Chance Constrained Programming Formulations for Stochastic Characterizations of Efficiency and Dominance in DEA

Pareto-Koopmans efficiency in Data Envelopment Analysis (DEA) is extended to stochastic inputs and outputs via probabilistic input-output vector comparisons in a given empirical production (possibility) set. In contrast to other approaches which have used Chance Constrained Programming formulations in DEA, the emphasis here is on joint chance constraints. An assumption of arbitrary but known probability distributions leads to the P-Model of chance constrained programming. A necessary condition for a DMU to be stochastically efficient and a sufficient condition for a DMU to be non-stochastically efficient are provided. Deterministic equivalents using the zero order decision rules of chance constrained programming and multivariate normal distributions take the form of an extended version of the additive model of DEA. Contacts are also maintained with all of the other presently available deterministic DEA models in the form of easily identified extensions which can be used to formalize the treatment of efficiency when stochastic elements are present.     

Generalized affine transform on pricing quanto range accrual note

This paper was to price and hedge a quanto floating range accrual note (QFRAN) by an affine term structure model with affine-jump processes. We first generalized the affine transform proposed by Duffie et al. (2000) under both the domestic and foreign risk-neutral measures with a change of measure, which provides a flexible structure to value quanto derivatives. Then, we provided semi-analytic pricing and hedging solutions for QFRAN under a four-factor affine-jump model with the stochastic mean, stochastic volatility, and jumps. The numerical results demonstrated that both the common and local factors significantly affect the value and hedging strategy of QFRAN. Notably,  the factor of stochastic mean plays the most important role in either valuation or hedging. This study suggested that ignorance of these factors in a term-structure model will result in significant pricing and hedging errors in QFRAN. In summary, this study provided flexible and easily implementable solutions in valuing quanto derivatives.     

A model of stochastic choice from lists

We study stochastic choice from lists. All lists present the same set of alternatives albeit in different orders. Faced with a list, the decision maker makes her choice in two stages. In the first stage she searches through the list till she sees $k$ alternatives. In the second stage she chooses from the alternatives she has seen. Both $k$ and the choice rule governing her second stage behavior are random. We show that the underlying primitives of our model are revealed by the decision maker’s choice frequencies from lists. We characterize the model and two of its special cases. In the first special case the decision maker deterministically chooses the best observed alternative according to a given preference. In the second, the decision maker maximizes random preferences.     

Satisficing with a variable threshold

We axiomatize a model of satisficing which features random thresholds and the possibility of choice abstention. Given a menu, the decision maker first randomly draws a threshold. Next, using a list order, she searches the menu for alternatives which are at least as good as the threshold. She chooses the first such alternative she finds, and if no such alternative exists, she abstains. Since the threshold is random, so is the resulting behavior. We characterize this model using two simple axioms. In general the revelation of the model’s primitives is incomplete. We characterize a specialization of the model for which the underlying preference and list ordering are uniquely identified by choice frequencies. We also show that our model is a special Random Utility Model.     

Note on positive lower bound of capital in the stochastic growth model

In the context of the classical stochastic growth model, we provide a simple proof that the optimal capital sequence is strictly bounded away from zero whenever the initial capital is strictly positive. We assume that the utility function is bounded below and the shocks affecting output are bounded. However, the proof does not require an interval shock space, thus, admitting both discrete and continuous shocks. Further, we allow for finite marginal product at zero capital. Finally, we use our result to show that any optimal capital sequence converges globally to a unique invariant distribution, which is bounded away from zero.     

Stochastic costly state verification and dynamic contracts

I consider a dynamic costly state verification environment in which a risk-averse agent enters into a contract with a risk-neutral principal. The agent has random income which is unknown to the principal but can be verified at a cost. The principal can commit to executing random verifications.I extend the standard recursive methods to study the problem and show that it is optimal to set verification probabilities strictly less than 1. If the agent׳s absolute risk aversion declines sufficiently slowly, the principal will use verification regardless of its cost. If the agent's income is verified then he would get consumption and continuation utility strictly higher than if his income were not verified.     

Shifts in volatility driven by large stock market shocks

This paper presents an extension of the stochastic volatility model which allows for level shifts in volatility of stock market returns, known as structural breaks. These shifts are endogenously driven by large return shocks (innovations), reflecting large pieces of market news. These shocks are identified from the data as being bigger in absolute terms than the values of two threshold parameters of the model: one for the negative shocks and one for the positive shocks. The model can be employed to investigate different sources of stock market volatility shifts driven by market news, without relying on exogenous information. In addition to this, it has a number of interesting features which enable us to study the effects of large return shocks on future levels of market volatility. The above properties of the model are shown based on a study for the US stock market volatility.     

Functional sunspot equilibria

Consider a one step forward looking model where agents believe that the equilibrium values of the state variable are determined by a function whose domain is the current value of the state variable and whose range is the value for the subsequent period. An agent’s forecast for the subsequent period uses the belief, where the function that is chosen is allowed to depend on the current realization of an extrinsic random process, and is made with knowledge of the past values of the state variable but not the current value. The paper provides (and characterizes) the conditions for the existence of sunspot equilibria for the model described.     

Engel's Law Reconsidered

Engel's Law expresses a negative stochastic association of the bivariate distribution of income and food share across a population. Among the many different definitions which can be found in the statistical literature four concepts are discussed and tested: Kendall's τ, quadrant dependence, stochastic decreasing conditional food share distribution function and decreasing regression. Only the last one is used in the economic literature, yet it does not imply useful information of the underlying distribution. For linking Engels's Law to micro-economics, stronger concepts of stochastic association are needed. This motivates the empirical study of the proposed alternative concepts of negative association.     

On the accuracy of bootstrap confidence intervals for efficiency levels in stochastic frontier models with panel data

We study the construction of confidence intervals for efficiency levels of individual firms in stochastic frontier models with panel data. The focus is on bootstrapping and related methods. We start with a survey of various versions of the bootstrap. We also propose a simple parametric alternative in which one acts as if the␣identity of the best firm is known. Monte Carlo simulations indicate that the parametric method works better than the␣percentile bootstrap, but not as well as bootstrap methods that make bias corrections. All of these methods are valid␣only for large time-series sample size (T), and correspondingly none of the methods yields very accurate confidence intervals except when T is large enough that the identity of the best firm is clear. We also present empirical results for two well-known data sets.      

Comparing and Combining Two Approaches for Chance Constrained DEA

This paper presents a comparison of two different models (Land et al (1993) and Olesen and Petersen (1995)), both designed to extend DEA to the case of stochastic inputs and outputs. The two models constitute two approaches within this area, that share certain characteristics. However, the two models behave very differently, and the choice between these two models can be confusing. This paper presents a systematic attempt to point out differences as well as similarities. It is demonstrated that the two models under some assumptions do have Lagrangian duals expressed in closed form. Similarities and differences are discussed based on a comparison of these dual structures. Weaknesses of the each of the two models are discussed and a merged model that combines attractive features of each of the two models is proposed.

Decomposing the declining volatility of long-term inflation expectations

The level and volatility of survey-based measures of long-term inflation expectations have come down dramatically over the past several decades. To capture these changes in inflation dynamics, we embed both short- and long-term expectations into a medium-scale VAR model with stochastic volatility. The model estimates attribute most of the marked decline in the volatility of expectations to smaller shocks to long-run inflation expectations. According to our estimates, the volatility of shocks plummeted in the early to mid-1980s, moved to a somewhat higher level that prevailed for much of the 1990s, and then declined to and remained at very low levels.     

Solving higher-dimensional continuous-time stochastic control problems by value function regression

The paper develops a method to solve higher-dimensional stochastic control problems in continuous time. A finite-difference-type approximation scheme is used on a coarse grid of low-discrepancy points, while the value function at intermediate points is obtained by regression. The stability properties of the method are discussed, and applications are given to test problems of up to 10 dimensions. Accurate solutions to these problems can be obtained on a personal computer.     

An Economist's Perspective on Probability Matching

The experimental phenomenon known as 'probability matching' is often offered as evidence in support of adaptive learning models and against the idea that people maximise their expected utility. Recent interest in dynamic-based equilibrium theories means the term re-appears in Economics. However, there seems to be conflicting views on what is actually meant by the term and about the validity of the data.
The purpose of this paper is therefore threefold: First, to introduce today's readers to what is meant by probability matching, and in particular to clarify which aspects of this phenomenon challenge the utility-maximisation hypothesis. Second, to familiarise the reader with the different theoretical approaches to behaviour in such circumstances, and to focus on the differences in predictions between these theories in light of recent advances. Third, to provide a comprehensive survey of repeated, binary choice experiments.     

Comments on “Pareto weights as wedges in two-country models” by D. Backus,C. Coleman,A. Ferriere and S. Lyon

Backus, Coleman, Ferriere and Lyon study how the formulations of preferences and shocks affect the behavior of macroeconomic and financial aggregates in a simple endowment economy with no frictions. Their exercise could be considered as a first step of a rich research program that can further our understanding of international business cycles. After discussing the fundamental propagation mechanisms in standard international business cycle models, I put their contribution in a broader context. I conclude with a summary of possible research questions to be explored in future work.     

Response to updated mortality forecasts in life cycle saving and labor supply

Historical evidence shows that demographic forecasts, including mortality forecasts, have often been grossly in error. One consequence of this is that forecasts are updated frequently. How should individuals or institutions react to updates, given that these are likewise expected to be uncertain? We discuss this problem in the context of a life cycle saving and labor supply problem, in which a cohort of workers decides how much to work and how much to save for mutual pensions. Mortality is stochastic and point forecasts are updated regularly. A Markovian approximation for the predictive distribution of mortality is derived. This renders the model computationally tractable, and allows us to compare a theoretically optimal rational expectations solution to a strategy in which the cohort merely updates the life cycle plan to match each updated mortality forecast. The implications of the analyses for overlapping generations modeling of pension systems are pointed out.     

The financial instability hypothesis: A stochastic microfoundation framework

This paper examines the dynamics of financial distress and in particular the mechanism of transmission of shocks from the financial sector to the real economy. The analysis is performed by representing the linkages between microeconomic financial variables and the aggregate performance of the economy by means of a microfounded model with firms that have heterogeneous capital structures. The model is solved both numerically and analytically, by means of a stochastic approximation that is able to replicate quite well the numerical solution. These methodologies, by overcoming the restrictions imposed by the traditional microfounded approach, enable us to provide some insights into the stabilization policies which may be effective in a financially fragile system.     

A spatial dominance approach to evaluate the performance of stocks and bonds: Does the investment horizon matter?

The common advice by practitioners is to allocate a greater proportion of stocks for long-term investors than for short-term investors. However, part of the academic literature disagrees with this advice. We use a spatial dominance test which is suited for comparing alternative investments for a given time horizon. Using daily data for the US from 1962 to 2012, we test for dominance of cumulative returns series for stocks versus bonds at different investment horizons from 1 to 15 years. We find evidence that bonds second order spatially dominate stocks for horizons from 1 to 4 years. In contrast, for horizons of 6 years and longer, we find evidence that stocks dominate bonds. The conclusion that bonds dominate stocks at short horizons, while stocks dominate bonds at long horizons is consistent across different periods and international markets. When different portfolios of stocks and bonds are compared, we find that for long investment horizons only those portfolios with a sufficiently high proportion of stocks are efficient in the sense of spatial dominance.