1. Justin van de Ven (justin.van@unimelb.edu.au), MIAESR & NIESR
Using Dynamic Programming Methods to Evaluate Relative Risk Aversion on Cross-sectional Data
Justin van de Ven MIAESR & NIESR
October 2013

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

3. Definitions Relative risk aversion:
Intertemporal elasticity of substitution:
CES utility:
Mankiw 1985 – RES
Mankiw et al (1985) - QJE

4. 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 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).
Mankiw 1985 – RES
Mankiw et al (1985) - QJE

5. 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

6. 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)

7. 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)

8. 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

9. The model endogenous decisions: CES preference relation:
consumption / saving
labour / leisure
pension scheme participation
CES preference relation:

10. 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

11. The model Uncertainty concerning: Returns are certain:
relationship transitions
wage potential & wage offer
survival
Returns are certain:

12. Margins for identification
Utility price of leisure (A), experience effects (B) and labour supply

13. Margins for identification
Intratemporal elasticity (e)
toward retirement utility maximising solution approximated by:
so that:

14. Margins for identification
Relative risk aversion (g), discount factor (d), and bequest motive (z) all identified jointly

15. Margins for identification
Discount factor(A), relative risk aversion (A), preference for bequests (B) and consumption

16. Margins for identification
Discount factor(-A), relative risk aversion (A), preference for bequests (A) and pension participation

17. Calibration results Utility price of leisure (a): 1.3
Intratemporal elasticity (e): 0.3
Discount factor (d): 0.959
Bequest motive (z): 5100
Relative Risk Aversion (g): 1.675
intertemporal elasticity at population averages –

18. Sensitivity of consumption to assumed value of RRA
Calibration results
Sensitivity of consumption to assumed value of RRA

19. Sensitivity of consumption to assumed value of discount factor
Calibration results
Sensitivity of consumption to assumed value of discount factor

20. Sensitivity of consumption to assumed value of bequest parameter
Calibration results
Sensitivity of consumption to assumed value of bequest parameter

21. A remaining puzzle

22. 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