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Consider the following model :

$$\begin{aligned} Crime &= α_0 + γ_1Police + α_1Unemp + α_2Income + α_3Gini + u_1 &(1) \\ Police &= β_0 + γ_2Crime + β_1Income + β_2Pub + u_2 &(2) \end{aligned}$$

where for suburb i, Crime is the crime rate (criminal cases per thousand residents),Police is the size of the police force, Unemp is the unemployment rate, Income is the median income of households, Gini is the Gini coefficient (a measure of inequality), and Pub is the number of pubs. Assume that all parameters are significantly different from zero. Only Crime and Police are jointly determined by this system.

I have to estimate these equations using SEM.

1)Can anyone help me in determining which equation here is identified and why? 2)Am I right to say that crime and police are both endogenous?

Any help here would be highly appreciated. Thank you very much.

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  • $\begingroup$ Can anyone please help me out at least in giving me some idea as to how I approach this problem? $\endgroup$ Commented Nov 3, 2015 at 16:33

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I think both these equations are identified (Either exactly or over). The intuition to say that these equations are identified is that in both equations there exists a variable which can be used as an instrumental variable i.e, there exists in both equations a variable which is not present in the other equation. The explanation is very layman and not very sound theoretically so I'll advice you to go through a textbook to exactly get the intuition behind identification.

Secondly, Yes both crime and police are endogenous because the value of both these variables are determined within the system. So a change is some specifics in the system you've modeled will have an impact on these variables so these variables are defined as endogenous. Hope it helps.

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