Simultaneous equation bias

Summary

Example

• Explaining consumption by GDP:

$$C_i=β_1+β_2GDP_i+ε_i , i=1,…,n$$

• GDP explains consumption but consumption also explains GDP ( $I$ is investment):

$$GDP_i=C_i+I_i, i=1,…,n$$

• Reduced form equations:

$$C_i= \frac{β_1}{1-β_2}+ \frac{β_2}{1-β_2}I_i+ \frac{ε_i}{1-β_2} , i=1,…,n$$

$${GDP}_i= \frac{β_1}{1-β_2}+ \frac{1}{1-β_2}I_i+ \frac{ε_i}{1-β_2} , i=1,…,n$$

• The second equation shows that ${GDP}_i$ is correlated with $ε_i$ and is endogenous in the consumption function.
• Estimation of the consumption function will lead to biased and inconsistent results. This bias is called simultaneous equation bias.