This paper studies semiparametric identification and estimation of the stochastic discount factor in consumption-based asset pricing models with latent state variables. We model consumption, dividends, and a multiplicative discount factor component via unknown functions of Markovian states describing aggregate output growth. For the case of affine state dynamics and polynomial approximation of the measurement and pricing equations, we provide rank conditions for identification and tractable algorithms for filtering, smoothing, and likelihood estimation. Empirically, we find sizable nonlinearities and interactions in the impacts of expected growth and volatility on the price-dividend ratio and the discount factor.
{"title":"Semiparametric Estimation of Latent Variable Asset Pricing Models","authors":"Jeroen Dalderop","doi":"10.2139/ssrn.3638365","DOIUrl":"https://doi.org/10.2139/ssrn.3638365","url":null,"abstract":"This paper studies semiparametric identification and estimation of the stochastic discount factor in consumption-based asset pricing models with latent state variables. We model consumption, dividends, and a multiplicative discount factor component via unknown functions of Markovian states describing aggregate output growth. For the case of affine state dynamics and polynomial approximation of the measurement and pricing equations, we provide rank conditions for identification and tractable algorithms for filtering, smoothing, and likelihood estimation. Empirically, we find sizable nonlinearities and interactions in the impacts of expected growth and volatility on the price-dividend ratio and the discount factor.","PeriodicalId":264857,"journal":{"name":"ERN: Semiparametric & Nonparametric Methods (Topic)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-08-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124562352","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}
Given an endogenous binary treatment D, an outcome Y and covariates Z, finding an instrument for D is far from easy. Instead, this paper deals with the endogeneity using two-wave (t=1,2) panel data, assuming that the endogeneity is caused by a time-constant error δ_{i}. We postulate that Y_{it} is generated by a semiparametric model with an unknown heterogeneous treatment effect μ_{D}(Z_{it}) where δ_{i} appears additively, so that δ_{i} drops out for ΔY_{i}≡Y_{i2}-Y_{i1}. The main difficulty with ΔY_{i} is that the resulting effect takes a differenced form Δμ_{D}(Z_{it}), not an additive form of μ_{D}(Z_{i1}) and μ_{D}(Z_{i2}). Despite this difficulty, however, a "variance- (or overlap-) weighted" average of μ_{D}(Z_{i1}) and μ_{D}(Z_{i2}) is estimated with the ordinary least squares estimator (OLS) of ΔY_{i} on the difference of the `propensity score residual', without a direct nonparametric estimation of μ_{D}(Z_{it}). Also, this finding answers an important practical question: what is estimated by the popular `fixed-effect/within-group' estimator for panel constant-effect linear models when the effect is actually not a constant? The answer is essentially the variance-weighted average of μ_{D}(Z_{i1}) and μ_{D}(Z_{i2}). Simulation and empirical studies are provided as well.
{"title":"Variance-Weighted Effect of Endogenous Treatment and the Estimand of Fixed-Effect Approach","authors":"Myoung‐jae Lee","doi":"10.2139/ssrn.3908263","DOIUrl":"https://doi.org/10.2139/ssrn.3908263","url":null,"abstract":"Given an endogenous binary treatment D, an outcome Y and covariates Z, finding an instrument for D is far from easy. Instead, this paper deals with the endogeneity using two-wave (t=1,2) panel data, assuming that the endogeneity is caused by a time-constant error δ_{i}. We postulate that Y_{it} is generated by a semiparametric model with an unknown heterogeneous treatment effect μ_{D}(Z_{it}) where δ_{i} appears additively, so that δ_{i} drops out for ΔY_{i}≡Y_{i2}-Y_{i1}. The main difficulty with ΔY_{i} is that the resulting effect takes a differenced form Δμ_{D}(Z_{it}), not an additive form of μ_{D}(Z_{i1}) and μ_{D}(Z_{i2}). Despite this difficulty, however, a \"variance- (or overlap-) weighted\" average of μ_{D}(Z_{i1}) and μ_{D}(Z_{i2}) is estimated with the ordinary least squares estimator (OLS) of ΔY_{i} on the difference of the `propensity score residual', without a direct nonparametric estimation of μ_{D}(Z_{it}). Also, this finding answers an important practical question: what is estimated by the popular `fixed-effect/within-group' estimator for panel constant-effect linear models when the effect is actually not a constant? The answer is essentially the variance-weighted average of μ_{D}(Z_{i1}) and μ_{D}(Z_{i2}). Simulation and empirical studies are provided as well.","PeriodicalId":264857,"journal":{"name":"ERN: Semiparametric & Nonparametric Methods (Topic)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131899033","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 paper, we propose a two-step semi-nonparametric estimator for the widely used random coefficient logit demand model. In the first step, exploiting the structure of logit choice probabilities, we transform the full demand system into a partial linear model and estimate the fixed (non-random) coefficients using standard linear sieve generalized method of moment (GMM). In the second step, we construct a sieve minimum distance (MD) estimator to uncover the distribution of random coefficients nonparametrically. We establish the asymptotic properties of the estimator and show the semi-nonparametric identification of the model in a large market environment. Monte Carlo simulations and empirical illustrations support the theoretical results and demonstrate the usefulness of our estimator in practice.
{"title":"Semi-Nonparametric Estimation of Random Coefficient Logit Model for Aggregate Demand","authors":"Zhentong Lu, Xiaoxia Shi, Jing Tao","doi":"10.2139/ssrn.3503560","DOIUrl":"https://doi.org/10.2139/ssrn.3503560","url":null,"abstract":"In this paper, we propose a two-step semi-nonparametric estimator for the widely used random coefficient logit demand model. In the first step, exploiting the structure of logit choice probabilities, we transform the full demand system into a partial linear model and estimate the fixed (non-random) coefficients using standard linear sieve generalized method of moment (GMM). In the second step, we construct a sieve minimum distance (MD) estimator to uncover the distribution of random coefficients nonparametrically. We establish the asymptotic properties of the estimator and show the semi-nonparametric identification of the model in a large market environment. Monte Carlo simulations and empirical illustrations support the theoretical results and demonstrate the usefulness of our estimator in practice.","PeriodicalId":264857,"journal":{"name":"ERN: Semiparametric & Nonparametric Methods (Topic)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130659809","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 study identification of ascending auctions with additively separable auction-level unobserved heterogeneity. Usual deconvolution approaches are inapplicable due to the lack of the highest bid; both unobserved heterogeneity and incomplete bid data contribute to the correlation among observed bids. We propose an identification strategy exploiting "within" independence of unobserved heterogeneity and private value. First, the ratio of two observed order statistics' characteristic functions identifies the private value distribution. Second, standard deconvolution with a known error distribution identifies the unobserved heterogeneity distribution.
{"title":"Accounting for Unobserved Heterogeneity in Ascending Auctions","authors":"Yao Luo, Ruli Xiao","doi":"10.2139/ssrn.3733211","DOIUrl":"https://doi.org/10.2139/ssrn.3733211","url":null,"abstract":"We study identification of ascending auctions with additively separable auction-level unobserved heterogeneity. Usual deconvolution approaches are inapplicable due to the lack of the highest bid; both unobserved heterogeneity and incomplete bid data contribute to the correlation among observed bids. We propose an identification strategy exploiting \"within\" independence of unobserved heterogeneity and private value. First, the ratio of two observed order statistics' characteristic functions identifies the private value distribution. Second, standard deconvolution with a known error distribution identifies the unobserved heterogeneity distribution.","PeriodicalId":264857,"journal":{"name":"ERN: Semiparametric & Nonparametric Methods (Topic)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-11-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117285587","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 paper, we estimate and leverage latent constant group structure to generate the point, set, and density forecasts for short dynamic panel data. We implement a nonparametric Bayesian approach to simultaneously identify coefficients and group membership in the random effects which are heterogeneous across groups but fixed within a group. This method allows us to incorporate subjective prior knowledge on the group structure that potentially improves the predictive accuracy. In Monte Carlo experiments, we demonstrate that our Bayesian grouped random effects (BGRE) estimators produce accurate estimates and score predictive gains over standard panel data estimators. With a data-driven group structure, the BGRE estimators exhibit comparable accuracy of clustering with the nonsupervised machine learning algorithm Kmeans and outperform Kmeans in a two-step procedure. In the empirical analysis, we apply our method to forecast the investment rate across a broad range of firms and illustrate that the estimated latent group structure facilitate forecasts relative to standard panel data estimators.
{"title":"Forecasting with Bayesian Grouped Random Effects in Panel Data","authors":"Boyuan Zhang","doi":"10.2139/ssrn.3681672","DOIUrl":"https://doi.org/10.2139/ssrn.3681672","url":null,"abstract":"In this paper, we estimate and leverage latent constant group structure to generate the point, set, and density forecasts for short dynamic panel data. We implement a nonparametric Bayesian approach to simultaneously identify coefficients and group membership in the random effects which are heterogeneous across groups but fixed within a group. This method allows us to incorporate subjective prior knowledge on the group structure that potentially improves the predictive accuracy. In Monte Carlo experiments, we demonstrate that our Bayesian grouped random effects (BGRE) estimators produce accurate estimates and score predictive gains over standard panel data estimators. With a data-driven group structure, the BGRE estimators exhibit comparable accuracy of clustering with the nonsupervised machine learning algorithm Kmeans and outperform Kmeans in a two-step procedure. In the empirical analysis, we apply our method to forecast the investment rate across a broad range of firms and illustrate that the estimated latent group structure facilitate forecasts relative to standard panel data estimators.","PeriodicalId":264857,"journal":{"name":"ERN: Semiparametric & Nonparametric Methods (Topic)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125622533","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 aims to establish asymptotic normality of the local linear kernel estimator for quantile regression under near epoch dependence, a useful concept in characterising time series dependence of extensive interests in Econometrics. In particular, near epoch dependence can cover a wide range of linear or nonlinear time series models that are even not of strong or $alpha$-mixing property (a property usually assumed in the nonlinear time series literature). Under the mild conditions, the Bahadur representation of the quantile regression estimators is established in weak convergence sense. The method provides much richer information than mean regression and covers much more processes, which do not satisfy general mixing conditions. Simulation and application to a real data set are studied, which demonstrate the usefulness of the introduced method for analysis of time series. The theoretical results of this paper will be of widely potential interest for time series econometric semiparametric quantile regression modelling.
{"title":"Local Linear Quantile Regression for Time Series Under Near Epoch Dependence","authors":"Xiaohang Ren, Zudi Lu","doi":"10.2139/ssrn.3555740","DOIUrl":"https://doi.org/10.2139/ssrn.3555740","url":null,"abstract":"This paper aims to establish asymptotic normality of the local linear kernel estimator for quantile regression under near epoch dependence, a useful concept in characterising time series dependence of extensive interests in Econometrics. In particular, near epoch dependence can cover a wide range of linear or nonlinear time series models that are even not of strong or $alpha$-mixing property (a property usually assumed in the nonlinear time series literature). Under the mild conditions, the Bahadur representation of the quantile regression estimators is established in weak convergence sense. The method provides much richer information than mean regression and covers much more processes, which do not satisfy general mixing conditions. Simulation and application to a real data set are studied, which demonstrate the usefulness of the introduced method for analysis of time series. The theoretical results of this paper will be of widely potential interest for time series econometric semiparametric quantile regression modelling.","PeriodicalId":264857,"journal":{"name":"ERN: Semiparametric & Nonparametric Methods (Topic)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-05-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133700178","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 develop a semiparametric model to track a large number of quantiles of a time series. The model satisfies the condition of non crossing quantiles and the defining property of fixed quantiles. A key feature of the specification is that the updating scheme for time varying quantiles at each probability level is based on the gradient of the check loss function, that forms a martingale difference sequence. Theoretical properties of the proposed model are derived, such as weak stationarity of the quantile process and consistency and asymptotic normality of the estimators of the fixed parameters. The model can be applied for filtering and prediction. We also illustrate a number of possible applications such as: i) semiparametric estimation of dynamic moments of the observables, ii) density prediction, and iii) quantile predictions.
{"title":"Semiparametric Modeling of Multiple Quantiles","authors":"Leopoldo Catania, A. Luati","doi":"10.2139/ssrn.3494995","DOIUrl":"https://doi.org/10.2139/ssrn.3494995","url":null,"abstract":"We develop a semiparametric model to track a large number of quantiles of a time series. The model satisfies the condition of non crossing quantiles and the defining property of fixed quantiles. A key feature of the specification is that the updating scheme for time varying quantiles at each probability level is based on the gradient of the check loss function, that forms a martingale difference sequence. Theoretical properties of the proposed model are derived, such as weak stationarity of the quantile process and consistency and asymptotic normality of the estimators of the fixed parameters. The model can be applied for filtering and prediction. We also illustrate a number of possible applications such as: i) semiparametric estimation of dynamic moments of the observables, ii) density prediction, and iii) quantile predictions.","PeriodicalId":264857,"journal":{"name":"ERN: Semiparametric & Nonparametric Methods (Topic)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125949066","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 isotonic regression discontinuity designs, the average outcome and the treatment assignment probability are monotone in the running variable. We introduce novel nonparametric estimators for sharp and fuzzy designs based on the bandwidth-free isotonic regression. The large sample distributions of introduced estimators are driven by Brownian motions originating from zero and moving in opposite directions. Since these distributions are not pivotal, we also introduce a novel trimmed wild bootstrap procedure, which is free from nonparametric smoothing, typically needed in such settings, and show its consistency. We illustrate our approach on the well-known dataset of Lee (2008), estimating the incumbency effect in the U.S. House elections.
{"title":"Isotonic Regression Discontinuity Designs","authors":"Andrii Babii, Rohit Kumar","doi":"10.2139/ssrn.3458127","DOIUrl":"https://doi.org/10.2139/ssrn.3458127","url":null,"abstract":"In isotonic regression discontinuity designs, the average outcome and the treatment assignment probability are monotone in the running variable. We introduce novel nonparametric estimators for sharp and fuzzy designs based on the bandwidth-free isotonic regression. The large sample distributions of introduced estimators are driven by Brownian motions originating from zero and moving in opposite directions. Since these distributions are not pivotal, we also introduce a novel trimmed wild bootstrap procedure, which is free from nonparametric smoothing, typically needed in such settings, and show its consistency. We illustrate our approach on the well-known dataset of Lee (2008), estimating the incumbency effect in the U.S. House elections.","PeriodicalId":264857,"journal":{"name":"ERN: Semiparametric & Nonparametric Methods (Topic)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-08-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133547793","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 propose two simple semiparametric estimation methods for ordered response models with an unknown error distribution. The proposed methods do not require users to choose any tuning parameter and they automatically incorporate the monotonicity restriction of the unknown distribution function. Fixing finite dimensional parameters in the model, we construct nonparametric maximum likelihood estimates (NPMLE) for the error distribution based on the related binary choice data or the entire ordered response data. We then obtain estimates for finite dimensional parameters based on moment conditions given the estimated distribution function. Our semiparametric approaches deliver root-n consistent and asymptotically normal estimators of the regression coefficient and threshold parameter. We also develop valid bootstrap procedures for inference. We apply our methods to the interdependent durations model in Honore and de Paula (2010), where the social interaction effect is directly related to the threshold parameter in the corresponding ordered response model. The advantages of our methods are borne out in simulation studies and a real data application to the joint retirement decision of married couples.
{"title":"Simple Semiparametric Estimation of Ordered Response Models: With an Application to the Interdependent Durations Model","authors":"Ruixuan Liu, Zhengfei Yu","doi":"10.2139/ssrn.3420906","DOIUrl":"https://doi.org/10.2139/ssrn.3420906","url":null,"abstract":"We propose two simple semiparametric estimation methods for ordered response models with an unknown error distribution. The proposed methods do not require users to choose any tuning parameter and they automatically incorporate the monotonicity restriction of the unknown distribution function. Fixing finite dimensional parameters in the model, we construct nonparametric maximum likelihood estimates (NPMLE) for the error distribution based on the related binary choice data or the entire ordered response data. We then obtain estimates for finite dimensional parameters based on moment conditions given the estimated distribution function. Our semiparametric approaches deliver root-n consistent and asymptotically normal estimators of the regression coefficient and threshold parameter. We also develop valid bootstrap procedures for inference. We apply our methods to the interdependent durations model in Honore and de Paula (2010), where the social interaction effect is directly related to the threshold parameter in the corresponding ordered response model. The advantages of our methods are borne out in simulation studies and a real data application to the joint retirement decision of married couples.","PeriodicalId":264857,"journal":{"name":"ERN: Semiparametric & Nonparametric Methods (Topic)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125295252","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 Horowitz’s smoothed maximum score estimator to discrete-time duration models. The estimator’s consistency and asymptotic distribution are derived. Monte Carlo simulations using various data generating processes with varying error distributions and shapes of the hazard rate are conducted to examine the finite sample properties of the estimator. The bias-corrected estimator performs reasonably well for the models considered with moderately-sized samples.
{"title":"Smoothed Maximum Score Estimation of Discrete Duration Models","authors":"Sadat Reza, Paul Rilstone","doi":"10.3390/JRFM12020064","DOIUrl":"https://doi.org/10.3390/JRFM12020064","url":null,"abstract":"This paper extends Horowitz’s smoothed maximum score estimator to discrete-time duration models. The estimator’s consistency and asymptotic distribution are derived. Monte Carlo simulations using various data generating processes with varying error distributions and shapes of the hazard rate are conducted to examine the finite sample properties of the estimator. The bias-corrected estimator performs reasonably well for the models considered with moderately-sized samples.","PeriodicalId":264857,"journal":{"name":"ERN: Semiparametric & Nonparametric Methods (Topic)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124519052","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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