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 (justin.van@unimelb.edu.au), MIAESR & NIESR October 2013

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: Mankiw 1985 – RES Mankiw et al (1985) - QJE

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

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: CES preference relation: consumption / saving labour / leisure pension scheme participation CES preference relation:

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: Returns are certain: relationship transitions wage potential & wage offer survival Returns are certain:

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

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

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

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

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

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 0.1875 – 0.2373

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

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

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

A remaining puzzle

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