Modelling reference dependence for repeated choices: A horse race between models of normalisation

In the logit model, a choice between options is driven by payoff differences. Existing evidence on repeated choices suggests that the way payoff differences are evaluated depends on historically observed differences. We capture such reference dependence using the value normalisation approach developed in neuroscience. We use experimental data and run a horse race between various models with normalisation, including widely used divisive and range normalisation. We show that a parsimonious logit model with maximum difference normalisation has both the best goodness of fit and a strong quasi-out-of-sample predictive power. In this structural parameter-free logit model, an agent makes a choice based on the difference in payoffs in the previous period, normalised by the maximum difference in payoffs in two previous periods. The model has a wide range of applications, from studying learning dynamics in repeated games to predicting retirement plans choices.     

Extended preferences and freedom of choice

The common choice theory in economics is based on the assumption that an individual is defined in terms of a binary preference relation. This preference relation is defined over alternatives without taking into account menu dependence and, in particular, freedom of choice or, more generally, the set that contains the alternatives. In this study we clarify the nature and the significance of freedom of choice which may positively or negatively affect the individual's welfare. Our proposed extended preference relation of the individual takes into account both the particular alternative and the opportunity set that he faces. This extended relation does not induce ranking of opportunity sets. Its restriction to a particular opportunity set is the paradigmatic preference relation and it can capture the dependence of preferences on freedom of choice. Our main result establishes the inconsistency between dependence of extended preferences on freedom of choice and the existence of a utility that represents the paradigmatic preference relation and any of its restrictions. Received: 30 December 1997/Accepted: 6 September 1999     

Modellvergleich und Ergebnisinterpretation in Logit- und Probit-Regressionen

In the social sciences logit and probit models are often used multivariate data analysis procedures for binary dependent variables. Both procedures can be thought of as resting on a linear model for an unobserved variable y* from which a nonlinear model for the probability of y?=?1 is derived. We first show that compared to linear models this nonlinearity leads to problems of interpreting results from such analysis. In particular odds ratios (exponentiated logit coefficients) often used in logistic regression are problematic in this respect. Instead we recommend using graphical procedures and reporting (corrected) average marginal effects (AME). Based on a series of Monte-Carlo simulations we next demonstrate that the regression coefficients from logit and probit models should not be compared between nested models. Because model building in the social sciences often employs a stepwise procedure a method allowing valid comparisons of effect sizes between models would be advantageous. Results from our simulation study show that average marginal effects and regression coefficients corrected by a method proposed by Karlson et al. (Sociological Methodology 42, 2012) lead to satisfactory results in many different scenarios. In contrast, y*-standardized coefficients are of limited utility and coefficients from a linear probability model should only be used with normally distributed variables.     

Political culture and monopoly price determination

In this paper we study the endogenous determination of monopoly price. Our proposed game of endogenous monopoly-price setting extends the literature on monopoly-price, monopoly rent-seeking contests and monopoly rent-seeking rent-avoidance contests by (i) determining the monopoly price such that it maximizes a composite utility function that depends on two components: expected social welfare and lobbying efforts. The welfare component has a positive or no effect on the utility while the lobbying efforts have a positive, negative or no effect on the utility (ii) introducing the political culture of the government and clarifying its role in the endogenous determination of monopoly price. In the proposed model the single parameter representing political culture is the weight assigned to the enhancement of social welfare. Our main concern is with the study of the relationship between this parameter and the proposed monopoly price and, in turn, the rent-seeking rent-avoidance efforts of the potential monopoly and the consumers and their aggregate expected benefit. We are grateful to the referees for their constructive and helpful comments.     

Freedom of choice and expected compromise

This article develops a new measure of freedom of choice based on the proposal that a set offers more freedom of choice than another if, and only if, the expected degree of dissimilarity between a random alternative from the set of possible alternatives and the most similar offered alternative in the set is smaller. Furthermore, a version of this measure is developed, which is able to take into account the values of the possible options.     

The triumph of hope over disappointment: A note on the utility value of good health expectations

In this paper, we present and test the empirical implications of competing theories about how expectations of outcomes affect utility. In the first utility formulation, which is consistent with particular interpretations of disappointment, prospect theory and regret theory, individuals receive negative utility from outcomes that were worse than expected. This directly implies that expectations themselves enter utility negatively. The second utility formulation incorporates anticipatory savoring, where positive expectations about the future directly lead to more utility today. We test which of these formulations best explains actual connections between health and welfare over time, using data from the Household Income and Labour Dynamics in Australia survey. Estimated coefficients from fixed-effects ordered logit models support a strong positive utility impact of positive expectations: expecting good health in the future increases happiness now. Our results are one argument for benevolent health care providers to allow individuals to maintain unrealistically positive expectations about the future.     

Empirical testing of the expected utility model

Suppose an individual is faced with a set of alternatives with uncertain money outcomes, then according to the expected utilily moded the alternative with the highest cxpected utility will be chosen. In the present paper this model is tested against the more general model given by Kahneman and Iversky (1979) and others. As contrasted with usual practice, the test is based on an exogenously measured utility function. The result of the test is that the expected utility model has to be rejected, both for a concavee and for an S-shaped specification of the utility function. The subjective evaluation of an objectve probability of 0.5 is in this study estimated at a value of 0.45 or 0.47. depending on the functional specification used.Our main conclusion is that although the hypotlicsis of expected utility has to be rejected, for practical purposes the difference between 0.5 and 0.45 (0.47) is so slight, that the hypothesis is a good working approximation. We do not know whether this remains true for valus of the objective probability considerably different from 0.5.     

Welfarist evaluations of decision rules under interstate utility dependencies

We provide welfarist evaluations of decision rules for federations of states and consider models, under which the interests of people from different states are stochastically dependent. We concentrate on two welfarist standards, viz. that the expected average utility for a person in the federation be maximized or that the expected utilities for the different people be equal. We discuss an analytical result that characterizes the decision rule with maximum expected average utility, set up a class of models that display interstate dependencies and run simulations for different dependency scenarios in the European Union. We find that the results that Beisbart and Bovens (Soc Choice Welf 29:581–608, 2007) established for two types of models without interstate dependencies are fairly stable if interstate dependencies are switched on. There are exceptions, though: sometimes the way in which alternative decision rules shape the welfare distribution is significantly affected by such dependencies. These exceptions particularly include cases in which the interests of people from different states are partly anti-correlated.     

Capabilities and achievements: An empirical study

This paper contributes to the development of the capabilities approach by showing that capabilities can, counter prevailing wisdom, be measured. By operationalising the capabilities element of Sen's non-welfarist theory, the paper develops the data required by this novel approach to welfare economics and by exploring relations to life-satisfaction (happiness) it also examines new economic co-variates of experienced utility. A postal questionnaire is designed to examine elements of Sen's theory of capabilities and implemented on a random sample of English voters. Analysis of survey results includes ordinal logistic regression models of overall capabilities, rank correlations between own capabilities and views about the distribution of capabilities, rank correlations between capabilities and achievements and a set of ordered logit models explaining achievements as a function of corresponding capabilities. Furthermore, results show that it is possible to make statistically significant distinctions between different capabilities, that perceptions of others’ capabilities are sometimes related to own capabilities and that achievements appear, in general, to be related to corresponding capabilities. Finally, and in keeping with oft-found paradoxes in the happiness literature, an examination of co-variates suggests that satisfaction with capabilities might be negatively related to objective measures of opportunity.     

Choosing subsets: a size-independent probabilistic model and the quest for a social welfare ordering

“Subset voting” denotes a choice situation where one fixed set of choice alternatives (candidates, products) is offered to a group of decision makers, each of whom is requested to pick a subset containing any number of alternatives. In the context of subset voting we merge three choice paradigms, “approval voting“ from political science, the “weak utility model” from mathematical psychology, and “social welfare orderings” from social choice theory. We use a probabilistic choice model proposed by Falmagne and Regenwetter (1996) built upon the notion that each voter has a personal ranking of the alternatives and chooses a subset at the top of the ranking. Using an extension of Sen's (1966) theorem about value restriction, we provide necessary and sufficient conditions for this empirically testable choice model to yield a social welfare ordering. Furthermore, we develop a method to compute Borda scores and Condorcet winners from subset choice probabilities. The technique is illustrated on an election of the Mathematical Association of America (Brams, 1988). Received: 18 August 1995 / Accepted: 13 February 1997     

On probabilistic rationalizability

This paper examines the problem of rationalizability of a choice system without imposing restrictions on the universal set of alternatives and the family of feasible sets. A choice system is the probabilistic counterpart of a choice function which is basic to much of the theory of individual choice behaviour in economics. We provide a necessary and sufficient condition for a choice system to be induced by a probability measure on a set of utility functions. I would like to thank the editor and two anonymous referees for helpful comments.     

A CROSS-SECTION ANALYSIS OF THE DEMAND FOR NEW AND USED AUTOMOBILES IN THE UNITED STATES

This paper investigates the effects of income and other family characteristics on the demand for new and used automobiles. The multinomial logit probability model is employed to explain a family's choice of age and number of automobiles. Two cross-section surveys are analyzed to ascertain how well these components of demand can be explained by socio-economic variables.     

Measures of freedom

According to the capability approach and more orthodox theories of individual well-being, freedom is an important ingredient of individual welfare. In operationalising these theories, therefore, it is crucial to have a practical measure of freedom. This paper analyses the measures of freedom proposed by Pattanaik and Xu, Steiner and Carter, Kramer, and Rosenbaum. We provide two interpretations of the first three measures. It is shown that one of these interpretations can be useful in empirical applications, while the other, together with additional arguments, considerably weakens Kramer's measure of freedom. Finally, it is shown that Rosenbaum's measure is not satisfactory as well because it yields counterintuitive results.     

Assent-maximizing social choice

We take a decision theoretic approach to the classic social choice problem, using data on the frequency of choice problems to compute social choice functions. We define a family of social choice rules that depend on the population’s preferences and on the probability distribution over the sets of feasible alternatives that the society will face. Our methods generalize the well-known Kemeny Rule. In the Kemeny Rule, it is known a priori that the subset of feasible alternatives will be a pair. We define a distinct social choice function for each distribution over the feasible subsets. Our rules can be interpreted as distance minimization—selecting the order closest to the population’s preferences, using a metric on the orders that reflects the distribution over the possible feasible sets. The distance is the probability that two orders will disagree about the optimal choice from a randomly selected available set. We provide an algorithmic method to compute these metrics in the case where the probability of a given feasible set is a function only of its cardinality.     

Conditionality of adaptiveness: Investigating the relationship between numeracy and adaptive behavior

Recent studies have illustrated that individuals with higher numeracy are more likely to make adaptive choices than individuals with lower numeracy. Highly numerate individuals can consistently make normatively superior choices by maximizing expected value (EV) in meaningful choice problems (high-payoff condition). However, in trivial problems (low-payoff condition), they can also adaptively change their strategy to make good enough choices and not follow a normatively superior strategy. Upon inspection of choice problems used in earlier studies, it was revealed that payoff was not the only varying factor between the two payoff conditions. Therefore, it is unclear whether payoff conditions alone can provide sufficient context for adaptive modulation in decision strategy. In two pre-registered studies (N = 343), we tested numerate individuals’ adaptiveness under high- and low-payoff conditions addressing the limitations of earlier studies. Results revealed that the presence of two payoff conditions together did not initiate adaptive strategy selection, regardless of participants’ numeracy. Instead, numerate individuals, compared to less numerate individuals, consistently made more EV-consistent choices in both payoff conditions. We identified that the change in EV consistency across payoff conditions was influenced more by the absolute difference than the relative difference in the expected reward.     

Strategic behaviour and a notion of ex ante efficiency in a voting model

A person is said to prefer in the stochastic dominance sense one lottery-over-outcomes over another lottery-over-outcomes if the probability of his (at least) first choice being selected in the first lottery is greater than or equal to the analogous probability in the second lottery, the probability of his at least second choice being selected in the first lottery is greater than or equal to the analogous probability in the second lottery, and so on, with at least one strict inequality. This (partial) preference relation is used to define straightforwardness of a social choice function that maps profiles of ordinal preferences into lotteries over outcomes. Given a prior probability distribution on profiles this partial preference ordering (taking into account the additional randomness) is used to induce a partial preference ordering over social choice functions for each individual. These are used in turn to define ex ante Pareto undominated (efficient) social choice functions. The main result is that it is impossible for a social choice function to be both ex ante efficient and straightforward. We also extend the result to cardinal preferences and expected utility evaluations.This work was supported by Grant #SOC 77-27403 and #SES 80-26086 from the National Science Foundation. It has been prepared at the University of Illinois and the University of Pennsylvania. We want to thank Steve Matthews and an anonymous referee for helpful comments     

FOUR USEFUL FINITE MIXTURE MODELS FOR REGRESSION ANALYSES OF PANEL DATA WITH A CATEGORICAL DEPENDENT VARIABLE

This paper describes and contrasts two useful ways to employ a latent class variable as a mixture variable in regression analyses of panel data with a categorical dependent variable. One way is to model unobserved heterogeneity in the trajectory, or change in the distribution, of the dependent variable. Two models that accomplish this are the latent trajectory model and latent growth curve model for a categorical dependent variable having ordered categories. Each latent class here represents a distinct trajectory of the dependent variable. The latent trajectory model introduces covariate effects on the composition of latent classes, while the latent growth curve model introduces covariate effects on both the "intercept" and the "slope" of growth in logit, which may vary among latent classes.
The other useful way is to model unobserved heterogeneity in the state dependence of the dependent variable. Two models that accomplish this are introduced for a simultaneous analysis of response probability and response stability, and the latent class variable is employed to distinguish two latent populations that differ in the stability of responses over time. One of them is the switching multinomial logit model with a time-lagged dependent variable as its separation indicator, and the other is the mover-stayer regression model.
By applying these four models to empirical data, this paper demonstrates the usefulness of these models for panel-data analyses. Example programs for specifying these models based on the LEM program are also provided.     

Paradoxe Folgen finanzieller Anreize zur Arbeitsaufnahme für die Beschäftigungsstabilität

Financial incentives to work (in-work benefits) are an instrument of labour market policy to motivate the unemployed to re-enter employment. Following neoclassical economic reasoning, such financial incentives should be effective, since the unemployed are expected to maximize financial utility. However, one common empirical finding is that such wage-subsidized employment is rather unstable. Applying Boudons cognitivist model to the ending of wage-subsidized employment the hypotheses are derived that firstly the in-work benefit is interpreted by the employee as a signal for the firm’s violation of the norm of reciprocity and secondly that the employee’s resulting sanctioning behaviour can raise the probability for job terminations. Survey data on in-work benefit recipients is used to test the hypotheses, performing ordered logit and event history analysis in combination with propensity score matching. Results from the empirical analysis support the hypotheses. It is concluded that labour market policy should be based not only on the assumption of economically rational behaviour, if labour market programmes are to be effective.     

The impact of AIDS on income and human capital

This paper studies the impact of HIV/AIDS on per capita income and education. It explores two channels on how HIV/AIDS affects income that have not been sufficiently stressed by previous literature: the reduction of the incentives to stay in school due to shorter expected longevity and the reduction in productivity of experienced workers. In the model, individuals live for three periods, may get infected in the second period, and with some probability die of AIDS before reaching the third period of their lives. Parents care for the welfare of the future generations so that they will maximize lifetime utility of their dynasty. The simulations predict that the most affected countries in Sub-Saharan Africa in the future will be, on average, 30% poorer than they would be without AIDS. Schooling will decline in some cases by 40%. These figures are dramatically reduced with widespread medical treatment, as it increases the survival probability and productivity of infected individuals.     

Neurobiological measurements of cardinal utility: Hedonimeters or learning algorithms?

A neurobiological argument has been used to defend the measurability and interpersonal comparability of cardinal utility. If true, a strong case could be made for the practical relevance of utility-based social welfare functions. In this paper I demonstrate that the current evidence does not corroborate the cardinal measurability and comparability of utility. Electrical stimulation of brain parts, or asymmetries in brain hemispherical activation, cannot be used to build a hedonimeter. The role of the neurotransmitter dopamine is that of a saliency detector or alternatively one validating adaptive learning models, but either way is not that of a general cardinal utility measure. Received: 3 March 2000/Accepted: 8 January 2001