Often socio-economic variables are measured on a discrete scale or rounded to protect confidentiality. Nevertheless, when exploring the effect of a relevant covariate on the whole outcome distribution of a discrete response variable, virtually all common quantile regression methods require the distribution of the covariate to be continuous. This paper departs from this basic requirement by presenting an algorithm for nonparametric estimation of conditional quantiles when both the response variable and the covariate are discretely distributed. Moreover, we allow the variables of interest to be pairwise correlated. For computational efficiency, we aggregate the data into smaller subsets by a binning operation, and make inference on the resulting prebinned data. Specifically, we propose two kernel-based binned conditional quantile estimators, one for untransformed discrete response data and one for rank-transformed response data. We establish asymptotic properties of both estimators. A practical procedure for jointly selecting band- and binwidth parameters is also presented. Simulation results show excellent estimation accuracy in terms of bias, mean squared error, and confidence interval coverage. Typically prebinning the data leads to considerable computational savings when large datasets are under study, as compared to direct (un)conditional quantile kernel estimation of multivariate data. With this in mind, we illustrate the proposed methodology with an application to a large real dataset concerning US hospital patients with congestive heart failure.
{"title":"Kernel-Smoothed Conditional Quantiles of Correlated Bivariate Discrete Data","authors":"J. De Gooijer, A. Yuan","doi":"10.2139/ssrn.1742230","DOIUrl":"https://doi.org/10.2139/ssrn.1742230","url":null,"abstract":"Often socio-economic variables are measured on a discrete scale or rounded to protect confidentiality. Nevertheless, when exploring the effect of a relevant covariate on the whole outcome distribution of a discrete response variable, virtually all common quantile regression methods require the distribution of the covariate to be continuous. This paper departs from this basic requirement by presenting an algorithm for nonparametric estimation of conditional quantiles when both the response variable and the covariate are discretely distributed. Moreover, we allow the variables of interest to be pairwise correlated. For computational efficiency, we aggregate the data into smaller subsets by a binning operation, and make inference on the resulting prebinned data. Specifically, we propose two kernel-based binned conditional quantile estimators, one for untransformed discrete response data and one for rank-transformed response data. We establish asymptotic properties of both estimators. A practical procedure for jointly selecting band- and binwidth parameters is also presented. Simulation results show excellent estimation accuracy in terms of bias, mean squared error, and confidence interval coverage. Typically prebinning the data leads to considerable computational savings when large datasets are under study, as compared to direct (un)conditional quantile kernel estimation of multivariate data. With this in mind, we illustrate the proposed methodology with an application to a large real dataset concerning US hospital patients with congestive heart failure.","PeriodicalId":264857,"journal":{"name":"ERN: Semiparametric & Nonparametric Methods (Topic)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2011-01-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129015346","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 quality of match of four statistical matches used in the LIMEW estimates for the United States for 1992 and 2007 is described. The first match combines the 1992 Survey of Consumer Finances (SCF) with the 1993 March Supplement to the Current Population Survey, or Annual Demographic Supplement (ADS). The second match combines the 1985 American Use of Time Project survey (AUTP) with the 1993 ADS. The third match combines the 2007 SCF with the 2008 March Supplement to the CPS, now called the Annual Social and Economics Supplement (ASEC). The fourth match combines the 2007 American Time Use Survey with the 2008 ASEC. In each case, the alignment of the two datasets is examined, after which various aspects of the match quality are described. Also in each case, the matches are of high quality, given the nature of the source datasets.
{"title":"Quality of Match for Statistical Matches Used in the 1992 and 2007 Limew Estimates for the United States","authors":"Thomas Masterson","doi":"10.2139/ssrn.1680409","DOIUrl":"https://doi.org/10.2139/ssrn.1680409","url":null,"abstract":"The quality of match of four statistical matches used in the LIMEW estimates for the United States for 1992 and 2007 is described. The first match combines the 1992 Survey of Consumer Finances (SCF) with the 1993 March Supplement to the Current Population Survey, or Annual Demographic Supplement (ADS). The second match combines the 1985 American Use of Time Project survey (AUTP) with the 1993 ADS. The third match combines the 2007 SCF with the 2008 March Supplement to the CPS, now called the Annual Social and Economics Supplement (ASEC). The fourth match combines the 2007 American Time Use Survey with the 2008 ASEC. In each case, the alignment of the two datasets is examined, after which various aspects of the match quality are described. Also in each case, the matches are of high quality, given the nature of the source datasets.","PeriodicalId":264857,"journal":{"name":"ERN: Semiparametric & Nonparametric Methods (Topic)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2010-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131291366","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 note illustrates that the typical parameter, beta, in a censored regression model can be used to calculate an interesting marginal effect even when the errors in the model and the explanatory variables are not independent. The result is relevant for cross sectional models such at the ones considered in Powell (1984), Powell (1986) and Chen and Khan (2000), as well as for panel data models such as the ones in Honore (1992) and Alan and Leth-Petersen (2006), and it applies with fixed as well as with random censoring.
{"title":"On Marginal Effects in Semiparametric Censored Regression Models","authors":"Bo E. Honoré","doi":"10.2139/ssrn.1394384","DOIUrl":"https://doi.org/10.2139/ssrn.1394384","url":null,"abstract":"This note illustrates that the typical parameter, beta, in a censored regression model can be used to calculate an interesting marginal effect even when the errors in the model and the explanatory variables are not independent. The result is relevant for cross sectional models such at the ones considered in Powell (1984), Powell (1986) and Chen and Khan (2000), as well as for panel data models such as the ones in Honore (1992) and Alan and Leth-Petersen (2006), and it applies with fixed as well as with random censoring.","PeriodicalId":264857,"journal":{"name":"ERN: Semiparametric & Nonparametric Methods (Topic)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2008-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121608689","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}
R. Brüggemann, W. Härdle, Julius Mungo, Carsten Trenkler
The implied volatility of an option as a function of strike price and time to maturity forms a volatility surface. Traders price according to the dynamics of this high dimensional surface. Recent developments that employ semiparametric models approximate the implied volatility surface (IVS) in a finite dimensional function space, allowing for a low dimensional factor representation of these dynamics. This paper presents an investigation into the stochastic properties of the factor loading time series using the vector autoregressive (VAR) framework and analyzes the dynamic relationship of these factors with economic indicators. Copyright The Author 2008. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oxfordjournals.org., Oxford University Press.
{"title":"VAR Modeling for Dynamic Loadings Driving Volatility Strings","authors":"R. Brüggemann, W. Härdle, Julius Mungo, Carsten Trenkler","doi":"10.1093/JJFINEC/NBN004","DOIUrl":"https://doi.org/10.1093/JJFINEC/NBN004","url":null,"abstract":"The implied volatility of an option as a function of strike price and time to maturity forms a volatility surface. Traders price according to the dynamics of this high dimensional surface. Recent developments that employ semiparametric models approximate the implied volatility surface (IVS) in a finite dimensional function space, allowing for a low dimensional factor representation of these dynamics. This paper presents an investigation into the stochastic properties of the factor loading time series using the vector autoregressive (VAR) framework and analyzes the dynamic relationship of these factors with economic indicators. Copyright The Author 2008. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oxfordjournals.org., Oxford University Press.","PeriodicalId":264857,"journal":{"name":"ERN: Semiparametric & Nonparametric Methods (Topic)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2008-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132106308","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 extends the existing fully parametric Bayesian literature on stochastic volatility to allow for more general return distributions. Instead of specifying a particular distribution for the return innovation, nonparametric Bayesian methods are used to flexibly model the skewness and kurtosis of the distribution while the dynamics of volatility continue to be modeled with a parametric structure. Our semiparametric Bayesian approach provides a full characterization of parametric and distributional uncertainty. A Markov chain Monte Carlo sampling approach to estimation is presented with theoretical and computational issues for simulation from the posterior predictive distributions. An empirical example compares the new model to standard parametric stochastic volatility models.
{"title":"Bayesian Semiparametric Stochastic Volatility Modeling","authors":"Mark J. Jensen, J. Maheu","doi":"10.2139/ssrn.1151239","DOIUrl":"https://doi.org/10.2139/ssrn.1151239","url":null,"abstract":"This paper extends the existing fully parametric Bayesian literature on stochastic volatility to allow for more general return distributions. Instead of specifying a particular distribution for the return innovation, nonparametric Bayesian methods are used to flexibly model the skewness and kurtosis of the distribution while the dynamics of volatility continue to be modeled with a parametric structure. Our semiparametric Bayesian approach provides a full characterization of parametric and distributional uncertainty. A Markov chain Monte Carlo sampling approach to estimation is presented with theoretical and computational issues for simulation from the posterior predictive distributions. An empirical example compares the new model to standard parametric stochastic volatility models.","PeriodicalId":264857,"journal":{"name":"ERN: Semiparametric & Nonparametric Methods (Topic)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2008-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129752132","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}
Daniel Egel, B. Graham, Cristine Campos de Xavier Pinto
We propose a new inverse probability weighting (IPW) estimator for moment condition models with missing data. Our estimator is easy to implement and compares favorably with existing IPW estimators, including augmented inverse probability weighting (AIPW) estimators, in terms of efficiency, robustness, and higher order bias. We illustrate our method with a study of the relationship between early Black-White differences in cognitive achievement and subsequent differences in adult earnings. In our dataset the early childhood achievement measure, the main regressor of interest, is missing for many units.
{"title":"Inverse Probability Tilting for Moment Condition Models with Missing Data","authors":"Daniel Egel, B. Graham, Cristine Campos de Xavier Pinto","doi":"10.1093/RESTUD/RDR047","DOIUrl":"https://doi.org/10.1093/RESTUD/RDR047","url":null,"abstract":"We propose a new inverse probability weighting (IPW) estimator for moment condition models with missing data. Our estimator is easy to implement and compares favorably with existing IPW estimators, including augmented inverse probability weighting (AIPW) estimators, in terms of efficiency, robustness, and higher order bias. We illustrate our method with a study of the relationship between early Black-White differences in cognitive achievement and subsequent differences in adult earnings. In our dataset the early childhood achievement measure, the main regressor of interest, is missing for many units.","PeriodicalId":264857,"journal":{"name":"ERN: Semiparametric & Nonparametric Methods (Topic)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2008-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125033127","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}
Bidirectional valuation models are based on numerical methods to obtain kernels of parabolic equations. Here we address the problem of robustness of kernel calculations vis a vis floating point errors from a theoretical standpoint. We are interested in kernels of one-dimensional diffusion equations with continuous coefficients as evaluated by means of explicit discretization schemes of uniform step h > 0 in the limit as h → 0. We consider both semidiscrete triangulations with continuous time and explicit Euler schemes with time step so small that the Courant condition is satisfied. We find uniform bounds for the convergence rate as a function of the degree of smoothness. We conjecture these bounds are indeed sharp. The bounds also apply to the time derivatives of the kernel and its first two space derivatives. The proof is constructive and is based on a new technique of path conditioning for Markov chains and a renormalization group argument. We make the simplifying assumption of time-independence and use longitudinal Fourier transforms in the time direction. Convergence rates depend on the degree of smoothness and Holder differentiability of the coefficients. We find that the fastest convergence rate is of order O(h2) and is achieved if the coefficients have a bounded second derivative. Otherwise, explicit schemes still converge for any degree of Holder differentiability except that the convergence rate is slower. Holder continuity itself is not strictly necessary and can be relaxed by an hypothesis of uniform continuity.
{"title":"Kernel Convergence Estimates for Diffusions with Continuous Coefficients","authors":"C. Albanese","doi":"10.2139/ssrn.1026612","DOIUrl":"https://doi.org/10.2139/ssrn.1026612","url":null,"abstract":"Bidirectional valuation models are based on numerical methods to obtain kernels of parabolic equations. Here we address the problem of robustness of kernel calculations vis a vis floating point errors from a theoretical standpoint. We are interested in kernels of one-dimensional diffusion equations with continuous coefficients as evaluated by means of explicit discretization schemes of uniform step h > 0 in the limit as h → 0. We consider both semidiscrete triangulations with continuous time and explicit Euler schemes with time step so small that the Courant condition is satisfied. We find uniform bounds for the convergence rate as a function of the degree of smoothness. We conjecture these bounds are indeed sharp. The bounds also apply to the time derivatives of the kernel and its first two space derivatives. The proof is constructive and is based on a new technique of path conditioning for Markov chains and a renormalization group argument. We make the simplifying assumption of time-independence and use longitudinal Fourier transforms in the time direction. Convergence rates depend on the degree of smoothness and Holder differentiability of the coefficients. We find that the fastest convergence rate is of order O(h2) and is achieved if the coefficients have a bounded second derivative. Otherwise, explicit schemes still converge for any degree of Holder differentiability except that the convergence rate is slower. Holder continuity itself is not strictly necessary and can be relaxed by an hypothesis of uniform continuity.","PeriodicalId":264857,"journal":{"name":"ERN: Semiparametric & Nonparametric Methods (Topic)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2007-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114420959","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}
It is difficult to define news, and many definitions are model-based since part of what is announced is anticipated. Therefore, news is typically defined as a residual within the context of some type of prediction model, and the prediction model locks in the sampling frequency that is the reference time scale for analyzing propagation mechanisms. We try to accomplish two goals: (1) characterize news as much as possible as a model-free observation, and (2) measure the impact of news over any arbitrary horizon of interest. We revisit the concept of news impact curves introduced by Engle and Ng (1993), in the current high frequency data environment of financial market time series. Instead of taking a single horizon fixed parametric specification, we recast many of the original ideas in a very flexible multi-horizon semi-parametric setting. Technically speaking we introduce semi-parametric MIDAS regressions and study their asymptotic properties. The analysis relates to and extends recent work by Linton and Mammen (2005). In addition we also introduce various new parametric models. We find that moderately good (intra-daily) news reduces volatility (the next day), while both very good news (unusual high positive returns) and bad news (negative returns) increase volatility, with the latter having a more severe impact. The asymmetries we find have profound implications for current volatility prediction models that are based on in-sample asymptotic analysis developed over recent years. In this context we discuss the link between diffusions and news impact curves.
{"title":"News - Good or Bad - and its Impact Over Multiple Horizons","authors":"Xilong Chen, Eric Ghysels","doi":"10.2139/ssrn.998209","DOIUrl":"https://doi.org/10.2139/ssrn.998209","url":null,"abstract":"It is difficult to define news, and many definitions are model-based since part of what is announced is anticipated. Therefore, news is typically defined as a residual within the context of some type of prediction model, and the prediction model locks in the sampling frequency that is the reference time scale for analyzing propagation mechanisms. We try to accomplish two goals: (1) characterize news as much as possible as a model-free observation, and (2) measure the impact of news over any arbitrary horizon of interest. We revisit the concept of news impact curves introduced by Engle and Ng (1993), in the current high frequency data environment of financial market time series. Instead of taking a single horizon fixed parametric specification, we recast many of the original ideas in a very flexible multi-horizon semi-parametric setting. Technically speaking we introduce semi-parametric MIDAS regressions and study their asymptotic properties. The analysis relates to and extends recent work by Linton and Mammen (2005). In addition we also introduce various new parametric models. We find that moderately good (intra-daily) news reduces volatility (the next day), while both very good news (unusual high positive returns) and bad news (negative returns) increase volatility, with the latter having a more severe impact. The asymmetries we find have profound implications for current volatility prediction models that are based on in-sample asymptotic analysis developed over recent years. In this context we discuss the link between diffusions and news impact curves.","PeriodicalId":264857,"journal":{"name":"ERN: Semiparametric & Nonparametric Methods (Topic)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2007-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123428577","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}
A covariance-stationary vector of variables has a Wold representation whose coefficients can be semiparametrically estimated by local projections (Jorda, 2005). Substituting the Wold representations for variables in model expressions generates restrictions that can be used by the method of minimum distance to estimate model parameters. We call this estimator projection minimum distance (PMD) and show that its parameter estimates are consistent and asymptotically normal. In many cases, PMD is asymptotically equivalent to maximum likelihood estimation (MLE) and nests GMM as a special case. In fact, models whose ML estimation would require numerical routines (such as VARMA models) can often be estimated by simple least-squares routines and almost as efficiently by PMD. Because PMD imposes no constraints on the dynamics of the system, it is often consistent in many situations where alternative estimators would be inconsistent. We provide several Monte Carlo experiments and an empirical application in support of the new techniques introduced.
{"title":"Estimation and Inference by the Method of Projection Minimum Distance","authors":"Ò. Jordà, S. Kozicki","doi":"10.2139/ssrn.1001957","DOIUrl":"https://doi.org/10.2139/ssrn.1001957","url":null,"abstract":"A covariance-stationary vector of variables has a Wold representation whose coefficients can be semiparametrically estimated by local projections (Jorda, 2005). Substituting the Wold representations for variables in model expressions generates restrictions that can be used by the method of minimum distance to estimate model parameters. We call this estimator projection minimum distance (PMD) and show that its parameter estimates are consistent and asymptotically normal. In many cases, PMD is asymptotically equivalent to maximum likelihood estimation (MLE) and nests GMM as a special case. In fact, models whose ML estimation would require numerical routines (such as VARMA models) can often be estimated by simple least-squares routines and almost as efficiently by PMD. Because PMD imposes no constraints on the dynamics of the system, it is often consistent in many situations where alternative estimators would be inconsistent. We provide several Monte Carlo experiments and an empirical application in support of the new techniques introduced.","PeriodicalId":264857,"journal":{"name":"ERN: Semiparametric & Nonparametric Methods (Topic)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2007-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126177112","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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