I discuss nonlinear difference-in-differences models, arguing their interpretation depends on the context of their application. When parallel trends are assumed in the natural scale of the dependent variable, I contend the treatment effect is the interaction effect (a cross-difference), while if parallel trends are assumed in the transformed scale, it is a single difference. Thus, interpretation is driven by the form of the parallel trends assumption. I further note that assuming parallel trends in one scale implies they do not hold in the other, except in special cases. Therefore, researchers should be careful about inadvertently making inconsistent assumptions when mixing models that imply different forms of parallel trends. Finally, I consider the special case of the log-linear model, providing a form of the treatment effect in percentage terms that is constant, easily calculated, and valid to compare across applications that might assume parallel trends in different scales.
{"title":"Interpretation of Nonlinear Difference-in-Differences: The Role of the Parallel Trends Assumption","authors":"Scott Barkowski","doi":"10.2139/ssrn.3772458","DOIUrl":"https://doi.org/10.2139/ssrn.3772458","url":null,"abstract":"I discuss nonlinear difference-in-differences models, arguing their interpretation depends on the context of their application. When parallel trends are assumed in the natural scale of the dependent variable, I contend the treatment effect is the interaction effect (a cross-difference), while if parallel trends are assumed in the transformed scale, it is a single difference. Thus, interpretation is driven by the form of the parallel trends assumption. I further note that assuming parallel trends in one scale implies they do not hold in the other, except in special cases. Therefore, researchers should be careful about inadvertently making inconsistent assumptions when mixing models that imply different forms of parallel trends. Finally, I consider the special case of the log-linear model, providing a form of the treatment effect in percentage terms that is constant, easily calculated, and valid to compare across applications that might assume parallel trends in different scales.","PeriodicalId":242950,"journal":{"name":"ERN: Truncated & Censored Models (Single) (Topic)","volume":"133 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121194733","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}
Over the last decade, researchers, practitioners, and regulators have had intense debates about how to treat the data collection threshold in operational risk modeling. Several approaches have been employed to fit the loss severity distribution: the empirical approach, the “naive” approach, the shifted approach, and the truncated approach. Since each approach is based on a different set of assumptions, different probability models emerge. Thus, model uncertainty arises. The main objective of this paper is to understand the impact of model uncertainty on the value-at-risk (VaR) estimators. To accomplish that, we take the bank’s perspective and study a single risk. Under this simplified scenario, we can solve the problem analytically (when the underlying distribution is exponential) and show that it uncovers similar patterns among VaR estimates to those based on the simulation approach (when data follow a Lomax distribution). We demonstrate that for a fixed probability distribution, the choice of the truncated approach yields the lowest VaR estimates, which may be viewed as beneficial to the bank, whilst the “naive” and shifted approaches lead to higher estimates of VaR. The advantages and disadvantages of each approach and the probability distributions under study are further investigated using a real data set for legal losses in a business unit (Cruz 2002).
{"title":"Model Uncertainty in Operational Risk Modeling Due to Data Truncation: A Single Risk Case","authors":"Daoping Yu, V. Brazauskas","doi":"10.3390/RISKS5030049","DOIUrl":"https://doi.org/10.3390/RISKS5030049","url":null,"abstract":"Over the last decade, researchers, practitioners, and regulators have had intense debates about how to treat the data collection threshold in operational risk modeling. Several approaches have been employed to fit the loss severity distribution: the empirical approach, the “naive” approach, the shifted approach, and the truncated approach. Since each approach is based on a different set of assumptions, different probability models emerge. Thus, model uncertainty arises. The main objective of this paper is to understand the impact of model uncertainty on the value-at-risk (VaR) estimators. To accomplish that, we take the bank’s perspective and study a single risk. Under this simplified scenario, we can solve the problem analytically (when the underlying distribution is exponential) and show that it uncovers similar patterns among VaR estimates to those based on the simulation approach (when data follow a Lomax distribution). We demonstrate that for a fixed probability distribution, the choice of the truncated approach yields the lowest VaR estimates, which may be viewed as beneficial to the bank, whilst the “naive” and shifted approaches lead to higher estimates of VaR. The advantages and disadvantages of each approach and the probability distributions under study are further investigated using a real data set for legal losses in a business unit (Cruz 2002).","PeriodicalId":242950,"journal":{"name":"ERN: Truncated & Censored Models (Single) (Topic)","volume":"48 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126532236","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}
In this study, we compare the parameter estimates of the mixed logit model obtained with maximum likelihood and with hierarchical Bayesian estimation. The choice of the priors in Bayesian estimation and of the type and the number of quasi-random draws for maximum likelihood estimation have a big impact on the estimates. Our main focus is on the effect of the prior for the covariance matrix in hierarchical Bayes estimation. We investigate several priors such as Inverse Wisharts, the Separation Strategy, Scaled Inverse Wisharts and the Huang Half-t priors and we compute the root mean square errors of the resulting estimates for the mean, covariance matrix and individual parameters in a large simulation study. We show that the default settings in many software packages can lead to very unreliable results and that it is important to check the robustness of the results.
{"title":"Estimating the Mixed Logit Model by Maximum Simulated Likelihood and Hierarchical Bayes","authors":"Deniz Akinc, M. Vandebroek","doi":"10.2139/ssrn.3052293","DOIUrl":"https://doi.org/10.2139/ssrn.3052293","url":null,"abstract":"In this study, we compare the parameter estimates of the mixed logit model obtained with maximum likelihood and with hierarchical Bayesian estimation. The choice of the priors in Bayesian estimation and of the type and the number of quasi-random draws for maximum likelihood estimation have a big impact on the estimates. Our main focus is on the effect of the prior for the covariance matrix in hierarchical Bayes estimation. We investigate several priors such as Inverse Wisharts, the Separation Strategy, Scaled Inverse Wisharts and the Huang Half-t priors and we compute the root mean square errors of the resulting estimates for the mean, covariance matrix and individual parameters in a large simulation study. We show that the default settings in many software packages can lead to very unreliable results and that it is important to check the robustness of the results.","PeriodicalId":242950,"journal":{"name":"ERN: Truncated & Censored Models (Single) (Topic)","volume":"24 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115802759","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 speed of convergence of the truncated realized covariance to the integrated covariation between the two Brownian parts of two semimartingales is heavily influenced by the presence of infinite activity jumps with infinite variation. Namely, the two processes small jumps play a crucial role through their degree of dependence, other than through their jump activity indices. This theoretical result is established when the semimartingales are observed discretely on a finite time horizon. The estimator in many cases is less efficient than when the model only has finite variation jumps. The small jumps of each semimartingale are assumed to be the small jumps of a Levy stable process, and to the two stable processes a parametric simple dependence structure is imposed, which allows to range from independence to monotonic dependence. The result of this paper is relevant in financial economics, since by the truncated realized covariance it is possible to separately estimate the common jumps among assets, which has important implications in risk management and contagion modeling.
{"title":"Truncated Realized Covariance When Prices Have Infinite Variation Jumps","authors":"C. Mancini","doi":"10.2139/ssrn.2443860","DOIUrl":"https://doi.org/10.2139/ssrn.2443860","url":null,"abstract":"The speed of convergence of the truncated realized covariance to the integrated covariation between the two Brownian parts of two semimartingales is heavily influenced by the presence of infinite activity jumps with infinite variation. Namely, the two processes small jumps play a crucial role through their degree of dependence, other than through their jump activity indices. This theoretical result is established when the semimartingales are observed discretely on a finite time horizon. The estimator in many cases is less efficient than when the model only has finite variation jumps. The small jumps of each semimartingale are assumed to be the small jumps of a Levy stable process, and to the two stable processes a parametric simple dependence structure is imposed, which allows to range from independence to monotonic dependence. The result of this paper is relevant in financial economics, since by the truncated realized covariance it is possible to separately estimate the common jumps among assets, which has important implications in risk management and contagion modeling.","PeriodicalId":242950,"journal":{"name":"ERN: Truncated & Censored Models (Single) (Topic)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127818110","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}
In reverse auctions, buyers often retain the right to bargain further concessions from the winner. The optimal form of such procurement is an English auction followed by an auctioneer's option to engage in ultimatum bargaining with the winner. We study behavior and performance in this procurement format using a laboratory experiment. Sellers closely follow the equilibrium strategy of exiting the auction at their costs and then accepting strictly profitable offers. Buyers generally exercise their option to bargain according to their equilibrium strategy, but their take-it-or-leave-it offers vary positively with auction prices when they should be invariant. We explain this deviation by modeling buyers' subjective posteriors regarding the winners' costs as distortions, calculated using a formulation of probability weighting, of the Bayesian posteriors. We show alternative models based upon risk aversion and anticipated regret can't explain these price dependencies.
{"title":"An Experimental Investigation of Auctions and Bargaining in Procurement","authors":"Jason M. Shachat, L. Tan","doi":"10.2139/ssrn.2170363","DOIUrl":"https://doi.org/10.2139/ssrn.2170363","url":null,"abstract":"In reverse auctions, buyers often retain the right to bargain further concessions from the winner. The optimal form of such procurement is an English auction followed by an auctioneer's option to engage in ultimatum bargaining with the winner. We study behavior and performance in this procurement format using a laboratory experiment. Sellers closely follow the equilibrium strategy of exiting the auction at their costs and then accepting strictly profitable offers. Buyers generally exercise their option to bargain according to their equilibrium strategy, but their take-it-or-leave-it offers vary positively with auction prices when they should be invariant. We explain this deviation by modeling buyers' subjective posteriors regarding the winners' costs as distortions, calculated using a formulation of probability weighting, of the Bayesian posteriors. We show alternative models based upon risk aversion and anticipated regret can't explain these price dependencies.","PeriodicalId":242950,"journal":{"name":"ERN: Truncated & Censored Models (Single) (Topic)","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125704554","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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