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.