Saving, Wealth and the Real Interest Rate

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[1]In trying to asses macroeconomic performance, one of the indicators is the amount of savings that occur in the macroeconomy. Broadly speaking, savings is important because its a form of insurance in cases of economic emergency. Further, it allows an economy to sustain future and long term goals. These goals might be the production of capital goods (such as factories, equipment and housing) and the resources to produce them are tightly tied to savings. [2]Savings is a flow variable, that is, it is measured over time.

[3]Savings form a type of asset, which is used to measure wealth. Wealth is a stock variable, that is it it measured at a point in time. In actual fact, wealth is a better measurement of macroeconomic performance as it is defined as:

Net Wealth = Value of Assets - Value of Liabilities
Where:
Assets are anything of value owned by an entity, be it physical (money, housing etc.) or non physical (patents etc.).
Liabilities are any debts an entity owes
Both assets and liabilities are measured in current market value rather than historical costs

Hence, wealth measures the overall value of an entity against its debt, and therefore a better measurement of macroeconomic performance. However, due to ease of calculation, more focus is put on savings which inadvertently gives an indication of wealth.

Contents

Textbook Readings

Bernanke, Olekalns and Frank, Principles of Macroeconomics, (3rd ed, Sydney, McGraw Hill, 2011), pp. 40-65.

Wealth and Savings

[4]Since wealth is measured by assets and liabilities, any money saved can be used to increase assets (by adding cash to an account) or to reduce a liability (by paying off a debt) and hence increase wealth. It is this property of savings that make it a great indicator of wealth and hence macroeconomic performance. Savings is defined as the difference between income and expenditure, that is:

Savings = Income - Expenditure

While the savings rate, the rate at which savings are earned is defined as:

Savings Rate = Savings/Income

[5]Now in order to measure the change in a wealth, we look at how much the market value of the assets and the liabilities have changed. These are referred to as capital gains or capital losses. In this way, change in wealth can be said to be:

ΔW = W2 - W1
= Savings + Capital Gains - Capital Losses
= Savings + Net Capital Gains

By rearranging the equation, it can be shown that wealth can be calculated by:

W2 = W1 + Savings + Net Capital Gains
Where:
W1 = Wealth at previous time period
W2 = Wealth at present time period

In general, capital gains and losses are too difficult to predict and hence the only way to measure or predict changes in wealth is by focusing on savings.

Reasons for Savings

[6]There are three general reasons as to why people save. They are:

  1. Life Cycle Saving - At some point, people will have to stop working and when they do that they will have no income. At this stage, their only support is their savings from when they were working.
  2. Precautionary Savings - People save so that they have some insurance against unexpected economic setbacks such as car breakdowns, loss of jobs etc. without having to incur any loans.
  3. Bequest Savings - People want to leave wealth to their close family and friends

Factors that reduce Savings

Some factors that reduce savings are:

  1. Availability of consumer credit, that is, the availability of loans means individuals are less likely to save knowing that they can take out loans pretty easily
  2. Demonstration effects, such as neighbours' consumption, often causes others to want to spend as well
  3. Government provisions (such as for pensions) mean people are less likely to save as they are already 'insured' against economic setbacks or already have a pension waiting for them

Savings and Interest Rates

Savings as a Function of Real Interest Rates
.[7]If one thinks of interest rates as a cost of consuming today against consuming tomorrow, then savings offer an opportunity cost. For example, one can either spend $500 on an item, or one can save it and make interest (of say 5% pa). By saving, one can make an extra $25, while by spending today one loses the opportunity of making $25.

For this reason most savings come in the form of a bank deposit or investments in shares or government bonds, all of which offer an interest rate. This interest rate is the real interest rate. Quite obviously, we can say that savings is related to interest rates, where higher interest rates generally means higher savings rates. This allows economists to model savings as an upward sloping function of real interest rates.

National Savings

[8]While the analysis so far has focused on individual and household savings, the same applies on a national scale. The difference is that savings occurs by:

  1. Households (C)
  2. Businesses (I)
  3. Governments (G)

In order to find national savings, the national income accounting identity is used, that is:

Y = C + I + G + NX

but for a closed economy with no exports or imports (for simplicity), NX = 0. Hence:

Y = C + I + G

Now since Savings = Current Income - Current Expenditure, and taking Y (output) to be a measure of income:

National Savings (S) = Y - C - G

Where the expenditure by businesses (I) is seen as investment, i.e. "savings" for future consumption.

Now in order to get a measure of private savings and public savings, that is savings made bu the private sector and savings made by the government, the following trick is used (notice the value of the identity doesn't change):

S = Y - C - G + T - T
Where
T = Taxes paid by private sector - Transfer payments from government to private sector - Interest payments from government to private sector

And by rearranging:

S = (Y - T - C) + (T - G)
That is:
Savings = Private Savings + Public Savings
Where:
Private Savings = Y - T - C
Public Savings = T - G

In general, the economy is said to be in surplus when public savings are greater than zero (T - G > 0) and in deficit when public savings are lower than zero (T - G < 0).

Investment and Capital Formation

Since national savings is a function of real interest rates, and national savings are used to buy capital and other goods and services, it is handy to make a connection between investment and real interest rates.

The analysis begins with the assumption that investment is equal to the amount of money firms use to purchase goods and services. That is,

Investment = Cost of Capital Goods and Services

Now, the cost of capital is related to the:

  1. Nominal interest rate on loans to pay for buying capital (i)
  2. Original cost of capital (Pk)
  3. Physical capital depreciation (δ)

Since capital changes value (capital gains and losses), the depreciation uses both original cost and changes to the value, denoted as Pk + ΔPk.

This relationship can therefore be expressed as:

Cost of Capital = Price + interest rate - depreciation
= Pk + i.Pk - (1-δ)(Pk + ΔPk)

By factoring out Pk,

Cost of Capital = Pk[1+ i - (1-δ) - (1-δ) ΔPk/Pk)}

And if we assume that the rate of change of capital depreciation, δ.ΔPk/Pk is very small, then

Cost of Capital = Pk(i + δ - ΔPk/Pk)

Now since ΔPk/Pk is a rate of change of capital, or a good, it is essentially the same as the inflation rate. Hence ΔPk/Pk = π and the equation becomes:

Cost of Capital = Pk(i + δ - π)
Investment as a Function of Real Interest Rates
But r = i - π (see Inflation and Interest Rates)

Therefore:

Cost of Capital = Pk(r + δ)

It can therefore be shown that the cost of capital is dependent primarily by the original cost and the value of real interest rates. From microeconomics, the assumption is made that firms will only make investments if the 'value of marginal product of capital' is greater than the cost of capital. Therefore firms will invest when the cost of capital is low, i.e. when the real interest rate is low.

Savings and Investment

Savings and Investment as Functions of Real Interest Rates
The culmination of this analysis is a model for national investment and savings. In macroeconomics, national savings equals investment (under a closed economy) so that equilibrium is attained. However this equilibrium may be shifted due to shifts in savings and increase to budget deficit amongst other reasons.

References

"Textbook" refers to Bernanke, Olekalns and Frank, Principles of Macroeconomics, (3rd ed, Sydney, McGraw Hill, 2011).

  1. Textbook, p. 42
  2. Textbook p. 44
  3. Textbook, p.42
  4. Textbook, p.44
  5. Textbook, p.45
  6. Textbook, p.48
  7. Textbook, pp. 48-50
  8. Textbook pp. 52 - 53.
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