Using Dynamic Programming Methods to Evaluate Relative Risk Aversion on Cross-sectional Data Justin...

Using Dynamic Programming Methods to Evaluate Relative Risk Aversion on Cross-sectional Data

Justin van de Ven ([email protected]), MIAESR & NIESROctober 2013

www.melbourneinstitute.com

Outline

Definitions Approaches to identification A new approach The model Margins for identification Results Summary and directions for further

research


Definitions Relative risk aversion:

Intertemporal elasticity of substitution:

CES utility:

t

tt

t

tt

r

cc

R

ccIE

/ln

ln

/ln 11

'

''

u

cuRRA

T

t

tt cU0

1

1


An empirical puzzle

There exists considerable controversy concerning the intertemporal elasticity (IE) of substitution (e.g. Attanasio and Webber, 2010).– Hall (1988) finds that the IE may not be very different from zero

• Dynan (1993), Grossman & Shiller (1981), and Mankiw (1985)

– Attanasio & Weber (1993) focus on the importance of liquidity constraints (0.8 for the UK)

• Attanasio & Weber (1995) find 0.6-0.7 for the US

– Other micro studies also find evidence of higher values:• Blundell et al. (1993) (0.5), Blundell et al. (1994) (0.75), Engelhardt &

Kumar (2007) (0.75), Hansen & Singleton (1983) and Mankiw et al. (1985) (just over 1).


An empirical puzzle

– Studies that explore the equity premium puzzle suggest very small elasiticities (e.g. Mehra & Prescott, 1985)

– Studies that explore the risk-free rate puzzle suggest elasticities > 0.5 (e.g. Lucas, 1990)

– Evidence from attitudinal surveys suggest that the IE is unlikely to be less than 0.2 (e.g. Barsky et al., 1997)

The willingness of people to substitute consumption through time is a fundamental

component in understanding savings decisions and is crucially important to a wide range of

practical questions including investment strategies and public policy design


Approaches to identification

Estimation of Euler conditions using standard linear regression techniques

Estimation of structural dynamic programming models (Deaton, 1991; Carroll, 1992)• Simulated Minimum Distance (Lee and Ingram, 1991)• Method of Simulated Moments (Stern, 1997)• Indirect Estimation (Gourieroux et al., 1993)• Efficient Method of Moments (Gallant and Tauchen,

1996)


Approaches to identification Focus on cohort specific models (Gourinchas and

Parker, 2002) Data considered for analysis:

– Data for observed cohorts (e.g. Attanasio et al 2005, 2008)

• Evolving policy environment / representativeness of selected cohorts

– Controlling for time and cohort effects (e.g. Sefton et al 2008)

– Growth adjusted cross-section (e.g. van de Ven, 2010)


A new approach

We are fundamentally interested in responses to uncertainty and willingness to substitute consumption through time– Solution requires use of dynamic programming

methods Empirical advantages of an OLG structure Empirical novelty and the choice of

methodological approach– calibration of a reasonably articulated structure


The model

endogenous decisions:– consumption / saving– labour / leisure– pension scheme participation

CES preference relation:

A

ajji

baajjiji

baaj

ajaai wlcuEU

1

,,1

,,,, 1,1

1

/11

1/11/1/11

,, , lclcu jiji ),0.1max( ,, jiji ww


The model Simulated characteristics:

– birth year– age (18-130)– relationship status (single/couple)– education level (graduate/non-graduate)– wage potential

• wage offer

– non-pension wealth– pension wealth– survival


The model Uncertainty concerning:

– relationship transitions– wage potential & wage offer

– survival Returns are certain:

tttttt lmmhh 1loglog 11

tttttt clhrwww )1(1


Margins for identification

Utility price of leisure (A), experience effects (B) and labour supply

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

15 25 35 45 55 65 75

prop

n no

t em

ploy

ed

age

adult couples

sample statistics simulated statistics

A

B

AA


Margins for identification Intratemporal elasticity

– toward retirement utility maximising solution approximated by:

– so that:

t

t

t hl

c 1

tj

ti

tj

tj

ti

ti

h

h

l

c

l

c

,

,

,

,

,

,


Margins for identification Relative risk aversion (), discount factor

and bequest motive all identified jointly



Discount factor(A), relative risk aversion (A), preference for bequests (B) and consumption

0

100

200

300

400

500

600

700

15 25 35 45 55 65 75

£(20

06)

per

wee

k

reference person age

geometric mean consumption by age - couples

Sample statistics simulated statistics

A A A

B



Discount factor(-A), relative risk aversion (A), preference for bequests (A) and pension

participation

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

15 25 35 45 55 65 75

prop

ortio

n of

cou

ples


proportion of couples contributing to private pensions

samplesimulated

A A A


Calibration results

Utility price of leisure 1.3 Intratemporal elasticity 0.3 Discount factor 0.959 Bequest motive 5100 Relative Risk Aversion 1.675

– intertemporal elasticity at population averages 0.1875 – 0.2373


Calibration results

0

100

200

300

400

500

600

700

20 30 40 50 60 70 80

£(20

06) p

er w

eek


sample gamma = 1.675 gamma = 1.25 gamma = 2.2

Sensitivity of consumption to assumed value of RRA


0

100

200

300

400

500

600

700

20 30 40 50 60 70 80

£(20

06) p

er w

eek


sample delta = 0.959 delta = 0.9 delta = 0.98

Calibration results

Sensitivity of consumption to assumed value of discount factor


0

100

200

300

400

500

600

700

20 30 40 50 60 70 80

£(20

06) p

er w

eek


sample zeta = 5100 zeta = 2424 zeta = 10682

Calibration results

Sensitivity of consumption to assumed value of bequest parameter


A remaining puzzle

0

50000

100000

150000

200000

250000

19 29 39 49 59 69 79

non-

pens

ion

wea

lth £

(200

6)

age of reference person

Age 18-21 Age 22-30 Age 31-40 Age 41-50Age 51-60 Age 61-70 Age 70+


Summary and next steps

An OLG model structure is sufficient to identify dynamic behavioural parameters and offers exciting possibilities for future research– variation of IE through time / between members

of the population (e.g. Fehr and Hoff, 2011) Simple models have very important limitations,

suggesting the need to exercise care when interpreting associated results– Econometric estimation

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