natural forecasting, asset pricing, and macroeconomic dynamics andreas fuster david laibson brock...
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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