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on Econometrics |
| By: | Chaohua Dong; Jiti Gao; Oliver Linton |
| Abstract: | Moment restriction semiparametric models, where both the dimension of parameter and the number of restrictions are divergent and an unknown function is involved, are studied using the generalized method of moments (GMM) and sieve method dealing with the nonparametric parameter. The consistency and normality for the GMM estimators are established. Meanwhile, a new test statistic is proposed for overidentification issue. Numerical examples are used to verify the established theory. |
| Keywords: | Generalized method of moments, high dimensional models, moment restriction, over-identification, sieve method. |
| JEL: | C12 C14 C22 C30 |
| Date: | 2017 |
| URL: | http://d.repec.org/n?u=RePEc:msh:ebswps:2017-17&r=ecm |
| By: | Wang, Xiaohu (The Chinese University of Hong Kong); Yu, Jun (School of Economics, Singapore Management University) |
| Abstract: | This paper develops the asymptotic theory of the ordinary least squares estimator of the autoregressive (AR) coefficient in various AR models, when data is generated from trend-stationary models in different forms. It is shown that, depending on how the autoregression is specified, the commonly used right-tailed unit root tests may tend to reject the null hypothesis of unit root in favor of the explosive alternative. A new procedure to implement the right-tailed unit root tests is proposed. It is shown that when the data generating process is trend-stationary, the test statistics based on the proposed procedure cannot find evidence of explosiveness. Whereas, when the data generating process is mildly explosive, the unit root tests find evidence of explosiveness. Hence, the proposed procedure enables robust bubble testing under deterministic trends. Empirical implementation of the proposed procedure using data from the stock and the real estate markets in the US reveals some interesting findings. While our proposed procedure flags the same number of bubbles episodes in the stock data as the method developed in Phillips, Shi and Yu (2015a, PSY), the estimated termination dates by the proposed procedure match better with the data. For real estate data, all negative bubble episodes flagged by PSY are no longer regarded as bubbles by the proposed procedure. |
| Keywords: | Autoregressive regressions; right-tailed unit root test; explosive and mildly explosive processes; deterministic trends; coefficient-based statistic; t-statistic. |
| JEL: | C12 C22 G01 |
| Date: | 2017–09–22 |
| URL: | http://d.repec.org/n?u=RePEc:ris:smuesw:2017_014&r=ecm |
| By: | Luís Silveira Santos; Isabel Proença |
| Abstract: | This paper presents a new method to approximate the inverse of the spatial lag operator matrix, used in the estimation of a spatial lag model with a binary dependent variable. The method is based on an approximation of the high order terms of the inverse series expansion. The proposed method is also applied to approximate other complex matrix operations and closed formulas for the elements of the approximated matrices are deduced. The approximated matrices are used in the gradients of a variant of Klier and McMillen's full GMM estimator, allowing to reduce the overall computational complexity of the estimation procedure. Monte Carlo experiments show that the new estimator performs well in terms of bias and root mean square error and exhibits a minimum trade-o between time and unbiasedness within a class of spatial GMM estimators. The new estimator is also applied to the analysis of competitiveness in the Metropolitan Statistical Areas of the United States of America. A new denition of binary competitiveness is proposed. Estimation of the spatial dependence parameter and the environmental eects are addressed as central issues. |
| Keywords: | Matrix approximation,matrix factorization, Spatial binary choice models, Spatial lag operator inverse, Spatial nonlinear models |
| Date: | 2017–11 |
| URL: | http://d.repec.org/n?u=RePEc:ise:remwps:wp0112017&r=ecm |
| By: | Mika Meitz; Pentti Saikkonen |
| Abstract: | Testing for regime switching when the regime switching probabilities are specified either as constants (`mixture models') or are governed by a finite-state Markov chain (`Markov switching models') are long-standing problems that have also attracted recent interest. This paper considers testing for regime switching when the regime switching probabilities are time-varying and depend on observed data (`observation-dependent regime switching'). Specifically, we consider the likelihood ratio test for observation-dependent regime switching in mixture autoregressive models. The testing problem is highly nonstandard, involving unidentified nuisance parameters under the null, parameters on the boundary, singular information matrices, and higher-order approximations of the log-likelihood. We derive the asymptotic null distribution of the likelihood ratio test statistic in a general mixture autoregressive setting using high-level conditions that allow for various forms of dependence of the regime switching probabilities on past observations, and we illustrate the theory using two particular mixture autoregressive models. The likelihood ratio test has a nonstandard asymptotic distribution that can easily be simulated, and Monte Carlo studies show the test to have satisfactory finite sample size and power properties. |
| Date: | 2017–11 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1711.03959&r=ecm |
| By: | Su, Liangjun (School of Economics, Singapore Management University); Ura, Takuya (Department of Economics, University of California Davis); Zhang, Yichong (School of Economics, Singapore Management University) |
| Abstract: | This paper studies non-separable models with a continuous treatment when the dimension of the control variables is high and potentially larger than the effective sample size. We propose a three-step estimation procedure to estimate the average, quantile, and marginal treatment effects. In the first stage we estimate the conditional mean, distribution, and density objects by penalized local least squares, penalized local maximum likelihood estimation, and penalized conditional density estimation, respectively, where control variables are selected via a localized method of L1-penalization at each value of the continuous treatment. In the second stage we estimate the average and the marginal distribution of the potential outcome via the plug-in principle. In the third stage, we estimate the quantile and marginal treatment effects by inverting the estimated distribution function and using the local linear regression, respectively. We study the asymptotic properties of these estimators and propose a weighted-bootstrap method for inference. Using simulated and real datasets, we demonstrate the proposed estimators perform well in finite samples. |
| Keywords: | Average treatment effect; High dimension; Least absolute shrinkage and selection operator (Lasso); Nonparametric quantile regression; Nonseparable models; Quantile treatment effect; Unconditional average structural derivative |
| JEL: | C21 I19 |
| Date: | 2017–09–28 |
| URL: | http://d.repec.org/n?u=RePEc:ris:smuesw:2017_015&r=ecm |
| By: | Buncic, Daniel (Financial Stability Department, Central Bank of Sweden) |
| Abstract: | Exponential smooth transition autoregressive (ESTAR) models are widely used in the international finance literature, particularly for the modelling of real exchange rates. We show that the exponential function is ill-suited as a regime weighting function because of two undesirable properties. Firstly, it can be well approximated by a quadratic function in the threshold variable whenever the transition function parameter , which governs the shape of the function, is ‘small’. This leads to an identification problem with respect to the transition function parameter and the slope vector, as both enter as a product into the conditional mean of the model. Secondly, the exponential regime weighting function can behave like an indicator function (or dummy variable) for very large values of the transition function parameter . This has the effect of ‘spuriously overfitting’ a small number of observations around the location parameter µ. We show that both of these effects lead to estimation problems in ESTAR models. We illustrate this by means of an empirical replication of a widely cited study, as well as a simulation exercise. |
| Keywords: | Exponential STAR; non-linear time series models; identification and estimation issues; exponential weighting function; real exchange rates; simulation analysis. |
| JEL: | C13 C15 C50 F30 F44 |
| Date: | 2017–10–01 |
| URL: | http://d.repec.org/n?u=RePEc:hhs:rbnkwp:0344&r=ecm |
| By: | AMBA OYON, Claude Marius; Mbratana, Taoufiki |
| Abstract: | This paper develops estimators for simultaneous equations with spatial autoregressive or spatial moving average error components. We derive a limited information estimator and a full information estimator. We give the generalized method of moments to get each coefficient of the spatial dependence of each equation in spatial autoregressive case as well as spatial moving average case. The results of our Monte Carlo suggest that our estimators are consistent. When we estimate the coefficient of spatial dependence it seems better to use instrumental variables estimator that takes into account simultaneity. We also apply these set of estimators on real data. |
| Keywords: | Panel data, SAR process, SMA process, Simultaneous equations, Spatial error components |
| JEL: | C13 C33 |
| Date: | 2017–10 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:82395&r=ecm |
| By: | Jentsch, Carsten; Weiß, Christian |
| Abstract: | Integer-valued autoregressive (INAR) time series form a very useful class of processes suitable to model time series of counts. In the common formulation of Du and Li (1991,JTSA), INAR models of order p share the autocorrelation structure with classical autoregressive time series. This fact allows to estimate the INAR coeffcients, e.g., by Yule-Walker estimators. However, contrary to the AR case, consistent estimation of the model coeffcients turns out to be not suffcient to compute proper `INAR residuals' to formulate a valid model-based bootstrap scheme. In this paper, we propose a general INAR-type bootstrap procedure. Based on mild regularity conditions and suitable meta assumptions, we prove bootstrap consistency of our pro- cedure for statistics belonging to the class of functions of generalized means. In particular, we discuss parametric and semi-parametric implementations of the INAR bootstrap scheme. The latter approach is based on a semi-parametric estimator suggested by Drost, van den Akker and Werker (2009, JRSSB) to estimate jointly the INAR coeffcients and the distribution of the innovations. In an extensive simulation study, we provide numerical evidence of our theoretical findings and illustrate the superiority of the proposed INAR bootstrap over some obvious competitors. We illustrate our method by an application to a real data set about iceberg orders for the Lufthansa stock. |
| Date: | 2017 |
| URL: | http://d.repec.org/n?u=RePEc:mnh:wpaper:42881&r=ecm |
| By: | Svetunkov, Ivan; Boylan, John Edward |
| Abstract: | Intermittent demand forecasting is an important supply chain task, which is commonly done using methods based on exponential smoothing. These methods however do not have underlying statistical models, which limits their generalisation. In this paper we propose a general state-space model that takes intermittence of data into account, extending the taxonomy of exponential smoothing models. We show that this model has a connection with conventional non-intermittent state space models and underlies Croston’s and Teunter-Syntetos-Babai (TSB) forecasting methods. We discuss properties of the proposed models and show how a selection can be made between them in the proposed framework. We then conduct experiments on simulated data and on two real life datasets, demonstrating advantages of the proposed approach. |
| Keywords: | Intermittent demand, supply chain, forecasting, state-space models |
| JEL: | C53 |
| Date: | 2017–11–07 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:82487&r=ecm |
| By: | Catalina Bolancé (RISKCENTER, Universitat de Barcelona); Raluca Vernic (Faculty of Mathematics and Informatics, Ovidius University of Constanta) |
| Abstract: | Starting from the question: “What is the accident risk of an insured?”, this paper considers a multivariate approach by taking into account three types of accident risks and the possible dependence between them. Driven by a real data set, we propose three trivariate Sarmanov distributions with generalized linear models (GLMs) for marginals and incorporate various individual characteristics of the policyholders by means of explanatory variables. Since the data set was collected over a longer time period (10 years), we also added each individual’s exposure to risk. To estimate the parameters of the three Sarmanov distributions, we analyze a pseudo-maximumlikelihood method. Finally, the three models are compared numerically with the simpler trivariate Negative Binomial GLM. |
| Keywords: | multivariate counting distribution, Sarmanov distribution, Negative Binomial distribution, Generalized Linear Model, ML estimation algorithm |
| Date: | 2017–11 |
| URL: | http://d.repec.org/n?u=RePEc:xrp:wpaper:xreap2017-07&r=ecm |
| By: | Biqing Cai; Jiti Gao |
| Abstract: | In this paper, we propose a simple approach to testing and modelling nonlinear predictability of stock returns using Hermite Functions. The proposed test suggests that there exists a kind of nonlinear predictability for the dividend yield. Furthermore, the out-of-sample evaluation results suggest the dividend yield has nonlinear predictive power for stock returns while the book-to-market ratio and earning-price ratio have little predictive power. |
| Keywords: | Hermite functions, out-of-sample forecast, return predictability, series estimator, unit root. |
| JEL: | C14 C22 G17 |
| Date: | 2017 |
| URL: | http://d.repec.org/n?u=RePEc:msh:ebswps:2017-18&r=ecm |
| By: | Dan A. Black; Joonhwi Joo; Robert LaLonde; Jeffrey Andrew Smith; Evan J. Taylor |
| Abstract: | We provide simple tests for selection on unobserved variables in the Vytlacil-Imbens-Angrist framework for Local Average Treatment Effects. The tests allow researchers not only to test for selection on either or both of the treated and untreated outcomes, but also to assess the magnitude of the selection effect. The tests are quite simple; undergraduates after an introductory econometrics class should be able to implement these tests. We illustrate our tests with two empirical applications: the impact of children on female labor supply from Angrist and Evans (1998) and the impact of training on adult women from the Job Training Partnership Act (JTPA) experiment. |
| Keywords: | instrumental variable, local average treatment effect, selection, test |
| Date: | 2017 |
| URL: | http://d.repec.org/n?u=RePEc:ces:ceswps:_6392&r=ecm |
| By: | Nithi Sopitpongstorn; Param Silvapulle; Jiti Gao |
| Abstract: | We propose a flexible and robust nonparametric local logit regression for modelling and predicting defaulted loans' recovery rates that lie in [0,1]. Applying the model to the widely studied Moody's recovery dataset and estimating it by a data-driven method, the local logit regression uncovers the underlying nonlinear relationship between the recovery and covariates, which include loan/borrower characteristics and economic conditions. We find some significant nonlinear marginal and interaction effects of conditioning variables on recoveries of defaulted loans. The presence of such nonlinear economic effects enriches the local logit model specification that supports the improved recovery prediction. This paper is the first to study a nonparametric regression model that not only generates unbiased and improved recovery predictions of defaulted loans relative to the parametric counterpart, it also facilitates reliable inference on marginal and interaction effects of loan/borrower characteristics and economic conditions. Moreover, incorporating these nonlinear marginal and interaction effects, we improve the specification of parametric regression for fractional response variable, which we call "calibrated" model, the predictive performance of which is comparable to that of local logit model. This calibrated parametric model will be attractive to applied researchers and industry professionals working in the risk management area and unfamiliar with nonparametric machinery. |
| Keywords: | Loss given default, credit risk, nonlinearity, kernel estimation, defaulted debt, simulation. |
| JEL: | C14 C53 G02 G32 |
| Date: | 2017 |
| URL: | http://d.repec.org/n?u=RePEc:msh:ebswps:2017-19&r=ecm |
| By: | Stanislav Anatolyev; Jozef Barunik |
| Abstract: | This paper presents a simple approach to forecasting conditional probability distributions of asset returns. We work with a parsimonious parametrization of ordered binary choice regression that quite precisely forecasts future conditional probability distributions of returns, using past indicator and past volatility proxy as predictors. Direct benefits of the proposed model are revealed in the empirical application to 29 most liquid U.S. stocks. The forecast probability distribution is translated to significant economic gains in a simple trading strategy. The model can therefore serve as useful risk management tool for investors monitoring tail risk, or even building trading strategies based on the entire conditional return distribution. Our approach can also be useful in many other applications where conditional distribution forecasts are desired. |
| Date: | 2017–11 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1711.05681&r=ecm |
| By: | Yuan Liao (Rutgers University); Xiye Yang (Rutgers University) |
| Abstract: | It has been well known in financial economics that factor betas depend on observed instruments such as firm specific characteristics and macroeconomic variables, and a key object of interest is the effect of instruments on the factor betas. One of the key features of our model is that we specify the factor betas as functions of time-varying observed instruments that pick up long-run beta fluctuations, plus an orthogonal idiosyncratic component that captures high-frequency movements in beta. It is often the case that researchers do not know whether or not the idiosyncratic beta exists, or its strengths, and thus uniformity is essential for inferences. It is found that the limiting distribution of the estimated instrument effect has a discontinuity when the strength of the idiosyncratic beta is near zero, which makes usual inferences fail to be valid and produce misleading results. In addition, the usual "plug-in" method using the estimated asymptotic variance is only valid pointwise. The central goal is to make inference about the effect on the betas of firms' instruments, and to conduct out-of-sample forecast of integrated volatilities using estimated factors. Both procedures should be valid uniformly over a broad class of data generating processes for idiosyncratic betas with various signal strengths and degrees of time-variant. We show that a cross-sectional bootstrap procedure is essential for the uniform inference, and our procedure also features a bias correction for the effect of estimating unknown factors. |
| Keywords: | Large dimensions, high-frequency data, cross-sectional bootstrap |
| JEL: | C33 C38 G12 |
| Date: | 2017–11–13 |
| URL: | http://d.repec.org/n?u=RePEc:rut:rutres:201711&r=ecm |