# Estimation of Life-Cycle Consumption - PowerPoint PPT Presentation

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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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## 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).

• An application of MSM to life-cycle consumption model (Gourinchas and Parker (2002)).

### 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.

### Model

• When working

• Income

• Transitory shock: takes 0 with probability

• and otherwise.

• Permanent shock:

### Model

• After retirement, no uncertainty.

• Illiquid wealth in the first year of retirement

• Retirement value function

• Consumption Rule (Merton (1971))

### Solution

• Normalization

• At retirement

• When working

### Solution

• In the last period of working

• In periods

### Numerical method

• Intertemporal budget constraint

• Two-dimensional Gauss-Hermite quadrature

### Estimation

• Objective

• Two step MSM:

• The first subset:

• The second subset:

• Expectation of log consumption,

• Approximation (Monte-Carlo)

### 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

### 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

### Estimation method

• This study,

• x is the set of parameters

• Dimension is T (time periods)

• Objective function is

• Hessian matrix

### Estimation Results

Figure 9. Life Cycle Consumption (Thousands in 1987 dollars)

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Raw data

Trust-region Newton

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L-M

Quasi-Newton

Global convergence

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Age