Endogenous Credit Cycles and Financial Dampening in an Adverse Selection Economy

We propose an adverse selection framework in which the financial sector has a dual role. It amplifies or dampens exogenous shocks and also generates endogenous fluctuations. We fully characterize constrained optimal contracts in a setting in which entrepreneurs need to borrow and are privately informed about the quality of their projects. Our characterization is novel in analyzing pooling and separating allocations in a context of multi-dimensional screening: specifically, the amounts of investment undertaken and of entrepreneurial net worth are used to screen projects. We then embed these results in a dynamic competitive economy. First, we show how endogenous regime switches in financial contracts may generate fluctuations in an economy that exhibits no dynamics under full information. Unlike previous models of endogenous cycles, our result does not rely on entrepreneurial net worth being counter-cyclical or inconsequential for determining investment. Secondly, the model shows the different implications of adverse selection as opposed to pure moral hazard. In particular, and contrary to standard results in the macroeconomic literature, the financial system may dampen exogenous shocks in the presence of adverse selection.

Revenue management under general discrete choice model of consumer behavior

Customer choice behavior, such as 'buy-up' and 'buy-down', is an importantphe-nomenon in a wide range of industries. Yet there are few models ormethodologies available to exploit this phenomenon within yield managementsystems. We make some progress on filling this void. Specifically, wedevelop a model of yield management in which the buyers' behavior ismodeled explicitly using a multi-nomial logit model of demand. Thecontrol problem is to decide which subset of fare classes to offer ateach point in time. The set of open fare classes then affects the purchaseprobabilities for each class. We formulate a dynamic program todetermine the optimal control policy and show that it reduces to a dynamicnested allocation policy. Thus, the optimal choice-based policy caneasily be implemented in reservation systems that use nested allocationcontrols. We also develop an estimation procedure for our model based onthe expectation-maximization (EM) method that jointly estimates arrivalrates and choice model parameters when no-purchase outcomes areunobservable. Numerical results show that this combined optimization-estimation approach may significantly improve revenue performancerelative to traditional leg-based models that do not account for choicebehavior.

Adaptive model selection using empirical complexities

Given $n$ independent replicates of a jointly distributed pair $(X,Y)\in {\cal R}^d \times {\cal R}$, we wish to select from a fixed sequence of model classes ${\cal F}_1, {\cal F}_2, \ldots$ a deterministic prediction rule $f: {\cal R}^d \to {\cal R}$ whose risk is small. We investigate the possibility of empirically assessingthe {\em complexity} of each model class, that is, the actual difficulty of the estimation problem within each class. The estimated complexities are in turn used to define an adaptive model selection procedure, which is based on complexity penalized empirical risk.The available data are divided into two parts. The first is used to form an empirical cover of each model class, and the second is used to select a candidate rule from each cover based on empirical risk. The covering radii are determined empirically to optimize a tight upper bound on the estimation error. An estimate is chosen from the list of candidates in order to minimize the sum of class complexity and empirical risk. A distinguishing feature of the approach is that the complexity of each model class is assessed empirically, based on the size of its empirical cover.Finite sample performance bounds are established for the estimates, and these bounds are applied to several non-parametric estimation problems. The estimates are shown to achieve a favorable tradeoff between approximation and estimation error, and to perform as well as if the distribution-dependent complexities of the model classes were known beforehand. In addition, it is shown that the estimate can be consistent,and even possess near optimal rates of convergence, when each model class has an infinite VC or pseudo dimension.For regression estimation with squared loss we modify our estimate to achieve a faster rate of convergence.

Risk management under a two-factor model of the term structure of interest rates

This paper presents several applications to interest rate risk managementbased on a two-factor continuous-time model of the term structure of interestrates previously presented in Moreno (1996). This model assumes that defaultfree discount bond prices are determined by the time to maturity and twofactors, the long-term interest rate and the spread (difference between thelong-term rate and the short-term (instantaneous) riskless rate). Several newmeasures of ``generalized duration" are presented and applied in differentsituations in order to manage market risk and yield curve risk. By means ofthese measures, we are able to compute the hedging ratios that allows us toimmunize a bond portfolio by means of options on bonds. Focusing on thehedging problem, it is shown that these new measures allow us to immunize abond portfolio against changes (parallel and/or in the slope) in the yieldcurve. Finally, a proposal of solution of the limitations of conventionalduration by means of these new measures is presented and illustratednumerically.

A model of collateral, investment and adverse selection

This paper characterizes the relationship between entrepreneurial wealth and aggregate investmentunder adverse selection. Its main finding is that such a relationship need not bemonotonic. In particular, three results emerge from the analysis: (i) pooling equilibria, in whichinvestment is independent of entrepreneurial wealth, are more likely to arise when entrepreneurialwealth is relatively low; (ii) separating equilibria, in which investment is increasing inentrepreneurial wealth, are most likely to arise when entrepreneurial wealth is relatively highand; (iii) for a given interest rate, an increase in entrepreneurial wealth may generate a discontinuousfall in investment.

Model selection and error estimation

We study model selection strategies based on penalized empirical loss minimization. We point out a tight relationship between error estimation and data-based complexity penalization: any good error estimate may be converted into a data-based penalty function and the performance of the estimate is governed by the quality of the error estimate. We consider several penalty functions, involving error estimates on independent test data, empirical {\sc vc} dimension, empirical {\sc vc} entropy, andmargin-based quantities. We also consider the maximal difference between the error on the first half of the training data and the second half, and the expected maximal discrepancy, a closely related capacity estimate that can be calculated by Monte Carlo integration. Maximal discrepancy penalty functions are appealing for pattern classification problems, since their computation is equivalent to empirical risk minimization over the training data with some labels flipped.

Reproductive and post-reproductive life history of wild-caught Drosophila melanogaster under laboratory conditions.

The life history of the fruit fly (Drosophila melanogaster) is well understood, but fitness components are rarely measured by following single individuals over their lifetime, thereby limiting insights into lifetime reproductive success, reproductive senescence and post-reproductive lifespan. Moreover, most studies have examined long-established laboratory strains rather than freshly caught individuals and may thus be confounded by adaptation to laboratory culture, inbreeding or mutation accumulation. Here, we have followed the life histories of individual females from three recently caught, non-laboratory-adapted wild populations of D. melanogaster. Populations varied in a number of life-history traits, including ovariole number, fecundity, hatchability and lifespan. To describe individual patterns of age-specific fecundity, we developed a new model that allowed us to distinguish four phases during a female's life: a phase of reproductive maturation, followed by a period of linear and then exponential decline in fecundity and, finally, a post-ovipository period. Individual females exhibited clear-cut fecundity peaks, which contrasts with previous analyses, and post-peak levels of fecundity declined independently of how long females lived. Notably, females had a pronounced post-reproductive lifespan, which on average made up 40% of total lifespan. Post-reproductive lifespan did not differ among populations and was not correlated with reproductive fitness components, supporting the hypothesis that this period is a highly variable, random 'add-on' at the end of reproductive life rather than a correlate of selection on reproductive fitness. Most life-history traits were positively correlated, a pattern that might be due to genotype by environment interactions when wild flies are brought into a novel laboratory environment but that is unlikely explained by inbreeding or positive mutational covariance caused by mutation accumulation.

The stationary distribution of a continuously varying strategy in a class-structured population under mutation-selection-drift balance.

Many traits and/or strategies expressed by organisms are quantitative phenotypes. Because populations are of finite size and genomes are subject to mutations, these continuously varying phenotypes are under the joint pressure of mutation, natural selection and random genetic drift. This article derives the stationary distribution for such a phenotype under a mutation-selection-drift balance in a class-structured population allowing for demographically varying class sizes and/or changing environmental conditions. The salient feature of the stationary distribution is that it can be entirely characterized in terms of the average size of the gene pool and Hamilton's inclusive fitness effect. The exploration of the phenotypic space varies exponentially with the cumulative inclusive fitness effect over state space, which determines an adaptive landscape. The peaks of the landscapes are those phenotypes that are candidate evolutionary stable strategies and can be determined by standard phenotypic selection gradient methods (e.g. evolutionary game theory, kin selection theory, adaptive dynamics). The curvature of the stationary distribution provides a measure of the stability by convergence of candidate evolutionary stable strategies, and it is evaluated explicitly for two biological scenarios: first, a coordination game, which illustrates that, for a multipeaked adaptive landscape, stochastically stable strategies can be singled out by letting the size of the gene pool grow large; second, a sex-allocation game for diploids and haplo-diploids, which suggests that the equilibrium sex ratio follows a Beta distribution with parameters depending on the features of the genetic system.

Postglacial recolonization at a snail's pace (Trochulus villosus): confronting competing refugia hypotheses using model selection.

The localization of Last Glacial Maximum (LGM) refugia is crucial information to understand a species' history and predict its reaction to future climate changes. However, many phylogeographical studies often lack sampling designs intensive enough to precisely localize these refugia. The hairy land snail Trochulus villosus has a small range centred on Switzerland, which could be intensively covered by sampling 455 individuals from 52 populations. Based on mitochondrial DNA sequences (COI and 16S), we identified two divergent lineages with distinct geographical distributions. Bayesian skyline plots suggested that both lineages expanded at the end of the LGM. To find where the origin populations were located, we applied the principles of ancestral character reconstruction and identified a candidate refugium for each mtDNA lineage: the French Jura and Central Switzerland, both ice-free during the LGM. Additional refugia, however, could not be excluded, as suggested by the microsatellite analysis of a population subset. Modelling the LGM niche of T. villosus, we showed that suitable climatic conditions were expected in the inferred refugia, but potentially also in the nunataks of the alpine ice shield. In a model selection approach, we compared several alternative recolonization scenarios by estimating the Akaike information criterion for their respective maximum-likelihood migration rates. The 'two refugia' scenario received by far the best support given the distribution of genetic diversity in T. villosus populations. Provided that fine-scale sampling designs and various analytical approaches are combined, it is possible to refine our necessary understanding of species responses to environmental changes.

Stationary states and phase diagram for a model of the Gunn effect under realistic boundary conditions

A general formulation of boundary conditions for semiconductor-metal contacts follows from a phenomenological procedure sketched here. The resulting boundary conditions, which incorporate only physically well-defined parameters, are used to study the classical unipolar drift-diffusion model for the Gunn effect. The analysis of its stationary solutions reveals the presence of bistability and hysteresis for a certain range of contact parameters. Several types of Gunn effect are predicted to occur in the model, when no stable stationary solution exists, depending on the value of the parameters of the injecting contact appearing in the boundary condition. In this way, the critical role played by contacts in the Gunn effect is clearly established.

Regression analysis of spatial data.

Many of the most interesting questions ecologists ask lead to analyses of spatial data. Yet, perhaps confused by the large number of statistical models and fitting methods available, many ecologists seem to believe this is best left to specialists. Here, we describe the issues that need consideration when analysing spatial data and illustrate these using simulation studies. Our comparative analysis involves using methods including generalized least squares, spatial filters, wavelet revised models, conditional autoregressive models and generalized additive mixed models to estimate regression coefficients from synthetic but realistic data sets, including some which violate standard regression assumptions. We assess the performance of each method using two measures and using statistical error rates for model selection. Methods that performed well included generalized least squares family of models and a Bayesian implementation of the conditional auto-regressive model. Ordinary least squares also performed adequately in the absence of model selection, but had poorly controlled Type I error rates and so did not show the improvements in performance under model selection when using the above methods. Removing large-scale spatial trends in the response led to poor performance. These are empirical results; hence extrapolation of these findings to other situations should be performed cautiously. Nevertheless, our simulation-based approach provides much stronger evidence for comparative analysis than assessments based on single or small numbers of data sets, and should be considered a necessary foundation for statements of this type in future.

APPRAISAL OF THE SNAP MODEL FOR PREDICTING NITROGEN MINERALIZATION IN TROPICAL SOILS UNDER EUCALYPTUS

The Soil Nitrogen Availability Predictor (SNAP) model predicts daily and annual rates of net N mineralization (NNM) based on daily weather measurements, daily predictions of soil water and soil temperature, and on temperature and moisture modifiers obtained during aerobic incubation (basal rate). The model was based on in situ measurements of NNM in Australian soils under temperate climate. The purpose of this study was to assess this model for use in tropical soils under eucalyptus plantations in São Paulo State, Brazil. Based on field incubations for one month in three, NNM rates were measured at 11 sites (0-20 cm layer) for 21 months. The basal rate was determined in in situ incubations during moist and warm periods (January to March). Annual rates of 150-350 kg ha-1 yr-1 NNM predicted by the SNAP model were reasonably accurate (R2 = 0.84). In other periods, at lower moisture and temperature, NNM rates were overestimated. Therefore, if used carefully, the model can provide adequate predictions of annual NNM and may be useful in practical applications. For NNM predictions for shorter periods than a year or under suboptimal incubation conditions, the temperature and moisture modifiers need to be recalibrated for tropical conditions.

Stationary states and phase diagram for a model of the Gunn effect under realistic boundary conditions

A general formulation of boundary conditions for semiconductor-metal contacts follows from a phenomenological procedure sketched here. The resulting boundary conditions, which incorporate only physically well-defined parameters, are used to study the classical unipolar drift-diffusion model for the Gunn effect. The analysis of its stationary solutions reveals the presence of bistability and hysteresis for a certain range of contact parameters. Several types of Gunn effect are predicted to occur in the model, when no stable stationary solution exists, depending on the value of the parameters of the injecting contact appearing in the boundary condition. In this way, the critical role played by contacts in the Gunn effect is clearly established.