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Academic Commons Search Resultsen-usInference On Two-Component Mixtures Under Tail Restrictions
https://academiccommons.columbia.edu/catalog/ac:199769
Jochmans, Koen; Henry, Marc; Salanie, Bernardhttp://dx.doi.org/10.7916/D8B27VCRTue, 07 Jun 2016 17:02:50 +0000Many econometric models can be analyzed as finite mixtures. We focus on two-component mixtures and we show that they are nonparametrically point identified by a combination of an exclusion restriction and tail restrictions. Our identification analysis suggests simple closed-form estimators of the component distributions and mixing proportions, as well as a specification test. We derive their asymptotic properties using results on tail empirical processes and we present a simulation study that documents their finite-sample performance.Economics, Mathematics, Econometrics--Mathematical models, Estimation theory--Asymptotic theorybs2237EconomicsWorking papersPartial Identification of Finite Mixtures in Econometric Models
https://academiccommons.columbia.edu/catalog/ac:184350
Henry, Marc; Kitamura, Yuichi; Salanie, Bernardhttp://dx.doi.org/10.7916/D8959GD4Tue, 10 Mar 2015 11:51:55 +0000We consider partial identification of finite mixture models in the presence of an observable source of variation in the mixture weights that leaves component distributions unchanged, as is the case in large classes of econometric models. We first show that when the number J of component distributions is known a priori, the family of mixture models compatible with the data is a subset of a J(J1)-dimensional space. When the outcome variable is continuous, this subset is defined by linear constraints, which we characterize exactly. Our identifying assumption has testable implications, which we spell out for J=2. We also extend our results to the case when the analyst does not know the true number of component distributions and to models with discrete outcomes. Keywords. Partial identification, finite mixture models. JEL classification. C24.Economics, Economic theorybs2237EconomicsArticlesInference in incomplete models
https://academiccommons.columbia.edu/catalog/ac:113244
Galichon, Alfred; Henry, Marchttp://hdl.handle.net/10022/AC:P:378Mon, 28 Mar 2011 09:35:16 +0000We provide a test for the specification of a structural model without identifying assumptions. We show the equivalence of several natural formulations of correct specification, which we take as our null hypothesis. From a natural empirical version of the latter, we derive a Kolmogorov-Smirnov statistic for Choquet capacity functionals, which we use to construct our test. We derive the limiting distribution of our test statistic under the null, and show that our test is consistent against certain classes of alternatives. When the model is given in parametric form, the test can be inverted to yield confidence regions for the identified parameter set. The approach can be applied to the estimation of models with sample selection, censored observables and to games with multiple equilibria.Economic theorymh530EconomicsWorking papersThe long range dependence paradigm for macroeconomics and finance
https://academiccommons.columbia.edu/catalog/ac:113855
Henry, Marc; Zaffaroni, Paolohttp://hdl.handle.net/10022/AC:P:404Tue, 22 Mar 2011 11:35:54 +0000The long range dependence paradigm appears to be a suitable description of the data generating process for many observed economic time series. This is mainly due to the fact that it naturally characterizes time series displaying a high degree of persistence, in the form of a long lasting effect of unanticipated shocks, yet exhibiting mean reversion. Whereas linear long range dependent time series models have been extensively used in macroeconomics, empirical evidence from financial time series prompted the development of nonlinear long range dependent time series models, in particular models of changing volatility. We discuss empirical evidence of long range dependence as well as the theoretical issues, both for economics and econometrics, such evidence has stimulated.Economic theorymh530EconomicsWorking papersNonparametric specification analysis of dynamic parametric models
https://academiccommons.columbia.edu/catalog/ac:113832
Henry, Marc; Scaillet, Olivierhttp://hdl.handle.net/10022/AC:P:403Tue, 22 Mar 2011 11:32:51 +0000Time series parametric models generally cater to a particular objective, such as forecasting, and it is therefore desirable to judge such models solely on the basis of their performance in the fullfillment of that objective. We propose a specification testing procedure which concentrates power on the parametric model's ability to estimate a set of characteristics of the finite dimensional distributions of the process. It is based on the comparison between a nonparametric estimate of the said characteristic and its parametric boot-strap analogue. Applications of this principle are proposed for the assessment of recursive dynamic models in the estimation of conditional means and conditional quantiles for mixing processes and for the estimation of dependence in long memory processes.Economic theorymh530EconomicsWorking papersEstimating ambiguity
https://academiccommons.columbia.edu/catalog/ac:113809
Henry, Marchttp://hdl.handle.net/10022/AC:P:402Tue, 22 Mar 2011 11:29:29 +0000We propose a measure of the degree of ambiguity associated with a belief function and a nonparametric method to estimate it. The degree of ambiguity associated with a belief function is measured by the Kullback-Leibler diameter of the set of probability measures compatible with it. It is shown that an estimator based on the empirical version of the unambiguous measure generating the belief function is consistent for the true value of the ambiguity measure. Applications to policy decision making under Knightian uncertainty are discussed.Economic theorymh530EconomicsWorking papersFormalization and applications of the precautionary principles
https://academiccommons.columbia.edu/catalog/ac:113710
Henry, Claude; Henry, Marchttp://hdl.handle.net/10022/AC:P:398Tue, 22 Mar 2011 11:18:34 +0000A formalization of the Precautionary Principle is given here: We formalize scientific knowledge on the likelihood of events in the state space and the concepts of scientifically unambiguous events and acts. We give a definition of a non-precautionary social planner as a Savage Expected Utility maximizer who evaluates acts relative to a baseline, called "business as usual," and who disregards scientifically ambiguous acts, and we show that, for a wide class of preferences for the representative agent, non-precautionary decision making is sub-optimal. A discussion of this formalization is given in the context of national and international debates on Precaution, in the fields of Climate Change, of WTO arbitrages, and of the safety regulations of chemical products.Economic theorymh530EconomicsWorking papersAveraged Periodogram Spectral Estimation with Long Memory Conditional Heteroscedasticity
https://academiccommons.columbia.edu/catalog/ac:100509
Henry, Marchttp://hdl.handle.net/10022/AC:P:15738Mon, 07 Mar 2011 10:39:03 +0000Semiparametric spectral methods seem particularly appropriate for the analysis of long financial time series, providing they are robust to a variety of forms of conditional heteroscedasticity, which is generally recognized as a dominant feature of financial returns. This paper analyses the averaged periodogram statistic in the framework of a generalized linear process with (possibly long memory) conditional heteroscedasticity in the innovations. It is shown that the averaged periodogram statistic is appropriate for a symptotically normal estimation of the spectrum of a weakly dependent process at frequency zero and for consistent estimation of long memory and stationary cointegration in strongly dependent processes. The asymptotic results are coupled with extensive small sample investigations of the performance of the estimates considered.Economic theorymh530EconomicsWorking papersIdentifying Finite Mixtures in Econometric Models
https://academiccommons.columbia.edu/catalog/ac:128353
Henry, Marc; Kitamura, Yuichi; Salanie, Bernardhttp://hdl.handle.net/10022/AC:P:9465Wed, 18 Aug 2010 14:21:07 +0000Mixtures of distributions are present in many econometric models, such as models with unobserved heterogeneity. It is thus crucial to have a general approach to identify them nonparametrically. Yet the literature so far only contains isolated examples, applied to specific models. We derive the identifying implications of a conditional independence assumption in finite mixture models. It applies for instance to models with unobserved heterogeneity, regime switching models, and models with mismeasured discrete regressors. Under this assumption, we derive sharp bounds on the mixture weights and components. For models with two mixture components, we show that if in addition the components behave differently in the tails of their distributions, then components and weights are fully nonparametrically identified. We apply our findings to the nonparametric identification and estimation of outcome distributions with a misclassified binary regressor. This provides a simple estimator that does not require instrumental variables, auxiliary data, symmetric error distributions or other shape restrictions.Economic theorybs2237EconomicsWorking papers