Simultaneous Equation Models Analysis Tool

Simultaneous Equation Models Analysis Tool

Model Specification

Equation 1 (Y₁):

Y₁ = + Y₂ + X₁ + ε₁

Equation 2 (Y₂):

Y₂ = + Y₁ + X₂ + ε₂

Data Generation

Sample Size: 200

Noise Level: 30

Estimation Results

Ordinary Least Squares (OLS)

Generate data to see results

Two-Stage Least Squares (2SLS)

Generate data to see results

Understanding Simultaneous Equations

This system has two endogenous variables (Y₁ and Y₂) that are determined simultaneously. The structural form is:

Y₁ = β₁₀ + β₁₁Y₂ + β₁₂X₁ + ε₁

Y₂ = β₂₀ + β₂₁Y₁ + β₂₂X₂ + ε₂

Because Y₁ and Y₂ appear on both sides of the equations, OLS estimates will be biased. Two-stage least squares (2SLS) provides consistent estimates by using instruments.