Questions: Simultaneous Equations Models and Identification
4 questions to test your understanding
Score: 0 / 4
Question 1 Multiple Choice
A model of the wheat market has supply q = a₁p + b₁·rain + u₁ and demand q = a₂p + b₂·income + u₂. Which variable identifies the demand equation?
AIncome, because it appears in the demand equation
BRain, because it shifts supply and is excluded from demand
CPrice, because it appears in both equations
DNeither; demand cannot be identified
To trace out the demand curve you need something that moves supply while leaving demand fixed. Rain is excluded from demand and appears in supply, so it serves as the instrument for price in the demand equation. Income likewise identifies the supply equation.
Question 2 True / False
An equation with two endogenous explanatory variables and one excluded exogenous variable satisfies the order condition.
TTrue
FFalse
Answer: False
The order condition requires at least as many excluded exogenous variables as included endogenous explanatory variables. One excluded variable cannot instrument for two endogenous regressors, so the equation is underidentified.
Question 3 Multiple Choice
Why is OLS biased when applied to the demand equation in a supply-and-demand system?
ABecause quantity is measured with error
BBecause a demand shock u₂ shifts the equilibrium price, so price is correlated with u₂
CBecause price is always nonstationary
DBecause the errors are heteroskedastic
When demand rises unexpectedly, both price and quantity rise. Price therefore moves with the demand error, which violates the OLS assumption that regressors are uncorrelated with the error. This is simultaneity bias.
Question 4 Short Answer
State the difference between the order condition and the rank condition for identifying an equation in a two-equation system.
Think about your answer, then reveal below.
Model answer: The order condition counts variables: the equation must exclude at least as many exogenous variables as it includes endogenous explanatory variables. The rank condition requires more: at least one of the excluded exogenous variables must actually appear with a nonzero coefficient in the other equation. Order is necessary; rank is necessary and sufficient.
An excluded variable that does not really shift the other equation cannot serve as an instrument, even though it passes the counting test.