4) Consider Becker's model of crime: (Refer to equation 1.3 in the textbook for details on each variable) Crime = Bo+Bwage + Bothinc + B3freqarr + Bfreqconv + Bavgsen + age + u For simplicity, let's rewrite the explanatory variables with X1, X2,etc. Obtaining: Crime Bo+B1X1 + B2X2 + B3x3 + B4X4 + B5X5 + 6X6 + u a) Taylor (Swift), an econometrics student, wants to use Becker's model to find the effect of wage on the frequency of criminal activity. Which coefficient will capture the partial effect of wage on crime? b) What sign should she expect the estimate to have? Briefly explain why. c) Suppose there is no data for X2 and it is omitted from the regression. Derive an equation for the magnitude of the bias that this omission causes. Speculate on the direction of the bias as well. d) After running a few regressions in Stata, Taylor Swift finds that R increases every time a new variable is added and decides to add as many explanatory variables as are available. Suppose the sample contains 400 observations. How many variables can she add? e) What is the problem with the method employed in d)? f) Suppose in the sample, for each observation, exactly 50% of arrests lead to conviction. This would imply that X4 = 0.5 * X3. Mathematically show how this linear dependance affects the OLS estimate. (Hint: What does 3 now capture?)