The variables we will use are listed in Table 7.5.

(a) Is the effect of age on fines non-linear? Assess this question by estimating a model with a quadratic age term, controlling for MPHover, Female, Black, and Hispanic. Interpret the coefficients on the age variables.

(b) Sketch the relationship between age and ticket amount from the foregoing quadratic model: calculate the fitted value for a white male with MPHover equals 0 (probably not many people going zero miles over the speed limit got a ticket, but this simplifies calculations a lot) for ages equal to \(20,25,30,35,40\), and 70 . (In Stata, the following displays the fitted value for a 20 -year-old, assuming all other independent variables equal zero: display _ b[_cons] + _b[Age]*20+_b[AgeSq]*20^2. In R, suppose that we name our OLS model in part

(a) "TicketOLS." Then the following displays the fitted value for a 20 -year-old, assuming all other independent variables equal zero: coef(TicketOLS) [1] + coef(TicketOLS) [2]*20 + coef(TicketOLS)[3]*(20^2).)

Use Equation 7.4 to calculate the marginal effect of age at ages 20,

\(\frac{\partial Y}{\partial X_1}=\beta_1+2 \beta_2 X_1 \tag{7.4}\)

(c) 35, and 70. Describe how these marginal effects relate to your sketch.

(d) Calculate the age that is associated with the lowest predicted fine based on the quadratic OLS model results given earlier.

(e) Do drivers from out of town and out of state get treated differently? Do state police and local police treat non-locals differently? Estimate a model that allows us to assess whether outof-towners and out-of-staters are treated differently and whether state police respond differently to out-of-towners and out-ofstaters. Interpret the coefficients on the relevant variables.

(f) Test whether the two state police interaction terms are jointly significant. Briefly explain the results.

TABLE 7.5 Variables for Speeding Ticket Data Variable name MP Hover Amount Age Female Black Hispanic State Pol Out Town OutState Description Miles per hour over the speed limit Assessed fine for the ticket Age of driver Equals for women and 0 for men Equals 1 for African-Americans and 0 otherwise Equals 1 for Hispanics and 0 otherwise Equals 1 if ticketing officer was state patrol officer Equals 1 if driver from out of town and 0 otherwise Equals 1 il driver from out of state and 0 otherwise