Crowding Out Through Higher Interest Rates

How a Fiscal Expansion Can Affect Private Investment

An increase in government spending or a tax reduction can support aggregate demand, but financing the resulting deterioration in the government budget can also affect private investment. In the loanable-funds model, a larger government deficit reduces national saving available to finance investment. The resulting increase in the equilibrium real interest rate can make some private investment projects less attractive.

This mechanism is called crowding out through higher interest rates. It is a comparative-static explanation: it compares equilibria before and after a fiscal change under specified assumptions. It does not mean that every fiscal expansion reduces investment by the same amount, or that a particular economy must follow the model exactly.

Definition: Private saving is household and business saving, represented in a simplified closed-economy model by $S_p=Y-T-C$, where $Y$ is output, $T$ is net taxes, and $C$ is consumption. Public saving is $S_g=T-G$, where $G$ is government purchases. National saving is their sum: $$ S=S_p+S_g=Y-C-G. $$ A government deficit, when $G>T$, means public saving is negative. A larger deficit reduces public saving and, other things equal, national saving.

The Loanable-Funds Model

The model treats national saving as the supply of loanable funds and planned private investment as the demand. The vertical axis of a loanable-funds diagram is the real interest rate, and the horizontal axis is the quantity of funds. In the basic closed-economy model, equilibrium requires saving to equal investment. Saving is assumed to rise with the real interest rate, while planned investment falls as the real interest rate rises.

For the fiscal comparison, hold output and net taxes fixed when government purchases rise. At any given real interest rate, the increase in $G$ reduces national saving by the same amount. Therefore the saving-supply curve shifts left. The new equilibrium has a higher real interest rate; because planned investment falls as the rate rises, private investment is lower.

The assumption that output is held fixed is important. It isolates the interest-rate channel rather than accounting for output changes that may accompany fiscal policy. Consumption is not held fixed as the real interest rate changes: in this model, the saving schedule reflects a behavioral response of saving to the rate. At a fixed rate, however, a rise in $G$ reduces $Y-C-G$ by the full increase in $G$, provided $Y$ and $C$ are unchanged at that rate.

Why the Saving Curve Shifts

The direction and size of the shift follow directly from the national-saving identity. Suppose output and taxes are fixed, and government purchases rise by $\Delta G>0$. At any given real interest rate, if consumption is unchanged, then:

\Delta S=\Delta(Y-C-G)=-\Delta G.

Thus the saving schedule moves left by $\Delta G$ at every rate. The equilibrium rate then adjusts, and consumption may respond to that rate change. The shift at a given rate must not be confused with the final change in equilibrium saving, which is determined jointly by the shifted supply schedule and the investment-demand schedule.

The interest-rate result can also be derived from simple linear schedules. Let saving initially be $S=S_0+sr$, and investment be $I=I_0-br$, where $s>0$, $b>0$, and $r$ is measured in a consistent unit, such as percentage points. A deficit increase of $D$ shifts saving to $S'=S_0-D+sr$. Equilibrium before the change satisfies $S=I$; afterward it satisfies $S'=I$. Solving the new equilibrium gives:

S_0-D+sr=I_0-br \qquad\Longrightarrow\qquad r'=\frac{I_0-S_0+D}{s+b}.

Before the change, $r=(I_0-S_0)/(s+b)$. Subtracting the two rates shows that the increase in the real interest rate is $D/(s+b)$. Since investment changes by $-b$ times the rate change, the decrease in investment is $bD/(s+b)$. This derivation explains why the deficit increase and the investment decrease need not be equal: the rate moves until saving and investment once again match.

Worked Example: A Spending Increase and the Saving Identity

In a hypothetical closed economy, output is held at $1{,}000$ billion dollars and net taxes are fixed. Initially, government purchases are $200$ billion dollars. The saving and investment schedules, with $r$ measured in percentage points, are $S=100+10r$ and $I=220-10r$, in billions of dollars. Government purchases rise by $30$ billion. Find the initial and new equilibria, the change in investment, and the consumption implied by the saving identity.

Method. First equate saving and investment in each situation. Then use $S=Y-C-G$ to check that the equilibrium saving is consistent with the accounting identity. The saving schedule means that consumption responds to the rate; it is not fixed across the two equilibria.

Initial equilibrium. Set $100+10r=220-10r$. Therefore $20r=120$, so $r=6$. Substitution gives $S=100+10(6)=160$ and $I=220-10(6)=160$ billion dollars.

New saving schedule. At any fixed rate, the spending increase lowers national saving by $30$ billion. The new schedule is $S'=70+10r$. Equating it to investment gives $70+10r=220-10r$, so $20r=150$ and $r=7.5$. At that rate, saving is $70+10(7.5)=145$, and investment is $220-10(7.5)=145$ billion dollars. Investment has fallen by $160-145=15$ billion dollars.

Accounting check. At the new equilibrium, $S=Y-C-G$, so $145=1{,}000-C-230$. Hence $C=625$ billion dollars. This gives $1{,}000-625-230=145$, exactly the saving found from the new schedule. Initially, consumption is $1{,}000-160-200=640$ billion dollars, also consistent with the initial equilibrium.

At the old rate of $6$, the new saving schedule gives $70+10(6)=130$, a $30$-billion decline from the original $160$. That is the shift at a fixed rate. At the new equilibrium, the rate has risen and consumption has fallen to $625$, so saving is $145$, not $130$. The method avoids treating consumption as fixed while also using an upward-sloping saving schedule.

Worked Example: A Tax Reduction and Lower Public Saving

Consider a hypothetical economy with output $Y=1{,}000$ billion dollars and government purchases $G=180$ billion. Initially, net taxes are $T=250$ billion, private saving is $S_p=80+10r$, and planned investment is $I=330-10r$, with $r$ in percentage points and quantities in billions. The government reduces net taxes by $20$ billion. Assume that at each given interest rate the tax reduction raises consumption by $20$ billion, leaving the private-saving schedule unchanged. Find both equilibria and verify the new saving with the accounting identity.

Method. The tax reduction lowers public saving $T-G$ by $20$ billion at every rate. Because private saving is assumed unchanged at each fixed rate, national saving shifts left by $20$ billion.

Initial equilibrium. Public saving is $250-180=70$ billion. National saving is therefore $S=(80+10r)+70=150+10r$. Equating saving and investment gives $150+10r=330-10r$, so $20r=180$ and $r=9$. Equilibrium saving and investment are both $150+10(9)=240$ billion dollars.

New equilibrium. After the tax reduction, public saving is $230-180=50$ billion, so the new national-saving schedule is $S'=80+10r+50=130+10r$. Then $130+10r=330-10r$, which gives $r=10$. Saving and investment are both $130+10(10)=230$ billion dollars. The interest rate has risen by one percentage point, and private investment has fallen by $240-230=10$ billion dollars.

Accounting check. At the new equilibrium, private saving is $80+10(10)=180$ billion, and public saving is $50$ billion, giving national saving of $230$ billion. The identity implies $C=Y-G-S=1{,}000-180-230=590$ billion. Directly, private saving is $Y-T-C=1{,}000-230-590=180$, as specified by its schedule. Initially, consumption is $1{,}000-180-240=580$ billion; the $20$-billion tax reduction and the higher rate together produce the stated new consumption.

The tax cut worsens the government budget position by $20$ billion relative to the initial situation. The size of the rate and investment changes follows from the slopes of both schedules, not from assuming that investment falls by the full tax reduction.

Worked Example: Calculating the Amount of Investment Displaced

In another hypothetical closed economy, the initial schedules are $S=90+6r$ and $I=270-9r$, in billions of dollars, with $r$ measured in percentage points. A deficit-financed increase in spending shifts saving left by $24$ billion at each rate. Calculate the initial and new rates and investment, then check the change using the linear-schedule result.

Initial equilibrium. Set $90+6r=270-9r$. Then $15r=180$, so $r=12$. Saving and investment are both $90+6(12)=162$ billion dollars.

New equilibrium. The new saving schedule is $S'=66+6r$. Set $66+6r=270-9r$, giving $15r=204$, or $r=13.6$. At that rate, saving is $66+6(13.6)=147.6$, and investment is $270-9(13.6)=147.6$ billion dollars. The rate rises by $13.6-12=1.6$ percentage points, while investment falls by $162-147.6=14.4$ billion dollars.

Slope check. Here $D=24$, $s=6$, and $b=9$. The derived rate change is $D/(s+b)=24/15=1.6$ percentage points. The predicted investment decline is $bD/(s+b)=9(24)/15=14.4$ billion dollars, agreeing with the direct calculation.

Reading the Result Carefully

A loanable-funds diagram makes the sequence visible: the deficit increase shifts saving supply left; the equilibrium moves up along the downward-sloping investment-demand curve; and the equilibrium quantity of private investment falls. Government borrowing and private borrowing compete for funds in this closed-economy representation. The real interest rate is the price that adjusts to reconcile saving and investment.

The conclusion depends on the model and assumptions just stated. In particular, it isolates the interest-rate channel with output held fixed and does not model changes in output or monetary-policy responses. It should therefore be read as a mechanism, not as a universal prediction that every fiscal expansion has an identical effect. The earlier material on fiscal multipliers and aggregate demand addresses the demand-side effects; the loanable-funds analysis here focuses on how financing can affect private investment.

Common exam trap: Do not treat the leftward shift in saving as the final equilibrium change in saving, and do not assume that private investment must fall dollar for dollar with the deficit. In Worked Example 1, at the original rate $r=6$, new saving is $130$, but investment at that rate remains $160$. Calling $130$ the new equilibrium would leave saving unequal to investment. Correctly solve the new equilibrium: $70+10r=220-10r$, so $r=7.5$ and both saving and investment equal $145$. The accounting identity then gives $C=625$, consistent with the rate-responsive saving schedule.

Key takeaway: In the basic closed-economy loanable-funds model, a larger deficit lowers national saving at a given real interest rate. The resulting leftward shift in saving supply raises the equilibrium real interest rate and reduces planned private investment. Always solve for the new equilibrium and check it against $S=Y-C-G$.

Check Your Understanding

For each question, keep track of whether a quantity is measured at a fixed interest rate or at the new equilibrium. Unless stated otherwise, rates are in percentage points and quantities are in billions of dollars.

Initially, $S=70+4r$ and $I=190-6r$. A deficit increase shifts saving left by $20$ at every rate. Find the initial and new equilibria and the decrease in investment. (Answer: Initially $r=12$, $S=I=118$; afterward $r=14$, $S=I=106$; investment falls by $12$.)
In the loanable-funds model, what happens to the saving-supply curve when a deficit-financed spending increase reduces public saving, and why does private investment fall in the new equilibrium? (Answer: Saving supply shifts left; the equilibrium real interest rate rises, and movement along downward-sloping investment demand lowers private investment.)
Let $S=120+8r$ and $I=280-12r$. A fiscal change reduces national saving by $15$ at each fixed rate. Calculate the change in the equilibrium rate and the investment decrease. (Answer: The rate rises from $8$ to $8.75$, an increase of $0.75$ percentage points; investment falls from $184$ to $175$, a decrease of $9$.)
Output is $800$, net taxes are $200$, and government purchases initially equal $150$. Private saving is $40+5r$, and investment is $210-5r$. Purchases increase by $20$. Find the new equilibrium and verify national saving using $S=Y-C-G$. (Answer: New saving is $70+5r$; $r=14$ and $S=I=140$. Private saving is $110$, public saving is $30$, and consumption is $490$, so $800-490-170=140$.)
For linear schedules $S=S_0+sr$ and $I=I_0-br$, a deficit increase shifts saving left by $D$. State the resulting interest-rate increase and investment decrease. (Answer: The rate increases by $D/(s+b)$; investment decreases by $bD/(s+b)$.)

What You'll Learn

How a Fiscal Expansion Can Affect Private Investment

The Loanable-Funds Model

Why the Saving Curve Shifts

Worked Example: A Spending Increase and the Saving Identity

Worked Example: A Tax Reduction and Lower Public Saving

Worked Example: A Tax Reduction and Lower Public Saving

Worked Example: Calculating the Amount of Investment Displaced

Worked Example: Calculating the Amount of Investment Displaced

Reading the Result Carefully

Check Your Understanding

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