|
on Econometrics |
| By: | Zongwu Cai; Huaiyu Xiong |
| Abstract: | We study a new class of semiparametric instrumental variables models with the structural function represented by a partially varying coefficient functional form. Under this representation, the models are linear in the endogenous/exogenous components with unknown constant or functional coefficients. As a result, the ill-posed inverse problem in a general nonparametric model with continuous endogenous variables does not exist under this setting. Efficient procedures are proposed to estimate both the constant and functional coefficients. Precisely, a three-step estimation procedure is proposed to estimate the constant parameters and the functional coefficients, we use the partial residuals and implement a nonparametric two-step estimation procedure. We establish the asymptotic properties for both estimators, including consistency and asymptotic normality. More importantly, it is also demonstrated that the constant parameters estimators are efficient, e.g., square root of n-consistent, and the functional coefficient estimators are oracle. A consistent estimation of the asymptotic covariance for both estimators is also provided. Finally, the high practical power of the resulting estimators is illustrated via both a Monte Carlo simulation study and an application to returns to education. |
| Keywords: | Endogenous variables; Functional-coefficient models; Instrumental variables; Local linear fitting; Nonparametric smoothing; Simultaneous equations. |
| Date: | 2013–10–14 |
| URL: | http://d.repec.org/n?u=RePEc:wyi:wpaper:001967&r=ecm |
| By: | Hisayuki Tsukuma (Faculty of Medicine, Toho University); Tatsuya Kubokawa (Faculty of Economics, The University of Tokyo) |
| Abstract: | 　　 This paper addresses the problem of estimating the mean vector of a singular multivariate normal distribution with an unknown singular covariance matrix. The maximum likelihood estimator is shown to be minimax relative to a quadratic loss weighted by the Moore-Penrose inverse of the covariance matrix. An unbiased risk estimator relative to the weighted quadratic loss is provided for a Baranchik type class of shrinkage estimators. Based on the unbiased risk estimator, a sufficient condition for the minimaxity is expressed not only as a differential inequality, but also as an integral inequality. Also, generalized Bayes minimax estimators are established by using an interesting structure of singular multivariate normal distribution. |
| Date: | 2014–04 |
| URL: | http://d.repec.org/n?u=RePEc:tky:fseres:2014cf930&r=ecm |
| By: | Harald Badinger (Department of Economics, Vienna University of Economics and Business); Peter Egger (Department of Management, Technology and Economics at ETH Zürich) |
| Abstract: | This paper develops a unified framework for fixed and random effects estimation of higher-order spatial autoregressive panel data models with spatial autoregressive disturbances and heteroskedasticity of unknown form in the idiosyncratic error component. We derive the moment conditions and optimal weighting matrix without distributional assumptions for a generalized moments (GM) estimation procedure of the spatial autoregressive parameters of the disturbance process and define both a random effects and a fixed effects spatial generalized two-stage least squares estimator for the regression parameters of the model. We prove consistency of the proposed estimators and derive their joint asymptotic distribution, which is robust to heteroskedasticity of unknown form in the idiosyncratic error component. Finally, we derive a robust Hausman-test of the spatial random against the spatial fixed effects model. |
| Keywords: | Higher-order spatial dependence, Generalized moments estimation, Heteroskedasticity, Two-stage least squares, Asymptotic statistics |
| JEL: | C13 C21 C23 |
| Date: | 2014–04 |
| URL: | http://d.repec.org/n?u=RePEc:wiw:wiwwuw:wuwp173&r=ecm |
| By: | Ying Chen; Bo Li; Linlin Niu |
| Abstract: | Our proposed local vector autoregressive (LVAR) model has time-varying parameters that allow it to be safely used in both stationary and non-stationary situations. The estimation is conducted over an interval of local homogeneity where the parameters are approximately constant. The local interval is identified in a sequential testing procedure. Numerical analysis and real data application are conducted to illustrate the monitoring function and forecast performance of the proposed model. |
| Keywords: | Adaptive estimation; Multivariate time series; Non-stationarity; Yield curve |
| JEL: | C32 C53 E43 E47 |
| URL: | http://d.repec.org/n?u=RePEc:wyi:wpaper:002208&r=ecm |
| By: | Koen Jochmans (Département d'économie) |
| Abstract: | This paper presents simple approaches to deal with sample selection in models with multiplicative errors. GMM estimators are constructed for both cross-section data and for panel data. These estimators build only on a specification of the conditional mean of the outcome of interest and are, therefore, semiparametric in nature. In particular, the distribution of unobservables is left unspecified. In the panel-data case, we further allow for group-specific fixed effects whose relation to covariates is left unrestricted. We derive distribution theory for both sampling situations and present Monte Carlo evidence on the finite-sample performance of the approach. |
| Date: | 2014–05 |
| URL: | http://d.repec.org/n?u=RePEc:spo:wpmain:info:hdl:2441/3vl5fe4i569nbr005tctlc8ll5&r=ecm |
| By: | Ying Fang |
| Abstract: | This chapter studies the asymptotic properties of estimation and inference with weak identification and near exogeneity in a GMM framework with instrumental variables. We obtained limiting results under weak identification and near exogeneity of general GMM estimators and some specific GMM estimators, such as one-step GMM estimator, two-step GMM estimator and continuous updating estimator. We also examine the asymptotic properties of the Anderson-Rubin type and the Kleibergen type tests under weak identification and near exogeneity. |
| Date: | 2013–10–14 |
| URL: | http://d.repec.org/n?u=RePEc:wyi:wpaper:001989&r=ecm |
| By: | Karyne B. Charbonneau |
| Abstract: | This paper considers the adaptability of estimation methods for binary response panel data models to multiple fixed effects. It is motivated by the gravity equation used in international trade, where important papers such as Helpman, Melitz and Rubinstein (2008) use binary response models with fixed effects for both importing and exporting countries. Econometric theory has mostly focused on the estimation of single fixed effects models. This paper investigates whether existing methods can be modified to eliminate multiple fixed effects for two specific models in which the incidental parameter problem has already been solved in the presence of a single fixed effect. We find that it is possible to generalize the conditional maximum likelihood approach of Rasch (1960, 1961) to include two fixed effects for the logit. Surprisingly, despite many similarities with the logit, Manski’s (1987) maximum score estimator for binary response models cannot be adapted to the presence of two fixed effects. Monte Carlo simulations show that the conditional logit estimator presented in this paper is less biased than other logit estimators without sacrificing on precision. This superiority is emphasized in small samples. An application to trade data using the logit estimator further highlights the importance of properly accounting for two fixed effects. |
| Keywords: | Econometric and statistical methods |
| JEL: | C23 C25 F14 |
| Date: | 2014 |
| URL: | http://d.repec.org/n?u=RePEc:bca:bocawp:14-17&r=ecm |
| By: | Gery Geenens; Arthur Charpentier; Davy Paindaveine |
| Abstract: | Copula modelling has become ubiquitous in modern statistics. Here, the problem of nonparametricallyestimating a copula density is addressed. Arguably the most popular nonparametric density estimator,the kernel estimator is not suitable for the unit-square-supported copula densities, mainly because it isheavily a↵ected by boundary bias issues. In addition, most common copulas admit unbounded densities,and kernel methods are not consistent in that case. In this paper, a kernel-type copula density estimatoris proposed. It is based on the idea of transforming the uniform marginals of the copula density intonormal distributions via the probit function, estimating the density in the transformed domain, whichcan be accomplished without boundary problems, and obtaining an estimate of the copula densitythrough back-transformation. Although natural, a raw application of this procedure was, however, seennot to perform very well in the earlier literature. Here, it is shown that, if combined with local likelihooddensity estimation methods, the idea yields very good and easy to implement estimators, fixing boundaryissues in a natural way and able to cope with unbounded copula densities. The asymptotic properties ofthe suggested estimators are derived, and a practical way of selecting the crucially important smoothingparameters is devised. Finally, extensive simulation studies and a real data analysis evidence theirexcellent performance compared to their main competitors. |
| Keywords: | copula density; transformation kernel density estimator; boundary bias; unbounded Density; local likelihood density estimation |
| Date: | 2014–04 |
| URL: | http://d.repec.org/n?u=RePEc:eca:wpaper:2013/159977&r=ecm |
| By: | Zongwu Cai; Qi Li |
| Abstract: | In this paper we survey some recent developments of nonparametric econometrics in the following areas: (i) Nonparametric estimation of regression models with mixed discrete and continuous data; (ii) Nonparametric models with nonstationary data; (iii) Nonparametric models with instrumental variables; (iv) Nonparametric estimation of conditional quantile functions. In each of the above areas we also point out some open research problems. |
| Date: | 2013–10–14 |
| URL: | http://d.repec.org/n?u=RePEc:wyi:wpaper:002008&r=ecm |
| By: | Lechner, Michael; Strittmatter, Anthony |
| Abstract: | This paper assesses the performance of common estimators adjusting for differences in covariates, like matching and regression, when faced with so-called common support problems. It also shows how different procedures suggested in the literature to tackle common support problems affect the properties of such estimators. Based on an Empirical Monte Carlo simulation design, a lack of common support is found to increase the root mean squared error (RMSE) of all investigated parametric and semiparametric estimators. Dropping observa¬tions that are off support usually improves their performance, although the amount of improvement depends on the particular method used. |
| Keywords: | Empirical Monte Carlo Study, matching estimation, regression, common support, outlier, small sample performance |
| JEL: | C21 J68 |
| Date: | 2014–04 |
| URL: | http://d.repec.org/n?u=RePEc:usg:econwp:2014:10&r=ecm |
| By: | Zongwu Cai; Bing-Yi Jing; Xin-Bing Kong; Zhi Liu |
| Abstract: | We study nonparametric estimation of regression function with nonstationary (integrated or nearly integrated) covariates and the error series of the regressor process following a fractional ARIMA model. A local linear estimation method is developed to estimate the unknown regression function. The asymptotic results of the resulting estimator at both interior points and boundaries are obtained. The asymptotic distribution is mixed normal, associated with the local time of an Ornstein-Uhlenbeck (O-U) fractional Brownian motion. Furthermore, we study the Nadaraya-Watson estimator and examine its asymptotic results. As a result, it shares exactly the same asymptotic results as those for the local linear estimator for the zero energy situation. But for the non-zero energy case, the local linear estimator is superior over the Nadaraya-Watson estimator in terms of optimal convergence rate. Moreover, a comparison of our results with the conventional results for stationary covariates is presented. Finally, a Monte Carlo simulation is conducted to illustrate the finite sample performance of the proposed estimator. |
| Keywords: | Asymptotics; kernel smoothing; local time of an Ornstein-Uhlenbeck fractional Brownian motion; nonlinearity; nonstationary covariates; unit root. |
| Date: | 2013–10–14 |
| URL: | http://d.repec.org/n?u=RePEc:wyi:wpaper:002020&r=ecm |
| By: | Federico Carlini (Aarhus University and CREATES); Katarzyna Lasak (VU Amsterdam & Tinbergen Institute) |
| Abstract: | In this paper we consider the Fractional Vector Error Correction model proposed in Avarucci (2007), which is characterized by a richer lag structure than models proposed in Granger (1986) and Johansen (2008, 2009). We discuss the identification issues of the model of Avarucci (2007), following the ideas in Carlini and Santucci de Magistris (2014) for the model of Johansen (2008, 2009). We propose a 4-step estimation procedure that is based on the switching algorithm employed in Carlini and Mosconi (2014) and the GLS procedure in Mosconi and Paruolo (2014). The proposed procedure provides estimates of the long run parameters of the fractional cointegrated system that are consistent and unbiased, which we demonstrate by a Monte Carlo experiment. |
| Keywords: | Error correction model, Gaussian VAR model, Fractional Cointegration, Estimation algorithm, Maximum likelihood estimation, Switching Algorithm, Reduced Rank Regression |
| JEL: | C13 C32 |
| Date: | 2014–04–29 |
| URL: | http://d.repec.org/n?u=RePEc:aah:create:2014-15&r=ecm |
| By: | Zongwu Cai; Jiancheng Jiang and Jingshuang Zhang |
| Abstract: | This paper provides a new methodology to test the superior predictive ability (SPA) of technical trading rules relative to the benchmark without potential data snooping bias. Unlike other previous methods, we explicitly approximate the covariance matrix through certain decomposition, which decreases the number of elements needed to be estimated. With the help of covariance matrix, we are able to exploit more information contained in the diagonal and off-diagonal terms and as a result, so that we improve the effectiveness of testing result. Due to the nuisance parameter in composite hypothesis, we choose the generalized likelihood ratio (GLR) test which is of uniform most power, to alleviate such problem and at the same time, to provide a pivotal distribution. Bootstrap procedure is employed in our simulation to obtain the power of the test. The result shows that the GLR test dominates the SPA test proposed by Hansen (2005) in terms of power and our GLR test is sensitive to the inclusion of superior models. Therefore, it increases the power faster than that of SPA test. The result also suggests that the GLR test is less conservative than SPA test. |
| Keywords: | Covariance matrix estimation; Data snooping; Generalized likelihood Ratio test; Reality check; SPA test; Technical trading rules. |
| Date: | 2013–10–14 |
| URL: | http://d.repec.org/n?u=RePEc:wyi:wpaper:002018&r=ecm |
| By: | Ying Fang; Sung Y. Park; Jinfeng Zhang |
| Abstract: | It is well known that the standard Lagrange multiplier (LM) test loses its local optimality when the true non-null model is not correctly specified. In this paper, we derive a score test robust to local and distributional misspecifications for spatial error autocorrelation and spatial lag dependence. The proposed test is general enough to include several popular tests for the spatial dependence as special cases. In our framework, we find that Burridge (1980) and Anselin, Bera, Florax and Yoon (1996)’s tests are automatically robust to distributional misspecification in some special cases. The size and power performances of our proposed score tests are investigated by a Monte-Carlo simulation. |
| Keywords: | �Spatial�dependence;�Score�test;�Robust�test;�Distribution�misspecification; |
| Date: | 2013–10–14 |
| URL: | http://d.repec.org/n?u=RePEc:wyi:wpaper:002027&r=ecm |
| By: | Stefan Skowronek; Stanislav Volgushev; Tobias Kley; Holger Dette; Marc Hallin |
| Keywords: | time series; spectral analysis; periodogram; quantile regression; copulas; ranks; local stationarity |
| Date: | 2014–04 |
| URL: | http://d.repec.org/n?u=RePEc:eca:wpaper:2013/159999&r=ecm |
| By: | Luo Xiao; Yingxing Li; David Ruppert |
| Abstract: | We propose a fast penalized spline method for bivariate smoothing. Univariate Pspline smoothers Eilers and Marx (1996) are applied simultaneously along both coordinates. The new smoother has a sandwich form which suggested the name “sandwich smoother†to a referee. The sandwich smoother has a tensor product structure that simplifies an asymptotic analysis and it can be fast computed. We derive a local central limit theorem for the sandwich smoother, with simple expressions for the asymptotic bias and variance, by showing that the sandwich smoother is asymptotically equivalent to a bivariate kernel regression estimator with a product kernel. As far as we are aware, this is the first central limit theorem for a bivariate spline estimator of any type. Our simulation study shows that the sandwich smoother is orders of magnitude faster to compute than other bivariate spline smoothers, even when the latter are computed using a fast GLAM (Generalized Linear Array Model) algorithm, and comparable to them in terms of mean squared integrated errors. We extend the sandwich smoother to array data of higher dimensions, where a GLAM algorithm improves the computational speed of the sandwich smoother. One important application of the sandwich smoother is to estimate covariance functions in functional data analysis. In this application, our numerical results show that the sandwich smoother is orders of magnitude faster than local linear regression. The speed of the sandwich formula is important because functional data sets are becoming quite large. |
| Keywords: | Asymptotics; Bivariate smoothing; Covariance function; GLAM; Nonparametric regression;Penalized splines; Sandwich smoother; Thin plate splines. |
| Date: | 2013–10–14 |
| URL: | http://d.repec.org/n?u=RePEc:wyi:journl:002174&r=ecm |
| By: | Ming Lin; Changjiang Liu; Linlin Niu |
| Abstract: | The Wishart autoregressive (WAR) process is a powerful tool to model multivariate stochastic volatility (MSV) with correlation risk and derive closed-form solutions in various asset pricing models. However, making inferences of the WAR stochastic volatility (WAR-SV) model is challenging because the latent volatility series does not have a closed-form transition density. Based on an alternative representation of the WAR process with lag order p=1 and integer degrees of freedom, we develop an effective two-step procedure to estimate parameters and the latent volatility series. The procedure can be applied to study other varying-dimension problems. We show the effectiveness of this procedure with a simulated example. Then this method is used to study the time-varying correlation of US and China stock market returns. |
| Keywords: | Bayesian posterior probability, Markov chain Monte Carlo, Multivariate stochastic volatility, Sequential Monte Carlo, Wishart autoregressive process |
| JEL: | G13 G17 C11 C58 |
| Date: | 2013–10–14 |
| URL: | http://d.repec.org/n?u=RePEc:wyi:wpaper:002054&r=ecm |
| By: | Ai Han; Yanan He; Yongmiao Hong; Shouyang Wang |
| Abstract: | We propose two parsimonious autoregressive conditional interval-valued (ACI) models to forecast crude oil prices. The ACI models are a new class of time series models proposed by Han et al. (2009). They can characterize the dynamics of economic variables in both level and range of variation in a unified framework and hence facilitate informative economic analysis. A minimum DK-distance estimation method can also simultaneously utilize rich information of level and range contained in interval-valued observations, thus enhancing parameter estimation efficiency and model forecasting ability. Compared to other existing methods, the ACI models deliver significantly better out-ofsample forecasts, not only for interval-valued prices but also for point-valued highs, lows, and ranges. In particular, we find that the oil price range information is more valuable than the oil price level information in forecasting crude oil prices, which is consistent with observed facts of price movements in crude oil markets. We also find that speculation has predictive power for oil prices in our interval framework.. |
| Keywords: | Interval-valued data, crude oil price, ACI model, minimum DK-distance estimation, range |
| Date: | 2013–10–14 |
| URL: | http://d.repec.org/n?u=RePEc:wyi:wpaper:002040&r=ecm |
| By: | Ahmed, Mumtaz; Zaman, Asad |
| Abstract: | Analytic evaluation of heteroskedasticity consistent covariance matrix estimates (HCCME) is difficult because of the complexity of the formulae currently available. We obtain new analytic formulae for the bias of a class of estimators of the covariance matrix of OLS in a standard linear regression model. These formulae provide substantial insight into the properties and performance characteristics of these estimators. In particular, we find a new estimator which minimizes the maximum possible bias and improves substantially on the standard Eicker-White estimate. |
| Keywords: | Eicker-White; OLS; Bias; Worst Case Bias |
| JEL: | C1 C2 |
| Date: | 2014 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:55724&r=ecm |
| By: | Jaeho Yun; Yongmiao Hong |
| Abstract: | In this article, we propose a simulation method to implement Hong and Li’s (2005) transition density based test for continuous-time models. The idea is to simulate a sequence of dynamic probability integral transforms, which is the key ingredient of Hong and Li’s (2005) test. The proposed procedure is generally applicable no matter whether or not the transition density of a continuous-time model has a closed form, and is simple and computationally inexpensive. A Monte Carlo study shows that the proposed simulation test has very similar sizes and powers to Hong and Li’s (2005) test using the closed form of the transition density (when available). Furthermore, the performance of the simulation test is robust to the choice of the number of simulation iterations and the number of discretization steps between adjacent observations. |
| Keywords: | Continuous-time model, Dynamic probability integral transform, Generalized residuals, Monte Carlo integration, Simulation, Transition density. |
| Date: | 2013–10–14 |
| URL: | http://d.repec.org/n?u=RePEc:wyi:wpaper:001985&r=ecm |
| By: | Cinzia Daraio (Department of Computer, Control and Management Engineering, Universita' degli Studi di Roma "La Sapienza"); LŽopold Simar (Institute of Statistics, Biostatistics et Actuarial Sciences, Universite' Catholique de Louvain, Louvain-la-Neuve, Belgium) |
| Abstract: | In efficiency analysis the assessment of the performance of Decision Making Units (DMUs) relays on the selection of the direction along which the distance from the efficient frontier is measured. Directional Distance Functions (DDFs) represent a flexible way to gauge the inefficiency of DMUs. Permitting the selection of a direction towards the efficient frontier is often useful in empirical applications. As a matter of fact, many papers in the literature have proposed specific DDFs suitable for different contexts of application. Nevertheless, the selection of a direction implies the choice of an efficiency target which is imposed to all the analyzed DMUs. Moreover, there exist many situations in which there is no a priori economic or managerial rationale to impose a subjective efficiency target. In this paper we propose a data-driven approach to find out an ÒobjectiveÓ direction along which to gauge the inefficiency of each DMU. Our approach permits to take into account for the heterogeneity of DMUs and their diverse contexts that may influence their input and/or output mixes. Our method is also a data driven technique for benchmarking each DMU. We describe how to implement our framework and illustrate its usefulness with simulated and real datasets. |
| Keywords: | DEA, benchmarking, directional distance functions, nonparametric estimation, heterogeneity, performance, productivity, organizational studies |
| Date: | 2014 |
| URL: | http://d.repec.org/n?u=RePEc:aeg:report:2014-07&r=ecm |
| By: | Nassim N Taleb; Raphael Douady |
| Abstract: | In fat-tailed domains, sample measures of top centile contributions to the total (concentration) are biased, unstable estimators extremely sensitive to sample size and concave in accounting for large deviations. They can vary over time merely from the increase of sample space, thus providing the illusion of structural changes in concentration. They are also inconsistent under aggregation and mixing distributions, as weighted concen- tration measures for A and B will tend to be lower than that from A + B. In addition, it can be shown that under fat tails, increases in the total sum need to be accompanied by increased measurement of concentration. We examine the bias and error under straight and mixed distributions. |
| Date: | 2014–05 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1405.1791&r=ecm |
| By: | Fukang Zhu; Zongwu Cai; Liang Peng |
| Abstract: | Researchers have constantly asked whether stock returns can be predicted by some macroeconomic data. However, it is known that macroeconomic data may exhibit nonstationarity and/or heavy tails, which complicates existing testing procedures for predictability. In this paper we propose novel empirical likelihood methods based on some weighted score equations to test whether the monthly CRSP value-weighted index can be predicted by the log dividend-price ratio or the log earnings-price ratio. The new methods work well both theoretically and empirically regardless of the predicting variables being stationary or nonstationary or having an infinite variance. |
| Date: | 2014–04 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1404.7642&r=ecm |
| By: | Zongwu Cai; Xian Wang |
| Date: | 2013–10–14 |
| URL: | http://d.repec.org/n?u=RePEc:wyi:wpaper:001958&r=ecm |
| By: | Ming Lin; Rong Chen; Jun S. Liu |
| Abstract: | Based on the principles of importance sampling and resampling, sequential Monte Carlo (SMC) encompasses a large set of powerful techniques dealing with complex stochastic dynamic systems. Many of these systems possess strong memory, with which future information can help sharpen the inference about the current state. By providing theoretical justification of several existing algorithms and introducing several new ones, we study systematically how to construct effient SMC algorithms to take advantage of the "future" information without creating a substantially high computational burden. The main idea is to allow for lookahead in the Monte Carlo process so that future information can be utilized in weighting and generating Monte Carlo samples, or resampling from samples of the current state. |
| Keywords: | Sequential Monte Carlo; Lookahead weighting; Lookahead sampling; Pilot lookahead; Multilevel; Adaptive lookahead. |
| Date: | 2013–10–14 |
| URL: | http://d.repec.org/n?u=RePEc:wyi:journl:002173&r=ecm |