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.

Credit constraints, firms' precautionary investment and the business cycle

This paper studies the macroeconomic implications of firms' investment composition choices in the presence of credit constraints. Following a negative andpersistent aggregate productivity shock, firms shift into short-term investments because they produce more pledgeable output and because they help alleviate futureborrowing constraints. This produces a short-run dampening of the effects of theshock, at the expense of lower long-term investment and future output, relativeto an economy with no credit market imperfections. The effects are exacerbatedby a steepening of the term structure of interest rates that further encourages ashift towards short-term investments in the short-run. Small temporary shocks tothe severity of financing frictions generate large and long-lasting effects on outputthrough their impact on the composition of investment. A positive financial shockproduces much stronger effects than an identical negative shock, while the responsesto positive and negative shocks to aggregate productivity are roughly symmetric.Finally, the paper introduces a novel explanation for the countercyclicality of financing constraints of firms.

Asset pricing with idiosyncratic risk and overlapping generations

A number of existing studies have concluded that risk sharing allocations supported by competitive, incomplete markets equilibria are quantitatively close to first-best. Equilibrium asset prices in these models have been difficult to distinguish from those associated with a complete markets model, the counterfactual features of which have been widely documented. This paper asks if life cycle considerations, in conjunction with persistent idiosyncratic shocks which become more volatile during aggregate downturns, can reconcile the quantitative properties of the competitive asset pricing framework with those of observed asset returns. We begin by arguing that data from the Panel Study on Income Dynamics support the plausibility of such a shock process. Our estimates suggest a high degree of persistence as well as a substantial increase in idiosyncratic conditional volatility coincident with periods of low growth in U.S. GNP. When these factors are incorporated in a stationary overlapping generations framework, the implications for the returns on risky assets are substantial. Plausible parameterizations of our economy are able to generate Sharpe ratios which match those observed in U.S. data. Our economy cannot, however, account for the level of variability of stock returns, owing in large part to the specification of its production technology.

Entrepreneurial risk, investment and innovation

In this paper I develop a general equilibrium model with risk averse entrepreneurialfirms and with public firms. The model predicts that an increase in uncertainty reducesthe propensity of entrepreneurial firms to innovate, while it does not affect thepropensity of public firms to innovate. Furthermore, it predicts that the negativeeffect of uncertainty on innovation is stronger for the less diversified entrepreneurialfirms, and is stronger in the absence of financing frictions in the economy. In thesecond part of the paper I test these predictions on a dataset of small and mediumItalian manufacturing firms.

Risk dominance selects the leader. An experimental analysis

Coordination games arise very often in studies of industrial organization and international trade. This type of games has multiple strict equilibria, and therefore the identification of testable predictions isvery difficult. We study a vertical product differentiation model with two asymmetric players choosing first qualities and then prices. This game has two equilibria for some parameter values. However, we apply the risk dominance criterion suggested by Harsanyi and Selten and show that it always selects the equilibrium where the leader is the firm having some initial advantage. We then perform an experimental analysis totest whether the risk dominance prediction is supported by the behaviour oflaboratory agents. We show that the probability that the risk dominance prediction is right depends crucially on the degree of asymmetry of the game. The stronger the asymmetries the higher the predictive power of the risk dominance criterion.

Credit derivatives in emerging markets

Credit Derivatives are securities that offer protection against credit or default risk ofbonds or loans. The credit derivatives emerging market has grown rapidly and creditderivatives are widely used. This paper describes the emerging credit derivativesmarket structure. The current market activity is analyzed through elementary pricingdynamics and the study of the term structure of default risk. Focusing on theperformance of credit derivatives in stress situation, including legal and market risks,we discuss the potential consequences of a debt restructuring in a large emergingmarket borrower. The contribution of credit derivatives to the risk sharing in emergingmarkets is also examined.

International capital flows and credit market imperfections: A tale of two frictions

The financial crisis of 2007-08 has underscored the importance of adverse selection in financialmarkets. This friction has been mostly neglected by macroeconomic models of financialimperfections, however, which have focused almost exclusively on the effects of limited pledgeability.In this paper, we fill this gap by developing a standard growth model with adverseselection. Our main results are that, by fostering unproductive investment, adverse selection:(i) leads to an increase in the economy s equilibrium interest rate, and; (ii) it generates a negativewedge between the marginal return to investment and the equilibrium interest rate. Underfinancial integration, we show how this translates into excessive capital inflows and endogenouscycles. We also extend our model to the more general case in which adverse selection and limitedpledgeability coexist. We conclude that both frictions complement one another and show thatlimited pledgeability exacerbates the effects of adverse selection.

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.

Hybrid risk adjustment for pharmaceutical benefits

This paper analyses the application of hybrid risk adjustment versus either prospective orconcurrent risk adjustment formulae in the context of funding pharmaceutical benefits for thepopulation of an integrated healthcare delivery organization in Catalonia during years 2002 and2003. We apply a mixed formula and find that a hybrid risk adjustment model increasesincentives for efficiency in the provision of low risk individuals at health organizations not only asa whole but also at each internal department compared to only prospective models by reducingwithin-group variation of drug expenditures.

Sovereign debt markets in turbulent times: Creditor discrimination and crowding-out effects

In 2007, countries in the Euro periphery were enjoying stable growth, low deficits, and lowspreads. Then the financial crisis erupted and pushed them into deep recessions, raising theirdeficits and debt levels. By 2010, they were facing severe debt problems. Spreads increased and,surprisingly, so did the share of the debt held by domestic creditors. Credit was reallocatedfrom the private to the public sectors, reducing investment and deepening the recessions evenfurther. To account for these facts, we propose a simple model of sovereign risk in which debtcan be traded in secondary markets. The model has two key ingredients: creditor discriminationand crowding-out effects. Creditor discrimination arises because, in turbulent times, sovereigndebt offers a higher expected return to domestic creditors than to foreign ones. This providesincentives for domestic purchases of debt. Crowding-out effects arise because private borrowingis limited by financial frictions. This implies that domestic debt purchases displace productiveinvestment. The model shows that these purchases reduce growth and welfare, and may lead toself-fulfilling crises. It also shows how crowding-out effects can be transmitted to other countriesin the Eurozone, and how they may be addressed by policies at the European level.

The mean-variance model from the inverse of the variance-covariance matrix

En este artículo, a partir de la inversa de la matriz de varianzas y covarianzas se obtiene el modelo Esperanza-Varianza de Markowitz siguiendo un camino más corto y matemáticamente riguroso. También se obtiene la ecuación de equilibrio del CAPM de Sharpe.

The mean-variance model from the inverse of the variance-covariance matrix

En este artículo, a partir de la inversa de la matriz de varianzas y covarianzas se obtiene el modelo Esperanza-Varianza de Markowitz siguiendo un camino más corto y matemáticamente riguroso. También se obtiene la ecuación de equilibrio del CAPM de Sharpe.

Calibration and application of the MN2D dynamics model to the avalanches of Las Leñas (Argentina)

During the winters of 1999 and 2000 large avalanches occurred in the ski resort of Las Leñas (Los Andes, Mendoza, Argentina). On 8 September 1999 an avalanche of new, dry snow ran over a path with a 1000 m vertical drop. On 30 June and on 1 July 2000 five avalanches of similar vertical drop, which start with new snow, entrained very wet snow during their descent, and evolved into dense snow avalanches. To use the MN2D dynamics model correctly, calibration of model parameters is necessary. Also, no previous works with the use of dynamics models exist in South America. The events used to calibrate the model occurred during the winters of 1999 and 2000 and are a good sample of the kind of avalanches which can occur in this area of the Andes range. By considering the slope morphology and topography, the snow and meteorological conditions and the results of the model simulations, it was estimated that these avalanches were not extreme events with a return period greater than one hundred years. This implies that, in natural conditions, bigger, extreme avalanches could happen. In this work, the MN2D dynamics model is calibrated with two different avalanches of the same magnitude: dry and wet. The importance of the topographic data in the simulation is evaluated. It is concluded that MN2D dynamics model can be used to simulate dry extreme avalanches in Argentinean Andes but not to simulate extreme wet avalanches, which are much more sensitive to the topography.

A Gain Scheduling Model Predictive Controller for Blood Glucose Control in Type 1 Diabetes

This paper presents a control strategy for blood glucose(BG) level regulation in type 1 diabetic patients. To design the controller, model-based predictive control scheme has been applied to a newly developed diabetic patient model. The controller is provided with a feedforward loop to improve meal compensation, a gain-scheduling scheme to account for different BG levels, and an asymmetric cost function to reduce hypoglycemic risk. A simulation environment that has been approved for testing of artificial pancreas control algorithms has been used to test thecontroller. The simulation results show a good controller performance in fasting conditions and meal disturbance rejection, and robustness against model–patient mismatch and errors in mealestimation

Disparities in work, risk and health between immigrants and native-born Spaniards

We analyse the impact of working and contractual conditions, particularly exposure to job risks, on the probability of acquiring a permanent disability, controlling for other personal and firm characteristics. We postulate a model in which this impact is mediated by the choice of occupation, with a level of risk associated with it. We assume this choice is endogenous, and that it depends on preferences and opportunities in the labour market, both of which may differ between immigrants and natives. To test this hypothesis we apply a bivariate probit model to data for 2006 from the Continuous Sample of Working Lives provided by the Spanish Social Security system, containing records for over a million workers. We find that risk exposure increases the probability of permanent disability arising from any cause - by almost 5%.