A researcher plans to study the causal effect of police crime using data from a random sample of U.S. counties. He plans to regress the county's crime rate on the (per capita) size of the country's police force.
Why is this regression likely to suffer from omitted variable bias?
A. There are other important determinants of a country's crime rate, including demographic characteristics of the population, that if left out of the regression would bias the estimated partial effect of the (per capita) size of the country's police force.
B. There are other important determinants of a country's crime rate, including demographic characteristics of the population, that if left out of the regression would increase the variance of the estimated coefficient for the (per capita) size of the country's police force.
C. Other regressors are likely perfectly collinear with the (per capita) size of the country's police force, so they should be included in the regression.
D. None of the above are correct.
Which of the following variables are likely useful to add to the regression to control for important omitted variables?
(Check all that apply)
A. The average income per capita of the county.
B. The average level of education in the county.
C. The fraction of young males in the county population.
D. The number of bowling alleys in the county.
Suppose that crime rate is positively affected by the fraction of young males in the population, and that counties with high crime rates tend to hire more police. Use the following expression for omitted variable bias to determine whether the regression will likely over- or underestimate the effect of police on the crime rate.
$$ \hat{\beta_1} = \beta_1 + \tilde{\delta_1} \frac{\text{Cov}(x_1, x_2)}{\text{Var}(x_1)} $$
A. The regression will likely overestimate $$ \beta_1 $$. That is, $$ \hat{\beta_1} $$ is likely to be larger than $$ \beta_1 $$.
B. The regression will likely underestimate $$ \beta_1 $$. That is, $$ \hat{\beta_1} $$ is likely to be smaller than $$ \beta_1 $$.
