Question

You have data on people convicted of crimes in California. You run a regression explaining the number of arrests of a person in 2018 (narrests) as a function of previous convictions (pcnv), the amount of prison time a person served in 2018(ptime) and the fraction of the labour force that is employed in their municipality of residence in 2018 (empfrac).

You obtain the following estimates:

narrests=0.2029+0.1676*pcnv-0.1111*ptime+0.3804*empfrac
N=8435 R-squared=0.066

1. a.) Interpret the coefficient on the variable ptime. Does it make sense? Why or why not? [ 2 marks]

2. b.) What fraction of the variance in the dependent variable is explained by this model? [1 mark]

3. c.) Underwhatconditionswouldtheestimatedcoefficientsbebiased?[2marks]

Answer 1

a.) Coefficient of ptime is -0.1111. This means that on an average, with every unit increase in ptime, narrests decreases by 0.1111 everything else remaining same. This makes sense. As, increasing the prison time will make it more difficult for the person to commit crime. We can give two reasons for this. Person getting harsher punishment is less likely to commit crime again and longer the prison time, lesser time for person to be out of prison and commit crime.

b.) Fraction of variance explained in the dependent variable is same as R-squared = 0.066.

c.) Below are the conditions for Unbiasedness. If these conditions are not met, the estimates will be biased.

1. Population model is linear in parameters. i.e. the linearity assumption made for the model has to be met.

2. No Sample selection bias. For example, only chain snatchers are taken and not murderers, then chances of recurrence of crime might be higher.

3. Explanatory variables should not uncorrelated with each other. Perfect correlation makes estimation impossible.

4. All explanatory variables are "exogenous". Variables should not be correlated with the error term.