1. Comment on the correctness of the following statements. You must fully explain your reasoning, not just correct/incorrect.
(a) (5 points) If an estimated regression is unbiased, the estimated coefficient in the sample is equal to the true population coefficient.
(b) (5 points) Heteroskedasticity leads to biased standard errors and coefficients.
(c) (10 points) The validity of a difference-in-differences estimation does not depend on treat- ment and control groups being similar to each other.
(d) (5 points) Omitted variable bias arises when we omit any variable that is important for explaining the y-variable.
2. Homicide rates vary considerably across states in the U.S. but so do laws that may serve to either increase or decrease homicides. One such law is called a “Castle Doctrine” or “Stand Your Ground” law, which many states started passing in 2006. These laws make it legal for people to defend themselves if they feel threatened without any need to make a reasonable effort to remove themselves from the threat. In other words, self defense is legal in all states, but in some states self defense is only legal if you cannot safely remove yourself from the threat, while in other states self defense is legal in response to any threat, regardless of whether you could reasonably avoid the threat (and, in some states, it is also legal to defend yourself against a perceived threat even if you initiated the confrontation to begin with). We’re going to look at the effect of Castle Doctrine laws passed in 2006 on homicides at the state level. Use the provided data to answer the following questions:
(a) (5 points) Estimate the following regression using OLS:
log(homicides) =β0 + β1log(populations) + β2polices + β3urates + β4incomes
+ β5northeasts + β6souths + β7wests + us
where homicide is the number of gun related homicides, population is the population of the state, police is the number of police per 100,000 residents, urate is the unemployment rate (unemployrt), income is state median income, and northeast, south, and west are dummies for whether a state is in one of those regions, with midwest being the omitted region.
(b) (15 points) Interpret the coefficients from the regression.
(c) (5 points) You should have found a positive relationship between the number of police and homicides in part b. Provide one reason why it is misleading to claim that this means that increasing the number of police increases homicides.
(d) (5 points) Reestimate 1, transforming the model so that β4 is an elasticity and interpret β4.
(e) (5 points) Add controls to 1 for whether a state adopts a Castle Doctrine law (treated) and for the time period after 2006 (after). Interpret the two new coefficients.
(f) (15 points) Estimate the difference-in-differences estimate of the effect of Castle Doctrine laws on log homicides, and interpret the resulting coefficient.
(g) (10 points) Replace the dependent variable with log of larceny. Larceny is theft of personal property. We might expect that if everyone knows that people have a right to defend themselves under any circumstances in which they feel threatened, that people will be less likely to steal things. Interpret the effect of Castle Doctrine on larceny.
(h) (5 points) Discuss what must be true about states that do and do not pass Castle Doctrine laws in order to interpret your difference-in-differences estimates as causal.
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