Arson and Abandonment: A Restatement

By Cloninger, Dale O. | Journal of Risk and Insurance, September 1990 | Go to article overview

Arson and Abandonment: A Restatement


Cloninger, Dale O., Journal of Risk and Insurance


Cloninger (1981) presents a model of arson abandonment that reconciles traditional abandonment models developed in the finance literature with criminal offense models developed in the economic literature. The 1981 article attempts to define the conditions under which abandonment by arson in the current period is the wealth maximizing alternative for risk neutral firms. Under those conditions, arson would also be the wealth maximizing alternative for risk averse firms as long as the risk of abandonment by arson is equal to or less than the risk of continued operation or the risk of abandonment by legitimate means. I The same conclusions hold even if the risk of arson exceeds the risks of continued operation or legitimate abandonment as long as the expected returns of arson are sufficiently large to offset the increased risks of arson. (See Cloninger, 1985).

Cloninger (1981) implies that the decision to abandon an asset by arson is made only after deciding to abandon the asset per se. This sequence is not required. Arson will be the wealth maximizing decision even though abandonment by other means is not financially justifiable as long as the risk adjusted present value of arson abandonment is greater than that of continued operation. That is, abandonment by arson may be justified even when abandonment by legitimate methods is not.

The arson offense rate model specified in the 1981 article is given by:

R = K Abl Bb2 Eb3 Qb4 eXp(U) 1)

where R = Arson rate; K = Constant; A = Objective probability of

arrest for arson; B = Business profit rate; E = Business failure rate and

Q = Property crime (burglary) rate.

As the 1981 article notes, the insured value of assets is their replacement value which, for most assets, is normally less than their going concern or market value. If the market value of assets exceeds their replacement value, the likelihood that the assets will be abandoned by arson diminishes. That is, if the present value of their future cash flows from operations exceeds the present value of the cash flow that would be generated by their piecemeal liquidation, the assets are less likely to be destroyed and their insured value claimed. On the other hand, if their market value is less than their replacement value, there is greater incentive to abandon them by arson. It would, therefore, be expected that the arson rate would vary inversely with the ratio of market value to replacement value of assets generally. This ratio is the familiar Tobin q. Because of the potential importance of this ratio in explaining arson offense rates, the earlier model is revised to include the q ratio (T). The model is now given by:

R = K Abl Bb2 Eb3 Qb4 Tb5 exp(u). (2)

The revised model is tested utilizing a sample that is approximately twice the size of the 1981 sample. Data are now available for the years 1964 - 1987 with the exception of 1976 when, for lack of reliable data, the National Fire Protection Association declined to publish or report the incidence of arson. Arson arrests and the burglary rate are obtained from the Uniform Crime Reports published by the FBI. The business failure rate is obtained from Dun and Bradstreet while the business profit rate (return on equity for the Standard and Poor 400) and Tobin's q (the market value of firms divided by the replacement value of their assets) is provided by the research department of Goldman, Sachs and Company.

Empirical tests replicating the same log-linear OLS regression technique used in the 1981 test are employed and the results are given in Table I along with the empirical results of the 1981 model.

The empirical results are consistent with the 1981 model and support the inclusion of Tobin's q as an explanatory variable. The sign of the coefficient for T is consistent with a priori expectations and is significant beyond the 001 level. The coefficient indicates, ceteris paribus, that the percentage change in the arson rate is just over half the change in the q ratio. …

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