Question

2-a-First, consider a regression where the independent variable is the neighborhood income around a school attendance zone and the dependent variable is student test scores. What is the likely sign of the coefficient on neighborhood income?

b-Now consider a regression where the independent variable is a measure of violent crime incidents around the school and the dependent variable is student test scores. What is the likely sign of the coefficient on violent crime?

c-Finally, consider a regression of violent crime incidents on area income levels. What is the likely sign of the coefficient on area income levels?

d-Now consider the sign of omitted variable bias in the first regression, neighborhood income levels on student test scores. What is the sign of omitted variable bias if we omit a measure of violent crime around a school? Explain.

Answer 1

a) the sign of neighbours income is likely to be positive as there is a positive relationship between Neighbourhoods income and test scores. A wealthy parent can get sources of study and tuition for his children. This would help him score more marks.

b) the sign of coefficient of violent crime is likely to be negative. Students are scared of crimes in their area and feel distracted. This diverts their mind from studying well and may also stop them from going to school.

c) the sign of coefficient on area income levels is negative. When income levels are high in the area, it is less likely that people commit crimes.

d) when we omit violent crime around a school there is downward bais. This is because violent crime and income levels are negatively related, also test score and violent crime are negatively related. This would lower the effect of income level on test score as income level not carries it's own effect but also negative effect of violent crime.