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.     

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.     

A theory of stochastic choice under uncertainty

In this paper we propose a characterization of stochastic choice under risk and under uncertainty. We presume that decision makers’ actual choices are governed by randomly selected states of mind, and study the representation of decision makers’ perceptions of the stochastic process underlying the selection of their state of mind. The connections of this work to the literatures on random choice, choice behavior when preference are incomplete; choice of menus; and grades of indecisiveness are also discussed.     

Mobility and optimal tenure choice

In this paper, we offer a dynamic model of the optimal tenure behavior of an individual who faces the possibility of moving multiple times during his lifetime. We also investigate the lifetime effects of such factors as income tax, property tax, transaction costs, and mortgage rates on the household’s tenure choice. The agents in the model utilize a genetic algorithm, a probabilistic search approach, to determine their optimal lifetime tenure choice path. The agents are forward looking in that they anticipate such possible events as changes in jobs, marital status, household size, or dissatisfaction with current residence. Our results suggest several housing policy implications and explain some of the empirical findings in the literature.     

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.     

Stochastic models for risky choices: A comparison of different axiomatizations

For a long time researchers have recognized the need for applying stochastic models for analyzing data generated from agents’ choice under risk. This paper compares and discusses recent axiomatizations of stochastic models for risky choice given by Blavatskyy (2008) and Dagsvik (2008). We show that some of Blavatskyy’s axioms are equivalent to some of Dagsvik’s axioms. We also propose new axioms and derive their implications. Specifically, we show that some of the results of Dagsvik (2008) can be derived under weaker axioms than those he proposed originally.     

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.     

Transitions between equilibria in bilingual games under logit choice

We study the effect of introducing a bilingual option on the long run equilibrium outcome in a class of two-strategy coordination games with distinct payoff and risk dominant equilibria under the logit choice rule. Existing results show that in the class of two-strategy games under consideration, the inefficient risk dominant equilibrium is selected in the long run under noisy best response models. We show that if the cost of the bilingual option is sufficiently low then the efficient payoff dominant equilibrium will be selected in the long run under the logit choice rule.     

A methodology for the choice of the best fitting continuous-time stochastic models of crude oil price

The crude oil price is generally considered as the fundamental factor in the valuation of undeveloped reserves but it is not the unique one. Undeveloped field value also depends on the uncertainty relating to the convenience yield and the risk-free interest rate. The purpose of this paper is to decide on the best continuous-time stochastic models for these risk factors. The Generalized Method of Moments and the Maximum Likelihood Estimation are implemented to fit the parameters of continuous-time stochastic processes. The results of unit root tests without breaks reveal a mean reversion in convenience yield series. Multiple structural change tests show that the risk-free interest rate can be considered constant. The simulation of continuous-time stochastic processes and the mean error between the simulated prices and the market ones show that the Geometric Brownian Motion with jumps is the best model for the oil price compared to the other commonly used processes.     

Consistent estimation of the fixed effects stochastic frontier model

In this paper we consider a fixed-effects stochastic frontier model. That is, we have panel data, fixed individual (firm) effects, and the usual stochastic frontier analysis (SFA) composed error.     

Maximum score estimation of the stochastic utility model of choice

This paper introduces a class of robust estimators of the parameters of a stochastic utility function. Existing maximum likelihood and regression estimation methods require the assumption of a particular distributional family for the random component of utility. In contrast, estimators of the ‘maximum score’ class require only weak distributional assumptions for consistency. Following presentation and proof of the basic consistency theorem, additional results are given. An algorithm for achieving maximum score estimates and some small sample Monte Carlo tests are also described.     

A stochastic dynamic model of trade and growth: Convergence and diversification

There is a growing literature that studies the properties of models that combine international trade and neoclassical growth theory, but mostly in a deterministic setting. In this paper we introduce uncertainty in a dynamic Heckscher-Ohlin model and characterize the equilibrium of a small open economy in such an environment. We show that, when trade is balanced period-by-period, the per capita output and consumption of a small open economy converge to an invariant distribution that is independent of the initial wealth. Further, at the invariant distribution, there are periods in which the small economy diversifies. Numerical simulations show that the speed of convergence increases with the size of the shocks. In the limit, when there is no uncertainty, there is no convergence and countries may specialize permanently. The paper highlights the role of market incompleteness, as a result of the period-by-period trade balance, in this setup. Through an analytical example we also illustrate the importance of country specific risk in delivering our results.     

Markov Perfect equilibria in repeated asynchronous choice games

This paper examines the issue of multiplicity of Markov Perfect equilibria in alternating move repeated games. Such games are canonical models of environments with repeated, asynchronous choices due to inertia or replacement. Our main result is that the number of Markov Perfect equilibria is generically finite with respect to stage game payoffs. This holds despite the fact that the stochastic game representation of the alternating move repeated game is “non-generic” in the larger space of state dependent payoffs. We further obtain that the set of completely mixed Markov Perfect equilibria is generically empty with respect to stage game payoffs.     

Equilibria in the spatial stochastic model of voting with party activists

Stochastic models of elections typically indicate that all parties, in equilibrium, will adopt positions at the electoral center. Empirical analyses discussed in this paper suggest that convergence of this kind is rarely observed. Here we examine a stochastic electoral model where parties differ in their valences – the electorally perceived, non-policy “quality” of the party leader. It is assumed that valence may either be exogenous, in the sense of being an intrinsic characteristic of the leader, or may be due to the contributions of party activists, who donate time and money and thus enhance electoral support for the party. Theorem 1 shows that vote maximization depends on balancing these two opposed effects. Theorem 2 provides the necessary and sufficient conditions for convergence to the electoral mean when activist valence is zero. The paper then examines empirical electoral models for the Netherlands circa 1980 and Britain in 1979, 1992 and 1997 and shows that party divergence from the electoral mean cannot be accounted for by exogenous valence alone. The balance condition suggests that the success of the Labour party in the election of 1997 can be attributed to a combination of high exogenous valence and pro-Europe activist support.     

Of songs and men: a model for multiple choice with herding

We propose a generic model for multiple choice situations in the presence of herding and compare it with recent empirical results from a Web-based music market experiment. The model predicts a phase transition between a weak imitation phase and a strong imitation, ‘fashion’ phase, where choices are driven by peer pressure and the ranking of individual preferences is strongly distorted at the aggregate level. The model can be calibrated to reproduce the main experimental results of Salganik et al. (Science, 311, 854–856 (2006)); we show in particular that the value of the social influence parameter can be estimated from the data. In one of the experimental situation, this value is found to be close to the critical value of the model.     

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.     

Filtering and identification of Heston's stochastic volatility model and its market risk

We study the filtering problem for the stochastic volatility model of Heston by using the nonlinear estimation theory. To solve the estimation problem for the stochastic volatility process, we use the random time change method. The derived basic equation for the filtering is the so-called Zakai equation and its numerically realized algorithm is proposed with the aid of the splitting-up method. Regarding the European call option problem, the identification of the market price of the volatility risk is also studied. Some numerical simulation studies are demonstrated to show the advantage of the proposed method.