This paper studies vector autoregressive models with parsimoniously time-varying parameters. The parameters are assumed to follow parsimonious random walks, where parsimony stems from the assumption that increments to the parameters have a non-zero probability of being exactly equal to zero. We estimate the sparse and high-dimensional vector of changes to the parameters with the Lasso and the adaptive Lasso. The parsimonious random walk allows the parameters to be modelled non parametrically, so that our model can accommodate constant parameters, an unknown number of structural breaks, or parameters varying randomly. We characterize the finite sample properties of the Lasso by deriving upper bounds on the estimation and prediction errors that are valid with high probability, and provide asymptotic conditions under which these bounds tend to zero with probability tending to one. We also provide conditions under which the adaptive Lasso is able to achieve perfectmodel selection. We investigate by simulations the properties of the Lasso and the adaptive Lasso in settings where the parameters are stable, experience structural breaks, or follow a parsimonious random walk. We use our model to investigate the monetary policy response to inflation and business cycle fluctuations in the US by estimating a parsimoniously time varying parameter Taylor rule. We document substantial changes in the policy response of the Fed in the 1970s and 1980s, and since 2007, but also document the stability of this response in the rest of the sample.
{"title":"Vector Autoregressions with Parsimoniously Time Varying Parameters and an Application to Monetary Policy","authors":"Laurent Callot, J. Kristensen","doi":"10.2139/ssrn.2520403","DOIUrl":"https://doi.org/10.2139/ssrn.2520403","url":null,"abstract":"This paper studies vector autoregressive models with parsimoniously time-varying parameters. The parameters are assumed to follow parsimonious random walks, where parsimony stems from the assumption that increments to the parameters have a non-zero probability of being exactly equal to zero. We estimate the sparse and high-dimensional vector of changes to the parameters with the Lasso and the adaptive Lasso. The parsimonious random walk allows the parameters to be modelled non parametrically, so that our model can accommodate constant parameters, an unknown number of structural breaks, or parameters varying randomly. We characterize the finite sample properties of the Lasso by deriving upper bounds on the estimation and prediction errors that are valid with high probability, and provide asymptotic conditions under which these bounds tend to zero with probability tending to one. We also provide conditions under which the adaptive Lasso is able to achieve perfectmodel selection. We investigate by simulations the properties of the Lasso and the adaptive Lasso in settings where the parameters are stable, experience structural breaks, or follow a parsimonious random walk. We use our model to investigate the monetary policy response to inflation and business cycle fluctuations in the US by estimating a parsimoniously time varying parameter Taylor rule. We document substantial changes in the policy response of the Fed in the 1970s and 1980s, and since 2007, but also document the stability of this response in the rest of the sample.","PeriodicalId":264857,"journal":{"name":"ERN: Semiparametric & Nonparametric Methods (Topic)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2014-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128627890","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 develops a dynamic model of consumer search that, despite placing very little structure on the dynamic problem faced by consumers, allows us to exploit intertemporal variation in within-period price and search cost distributions to estimate the population distribution from which consumers' search costs are initially drawn. We show that static approaches to estimating this distribution generally suffer from a dynamic sample selection bias because forward-looking consumers with unit demand for a good may delay their purchase in a way that depends on their individual search cost. We analyze identification of the population search cost distribution using only price data and develop estimable nonparametric upper and lower bounds on the distribution function and a nonlinear least squares estimator for parametric models. We also consider the additional identifying power of weak assumptions such as monotonicity of purchase probabilities in search costs. We apply our estimators to analyze the online market for two widely used econometrics textbooks. Our results suggest that static estimates of the search cost distribution are biased upwards, in a distributional sense, relative to the true population distribution. In a small-scale simulation study, we show that this is typical in a dynamic setting where consumers with high search costs are more likely to delay purchase than those with lower search costs.
{"title":"Dynamic Selection and Distributional Bounds on Search Costs in Dynamic Unit-Demand Models","authors":"Jason R. Blevins, Garrett T. Senney","doi":"10.2139/ssrn.2516601","DOIUrl":"https://doi.org/10.2139/ssrn.2516601","url":null,"abstract":"This paper develops a dynamic model of consumer search that, despite placing very little structure on the dynamic problem faced by consumers, allows us to exploit intertemporal variation in within-period price and search cost distributions to estimate the population distribution from which consumers' search costs are initially drawn. We show that static approaches to estimating this distribution generally suffer from a dynamic sample selection bias because forward-looking consumers with unit demand for a good may delay their purchase in a way that depends on their individual search cost. We analyze identification of the population search cost distribution using only price data and develop estimable nonparametric upper and lower bounds on the distribution function and a nonlinear least squares estimator for parametric models. We also consider the additional identifying power of weak assumptions such as monotonicity of purchase probabilities in search costs. We apply our estimators to analyze the online market for two widely used econometrics textbooks. Our results suggest that static estimates of the search cost distribution are biased upwards, in a distributional sense, relative to the true population distribution. In a small-scale simulation study, we show that this is typical in a dynamic setting where consumers with high search costs are more likely to delay purchase than those with lower search costs.","PeriodicalId":264857,"journal":{"name":"ERN: Semiparametric & Nonparametric Methods (Topic)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2014-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131381291","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}
M. Gámiz, E. Mammen, M. D. Martínez-Miranda, J. Nielsen
This paper brings together the theory and practice of local linear kernel hazard estimation. Bandwidth selection is fully analysed, including Do-validation that is shown to have good practical and theoretical properties. Insight is provided into the choice of the weighting function in the local linear minimization and it is pointed out that classical weighting sometimes lacks stability. A new semi-parametric hazard estimator transforming the survival data before smoothing is introduced and shown to have good practical properties.
{"title":"Do-Validating Local Linear Hazards","authors":"M. Gámiz, E. Mammen, M. D. Martínez-Miranda, J. Nielsen","doi":"10.2139/ssrn.2504497","DOIUrl":"https://doi.org/10.2139/ssrn.2504497","url":null,"abstract":"This paper brings together the theory and practice of local linear kernel hazard estimation. Bandwidth selection is fully analysed, including Do-validation that is shown to have good practical and theoretical properties. Insight is provided into the choice of the weighting function in the local linear minimization and it is pointed out that classical weighting sometimes lacks stability. A new semi-parametric hazard estimator transforming the survival data before smoothing is introduced and shown to have good practical properties.","PeriodicalId":264857,"journal":{"name":"ERN: Semiparametric & Nonparametric Methods (Topic)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2014-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132355874","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 discusses partial identification in a nonparametric triangular system with discrete endogenous regressors and nonseparable errors. Recently, Jun et al. (2011, JPX) provide bounds on the structural function evaluated at particular values using exclusion, exogeneity and rank conditions. We propose a simple idea that often allows to improve the JPX bounds without invoking a new set of assumptions. Moreover, we show how our idea can be used to tighten existing bounds on the structural function in more general triangular systems.
{"title":"Tightening Bounds in Triangular Systems","authors":"Désiré Kédagni, Ismael Mourifié","doi":"10.2139/ssrn.2457275","DOIUrl":"https://doi.org/10.2139/ssrn.2457275","url":null,"abstract":"This note discusses partial identification in a nonparametric triangular system with discrete endogenous regressors and nonseparable errors. Recently, Jun et al. (2011, JPX) provide bounds on the structural function evaluated at particular values using exclusion, exogeneity and rank conditions. We propose a simple idea that often allows to improve the JPX bounds without invoking a new set of assumptions. Moreover, we show how our idea can be used to tighten existing bounds on the structural function in more general triangular systems.","PeriodicalId":264857,"journal":{"name":"ERN: Semiparametric & Nonparametric Methods (Topic)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2014-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130796604","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 article proposes a general empirical method for the estimation of marginal cost of individual firms. The new method employs the smooth coefficient model, which has a number of appealing features when applied to cost functions. The empirical analysis uses data from a unique sample from which we observe marginal cost. We compare the estimates from the proposed method with the true values of marginal cost, and the estimates of marginal cost that we obtain through conventional parametric methods. We show that the proposed method produces estimated values of marginal cost that very closely approximate the true values of marginal cost. In contrast, the results from conventional parametric methods are significantly biased and provide invalid inference.
{"title":"On the Estimation of Marginal Cost","authors":"M. Delis, Maria Iosifidi, E. Tsionas","doi":"10.2139/ssrn.2857561","DOIUrl":"https://doi.org/10.2139/ssrn.2857561","url":null,"abstract":"This article proposes a general empirical method for the estimation of marginal cost of individual firms. The new method employs the smooth coefficient model, which has a number of appealing features when applied to cost functions. The empirical analysis uses data from a unique sample from which we observe marginal cost. We compare the estimates from the proposed method with the true values of marginal cost, and the estimates of marginal cost that we obtain through conventional parametric methods. We show that the proposed method produces estimated values of marginal cost that very closely approximate the true values of marginal cost. In contrast, the results from conventional parametric methods are significantly biased and provide invalid inference.","PeriodicalId":264857,"journal":{"name":"ERN: Semiparametric & Nonparametric Methods (Topic)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2014-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123575782","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 explore the application of Generalised Additive Models of Location, Scale and Shape for the analysis of conditional income distributions in Germany following the reunification. We find that conditional income distributions can generally be modelled using the three parameter Dagum distribution and our results hint at an even more pronounced effect of skill-biased technological change than can be observed by standard mean regression.
{"title":"A New Semiparametric Approach to Analysing Conditional Income Distributions","authors":"Alexander Sohn, N. Klein, T. Kneib","doi":"10.2139/ssrn.2404335","DOIUrl":"https://doi.org/10.2139/ssrn.2404335","url":null,"abstract":"In this paper we explore the application of Generalised Additive Models of Location, Scale and Shape for the analysis of conditional income distributions in Germany following the reunification. We find that conditional income distributions can generally be modelled using the three parameter Dagum distribution and our results hint at an even more pronounced effect of skill-biased technological change than can be observed by standard mean regression.","PeriodicalId":264857,"journal":{"name":"ERN: Semiparametric & Nonparametric Methods (Topic)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2014-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128483951","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 consider a semiparametric single-index panel data model with cross-sectional dependence and stationarity. Meanwhile, we allow fixed effects to be correlated with the regressors to capture unobservable heterogeneity. Under a general spatial error dependence structure, we then establish some consistent closed-form estimates for both the unknown parameters and the link function for the case where both cross-sectional dimension (N) and temporal dimension (T) go to infinity. Rates of convergence and asymptotic normality are established for the proposed estimates. Our experience suggests that the proposed estimation method is simple and thus attractive for finite-sample studies and empirical implementations. Moreover, both the finite-sample performance and the empirical applications show that the proposed estimation method works well when the cross-sectional dependence exists in the data set.
{"title":"Semiparametric Single-Index Panel Data Models with Cross-Sectional Dependence","authors":"B. Peng, Chaohua Dong, Jiti Gao","doi":"10.2139/ssrn.2401476","DOIUrl":"https://doi.org/10.2139/ssrn.2401476","url":null,"abstract":"In this paper, we consider a semiparametric single-index panel data model with cross-sectional dependence and stationarity. Meanwhile, we allow fixed effects to be correlated with the regressors to capture unobservable heterogeneity. Under a general spatial error dependence structure, we then establish some consistent closed-form estimates for both the unknown parameters and the link function for the case where both cross-sectional dimension (N) and temporal dimension (T) go to infinity. Rates of convergence and asymptotic normality are established for the proposed estimates. Our experience suggests that the proposed estimation method is simple and thus attractive for finite-sample studies and empirical implementations. Moreover, both the finite-sample performance and the empirical applications show that the proposed estimation method works well when the cross-sectional dependence exists in the data set.","PeriodicalId":264857,"journal":{"name":"ERN: Semiparametric & Nonparametric Methods (Topic)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2014-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130940766","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 extend Bossaerts’ (2004) analysis of the implications of the efficient learning market hypothesis (ELM) for asset prices by reformulating it in a GMM setting. Our representation is more amenable to widespread application and allows the econometrician, in testing ELM, to make use of the full range of specification tests that have been developed by the empirical literature in the context of tests of the more restrictive Efficient Market Hypothesis (EMH). We apply this framework to test for efficient learning in the pricing of small capitalization stocks. We find evidence of mispricing of small stocks but we cannot rule out that, in spite of possibly incorrect priors about the future payoffs of small firms, the market efficiently processes information as it becomes available over time. That is, our evidence contradicts the Efficient Market Hypothesis (EMH) but it is not incompatible with efficient learning in the manner of Bossaerts (2004).
{"title":"GMM-Based Tests of Efficient Market Learning and an Application to Testing for a Small Firm Effect in Equity Pricing","authors":"Valerio Potì, Akhtar Siddique","doi":"10.2139/ssrn.2212482","DOIUrl":"https://doi.org/10.2139/ssrn.2212482","url":null,"abstract":"In this paper, we extend Bossaerts’ (2004) analysis of the implications of the efficient learning market hypothesis (ELM) for asset prices by reformulating it in a GMM setting. Our representation is more amenable to widespread application and allows the econometrician, in testing ELM, to make use of the full range of specification tests that have been developed by the empirical literature in the context of tests of the more restrictive Efficient Market Hypothesis (EMH). We apply this framework to test for efficient learning in the pricing of small capitalization stocks. We find evidence of mispricing of small stocks but we cannot rule out that, in spite of possibly incorrect priors about the future payoffs of small firms, the market efficiently processes information as it becomes available over time. That is, our evidence contradicts the Efficient Market Hypothesis (EMH) but it is not incompatible with efficient learning in the manner of Bossaerts (2004).","PeriodicalId":264857,"journal":{"name":"ERN: Semiparametric & Nonparametric Methods (Topic)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2013-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124016368","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 Cross Entropy method is a well-known adaptive importance sampling method for rare-event probability estimation, which requires estimating an optimal importance sampling density within a parametric class. In this article we estimate an optimal importance sampling density within a wider semiparametric class of distributions. We show that this semiparametric version of the Cross Entropy method frequently yields efficient estimators. We illustrate the excellent practical performance of the method with numerical experiments and show that for the problems we consider it typically outperforms alternative schemes by orders of magnitude.
{"title":"Semiparametric Cross Entropy for Rare-Event Simulation","authors":"Z. Botev, Ad Ridder, L. Rojas-Nandayapa","doi":"10.2139/ssrn.2319292","DOIUrl":"https://doi.org/10.2139/ssrn.2319292","url":null,"abstract":"The Cross Entropy method is a well-known adaptive importance sampling method for rare-event probability estimation, which requires estimating an optimal importance sampling density within a parametric class. In this article we estimate an optimal importance sampling density within a wider semiparametric class of distributions. We show that this semiparametric version of the Cross Entropy method frequently yields efficient estimators. We illustrate the excellent practical performance of the method with numerical experiments and show that for the problems we consider it typically outperforms alternative schemes by orders of magnitude.","PeriodicalId":264857,"journal":{"name":"ERN: Semiparametric & Nonparametric Methods (Topic)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2013-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130477543","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 at improved accuracy in testing for long-run predictability in noisy series, such as stock market returns. Long-horizon regressions have previously been the dominant approach in this area. We suggest an alternative method that yields more accurate results. We find evidence of predictability in S&P 500 returns even when the confidence intervals are constructed using model-free methods based on subsampling.
{"title":"A Frequency-Domain Alternative to Long-Horizon Regressions with Application to Return Predictability","authors":"N. Sizova","doi":"10.2139/ssrn.2297934","DOIUrl":"https://doi.org/10.2139/ssrn.2297934","url":null,"abstract":"This paper aims at improved accuracy in testing for long-run predictability in noisy series, such as stock market returns. Long-horizon regressions have previously been the dominant approach in this area. We suggest an alternative method that yields more accurate results. We find evidence of predictability in S&P 500 returns even when the confidence intervals are constructed using model-free methods based on subsampling.","PeriodicalId":264857,"journal":{"name":"ERN: Semiparametric & Nonparametric Methods (Topic)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2013-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114663271","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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