BOMBOLLES ESPECULATIVES

Jaume VenturaCREI, UPF & Barcelona GSE

Bojos per l’economia! Març 2014

AN ECONOMIC MODEL OF ASSET PRICES

Assumptions1. Time is a sequence of dates t=0,1,2,…,∞.2. There is a market with traders willing to borrow

and lend at the expected return of 1+r per period.

Question1. What is the price of an asset that delivers pay-

offs dt in date t?

2. Assume this asset is traded only in date 0.

...,, 321 ddd

What future payments does the asset promise?

What is the expected value of these future payments?

How much are traders willing to pay today for these future payments?

,...,...,, 21 nddd

,...,...,, 02010 ndEdEdE

,...)1(

,...,)1(

,1

022010

nn

rdE

rdE

rdE

MARKET EQUILIBRIUM!!!

Let xn be today’s value of payment at time n. Then,

.

.

.

101 )1( dErx rdEx

1

101

202 )1)(1( dErrx 2)1(20

2r

dEx

nn dErrrx 0)1)...(1)(1( nr

dEx nn

)1(0

How much are traders willing to pay today for these future payments?

How much are traders willing to pay today for the asset?

Thus, the price of the asset is

,...)1(

,...,)1(

,1

022010

nn

rdE

rdE

rdE

...)1(

...)1(1

022010

nn

rdE

rdE

rdE

1

00 )1(t

tt

rdEp

o Asset prices are high when expected payments are high and interest rates are low.

1

00 )1(t

tt

rdEp

MODIFYING OUR ECONOMIC MODEL OF ASSET PRICES

We have assumed so far that the asset is traded at time 0 only.

Assume from now on that the asset is traded in all periods.

Can the ability to resell the asset modify its value?

NEW MARKET EQUILIBRIUM!!!

Let pn be the price of the asset in date n. Then:

.

.

.

.

.Iterating forever…

1010)1( pEdErpo rpE

rdEp

111010

0

202010 )1( pEdErpE 220

22010

0 )1()1(1 rpE

rdE

rdEp

10100 )1( nnn pEdErpE nn

nn

rpE

rdE

rdE

rdEp

)1()1(...

)1(100

22010

0

1

000 )1(

lim)1(t

nn

ntt

rpE

rdEp

Asset prices have a fundamental and a bubble component.

The bubble component is a pyramid scheme.

Self-fulfilling expectations play a crucial role in asset price fluctuations.

1

000 )1(

lim)1(t

nn

ntt

rpE

rdEp

Fundamental Bubble

CALCULATING FUNDAMENTAL AND BUBBLE COMPONENTS

1. Measure the cash-flows that US productive assets generate as capital income, net of taxes and investment.

2. Compute the expected present discounted value of these cash-flows by assuming –

a. The interest rate is constant for all time horizons (equal to the 1950-2010 period average); and

b. Out-of-sample cash-flows grow at a constant rate (equal to the 1950-2010 period average), and resort to perfect foresight for within-sample cash-flows.

Household Savings

Firm Savings

Investment Growth

Household Savings

Firm Savings

Investment Growth

Credit!!!

Household Savings

Firm Savings

Investment Growth

Credit!!!

BACK TO THEORY (WITHOUT EQUATIONS!!) Two effects of bubbles on investments

1. An increase in the size of bubbles today absorbs credit and lowers investment – CROWDING-OUT EFFECT.

2. An increase in the size of bubbles tomorrow provides collateral and raises investment – CROWDING-IN EFFECT.

What effects dominates?1. If bubbles are not too large, the crowding-in effect

dominates and bubbles raise investment and growth.2. If bubbles become too large, the crowding-out effect

dominates and bubbles lower investment and growth.

SIMULATED ECONOMY WITHOUT PRODUCTIVITY SHOCKS AND POLICY

SIMULATED ECONOMY WITH PRODUCTIVITY SHOCKS AND WITHOUT POLICY

POLICY IMPLICATIONS FOR CENTRAL BANKS

The behavior of the economy depends on self-fulfilling expectations and the bubble is sometimes too small and sometimes too large.

Central Banks can manage bubbles by taxing credit when the bubble is too large and subsidizing credit when the bubble is too low.

This policy raises welfare and has no fiscal cost.

SIMULATED ECONOMY WITHOUT PRODUCTIVITY SHOCKS AND WITH POLICY

SIMULATED ECONOMY WITH PRODUCTIVITY SHOCKS AND POLICY

BOMBOLLES ESPECULATIVES

Jaume VenturaCREI, UPF & Barcelona GSE

Bojos per l’economia! Març 2014