Consistency and Monotonicity in One-Sided Assignment Problems

One-sided assignment problems combine important features of two well-known matching models. First, as in roommate problems, any two agents can be matched and second, as in two-sided assignment problems, the payoffs of a matching can be divided between the agents. We take a similar approach to one-sided assignment problems as Sasaki (1995) for two-sided assignment problems and we analyze various desirable properties of solutions including consistency and weak pairwise-monotonicity. We show that for the class of solvable one-sided assignment problems (i.e., the subset of one-sided assignment problems with a non-empty core), if a subsolution of the core satisfies [indifference with respect to dummy agents, continuity, and consistency] or [Pareto indifference and consistency], then it coincides with the core (Theorems 1 and 2). However, we also prove that on the class of all one-sided assignment problems (solvable or not), no solution satisfies consistency and coincides with the core whenever the core is non-empty (Theorem 3). Finally, we comment on the difficulty in obtaining further positive results for the class of solvable one-sided assignment problems in line with Sasaki's (1995) characterizations of the core for two-sided assignment problems.(One-sided) assignment problems, consistency, core, matching.

Consistency in one-sided assignment problems

One-sided assignment problems combine important features of two well-known matching models. First, as in roommate problems, any two agents can be matched and second, as in two-sided assignment problems, the division of payoffs to agents is flexible as part of the solution. We take a similar approach to one-sided assignment problems as Sasaki (Int J Game Theory 24:373-397, 1995) for two-sided assignment problems, and we analyze various desirable properties of solutions including consistency and weak pairwise-monotonicity. We show that for the class of solvable one-sided assignment problems (i.e., the subset of one-sided assignment problems with a non-empty core), if a subsolution of the core satisfies [Pareto indifference and consistency] or [invariance with respect to unmatching dummy pairs, continuity, and consistency], then it coincides with the core (Theorems 1 and 2). However, we also prove that on the class of all one-sided assignment problems (solvable or not), no solution satisfies consistency and coincides with the core whenever the core is non-empty (Theorem 4). Finally, we comment on the difficulty in obtaining further positive results for the class of solvable one-sided assignment problems in line with Sasaki's (1995) characterizations of the core for two-sided assignment problem

Financial literacy and mortgage equity withdrawals

The recent U.S. consumption boom and the subsequent surge in mortgage defaults have been linked to mortgage equity withdrawals (MEWs). MEWs are correlated with covariates consistent with a permanent income framework augmented for credit-constraints. Nevertheless, many households are financially illiterate. We assess the unexplored linkages between “active MEW” and measures of financial literacy using panel data from the Health and Retirement Study (HRS). Findings indicate that declines in mortgage interest rates encouraged MEWs. Nevertheless, financially illiterate households were significantly more likely to withdraw housing equity via traditional first or second mortgages (including cash-out mortgage refinancings but not home equity loans).> ; We find that the financially less savvy are 3–5 percentage points more likely to engage in this type of MEW relative to those who answered financial literacy questions correctly. Also significant were state differences in debtor versus creditor interests in bankruptcy, with loan demand effects outweighing loan supply effects across states.Consumption (Economics) - United States ; Credit control

Private Information in Large Games

Nash equilibrium, ex-post Nash,anonymous games, market games, rational expectations, extensive robustness, information proofness, web games

Labor Force Participation and Crime among Serious and Violent Former Prisoners

This project examines the relationship between work and crime among male former prisoners. Criminological theories and observational studies suggest that work reduces crime, but recent studies cast doubt on the ability of employment programs to reduce recidivism among former prisoners. Ongoing weak evaluations may imperil support for employment-focused rehabilitative programming. Using data from the Serious and Violent Offender Reentry Initiative (n = 1,575), this study examines whether selection bias and unobserved heterogeneity contribute to weak evaluation findings. First, this study tests whether unobserved heterogeneity contributes to jobs programs\u27 weak treatment effects. It uses group-based trajectory modeling and propensity score methods to balance participants and nonparticipants on demographic and criminal risk factors. Lifetime arrest data from administrative records are used to model respondents\u27 prior offending trajectories. Baseline interview data are used to balance respondents on the propensity to receive employment-focused services. After balancing respondents, this study employs duration models to test the effects of educational and employment programming on time to rearrest. Second, this study tests whether financial problems mediate the work-crime relationship. Longitudinal structural equation modeling is used to model men\u27s labor force attachment, job quality, financial needs, and emotional wellbeing. Models test whether financial problems diminish the crime-reducing effects of employment for men who remain weakly attached to the labor force. Multiple indicators for each latent construct reduce bias due to measurement error. Results of this study show that education and employment programs in United States prisons have limited effects on the likelihood that participants maintain employment and avoid criminal justice involvement. Male prisoners recruited into the Serious and Violent Offender Reentry Initiative faced multiple barriers to employment before entering prison, due to extensive criminal records, low educational attainment, and limited work experience. Before matching men on the probability of receiving employment-focused services, program participants differed from nonparticipants across an array of demographic and risk factors. The group-based trajectory model derived three latent trajectory groups from the sample that exhibited distinctive demographic characteristics and pre-prison offending trajectories. Due to significant variation at the state-level, a multilevel logit model was used to model the probability of receiving education and employment services. Nearest neighbor matching with caliper resulted in a sample that exhibited balance across multiple demographic, criminal record, employment, and health measures. After matching, employment program participants were slightly more likely than education participants and nonparticipants to maintain stable employment, and employment program participants exhibited lower rates of rearrest during the first 9 months after release. After that point, there were no significant differences between employment-focused program participants and nonparticipants in labor force and criminal activity. The longitudinal structural equation model results show that criminal activity has cascading effects on financial and emotional wellbeing, subsequent labor force activity, and ongoing criminal justice involvement. Engagement in crime during the early months of release reduced labor force participation, limited men\u27s ability to obtain higher-quality employment, and increased their financial needs and feelings of psychological distress. In contrast, stable employment led to improved job quality and reduced financial needs over time. Employment did not reduce men\u27s later involvement in criminal activity, however. In fact, employment during the first 9 months of release was associated with increased odds of reporting committing new crimes during the subsequent 6-month period. Overall, the path model results provide no evidence to suggest that stable employment reduces criminal activity among serious and violent former prisoners. The results of this study cast doubt on theories of crime that presuppose causal associations between work and crime. Observational studies that show associations between stable labor force participation and desistance from crime may be capturing maturation effects that simultaneously directed individuals toward legal work and away from crime. If desistance from crime actually precedes stable labor force attachment for most former prisoners, this may explain the weak empirical evidence for prison-based employment programs. The findings may inform modifications to employment and transitional jobs programs to identify participants on the path to desistance who may be most responsive to these services

Influence of Context on Item Parameters in Forced-Choice Personality Assessments

A fundamental assumption in computerized adaptive testing (CAT) is that item parameters are invariant with respect to context – items surrounding the administered item. This assumption, however, may not hold in forced-choice (FC) assessments, where explicit comparisons are made between items included in the same block. We empirically examined the influence of context on item parameters by comparing parameter estimates from two FC instruments. The first instrument was compiled of blocks of three items, whereas in the second, the context was manipulated by adding one item to each block, resulting in blocks of four. The item parameter estimates were highly similar. However, a small number of significant deviations were observed, confirming the importance of context when designing adaptive FC assessments. Two patterns of such deviations were identified, and methods to reduce their occurrences in a FC CAT setting were proposed. It was shown that with a small proportion of violations of the parameter invariance assumption, score estimation remained stable