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Context-Dependent Heterogeneous Preferences: A Comment on Barseghyan and Molinari (2023) 语境依赖的异质性偏好:对Barseghyan和Molinari(2023)的评析
2区 数学
Journal of Business & Economic Statistics Pub Date : 2023-10-02 DOI: 10.1080/07350015.2023.2216740
Matias D. Cattaneo, Xinwei Ma, Yusufcan Masatlioglu
{"title":"Context-Dependent Heterogeneous Preferences: A Comment on Barseghyan and Molinari (2023)","authors":"Matias D. Cattaneo, Xinwei Ma, Yusufcan Masatlioglu","doi":"10.1080/07350015.2023.2216740","DOIUrl":"https://doi.org/10.1080/07350015.2023.2216740","url":null,"abstract":"Abstract–Barseghyan and Molinari give sufficient conditions for semi-nonparametric point identification of parameters of interest in a mixture model of decision-making under risk, allowing for unobserved heterogeneity in utility functions and limited consideration. A key assumption in the model is that the heterogeneity of risk preferences is unobservable but context-independent. In this comment, we build on their insights and present identification results in a setting where the risk preferences are allowed to be context-dependent.KEYWORDS: Discrete choiceRandom limited considerationRandom utilitySemi-nonparametric identification AcknowledgmentsWe thank Francesca Molinari and the participants at the 2023 ASSA meetings (JBES Session: Risk Preference Types, Limited Consideration, and Welfare) for comments.Disclosure StatementThe authors report there are no competing interests to declare.Additional informationFundingCattaneo gratefully acknowledges financial support from the National Science Foundation through grants SES-1947805 and SES-2241575.","PeriodicalId":50247,"journal":{"name":"Journal of Business & Economic Statistics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135900503","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Discussion of “Risk Preference Types, Limited Consideration, and Welfare” by Levon Barseghyan and Francesca Molinari Levon Barseghyan和Francesca Molinari对“风险偏好类型、有限考虑和福利”的讨论
2区 数学
Journal of Business & Economic Statistics Pub Date : 2023-10-02 DOI: 10.1080/07350015.2023.2216255
Cristina Gualdani
{"title":"Discussion of “Risk Preference Types, Limited Consideration, and Welfare” by Levon Barseghyan and Francesca Molinari","authors":"Cristina Gualdani","doi":"10.1080/07350015.2023.2216255","DOIUrl":"https://doi.org/10.1080/07350015.2023.2216255","url":null,"abstract":"This article is part of an impressive research agenda by the authors which develops tools to identify models of risk preferences (Barseghyan, Prince, and Teitelbaum 2011; Barseghyan et al. 2013, 2018, 2021; Barseghyan, Molinari, and Teitelbaum 2016; Barseghyan, Teitelbaum, and Xu 2018; Barseghyan, Molinari, and Thirkettle 2021). Such work is prominent in industrial organization, development, health, labor, finance, and public economics because it is pivotal to studying incentives and assessing the welfare impact of policy interventions in insurance markets. In this article, the authors provide a novel method to identify a static model of decision-making under risk, where agents choose insurance bundles over multiple lines of property coverage, belong to different preference types, display unobserved heterogeneity in attitudes toward risk, and may consider a limited amount of bundles when making their choices. This rich framework is critical for rationalizing data patterns but introduces substantial econometric challenges. The crucial insight consists of exploiting the single crossing property (SCP) that the model features within each coverage context and an exclusion restriction to characterize the response to changes in the covariates of the choice probability of the cheapest bundle. From these elasticities, we can identify the type shares and the distribution of unobserved heterogeneity and consideration sets for each type. I devote the first part of the discussion to summarizing the identification strategy and giving context to the novelty of the arguments. In doing so, I applaud the authors for expertly and smoothly guiding us throughout their overarching research agenda to learn econometric tools that prove extremely useful for the specific setting at hand and, more generally, for employment by structural economists and other applied researchers. In the second part of the discussion, I suggest additional aspects that could play an important empirical role in the functioning of property insurance markets, namely private information about risk and supply-side issues, and pave the way for possible approaches to introduce them into the authors’ framework.","PeriodicalId":50247,"journal":{"name":"Journal of Business & Economic Statistics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135901021","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Rejoinder 反驳
2区 数学
Journal of Business & Economic Statistics Pub Date : 2023-10-02 DOI: 10.1080/07350015.2023.2239870
Levon Barseghyan, Francesca Molinari
{"title":"Rejoinder","authors":"Levon Barseghyan, Francesca Molinari","doi":"10.1080/07350015.2023.2239870","DOIUrl":"https://doi.org/10.1080/07350015.2023.2239870","url":null,"abstract":"Click to increase image sizeClick to decrease image size Notes1 Our analysis, available upon request, allows for endogenous loss probabilities via a linear function of effort, (1−e)μ. The effort level, e, is in turn associated with a (potentially heterogeneous across agents) quadratic cost function. The analysis shows that for deductible levels as in our data, the choice of $200 in collision is not rationalizable, even in the presence of endogenous loss probabilities.","PeriodicalId":50247,"journal":{"name":"Journal of Business & Economic Statistics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135901019","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Discussion of “Risk Preference Types, Limited Consideration, and Welfare” by Levon Barseghyan and Francesca Molinari Levon Barseghyan和Francesca Molinari对“风险偏好类型、有限考虑和福利”的讨论
2区 数学
Journal of Business & Economic Statistics Pub Date : 2023-10-02 DOI: 10.1080/07350015.2023.2217870
Elisabeth Honka
{"title":"Discussion of “Risk Preference Types, Limited Consideration, and Welfare” by Levon Barseghyan and Francesca Molinari","authors":"Elisabeth Honka","doi":"10.1080/07350015.2023.2217870","DOIUrl":"https://doi.org/10.1080/07350015.2023.2217870","url":null,"abstract":"Click to increase image sizeClick to decrease image size Disclosure StatementI state that there are no competing interests to declare.Notes1 Throughout the economics and marketing literature, consideration sets have also been called “search sets,” “evoked sets,” or “(endogenous) choice sets.”2 For example, see Hauser and Wernerfelt (Citation1990) for a variety of grocery store products, Roberts and Lattin (Citation1991) for cereal, De los Santos, Hortçsu, and Wildenbeest (Citation2012) for books, Honka (Citation2014) for auto insurance, Koulayev (Citation2014) and Ursu (Citation2018) for hotels, Bronnenberg, Kim, and Mela (Citation2016) for digital cameras, Honka, Hortçsu, and Vitorino (Citation2017) for savings accounts, Ursu, Wang, and Chintagunta (Citation2020) for restaurants, Kapor (Citation2020) for colleges, Yavorsky, Honka, and Chen (Citation2021), Gardete and Hunter (Citation2020), and Moraga-González et al. (Citation2022) for cars, Morozov et al. (Citation2021) for cosmetics, and Zhang et al. (Citation2023) for shoes.3 For example, consumers’ average consideration set sizes are 2.4 for auto insurance (Honka Citation2014), 2.8–6.4 for digital cameras (Bronnenberg, Kim, and Mela Citation2016), 2.5 for savings accounts (Honka, Hortçsu, and Vitorino Citation2017), 2.3 for online used cars (Gardete and Hunter Citation2020), 1.4 for cosmetics (Morozov et al. Citation2021), 1.1 for new car purchases (Yavorsky, Honka, and Chen Citation2021), 1.7 for home improvement products (Amano, Rhodes, and Seiler Citation2022), and 1.9 for shoes (Zhang et al. Citation2023).","PeriodicalId":50247,"journal":{"name":"Journal of Business & Economic Statistics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135901686","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Testing For Global Covariate Effects in Dynamic Interaction Event Networks 动态交互事件网络中全局协变量效应的检验
2区 数学
Journal of Business & Economic Statistics Pub Date : 2023-09-26 DOI: 10.1080/07350015.2023.2263537
Alexander Kreiss, Enno Mammen, Wolfgang Polonik
{"title":"Testing For Global Covariate Effects in Dynamic Interaction Event Networks","authors":"Alexander Kreiss, Enno Mammen, Wolfgang Polonik","doi":"10.1080/07350015.2023.2263537","DOIUrl":"https://doi.org/10.1080/07350015.2023.2263537","url":null,"abstract":"AbstractIn statistical network analysis it is common to observe so called interaction data. Such data is characterized by actors forming the vertices and interacting along edges of the network, where edges are randomly formed and dissolved over the observation horizon. In addition covariates are observed and the goal is to model the impact of the covariates on the interactions. We distinguish two types of covariates: global, system-wide covariates (i.e. covariates taking the same value for all individuals, such as seasonality) and local, dyadic covariates modeling interactions between two individuals in the network. Existing continuous time network models are extended to allow for comparing a completely parametric model and a model that is parametric only in the local covariates but has a global non-parametric time component. This allows, for instance, to test whether global time dynamics can be explained by simple global covariates like weather, seasonality etc. The procedure is applied to a bike-sharing network by using weather and weekdays as global covariates and distances between the bike stations as local covariates.Keywords: Dynamic NetworksCounting ProcessesDependenceDisclaimerAs a service to authors and researchers we are providing this version of an accepted manuscript (AM). Copyediting, typesetting, and review of the resulting proofs will be undertaken on this manuscript before final publication of the Version of Record (VoR). During production and pre-press, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal relate to these versions also.","PeriodicalId":50247,"journal":{"name":"Journal of Business & Economic Statistics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134886537","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Reduced-rank envelope vector autoregressive model 降秩包络向量自回归模型
2区 数学
Journal of Business & Economic Statistics Pub Date : 2023-09-21 DOI: 10.1080/07350015.2023.2260862
S. Yaser Samadi, H. M. Wiranthe B. Herath
{"title":"Reduced-rank envelope vector autoregressive model","authors":"S. Yaser Samadi, H. M. Wiranthe B. Herath","doi":"10.1080/07350015.2023.2260862","DOIUrl":"https://doi.org/10.1080/07350015.2023.2260862","url":null,"abstract":"Abstract–The standard vector autoregressive (VAR) models suffer from overparameterization which is a serious issue for high-dimensional time series data as it restricts the number of variables and lags that can be incorporated into the model. Several statistical methods, such as the reduced-rank model for multivariate (multiple) time series (Velu et al., 1986; Reinsel and Velu, 1998; Reinsel et al., 2022) and the Envelope VAR model (Wang and Ding, 2018), provide solutions for achieving dimension reduction of the parameter space of the VAR model. However, these methods can be inefficient in extracting relevant information from complex data, as they fail to distinguish between relevant and irrelevant information, or they are inefficient in addressing the rank deficiency problem. We put together the idea of envelope models into the reduced-rank VAR model to simultaneously tackle these challenges, and propose a new parsimonious version of the classical VAR model called the reduced-rank envelope VAR (REVAR) model. Our proposed REVAR model incorporates the strengths of both reduced-rank VAR and envelope VAR models and leads to significant gains in efficiency and accuracy. The asymptotic properties of the proposed estimators are established under different error assumptions. Simulation studies and real data analysis are conducted to evaluate and illustrate the proposed method.Keywords: Reduced-rank autoregressionEnvelope modelVector autoregressive model.DisclaimerAs a service to authors and researchers we are providing this version of an accepted manuscript (AM). Copyediting, typesetting, and review of the resulting proofs will be undertaken on this manuscript before final publication of the Version of Record (VoR). During production and pre-press, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal relate to these versions also.","PeriodicalId":50247,"journal":{"name":"Journal of Business & Economic Statistics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136153379","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Modeling extreme events: time-varying extreme tail shape* 极端事件建模:时变极端尾形*
2区 数学
Journal of Business & Economic Statistics Pub Date : 2023-09-21 DOI: 10.1080/07350015.2023.2260439
Bernd Schwaab, Xin Zhang, Andre Lucas
{"title":"Modeling extreme events: time-varying extreme tail shape*","authors":"Bernd Schwaab, Xin Zhang, Andre Lucas","doi":"10.1080/07350015.2023.2260439","DOIUrl":"https://doi.org/10.1080/07350015.2023.2260439","url":null,"abstract":"We propose a dynamic semi-parametric framework to study time variation in tail parameters. The framework builds on the Generalized Pareto Distribution (GPD) for modeling peaks over thresholds as in Extreme Value Theory, but casts the model in a conditional framework to allow for time-variation in the tail parameters. We establish parameter regions for stationarity and ergodicity and for the existence of (unconditional) moments and consider conditions for consistency and asymptotic normality of the maximum likelihood estimator for the deterministic parameters in the model. Two empirical datasets illustrate the usefulness of the approach: daily U.S. equity returns, and 15-minute euro area sovereign bond yield changes.","PeriodicalId":50247,"journal":{"name":"Journal of Business & Economic Statistics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136102134","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A Modified Randomization Test for the Level of Clustering 聚类水平的改进随机化检验
2区 数学
Journal of Business & Economic Statistics Pub Date : 2023-09-19 DOI: 10.1080/07350015.2023.2261567
Yong Cai
{"title":"A Modified Randomization Test for the Level of Clustering","authors":"Yong Cai","doi":"10.1080/07350015.2023.2261567","DOIUrl":"https://doi.org/10.1080/07350015.2023.2261567","url":null,"abstract":"AbstractSuppose a researcher observes individuals within a county within a state. Given concerns about correlation across individuals, it is common to group observations into clusters and conduct inference treating observations across clusters as independent. However, a researcher that has chosen to cluster at the county level may be unsure of their decision, given knowledge that observations are independent across states. This paper proposes a modified randomization test as a robustness check for the chosen level of clustering in a linear regression setting. Existing tests require either the number of states or number of counties to be large. Our method is designed for settings with few states and few counties. While the method is conservative, it has competitive power in settings that may be relevant to empirical work.Keywords: Linear RegressionClustered Standard ErrorsSmall-Cluster AsymptoticsDisclaimerAs a service to authors and researchers we are providing this version of an accepted manuscript (AM). Copyediting, typesetting, and review of the resulting proofs will be undertaken on this manuscript before final publication of the Version of Record (VoR). During production and pre-press, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal relate to these versions also.","PeriodicalId":50247,"journal":{"name":"Journal of Business & Economic Statistics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135011351","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 4
Risk Preference Types, Limited Consideration, and Welfare 风险偏好类型、有限考虑和福利
2区 数学
Journal of Business & Economic Statistics Pub Date : 2023-09-18 DOI: 10.1080/07350015.2023.2239949
Levon Barseghyan, Francesca Molinari
{"title":"Risk Preference Types, Limited Consideration, and Welfare","authors":"Levon Barseghyan, Francesca Molinari","doi":"10.1080/07350015.2023.2239949","DOIUrl":"https://doi.org/10.1080/07350015.2023.2239949","url":null,"abstract":"AbstractWe provide sufficient conditions for semi-nonparametric point identification of a mixture model of decision making under risk, when agents make choices in multiple lines of insurance coverage (contexts) by purchasing a bundle. As a first departure from the related literature, the model allows for two preference types. In the first one, agents behave according to standard expected utility theory with CARA Bernoulli utility function, with an agent-specific coefficient of absolute risk aversion whose distribution is left completely unspecified. In the other, agents behave according to the dual theory of choice under risk combined with a one-parameter family distortion function, where the parameter is agent-specific and is drawn from a distribution that is left completely unspecified. Within each preference type, the model allows for unobserved heterogeneity in consideration sets, where the latter form at the bundle level—a second departure from the related literature. Our point identification result rests on observing sufficient variation in covariates across contexts, without requiring any independent variation across alternatives within a single context. We estimate the model on data on households’ deductible choices in two lines of property insurance, and use the results to assess the welfare implications of a hypothetical market intervention where the two lines of insurance are combined into a single one. We study the role of limited consideration in mediating the welfare effects of such intervention.KEYWORDS: (Non-)expected utilityRisk preferencesSemi-nonparametric identificationUnobserved consideration sets AcknowledgmentsWe thank the editor, Ivan Canay, two anonymous reviewers, Matias Cattaneo, Cristina Gualdani, Elisabeth Honka, Xinwei Ma, Yusufcan Masatlioglu, Julie Mortimer, Deborah Doukas, Roberta Olivieri, and conference participants at FUR22 and at the JBES session at the ESWM23 for helpful comments.Disclosure StatementThe authors report there are no competing interests to declare.Notes1 This assumption is sometimes viewed as an aspect of rationality (e.g., Kahneman Citation2003), and is credible in our empirical study of demand in very similar contexts (collision and comprehensive deductible insurance).2 Within a single insurance company, typically in a given context if an agent faces a larger price than another agent for one alternative, the first agent faces a (proportionally) larger price for all other alternatives.3 See Barseghyan, Molinari, and Thirkettle (Citation2021b) for a formal discussion and Section 4.3 for further details.4 See Section 4.2 for additional information on the data.5 The multiplicative factors {glj:l∈Dj} are known as the deductible factors and δj is a small markup known as the expense fee.6 Multiple preference types are a focus of the literature that estimates risk preferences using experimental data (e.g., Bruhin, Fehr-Duda, and Epper Citation2010; Harrison, Humphrey, and Verschoor Citation2010; Conte","PeriodicalId":50247,"journal":{"name":"Journal of Business & Economic Statistics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135110688","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 4
FNETS: Factor-adjusted network estimation and forecasting for high-dimensional time series 高维时间序列的因子调整网络估计与预测
2区 数学
Journal of Business & Economic Statistics Pub Date : 2023-09-14 DOI: 10.1080/07350015.2023.2257270
Matteo Barigozzi, Haeran Cho, Dom Owens
{"title":"FNETS: Factor-adjusted network estimation and forecasting for high-dimensional time series","authors":"Matteo Barigozzi, Haeran Cho, Dom Owens","doi":"10.1080/07350015.2023.2257270","DOIUrl":"https://doi.org/10.1080/07350015.2023.2257270","url":null,"abstract":"–We propose FNETS, a methodology for network estimation and forecasting of high-dimensional time series exhibiting strong serial- and cross-sectional correlations. We operate under a factor-adjusted vector autoregressive (VAR) model which, after accounting for pervasive co-movements of the variables by common factors, models the remaining idiosyncratic dynamic dependence between the variables as a sparse VAR process. Network estimation of FNETS consists of three steps: (i) factor-adjustment via dynamic principal component analysis, (ii) estimation of the latent VAR process via-regularised Yule-Walker estimator, and (iii) estimation of partial correlation and long-run partial correlation matrices. In doing so, we learn three networks underpinning the VAR process, namely a directed network representing the Granger causal linkages between the variables, an undirected one embedding their contemporaneous relationships and finally, an undirected network that summarises both lead-lag and contemporaneous linkages. In addition, FNETS provides a suite of methods for forecasting the factor-driven and the idiosyncratic VAR processes. Under general conditions permitting tails heavier than the Gaussian one, we derive uniform consistency rates for the estimators in both network estimation and forecasting, which hold as the dimension of the panel and the sample size diverge. Simulation studies and real data application confirm the good performance of FNETS.","PeriodicalId":50247,"journal":{"name":"Journal of Business & Economic Statistics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135487683","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 9
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