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Estimation of Life-Cycle Consumption Zhe Li (PhD Student) Stony Brook University.

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Presentation on theme: "Estimation of Life-Cycle Consumption Zhe Li (PhD Student) Stony Brook University."— Presentation transcript:

1 Estimation of Life-Cycle Consumption Zhe Li (PhD Student) Stony Brook University

2 Introduction A CLASSICAL METHOD of moments estimator Instead using analytically form, replace the expected response function by a simulation result ---- the method of simulated moments (MSM). An application of MSM to life-cycle consumption model (Gourinchas and Parker (2002)).

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4 Model Live t= 0----N, and work for periods T

5 Model When working Income Transitory shock: takes 0 with probability and otherwise. Permanent shock:

6 Model After retirement, no uncertainty. Illiquid wealth in the first year of retirement Retirement value function Consumption Rule (Merton (1971))

7 Solution Normalization At retirement When working

8 Solution In the last period of working In periods

9 Numerical method Intertemporal budget constraint Two-dimensional Gauss-Hermite quadrature

10 Simulation ParametersDescriptionValue Rate of time preference0.96 Rate of risk aversion0.514, where h is the ratio of illiquid wealth to the permanent component of income at retirement Marginal propensity to consume at retirement0.071 RInterest rate pProbability of unemployment Variance of permanent shock Variance of transitory shock Initial log normalized wealth at age (1.784)

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16 Estimation Objective Two step MSM: The first subset: The second subset: Expectation of log consumption, Approximation (Monte-Carlo)

17 Estimation Find that minimize Where W is a T*T weighting matrix: –Inverse of the sample counterpart of –Corrected by the variance-covariance matrix for the first-stage estimation

18 Estimation Method Start at a point x in N-dimensional space, and proceed from there in some vector direction p Any function of N variables f(x) can be minimized along the line p, say finding the scalar a that minimizes f(x+ap) Replace x by x+ap, and start a new iteration until convergence occurs Example: Newton method

19 Estimation method This study, –x is the set of parameters –Dimension is T (time periods) –Objective function is –Gradient –Hessian matrix

20 Estimation Results Parameters Trust-Region Newton L-MQuasi-NewtonGlobal convergence (0.0390)(0.0385)(0.0313)(0.0556) (3.9409)(2.6876)(3.6892)(5.0803) Retirement Rule: (7.3221)(6.7996)(6.5953)(1.8346) (0.6604)(0.6086)(0.3639)(0.4741) fmin

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