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REVISION: Anthropocene Agricultural Law
(April 21, 2016)
Agricultural controversies in affluent, comfortably fed countries increasingly emphasize the esthetic or expressive elements of food. Consumer advocates can indulge in litigation over foie gras, for instance, or coffee production certification. This expressive turn elevates the ornamental aspects of food at the expense of agriculture's utilitarian purposes. The modernist principles articulated in Adolf Loos's "Ornament und Verbrechung" urge the subordination of agriculture's ornamental aspects in favor of its original instrumentalist underpinnings.
Meanwhile, ecological disaster looms. Human ecological impacts are so severe that geological history has arguably entered a new epoch, the Anthropocene. Exhaustion of vital inputs (petroleum, phosphorus) and evolutionary calamity (mass extinctions, herbicide and pesticide resistance) threatens future agricultural productivity. Food security and the economic foundations of civilization hang precariously in the balance.
Human beings, ...
New: Legal Quanta: A Mathematical Romance of Many Dimensions
(April 7, 2016)
Many things can be measured and expressed numerically. Nature speaks in the language of mathematics. Mathematical analysis of law is often associated with the application of established empirical techniques to ever-growing bodies of legal data. Other distinct applications of mathematics to law include machine learning, legal networks, and analytical modeling. Mathematical analysis of law ultimately follows not only the data describing the legal world as we find it, but also the own internal logic of mathematics.
REVISION: Inflation-Based Adjustments in Federal Civil Monetary Penalties
(April 7, 2016)
Civil monetary penalties play a vital role in federal law. The Federal Civil Penalties Inflation Adjustment Act of 1990, Pub. L. No. 101-410, prescribes rules for the regular adjustment of federal civil monetary penalties in response to inflation. Three statutory defects have undermined the Inflation Adjustment Act. First, the Act's 10 percent cap on initial adjustments creates an "inflation gap" relative to the level that would properly reflect inflation. Second, the Act directs federal agencies to use Consumer Price Index data that are at least 7 months and as many as 18 months out of date. This creates "CPI lag" in the adjustment of civil monetary penalties. Third, the Act's rounding rules can force some agencies to wait 15 years or more between adjustments.
Originally prepared as a report for the Administrative Conference of the United States, this article examines the Inflation Adjustment Act and recommends possible legislative remedies for the Act's defects.
REVISION: Scholarships at Risk: The Mathematics of Merit Stipulations in Financial Aid Awards
(March 14, 2016)
Many law schools in the United States condition financial aid grants on the recipients’ maintenance of a certain grade point average. These merit stipulations require students to meet or exceed minimum academic standards in order to keep all or part of their financial aid. Law students should take merit stipulations into account when they decide whether to accept an offer of admission paired with a conditional grant of financial aid. By all accounts, they do not. Law schools should transparently disclose the likely effect of merit stipulations on their financial aid awards. By all accounts, law schools do no such thing. Absent external coercion, they are unlikely to change their current practices. In the absence of industry-wide standards counseling full disclosure of financial aid practices, this article will try to equip law school applicants with the mathematical tools to assess the real impact of merit stipulations on their financial well being.
This article first presents very ...
REVISION: Momentary Lapses of Reason: The Psychophysics of Law and Behavior
(February 22, 2016)
The conventional capital asset pricing model (CAPM) remains the preferred approach to risk management in a wide range of economic settings. At the same time, the neoclassical assumptions underlying the CAPM have come under severe attack by behavioral economics. In sharp contrast with the purely rational agents of neoclassical economics, real humans make decisions under the constraints imposed by their innate heuristics. The tension between conventional asset pricing theory and behavioral economics puts particular pressure on law. As an applied branch of social science, law purports to subject human conduct to rules that should optimize objective well-being as well as subjective satisfaction.
This paper proposes a mathematically expedient method of alleviating this tension. A four-moment capital asset pricing model captures the emotional impact of odd and even moments of statistical distributions. Critically, a four-moment CAPM transcends the limits of financial models that ...
New: Fables of the Reconstruction: Human Emotion and Behavioral Heuristics in Environmental Economics
(December 19, 2015)
Environmental economics provides an especially rich source of insights into the impact of emotion, cognitive bias, and behavioral heuristics on risk assessment and management. In contrast with the ambivalent reception of behavioral psychology within mathematical finance, the impact of emotion and innate heuristics on environmental decision making has never been doubted. From the affect heuristic to the endowment effect and disaster psychology, environmental choices harbor the richest trove of economic departures from strict rationality.
REVISION: Indexing Inflation: The Impact of Methodology on Econometrics and Macroeconomic Policy
(October 8, 2015)
Because there is no perfect gauge of inflation, the macroeconomic enterprise of indexing inflation ultimately dissolves into a choice among imperfect methodologies. But that choice still matters. This article will highlight the practical significance of methodological choices made in the course of indexing inflation. It will focus on two different indexes of inflation in the United States: the Consumer Price Index (CPI) and the implicit price deflator of the gross domestic product (IPD). This article identifies a long-term gap in these competing indexes’ measurement of inflation. To explain why the CPI appears to overstate inflation, relative to the IPD, by roughly two-thirds of a percentage point each year, this article more fully describes the distinct methodologies underlying the CPI and the IPD. Lawmakers should adopt the implicit price deflator of the GDP, or some other inflation index that shares its best methodological features, as the best practicable measure of real ...
REVISION: Leaps, Metes, and Bounds: Innovation Law and Its Logistics
(October 8, 2015)
Economic analysis of technological innovation, diffusion, and decline often proceeds according to sigmoid (S-shaped) models, either directly or as a component in more elaborate mathematical representations of the creative process. Three distinct aspects of American innovation policy — Aereo’s failed attempt to retransmit television broadcasts, agricultural biotechnology, and network neutrality — invite analysis according to one variant or another of the logistic function. Innovation and legal policies designed to foster it follow the leaps, metes, and bounds of sigmoid functions.
Part I introduces the logistic function as the simplest analytical expression of a sigmoid function. Its parameters provide very clear interpretations grounded in physical principles. Part II evaluates the Aereo controversy and agricultural biotechnology as instances of logistic substitution between competing products. The deployment of plant-incorporated pesticides and herbicide-resistant crops ...
New: Law on the Market? Evaluating the Securities Market Impact of Supreme Court Decisions
(August 24, 2015)
Do judicial decisions affect the securities markets in discernible and perhaps predictable ways? In other words, is there “law on the market” (LOTM)? This is a question that has been raised by commentators, but answered by very few in a systematic and financially rigorous manner. Using intraday data and a multiday event window, this large scale event study seeks to determine the existence, frequency and magnitude of equity market impacts flowing from Supreme Court decisions.
We demonstrate that, while certainly not present in every case, "law on the market" events are fairly common. Across all cases decided by the Supreme Court of the United States between the 1999-2013 terms, we identify 79 cases where the share price of one or more publicly traded company moved in direct response to a Supreme Court decision. In the aggregate, over fifteen years, Supreme Court decisions were responsible for more than 140 billion dollars in absolute changes in wealth. Our analysis not only ...
REVISION: Sinking, Fast and Slow: Bifurcating Beta in Financial and Behavioral Space
(August 2, 2015)
Modern portfolio theory accords symmetrical treatment to all deviations from expected return, positive or negative. This assumption is vulnerable on both descriptive and behavioral grounds. Many of the predictive flaws in contemporary finance stem from mathematically elegant but empirically flawed Gaussian models. In reality, returns are skewed. The presumption that returns and volatility are symmetrical also defies human behavior. Losing hurts worse than winning feels good; investors do not react equally to upside gain and downside loss. Moreover, correlation tightening during bear markets, not offset by changes in correlation during bull markets, suggest that standard diversification strategies may erode upside returns without providing adequate protection during times of stress.
This article outlines mathematical tools for calculating volatility, variance, covariance, correlation, and beta, not merely across the entire spectrum of returns, but also on either side of mean ...
REVISION: The Promise and the Peril of Parametric Value-at-Risk (VaR) Analysis
(July 8, 2015)
Leptokurtosis, or the risk lurking in “fat tails,” poses the deepest epistemic threat to economic forecasting. Parametric value-at-risk (VaR) models are extremely vulnerable to kurtosis in excess of the levels associated with a normal, Gaussian distribution. This article provides step-by-step guidance on the use of Student’s t-distribution to enhance the statistical robustness of VaR forecasts. For degrees of freedom greater than 4, Student’s t-distribution can emulate any level of kurtosis exceeding that of a Gaussian distribution. Because VaR is elicitable from historical data, observed levels of excess kurtosis can inform the proper use of Student’s t-distribution to measure value-at-risk. In addition, the calculation of parametric VaR according to the number of degrees of freedom implied by historical levels of excess kurtosis leads directly to the corresponding value of expected shortfall. Conducted in this fashion, parametric VaR not only exploits the elicitability of that ...
New: Legal Signal Processing
(June 4, 2015)
It makes far more economic sense to prepare for disaster in advance than it does to stage heroic relief efforts after calamity strikes. For reasons rooted in politics and emotion, the law does exactly the opposite. Ad hoc relief, as expensive as it is spontaneous, dominates disaster law and policy.
The President’s unilateral power to declare a federal disaster under the Stafford Act invites political manipulation. To test whether presidential disaster declarations track the four-year presidential electoral cycle, this paper devises a generalized polynomial and multi-sinusoidal model for detecting cyclical patterns. This model draws heavily upon Fourier analysis and digital signal processing.
Presidential disaster declarations since 1953 reveal not one but two forms of periodicity. As expected, a “short wave” of four years shows how disaster declarations track the presidential election cycle. The effect is most pronounced not in election years (when declarations do spike), but in ...
New: Gini's Crossbow
(May 21, 2015)
The Gini coefficient remains a popular gauge of inequality throughout the social and natural sciences because it is visually striking and geometrically intuitive. It measures the “gap” between a hypothetically equal distribution of income or wealth and the actual distribution. But not all inequality curves yielding the same Gini coefficient are unequal in the same way. The Lorenz asymmetry coefficient, a second-order measure of asymmetry, provides further information about the distribution of income or wealth. To add even more interpretive power, this paper proposes a new angular measure derived from the Lorenz asymmetry coefficient. Adjusted azimuthal asymmetry is the angular distance of the Lorenz asymmetry coefficient from the axis of symmetry, divided by the maximum angular distance that can be attained for any given Gini coefficient.