A researcher plans to study the causal effect of police on crime using data from

Question

A researcher plans to study the causal effect of police on crime using data from a random sample of U.S. counties. She plans to regress the county's crime rate on the per capita size of the county's police force. 2. a. Explain why this regression is likely to suffer from omitted variable bias. Give one specific example of a variable that you would add to the regression and why it satisfies the conditions of omitted variable bias. Variables will differ across student answers, and this will be graded based on the discussion. Use your answer in (a) to determine whether the regression will likely over- or underestimate the effect of police on the crime rate. (i.e. Explain whether B1> B1 or B1 1 and provide intuition based on the specific omitted variable that you identified in part (a).) Recall that the formula for omitted variable bias is B1 B1 pu, which says that the estimate of B1 converges in probability to the true value of B1 plus the ratio of the standard deviation of the error term, ??, and the standard deviation of the independent variable x, ? x, multiplied by the correlation between the error term and the x variable, Pux. Therefore, your answer will depend on Pux b. Or

Explanation / Answer

A researcher plans to study the causal effect of police on 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 county’s police forces.

(a) Explain why this regression is likely to suffer from omitted variable bias. Which variables

would you add to the regression to control for important variables?

There are other important determinants of a country’s crime rate, including demographic

characteristics of the population.

(b) Use you answer to (a) and the expression for omitted variable bias to determine whether the

regression will likely over-or underestimate the effect of police on the crime rate.

Suppose that the 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.

In this case, the size of the police force is likely to be positively correlated with the fraction of young males in the population leading to a positive value for the omitted variable bias so that

beta' 1>beta 2

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