Question

ln(crime per capita) = beta0 +beta1(police per capita) + u

est beta1 = 0.002 and r2 = 0.60

Q. what would be an improved model to analyse the relation between crime rate and policing?

Answer 1

Solution:

The given model analyze only the impact of policing on crime, but clearly there are many other variables, independent of the policing factor, which can directly impact the crime per capita variable. One way of improving the model could then be inclusion of such variables can give a better model estimation, thereby giving a better estimate for finding impact of policing on crime.

Some of such variables could be:

1. Education: A higher education is expected to decrease the crime rate, though it is not related with policing.

2. Indicators such as job availability or poverty or income levels: One might expect that a better living will reduce the chance of a person to get engaged into crimes such as thievery, burglary, etc. Also, these indicators are not influenced by policing in any way, so their inclusion will not create problem of multi-collinearity.

More job availability or higher income can result in lower crime rates, while poverty is positively related with poverty. Poverty can be included as a dummy variable; whether person lies below poverty or not.

There can be many other such variables which can be included in the model.

Thus, an improved model to estimate could be:

ln (crime per capita) = beta0 + beta1*police per capita + beta2*education + beta3*income + u