To test both the alternative explanation and the hypothesis that the relation between selfinsurance and state insurer taxes varies with the elasticity of demand, equation (1) is reestimated twice, once with the natural logarithm of liability insured losses as the dependent variable and once with the natural logarithm of physical insured losses as the dependent variable. An inverse relation between physical losses and state taxes will be interpreted as contrary to the alternative explanation and support for the original inference that self-insurance is increasing in state taxes. A finding that the relation between liability losses and taxes is less negative than the relation between physical losses and taxes is consistent with the demand curve being more inelastic for liability insurance. Greater inelasticity for liability insurance is expected to impede a shift to self-insurance in response to higher state taxes.

Three additional control variables are added to the regression equation to capture potential sources of state variation unique to automobile insurance. DENSITY is state i’s population per square mile in 1990. THEFT is state i’s annual total motor vehicle thefts. Insured losses are expected to be increasing in the natural logarithms of both the density of the population and the number of automobile thefts.

COMPULSORY is a categorical variable equaling one if automobile liability insurance is mandatory in state i. Although almost all motorists carry liability insurance in noncompulsory states, the option to self-insure is expected to introduce elasticity in the demand curve. Thus, liability insured losses are expected to be greater in compulsory states. Whether the state requires liability coverage is not expected to affect physical insured losses. Thus, the coefficient on COMPULSORY in the physical loss regression is expected to be insignificantly different from zero.

Table 4 presents summary statistics from the two automobile insurance regressions. As expected, the regression coefficient estimates on the natural logarithm of TAX are negative when the dependent variable is the natural logarithm of automobile physical insured losses. The regression coefficient estimates are -0.17 in 1993, -0.18 in 1994, and -0.14 in 1995. The coefficients are significantly less than zero at the 5 percent level in 1993 and 1994 and at the 10 percent level in 1995. These findings are not consistent with the alternative explanation. Instead they provide additional evidence that self-insurance is increasing in state taxes.

As in the prior results, the TAX coefficients enable us to approximate the effects on selfinsurance of a change in state tax rates. Using the same parameters as before, the regression coefficient estimate for 1993 implies that a one-half percentage point increase in tax rates lowers insured losses by $22 million, a 5.3 percent reduction in coverage. As indicated above, these calculations are imprecise at best and should be interpreted with care.

**Table 4 – OLS regression coefficient estimates (standard errors) [^-statistics] Dependent variable: natural logarithm of automobile insured losses, dichotomized by liability and physical n=50 states**

1993 | 1994 | 1995 | ||||

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

13.70 | 11.21 | 13.46 | 10.90 | 13.11 | 10.34 | |

Intercept | (0.78) | (0.72) | (0.80) | (0.80) | (0.73) | (0.94) |

[17.61] | [15.50] | [16.76] | [13.54] | [18.07] | [10.98] | |

0.09 | –0.17 | 0.07 | –0.18 | 0.03 | –0.14 | |

In (TAX) | (0.07) | (0.07) | (0.08) | (0.07) | (0.08) | (0.09) |

[1.21] | [-2.40] | [0.97] | [-2.39] | [0.36] | [-161] | |

0.89 | 1.01 | 0.93 | 1.02 | 0.89 | 1.04 | |

In (POP) | (0.05) | (0.05) | (0.04) | (0.04) | (0.04) | (0.04) |

[17.87] | [21.84] | [20.88] | [22.81] | [24.38] | [23.11] | |

0.51 | 0.08 | 0.49 | 0.04 | 0.41 | –0.12 | |

ln (WEALTH) | (0.15) | (0.14) | (0.16) | (0.16) | (0.15) | (0.19) |

[3.35] | [0.54] | [2.98] | [0.26] | [2.68] | [-0.63] | |

0.01 | 0.02 | –0.01 | 0.01 | –0.00 | 0.01 | |

ln (CAT) | (0.02) | (0.02) | (0.02) | (0.02) | (0.01) | (0.01) |

[0.24] | [1.08] | [-0.92] | [0.74] | [-0.23] | [0.80] | |

0.08 | –0.04 | 0.09 | –0.03 | 0.07 | –0.04 | |

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

[3.81] | [-2.10] | [4.16] | [-1.44] | [4.07] | [-1.78] | |

0.19 | –0.06 | 0.16 | –0.04 | 0.19 | –0.01 | |

ln (THEFT) | (0.06) | (0.06) | (0.06) | (0.06) | (0.05) | (0.07) |

[2.98] | [-1.02] | [2.64] | [-0.69] | [3.83] | [-0.19] | |

0.19 | 0.06 | 0.14 | 0.05 | 0.14 | 0.07 | |

COMPULSORY | (0.06) | (0.05) | (0.05) | (0.05) | (0.05) | (0.06) |

[3.19] | [1.03] | [2.54] | [1.01] | [3.14] | [1.07] | |

Adj. R^{2} |
0.98 | 0.98 | 0.98 | 0.98 | 0.98 | 0.97 |