**3.7. Univariate Analysis**

Table 2 presents Pearson correlation coefficient estimates for each of the regression variables using 1993 data expressed in natural logarithms. The correlation coefficient estimate between TAX and LOSS is negative and highly significant; however, so is the correlation between TAX and POP. Because LOSS and POP are highly positively correlated, inferences about the relation between taxes and coverage must be deferred until the multivariate analysis is completed. Correlations are qualitatively similar in 1994 and 1995.

**4. Empirical Results
4.1. Primary findings**

Regressions are conducted separately for the automobile lines and the other lines of business because the demand curve for automobile liability insurance is expected to be less elastic than the demand curve for other property-casualty lines. Initial tests are conducted on the non-automobile lines of property-casualty insurance where a downward sloping demand is predicted.

The regression results in Table 3 present evidence consistent with state taxes suppressing coverage for property-casualty lines, other than automobile. The coefficient estimates on the natural logarithm of TAX are -0.24 in 1993 (significantly less than zero at the 5 percent level using a one-tailed test), -0.28 (1 percent significance) and -0.18 (10 percent significance). The coefficient estimates on the control variables are always positive, as predicted, and stable across years.

The TAX coefficients enable us to estimate the effects on self-insurance of a change in state tax rates. Suppose a state with a 1993 mean tax rate of 1.6 percent increases its tax rate by one standard deviation. Using the 1993’s standard derivation for TAX of 0.5 percent and the mean state’s 1993 non-automobile losses of $1.87 billion, the regression coefficient estimate for 1993 implies that insured losses in the state would decrease by $140 million, a 7.5 percent reduction in insurance coverage.

This rough approximation provides an indication of the economic significance of the regression coefficient estimates. However, it ignores important general equilibrium effects, including likely responses by insurance companies, consumers, and other states to a change in tax rates. It also ignores any behavioral response to self-insurance, namely, a tendency toward increased loss prevention, reducing moral hazard concerns (Pauly, 1968).

These findings carry important social welfare implications to the extent sub-optimal risk sharing arises as residents shift to self-insurance. Among other effects, high levels of selfinsurance jeopardize a state’s ability to weather catastrophic damage. Additional analysis, however, is needed to determine whether the social benefits from the tax revenue offsets the suboptimalities introduced by the taxes.

**Table 1 Descriptive Statistics 50 states, 1993**

Mean | Std. Dev. | Minimum | Median | Maximum | |

LOSS: Automobile Liability | 1000 | 1160 | 66 | 695 | 5380 |

LOSS: Automobile Physical | 420 | 476 | 39 | 283 | 2620 |

LOSS: Other | 1870 | 2600 | 108 | 1100 | 15500 |

TAX | 1.6% | 0.5% | 0.6% | 1.6% | 2.7% |

POP | 5144 | 5680 | 470 | 3598 | 31220 |

WEALTH | 0.024 | 0.005 | 0.017 | 0.023 | 0.042 |

CAT | 115 | 216 | 0 | 47 | 1082 |

**Table 2 – Pearson correlation coefficient estimates (two-sided significance levels) for the regression variables in equation (1) 50 states, 1993**

In (TAX) | In (POP) | In (WEALTH) | In (CAT) | |

In (POP) | -0.42(0.002) | |||

In (WEALTH) | -0.20(0.17) | 0.02(0.89) | ||

In (CAT) | -0.21(0.14) | 0.76(0.001) | -0.06(0.67) | |

In (LOSS) | -0.48(0.001) | 0.96(0.001) | 0.13(0.35) | 0.76(0.001) |

**Table 3 – OLS regression coefficient estimates (standard errors) [^-statistics] Dependent variable: natural logarithm of non-automobile insured losses n=50 states**

1993 | 1994 | 1995 | ||

14.84 | 13.79 | 13.91 | ||

Intercept | (0.98) | (102) | (109) | |

[15.19] | [13.43] | [12.71] | ||

-0.24 | -0.28 | -0.18 | ||

In (TAX) | (-) | (0.11) | (0.11) | (0.11) |

[-2.19] | [-2.52] | [-158] | ||

0.88 | 0.89 | 0.99 | ||

In (POP) | (+) | (0.06) | (0.05) | (0.06) |

[14.88] | [16.62] | [17.09] | ||

0.65 | 0.43 | 0.54 | ||

ln (WEALTH) | (+) | (0.21) | (0.23) | (0.26) |

[3.16] | [190] | [2.09] | ||

0.07 | 0.07 | 0.02 | ||

ln (CAT) | (+) | (0.03) | (0.02) | (0.02) |

[2.12] | [3.17] | [0.91] | ||

Adj. R^{2} |
0.95 | 0.95 | 0.95 |