We propose a new method for learning causal structures from observational data, a process known as causal discovery. Our method takes as input observational data over a set of variables and returns a graph in which causal relations are specified by directed edges. We consider a highly general search space that accommodates latent confounders and feedback cycles, which few extant methods do. We formulate the discovery problem as an integer program, and propose a solution technique that leverages the conditional independence structure in the data to identify promising edges for inclusion in the output graph. In the large-sample limit, our method recovers a graph that is equivalent to the true data-generating graph. Computationally, our method is competitive with the state-of-the-art, and can solve in minutes instances that are intractable for alternative causal discovery methods. We demonstrate our approach by showing how it can be used to examine the validity of instrumental variables, which are widely used for causal inference. In particular, we analyze US Census data from the seminal paper on the returns to education by Angrist and Krueger (1991), and find that the causal structures uncovered by our method are consistent with the literature.
{"title":"Discovering Causal Models with Optimization: Confounders, Cycles, and Feature Selection","authors":"F. Eberhardt, Nur Kaynar, Auyon Siddiq","doi":"10.2139/ssrn.3873034","DOIUrl":"https://doi.org/10.2139/ssrn.3873034","url":null,"abstract":"We propose a new method for learning causal structures from observational data, a process known as causal discovery. Our method takes as input observational data over a set of variables and returns a graph in which causal relations are specified by directed edges. We consider a highly general search space that accommodates latent confounders and feedback cycles, which few extant methods do. We formulate the discovery problem as an integer program, and propose a solution technique that leverages the conditional independence structure in the data to identify promising edges for inclusion in the output graph. In the large-sample limit, our method recovers a graph that is equivalent to the true data-generating graph. Computationally, our method is competitive with the state-of-the-art, and can solve in minutes instances that are intractable for alternative causal discovery methods. We demonstrate our approach by showing how it can be used to examine the validity of instrumental variables, which are widely used for causal inference. In particular, we analyze US Census data from the seminal paper on the returns to education by Angrist and Krueger (1991), and find that the causal structures uncovered by our method are consistent with the literature.","PeriodicalId":11485,"journal":{"name":"Econometrics: Applied Econometrics & Modeling eJournal","volume":"4 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91524534","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract Decision-makers often collect and aggregate experts’ point predictions about continuous outcomes, such as stock returns or product sales. In this article, we model experts as Bayesian agents and show that means, including the (weighted) arithmetic mean, trimmed means, median, geometric mean, and essentially all other measures of central tendency, do not use all information in the predictions. Intuitively, they assume idiosyncratic differences to arise from error instead of private information and hence do not update the prior with all available information. Updating means in terms of unused information improves their expected accuracy but depends on the experts’ prior and information structure that cannot be estimated based on a single prediction per expert. In many applications, however, experts consider multiple stocks, products, or other related items at the same time. For such contexts, we introduce ANOVA updating – an unsupervised technique that updates means based on experts’ predictions of multiple outcomes from a common population. The technique is illustrated on several real-world datasets.
{"title":"Improving the Wisdom of Crowds with Analysis of Variance of Predictions of Related Outcomes","authors":"Ville A. Satopää","doi":"10.2139/ssrn.3786074","DOIUrl":"https://doi.org/10.2139/ssrn.3786074","url":null,"abstract":"Abstract Decision-makers often collect and aggregate experts’ point predictions about continuous outcomes, such as stock returns or product sales. In this article, we model experts as Bayesian agents and show that means, including the (weighted) arithmetic mean, trimmed means, median, geometric mean, and essentially all other measures of central tendency, do not use all information in the predictions. Intuitively, they assume idiosyncratic differences to arise from error instead of private information and hence do not update the prior with all available information. Updating means in terms of unused information improves their expected accuracy but depends on the experts’ prior and information structure that cannot be estimated based on a single prediction per expert. In many applications, however, experts consider multiple stocks, products, or other related items at the same time. For such contexts, we introduce ANOVA updating – an unsupervised technique that updates means based on experts’ predictions of multiple outcomes from a common population. The technique is illustrated on several real-world datasets.","PeriodicalId":11485,"journal":{"name":"Econometrics: Applied Econometrics & Modeling eJournal","volume":"8 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88250187","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We develop a novel approach based on the canonical correlation analysis to identify the number of global factors in the multilevel factor model. We propose the two consistent selection criteria, the canonical correlations difference (CCD) and the modified canonical correlations (MCC). Via Monte Carlo simulations, we show that CCD and MCC select the number of global factors correctly even in small samples, and they are robust to the presence of serially correlated and weakly cross-sectionally correlated idiosyncratic errors as well as the correlated local factors. Finally, we demonstrate the utility of our approach with an application to the multilevel asset pricing model for the stock return data in 12 industries in the U.S.
{"title":"Canonical Correlation-based Model Selection for the Multilevel Factors","authors":"In Choi, Rui Lin, Y. Shin","doi":"10.2139/ssrn.3590109","DOIUrl":"https://doi.org/10.2139/ssrn.3590109","url":null,"abstract":"We develop a novel approach based on the canonical correlation analysis to identify the number of global factors in the multilevel factor model. We propose the two consistent selection criteria, the canonical correlations difference (CCD) and the modified canonical correlations (MCC). Via Monte Carlo simulations, we show that CCD and MCC select the number of global factors correctly even in small samples, and they are robust to the presence of serially correlated and weakly cross-sectionally correlated idiosyncratic errors as well as the correlated local factors. Finally, we demonstrate the utility of our approach with an application to the multilevel asset pricing model for the stock return data in 12 industries in the U.S.","PeriodicalId":11485,"journal":{"name":"Econometrics: Applied Econometrics & Modeling eJournal","volume":"9 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80174650","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We use a decision-theoretic framework to study the problem of forecasting discrete outcomes when the forecaster is unable to discriminate among a set of plausible forecast distributions because of partial identification or concerns about model misspecification or structural breaks. We derive "robust" forecasts which minimize maximum risk or regret over the set of forecast distributions. We show that for a large class of models including semiparametric panel data models for dynamic discrete choice, the robust forecasts depend in a natural way on a small number of convex optimization problems which can be simplified using duality methods. Finally, we derive "efficient robust" forecasts to deal with the problem of first having to estimate the set of forecast distributions and develop a suitable asymptotic efficiency theory. Forecasts obtained by replacing nuisance parameters that characterize the set of forecast distributions with efficient first-stage estimators can be strictly dominated by our efficient robust forecasts.
{"title":"Robust Forecasting","authors":"T. Christensen, H. Moon, F. Schorfheide","doi":"10.2139/ssrn.3737629","DOIUrl":"https://doi.org/10.2139/ssrn.3737629","url":null,"abstract":"We use a decision-theoretic framework to study the problem of forecasting discrete outcomes when the forecaster is unable to discriminate among a set of plausible forecast distributions because of partial identification or concerns about model misspecification or structural breaks. We derive \"robust\" forecasts which minimize maximum risk or regret over the set of forecast distributions. We show that for a large class of models including semiparametric panel data models for dynamic discrete choice, the robust forecasts depend in a natural way on a small number of convex optimization problems which can be simplified using duality methods. Finally, we derive \"efficient robust\" forecasts to deal with the problem of first having to estimate the set of forecast distributions and develop a suitable asymptotic efficiency theory. Forecasts obtained by replacing nuisance parameters that characterize the set of forecast distributions with efficient first-stage estimators can be strictly dominated by our efficient robust forecasts.","PeriodicalId":11485,"journal":{"name":"Econometrics: Applied Econometrics & Modeling eJournal","volume":"2 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73074349","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Recent studies report that the size effect in the cross-section of stock returns has disappeared after the early 1980s. This paper shows that the disappearance of the size effect from realized returns can be attributed to unexpected shocks to the profitability of small and big firms. We find that small firms experience large negative profitability shocks after the early 1980s, while big firms experience large positive shocks. As a result, realized returns of small and big firms over this period differ substantially from expected returns. After adjusting for the price impact of profitability shocks, we find that there still is a robust size effect in the cross-section of expected returns. Our results highlight the importance of in-sample cash flow shocks for understanding cross-sectional return predictability.
{"title":"Resurrecting the Size Effect: Firm Size, Profitability Shocks, and Expected Stock Returns","authors":"Kewei Hou, Mathijs A. Van Dijk","doi":"10.2139/ssrn.1536804","DOIUrl":"https://doi.org/10.2139/ssrn.1536804","url":null,"abstract":"Recent studies report that the size effect in the cross-section of stock returns has disappeared after the early 1980s. This paper shows that the disappearance of the size effect from realized returns can be attributed to unexpected shocks to the profitability of small and big firms. We find that small firms experience large negative profitability shocks after the early 1980s, while big firms experience large positive shocks. As a result, realized returns of small and big firms over this period differ substantially from expected returns. After adjusting for the price impact of profitability shocks, we find that there still is a robust size effect in the cross-section of expected returns. Our results highlight the importance of in-sample cash flow shocks for understanding cross-sectional return predictability.","PeriodicalId":11485,"journal":{"name":"Econometrics: Applied Econometrics & Modeling eJournal","volume":"50 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72736685","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The Securities and Exchange Commission’s 2008 emergency order introduced a shorting ban of some 800 financials traded in the US. This paper provides an empirical analysis of the options market around the ban period. Using transaction level data from OPRA (The Options Price Reporting Authority), we study the options volume, spreads, pricing measures and option trade volume informativeness during the ban. We also consider the put–call parity relationship. While mostly statistically significant, economic magnitudes of our results suggest that the impact of the ban on the equity options market was likely not as dramatic as initially thought.
{"title":"Equity Options During the Shorting Ban of 2008","authors":"Nusret Cakici, G. Goswami, Sinan Tan","doi":"10.2139/ssrn.1618873","DOIUrl":"https://doi.org/10.2139/ssrn.1618873","url":null,"abstract":"The Securities and Exchange Commission’s 2008 emergency order introduced a shorting ban of some 800 financials traded in the US. This paper provides an empirical analysis of the options market around the ban period. Using transaction level data from OPRA (The Options Price Reporting Authority), we study the options volume, spreads, pricing measures and option trade volume informativeness during the ban. We also consider the put–call parity relationship. While mostly statistically significant, economic magnitudes of our results suggest that the impact of the ban on the equity options market was likely not as dramatic as initially thought.<br>","PeriodicalId":11485,"journal":{"name":"Econometrics: Applied Econometrics & Modeling eJournal","volume":"90 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82741661","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper constructs a new measure of attention allocation by local investors relative to nonlocals using aggregate search volume from Google. We first present a conceptual framework in which local investors optimally choose to focus their attention on local stocks when they receive private news, leading to an asymmetric allocation of attention between local and nonlocal investors. Consistent with the main prediction of this framework, we find that firms attracting abnormally high asymmetric attention from local relative to nonlocal investors earn higher returns. A portfolio that goes long in stocks with high asymmetric attention and short in stocks with low asymmetric attention has an alpha of 32 basis points per month. The results are stronger for stocks with a greater degree of information friction. The new measure of asymmetric attention allows one to infer the arrival of unobservable private information by observing investors’ attention allocation behavior. This paper was accepted by Karl Diether, finance.
{"title":"Asymmetric Attention and Stock Returns","authors":"P. Cziraki, J. Mondria, Thomas Wu","doi":"10.2139/ssrn.1772821","DOIUrl":"https://doi.org/10.2139/ssrn.1772821","url":null,"abstract":"This paper constructs a new measure of attention allocation by local investors relative to nonlocals using aggregate search volume from Google. We first present a conceptual framework in which local investors optimally choose to focus their attention on local stocks when they receive private news, leading to an asymmetric allocation of attention between local and nonlocal investors. Consistent with the main prediction of this framework, we find that firms attracting abnormally high asymmetric attention from local relative to nonlocal investors earn higher returns. A portfolio that goes long in stocks with high asymmetric attention and short in stocks with low asymmetric attention has an alpha of 32 basis points per month. The results are stronger for stocks with a greater degree of information friction. The new measure of asymmetric attention allows one to infer the arrival of unobservable private information by observing investors’ attention allocation behavior. This paper was accepted by Karl Diether, finance.","PeriodicalId":11485,"journal":{"name":"Econometrics: Applied Econometrics & Modeling eJournal","volume":"10 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2017-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76379858","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We introduce a novel economic indicator, named excess idle time (EXIT), measuring the extent of sluggishness in financial prices. Under a null and an alternative hypothesis grounded in no‐arbitrage (the null) and market microstructure (the alternative) theories of price determination, we derive a limit theory for EXIT leading to formal tests for staleness in the price adjustments. Empirical implementation of the theory indicates that financial prices are often more sluggish than implied by the (ubiquitous, in frictionless continuous‐time asset pricing) semimartingale assumption. EXIT is interpretable as an illiquidity proxy and is easily implementable, for each trading day, using transaction prices only. By using EXIT, we show how to estimate structurally market microstructure models with asymmetric information.
{"title":"EXcess Idle Time","authors":"F. Bandi, Davide Pirino, R. Renò","doi":"10.2139/ssrn.2199468","DOIUrl":"https://doi.org/10.2139/ssrn.2199468","url":null,"abstract":"We introduce a novel economic indicator, named excess idle time (EXIT), measuring the extent of sluggishness in financial prices. Under a null and an alternative hypothesis grounded in no‐arbitrage (the null) and market microstructure (the alternative) theories of price determination, we derive a limit theory for EXIT leading to formal tests for staleness in the price adjustments. Empirical implementation of the theory indicates that financial prices are often more sluggish than implied by the (ubiquitous, in frictionless continuous‐time asset pricing) semimartingale assumption. EXIT is interpretable as an illiquidity proxy and is easily implementable, for each trading day, using transaction prices only. By using EXIT, we show how to estimate structurally market microstructure models with asymmetric information.","PeriodicalId":11485,"journal":{"name":"Econometrics: Applied Econometrics & Modeling eJournal","volume":"48 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2017-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85620778","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The traditional estimated return for the Markowitz mean-variance optimization has been demonstrated to be seriously departed from its theoretic value. We prove that this phenomenon is natural and the estimated optimal return is always larger than its theoretic parameter. Thereafter, we develop new bootstrap estimators for the optimal return and its asset allocation and prove that these bootstrap estimates are consistent with their counterpart parameters. Our simulation confirms the consistency; implying the essence of the portfolio analysis problem could be adequately captured by our proposed estimates. This greatly enhances the Markowitz meanvariance optimization procedure to be practically useful.
{"title":"Making Markowitz's Portfolio Optimization Theory Practically Useful","authors":"Z. Bai, Huixia Liu, W. Wong","doi":"10.2139/ssrn.900972","DOIUrl":"https://doi.org/10.2139/ssrn.900972","url":null,"abstract":"The traditional estimated return for the Markowitz mean-variance optimization has been demonstrated to be seriously departed from its theoretic value. We prove that this phenomenon is natural and the estimated optimal return is always larger than its theoretic parameter. Thereafter, we develop new bootstrap estimators for the optimal return and its asset allocation and prove that these bootstrap estimates are consistent with their counterpart parameters. Our simulation confirms the consistency; implying the essence of the portfolio analysis problem could be adequately captured by our proposed estimates. This greatly enhances the Markowitz meanvariance optimization procedure to be practically useful.","PeriodicalId":11485,"journal":{"name":"Econometrics: Applied Econometrics & Modeling eJournal","volume":"48 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2016-10-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81279537","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Allen N. Berger, Christa H. S. Bouwman, Thomas K. Kick, K. Schaeck
We study the effects of regulatory interventions and capital support (bailouts) on banks’ liquidity creation. We rely on instrumental variables to deal with possible endogeneity concerns. Our key findings, which are based on a unique supervisory German dataset, are that regulatory interventions robustly trigger decreases in liquidity creation, while capital support does not affect liquidity creation. Additional results include the effects of these actions on different components of liquidity creation, lending, and risk taking. Our findings provide new and important insights into the debates about the design of regulatory interventions and bailouts.
{"title":"Bank Liquidity Creation Following Regulatory Interventions and Capital Support","authors":"Allen N. Berger, Christa H. S. Bouwman, Thomas K. Kick, K. Schaeck","doi":"10.2139/ssrn.1908102","DOIUrl":"https://doi.org/10.2139/ssrn.1908102","url":null,"abstract":"We study the effects of regulatory interventions and capital support (bailouts) on banks’ liquidity creation. We rely on instrumental variables to deal with possible endogeneity concerns. Our key findings, which are based on a unique supervisory German dataset, are that regulatory interventions robustly trigger decreases in liquidity creation, while capital support does not affect liquidity creation. Additional results include the effects of these actions on different components of liquidity creation, lending, and risk taking. Our findings provide new and important insights into the debates about the design of regulatory interventions and bailouts.","PeriodicalId":11485,"journal":{"name":"Econometrics: Applied Econometrics & Modeling eJournal","volume":"7 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2016-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86172095","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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