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Refer to Example 13.9 and the data in CRIME 4(i) Suppose that, after differencing to remove the unobserved effect, you think $\Delta \log (p o l p c)$ is simultaneously determined with $\Delta \log ($crmrte$) ;$ in particular, increases in crime are associated with increases in police officers. How does this help to explain the positive coefficient on $\Delta \log ($polpc$)$ in equation $(13.33) ?$(ii) The variable $t a x p c$ is the taxes collected per person in the county. Does it seem reasonable to exclude this from the crime equation?(iii) Estimate the reduced form for $\Delta \log (p o l p c)$ using pooled OLS, including the potential IV, Llog (taxpc). Does it look like $\Delta \log ($taxpc$)$ is a good IV candidate? Explain.(iv) Suppose that, in several of the years, the state of North Carolina awarded grants to some counties to increase the size of their county police force. How could you use this information to estimate the effect of additional police officers on the crime rate?

(i) possibly more police are hired to counteract crime (ii) maybe (iii) (iv) see video

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Chapter 16

Simultaneous Equations Models

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part one. So the coefficient of variable delta log police per capita is positive, meaning there is a positive relationship between the change in crime rate and the change in the amount of the number of police per capita. This positive relationship can be explained by common sense. If the administrators of the county predict that crime rates will increase in the future, then they may hire more police to curb the crime are too. It may be reasonable to exclude variable tax pC from the equation. It's just maybe though, because this variable depends on part of party on income and sales taxes. Mhm. And these factors further depends on the economic situation in that can influence crime rates. R. Three. The reduced form for the change in log of police per capita is so on the left hand side you have the change of lock of police per capita and on the right hand side you have an intercept, you have ford ear dummies of the year 1983 to 1987 And you have five explanatory variables P r B A r p r b c O N V, PRB, Pr I S and a b g S E N and finally tax per capita. So we need, yeah the coefficient of tax book capita, mhm positive. No not necessary. We need this coefficient to be different from zero. We needed to be non-0. So the variable tax per capita can be a reasonable ivy for the change in um police per capita. When we estimate the reduced form equation by pool O. L. S. Yeah, we have nighty counties six years and That makes 540 observations. We get the estimate on variable lot of tax. The change in lock of tax, B C. To be .0052 with a T statistic of 0.8 a very small T statistic. So we are unable to reject the null hypothesis that the coefficient of this variable is zero and so tax per capita is not a good instrument for police per capita Part four. If the grants are awarded randomly, the correlation between brand and delta. U. Sub. It is zero and Delta use A. It is the change in an observant growth that effect county crime rates. By the definition, the correlation between grants and police per capita is not zero. These factors are correlated across county and time. So this means we have an exogenous variable that can be submitted from the crime equation and also partially correlated with the endogenous explanatory variable. So we could re estimate equation 13.33 by instrumental variable method.

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