Question

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 force. (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 omitted variables

Answer 1

The planned regression is subject to omitted variable bias, which can skew the results. Additional variables such as poverty, unemployment, diversity, residential mobility, educational attainment, region, average age, and police expenditures should be added to create a more accurate model of the relationship between police force size and crime rates.

Step-by-step explanation:

The regression that the researcher plans to conduct, using crime rates and the size of the police force, is likely to suffer from omitted variable bias. This bias occurs because there are other important variables that influence crime rates that are not being included in the analysis. To address omitted variable bias, we should consider adding additional control variables such as poverty levels, employment rates, ethnic diversity, residential mobility, and educational attainment. These variables can have a significant impact on crime rates and add complexity to the simple relationship between police presence and crime.

Moreover, variables like region and average age of the population, along with police expenditures, can also play a critical role in shaping crime rates. Including these variables in the regression would help to control for important confounding factors that might otherwise lead to distorted results, enabling a more accurate estimation of the causal effect of police on crime.

Answer 2

Answer and Step-by-step explanation:

This regression can generate an omitted variable bias, because the researcher did not determine any parameters or real data to measure it. In this case, the researcher determined the crime rate as a dependent variable, but did not establish the facts that influence it and that promote an observable result. In this way, he omitted the independent variable and his research will be inaccurate and incorrect. To control this bias, it is necessary for the researcher to provide a dependent variable such as the level of education in the region, the income distribution in the region, the unemployment rate, the fraction of young men, among others.