Counting growth types of automorphisms of free groups

Given an automorphism of a free group $F_n$, we consider the following invariants: $e$ is the number of exponential strata (an upper bound for the number of different exponential growth rates of conjugacy classes); $d$ is the maximal degree of polynomial growth of conjugacy classes; $R$ is the rank of the fixed subgroup. We determine precisely which triples $(e,d,R)$ may be realized by an automorphism of $F_n$. In particular, the inequality e\le (3n-2)/4} (due to Levitt-Lustig) always holds. In an appendix, we show that any conjugacy class grows like a polynomial times an exponential under iteration of the automorphism.Comment: final version, to appear in GAFA; proof of 3.1 simplified thanks to the refere

Testing Theories of Discrimination: Evidence from "Weakest Link"

In most settings, it is difficult to measure discrimination, and even more challenging to distinguish between competing theories of discrimination (taste-based versus information-based). Using contestant voting behavior on the television game show Weakest Link, one can in principle empirically address both of these questions. On the show, contestants answer questions and vote off other players, competing for a winner-take-all prize. In early rounds, strategic incentives encourage voting for the weakest competitors. In later rounds, the incentives reverse, and the strongest competitors become the logical target. Controlling for other observable characteristics including the number of correct answers thus far, both theories of discrimination predict that in early rounds, excess votes will be made against groups targeted for discrimination. In later rounds, however, taste-based models predict continued excess votes, whereas statistical discrimination predicts fewer votes against the target group. Empirically, I find some evidence of information-based discrimination towards Hispanics (i.e., other players perceive them as having low ability) and taste-based discrimination against older players (i.e., other players treat them with animus). There is little in the data to suggest discrimination against women and Blacks.

Osteopathic Digest (September 1946)

The September 1946 issue of the Osteopathic Digest includes the following articles: The President\u27s Editorial There are Two Seas a Parabe by Bruce Barton The Osteopathic Foundation of Philadelphia Activities of the Faculty: College News P. C. O. Commencement October 18 Osteopathic Hospital Review and Forecast Student Activities Osteopathic Meetings On the Firing Line! Alexander Levitt, D. O. Activities of the P. C. O. Alumni in the Field Obituaryhttps://digitalcommons.pcom.edu/digest/1049/thumbnail.jp

Market Distortions when Agents are Better Informed: The Value of Information in Real Estate Transactions

Agents are often better informed than the clients who hire them and may exploit this informational advantage. Real-estate agents, who know much more about the housing market than the typical homeowner, are one example. Because real estate agents receive only a small share of the incremental profit when a house sells for a higher value, there is an incentive for them to convince their clients to sell their houses too cheaply and too quickly. We test these predictions by comparing home sales in which real estate agents are hired by others to sell a home to instances in which a real estate agent sells his or her own home. In the former case, the agent has distorted incentives; in the latter case, the agent wants to pursue the first-best. Consistent with the theory, we find homes owned by real estate agents sell for about 3.7 percent more than other houses and stay on the market about 9.5 days longer, even after controlling for a wide range of housing characteristics. Situations in which the agent's informational advantage is larger lead to even greater distortions.

An Empirical Analysis of Imprisoning Drug Offenders

The number of prisoners incarcerated on drug-related offenses rose fifteen-fold between 1980 and 2000. This paper provides the first systematic empirical analysis of the implications of that dramatic shift in public policy. We show that the increase in drug prisoners led to reductions in expected time served for other crimes, especially for less serious offenses. Reductions in time served, however, increased other crimes by no more than a few percent. Moreover, incarcerating drug offenders is found to be almost as effective in reducing violent and property crime as locking up other types of offenders. We estimate that cocaine prices are 10-15 percent higher today as a consequence of increases in drug punishment since 1985. Based on previous estimates of the price elasticity of demand for cocaine, this implies a reduction in cocaine consumed of as much as 20 percent.

An Economic Analysis of a Drug-Selling Gang's Finances

We analyze a unique data set detailing the financial activities of a drug-selling street gang on a monthly basis over a four-year period in the recent past. The data, originally compiled by the gang leader to aid in managing the organization, contain detailed information on both the sources of revenues (e.g. drug sales, extortion) and expenditrues (e.g. costs of drugs sold, weapons, tribute to the central gang organization, wages paid to various levels of the gang). Street-level drug dealing appears to be less lucrative than is generally though. We estimate the average wage in the organization to rise from roughly $6 per hour to$11 per hour over the time period studied. The distribution of wages, however, is extremely skewed. Gang leaders earn far more than they could in the legitimate sector, but the actual street-level dealers appear to earn less than the minimum wage throughout most of our sample, in spite of the substantial risks associated with such activities (the annual violent death rate in our sample is 0.07), There is some evidence consistent both with compensating differentials and efficiency wages. The markup on drugs suggests that the gang has substantial local market power. Gang wars appear to have an important strategic component: violence on another gang's turf shifts demand away from that area. The gang we observe responds to such attacks by pricing below marginal cost, suggesting either economic punishment for the rival gang or the presence of switching for users that makes market share maintenance valuable. We investigate a range of alternative methods for estimating the willingness of gang members to accept risks of death, all of which suggest that the implicit value that gang members place on their own lives is very low.

Rotten Apples: An Investigation of the Prevalence and Predictors of Teacher Cheating

We develop an algorithm for detecting teacher cheating that combines information on unexpected test score fluctuations and suspicious patterns of answers for students in a classroom. Using data from the Chicago Public Schools, we estimate that serious cases of teacher or administrator cheating on standardized tests occur in a minimum of 4-5 percent of elementary school classrooms annually. Moreover, the observed frequency of cheating appears to respond strongly to relatively minor changes in incentives. Our results highlight the fact that incentive systems, especially those with bright line rules, often induce behavioral distortions such as cheating. Statistical analysis, however, may provide a means of detecting illicit acts, despite the best attempts of perpetrators to keep them clandestine.

Catching Cheating Teachers: The Results of an Unusual Experiment in Implementing Theory

This paper reports on the results of a prospective implementation of methods for detecting teacher cheating. In Spring 2002, over 100 Chicago Public Schools elementary classrooms were selected for retesting based on the cheating detection algorithm. Classrooms prospectively identified as likely cheaters experienced large test score declines. In contrast, classes that had large test score gains on the original test, but were prospectively identified as being unlikely to have cheated, maintained their original gains. Randomly selected classrooms also maintained their gains. The cheating detection tools were thus demonstrated to be effective in distinguishing between classrooms that achieved large test-score gains as a consequence of cheating versus those whose gains were the result of outstanding teaching. In addition, the data generated by the implementation experiment highlight numerous ways in which the original cheating detection methods can be improved in the future.

Crime, Urban Flight, and the Consequences for Cities

This paper demonstrates that rising crime rates in cities are correlated with city depopulation. Instrumental variables estimates, using measures of the certainty and severity of a state?s criminal justice system as instruments for city crime rates, imply that the direction of causality runs from crime to urban flight. Using annual city-level panel data, our estimates suggest that each additional reported crime is associated with a one person decline in city residents. There is some evidence that increases in suburban crime tend to keep people in cities, although the magnitude of this effect is small. Analysis of individual-level data from the 1980 census confirms the city-level results and demonstrates that almost all of the crime-related population decline is attributable to increased outmigration rather than a decrease in new arrivals to a city. Those households that leave the city because of crime are much more likely to remain within the SMSA than those leaving the city for other reasons. The migration decisions of high-income households and those with children are much more responsive to changes in crime than other households. Crime-related mobility imposes costs on those who choose to remain in the city through declining property values and a shrinking tax base.