crime = β0 + β1unem + β2police_exp + u I am trying to estimate the causal effect of government expenditure on the local police force (police_exp) on crime rates (crime). But, it can be hard to estimate the causal effect of police expenditure on crime, even after controlling for the local area unemployment rate (unem). The reason is that crime rates and expenditure on the police are simultaneously determined, or in other words that there are many omitted factors that drive the crime rate in a local area and that are also related to expenditure on police. So expenditure on police is endogenous in this model. I am planning to use the local area crime rate from three years ago (crime−3) as a proxy for these omitted local area characteristics. Which of the following assumptions must my proxy variable crime−3 satisfy to ensure that I can consistently estimate the effect of police expenditure on crime? a) E (crime−3 | unem,police_exp) = 0 b) Corr(crime−3,crime) = 0 c) Corr(crime−3,u) = 0 d) Corr(crime−3,u) ≠ 0
I have the following model for local area crime rates:
crime = β0 + β1unem + β2police_exp + u
I am trying to estimate the causal effect of government expenditure on the local police force (police_exp) on crime rates (crime).
But, it can be hard to estimate the causal effect of police expenditure on crime, even after controlling for the local area
The reason is that crime rates and expenditure on the police are simultaneously determined, or in other words that there are many omitted factors that drive the crime rate in a local area and that are also related to expenditure on police. So expenditure on police is endogenous in this model.
I am planning to use the local area crime rate from three years ago (crime−3) as a proxy for these omitted local area characteristics.
Which of the following assumptions must my proxy variable crime−3 satisfy to ensure that I can consistently estimate the effect of police expenditure on crime?
a) E (crime−3 | unem,police_exp) = 0
b) Corr(crime−3,crime) = 0
c) Corr(crime−3,u) = 0
d) Corr(crime−3,u) ≠ 0
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