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.     

Hazard rate,stochastic choice and consideration sets

Manzini and Mariotti (2014) define the menu-independent random consideration set rule, where the decision maker considers each alternative with a menu-independent probability known as the attention function. We relax the assumption of menu-independence and allow for any restriction to be imposed on the attention function. We show that there is an equivalence between the attention function and the hazard rate. This equivalence is used to characterize the menu dependent random consideration set rules that correspond to (i) specific conditions on the probability rule, and (ii) different stochastic choice models from the literature.     

Similarity-based mistakes in choice

We characterize the following choice procedure. The decision maker is endowed with two binary relations over alternatives, a preference and a similarity. In every choice problem she includes in her choice set all alternatives which are similar to the best feasible alternative. Hence she can, by mistake, choose an inferior option because it is similar to the best. We characterize this boundedly rational behavior by suitably weakening the rationalizability axiom of Arrow (1959). We also characterize a variation where the decision maker chooses alternatives on the basis of their similarities to attractive yet infeasible options. We show that similarity-based mistakes of either kind lead to cyclical behavior. Finally, we reinterpret our procedure as a method for choosing a bundle given a set of individual items, in which the decision maker combines the best feasible item with those that complement it.     

Models of stochastic choice and decision theories: why both are important for analyzing decisions

We select a menu of seven popular decision theories and embed each theory in five models of stochastic choice, including tremble, Fechner and random utility model. We find that the estimated parameters of decision theories differ significantly when theories are combined with different models. Depending on the selected model of stochastic choice we obtain different rankings of decision theories with regard to their goodness of fit to the data. The fit of all analyzed decision theories improves significantly when they are embedded in a Fechner model of heteroscedastic truncated errors or a random utility model. Copyright © 2009 John Wiley & Sons, Ltd.     

Disentangling preferences and limited attention: Random-utility models with consideration sets

This paper presents a model of choice with limited attention. The decision-maker forms a consideration set, from which she chooses her most preferred alternative. Both preferences and consideration sets are stochastic. While we present axiomatisations for this model, our focus is on the following identification question: to what extent can an observer retrieve probabilities of preferences and consideration sets from observed choices? Our first conclusion is a negative one: if the observed data are choice probabilities, then probabilities of preferences and consideration sets cannot be retrieved from choice probabilities. We solve the identification problem by assuming that an “enriched” dataset is observed, which includes choice probabilities under two frames. Given this dataset, the model is “fully identified”, in the sense that we can recover from observed choices (i) the probabilities of preferences (to the same extent as in models with full attention) and (ii) the probabilities of consideration sets. While a number of recent papers have developed models of limited attention that are, in a similar sense, “fully identified”, they obtain this result not by using an enriched dataset but rather by making a restrictive assumption about the default option, which our paper avoids.     

The structure of strategy-proof random social choice functions over product domains and lexicographically separable preferences

We characterize the class of dominant-strategy incentive-compatible (or strategy-proof) random social choice functions in the standard multi-dimensional voting model where voter preferences over the various dimensions (or components) are lexicographically separable. We show that these social choice functions (which we call generalized random dictatorships) are induced by probability distributions on voter sequences of length equal to the number of components. They induce a fixed probability distribution on the product set of voter peaks. The marginal probability distribution over every component is a random dictatorship. Our results generalize the classic random dictatorship result in Gibbard (1977) and the decomposability results for strategy-proof deterministic social choice functions for multi-dimensional models with separable preferences obtained in LeBreton and Sen (1999).     

Increasing sales by introducing non‐salable items

Rationality implies that adding ‘irrelevant’ and, in particular, inferior alternatives to the opportunity set cannot increase the choice probability of some other alternative. In this study, we propose a novel approach that can rationalize an intended addition of such alternatives because it strictly increases the choice probability of some existing alternative. The driving force behind the existence and extent of such an increase is the random nature of individual preferences, that implies intransitivity, and the random nature of the applied choice procedures. We study the case of a firm interested in increasing the sales of some of its existing products by introducing a new and inferior (non‐salable) product. Our main results focus on the feasibility and potential advantage of a successful such strategy. We first establish necessary and sufficient conditions for an increase in the sale probability and then derive the maximal possible absolute and relative increase in this probability, when the firm has extremely limited information on the characteristics of the consumers. We then derive analogous results, assuming that the existing line of products consists of just two items and that the firm has accurate information on the consumers' stochastic preferences over the existing products. These later results are illustrated using some experimental evidence. The applicability of the approach is finally briefly discussed in the context of branding policy. Copyright © 2006 John Wiley & Sons, Ltd.     

Alternative estimation method of earnings growth rate for PEGR strategy

The ambiguous return pattern for the PEGR (the ratio of the stock’s price/earnings to its estimated earnings growth rate) strategy has been documented in literature for the US stock markets. As stock prices and earnings per share (EPS) are objective data, earnings growth rate, however, is estimated by analyst whose method partial explains the PEGR vague return pattern. The purpose of this study is not to deny or substitute analysts’ estimation, but rather, to provide a simple and popular method, log-linear regression model, to forecast the earnings growth rate (G), and examine whether the typical PEGR effect, such as PER (price/earnings ratio) or PBR (price/book ratio) effect, exists by using our alternative estimation method. Our evidence indeed shows that returns on the lowest PEGR portfolio not only dominate over all higher PEGR portfolios, but also beat the market with stochastic dominance (SD) analysis, which is consistent with our prediction. Our results, at least, imply that using the log-linear regression model to construct the PEGR-sorted portfolios can benefit investors and the model is also a good choice for analysts in their forecasting.     

Can a stochastic cusp catastrophe model explain stock market crashes?

This paper is the first attempt to fit a stochastic cusp catastrophe model to stock market data. We show that the cusp catastrophe model explains the crash of stock exchanges much better than other models. Using the data of U.S. stock markets we demonstrate that the crash of October 19, 1987, may be better explained by cusp catastrophe theory, which is not true for the crash of September 11, 2001. With the help of sentiment measures, such as the index put/call options ratio and trading volume (the former models the chartists, the latter the fundamentalists), we have found that the 1987 returns are bimodal, and the cusp catastrophe model fits these data better than alternative models. Therefore we may say that the crash has been led by internal forces. However, the causes for the crash of 2001 are external, which is also evident in much weaker presence of bifurcations in the data. In this case, alternative models explain the crash of stock exchanges better than the cusp catastrophe model.     

When to haggle,when to hold firm? Lessons from the used‐car retail market

Though haggling has been the conventional way for auto retailers to sell cars, the last two decades have witnessed the systematic adoption of no‐haggle prices by many large dealerships, including the largest new‐ and used‐car dealership chains. This paper develops a structural empirical model to estimate sellers' profits under posted price and haggling, and investigates how market conditions affect sellers' optimal pricing formats. The model incorporates a simple class of bargaining mechanisms into a standard random‐coefficient discrete‐choice model. With the extension, the product‐level demand system is estimated using data with only list prices, and the unobserved price discounts are also recovered in the estimation. The counterfactual experiments yield a few interesting findings. First, dealers' adopted pricing formats seem superior to the alternative ones. Second, dealers enjoying larger market power through vertical differentiation and carrying a large number of models are more likely to have posted price as their optimal pricing format.     

Optimal mechanisms with simple menus

We consider revenue-optimal mechanism design for the case with one buyer and two items, when the buyer’s valuations are independent and additive. We obtain two sets of structural results of the optimal mechanisms, which can be summarized in one conclusion: under certain distributional conditions, the optimal mechanisms have simple menus.The first set of results states that, under a condition that requires that the types are concentrated on lower values, the optimal menu can be sorted in ascending order. Applying the theorem, we derive a revenue-monotonicity theorem which states that stochastically dominated distributions yield less revenue.The second set of results states that, under certain conditions which require that types are distributed more evenly or are concentrated on higher values, the optimal mechanisms have a few menu items. Our first result states that, for certain such distributions, the optimal menu contains at most 4 menu items. The condition admits power density functions. Our second result works for a weaker condition, under which the optimal menu contains at most 6 menu items. Our last result in this set works for the unit-demand setting, it states for uniform distributions, the optimal menu contains at most 5 items.     

The evolution of free trade networks

This paper considers the evolutionary dynamics of a free trade agreement (FTA) network formation game among N countries. We first explore the static model introduced by Goyal and Joshi (2006) and precisely characterize the set of pairwise stable FTA networks. Then, we develop a dynamic model under random perturbations and identify long-run outcomes to remove prediction uncertainty inherited from static analysis. The results show that both partial free trade and global free trade will result when there are only three countries. However, when more countries are involved, only the complete FTA network emerges.     

The heterogeneous behaviour of the inflation hedging property of cocoa

In this paper, we examine distinctly the inflation hedging potential of cocoa in net cocoa-exporting and net cocoa-importing countries. The choice of cocoa is motivated by its significance as a key ingredient in the production of chocolate which is largely consumed at every household and therefore serves as a major source of revenue to cocoa investors in exporting and importing countries. Based on our preliminary analyses including panel causality tests, we formulate both panel threshold regression model and panel smooth transition regression model in order to account for any inherent nonlinearity, time-variation and structural breaks in the inflation-cocoa returns nexus. We find that cocoa offers better inflation hedging characteristics in cocoa importing countries than their cocoa exporting counterparts. While the results are robust to alternative frequency and market size, we are able to establish that ignoring the presence of threshold effects may lead to wrong conclusions.     

A theory of iterative choice in lists

In a list, alternatives appear according to an order and the decision maker follows this order to evaluate alternatives. He records the first alternative as the initial survivor and then at every stage, he compares the current survivor with the next alternative in the list to determine whether the next alternative replaces that to become the new survivor. When the entire list is exhausted in this manner, the agent chooses the survivor in the last stage. We call this procedure “iterative” and provide an axiomatic characterization for it when the order in every list is observable. Then, we also study characterizations of the iterative procedure that is prone to the well-known primacy and recency effects. Finally, we analyze situations where the order of alternatives is unknown to an outside observer and provide a characterization result that enables such an outsider with limited information to understand whether the decision maker can indeed be an iterative list chooser for some order.     

Testing the specification of multivariate models in the presence of alternative hypotheses

In this paper we propose a non-nested hypothesis test for testing the specification of a multivariate econometric model in the presence of an alternative model which purports to explain the same phenomenon. We demonstrate that the new test statistic tends to minus the same random variable as the CPD test statistic introduced by Pesaran and Deaton (1978), provided that the truth is ‘close’ to the null hypothesis. Since the new test is simpler to compute than the multivariate CPD test, it would seem to be the procedure of choice.     

A general endogenous grid method for multi-dimensional models with non-convexities and constraints

The endogenous grid method (EGM) significantly speeds up the solution of stochastic dynamic programming problems by simplifying or completely eliminating root-finding. We propose a general and parsimonious EGM extended to handle (1) multiple continuous states and choices, (2) multiple occasionally binding constraints, and (3) non-convexities such as discrete choices. Our method enjoys the speed gains of the original one-dimensional EGM, while avoiding expensive interpolation on multi-dimensional irregular endogenous grids. We explicitly define a broad class of models for which our solution method is applicable, and illustrate its speed and accuracy using a consumption–saving model with both liquid assets and illiquid pension assets and a discrete retirement choice.     

Sectoral labour supply,choice restrictions and functional form

In this paper we discuss a general framework for analysing labour supply behaviour in the presence of complicated budget and quantity constraints, of which some are unobserved. The individual's labour supply decision is viewed as a choice from a set of discrete alternatives (jobs). These jobs are characterized by attributes such as hours of work, sector‐specific wages and other sector‐specific aspects of the jobs. The labour supply model for married women is estimated on Norwegian data. Wage elasticities and the outcome of a tax reform experiment show that overall labour supply is moderately elastic, but these modest overall responses shadow for much stronger inter‐sectoral changes. Our model is compared with a discrete choice model in which the utility is assumed to be a polynomial. We show that our estimated model has a more economically sensible interpretation and fits the data as well as the alternative approach. Copyright © 2006 John Wiley & Sons, Ltd.     

The valuation of barrier options under a threshold rough Heston model

In this paper, we propose a novel model for pricing double barrier options, where the asset price is modeled as a threshold geometric Brownian motion time changed by an integrated activity rate process, which is driven by the convolution of a fractional kernel with the CIR process. The new model both captures the leverage effect and produces rough paths for the volatility process. The model also nests the threshold diffusion, Heston and rough Heston models. We can derive analytical formulas for the double barrier option prices based on the eigenfunction expansion method. We also implement the model and numerically investigate the sensitivities of option prices with respect to the parameters of the model.     

Context dependent beliefs

This paper examines a model where the set of available outcomes from which a decision maker must choose alters his perception of uncertainty. Specifically, this paper proposes a set of axioms such that each menu induces a subjective belief over an objective state space. The decision maker’s preferences are dependent on the realization of the state. The resulting representation is analogous to state-dependent expected utility within each menu; the beliefs are menu dependent and the utility index is not. Under the interpretation that a menu acts as an informative signal regarding the true state, the paper examines the behavioral restrictions that coincide with different signal structures: elemental (where each element of a menu is a conditionally independent signal) and partitional (where the induced beliefs form a partition of the state space).