DOES NEAR‐RATIONALITY MATTER IN FIRST‐ORDER APPROXIMATE SOLUTIONS? A PERTURBATION APPROACH

This paper studies first‐order approximate solutions to near‐rational dynamic equilibrium models. Under near‐rationality, agents' subjective beliefs are distorted away from rational expectations via a change of measure process which fulfills some regularity conditions. In most applications, the beliefs distortion process is also directly observed by (a subset of) the decision‐makers – e.g., ambiguity‐averse households or policy‐makers with a concern for robustness – and therefore included into their optimization problems. We investigate conditions for existence and local uniqueness of solutions under endogenous distortions, as well as the relation with their rational expectations counterparts. We show that linearly perturbed solutions may well be affected by the presence of distorted beliefs, depending on the underlying model economy. In particular, while directly affecting first‐order decision rules, near‐rationality may also induce failure of the certainty equivalence principle. Moreover, the martingale representation of distorted beliefs might prove non‐unique, pointing to a subtle form of equilibrium indeterminacy.     

Endogenous private information structures

We formally incorporate the option to gather information into a game and thus endogenize the information structure. We ask whether models with exogenous information structures are robust with respect to this endogenization. Any Nash equilibrium of the game with information acquisition induces a Nash equilibrium in the corresponding game with an exogenous structure. We provide sufficient conditions on the structure of the game for which this remains true when ‘Nash’ is replaced by ‘sequential’. We characterize the (sequential) Nash equilibria of games with exogenous information structures that can arise as a (sequential) Nash equilibrium of games with endogenous information acquisition.     

Robust control and model misspecification

A decision maker fears that data are generated by a statistical perturbation of an approximating model that is either a controlled diffusion or a controlled measure over continuous functions of time. A perturbation is constrained in terms of its relative entropy. Several different two-player zero-sum games that yield robust decision rules are related to one another, to the max-min expected utility theory of Gilboa and Schmeidler [Maxmin expected utility with non-unique prior, J. Math. Econ. 18 (1989) 141-153], and to the recursive risk-sensitivity criterion described in discrete time by Hansen and Sargent [Discounted linear exponential quadratic Gaussian control, IEEE Trans. Automat. Control 40 (5) (1995) 968-971]. To represent perturbed models, we use martingales on the probability space associated with the approximating model. Alternative sequential and nonsequential versions of robust control theory imply identical robust decision rules that are dynamically consistent in a useful sense.     

Amenity driven price effects and conservation reserve site selection: A dynamic linear integer programming approach

Most conservation reserve design models presented in the literature are static and ignore the dynamic economic aspects of site selection. Typically conservation programs operate under time-related (e.g. annual) budgets and purchase land over time in a sequential manner. The uncertainty of land development has been incorporated in a few dynamic reserve selection formulations using stochastic dynamic programming. However, the existing formulations do not explicitly deal with inter-temporal price and location linkages. We address this issue here and present a two-period linear integer programming model for conservation reserve design that incorporates amenity driven price feedback effects inherent in the reserve development problem. In addition, the model includes spatial and ecological criteria. We then use this model to answer the question “How suboptimal is ignoring amenity driven price effects in reserve design models?” We apply the model to artificially generated data sets and compare the results with the results of an iterated static model that considers only one period at a time. We find that the dynamic model with price feedback effects selects sites at a lower per-site cost. The policy implication of this finding is that conservation programs should avoid purchasing land in the same neighborhood over multiple time periods.     

WHAT AFFECTS EFFICIENCY IN LABOUR MARKET MATCHING AT DIFFERENT TERRITORIAL AGGREGATION LEVELS IN POLAND?

We analyse efficiency of a labour market matching process at different levels of territorial aggregation and in different time horizons. We apply a stochastic matching frontier to random, job queuing and stock‐flow models. We use data for Poland, a country with highly regionally diversified unemployment. We find that search and matching mechanisms significantly differ with territorial aggregation. Higher efficiency in small regions results from lower frictions. Larger regions enjoy better structural matching if only labour market participants have time to search. Different policy measures should be designed to improve labour market matching efficiency at different regional levels.     

A new axiomatization of the Banzhaf semivalue

A new characterization of the Banzhaf semivalue on the domain of monotonic simple games is given. We use the well-known valuation and dummy axioms plus two additional properties. The first one simply requires that the power-index be bigger for those players belonging to more winning coalitions. The second one is the proportionality axiom introduced by Owen in (1982) which is suitable for those simple games that represent an indirect voting process.     

Social Organization in an Endogenous Growth Model

We develop an endogenous growth model in which individuals form matches in order to consume goods that are not explicitly traded. The matching process endogenously generates a concern for relative wealth and is thereby beneficial for capital accumulation and economic growth. We then study how social segmentation in the matching process affects economic growth. Under strong segmentation, social competition over mates occurs inside homogeneous groups. This homogeneity increases the severity of the "rat race" of wealth accumulation and fosters economic growth.     

Non-self-averaging and the statistical mechanics of endogenous macroeconomic fluctuations

Strong fluctuation phenomena are an endogenous feature of economic systems if they are non-self-averaging. We show that an important consequence of non-self-averaging is that current forms of economic policy can be rendered useless. We also find non-self-averaging both to exist in microeconomic models of cluster development within economies and to be consistent with observed economic power laws. These results suggest the need for straightforward identification of non-self-averaging in economic systems and to this end we present a sufficient condition for non-self-averaging in terms familiar to financial risk management.     

TESTING THE SEQUENTIAL LOGIT MODEL AGAINST THE NESTED LOGIT MODEL*

In this paper, we show that the sequential logit (SL) model, in which a choice process is characterized as a sequence of independent multinomial logit models, is a limiting case of the nested logit (NL) model. For testing the SL model against the NL model, we propose Wald, likelihood ratio and Lagrange multiplier tests after suitably reparameterizing the NL model. It is found that when the NL model parameters are “weakly identified”, the Wald test severely underrejects the true model, whereas the sizes of the LR and LM tests are not significantly affected.     

A two-person game of information transmission

We consider a statistical decision problem faced by a two player organization whose members may not agree on outcome evaluations and prior probabilities. One player is specialized in gathering information and transmitting it to the other, who takes the decision. This process is modeled as a game. Qualitative properties of the equilibria are analyzed. The impact of improving the quality of available information on the equilibrium welfares of the two individuals is studied. Better information generally may not improve welfare. We give conditions under which it will.     

On the Problem of Constructing Rational Preferences

In standard models it is typically taken for granted that preferences are given and defined over the alternatives alone, and the possibility of making a rational choice is a matter of assumption. I generalise this aspect of the economic model so that preferences over alternatives are constructed from given preferences defined over various characteristics of the alternatives under consideration. I characterise the decision problem before investigating what conditions a procedure for aggregating preferences over attributes into preferences over alternatives must satisfy in order for the latter to be rational. I then consider what the implications of these conditions for the procedural rationality of the aggregation process.     

New results on rational random behavior

This letter deals with conditions under which it is preferable to buy a zero amount of information; with a proportionality of the information and loss variances associated with two different decision distributions; and with a limiting chi-square distribution of the decision maker's loss when the marginal cost of information is small.     

Matching and bargaining models of markets: approximating small markets by large markets

Summary. We show that the equilibrium of a matching and bargaining model of a market in which there is a finite number of agents at each date need not be near the equilibrium of a market with a continuum of agents, although matching probabilities are the same in both markets. Holding the matching process fixed, as the finite market becomes large its equilibrium approaches the equilibrium of its continuum limit.Received: January 22, 1996; revised version: September 24, 1996This revised version was published online in February 2005 with corrections to the cover date.     

Robust estimation and control under commitment

In a Markov decision problem with hidden state variables, a decision maker expresses fear that his model is misspecified by surrounding it with a set of alternatives that are nearby as measured by their expected log likelihood ratios (entropies). Sets of martingales represent alternative models. Within a two-player zero-sum game under commitment, a minimizing player chooses a martingale at time 0. Probability distributions that solve distorted filtering problems serve as state variables, much like the posterior in problems without concerns about misspecification. We state conditions under which an equilibrium of the zero-sum game with commitment has a recursive representation that can be cast in terms of two risk-sensitivity operators. We apply our results to a linear quadratic example that makes contact with findings of T. Ba?ar and P. Bernhard [H^∞-Optimal Control and Related Minimax Design Problems, second ed., Birkhauser, Basel, 1995] and P. Whittle [Risk-sensitive Optimal Control, Wiley, New York, 1990].     

Prior symmetry, similarity-based reasoning, and endogenous categorization

This paper presents a rational theory of categorization and similarity-based reasoning. I study a model of sequential learning in which the decision maker infers unknown properties of an object from information about other objects. The decision maker may use the following heuristics: divide objects into categories with similar properties and predict that a member of a category has a property if some other member of this category has this property. The environment is symmetric: the decision maker has no reason to believe that the objects and properties are a priori different. In symmetric environments, categorization is an optimal solution to an inductive inference problem. Any optimal solution looks as if the decision maker categorizes. Various experimental observations about similarity-based reasoning coincide with the optimal behavior in my model.     

Bidding for money

We analyze monetary exchange in a model that allows for directed search and multilateral matches. We consider environments with divisible goods and indivisible money, and compare the results with those in models that use random matching and bilateral bargaining. Two different pricing mechanisms are used: ex ante price posting, and ex post bidding (auctions). Also, we consider settings both with and without lotteries. We find that the model generates very simple and intuitive equilibrium allocations that are similar to those with random matching and bargaining, but with different comparative static and welfare properties.     

Kept back to get ahead? Kindergarten retention and academic performance

While most existing research concludes that grade retention generates no benefits for the retainees’ academic performance, holding low-achieving children back has been a popular practice for decades. Drawing on a recently collected nationally representative dataset in the US, this paper estimates the causal effect of repeating kindergarten on the retained children's academic performance. Since we observe children being held back only when they enroll in schools that permit kindergarten retention, this paper jointly models the choice of enrolling in a school that allows kindergarten retention, the decision of repeating kindergarten, and children's academic performance in higher grades. A control function approach is developed to estimate the resulting double-hurdle treatment model, which accounts for unobserved heterogeneity in the retention effect. A nearest-neighbor matching estimator is also implemented. Holding children back in kindergarten is found to have positive but diminishing effects on their academic performance up to third grade.     

Efficient delays in a stochastic model of bargaining

Summary. We consider a k-player sequential bargaining model in which both the cake size and the identity of the proposer are determined by a stochastic process. For the case where the cake is a simplex (of random size) and the players share a common discount factor, we establish the existence of a unique stationary subgame perfect payoff which is efficient and characterize the conditions under which agreement is delayed. We also investigate how the equilibrium payoffs depend on the order in which the players move and on the correlation between the identity of the proposer and the cake size.Received: November 5, 1996; revised version: December 31, 1996This revised version was published online in February 2005 with corrections to the cover date.     

Modelling the participation decision and duration of sporting activity in Scotland

Motivating individuals to actively engage in physical activity due to its beneficial health effects has been an integral part of Scotland's health policy agenda. The current Scottish guidelines recommend individuals participate in physical activity of moderate vigour for 30 min at least five times per week. For an individual contemplating the recommendation, decisions have to be made in regard of participation, intensity, duration and multiplicity. For the policy maker, understanding the determinants of each decision will assist in designing an intervention to effect the recommended policy. With secondary data sourced from the 2003 Scottish Health Survey (SHeS) we statistically model the combined decisions process, employing a copula approach to model specification. In taking this approach the model flexibly accounts for any statistical associations that may exist between the component decisions. Thus, we model the endogenous relationship between the decision of individuals to participate in sporting activities and, amongst those who participate, the duration of time spent undertaking their chosen activities. The main focus is to establish whether dependence exists between the two random variables assuming the vigour with which sporting activity is performed to be independent of the participation and duration decision. We allow for a variety of controls including demographic factors such as age and gender, economic factors such as income and educational attainment, lifestyle factors such as smoking, alcohol consumption, healthy eating and medical history. We use the model to compare the effect of interventions designed to increase the vigour with which individuals undertake their sport, relating it to obesity as a health outcome.