Comprehensive Study Notes on National Saving, Intertemporal Consumption, and Macroeconomic Policy

Administrative Announcements & Federal Reserve Monetary Policy

• The midterm examination remains scheduled for next Wednesday, with further details to be provided on Monday.

• Federal Reserve Funds Rate Target and Benchmark:

  • Target range for the Fed funds rate: $3.75\%$ to $4.00\%$.

  • Actual benchmark rate: $3.9\%$.

  • Recent rate adjustment: The Federal Reserve increased the benchmark rate by $25\, \text{basis points}$ ($0.25\%$).

  • Definition of basis points: $100\, \text{basis points} = 1.0\, \text{percentage point}$.

  • Future monetary policy expectations: An additional rate hike of $25\, \text{basis points}$ is anticipated following the late October Federal Open Market Committee (FOMC) meeting, with further increases expected before the end of the calendar year.

Goods Market Equilibrium & National Saving Fundamentals

• Closed Economy Framework Assumptions:

  • Net exports ($NX$) are assumed to be $0$ due to zero international trade.

  • Total national output ($Y$) is generated through the labor market production function.

  • Total demand for produced output consists of household consumption ($C$), gross private investment ($I$), and government purchases ($G$).

• National Saving Formula and Structure:

  • Total National Saving ($S_{national}$) ignores net factor payments ($NFP$) in a closed economy and is defined as:

$S_{national} = Y - C - G$

• National Saving is composed of Private Saving ($S_p$) and Government Saving ($S_g$):

$S_{national} = S_p + S_g$

• Private Saving ($S_p$) represents aggregate household disposable income after taxes, transfers, and consumption (excluding transfer payments $TR$ and interest payments $INT$):

$S_p = (Y - T) - C$

• Government Saving ($S_g$) represents net tax revenue minus government purchases:

$S_g = T - G$

• Equilibrium condition in the loanable funds / goods market:

$S_{national} = I$

Intertemporal Consumption Model & Permanent Income Hypothesis

• Intertemporal Choice Framework:

  • Households maximize lifetime utility $U(c, c_f)$ subject to a lifetime budget constraint, where $c$ represents current consumption and $c_f$ represents future consumption.

  • Model simplification: Setting the real interest rate $r = 0$ yields the simplified Lifetime Budget Constraint:

$c + c_f = (Y - T) + (Y_f - T_f) + a$

• Present Value of Lifetime Resources ($PVLR$) combines current disposable income, expected future disposable income ($Y_f - T_f$), and current real wealth ($a$), where $a$ includes real assets minus liabilities (e.g., housing value, stock portfolios, Bitcoin):

$PVLR = (Y - T) + (Y_f - T_f) + a$

• Present Value of Lifetime Consumption ($PVLC$):

$PVLC = c + c_f$

• Permanent Income Hypothesis ($Y_p$):

  • Household consumption decisions are driven by total lifetime resources ($PVLR$) rather than current income ($Y$) alone.

  • Absence of Bequests: Individuals consume all lifetime resources over their lifespan without leaving assets for heirs.

  • Marginal Propensity to Consume ($MPC$):

  • $MPC$ out of Permanent Income ($PVLR$) equals $1.0$ when allocated over the full lifetime horizon.

  • $MPC$ out of temporary changes in income is significantly less than $1.0$ because households spread the windfall over all remaining periods.

• Consumption Smoothing Hypothesis:

  • Households prefer a uniform consumption path across all time periods ($c = c_f$).

  • Hypothetical calculation example: If an individual has $PVLR = \$2,000,000$ across a $100\text{-year}$ lifespan, perfect consumption smoothing dictates an annual consumption of:

c = \frac{\2,000,000}{100\, \text{years}} = \$20,000\, \text{per year}$

Five Determinants and Shocks to National Saving

• Current Real GDP Increase ($Y \uparrow$):

  • Mechanism: An increase in current output raises $PVLR$ by $\Delta Y$.

  • Household response: Consumption smoothing leads households to increase current consumption ($c$) and future consumption ($c_f$) by less than $\Delta Y$ (e.g., $50\%$ of $\Delta Y$).

  • Impact on Private Saving: Because $Y$ rises by more than $c$, private saving $S_p = (Y - T) - C$ increases.

  • Impact on National Saving: $S_{national}$ increases.

• Expected Future Real GDP Increase ($Y_f \uparrow$):

  • Mechanism: Expecting higher future income increases current $PVLR$ without changing current real output ($Y$).

  • Household response: Households feel wealthier today and immediately increase current consumption ($c \uparrow$).

  • Impact on Private Saving: With $Y$ fixed and $c$ higher, $S_p = (Y - T) - C$ decreases.

  • Impact on National Saving: $S_{national}$ decreases.

• Real Wealth Increase ($a \uparrow$):

  • Mechanism: Asset appreciation (e.g., housing boom, stock market gains, cryptocurrency expansion) increases $a$ and raises $PVLR$.

  • Household response: Current consumption ($c$) increases.

  • Impact on Private Saving: Current income $Y$ does not change; thus, $S_p = (Y - T) - C$ decreases.

  • Impact on National Saving: $S_{national}$ decreases.

• Government Purchases Increase ($G \uparrow$):

  • Example scenario: An extra $\$10,000,000,000$ in defense spending (e.g., military aircraft, drones) under the Trump administration.

  • Financing Case A (Current Tax Increase, $\Delta T = \Delta G$):

  • Household disposable income drops by $\Delta T$, causing $PVLR$ to drop.

  • Due to consumption smoothing, households reduce current consumption $c$ by less than $\Delta T$ (e.g., a $\$1,000,000,000$ tax increase reduces consumption by $\$500,000,000$).

  • Since $c$ decreases by less than $G$ increases, total national saving $S_{national} = Y - C - G$ falls.

  • Financing Case B (Government Borrowing / Bond Issuance, $\Delta T = 0$, $\Delta T_f > 0$):

  • Government runs a budget deficit ($S_g = T - G$ falls by $\Delta G$).

  • Forward-looking households recognize future taxes ($T_f$) will rise to service public debt, reducing $PVLR$.

  • Household consumption $c$ drops slightly, causing private saving $S_p$ to rise slightly, but by less than the full increase in $\Delta G$ ($\$1,000,000,000$ deficit leads to $\$500,000,000$ private saving increase).

  • Net effect: Total national saving $S_{national}$ falls.

  • Conclusion: An increase in government purchases ($G \uparrow$) unambiguously decreases National Saving ($S_{national}$).

Ricardian Equivalence Proposition

• Core Theory of Ricardian Equivalence:

  • Proposed by classical economists, stating that a lump-sum tax cut financed by government borrowing has zero impact on aggregate demand, current consumption, or national saving.

  • Government Budget Constraint:

$G + \frac{G_f}{1+r} = T + \frac{T_f}{1+r}$

• Substituting the government constraint into the household budget constraint shows that total tax timing does not alter lifetime purchasing power.

  • Outcomes Under Ricardian Equivalence:

• A current tax cut of $\$100$ ($\Delta T = -\$100$) creates a government budget deficit but implies a future tax increase of $\$100$ in present value ($\Delta T_f = +\$100$).

• Rational households save $100\%$ of the tax rebate check to pay future taxes.

• Current consumption remains completely unchanged ($\Delta c = 0$).

• Private saving increases by the exact amount of the tax cut ($\Delta S_p = -\Delta T$), perfectly offsetting the fall in government saving ($\Delta S_g = \Delta T$).

• National Saving ($S_{national}$) remains unchanged.

  • Outcomes When Ricardian Equivalence Fails (Keynesian / Non-Classical View):

• Reasons for Failure:

  • Borrowing Constraints: Credit-constrained households cannot borrow against future income; a tax cut provides liquidity to increase immediate consumption.

  • Finite Lifespans / Generational Disconnect: Current taxpayers expect to die before future tax hikes occur, shifting the tax burden onto future generations.

  • Myopia and Irrationality: Taxpayers view rebate checks as pure windfalls rather than future liabilities.

• Impact of Tax Cut when Ricardian Equivalence Fails:

  • Households increase current consumption ($c \uparrow$).

  • Private saving increases by less than the full tax cut.

  • National Saving ($S_{national}$) decreases (and conversely, a tax increase causes National Saving to increase).

Real Interest Rates and the National Saving Curve

• Intertemporal Price of Consumption:

  • Discounted Budget Constraint:

$c + \frac{c_f}{1+r} = (Y - T) + \frac{Y_f - T_f}{1+r} + a$

• The real interest rate ($r$) represents the relative price of current consumption in terms of future consumption.

  • Dual Effects of Real Interest Rate Changes ($r \uparrow$):

• Substitution Effect: Higher $r$ increases the yield on saving, making current consumption relatively more expensive. Households substitute away from current consumption toward saving ($c \downarrow$, $S \uparrow$).

• Income Effect: For net savers, higher $r$ increases net interest receipts, expanding overall lifetime wealth ($PVLR$) and encouraging higher current consumption ($c \uparrow$, $S \downarrow$).

  • Empirical Assumption & Curve Slope:

• The substitution effect empirically dominates the income effect.

• The National Saving Curve ($S_{national}$) is upward-sloping in $(S, r)$ space, where real interest rate ($r$) is on the vertical axis and saving ($S$) is on the horizontal axis.

Life Cycle Hypothesis and Demographics

• Model Formulation (Franco Modigliani):

  • Income profile across a lifespan is hump-shaped (peaking during middle age), while consumption remains flat and smooth.

• Numerical Life Cycle Example:

  • Lifespan structure: Total horizon of $60\, \text{years}$ (ages $20$ to $80$), divided into three $20\text{-year}$ phases:

  • Young / Student Phase (Ages $20 - 40$): Income $Y = \$20,000\, \text{per year}$.

  • Middle Age Phase (Ages $40 - 65$): Income $Y = \$60,000\, \text{per year}$.

  • Retirement / Old Age Phase (Ages $65 - 80$): Income $Y = \$10,000\, \text{per year}$ (Social Security benefits).

  • Total Present Value of Lifetime Resources ($PVLR$):

PVLR = (20 \times \20,000) + (20 \times \$60,000) + (20 \times \$10,000) = \$400,000 + \$1,200,000 + \$200,000 = \$1,800,000$

• Annual Smooth Consumption ($c$):

c = \frac{\1,800,000}{60\, \text{years}} = \$30,000\, \text{per year}$

• Period-by-Period Saving Patterns:

  • Youth Saving: $S_{young} = \$20,000 - \$30,000 = -\$10,000\, \text{per year}$ (dis-saving / borrowing).

  • Middle Age Saving: $S_{middle} = \$60,000 - \$30,000 = +\$30,000\, \text{per year}$ (paying off youth debt and accumulating retirement wealth).

  • Retirement Saving: $S_{old} = \$10,000 - \$30,000 = -\$20,000\, \text{per year}$ (dis-saving accumulated wealth).

  • Macroeconomic & Demographic Implications:

• Aging populations (e.g., retiring baby boomers) increase the proportion of dis-savers, causing overall aggregate national saving to drop.

• High concentration of middle-aged workers raises aggregate national saving.

Borrowing Constraints and Consumption Smoothing Limitations

• Imposition of Credit Constraints:

  • Banks (e.g., MSU Federal Credit Union) may refuse loan applications to young individuals due to lacking credit history or unverified future earning capacity.

• Impact on Young Phase:

  • Young individuals cannot borrow the desired $\$10,000\, \text{per year}$.

  • Young consumption is forced down to current disposable income: $c = \$20,000\, \text{per year}$.

  • Young saving is constrained to $S = \$0\, \text{per year}$.

• Adjustment to Remaining Life Cycle (Ages $40 - 80$, $40\, \text{years}$ remaining):

  • Remaining Lifetime Resources:

PVLR_{remaining} = (20 \times \60,000) + (20 \times \$10,000) = \$1,200,000 + \$200,000 = \$1,400,000$

• Adjusted Annual Smooth Consumption for Middle and Old Age:

c_{adjusted} = \frac{\1,400,000}{40\, \text{years}} = \$35,000\, \text{per year}$

• Adjusted Middle Age Saving: $S_{middle} = \$60,000 - \$35,000 = +\$25,000\, \text{per year}$.

• Adjusted Retirement Dis-saving: $S_{old} = \$10,000 - \$35,000 = -\$25,000\, \text{per year}$.

Questions & Discussion

• Student Question: Do presidents deliberately manipulate tax timing by keeping taxes low during their presidency to leave tax increases for future administrations?

  • Explanation: Administrations often face short-term electoral incentives. Because politicians may operate over shorter time horizons than the overall life of the nation, debt accumulation can be passed to future generations, leading to potential future tax hikes, debt monetization (inflationary money printing), or default.

• Student Question: What review materials will be provided prior to the midterm exam?

  • Explanation: A two-page study review outline will be published on Wednesday. Additionally, a new problem set containing numerical exercises matching the format of exam questions will be assigned on Wednesday.