Discussion Paper No. 368
January 20, 2023
Optimal Trade Execution under Endogenous Order Flow
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Abstract:
We consider an optimal liquidation model in which an investor is required to execute meta-orders during intraday trading periods, and his trading activity triggers child orders and endogenously affects future order flow, both instantaneously and permanently. Under the assumptions of risk neutrality and deterministic constants of the impact parameters, we provide closed-form solutions and illustrate the relationship between trading strategies and feedback effects. The optimal trading strategy is of hyperbolic form if the feedback effect of current trading on future order flow is not too strong. If the feedback effect becomes too dominating, a cyclic strategy with possible beneficial round-trips may emerge. We set up an estimation framework so that parameter estimates can be made directly from public data and are consistent with the theoretical model. When implementing our model on 110 NASDAQ stocks, the empirical analysis shows that as the level of endogeneity increases, our strategy provides increasingly better performance than the commonly adopted trading strategy. The empirical analysis also shows that too strong feedback effects do not exist in practice, thus ruling out statistical arbitrage.
Keywords:
liquidity risk; optimal trading strategy; portfolio liquidation; Hawkes process;
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Discussion Paper No. 367
An Experimental Test of the Global-Game Selection in Coordination Games with Asymmetric Players
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In symmetric binary-choice coordination games, the global-game selection (GGS) has been proven to predict a high proportion of observed choices correctly. In these games, the GGS is identical to the best response to Laplacian beliefs about the fraction of players choosing either action. This paper presents an experiment on asymmetric games in which the GGS differs from the best response to Laplacian beliefs. It shows that the best response to Laplacian beliefs is a better predictor of behavior in these games than the GGS. In the considered games, the GGS provides poor guidance and also fails to give the right qualitative comparative statics predictions. Simple cognitive hierarchy models yield better predictions. The best response to a Laplacian belief about the distribution of other players' actions yields the best prediction. Comparing maximum likelihood estimates for four probabilistic models shows that an estimated global-game equilibrium fits worse than a rather simple level-k or Laplacian-belief model combined with a standard error-response function.
Keywords:
coordination games; equilibrium selection; global game; Laplacian beliefs; private information; network effects;
JEL-Classification:
C72; C91; D81;
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Discussion Paper No. 371
Home alone: Widows' Well-Being and Time
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Abstract:
Using data from the Survey of Health, Ageing and Retirement in Europe (SHARE, 2004-17) and time diaries from Poland (2013), the U.S. (2006-16), the U.K. (2014-15) and France (2009-10), we examine differences between widowed and partnered older women in well-being and its development in widowhood. Most importantly, our analysis accounts for time use, an aspect which has not been studied previously. We trace the evolution of well-being of women who become widowed by comparing them with their matched non-widowed ‘statistical twins’ and examine the role of an exceptionally broad set of potential moderators of widowhood’s impact on well-being. We confirm a dramatic decrease in mental health and life satisfaction after the loss of partner, followed by a slow partial recovery over a five-year period. An extensive set of controls recorded prior to widowhood, including detailed family ties and social networks, provides little help in explaining the deterioration in well-being. Unique data from time-diaries kept by older women in several European countries and the U.S. tell us why: the key factor behind widows’ reduced well-being is increased time spent alone.
Keywords:
widowhood; well-being; social networks; time use;
JEL-Classification:
I31; I19; J14;
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Discussion Paper No. 366
January 4, 2023
Everyone Likes to Be Liked: Experimental Evidence from Matching Markets
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Abstract:
Matching markets can be unstable when individuals prefer to be matched to a partner who also wants to be matched with them. Through a pre-registered and theory-guided laboratory experiment, we provide evidence that such reciprocal preferences exist, significantly decrease stability in matching markets, and are driven both by belief-based and preference-based motives. Participants expect partners who want to be matched with them to be more cooperative, and are more altruistic themselves. This leads to higher cooperation and larger profits when participants can consider each other's preferences.
Keywords:
experiment; market design; matching; reciprocal preferences; incomplete information; Gale-Shapley deferred acceptance mechanism;
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Discussion Paper No. 365
Biased Beliefs in Search Markets
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Abstract:
We study the implications of biased consumer beliefs for search market outcomes in the seminal framework due to Diamond (1971). Biased consumers base their search strategy on a belief function which specifies for any (true) distribution of utility offers in the market a possibly incorrect distribution of utility offers. If biased consumers overestimate the best offer in the market, a novel type of equilibrium may emerge in which firms make exceptionally favourable offers in order to meet biased consumers' unreasonable high expectations which then become partially self-fulfilling. Consequently, the presence of biased consumers may improve the welfare of all consumers.
Keywords:
consumer search; bounded rationality; cursed beliefs;
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Discussion Paper No. 364
Competition in Search Markets with Naive Consumers
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We study the interplay between quality provision and consumer search in a search market where firms may design products of inferior quality to promote them to naive consumers who fail to fully understand product characteristics. We derive an equilibrium in which both superior and inferior quality is offered and show that as search frictions vanish, the share of firms offering superior goods in the market goes to zero. The presence of inferior products harms sophisticated consumers, as it forces them to search longer to find a superior product. We argue that policy interventions that reduce search frictions such as the standardization of price and package formats may harm welfare. In contrast, reducing the number of naive consumers through transparency policies and education campaigns as well as a minimum quality standard can improve welfare.
Keywords:
inferior products; competition; naivete; consumer search;
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Discussion Paper No. 363
The Effect of Pension Wealth on Employment
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This study provides novel evidence about the pension wealth elasticity of employment. For the identification we exploit reform-induced variation of pension wealth that is related to the number of children but which does not affect the implicit tax rate of employment. We use a difference-in-differences estimator based on administrative data from the German pension insurance and find that, on average, the negative employment effect of pension wealth is significant and economically important. Heterogeneity analyses document a strong age pattern showing that the employment effects are driven by behavioral responses of women close to retirement. The age pattern is partly explained by the positive effect of pension wealth on disability pensions after the age of 60.
Keywords:
pension reform; pension wealth elasticity; female labour supply; retirement; difference in differences;
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Discussion Paper No. 362
Approximate Bayesian Implementation and Exact Maxmin Implementation: An Equivalence
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This paper provides a micro-foundation for approximate incentive compatibility using ambiguity aversion. In particular, we propose a novel notion of approximate interim incentive compatibility, approximate local incentive compatibility, and establish an equivalence between approximate local incentive compatibility in a Bayesian environment and exact interim incentive compatibility in the presence of a small degree of ambiguity. We then apply our result to the implementation of efficient allocations. In particular, we identify three economic settings—including ones in which approximately efficient allocations are implementable, ones in which agents are informationally small, and large double auctions—in which efficient allocations are approximately locally implementable when agents are Bayesian. Applying our result to those settings, we conclude that efficient allocations are exactly implementable when agents perceive a small degree of ambiguity.
Keywords:
approximate local incentive compatibility; ambiguity aversion; efficiency; informational size; modified VCG mechanism; double auction;
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Discussion Paper No. 361
Intertemporal Hedging and Trade in Repeated Games with Recursive Utility
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Abstract:
Recursive preferences have found widespread application in representative-agent asset-pricing models and general equilibrium. A majority of these applications exploit two decision-theoretic properties not shared by the standard model of intertemporal choice: (i) agents care about the intertemporal distribution of risk and (ii) rates of time preference, rather than being exogenously fixed, may vary with the level of consumption. We investigate what these features imply in the context of a repeated strategic interaction. Specifically, we identify novel opportunities for the players to manage risk and trade intertemporally, and characterize when such opportunities lead to an expansion of the fea- sible set of payoffs. Sharp implications for equilibrium behavior and the folk theorem are also deduced.
Keywords:
recursive utility; repeated games; correlation aversion; endogenous discounting; intertemporal trade; intertemporal hedging;
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Discussion Paper No. 360
Sufficient Statistics for Nonlinear Tax Systems with General Across-income Heterogeneity
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Abstract:
This paper provides general and empirically implementable sufficient statistics formulas for optimal nonlinear tax systems in the presence of across-income heterogeneity in preferences, inheritances, income-shifting capabilities, and other sources. We study unrestricted tax systems on income and savings (or other commodities) that implement the optimal direct-revelation mechanism, as well as simpler tax systems that impose common restrictions like separability between earnings and savings taxes. We characterize the optimum using familiar elasticity concepts and a sufficient statistic for general across-income heterogeneity: the difference between the cross-sectional variation of savings with income, and the causal effect of income on savings. The Atkinson-Stiglitz Theorem is a knife-edge case corresponding to zero difference, and a number of other key results in optimal tax theory are subsumed as special cases. We provide tractable extensions of these results that include multidimensional heterogeneity, additional efficiency rationales for taxing heterogeneous returns, and corrective motives to encourage more saving. Applying these formulas in a calibrated model of the U.S. economy, we find that the optimal savings tax is positive and progressive.
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