natural forecasting, asset pricing, and macroeconomic dynamics andreas fuster david laibson brock...
TRANSCRIPT
![Page 1: Natural Forecasting, Asset Pricing, and Macroeconomic Dynamics Andreas Fuster David Laibson Brock Mendel Harvard University May 2010](https://reader031.vdocument.in/reader031/viewer/2022012918/56649c425503460f948f134d/html5/thumbnails/1.jpg)
Natural Forecasting, Asset Pricing, and
Macroeconomic Dynamics
Andreas FusterDavid LaibsonBrock Mendel
Harvard UniversityMay 2010
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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
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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
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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
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The Japanese Bubble
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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
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8
-$63 = (Share price of 3Com) - (1.5)*(Share price of Palm)
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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
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Housing prices and trade deficits
Turkey
Japan
Germany
Laibson and Mollerstrom, 2010
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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
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Lehman’s forecasts in 2005HPA = House Price Appreciation
Source: Gerardi et al (BPEA, 2008)
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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)
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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
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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
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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
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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
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Real Estate in Phoenix and Las VegasJan 1987 – January 2010
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Long-run horizontal supply curve
Phoenix
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Long-run horizontal supply curve
Phoenix
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Long-run horizontal supply curve
8 miles
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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
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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
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S&P 500 Case-Shiller IndexJanuary 1987-January 2010
226.7
April2006
January1987
January2010
May2009
January2000
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Housing Prices
Source: Robert Shiller
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Household net worth divided by GDP
1952 Q1 – 2008 Q4
Source: Flow of Funds, Federal Reserve Board ; GDP, BEA.
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Today
• A formal model of non-rational bubbles• Microfoundations• Testable predictions• Goal: Study non-rational expectations with a
parsimonious and generalizable model.
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Outline
1. Two building blocks– Natural forecasting– Hump-shaped impulse response
2. Tree model3. Simulations, predictions, empirical evaluation4. Counterfactuals5. Extensions
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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
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(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
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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
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(b) True data generating process with hump-shaped impulse response
Impulse response functions
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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)
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Ln(Real GDP)Four-year horizon (quarterly data)
ARIMA(1,1,0)
ARIMA(0,1,12)
ARIMA(0,1,8)
ARIMA(0,1,4)
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Unemployment Four-year horizon (quarterly data)
ARIMA(1,1,0)
ARIMA(0,1,12)
ARIMA(0,1,8)
ARIMA(0,1,4)
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Ln(Real earnings) Four-year horizon (quarterly data)
ARIMA(1,1,0)
ARIMA(0,1,12)
ARIMA(0,1,8)
ARIMA(0,1,4)
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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)
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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
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Impulse response functions: 1 year
θ = 1θ = 0.75θ = 0.5θ = 0.25θ = 0
1.45 0.5 0.475
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Impulse response functions: 4 years
θ = 1
θ = 0.75
θ = 0.5
θ = 0.25
θ = 0
1.45 0.5 0.475
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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
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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
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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
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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
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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
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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)
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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
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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
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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
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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
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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
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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).
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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%.
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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)
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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
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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
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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
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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
![Page 59: Natural Forecasting, Asset Pricing, and Macroeconomic Dynamics Andreas Fuster David Laibson Brock Mendel Harvard University May 2010](https://reader031.vdocument.in/reader031/viewer/2022012918/56649c425503460f948f134d/html5/thumbnails/59.jpg)
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