**3. Research Design
3.1. Regression equation**

To test the proposition that self-insurance is increasing in state taxes, we estimate the following regression equation at the state-level:

*LOSS, = A, + A TAX, + b2 POP, + A WEALTH + A CAT,+ e (1)*

where LOSS, is the property-casualty industry’s insured losses in state i; TAX, is the total insurance taxes collected in state i in the three preceding years (i.e., years t-3, t-2 and t-1) divided by the total premiums earned in state i in the same three preceding years; POP, is state i’s population; WEALTH, is state i’s gross state product per capita; and CAT, is state i’s estimated catastrophic losses.

A negative coefficient on TAX will be interpreted as evidence that the demand for property-casualty insurance is elastic, causing self-insurance to increase with state taxes. To facilitate coefficient interpretation, the model is estimated in log-linear form. The regression is conducted separately for 1993, 1994 and 1995. Multiple years are examined to mitigate concerns that the results are period-specific.

The model specification relies on Klassen and Shackelford’s (1998) rejection of simultaneous determination of subnational tax revenues and rates. Klassen and Shackelford (1998) jointly estimate a model of U.S. state and Canadian provincial corporate income tax revenues and a model of U.S. state and Canadian provincial corporate income tax rates. They find that the inferences drawn from the simultaneous equations are qualitatively indifferent from those drawn from ordinary least squares.

Consequently, this paper assumes states exogenously levy taxes on the insurance industry, and insurers and consumers endogenously make decisions that determine the taxes paid. However, to the extent Klassen and Shackelford’s findings do not generalize to the state insurer tax setting and simultaneity exists, the determinants of tax rates could be correlated with the factors affecting coverage. If so, ordinary least square estimates of equation (1) could produce erroneous inferences.

One similarity between the corporate income taxes that Klassen and Shackelford (1998) examine and the insurer taxes in this study is that in both settings, tax rates change very infrequently. Thus, even if rates were originally set in response to factors affecting coverage, such as cross-state differences in risk preferences, those factors may now be relatively unimportant. For example, the current discriminatory state taxes levied on out-of-state insurers date back to the 1800s when southern and western states attempted to soak the industry, which at that time was predominantly located in northeastern states.