**4.5. Sensitivity tests**

The automobile regression results were subjected to same sensitivity tests applied to the non-automobile lines. Again, findings are robust to alternative specifications and control variables. Results are insensitive to estimating the automobile regression equations in log-linear expression. Conclusions are qualitatively unaltered when the regression variables, other than TAX, WEALTH, and COMPULSORY, are scaled by population. The TAX coefficients remain negative and significantly less than zero in the automobile physical regression. They also are more negative than the TAX coefficients in the automobile liability regressions, which are never significantly different from zero. Also, results again hold when rank regressions are employed.

The regressions also were estimated using several control variables that were discarded because their estimated regression coefficients were not significantly different from zero and they did not affect the inferences drawn from the TAX coefficients. These control variables include the discarded control variables detailed in section 4.2. and a categorical variable indicating whether the state has no-fault automobile insurance, as reported by The Fact Book. Another robustness check involves substituting premiums for incurred losses in the regression equation. Recall that this study uses incurred losses as the proxy for coverage because reported premiums were expected to suffer from tax and regulatory management. Since Petroni and Shackelford (1999) document no such manipulation for automobile premiums, they should measure automobile coverage without bias.

An advantage of using premiums is that premiums are an ex-ante measure of coverage, rather than an ex-post measure like losses. Thus, no control is needed for unanticipated states of nature, such as catastrophes. However, a disadvantage of using premiums is that reported premiums include the premium tax. Thus, using premiums as a measure of coverage biases against rejecting the null hypothesis because reported premiums are greater in high premium tax states, ceteris paribus. Another possible disadvantage of using premiums is that they include insurer profits, which could vary across states if regulation or other factors create barriers to entry.

The mean premiums earned from automobile liability (physical) insurance is $1.4 (0.7) billion. Table 5 presents summary statistics from reestimating the automobile regressions using the natural logarithm of premiums as the dependent variable and dropping CAT as a control variable. As expected, the physical TAX coefficients are always negative. They are significant at the 1 percent level in 1993 and the 10 percent level in 1994, but not significant in 1995. In addition, they are always significantly less than the liability TAX coefficients, which are never significantly different from zero. In brief, the premium regressions confirm the inferences drawn from the insured losses regressions.

**Table 5 – OLS regression coefficient estimates (standard errors) [^-statistics] Dependent variable: natural logarithm of automobile premiums earned, dichotomized by liability and physical n=50 states**

1993 | 1994 | 1995 | ||||

Liability | Physical | Liability | Physical | Liability | Physical | |

13.44 | 12.20 | 13.35 | 12.39 | 13.49 | 12.24 | |

Intercept | (0.63) | (0.51) | (0.71) | (0.62) | (0.65) | (0.61) |

[21.37] | [23.86] | [18.86] | [20.15] | [20.91] | [20.06] | |

0.01 | –0.13 | –0.00 | –0.08 | 0.02 | –0.07 | |

In (TAX) | (0.06) | (0.05) | (0.06) | (0.05) | (0.06) | (0.06) |

[0.21] | [-2.72] | [-0.06] | [-156] | [0.37] | [-1.28] | |

0.87 | 0.96 | 0.86 | 0.96 | 0.88 | 0.97 | |

In (POP) | (0.03) | (0.02) | (0.03) | (0.03) | (0.03) | (0.03) |

[28.49] | [38.77] | [28.62] | [36.90] | [30.62] | [35.75] | |

0.43 | 0.17 | 0.41 | 0.17 | 0.41 | 0.13 | |

ln (WEALTH) | (0.12) | (0.10) | (0.14) | (0.13) | (0.13) | (0.12) |

[3.45] | [171] | [2.86] | [1.35] | [3.12] | [1.06] | |

0.10 | 0.00 | 0.09 | –0.00 | 0.09 | 0.00 | |

ln (DENSITY) | (0.02) | (0.01) | (0.02) | (0.01) | (0.02) | (0.02) |

[5.58] | [0.14] | [5.34] | [-0.17] | [5.39] | [0.01] | |

0.21 | 0.01 | 0.22 | 0.01 | 0.19 | 0.02 | |

ln (THEFT) | (0.05) | (0.04) | (0.05) | (0.04) | (0.05) | (0.04) |

[4.10] | [0.35] | [4.41] | [0.29] | [4.19] | [0.49] | |

0.14 | –0.01 | 0.13 | 0.01 | 0.14 | 0.02 | |

COMPULSORY | (0.05) | (0.04) | (0.05) | (0.04) | (0.05) | (0.04) |

[3.01] | [-0.22] | [2.73] | [0.32] | [3.03] | [0.52] | |

Adj. R^{2} |
0.98 | 0.99 | 0.98 | 0.99 | 0.99 | 0.99 |