Control Variable

Study guide: Exam MAS-I

A Control Variable is a predictor included in an insurance Generalized Linear Model to account for a real, known effect on the response — preventing that effect from being incorrectly absorbed into the coefficients of the rating variables — even though the control variable itself will not be used to set the final rate.

\hat{\beta}_{\text{rating}}\big|_{\text{control omitted}} \;\neq\; \hat{\beta}_{\text{rating}}\big|_{\text{control included}} \quad \text{if the rating and control variables are correlated}

• The common control variable in ratemaking is a temporal variable such as accident year or calendar year, which picks up trend, loss development and rate changes the target has not been adjusted for
• A territory or class that is priced separately outside the model is not a control variable: it enters as an offset, with its coefficient fixed, so the other variables are fitted in its presence
• Omitting a relevant control variable causes omitted variable bias: correlated rating variables' coefficients absorb some of the missing variable's true effect, distorting the indicated rate relativities
• A control variable's coefficient is estimated from the data, unlike an Offset Variable, whose coefficient is fixed at 1

Including a Control Variable to Avoid Bias An actuary fits a Poisson frequency GLM with vehicle age as the only rating variable. Calendar year is known to affect frequency (due to changing claim-reporting patterns) and is correlated with the vehicle-age mix of the book, but calendar year will not be used to set rates. Should calendar year be included in the model?

Answer Yes — calendar year should be included as a control variable. Because it is correlated with vehicle age and has a real effect on frequency, omitting it would let part of the calendar-year effect leak into the vehicle-age coefficient, biasing the indicated vehicle-age relativities. Including it (without using its coefficient for rating) isolates the true vehicle-age effect.