0) Negative
Investment (c0) Positive
Government Spending Positive
Taxes (tax rate) Negative
Budget Deficit (govt. spending - taxes) Positive
Exports Positive
Imports Negative
Trade Deficit (imports -exports) Negative
Nominal Interest Rate in the Long Run
Assuming people have correct expectations about inflation in the long run, the nominal market interest rate is equal to the natural interest rate plus the inflation rate.
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Rt = rnt + Pt (Long Run = full equilibrium)