Computational Economics (Link to GitHub Repository)
This repository contains implementations of numerical methods for solving dynamic economic models, focusing on Projection Methods (Chebyshev Polynomials) and their application to the Neoclassical Growth Model (NGM).
Project Overview
The project is structured to demonstrate:
- Direct Implementation of Projection Methods: Using Chebyshev polynomials to approximate value and policy functions.
- Application: Solving the Stochastic NGM with Endogenous Labor Supply using global solution methods.
1. Function Approximation & Teaching Material
The following figures illustrate the core concepts of function approximation, demonstrating the convergence properties and structural advantages of Chebyshev projection methods.
Example 1: Convergence with Number of Points
Chebyshev Approximation: Smooth vs Non-Smooth Functions
Chebyshev vs Taylor Polynomial: Exponential Function
Chebyshev Approximation: Curvy Function
Taylor Polynomial Approximation: Curvy Function
2. Neoclassical Growth Model (NGM)
Calibration Parameters
The model is calibrated using standard quarterly parameters:
| Parameter | Value | Description |
|---|---|---|
| $\beta$ | 0.99 | Discount Factor |
| $\alpha$ | 0.33 | Capital Share |
| $\delta$ | 0.025 | Depreciation Rate |
| $\nu$ | 1.0 | Frisch Elasticity |
| $\rho$ | 0.95 | Persistence of Productivity Shock |
| $\sigma$ | 0.02 | Std. Dev. of Innovation |
| $L_{ss}$ | 0.33 | Target Labor Supply (Steady State) |
Deterministic Solution Comparison
Stochastic NGM with Endogenous Labor Supply
Policy Functions & Results
The stochastic solution provides the policy functions for $c(k,z)$ and $l(k,z)$.
Euler Equation Errors: Convergence and Accuracy
Measurement of numerical precision as a function of the polynomial degree ($n$). As $n$ increases, the Euler residuals vanish, demonstrating high global accuracy.
| Degree $n=3$ | Degree $n=5$ |
|---|---|
 |  |
| Degree $n=10$ | Degree $n=20$ |
 |  |
Repository Structure
./: Core implementations and comparisons.chebyshev_loglinear_comparison/: Codes for the comparison study.solve_NGM_model/: Stochastic NGM with endogenous labor.
Requirements
- Python 3.x
NumPy, SciPy, Matplotlib
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