Partial mean processes with generated regressors arise in several important econometric problems, such as the distribution of potential outcomes with continuous treatments and the quantile structural function in a nonseparable triangular model. This paper proposes a fully nonparametric estimator for the partial mean process, where the second step consists of a kernel regression on regressors that are estimated in the first step. The main contribution is a uniform expansion that characterizes in detail how the estimation error associated with the generated regressor affects the limiting distribution of the marginal integration estimator. The general results are illustrated with three examples: control variables in triangular models (Newey, Powell, and Vella, 1999; Imbens and Newey, 2009), the generalized propensity score for a continuus treatment (Hirano and Imbens, 2004), and the propensity score for sample selection (Das, Newey, and Vella, 2003).
产生回归量的偏均值过程出现在几个重要的计量经济学问题中，例如连续处理的潜在结果的分布和不可分三角模型中的分位数结构函数。本文针对偏均值过程提出了一个完全非参数估计器，其中第二步是对第一步估计的回归量进行核回归。主要贡献是统一展开，详细描述了与生成的回归量相关的估计误差如何影响边际积分估计量的极限分布。一般结果用三个例子来说明:三角模型中的控制变量(Newey, Powell, and Vella, 1999;Imbens和Newey, 2009)，连续治疗的广义倾向得分(Hirano和Imbens, 2004)，以及样本选择的倾向得分(Das, Newey, and Vella, 2003)。
{"title":"Partial Mean Processes with Generated Regressors: Continuous Treatment Effects and Nonseparable Models","authors":"Ying-Ying Lee","doi":"10.2139/ssrn.3250485","DOIUrl":"https://doi.org/10.2139/ssrn.3250485","url":null,"abstract":"Partial mean processes with generated regressors arise in several important econometric problems, such as the distribution of potential outcomes with continuous treatments and the quantile structural function in a nonseparable triangular model. This paper proposes a fully nonparametric estimator for the partial mean process, where the second step consists of a kernel regression on regressors that are estimated in the first step. The main contribution is a uniform expansion that characterizes in detail how the estimation error associated with the generated regressor affects the limiting distribution of the marginal integration estimator. The general results are illustrated with three examples: control variables in triangular models (Newey, Powell, and Vella, 1999; Imbens and Newey, 2009), the generalized propensity score for a continuus treatment (Hirano and Imbens, 2004), and the propensity score for sample selection (Das, Newey, and Vella, 2003).","PeriodicalId":273058,"journal":{"name":"ERN: Model Construction & Estimation (Topic)","volume":"49 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124576648","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 new practical numerical method to estimate conditional distributions, p(y|x), where y is the value of a continuous random variable supported on R^{N_y} and x is in R^{N_x}, via the Maximum Entropy Principal. We are not aware of other practical robust methods to tackle this problem. We also introduce a new practical numerical method to estimate p(y|x), when the (multivariate) data associated with y are fat-tailed, by maximizing U-entropy, a generalization of entropy. The maximization procedures are convex programming problems and are therefore amenable to robust numerical solution. The models that result are provably robust in a certain decision-theoretic sense, and the U-entropy problem solutions are optimal with respect to Tsallis, Renyi and power f-entropy. In our approach, we do not make use of models for x or joint models of x and y. We benchmark our models against various alternative models on financial data and show that our approach produces models that outperform the benchmarks with respect to out-of-sample likelihood.
{"title":"Estimating Multivariate Conditional Models via Entropic Methods","authors":"Wenbo Cao, Craig Friedman","doi":"10.2139/ssrn.2379080","DOIUrl":"https://doi.org/10.2139/ssrn.2379080","url":null,"abstract":"We introduce a new practical numerical method to estimate conditional distributions, p(y|x), where y is the value of a continuous random variable supported on R^{N_y} and x is in R^{N_x}, via the Maximum Entropy Principal. We are not aware of other practical robust methods to tackle this problem. We also introduce a new practical numerical method to estimate p(y|x), when the (multivariate) data associated with y are fat-tailed, by maximizing U-entropy, a generalization of entropy. The maximization procedures are convex programming problems and are therefore amenable to robust numerical solution. The models that result are provably robust in a certain decision-theoretic sense, and the U-entropy problem solutions are optimal with respect to Tsallis, Renyi and power f-entropy. In our approach, we do not make use of models for x or joint models of x and y. We benchmark our models against various alternative models on financial data and show that our approach produces models that outperform the benchmarks with respect to out-of-sample likelihood.","PeriodicalId":273058,"journal":{"name":"ERN: Model Construction & Estimation (Topic)","volume":"32 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121566843","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}
Pub Date : 2014-03-14DOI: 10.5585/REMARK.V13I2.2718
J. Hair, M. Gabriel, V. Patel
Structural equation modeling (SEM) is increasingly a method of choice for concept and theory development in the social sciences, particularly the marketing discipline. In marketing research there increasingly is a need to assess complex multiple latent constructs and relationships. Second-order constructs can be modeled providing an improved theoretical understanding of relationships as well as parsimony. SEM in particular is well suited to investigating complex relationships among multiple constructs. The two most prevalent SEM based analytical methods are covariance-based SEM (CB-SEM) and variance-based SEM (PLS-SEM). While each technique has advantages and limitations, in this article we focus on CB-SEM with AMOS to illustrate its application in examining the relationships between customer orientation, employee orientation, and firm performance. We also demonstrate how higher-order constructs are useful in modeling both responsive and proactive components of customer and employee orientation.
{"title":"AMOS Covariance-Based Structural Equation Modeling (CB-SEM): Guidelines on Its Application as a Marketing Research Tool","authors":"J. Hair, M. Gabriel, V. Patel","doi":"10.5585/REMARK.V13I2.2718","DOIUrl":"https://doi.org/10.5585/REMARK.V13I2.2718","url":null,"abstract":"Structural equation modeling (SEM) is increasingly a method of choice for concept and theory development in the social sciences, particularly the marketing discipline. In marketing research there increasingly is a need to assess complex multiple latent constructs and relationships. Second-order constructs can be modeled providing an improved theoretical understanding of relationships as well as parsimony. SEM in particular is well suited to investigating complex relationships among multiple constructs. The two most prevalent SEM based analytical methods are covariance-based SEM (CB-SEM) and variance-based SEM (PLS-SEM). While each technique has advantages and limitations, in this article we focus on CB-SEM with AMOS to illustrate its application in examining the relationships between customer orientation, employee orientation, and firm performance. We also demonstrate how higher-order constructs are useful in modeling both responsive and proactive components of customer and employee orientation.","PeriodicalId":273058,"journal":{"name":"ERN: Model Construction & Estimation (Topic)","volume":"52 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124058734","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}
I conduct a comprehensive nonparametric study of volatility jumps and leverage effect by examining high-frequency data on the VIX and S&P 500 from 1992 to 2010. I argue that the VIX data prior to 1998 are too noisy to provide a reliable inference. After 1999, the dataset is cleaner but still controversial. More specifically, the high-frequency dynamics of the VIX jumps challenges the assumptions of commonly used stochastic volatility jump-diffusion models. I explain this phenomenon by hypothesizing that most jump-like movements in the VIX are "pseudo-jumps" i.e., these jumps are large but temporary deviations from fundamental values.
{"title":"Understanding Jumps in the High-Frequency VIX","authors":"Inna Khagleeva","doi":"10.2139/ssrn.2277324","DOIUrl":"https://doi.org/10.2139/ssrn.2277324","url":null,"abstract":"I conduct a comprehensive nonparametric study of volatility jumps and leverage effect by examining high-frequency data on the VIX and S&P 500 from 1992 to 2010. I argue that the VIX data prior to 1998 are too noisy to provide a reliable inference. After 1999, the dataset is cleaner but still controversial. More specifically, the high-frequency dynamics of the VIX jumps challenges the assumptions of commonly used stochastic volatility jump-diffusion models. I explain this phenomenon by hypothesizing that most jump-like movements in the VIX are \"pseudo-jumps\" i.e., these jumps are large but temporary deviations from fundamental values.","PeriodicalId":273058,"journal":{"name":"ERN: Model Construction & Estimation (Topic)","volume":"18 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130303666","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 considers asset pricing models with stochastic differential utility incorporating decision makers' concern with ambiguity on true probability measure. Under a representative agent setting, we empirically evaluate alternative preference specifications including a multiple-priors recursive utility. Our empirical findings are summarized as follows: Relative risk aversion is estimated around 1-8 with ambiguity aversion and 7.4-15 without ambiguity aversion. Estimated ambiguity aversion is both economically and statistically significant and can explain up to 45% of the average equity premium. The elasticity of intertemporal substitution is higher than 1 but its identification appears to be weak, as observed by previous authors.
{"title":"Does Ambiguity Matter? Estimating Asset Pricing Models with a Multiple-Priors Recursive Utility","authors":"Daehee Jeong, Hwagyun Kim, Joon Y. Park","doi":"10.2139/ssrn.1573139","DOIUrl":"https://doi.org/10.2139/ssrn.1573139","url":null,"abstract":"This paper considers asset pricing models with stochastic differential utility incorporating decision makers' concern with ambiguity on true probability measure. Under a representative agent setting, we empirically evaluate alternative preference specifications including a multiple-priors recursive utility. Our empirical findings are summarized as follows: Relative risk aversion is estimated around 1-8 with ambiguity aversion and 7.4-15 without ambiguity aversion. Estimated ambiguity aversion is both economically and statistically significant and can explain up to 45% of the average equity premium. The elasticity of intertemporal substitution is higher than 1 but its identification appears to be weak, as observed by previous authors.","PeriodicalId":273058,"journal":{"name":"ERN: Model Construction & Estimation (Topic)","volume":"117 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-12-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117334996","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 studies panel data models with unobserved group factor structures. The group membership of each unit and the number of groups are left unspecified. We estimate the model by minimizing the sum of least squared errors with a shrinkage penalty. The regressions coefficients can be homogeneous or group specific. The consistency and asymptotic normality of the estimator are established. We also introduce new Cp-type criteria for selecting the number of groups, the numbers of group-specific common factors and relevant regressors. Monte Carlo results show that the proposed method works well. We apply the method to the study of US mutual fund returns under homogeneous regression coefficients, and the China mainland stock market under group-specific regression coefficients.
{"title":"Panel Data Models with Grouped Factor Structure Under Unknown Group Membership","authors":"T. Ando, Jushan Bai","doi":"10.2139/ssrn.2373629","DOIUrl":"https://doi.org/10.2139/ssrn.2373629","url":null,"abstract":"This paper studies panel data models with unobserved group factor structures. The group membership of each unit and the number of groups are left unspecified. We estimate the model by minimizing the sum of least squared errors with a shrinkage penalty. The regressions coefficients can be homogeneous or group specific. The consistency and asymptotic normality of the estimator are established. We also introduce new Cp-type criteria for selecting the number of groups, the numbers of group-specific common factors and relevant regressors. Monte Carlo results show that the proposed method works well. We apply the method to the study of US mutual fund returns under homogeneous regression coefficients, and the China mainland stock market under group-specific regression coefficients.","PeriodicalId":273058,"journal":{"name":"ERN: Model Construction & Estimation (Topic)","volume":"4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117055769","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 discusses the different concepts of measuring multinational corporations' activities to provide empirical researchers helpful guidelines about which measures to use in their work. I discuss which economic relations exist between the measures and show that a tight relationship can be established in theory and is indeed present in the actual data. A main conclusion is that foreign direct investment (FDI) stock data is generally recommendable to measure the importance of multinational firms but the preferred measure depends on the analytical question under investigation. The second part of the paper argues that estimating the determinants of multinational firms by using static equilibrium models can be quantitatively misleading and hence be problematic for our understanding of multinational firms and for the design of policy. In this context, I suggest some guidelines how data on multinationals could and should be used for empirical estimation. JEL Classification: C51, F2, E01
{"title":"On the Measurement of Foreign Direct Investment and Its Relationship to Activities of Multinational Corporations","authors":"K. Wacker","doi":"10.2139/ssrn.2354249","DOIUrl":"https://doi.org/10.2139/ssrn.2354249","url":null,"abstract":"This paper discusses the different concepts of measuring multinational corporations' activities to provide empirical researchers helpful guidelines about which measures to use in their work. I discuss which economic relations exist between the measures and show that a tight relationship can be established in theory and is indeed present in the actual data. A main conclusion is that foreign direct investment (FDI) stock data is generally recommendable to measure the importance of multinational firms but the preferred measure depends on the analytical question under investigation. The second part of the paper argues that estimating the determinants of multinational firms by using static equilibrium models can be quantitatively misleading and hence be problematic for our understanding of multinational firms and for the design of policy. In this context, I suggest some guidelines how data on multinationals could and should be used for empirical estimation. JEL Classification: C51, F2, E01","PeriodicalId":273058,"journal":{"name":"ERN: Model Construction & Estimation (Topic)","volume":"96 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115072136","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}
Financial time series often exhibit properties that depart from the usual assumptions of serial independence and normality. These include volatility clustering, heavy-tailedness and serial dependence. A voluminous literature on different approaches for modeling these empirical regularities has emerged in the last decade. In this paper we review the estimation of a variety of highly flexible stochastic volatility models, and introduce some efficient algorithms based on recent advances in state space simulation techniques. These estimation methods are illustrated via empirical examples involving precious metal and foreign exchange returns. The corresponding Matlab code is also provided.
{"title":"Estimation of Stochastic Volatility Models with Heavy Tails and Serial Dependence","authors":"J. Chan, C. Hsiao","doi":"10.2139/ssrn.2359838","DOIUrl":"https://doi.org/10.2139/ssrn.2359838","url":null,"abstract":"Financial time series often exhibit properties that depart from the usual assumptions of serial independence and normality. These include volatility clustering, heavy-tailedness and serial dependence. A voluminous literature on different approaches for modeling these empirical regularities has emerged in the last decade. In this paper we review the estimation of a variety of highly flexible stochastic volatility models, and introduce some efficient algorithms based on recent advances in state space simulation techniques. These estimation methods are illustrated via empirical examples involving precious metal and foreign exchange returns. The corresponding Matlab code is also provided.","PeriodicalId":273058,"journal":{"name":"ERN: Model Construction & Estimation (Topic)","volume":"139 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132393095","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}
Modeling dependence among operational loss frequencies is a natural way of trying to capture possible relationships between losses, which are categorized differently with respect to the business line or the event type, but which have occurred simultaneously.We propose a model that explicitly accounts for such dependence and allows modeling it in a heterogeneous way to capture the wide spectrum of dependence structures operational losses exhibit.Our model relies on a pair copula construction, which flexibly combines different bivariate copulas, to estimate efficiently the joint multivariate distribution and then determine the total risk capital.Empirical results on real-world data show that such flexible explicit dependence modeling might have a significant impact on the risk capital, leading to a clear diversification benefit compared to the standard Basel comonotonicity assumption.
{"title":"Modeling Dependence of Operational Loss Frequencies","authors":"E. Brechmann, C. Czado, S. Paterlini","doi":"10.2139/ssrn.2345342","DOIUrl":"https://doi.org/10.2139/ssrn.2345342","url":null,"abstract":"Modeling dependence among operational loss frequencies is a natural way of trying to capture possible relationships between losses, which are categorized differently with respect to the business line or the event type, but which have occurred simultaneously.We propose a model that explicitly accounts for such dependence and allows modeling it in a heterogeneous way to capture the wide spectrum of dependence structures operational losses exhibit.Our model relies on a pair copula construction, which flexibly combines different bivariate copulas, to estimate efficiently the joint multivariate distribution and then determine the total risk capital.Empirical results on real-world data show that such flexible explicit dependence modeling might have a significant impact on the risk capital, leading to a clear diversification benefit compared to the standard Basel comonotonicity assumption.","PeriodicalId":273058,"journal":{"name":"ERN: Model Construction & Estimation (Topic)","volume":"64 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121527168","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 proposes a moment-matching method for approximating vector autoregressions by finite-state Markov chains. The Markov chain is constructed by targeting the conditional moments of the underlying continuous process. The proposed method is more robust to the number of discrete values and tends to outperform the existing methods for approximating multivariate processes over a wide range of the parameter space, especially for highly persistent vector autoregressions with roots near the unit circle.
{"title":"A Moment-Matching Method for Approximating Vector Autoregressive Processes by Finite-State Markov Chains","authors":"Nikolay Gospodinov, D. Lkhagvasuren","doi":"10.2139/ssrn.2478493","DOIUrl":"https://doi.org/10.2139/ssrn.2478493","url":null,"abstract":"This paper proposes a moment-matching method for approximating vector autoregressions by finite-state Markov chains. The Markov chain is constructed by targeting the conditional moments of the underlying continuous process. The proposed method is more robust to the number of discrete values and tends to outperform the existing methods for approximating multivariate processes over a wide range of the parameter space, especially for highly persistent vector autoregressions with roots near the unit circle.","PeriodicalId":273058,"journal":{"name":"ERN: Model Construction & Estimation (Topic)","volume":"52 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123468211","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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