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Estimation of Life-Cycle Consumption

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

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Estimation of Life-Cycle Consumption

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  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)).

  3. Model • Live t= 0----N, and work for periods T<N. T and N are exogenous. • The households maximize • Utility is of CRRA form, and multiplicatively separable in Z.

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

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

  6. Solution • Normalization • At retirement • When working

  7. Solution • In the last period of working • In periods

  8. Numerical method • Intertemporal budget constraint • Two-dimensional Gauss-Hermite quadrature

  9. Simulation

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

  11. 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

  12. 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

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

  14. Estimation Results

  15. Figure 9. Life Cycle Consumption (Thousands in 1987 dollars) 25 Raw data Trust-region Newton 24 L-M Quasi-Newton Global convergence 23 22 21 20 19 18 17 25 30 35 40 45 50 55 60 65 Age

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