Discussion Paper No. 78
November 4, 2021
The Axiomatic Foundation of Logit
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Abstract:
Multinomial logit is the canonical model of discrete choice but widely criticized for requiring functional form assumptions as foundation. The present paper shows that logit is behaviorally founded without such assumptions. Logit's functional form obtains if relative choice probabilities are independent of irrelevant alternatives and invariant to utility translation, to relabeling options (presentation independence), and to changing utilities of third options (context independence). Reviewing behavioral evidence, presentation and context independence seem to be violated in typical experiments, though not IIA and translation invariance. Relaxing context independence yields contextual logit (Wilcox, 2011), relaxing presentation independence allows to capture "focality" of options.
Keywords:
stochastic choice; logit; axiomatic foundation; behavioral evidence; utility estimation;
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Discussion Paper No. 77
Specification Testing in Random Coefficient Models
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In this paper, we suggest and analyze a new class of specification tests for random coefficient models. These tests allow to assess the validity of central structural features of the model, in particular linearity in coefficients, generalizations of this notion like a known nonlinear functional relationship, or degeneracy of the distribution of a random coefficient, i.e., whether a coefficient is fixed or random, including whether an associated variable can be omitted altogether. Our tests are nonparametric in nature, and use sieve estimators of the characteristic function. We provide formal power analysis against global as well as against local alternatives. Moreover, we perform a Monte Carlo simulation study, and apply the tests to analyze the degree of nonlinearity in a heterogeneous random coefficients demand model. While we find some evidence against the popular QUAIDS specification with random coefficients, it is not strong enough to reject the specification at the conventional significance level.
Keywords:
nonparametric; specification; testing; random coefficients; unobserved heterogeneity; sieve estimation; characteristic function; consumer demand;
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Discussion Paper No. 76
On the Relationship Between Cognitive Ability and Risk Preference
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This paper focuses on the relationship between cognitive ability and decision making under risk and uncertainty. We begin by clarifying some important distinctions between concepts and measurement of risk preference and cognitive ability and then take stock of what is known empirically on the connections between cognitive ability and measured risk preferences.
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Discussion Paper No. 75
Job Search with Subjective Wage Expectations
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This paper analyzes how subjective expectations about wage opportunities influence the job search decision. We match data on subjective wage expectations with administrative employment records. The data reveal that unemployed individuals over-estimate their future net re-employment wage by 10% on average. In particular, the average individual does not anticipate that wage offers decline in value with their elapsed time out of em- ployment. How does this optimism affect job finding? We analyze this question using a structural job search framework in which subjective expectations about future wage offers are not constrained to be consistent with reality. Results show that wage optimism has highly dynamic effects: upon unemployment entry, optimism decreases job finding by about 8%. This effect weakens over the unemployment spell and eventually switches sign after about 8 months of unemployment. From then onward, optimism prevents un- employed individuals from becoming discouraged and thus increases search. On average, optimism increases the duration of unemployment by about 6.5%.
Keywords:
job search; subjective expectations; structural estimation;
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Discussion Paper No. 74
A Compact Topology for Sigma-Algebra Convergence
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We propose a sequential topology on the collection of sub-sigma-algebras included in a separable probability space. We prove compactness of the conditional expectations with respect to L2-bounded random variables along sequences of sub-sigma-algebras. The varying index of measurability is captured by a bundle space construction. As a consequence, we establish the compactness of the space of sub-sigma-algebras. The proposed topology preserves independence and is compatible with join and meet operations. Finally, a new application to information economics is discussed.
Keywords:
convergence of sigma-algebras; compactness of sub-sigma-algebras; conditional expectation; fiber bundle; information economics;
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Discussion Paper No. 73
An Experiment on Social Mislearning
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We investigate experimentally whether social learners appreciate the redundancy of information conveyed by their observed predecessors' actions. Each participant observes a private signal and enters an estimate of the sum of all earlier-moving participants' signals plus her own. In a first treatment, participants move single-file and observe all predecessors' entries; Bayesian Nash Equilibrium (BNE) predicts that each participant simply add her signal to her immediate predecessor's entry. Although 75% of participants do so, redundancy neglect by the other 25% generates excess imitation and mild inefficiencies. In a second treatment, participants move four per period; BNE predicts that most players anti-imitate some observed entries. Such anti-imitation occurs in 35% of the most transparent cases, and 16% overall. The remaining redundancy neglect creates dramatic excess imitation and inefficiencies: late-period entries are far too extreme, and on average participants would earn substantially more by ignoring their predecessors altogether.
Keywords:
social learning; redundancy neglect; experiments; higher-order beliefs;
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Discussion Paper No. 72
The Term Structure of Sharpe Ratios and Arbitrage-Free Asset Pricing in Continuous Time
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Recent empirical studies suggest a downward sloping term structure of Sharpe ratios. We present a theoretical framework in continuous time that can cope with such a non-flat forward curve of risk prices. The approach departs from an arbitrage-free and incomplete market setting when different pricing measures are possible. Involved pricing measures now depend on the time of evaluation or the maturity of payoffs. This results in a time inconsistent pricing scheme. The dynamics can be captured by a time-delayed backward stochastic Volterra integral equation, which to the best of our knowledge, has not yet been studied.
Keywords:
term structures; sharpe ratio; incomplete markets; asset pricing; time inconsistency; arbitrage; (time-delayed) volterra equations;
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Discussion Paper No. 71
The Effect of Incentives in Non-Routine Analytical Team Tasks - Evidence From a Field Experiment
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Despite the prevalence of non-routine analytical team tasks in modern economies, little is known about how incentives influence performance in these tasks. In a field experiment with more than 3000 participants, we document a positive effect of bonus incentives on the probability of completion of such a task. Bonus incentives increase performance due to the reward rather than the reference point (performance threshold) they provide. The framing of bonuses (as gains or losses) plays a minor role. Incentives improve performance also in an additional sample of presumably less motivated workers. However, incentives reduce these workers' willingness to "explore" original solutions.
Keywords:
team work; bonus; incentives; loss; gain; non-routine; exploration;
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Discussion Paper No. 69
The Impact of a Negative Labor Demand Shock on Fertility - Evidence From the Fall of the Berlin Wall
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How does a negative labor demand shock impact fertility? I analyze this question in the context of the East German fertility decline after the fall of the Berlin Wall in 1989. I exploit differential pressure for restructuring across East German industries which led to unexpected, exogenous, and permanent changes to labor demand. I find that throughout the 1990s, women more severely impacted by the demand shock had relatively more children than their less-severely-impacted counterparts. Thus, the demand shock did not only depress the aggregate fertility level but also changed the composition of mothers. My paper shows that these two effects do not necessarily operate in the same direction.
Keywords:
J13; J23; P36;
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Discussion Paper No. 70
Signal Sell: Product Lines when Consumers Differ Both in Taste for Quality and Image Concern
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This paper analyzes optimal product lines when consumers differ both in their taste for quality and in their desire for social image. The market outcome features partial pooling and product differentiation that is not driven by heterogeneous valuations for quality but by image concerns. A typical monopoly outcome is a two-tier product line resembling a "masstige" strategy as observed in luxury goods markets. Products can have identical quality and differ only in price and image, thereby rationalizing quality-equivalent line extensions. Under competition, both average quality and market coverage are (weakly) higher but monopoly can yield higher welfare than competition.
Keywords:
image concern; conspicuous consumption; two-dimensional screening; nonlinear pricing;
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