Legal signal processing: A case study in the public financing of disaster relief

Financial preparedness for catastrophes is an essential component of disaster law.  Climate change will likely increase the scale and the probability of losses attributable to extreme environmental events.  In  "Correlation, Coverage, and Catastrophe," http://ssrn.com/abstract=2468361. I showed how governments, as a matter of behavioral economics and public choice theory, typically prefer politically salient, emotionally “heroic,” but financially ruinous disbursements for disaster relief.  Such profligate expenditures are almost always better directed toward disaster preparedness ex ante.

This paper also addresses a methodological shortcoming in conventional economic analyses of law.  Empirical analysis of law filters raw data in search of trends, patterns, and other insights.  Analytical techniques derived from engineering can reveal astonishing amounts of useful information that had been regarded (and therefore disregarded) as noise.

Time series pervade the law.  By and large, the law and economics movement has been content to analyze temporal effects according to some variant of the linear autoregressive model.  But inherently cyclical aspects of time demand nonlinear analysis.

This paper proposes a generalized approach to time series analysis in law.  Such an approach would combine linear or polynomial regression with spectral analysis.  One implication of the Taylor series is that the rigorous, systematic application of polynomial regressions, from linear to quadratic, cubic, and quartic fits, may reveal cyclical patterns more fruitfully evaluated through periodic regression.  Inspired in theory by Fourier analysis and in practice by digital signal processing, this paper outlines a systematic approach to time series that simultaneously exhibits linear and periodic effects.

Public finance of disaster relief in the United States illustrates these effects.  The President’s unilateral power to declare a federal disaster under the Stafford Act invites political manipulation.  Indeed, a single presidential disaster declaration appears to be worth one or two percentage points in the affected state.  To test whether disaster declarations coincide with presidential election years, I applied my time series analysis to the history of Presidential disaster declarations

The graphic posted at http://www.jurisdynamics.net/files/images/FourierDisasterDeclarationModel.png summarizes my results.  This parsimonious model consists of (1) one linear regression, (2) two third-order partial Fourier series, and (3) one parametric amplitude adjustment.  The resulting univariate time series achieves 75 percent accuracy in modeling presidential disaster declarations.  It confirms the presence of a four-year cycle, peaking in presidential election years.  Intriguingly, disaster declarations may also reflect a grand 44-year cycle evocative of Arthur Schlesinger's theory of generational ages in American politics.