Natural Forecasting, Asset Pricing, and

Macroeconomic Dynamics

Andreas FusterDavid LaibsonBrock Mendel

Harvard UniversityMay 2010

Financial crises

Key ingredients (Kindleberger 1978)• Improving fundamentals • Rising asset prices• Rising leverage supporting consumption and

investment• Falling asset prices and deleveraging• Banking crisis• Recession/Depression

Financial crises

Key ingredients (Kindleberger 1978)• Improving fundamentals • Rising asset prices (“bubble”)• Rising leverage supporting consumption and

investment• Falling asset prices and deleveraging• Banking crisis• Recession/Depression

Bubbles

• Neo-classical economic view:– Non-rational bubbles don’t exist– Non-rational bubbles only appear to exist because of

hindsight bias (fundamentals sometimes unexpectedly deteriorate)

– Rational bubbles may exist in special circumstances (Tirole, 1985)

• Today:– bubbles are (at least partially) not rational– bubbles explain macro dynamics

The Japanese Bubble

7

Dot com bubble Lamont and Thaler (2003)

• March 2000• 3Com owns 95% of Palm and lots of other net

assets, but...• Palm has higher market capitalization than

3Com

$Palm > $3Com = $Palm + $Other Net Assets

8

-$63 = (Share price of 3Com) - (1.5)*(Share price of Palm)

Four classes of explanations for the most recent crisis:

• Savings glut (e.g., Bernanke 2003)– But see Laibson and Mollerstrom (2010): worldwide savings did not rise

• Rational bubbles (e.g., Caballero et al 2006)• Agency problems– But see Connor, Flavin, and O’Kelly 2010: Ireland did not have exotic

mortgages and CMO’s

• Non-rational bubbles

Housing prices and trade deficits

Turkey

Japan

Germany

Laibson and Mollerstrom, 2010

Four classes of explanations for the most recent crisis:

• Savings glut (e.g., Bernanke 2003)– But see Laibson and Mollerstrom (2010): worldwide savings did not rise

• Rational bubbles (e.g., Caballero et al 2006)• Agency problems– But see Connor, Flavin, and O’Kelly 2010: Ireland did not have exotic

mortgages and CMO’s

• Non-rational bubbles

Lehman’s forecasts in 2005HPA = House Price Appreciation

Source: Gerardi et al (BPEA, 2008)

Alan Greenspan• “While local economies may experience significant

speculative price imbalances, a national severe price distortion seems most unlikely in the United States, given its size and diversity.” (October, 2004)

• If home prices do decline, that “likely would not have substantial macroeconomic implications.” (June, 2005)

• Though housing prices are likely to be lower than the year before, “I think the worst of this may well be over.” (October, 2006)

Four classes of explanations for the most recent crisis:

• Savings glut (e.g., Bernanke 2003)– But see Laibson and Mollerstrom (2010): worldwide savings did not rise

• Rational bubbles (e.g., Caballero et al 2006)• Agency problems– But see Connor, Flavin, and O’Kelly 2010: Ireland did not have exotic

mortgages and CMO’s

• Non-rational bubbles

Bubbles form: 1995-2007

• I’ll focus on the US• Related bubbles existed in many other countries• The US bubble had two main components: – Prices of publicly traded companies– Prices of residential real estate

• And many minor contributors:– Prices of private equity– Commodities– Hedge funds

Fundamental Catalysts: 1990’s

• End of the cold war• Deregulation• High productivity growth• Weak labor unions• Low energy prices ($11 per barrel avg. in 1998)• IT revolution• Low nominal and real interest rates• Congestion and supply restrictions in coastal

cities

P/E ratio: Cambell and Shiller (1998a,b)Real index value divided by 10-year average of real earnings

Jan 1881 to April 2010

Dec1920

Sept1929

July1982

Jan1966

Dec 1999

Average: 16.34Source: Robert Shiller

Real Estate in Phoenix and Las VegasJan 1987 – January 2010

Long-run horizontal supply curve

Phoenix

Long-run horizontal supply curve

Phoenix

Long-run horizontal supply curve

8 miles

Demand

BubbleDemand

Long-run horizontal supply curve

LR Supply

SR Supply

Arbitrage: Buy your house now for $400,000 or in 3 years at $300,000

Price

Quantity

Demand

BubbleDemand

“Over-shooting”

LR Supply

SR Supply

Arbitrage: Buy your house now for $400,000 or in 3 years at $200,000

Price

Quantity

DWL

S&P 500 Case-Shiller IndexJanuary 1987-January 2010

226.7

April2006

January1987

January2010

May2009

January2000

Housing Prices

Source: Robert Shiller

Household net worth divided by GDP

1952 Q1 – 2008 Q4

Source: Flow of Funds, Federal Reserve Board ; GDP, BEA.

Today

• A formal model of non-rational bubbles• Microfoundations• Testable predictions• Goal: Study non-rational expectations with a

parsimonious and generalizable model.

Outline

1. Two building blocks– Natural forecasting– Hump-shaped impulse response

2. Tree model3. Simulations, predictions, empirical evaluation4. Counterfactuals5. Extensions

Related Literature• Barberis, Shleifer, and Vishny (1998): extrapolative dividend forecasts• Barsky and De Long (1993): extrapolation and excess volatility• Benartzi (2001): extrapolation and company stock• Black (1986): noise traders• Campbell and Shiller (1988a,b): P/E ratio and return predictability• Choi (2006): extrapolation and asset pricing• Choi, Laibson, and Madrian (2009): positive feedback in investment• Cutler, Poterba, and Summers (1991): return autocorrelations• De Long, et al (1990): noise traders and positive feedback• Hong and Stein (1999): forecasting biases• Keynes (1936): animal spirits• LaPorta (1996): Growth expectations have insufficient mean reversion• Leroy and Porter (1981): excess volatility in stock prices• Lettau and Ludvigson (1991): W/C correlates negatively with future returns• Lo and MacKinlay (1988): variance ratio tests • Loewenstein, O’Donoghue, and Rabin (2003): projection bias• Piazessi and Schneider (2009): extrapolative beliefs in the housing market• Previterro (2001): extrapolative beliefs and annuity investment• Shiller (1981): excess volatility in stock prices• Summers (1986): power problems in financial econometrics• Tortorice (2010): extrapolative beliefs in unemployment forecasts

(a) Natural forecasting bias

1

11

1

1

N

N 1 EEt t

t t

t

t

tt t

x

x x

x

x

E[] repres

N[] represe

ents the be

nts the natural foreca

havioral forecasting o

E[] represents the rational fo

is calculated

sting operator

from historic

recast

al dat

ing operator

a (best fit)

perat

i a

or

s

"free" parameter

Model nests rational expectations: =0

is an index of imperfect rationality

Natural forecasting

1 1

11 1

N

N

t t t

t t t

x x

x x

• Natural forecasting requires minimal memory• Natural forecasting has no free parameters• Natural forecasting nests:o random walk:o frictionless momentum on a surface:

0 1

(b) True data generating process with hump-shaped impulse response

Impulse response functions

Hump-shaped impulse response

1

1

( ) ( )

( ) ( )

( ) ( ) ( )

0 for

0 for 1

t t

t t

i

i

A L x B L

x A L B L

A L B L L

i I

i I

ARIMA(p,1,q)

ARIMA(0,1,Q)

Ln(Real GDP)Four-year horizon (quarterly data)

ARIMA(1,1,0)

ARIMA(0,1,12)

ARIMA(0,1,8)

ARIMA(0,1,4)

Unemployment Four-year horizon (quarterly data)

ARIMA(1,1,0)

ARIMA(0,1,12)

ARIMA(0,1,8)

ARIMA(0,1,4)

Ln(Real earnings) Four-year horizon (quarterly data)

ARIMA(1,1,0)

ARIMA(0,1,12)

ARIMA(0,1,8)

ARIMA(0,1,4)

Ln(S&P Gross Return) Four-year horizon (monthly data)

ARIMA(1,1,0)

ARIMA(0,1,12)ARIMA(0,1,8)

ARIMA(0,1,4)

Interacting Natural Forecasting and Hump-Shaped Impulse Responses

1 2

1

2 1 1

2 1

t t t t

t t t

x x x

x x

Data generating process

Natural forecasting model

Best fit value for φ

Impulse response functions: 1 year

θ = 1θ = 0.75θ = 0.5θ = 0.25θ = 0

1.45 0.5 0.475

Impulse response functions: 4 years

θ = 1

θ = 0.75

θ = 0.5

θ = 0.25

θ = 0

1.45 0.5 0.475

2. Illustrative Model

• Equity tree, with dividends:

• Labor tree (non-stochastic): yt• Quadratic preferences• Study limit in which curvature → 0

o but do not pass to the limit• Discount factor δ

1 2t t t td d d

Model continued

• Elastic supply of foreign capital with gross return R.

• Assume that δR=1.• Assume foreign agents don’t hold domestic capital– Home bias– Moral hazard– Adverse selection– Expropriation risk

• Natural forecasting with weighting parameter θ

1t t t t tB c RB d y

Consumption function

0 0

1 1 1

11

1

t s t stt ts s

s s

t s t s t st t ts s s

s s s

yc E R

d

d d d

BR R R

E N ER R R

Natural forecasting asset pricing

11

2

1

11 1 1 1

1 1

2 1

t s tt t ts

s

d R Rdd

N dR R

R R

Rational expectations asset pricing2

1

2

2

2 11

1 2

1 12

1 2

1 2

1 21 1 1

4

2

4

2

1

t st

t

t t

tt

t t

s

t

s

r r

R RA Br rR RR R

r

r

y r yA r

r r

r y yB r

r r

dE

Calibration1.015 ( quarterly return on risky capital)

1.45 ( estimate from NIPA data)

0.5 ( estimate from NIPA data)

0.035 (set to generate standard deviation of equity returns)

0.33 ( capit

R

y

al income share)

0.5 (free parameter)

Data and Simulations (N=5000)

τ Data Sim Data Sim Data Sim Data Sim

1 -0.03 0.00 0.09 0.01 -0.12 -0.14 -0.07 -0.14

2 0.01 -0.01 -0.06 -0.01 -0.13 -0.15 -0.12 -0.16

3 -0.08 -0.04 -0.04 -0.02 -0.14 -0.14 -0.15 -0.14

4 -0.21 -0.07 -0.03 -0.06 -0.14 -0.13 -0.18 -0.13

5 -0.05 -0.05 -0.06 -0.05 -0.13 -0.12 -0.22 -0.14

6 -0.01 -0.03 -0.06 -0.05 -0.11 -0.12 -0.23 -0.12

7 -0.13 -0.03 -0.13 -0.06 -0.10 -0.11 -0.25 -0.11

8 -0.12 -0.04 0.01 -0.03 -0.08 -0.10 -0.27 -0.10

9 -0.07 -0.04 0.01 -0.03 -0.08 -0.08 -0.24 -0.11

10 0.07 0.00 0.04 -0.03 -0.07 -0.07 -0.23 -0.11

( ln , )t tC R ( , )t tR R

,tt

t

WR

C

, lntt

t

WC

C

τ Data Sim1 -0.03 0.002 0.01 -0.013 -0.08 -0.044 -0.21 -0.075 -0.05 -0.056 -0.01 -0.037 -0.13 -0.038 -0.12 -0.049 -0.07 -0.04

10 0.07 0.00

( ln , )t tC R

τ Data Sim1 0.09 0.012 -0.06 -0.013 -0.04 -0.024 -0.03 -0.065 -0.06 -0.056 -0.06 -0.057 -0.13 -0.068 0.01 -0.039 0.01 -0.03

10 0.04 -0.03

( , )t tR R

τ Data Sim1 -0.12 -0.142 -0.13 -0.153 -0.14 -0.144 -0.14 -0.135 -0.13 -0.126 -0.11 -0.127 -0.10 -0.118 -0.08 -0.109 -0.08 -0.08

10 -0.07 -0.07

,tt

t

WR

C

τ Data Sim1 -0.07 -0.142 -0.12 -0.163 -0.15 -0.144 -0.18 -0.135 -0.22 -0.146 -0.23 -0.127 -0.25 -0.118 -0.27 -0.109 -0.24 -0.11

10 -0.23 -0.11

, lntt

t

WC

C

Summary so far:• Improvement in fundamentals causes overreaction in

asset prices• Consumption also rises “too much”• Then asset prices and consumption tend to fall: agents

are disappointed by future realizations of fundamentals• Intertemporal dependencies are very weak: correlation

of 0.1 implies R2 of 0.01.• With 200 quarters of data, could not reject null

hypothesis of random walk in consumption and iid asset returns.

• Prior dominates inference (Summers 1986).

Counterfactuals

Suppose agents had rational expectations (θ=0)? What would economy look like?

• Asset returns would be iid• Consumption would be a random walk• Standard deviation asset returns falls by 75%.• Standard deviation of ΔlnC falls by 75%.

Extensions

• Add a persistent component to dividends to better match true DGP (little changes)

• Add other sources of stochasticity (labor income)

• Add quantitatively meaningful risk aversion• Add a mechanism for delayed adjustment in

consumption (see next slide)

τ Data Sim1 -0.03 0.002 0.01 -0.013 -0.08 -0.044 -0.21 -0.075 -0.05 -0.056 -0.01 -0.037 -0.13 -0.038 -0.12 -0.049 -0.07 -0.04

10 0.07 0.00

( ln , )t tC R

-0.02-0.04-0.08-0.08-0.06-0.07-0.06-0.06-0.04-0.03

Sim Habit

τ Data Sim1 0.09 0.012 -0.06 -0.013 -0.04 -0.024 -0.03 -0.065 -0.06 -0.056 -0.06 -0.057 -0.13 -0.068 0.01 -0.039 0.01 -0.03

10 0.04 -0.03

( , )t tR R

τ Data Sim1 -0.12 -0.142 -0.13 -0.153 -0.14 -0.144 -0.14 -0.135 -0.13 -0.126 -0.11 -0.127 -0.10 -0.118 -0.08 -0.109 -0.08 -0.08

10 -0.07 -0.07

,tt

t

WR

C

-0.18-0.18-0.18-0.16-0.14-0.12-0.11-0.09-0.08-0.07

Sim Habit

τ Data Sim1 -0.07 -0.142 -0.12 -0.163 -0.15 -0.144 -0.18 -0.135 -0.22 -0.146 -0.23 -0.127 -0.25 -0.118 -0.27 -0.109 -0.24 -0.11

10 -0.23 -0.11

, lntt

t

WC

C

-0.02-0.18-0.23-0.25-0.25-0.24-0.21-0.21-0.20-0.18

Sim Habit

Conclusion• Parsimonious model of quasi-rational expectations• Portable to other settings• Generates testable predictions• Matches key moments– Autocorrelation of asset returns– Co-movement of wealth, asset returns and

consumption• Much work remains to be done!• Policy implications?• Comments and suggestions welcome