Discussion Paper No. 59
November 4, 2021
Testing Missing At Random Using Instrumental Variables
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Abstract:
This paper proposes a test for missing at random (MAR). The MAR assumption is shown to be testable given instrumental variables which are independent of response given potential outcomes. A nonparametric testing procedure based on integrated squared distance is proposed. The statistic's asymptotic distribution under the MAR hypothesis is derived. In particular, our results can be applied to testing missing completely at random (MCAR). A Monte Carlo study examines finite sample performance of our test statistic. An empirical illustration analyzes the nonresponse mechanism in labor income questions.
Keywords:
C12; C14;
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Discussion Paper No. 58
Nonparametric Estimation in Case of Endogenous Selection
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Abstract:
This paper addresses the problem of estimation of a nonparametric regression function from selectively observed data when selection is endogenous. Our approach relies on independence between covariates and selection conditionally on potential outcomes. Endogeneity of regressors is also allowed for. In the exogenous and endogenous case, consistent two-step estimation procedures are proposed and their rates of convergence are derived. Pointwise asymptotic distribution of the estimators is established. In addition, bootstrap uniform confidence bands are obtained. Finite sample properties are illustrated in a Monte Carlo simulation study and an empirical illustration.
Keywords:
endogenous selection; instrumental variable; sieve minimum distance; regression estimation; inverse problem; inverse probability weighting; convergence rate; asymptotic normality; bootstrap uniform confidence bands;
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Discussion Paper No. 50
November 3, 2021
Why Should Majority Voting Be Unfair?
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Abstract:
The common use of majority rule in group decision making is puzzling. In theory, it inequitably favors the proposer, and paradoxically, it disadvantages voters further if they are inequity averse. In practice, however, outcomes are equitable. The present paper analyzes data from a novel experimental design to identify the underlying social preferences. Our experiment compares one-shot and indefinite horizon versions of random-proposer majority bargaining (the Baron-Ferejohn game) which allow us to disentangle behaviors compatible with altruism, inequity aversion, and reference dependent altruism. Most subjects are classified as reference-dependent altruists, around 10% are inequity averse. Subjects are egoistic when their payoff is below their reference point, they become efficiency concerned when satisfied, and the reference point is either the ex ante expectation or the opponent's payoff. Finally, we successfully test RDA out-of-sample on a number of distribution and bargaining games from three seminal social preference experiments.
Keywords:
bargaining; voting; experiment; social preferences; quantal response equilibrium;
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Discussion Paper No. 38
Time Preferences and Bargaining
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Abstract:
This paper presents an analysis of general time preferences in the canonical Rubinstein (1982) model of bargaining, allowing for arbitrarily history-dependent strategies. I derive a simple sufficient structure for optimal punishments and thereby fully characterize (i) the set of equilibrium outcomes for any given preference profile, and (ii) the set of preference profiles for which equilibrium is unique. Based on this characterization, I establish that a weak notion of present bias—implied, e.g., by any hyperbolic or quasi-hyperbolic discounting—is sufficient for equilibrium to be unique, stationary and efficient. Conversely, I demonstrate how certain violations of present bias give rise to multiple (non-stationary) equilibria that feature delayed agreement under gradually increasing offers.
Keywords:
time preferences; dynamic inconsistency; alternating offers; bargaining; optimal punishments; delay;
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Discussion Paper No. 36
Knowing Me, Imagining You: Projection and Overbidding in Auctions
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Overbidding in auctions has been attributed to e.g. risk aversion, loser regret, level-k, and cursedness, relying on varying identifying assumptions. I argue that “type projection” organizes these findings and largely captures observed behavior. Type projection formally models that people tend to believe others have object values similar to their own—a robust psychological phenomenon that naturally applies to auctions. First, I show that type projection generates the main behavioral phenomena observed in auctions, including increased sense of competition (“loser regret”) and broken Bayesian updating (“cursedness”). Second, re-analyzing data from seven experiments, I show that type projection explains the stylized facts of behavior across private and common value auctions. Third, in a structural analysis relaxing the identifying assumptions made in earlier studies, type projection consistently captures behavior best, in-sample and out-of-sample. The results reconcile bidding patterns across conditions and have implications for behavioral and empirical analyses as well as policy.
Keywords:
auctions; overbidding; projection; risk aversion; cursed equilibrium; depth of reasoning;
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Discussion Paper No. 35
Discrete Choice with Presentation Effects
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Experimenters have to make theoretically irrelevant decisions concerning user inter- faces and ordering or labeling of options. Such presentation decisions affect behavior and cause results to appear contradictory across experiments, obstructing utility esti- mation and policy recommendations. The present paper derives a model of choice allowing analysts to control for both presentation effects and stochastic errors in econometric analyses. I test the model in a comprehensive re-analysis of dictator game experiments. Controlling for presentation effects, preference estimates are con- sistent across experiments and predictive out-of-sample, highlighting the fundamen- tal role of presentation for choice, and this notwithstanding the possibility of reliable estimation and prediction.
Keywords:
discrete choice; presentation effects; utility estimation; counterfactual predictions; laboratory experiment;
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Discussion Paper No. 13
Measuring Applicant Quality to Detect Discrimination In Peer-to-Peer Lending
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Abstract:
We measure the quality of applications for online peer-to-peer lend- ing in Germany and relate it to gender discrimination. The data context allows summarizing application quality as a single numeric measure, the expected internal rate of return. The measure serves as a control variable and is interacted with the applicants’ gender. We find that women enjoy higher funding rates than men, mainly be- cause they are less punished when they offer a low application qual- ity. The evidence is consistent with the hypothesis that the predom- inantly male lenders have a less precise understanding of women’s applications than of men’s applications.
Keywords:
gender discrimination; household finance; irrational beliefs;
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