Flocking with discrete symmetry: the 2d Active Ising Model

We study in detail the active Ising model, a stochastic lattice gas where collective motion emerges from the spontaneous breaking of a discrete symmetry. On a 2d lattice, active particles undergo a diffusion biased in one of two possible directions (left and right) and align ferromagnetically their direction of motion, hence yielding a minimal flocking model with discrete rotational symmetry. We show that the transition to collective motion amounts in this model to a bona fide liquid-gas phase transition in the canonical ensemble. The phase diagram in the density/velocity parameter plane has a critical point at zero velocity which belongs to the Ising universality class. In the density/temperature "canonical" ensemble, the usual critical point of the equilibrium liquid-gas transition is sent to infinite density because the different symmetries between liquid and gas phases preclude a supercritical region. We build a continuum theory which reproduces qualitatively the behavior of the microscopic model. In particular we predict analytically the shapes of the phase diagrams in the vicinity of the critical points, the binodal and spinodal densities at coexistence, and the speeds and shapes of the phase-separated profiles.Comment: 20 pages, 25 figure

Two-Sample Instrumental Variables Estimators

Following an influential article by Angrist and Krueger (1992) on two-sample instrumental variables (TSIV) estimation, numerous empirical researchers have applied a computationally convenient two-sample two-stage least squares (TS2SLS) variant of Angrist and Krueger's estimator. In the two-sample context, unlike the single-sample situation, the IV and 2SLS estimators are numerically distinct. Our comparison of the properties of the two estimators demonstrates that the commonly used TS2SLS estimator is more asymptotically efficient than the TSIV estimator and also is more robust to a practically relevant type of sample stratification.

The Intuitive Appeal of Explainable Machines

Algorithmic decision-making has become synonymous with inexplicable decision-making, but what makes algorithms so difficult to explain? This Article examines what sets machine learning apart from other ways of developing rules for decision-making and the problem these properties pose for explanation. We show that machine learning models can be both inscrutable and nonintuitive and that these are related, but distinct, properties. Calls for explanation have treated these problems as one and the same, but disentangling the two reveals that they demand very different responses. Dealing with inscrutability requires providing a sensible description of the rules; addressing nonintuitiveness requires providing a satisfying explanation for why the rules are what they are. Existing laws like the Fair Credit Reporting Act (FCRA), the Equal Credit Opportunity Act (ECOA), and the General Data Protection Regulation (GDPR), as well as techniques within machine learning, are focused almost entirely on the problem of inscrutability. While such techniques could allow a machine learning system to comply with existing law, doing so may not help if the goal is to assess whether the basis for decision-making is normatively defensible. In most cases, intuition serves as the unacknowledged bridge between a descriptive account and a normative evaluation. But because machine learning is often valued for its ability to uncover statistical relationships that defy intuition, relying on intuition is not a satisfying approach. This Article thus argues for other mechanisms for normative evaluation. To know why the rules are what they are, one must seek explanations of the process behind a model’s development, not just explanations of the model itself

Earnings Dynamics and Inequality among Canadian Men, 1976-1992: Evidence from Longitudinal Income Tax Records

Several recent studies have found that earnings inequality in Canada has grown considerably since the late 1970's. Using an extraordinary data base drawn from longitudinal income tax records, we decompose this growth in earnings inequality into its persistent and transitory components. We find that the growth in earnings inequality reflects both an increase in long-run inequality and an increase in earnings instability. The large size of our earnings panel allows us to estimate and test richer models of earnings dynamics than could be supported by the relatively small panel surveys used in U.S. research. The Canadian data strongly reject several restrictions commonly imposed in the U.S. literature, and they also suggest that imposing these evidently false restrictions may lead to distorted inferences about earnings dynamics and inequality trends.

Wage Bargaining, Labor Turnover, and the Business Cycle: A Model with Asymmetric Information

This paper presents a wage bargaining model in which the employer and employee are each uncertain about the other's reservation wage. Under specified circumstances, the model's equilibrium is shown to involve unilateral wage setting and inefficient labor turnover. In addition, aggregate demand shocks affect the equilibrium in a way that produces procyclical quits and countercyclical layoffs.These results are obtained without resorting to assumptions of nominal wage rigidity, long-term contracting, or aggregate price misperceptions.

Life-Cycle Variation in the Association between Current and Lifetime Earnings

Researchers in a variety of important economic literatures have assumed that current income variables as proxies for lifetime income variables follow the textbook errors-in-variables model. In an analysis of Social Security records containing nearly career-long earnings histories for the Health and Retirement Study sample, we find that the relationship between current and lifetime earnings departs substantially from the textbook model in ways that vary systematically over the life cycle. Our results can enable more appropriate analysis of and correction for errors-in-variables bias in a wide range of research that uses current earnings to proxy for lifetime earnings.

Phase transition in protocols minimizing work fluctuations

For two canonical examples of driven mesoscopic systems - a harmonically-trapped Brownian particle and a quantum dot - we numerically determine the finite-time protocols that optimize the compromise between the standard deviation and the mean of the dissipated work. In the case of the oscillator, we observe a collection of protocols that smoothly trade-off between average work and its fluctuations. However, for the quantum dot, we find that as we shift the weight of our optimization objective from average work to work standard deviation, there is an analog of a first-order phase transition in protocol space: two distinct protocols exchange global optimality with mixed protocols akin to phase coexistence. As a result, the two types of protocols possess qualitatively different properties and remain distinct even in the infinite duration limit: optimal-work-fluctuation protocols never coalesce with the minimal work protocols, which therefore never become quasistatic.Comment: 6 pages, 6 figures + SI as ancillary fil

Earnings Dynamics and Inequality among Canadian Men, 1976-1992: Evidence from Longitudinal Income Tax Records

Several recent studies have found that earnings inequality in Canada has grown considerably since the late 1970's. Using an extraordinary data base drawn from longitudinal income tax records, we decompose this growth in earnings inequality into its persistent and transitory components. We find that the growth in earnings inequality reflects both an increase in long-run inequality and an increase in earnings instability. Our large sample size enables us to estimate and test richer models than could be supported by the relatively small panel surveys used in most previous research on earnings dynamics. For example, we are able to incorporate both heterogeneous earnings growth and a random-walk process in the same model, and we find that both are empirically significant.

A Portmanteau Test for Serially Correlated Errors in Fixed Effects Models

We propose a portmanteau test for serial correlation of the error term in a fixed effects model. The test is derived as a conditional Lagrange multiplier test, but it also has a straightforward Wald test interpretation. In Monte Carlo experiments, the test displays good size and power properties.