© 2020 EMANUEL GOMES CONFIDENTIAL AND PROPRIETARYMiguel Lebre de Freitas

(1)

Miguel Lebre de Freitas

Endowment economy

MACROECONOMIC ANALYSIS

Kathleen Petyarre, 'Sandhills', 2007

(2)

•

Many decisions are intertemporal They refer to choices regarding the

allocation of resources over time, such as borrowing and lending.

•

The inter-temporal model is fundamental to understand agents’

incentives to save and invest.

•

Role of temporary versus permanent shocks

Why the time dimension?

The Endowment Economy

Questions to be addressed

• How households decide how much of their income to consume today and how much to save for the future?

• How different variables affect consumption decisions?

• How is the macroeconomic equilibrium determined by consumption decisions?

• How different variables impacts on the macroeconomic equilibrium?

(3)

The Endowment Economy

Main assumptions

• Single homogenous good (numeraire)

• Production is exogenous

(no investment, no working decision)

• Representative agent

• Two period economy

• Perfect information

• Open, closed

• Government, lump sum.

• Flexible prices

Departures from these assumptions to be explored

(4)

•

INTERTEMPORAL BUDGET CONSTRAINTS

•

OPTIMAL CONSUMPTION

•

CONSUMPTION AND THE INTEREST RATE

•

RICARDIAN EQUIVALENCE

•

MACROECONOMIC EQUILIBRIUM WITH FLEXIBLE PRICES

•

COMPARATIVE STATICS

•

THE WORLD INTEREST RATE

•

FAILURE OF RICARDIAN EQUIVALENCE

•

BEYOUND THE TWO-PERIOD MODEL

The endowment economy

(5)

•

OPTIMAL CONSUMPTION

•

COMPARATIVE STATICS

•

• The endowment economy

(6)

Two period economy: private sector The endowment economy

At the end of period 2 all debts owed or owing must be paid off

2

(1

1

)

1 2 2 2

0 b   r b  Q   T C 

1

(1

0

)

0 1 1 1

b   r b  Q T   C

2 2 2

1 0 0 1 1

1 he present value of 1

assets

Present value of Present value of

household present and future

consumption disposable income

Household' life

(1 )

(1 ) (1 )

T inherited

C Q T

C r b Q T

r r

      

   

 

time wealth ( )

  

The two-period budget constraint of the private sector equals: 1/(1 + r) is the relative price of future consumption

• When a household borrows, it gets the right to purchase some quantity of consumption at present in return for repayment of some larger

quantity in the future.

Budget constraints

(7)

Graphical illustration The endowment economy

Endowments are points, wealth is a segment

2

1 1

(1

1

) C C

 r  



C

₁

C

₂

0 slope =-(1+r

₁

)

Endowment point



₁

E

 1  r b

0



0

 Q

1

 T

1

Q

₂

 T

₂

 

² ²

1 0 0 1 1

1

1 1

Q T r b Q T

r

      



Budget constraint

Lifetime wealth

Budget constraints

(8)

Two period economy: government sector The endowment economy

At the end of period 2 all debts owed or owing must be paid off

The two-period budget constraint of the government sector equals:

1

(1

0

)

0 1 1

d   r d  G T 

2

(1

1

)

1 2 2

0 d   r d  G   T

2 2

1 1 0 0

1 1 he present value of

initial debt Present value of Present value of

present and future government

taxes expenditures

(1 )

1 (1 )

T

T G

T G r d

r r

    

  

 

Budget constraints

(9)

Two period economy: the economy budget constraint The endowment economy

At the end of period 2 all debts owed or owing must be paid off

The two-period budget constraint of the

economy equals:

* * *

1

(1

0

)

0 1

b   r b  TB

2 *

1 * 0 0

1 he present value of inherited NIIP Present value of

present and future taxes

(1 ) 0

1

T

TB TB r b

 r   

 



* * *

2

(1

1

)

1 2

0 b   r b  TB  Or, in alternative:

* * 2 2

0 0 1 * 1 *

1 1

he present value of

NIIP Present value of Present value of present and future present and future GDP Absorption (national expenditure)

(1 )

(1 ) (1 )

T inherited

Q A

r b Q A

r r

    

 



 

Budget constraints

 

t t t t t t

TB  Q  C G   Q  A

(10)

•

OPTIMAL CONSUMPTION

•

COMPARATIVE STATICS

•

• The endowment economy

(11)

The first order conditions imply the equality between the MRS and the relative price The household maximizes his life-time

utility function

Subject to the budget constraint

(Note that all terms inside omega are exogenous)

Consumer problem

Optimal Consumption

The endowment economy

U  u C  

₁

^ ^{u C}  

²

1 r

2

1 1

1

C C

 r  



    

¹



1 2

' 1 1

'

u C r

u C  r  

(Euler equation)

(12)

When the instantaneous utility function is logarithmic

The Euler equation simplifies to:

Consumption will be increasing

(decreasing) over time if the interest rate is greater (smaller) than the rate of time preference

Consumer problem

Optimal Consumption

   

2 1

ln ln

1 U C C

  r



Solving together the Euler equation and the budget constraint, we get

Replacing the exogenous omega:

C

₁

 1 r 2  r ^

¹

 

² ²

1 0 0 1 1

1

1 1

2 1

Q T

C r b Q T

r r

r

  

           

2 1

1

1 1

C r

 



(13)

Graphical illustration

Optimal Consumption

Borrowing and repayment:

E

 ¹ ^ ^r

¹



Optimal consumption when the indifference curve is tangent to the budget constraint



0



0

1 1

1 r b Q T

 

 

2 2

Q  T

In this case, the household : (i) Borrows from the future

(ii) To increase consumption today

C 

2

C

2

C

1

C 

1

(i) C

(ii)

Income expansion path (Euler)

(14)

Borrowing Constraints

Optimal Consumption

Shadow interest rate (MRS)

C2

 1  r

1



 1  r

1



     

2 2 2

1

1 0 0 1 1

1 1 1

1 C Q T

r C r r r b ^ Q T

    

  

C1

With credit constraint, the choice set is reduced

 1  r b

0



0

 Q

1

 T

1

2 2

Q  T E

•

Consumption smoothing requires well-functioning financial markets to allow agents to borrow and lend across periods.

•

Although individuals may form expectations about their future

disposable incomes in a systematic way, liquidity constraint

may prevent them from acting on these expectations.

(15)

•

OPTIMAL CONSUMPTION

•

COMPARATIVE STATICS

•

• The endowment economy

(16)

Changes in the interest rate

Consumption and the interest rate

The intertemporal budget constraint is different from conventional, in that the price (interest rate) is both on the left-hand side and on the right-hand side

 

2 2 2

1 0 0 1 1

1 1

1 1 1

C Q T

C r b Q T

r r

      

 

2

1 1 1

1

C C r

r

 



       

Three potentially opposing effects on C1

• Conventional:

• Substitution effect: C2 relatively cheaper

• Income effect: positive because C2 is cheaper

• With logarithmic utility these two effects cancel out

• Wealth effect: The value of life-time wealt declines: if Q2>0, C1 falls!



When the interest rate increases, lifetime wealth falls

What happens when the interest rate increases?

(17)

Effect of an increase in the interest rate The endowment economy

 

C1

E E

A A

C

 ´

_C1

C2 C2

Borrowers are made poorer: the positive income effect is offset

by the negative wealth effect

Lenders are made richer: ifthe elasticity of substitution is less than one, the positive income

effect may be offset by the negative wealth effect

Along this course, we assume that C1 responds negatively to an increase in the interest rate

Consumption and the interest

rate

(18)

•

OPTIMAL CONSUMPTION

•

COMPARATIVE STATICS

•

• The endowment economy

(19)

The household maximizes his life-time utility function

Subject to the budget constraint

The solution to this problem is:

Revisit Consumer problem

Optimal consumption

   

2 1

ln ln

1 U C C

  r



2

1 1

1

C C

 r  



C

₁

 1 r 2  r ^

¹

• All terms inside omega are exogenous in respect to the consumer decision

• What matters for consumption is the current value of lifetime wealth, omega.

• Whether the value of omega

corresponds to income today or in the future it does not matter

 

² ²

1 0 0 1 1

1

1 1

Q T r b Q T

r

      



(20)

Private sector’ s wealth and government debt The endowment economy

Households’ lifetime wealth

As long as the government respects its budget constraint, its spending will be paid for by taxes, now or in the future.

If the private sector fully internalizes the public sector budget constraint :

•

Government bonds are not private wealth:

households buy bonds today to hedge future taxation

•

The pattern of taxation over time has no effect on private wealth

• Consumption does not depend on the timing of taxation

•

Consumption is however affected by government expenditures (omega affected)

 

² ²

1 0 0 1 1

1

1 1

Q T r b Q T

r

      



2 2

1 1 0 0

1 1

(1 )

1 (1 )

T G

T G r d

r r

    

 



^*



^* ² ²

1 0 0 1 1

1

1 1

Q G r b Q G

r

      



The Ricardian Equivalence

(21)

•

OPTIMAL CONSUMPTION

•

COMPARATIVE STATICS

•

• The endowment economy

(22)

The macroeconomic equilibrium will depend on whether the economy is open or closed :

•

Open economy:

•

Closed Economy (autarky interest rate endogenous)

eventually Private consumption

National expenditure

National income

Expenditure, income, and the current account

Macroeconomic equilibrium



^*



^* ² ²

1 0 0 1 1

1

1 1

2 1

Q G

C r b Q G

r r

r

  

           



^*



1 1 1

; ,

1 2

, ,

1 2

, ,

0 1

A  C r Q Q G G r b  G



^*



1 1 1 1

,...

CA   Y A r

*

1 0 0 1

Y  r b  Q

 

1 1 1^a

,...

Y  A r

*

0

0 b 

(23)

1  r

1

1 1 1

CA   Y A

1  r

1

Y

1

Q

1

1 1 1

A  C  G 1  r

1^a

Macroeconomic equilibrium

The endowment economy Numerical example:

*

0 1 2

0 b   r G  G 

1

100 Q 

2

80 Q 

“Dark future”

1 1

1

1 80

2 100 1

C A

r

 

       

1

50 40 CA 1

  r



The macroeconomic equilibrium will

depend on whether the economy is

open or closed

(24)

Numerical example:

Macroeconomic equilibrium

1  r

1

CA

1

1  r

1

Y

1

1.25 Q

1

1 1

A  C

*

1  r

1

18 CA 

open economy •

the interest rate is exogenous, the current account is endogenous

1

50 40 82 C 1

  r 



1

50 40 18 CA 1

  r 



*

1   r

1

1.25 82 100

  ^ ^

* *

2 1

1

1 2

18 1.25 80 102.5 C  b  r  Q   

 

* *

2 1 1 2

18 0.25 80 84.5 Y  b r  Q   

•

Future:

2 2 2

84.5 102.5 18 S   Y C    

 

* * * *

2 2 1 1 2 2 1 1

18 CA  TB  r b  Q  C  r b  

(25)

Macroeconomic equilibrium

1  r

1

CA

1

1  r

1

Y

1

1 1 1

A  C  G

closed economy •

Closed Economy: the current account must be zero, the interest rate is endogenous

1  r

1^a

Autarky interest rate:

1

1 40 0.8

50 r

a

  

0.8

1

50 40 0

1

^a

CA   r 



Example: two agents

1^A

60 Q 

2^A

40 Q 

1^B 40 Q 

1

1 40

60 55

2 0.8

CA     

1

1 40

40 45

2 0.8

CB    

1Â 1Â 1Â 5

S Q C 

1^B 1^B 1^B 5

S Q C  

(26)

•

OPTIMAL CONSUMPTION

•

COMPARATIVE STATICS

•

BEYOUND THE TWO-PERIOD MODEL THE ENDOWMENT ECONOMY

AGENDA

(27)

Temporary increase in output

1  r

1

CA

1

1  r

1

Y

1

*

1  r

1

1 1 1

A  C  G

• Assume CA=0 before the shock

 (closed=open)

*

1  r

1

Q

1

Experiment 1

1 0

 Q THE ENDOWMENT ECONOMY

Comparative statics

(28)

CA

1

1 1 1

A  C  G

1

0 CA 

 (closed=open)

• Temporary shock (open economy):

• At a constant interest rate

1

0 CA 

C

₁

Q

₁

 1 r 2  r ^< ¹

1 1

1 1 0

2 CA

Q

r r

 

  

 

open economy

*

1  r

1

Q

1

1  r

1

*

1  r

1

Temporary increase in output

Experiment 1

THE ENDOWMENT ECONOMY

1 0

 Q

1  r

1

Y

1

Comparative statics

(29)

CA

1

1  r

1^a

1 1 1

A  C  G 1  r

1^a

'

• Temporary shock (closed economy):

• The autarky interest rate must fall to induce an expansion of current

consumption equal to the increase in output.

Q

1

1  r

1

Temporary increase in output  Q₁ 0

Experiment 1

closed economy

1  r

1

Y

1

Comparative statics

(30)

CA

1

* *

1 1 o 0

Y  Q  r b

1 1 1

A  C  G

*

1  r

1

2 0

Q 

 (closed=open)

Q

1

Anticipated (future) output expansion

Experiment 2

1  r

1

*

1  r

1

1  r

1₁

1  r

Comparative statics

(31)

CA

1

1 1 1

A  C  G

*

1  r

1

0 CA <

1

0 CA <

• Private wealth increases

• At a constant interest rate (open economy):

1

*

2 1

1 1

2 1 0 C

Q r

r r

   

  

1

*

2 1

1 1 0

2 1

CA

Q r

r r

 

  <

  

Q

1

1  r

1

*

1  r

1

2 0

Q 

Experiment 2

open economy

* *

1 1 o 0

Y  Q  r b 1  r

₁

Comparative statics

(32)

CA

1

1  r

1^a

1 1 1

A  C  G

*

1  r

1

The autarky interest rate must increase to prevent consumers from expanding current consumption, ahead of future income.

1  r

1^a

'

Q

1

closed economy

Experiment 2

2 0

Q 

1  r

1 ^{* *}

1 1 o 0

Y  Q  r b 1  r

₁

Comparative statics

(33)

1 1 1

A  C  G

1 2 0

Q Q Q

     

Q

1

Permanent output expansion

Experiment 3

1  r

1

*

1  r

1

Y

1

*

r

1

r 

Comparative statics

(34)

Y

1

1 1 1

A  C  G

*

1 1

*

1 1

2 1 1 0

2 1

CA r

Q r

r r

 

  

    

    

*

1 1

*

2 1

1 2

2 1 1

C r

Q r

r r

    

  

In case

• Impact on consumption (1:1)

• No need to smooth borrowing or lending abroad

*

r

1

r 

*

r

1

r 

Q

1

1 2 0

Q Q Q

      Permanent output expansion

Experiment 3

1  r

1

*

1  r

1

open economy

Comparative statics

(35)

1  r

1^a

1 1 1

A  C  G

• At a constant interest rate • The autarky interest rate may change, depending on the time profile of government

expenditures

   

2 2 2

1

1 1 1

1

^a

C 1 Q G 1

r C r Q G ^ r

    



Q

1

1  r

1

1 2 0

Q Q Q

      Permanent output expansion

Experiment 3

closed economy

Y

1

Comparative statics

(36)

1  r

1

CA

1

Y

1

1 1 1

A  C  G

*

1  r

1

 (closed=open)

1 0

 G

Q

1

Temporary fiscal expansion

Experiment 4

1  r

1

*

1  r

1

Comparative statics

(37)

CA

1

1 1 1

A  C  G

*

1  r

1

0 CA <

 (closed=open)

1 1

1 1 0

2 CA A

G G

r r

  

     <

  

1

0 CA <

C

₁

G

₁

  1 r 2  r ^< ⁰

Q

1

1 0

 G Temporary fiscal expansion

Experiment 4

open economy

1  r

1

*

1  r

1

1  r

1

Y

1

Comparative statics

(38)

1  r

1

Y

1

CA

1

1  r

1^a

1 1 1

A  C  G

• The increase in government spending cannot be matched by imports

• Private consumption must be completely crowded out

• The autarky interest rate must rise to induce the fall in current consumption

• Rationale: savings decline in the market for loanable funds

1  r

1^a

'

Q

1

1  r

1

1 0

 G Temporary fiscal expansion

Experiment 4

closed economy

Comparative statics

(39)

1  r

1

Y

1

1  r

1

*

1  r

1

1 1 1

A  C  G

*

1  r

1

0 CA <

1

0 CA <

*

0 0

 b



^*



1

* 0 0

1 1 0

2 C r

b

r r

 

  







⁰^*



1

* 0

1 0

2 CA r

b

r r

  

  <



1

 Q

CA

1

Increase in NIIP:

Experiment 5

open economy

Comparative statics

1 *

* 0 0

Y 0 b r

  



(40)

CA

1

1 1 1

A  C  G

1

0 CA 

• Temporary TOT shock

• Same as a temporary output shock

• Increase in consumption today

• Improvement in the Current Account

• The positive relationship between terms of trade, savings and the Current Account is known as the Harberger-Laursen-Metzler effect

1

0 CA 

*

1  r

1

Q

1

1  r

1

*

1  r

1

Terms of trade improvement

Experiment 6

1

0  TT  1  r

1

Y

1

Comparative statics

 

* * 2 2 2

1 0 0 1 1 1 *

1

1 1

TT Q G b r TT Q G

r

      



Q C

TT  P P

open economy

(41)

•

OPTIMAL CONSUMPTION

•

COMPARATIVE STATICS

•

• The endowment economy

(42)

Macroeconomic equilibrium

CA

₁

S

₁

*

CA

1

1  r

1

1 r

₁^a _A

*

1  r

1

1^A

0 CA < CA

₁^B

 0

*

1  r

1

• The world interest rate is the one that clears the world market for loanable funds

(World=closed economy)

• The small open economy is negligible: it takes the interest rate as given.

• In the figure, at the world interest rate, the home economy is running a deficit.

• Note that the autarky interest rate is above the international interest rate.

• This reflects scarcity of loanable funds at home

Small open economy and the world interest rate

(43)

• In the figure, the world interest rate is increasing, reflecting for instance, an increase in r(impatience).

• The increase in the world interest rate caused the home economy (left panel) to move from a CA deficit into a

surplus

• Note that the world interest rate jumped ahead of the autarky interest

Macroeconomic equilibrium

CA

₁

S

₁

*

CA

1

1  r

1

1  r

₁^a

A A

B

*

1  r

1

B

1^A

0 CA < CA

₁^B

 0

*

1  r

1

• When the world interest rate increases Experiment 1

Small open economy and the world interest rate

(44)

Sudden Stop

On occasion, capital flows can suddenly stop, meaning that those who wish to borrow anew or roll over an existing loan will be unable to obtain financing.

These capital market shutdowns occur much more frequently in emerging markets.

• financial account surplus rapidly shrinks,

• requiring a decrease in current account deficit,

• requiring a sudden cut in expenditures (GNE) relative to production (GDP).

Macroeconomic equilibrium

(45)

Sudden stop

Macroeconomic equilibrium

1  r

1

CA

1

1  r

1

Y

1

*

1  r

1

1 1 1

A  C  G

*

1  r

1

1  r

1

A Sudden Stop materializes as a decline in the amount a country can borrow abroad.

The current account is forced to shrink, to meet that amount.

In this case, the domestic interest rate increases above the international interest rate, reflecting the scarcity of loanable funds in the home economy.

Q

1

_CA

₁

_< ₀

1

0 CA <

Experiment 2

(46)

Capital flow reversal

Macroeconomic equilibrium

1  r

1

CA

1

1  r

1

Y

1

*

1  r

1

1 1 1

A  C  G

*

1  r

1

1  r

1

In a more extreme case where the country

is forced to pay back existing debt (say, short term debt maturing at the time of the capital flow), the CA is forced to a positive level, and the domestic interest rate (or the shadow cost of borrowing) increases even further

Q

1

0 CA 

1

0 CA 

Experiment 2

(47)

Macroeconomic equilibrium

1^L

0 CA <

1

CA

RW

1  r

1

*

1

0 CA 

1^L 1^RW

0 CA  CA 

1

CA

L

1  r

1

*

1  r

1

• The World interest rate must be such that the deficit in the large home economy (L) matches the surplus in the rest of the world Large economy

• The world interest rate is the one that clears the world market for loanable funds

• The large economy influences the world interest rate.

(48)

• Suppose that the home (L) economy is hit by a temporary output expansion

• The CA schedule shifts to the right Large economy:

Macroeconomic equilibrium

1^L

0 CA <

1  r

1

*

1

0 CA 

1

CA

L

1  r

1

Temporary output expansion in L.

*

1  r

1

1^L 1^RW

0 CA  CA 

1

CA

RW

Experiment 3

(49)

• Suppose that the home (L) economy is hit by a temporary output expansion

• The CA schedule shifts to the right

• At a constant interest rate, the CA deficit will decrease, causing an excess supply of loanable funds in the world economy

• The world interest rate must fall to clear the market for loanable funds.

Large economy:

Macroeconomic equilibrium

1^L

0 CA <

1  r

1

*

1  r

1

*

1

0 CA 

1

CA

L

1  r

1

*

1  r

1

'

1^L 1^RW

0 CA  CA 

1

CA

RW

Experiment 3

Temporary output expansion in L.

(50)

•

OPTIMAL CONSUMPTION

•

COMPARATIVE STATICS

•

BEYOUND THE TWO-PERIOD MODEL THE ENDOWMENT ECONOMY

AGENDA

(51)

Private sector’ s wealth and government debt The endowment economy

Households’ lifetime wealth

As long as the government respects its budget constraint, its spending will be paid for by taxes, now or in the future.

If the private sector fully internalizes the public sector budget constraint :

•

Government bonds are not private wealth:

households buy bonds today to hedge future taxation

•

The pattern of taxation over time has no effect on private wealth

• Consumption does not depend on the timing of taxation

•

Consumption is however affected by government expenditures (omega affected)

 

² ²

1 0 0 1 1

1

1 1

Q T r b Q T

r

      



2 2

1 1 0 0

1 1

(1 )

1 (1 )

T G

T G r d

r r

    

 



^*



^* ² ²

1 0 0 1 1 *

1

1 1

Q G r b Q G

r

      



The Ricardian Equivalence

(52)

Change in the timing of taxation The endowment economy

All else equal, if the government decreases taxes today, government debt will increase

Since this debt must be repaid in period 2, taxes must increase in period 2:

All in all, the government shifted taxes to the future, without altering the current value of total revenues (that must equal the current value of expenditures)

•

Changing the profile of taxation had no impact on the private sector lifetime wealth:

The Ricardian Equivalence

1 2

1

1 0 T T

r

   



1

0  < T

1 1

0 d T

   

   

2 1

1

1 1

1

T d r T r

      

 

² ²

1 0 0 1 1

1

1 1

Q T r b Q T

r

      



1 1 2

1

1 0 T T

r

     



(53)

Since private consumption does not change, national savings are not impacted

However, the tax cut today impacts positively on the private sector disposable income. Since consumption does not change, this means that private savings must increase:

This will match the fall in government savings:

The Ricardian Equivalence

1 0 0 1 1 1

S

P

 r b  Q   T C

1 1 1 0 0

S

G

  T G  r d

 

1

*

1 1 0 0 1 1

Y

S  Q   r b   C  G

Change in the timing of taxation

1^P 1

0 S T

   

1

0  < T

1^G 1

0 S T

   <

In sum:

• A fall in government saving caused by temporary

tax cut is fully offset by a contemporaneous rise in private saving.

•

In effect, the private sector will save buying the

government bonds that the government is selling.

(54)

In the real life, there are many reasons why the Ricardian equivalence fails.

In what follows, we focus on three cases.

The Ricardian Equivalence will not hold exactly when:

(i) lump sum taxes are not available;

(ii) the private sector faces borrowing constraints or higher interest rates than the government sector;

(iii) households have shorter horizons than governments.

Failure of Ricardian equivalence

(55)

Failure of Ricardian equivalence

(56)

Assume that the Government subsidizes rises a consumption tax taxes today to finance a subsidy on consumption expenditures next year.

Also assume that

Since the government meets its budget constraint

…the timing of taxation does not affect private wealth.

Still, taxes now affect the relative price of consumption today versus future.

*

1 2 0

0 G  G  b 

C₁

 

1

t

₁ ^^C²



^1

^t

²



1r₁ Q₁ Q₂ 1r₁

t

₁

C

₁

 t

₂

C

₂

1 r  0

Distortionary taxation

Failure of Ricardian equivalence

The Euler equation is:

Substituting in the budget constraint, we see that current consumption depends on the tax rate.

C₁  1

r

2

r



 

 1 1

t

₁^¹

 

²



1



¹

1 2

1 1 1

1 C r

C r t

t

   



(57)

1  r

1

CA

1

1  r

1

Y

1

*

1  r

1

,

1

Y A

1 1 1

A  C  G

*

1  r

1

0 CA <

• Now consider a tax cut today to be financed by an increase in the tax rate tomorrow.

• In the open economy, private consumption increases, and a CA deficit emerges.

• In the closed economy, the interest rate must increase to offset the higher desire for consumption today.

1

0 CA <

'

1  r

1^a

C

₁

 1 r 2  r



  

  1 1 t

₁

^

¹

1

0 t

 <

Tax Cut under distortionary taxation THE ENDOWMENT ECONOMY

Failure of Ricardian equivalence

(58)

Failure of Ricardian equivalence

(59)

C2

E

• Households often face restriction in the

access to credit markets.

• A tax cut today offset with more taxes tomorrow will impact one-to-one on current consumption of constrained (Hand- to-mouht) households.

1

0  < T

Tax cut open economy

Borrowing constraints

Failure of Ricardian equivalence

2 2 2

C  Q  T

 1  r

1



1 1 1

C1

C  Q T 

(60)

Assume that some fraction lof households in our economy are constrained on borrowing, while the remaining fraction 1-lis borrowing normally.

Also assume that

Aggregate consumption will be:

*

1 2 0

0 G  G  b 

   

²

1 1 1 1 *

1

1 1

2 1

C Q T Q Q

r

l l r

r

 

  

           Heterogeneous agents

Failure of Ricardian equivalence

(61)

Also assume that

*

1 2 0

0 G  G  b 

   

²

1 1 1 1 *

1

1 1

2 1

C Q T Q Q

r

l l r

r

 

  

Failure of Ricardian equivalence

1 1 1

CA  Q C 

1

0  < T

Tax cut

Tax cut:

• Private consumption increases, in the proportion of constrained households, giving rise to CA<0.

• Private saving increase in the proportion of Ricardian households

• The share of government debt that is not financed by Ricardian consumers is financed by foreigners open economy

1 1

0 C T l

     CA

₁

  T

₁

l < 0

(62)

Also assume that

*

1 2 0

0 G  G  b 

   

²

1 1 1 1 *

1

1 1

2 1

C Q T Q Q

r

l l r

r

 

  

Failure of Ricardian equivalence

1 1 1

CA  Q C 

1

0  < T

Tax cut

• In the closed economy, national expenditure cannot increase. Hence the interest rate must rise.

• The rise in the interest rate induces Ricardian consumers to save more to buy the government bonds and finance the policy.

• Consumption of Ricardian households is crowded out by the increase in the consumption of non- ricardians.

closed economy

(63)

Failure of Ricardian equivalence

(64)

• Governments are infinitely lived, while households are not.

• In the real world, it may be that governments engage in debt finance for long period of time, before rising taxes in the distant future.

• In that case, the future tax increase will not be paid by current households that are to die before this day happens.

• These households will see the tax cut as a true increase in their lifetime wealth.

Failure of Ricardian equivalence

Heterogeneous agents

• Suppose that each household lives one period only, while the government lives two periods.

• If the government decreases taxes today – on the current generation - to be paid in the future – by the next generation, then the disposable income of current generation increases and so will do current consumption.

• If lis the fraction of households that are to die in the current period:

1 1

C T l

  

(65)

Heterogeneous agents The endowment economy

Failure of Ricardian Equivalence

1 1

C T l

  

•

Suppose that each household lives one period only, while the government lives two periods.

•

If the government decreases taxes today – on the current generation - to be paid in the future – by the next generation, then the disposable income of

current generation increases and so will do current consumption.

•

If l is the fraction of households that are to die in the current period:

•

Governments are infinitely lived, while households are not.

•

In the real world, it may be that governments engage in debt finance for long period of time, before rising taxes in the distant future.

•

In that case, the future tax increase will not be paid by current households that are to die before this day happens.

•

These households will see the tax cut as a true increase in

their lifetime wealth.