Macroeconomics: Saving and Capital Formation

Fundamentals of Saving and Wealth

Saving and Saving Rate * Saving is defined as current income minus spending on current needs. * The saving rate is calculated by dividing saving by income.
Wealth and the Balance Sheet * Wealth is the value of assets minus liabilities. * Assets represent anything of value that an individual or entity owns. * Liabilities represent the debts an individual or entity owes. * A balance sheet is a formal list of an economic unit’s (e.g., household or business) assets and liabilities at a specific date.

Case Study: Consuelo’s Balance Sheet

Assets * Cash: $80$ * Checking account: $1,200$ * Shares of stock: $1,000$ * Car (market value): $3,500$ * Furniture (market value): $500$ * Total Assets: $6,280$
Liabilities * Student loan: $3,000$ * Credit card balance: $250$ * Total Liabilities: $3,250$
Net Worth * Net worth is defined as total assets minus total liabilities. * Consuelo's Net Worth: $6,280 - 3,250 = 3,030$

Flow Values and Stock Values

Flow Values * Flow values are defined per unit of time. * Examples include: * Income * Spending * Saving * Wage
Stock Values * Stock values are defined at a specific point in time. * Examples include: * Wealth * Debt
Relationship Between Flow and Stock * The flow of savings causes the stock of wealth to change. * Every dollar saved adds directly to an individual's wealth. * A high rate of saving in the present leads to an improved standard of living in the future.

Capital Gains and Losses

Wealth changes when the value of existing assets changes, independent of the flow of saving.
Capital Gains: These increase the value of existing assets (e.g., a higher market value for owned stock).
Capital Losses: These decrease the value of existing assets (e.g., a car accident that damages a bumper and headlight, reducing the vehicle's market value).
Change in Wealth Formula: * $\text{Change in Wealth} = \text{Saving} + \text{Capital Gains} - \text{Capital Losses}$

Historical Trends in American Household Wealth

The 1990s and Stock Market Growth * Stock ownership increased via direct purchases, mutual funds, and pension/retirement funds. * Rapidly rising stock prices generated significant capital gains, increasing household wealth. * Evidence suggests these capital gains may have decreased the motivation for active household savings.
2000–2002 Transitions * The stock market declined, but household savings remained low. * The value of privately owned homes increased rapidly during this period.
2012–Present Dynamics * Household saving reached a peak in 2012 when the housing market hit its bottom. * A steep increase in saving occurred in 2020 because spending slowed and the government provided COVID-19 stimulus payments, temporarily increasing household incomes. * Saving rates have recently fallen again as stock and home values reached new historical highs.

Three Reasons for Household Saving

Life-cycle Saving: This is done to meet long-term objectives such as retirement, funding children’s college attendance, or purchasing a home.
Precautionary Saving: This acts as protection against unforeseen setbacks, such as the loss of a job or a medical emergency.
Bequest Saving: This is saving intended to leave an inheritance, a behavior seen primarily among higher-income groups.

Case Study: Household Saving in China

Chinese households save approximately $25\%$ of their disposable income.
This is a relatively new phenomenon, as the rate was only $10\%$ until the late 1980s.
Drivers of the Chinese Saving Rate: * Life-cycle and Precautionary Motives: Chinese wealth is a recent development; young people are often richer than older generations, and the saving of the young outweighs the dissaving of the old. * Social Safety Net: High saving is driven by a limited social safety net. * Borrowing Constraints: Individuals have little opportunity to borrow, making savings necessary for large purchases. * Economic Reform: Before reforms, there were fewer opportunities and less perceived need for precautionary saving.

Saving and the Real Interest Rate

Saving often takes the form of financial assets that pay a return, such as interest-bearing checking accounts, bonds, savings accounts, CDs, mutual funds, and stocks.
Real Interest Rate ( $r$ ): This is the nominal interest rate ( $i$ ) minus the rate of inflation ( $\pi$ ). * $r = i - \pi$
The real interest rate represents the increase in purchasing power from a financial asset and is the marginal benefit of extra saving.

Comparison: Thrifts vs. Spends

Consider two identical families starting in 2005 with a real income of $40,000$ and a real interest rate of $8\%$ .
Spends Household: * Savings Rate: $5\%$ * Initial Consumption (2005): $38,000$ * Accumulated Savings by 2040: $77,000$
Thrifts Household: * Savings Rate: $20\%$ * Initial Consumption (2005): $32,000$ * By 2020, Thrifts begin to consume more than Spends due to unearned income from interest. * Accumulated Savings by 2040: $385,000$ * By 2040, the Thrift's consumption is $12,000$ higher than the Spend's consumption.
Bottom Line: A high savings rate pays off significantly in the long run.

Savings Perspective and Psychology

Target Savers: If people save for a specific goal (e.g., $25,000$ in five years), a higher interest rate actually lowers the required saving rate. * At $5\%$ , one must save $4,309$ per year. * At $10\%$ , one must save only $3,723$ per year.
Aggregate Data: Real-world data shows that higher real interest rates generally increase savings, but only modestly.
Self-Control: Psychologists suggest individual self-control may be too weak for rational outcomes in smoking, obesity, gambling, and spending.
Commitment Devices: Devices to support saving include making saving automatic and making withdrawals costly (e.g., penalties for early withdrawal of IRA funds).
Easy Borrowing: High current spending is supported by credit cards and home equity loans.

Factors Depressing the U.S. Household Savings Rate

Availability of Social Security, Medicare, and other government programs for the elderly.
Mortgages requiring small or no down payments.
Confidence in a prosperous future.
Increasing values of stocks and homes.
Readily available home equity loans.
Demonstration Effects: The pressure to buy status goods to keep up with others.

National Savings

Aggregate Income Formula: * $Y = C + I + G + NX$ * $Y$ = aggregate income (GDP) * $C$ = consumption expenditure * $I$ = investment spending * $G$ = government purchases of goods and services * $NX$ = net exports
National Savings ( $S$ ): Current income less spending on current needs. * Assuming $NX = 0$ for simplicity. * We assume all of $C$ and all of $G$ are for current needs and exclude investment ( $I$ ). * $S = Y - C - G$
Historical National Savings Rate (1960–2022): Historically fluctuated between $12\%$ and $14\%$ , which is less volatile than household saving.

Components of Private and Public Saving

Private Saving ( $S_{\text{private}}$ ): Saving by households and businesses. * $S_{\text{private}} = Y - T - C$ * $T$ = Net Taxes, defined as $\text{Taxes} - \text{Transfers} - \text{Government interest payments}$ . * Business saving accounts for the majority of private saving in the U.S. and is defined as: $\text{Revenues} - \text{Operating costs} - \text{Dividends}$ .
Public Saving ( $S_{\text{public}}$ ): Income of the public sector not spent on current needs. * $S_{\text{public}} = T - G$
National Saving Identity: * $S = S_{\text{private}} + S_{\text{public}}$ * $S = (Y - T - C) + (T - G) = Y - C - G$

The Government Budget

Balanced Budget: Occurs when $G = T$ .
Government Budget Surplus: Excess of net tax collections over spending ( $T - G$ ); this is equivalent to public saving.
Government Budget Deficit: Excess of spending over net tax collections ( $G - T$ ); this represents public dissaving.
Historical Data Points (Billions of Dollars): * 2000: * Federal Receipts: $2,067.8$ ; Expenditures: $1,908.1$ * State/Local Receipts: $1,304.3$ ; Expenditures: $1,345.0$ * 2021: * Federal Receipts: $4,319.0$ ; Expenditures: $7,154.4$ * State/Local Receipts: $3,525.0$ ; Expenditures: $3,300.1$

Investment and Capital Formation

Investment is the creation of new capital goods and housing.
Firms decide to buy new capital to increase profits based on the Cost-Benefit Principle. * Cost: The cost of using the machine or capital (influenced by the price of capital goods and the real interest rate ( $r$ )). * Benefit: The Value of the Marginal Product of the capital (VMP).
Lauren’s Lawn Care Example: * Cost of mower: $4,000$ (Interest on loan: $6\%$ ). Assume the mower can be resold for the same price. * Net revenue: $6,000$ per summer; Taxes: $20\%$ \ ( $1,200$ ). * Opportunity cost: Working elsewhere for $4,400$ . * VMP of lawnmower: $6,000 - 1,200 - 4,400 = 400$ . * Interest cost: $6\% \times 4,000 = 240$ . * Net benefit: $400 - 240 = 160$ . (Lauren should start the business).

Saving, Investment, and Financial Markets

Supply of Savings ( $S$ ): Provided by households, businesses, and the government. The quantity supplied increases as the real interest rate ( $r$ ) increases.
Demand for Investment ( $I$ ): The amount firms want to borrow for capital. The quantity demanded is inversely related to the real interest rate ( $r$ ).
Equilibrium Interest Rate: The rate where the amount of saving equals the investment funds demanded. * If $r$ is above equilibrium: Surplus of savings. * If $r$ is below equilibrium: Shortage of savings.
Shifts in Financial Markets: * Technological Improvement: Raises the marginal productivity of capital, increasing the demand for investment ( $I$ ). This move causes a higher interest rate and a higher level of savings and investment. * Government Budget Deficit Increases: Reduces national saving (shifting the supply of savings curve). This results in a higher interest rate and a lower level of saving and investment. Private investment is "crowded out."

Policy Implications to Increase National Saving

Reducing the government budget deficit increases national saving.
Increase incentives for households through: * Federal consumption taxes. * Reducing taxes on dividends and investment income.
Higher national saving leads to greater investment in new capital goods and a higher standard of living.