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on Econometrics |
| By: | Badi Baltagi (Center for Policy Research, Maxwell School, Syracuse University, 426 Eggers Hall, Syracuse, NY 13244); Chihwa Kao (Center for Policy Research, Syracuse University); Long Liu (University of Texas at San Antonio) |
| Abstract: | This paper studies test of hypotheses for the slope parameter in a linear time trend panel data model with serially correlated error component disturbances. We propose a test statistic that uses a bias corrected estimator of the serial correlation parameter. The proposed test statistic which is based on the corresponding fixed effects feasible generalized least squares (FE-FGLS) estimator of the slope parameter has the standard normal limiting distribution which is valid whether the remainder error is I(0) or I(1). This performs well in Monte Carlo experiments and is recommended. |
| Keywords: | Panel Data, Generalized Least Squares, Time Trend Model, Fixed Effects, First Difference, and Nonstationarity |
| JEL: | C23 C33 |
| Date: | 2014–07 |
| URL: | http://d.repec.org/n?u=RePEc:max:cprwps:170&r=ecm |
| By: | Arnaud Dufays (École Nationale de la Statistique et de l'Administration Économique, CREST) |
| Abstract: | Sequential Monte Carlo (SMC) methods are widely used for filtering purposes of non-linear economic or financial models. Nevertheless the SMC scope encompasses wider applications such as estimating static model parameters so much that it is becoming a serious alternative to Markov- Chain Monte-Carlo (MCMC) methods. Not only SMC algorithms draw posterior distributions of static or dynamic parameters but additionally provide an estimate of the normalizing constant. The tempered and time (TNT) algorithm, developed in the paper, combines (off-line) tempered SMC inference with on-line SMC inference for estimating many slightly different distributions. The method encompasses the Iterated Batch Importance Sampling (IBIS) algorithm and more generally the Resample Move (RM) algorithm. Besides the number of particles, the TNT algorithm self-adjusts its calibrated parameters and relies on a new MCMC kernel that allows for particle interactions. The algorithm is well suited for efficiently back-testing models. We conclude by comparing in-sample and out-of-sample performances of complex volatility models. |
| Keywords: | Bayesian inference, Sequential Monte Carlo, Annealed Importance sampling, Differential Evolution, Volatility models, Multifractal model, Markov-switching model |
| JEL: | C11 C15 C22 C58 |
| Date: | 2014–09 |
| URL: | http://d.repec.org/n?u=RePEc:nbb:reswpp:201409-263&r=ecm |
| By: | Tae-Hwy Lee (Department of Economics, University of California Riverside); Yundong Tu (Peking University, Beijing, China); Aman Ullah (University of California, Riverside) |
| Abstract: | This paper considers nonparametric and semiparametric regression models subject to monotonicity constraint. We use bagging as an alternative approach to Hall and Huang (2001). Asymptotic properties of our proposed estimators and forecasts are established. Monte Carlo simulation is conducted to show their finite sample performance. An application to predicting equity premium is taken for illustration. We introduce a new forecasting evaluation criterion based on the second order stochastic dominance in the size of forecast errors and compare models over different sizes of forecast errors. Imposing monotonicity constraint can mitigate the chance of making large size forecast errors. |
| Keywords: | Local monotonicity, Bagging, Asymptotic mean squared errors, Second order stochastic dominance, Equity premium prediction. |
| JEL: | C14 C50 C53 G17 |
| Date: | 2014–09 |
| URL: | http://d.repec.org/n?u=RePEc:ucr:wpaper:201404&r=ecm |
| By: | Weixuan Zhu; Juan Miguel Marín Diazaraque; Fabrizio Leisen |
| Abstract: | Recently, an increasingly amount of literature focused on Bayesian computational methods to address problems with intractable likelihood. These algorithms are known as Approximate Bayesian Computational (ABC) methods. One of the problems of these algorithms is that the performance depends on the tuning of some parameters, such as the summary statistics, distance and tolerance level. To bypass this problem, an alternative method based on empirical likelihood was introduced by Mengersen et al. (2013), which can be easily implemented when a set of constraints, related with the moments of the distribution, is known. However, the choice of the constraints is crucial and sometimes challenging in the sense that it determines the convergence property of the empirical likelihood. To overcome this problem, we propose an alternative method based on a bootstrap likelihood approach. The method is easy to implement and in some cases it is faster than the other approaches. The performance of the algorithm is illustrated with examples in Population Genetics, Time Series and a recent non-explicit bivariate Beta distribution. Finally, we test the method on simulated and real data random fields. |
| Keywords: | Approximate Bayesian Computational methods, Bootstrap likelihood, Empirical likelihood, Bivariate Beta distribution, Population genetics |
| Date: | 2014–09 |
| URL: | http://d.repec.org/n?u=RePEc:cte:wsrepe:ws142517&r=ecm |
| By: | M. E. Bontempi; I. Mammi |
| Abstract: | The problem of instrument proliferation and its consequences (overfitting of the endogenous explanatory variables, biased IV and GMM estimators, weakening of the power of the overidentification tests) are well known. This paper introduces a statistical method to reduce the instrument count. The principal component analysis (PCA) is applied on the instrument matrix, and the PCA scores are used as instruments for the panel generalized method-of-moments (GMM) estimation. This strategy is implemented through the new command pca2. |
| JEL: | C13 C15 C33 C36 C63 |
| Date: | 2014–08 |
| URL: | http://d.repec.org/n?u=RePEc:bol:bodewp:wp960&r=ecm |
| By: | Leschinski, Christian; Sibbertsen, Philipp |
| Abstract: | We propose an automatic model order selection procedure for k-factor GARMA processes. The procedure is based on sequential tests of the maximum of the periodogram and semiparametric estimators of the model parameters. As a byproduct, we introduce a generalized version of Walker's large sample g-test that allows to test for persistent periodicity in stationary ARMA processes. Our simulation studies show that the procedure performs well in identifying the correct model order under various circumstances. An application to Californian electricity load data illustrates its value in empirical analyses and allows new insights into the periodicity of this process that has been subject of several forecasting exercises. |
| Keywords: | seasonal long memory, k-factor GARMA, model selection, electricity loads |
| JEL: | C22 C52 |
| Date: | 2014–09 |
| URL: | http://d.repec.org/n?u=RePEc:han:dpaper:dp-535&r=ecm |
| By: | Aman Ullah (Department of Economics, University of California Riverside); Yong Bao (Purdue University); Yun Wang (University of International Business and Economics, China) |
| Abstract: | Econometricians have recently been interested in estimating and testing the mean reversion parameter (κ) in linear diffusion models. It has been documented that the maximum likelihood estimator (MLE) of κ tends to over estimate the true value. Its asymptotic distribution, on the other hand, depends on how the data are sampled (under expanding, infill, or mixed domain) as well as how we spell out the initial condition. This poses a tremendous challenge to practitioners in terms of estimation and inference. In this paper, we provide new and significant results regarding the exact distribution of the MLE of κ in the Ornstein-Uhlenbeck process under different scenarios: known or unknown drift term, fixed or random start-up value, and zero or positive κ. In particular, we employ numerical integration via analytical evaluation of a joint characteristic function. Our numerical calculations demonstrate the remarkably reliable performance of our exact approach. It is found that the true distribution of the MLE can be severely skewed in finite samples and that the asymptotic distributions in general may provide misleading results. Our exact approach indicates clearly the non-mean-reverting behavior of the real federal fund rate. |
| Keywords: | Distribution, Mean Reversion Estimator, Ornstein-Uhlenbeck Process. |
| JEL: | C22 C46 C58 |
| Date: | 2014–09 |
| URL: | http://d.repec.org/n?u=RePEc:ucr:wpaper:201413&r=ecm |
| By: | Tae-Hwy Lee (Department of Economics, University of California Riverside); Zhou Xi (University of California, Riverside); Ru Zhang (University of California, Riverside) |
| Abstract: | This paper makes a simple but previously neglected point with regard to an empirical application of the test of White (1989) and Lee, White and Granger (LWG, 1993), for neglected nonlinearity in conditional mean, using the feedforward single layer artificial neural network (ANN). Because the activation parameters in the hidden layer are not identified under the null hypothesis of linearity, LWG suggested to activate the ANN hidden units based on the randomly generated activation parameters. Their Monte Carlo experiments demonstrated the excellence performance (good size and power), even if LWG considered a fairly small number (10 or 20) of random hidden unit activations. However, in this paper we note that the good size and power of Monte Carlo experiments are the average frequencies of rejecting the null hypothsis over multiple replications of the data generating process. The average over many simulations in Monte Carlo smooths out the randomness of the activations. In an empirical study, unlike in a Monte Carlo study, multiple realizations of the data are not possible or available. In this case, the ANN test is sensitive to the randomly generated activation parameters. One solution is the use of Bonferroni bounds as suggested in LWG (1993), which however still exhibit some excessive dependence on the random activations (as shown in this paper). Another solution can be to integrate the test statistic over the nuisance parameter space, for which however, bootstrap or simulation should be used to obtain the null distribution of the integrated statistic. In this paper, we consider a much simpler solution that is shown to work very well. That is, we simply increase the number of randomized hidden unit activations to a (very) large number (e.g., 1000). We show that using many randomly generated activation parameters can robustify the performance of the ANN test when it is applied to a real empirical data. This robustification is reliable and useful in practice, and can be achieved at no cost as increasing the number of random activations is almost costless given today's computer technology. |
| Keywords: | Many Activations. Randomized Nuisance Parameters. Boferroni Bounds. Principal Components. |
| JEL: | C1 C4 C5 |
| Date: | 2014–09 |
| URL: | http://d.repec.org/n?u=RePEc:ucr:wpaper:201411&r=ecm |
| By: | Carsten Bormann; Melanie Schienle; Julia Schaumburg; |
| Abstract: | In practice, multivariate dependencies between extreme risks are often only assessed in a pairwise way. We propose a test to detect when tail dependence is truly high{dimensional and bivariate simplications would produce misleading results. This occurs when a signicant portion of the multivariate dependence structure in the tails is of higher dimension than two. Our test statistic is based on a decomposition of the stable tail dependence function, which is standard in extreme value theory for describing multivariate tail dependence. The asymptotic properties of the test are provided and a bootstrap based nite sample version of the test is suggested. A simulation study documents the good performance of the test for standard sample sizes. In an application to international government bonds, we detect a high tail{risk and low return situation during the last decade which can essentially be attributed to increased higher{order tail risk. We also illustrate the empirical consequences from ignoring higher-dimensional tail risk. |
| Keywords: | decomposition of tail dependence; multivariate extreme values; stable tail dependence function; subsample bootstrap; tail correlation |
| JEL: | C01 C46 C58 |
| Date: | 2014–09 |
| URL: | http://d.repec.org/n?u=RePEc:hum:wpaper:sfb649dp2014-042&r=ecm |
| By: | Timothy B. Armstrong (Cowles Foundation, Yale University) |
| Abstract: | We consider the problem of inference on a regression function at a point when the entire function satisfies a sign or shape restriction under the null. We propose a test that achieves the optimal minimax rate adaptively over a range of Holder classes, up to a log log n term, which we show to be necessary for adaptation. We apply the results to adaptive one-sided tests for the regression discontinuity parameter under a monotonicity restriction, the value of a monotone regression function at the boundary, and the proportion of true null hypotheses in a multiple testing problem. |
| Keywords: | Adaptive inference, Regression discontinuity, Identification at infinity |
| JEL: | C14 C12 |
| Date: | 2014–08 |
| URL: | http://d.repec.org/n?u=RePEc:cwl:cwldpp:1957&r=ecm |
| By: | Atsushi Inoue; Lu Jin; Barbara Rossi |
| Abstract: | While forecasting is a common practice in academia, government and business alike, practitioners are often left wondering how to choose the sample for estimating forecasting models. When we forecast in ation in 2014, for example, should we use the last 30 years of data or the last 10 years of data? There is strong evidence of structural changes in economic time series, and the forecasting performance is often quite sensitive to the choice of such window size". In this paper, we develop a novel method for selecting the estimation window size for forecasting. Specically, we propose to choose the optimal window size that minimizes the forecaster's quadratic loss function, and we prove the asymptotic validity of our approach. Our Monte Carlo experiments show that our method performs quite well under various types of structural changes. When applied to forecasting US real output growth and in ation, the proposed method tends to improve upon conventional methods. |
| Keywords: | Macroeconomic forecasting; parameter instability; nonparametric estimation; band-width selection. |
| Date: | 2014–06 |
| URL: | http://d.repec.org/n?u=RePEc:upf:upfgen:1435&r=ecm |
| By: | Roberto Leon-Gonzalez (National Graduate Institute for Policy Studies (GRIPS) and The Rimini Centre for Economic Analysis (RCEA)) |
| Abstract: | This paper develops a novel and efficient algorithm for Bayesian inference in inverse Gamma Stochastic Volatility models. It is shown that by conditioning on auxiliary variables, it is possible to sample all the volatilities jointly directly from their posterior conditional density, using simple and easy to draw from distributions. Furthermore, this paper develops a generalized inverse Gamma process with more flexible tails in the distribution of volatilities, which still allows for simple and efficient calculations. Using several macroeconomic and financial datasets, it is shown that the inverse Gamma and Generalized inverse Gamma processes can greatly outperform the commonly used log normal volatility processes with student-t errors. |
| Date: | 2014–09 |
| URL: | http://d.repec.org/n?u=RePEc:rim:rimwps:19_14&r=ecm |
| By: | Jones, A.;; Lomas, J.;; Rice, N.; |
| Abstract: | Understanding the data generating process behind healthcare costs remains a key empirical issue. Although much research to date has focused on the prediction of the conditional mean cost, this can potentially miss important features of the full conditional distribution such as tail probabilities. We conduct a quasi-Monte Carlo experiment using English NHS inpatient data to compare 14 approaches to modelling the distribution of healthcare costs: nine of which are parametric, and have commonly been used to fit healthcare costs, and five others designed specifically to construct a counterfactual distribution. Our results indicate that no one method is clearly dominant and that there is a trade-off between bias and precision of tail probability forecasts. We find that distributional methods demonstrate significant potential, particularly with larger sample sizes where the variability of predictions is reduced. Parametric distributions such as log-normal, generalised gamma and generalised beta of the second kind are found to estimate tail probabilities with high precision, but with varying bias depending upon the cost threshold being considered. |
| Keywords: | healthcare costs; heavy tails; counterfactual distributions; quasi-Monte Carlo |
| JEL: | C1 C5 |
| Date: | 2014–08 |
| URL: | http://d.repec.org/n?u=RePEc:yor:hectdg:14/26&r=ecm |
| By: | van der Weide, Roy |
| Abstract: | This note adapts results by Huang and Hidiroglou (2003) on Generalized Least Squares estimation and Empirical Bayes prediction for linear mixed models with sampling weights. The objective is to incorporate these results into the poverty mapping approach put forward by Elbers et al. (2003). The estimators presented here have been implemented in version 2.5 of POVMAP, the custom-made poverty mapping software developed by the World Bank. |
| Keywords: | Statistical&Mathematical Sciences,Crops and Crop Management Systems,Poverty Monitoring&Analysis,Science Education,Scientific Research&Science Parks |
| Date: | 2014–09–01 |
| URL: | http://d.repec.org/n?u=RePEc:wbk:wbrwps:7028&r=ecm |
| By: | Yevgeniy Kovchegov; Nese Yildiz |
| Abstract: | We develop an approach that resolves a {\it polynomial basis problem} for a class of models with discrete endogenous covariate, and for a class of econometric models considered in the work of Newey and Powell (2003), where the endogenous covariate is continuous. Suppose $X$ is a $d$-dimensional endogenous random variable, $Z_1$ and $Z_2$ are the instrumental variables (vectors), and $Z=\left(\begin{array}{c}Z_1 \\Z_2\end{array}\right)$. Now, assume that the conditional distributions of $X$ given $Z$ satisfy the conditions sufficient for solving the identification problem as in Newey and Powell (2003) or as in Proposition 1.1 of the current paper. That is, for a function $\pi(z)$ in the image space there is a.s. a unique function $g(x,z_1)$ in the domain space such that $$E[g(X,Z_1)~|~Z]=\pi(Z) \qquad Z-a.s.$$ In this paper, for a class of conditional distributions $X|Z$, we produce an orthogonal polynomial basis $Q_j(x,z_1)$ such that for a.e. $Z_1=z_1$, and for all $j \in \mathbb{Z}_+^d$, and a certain $\mu(Z)$, $$P_j(\mu(Z))=E[Q_j(X, Z_1)~|~Z ],$$ where $P_j$ is a polynomial of degree $j$. This is what we call solving the {\it polynomial basis problem}. Assuming the knowledge of $X|Z$ and an inference of $\pi(z)$, our approach provides a natural way of estimating the structural function of interest $g(x,z_1)$. Our polynomial basis approach is naturally extended to Pearson-like and Ord-like families of distributions. |
| Date: | 2014–09 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1409.1620&r=ecm |
| By: | Knut Are Aastveit (Norges Bank (Central Bank of Norway)); Andrea Carriero (Queen Mary, University of London); Todd E. Clark (Federal Reserve Bank of Cleveland); Massimiliano Marcellino (Bocconi University, IGIER and CEPR) |
| Abstract: | Small or medium-scale VARs are commonly used in applied macroeconomics for forecasting and evaluating the shock transmission mechanism. This requires the VAR parameters to be stable over the evaluation and forecast sample, or to explicitly consider parameter time variation. The earlier literature focused on whether there were sizable parameter changes in the early 1980s, in either the conditional mean or variance parameters, and in the subsequent period till the beginning of the new century. In this paper we conduct a similar analysis but focus on the e ects of the recent crisis. Using a range of techniques, we provide substantial evidence against parameter stability. The evolution of the unemployment rate seems particularly different relative to its past behavior. We then discuss and evaluate alternative methods to handle parameter instability in a forecasting context. While none of the methods clearly emerges as best, some techniques turn out to be useful to improve the forecasting performance. |
| Keywords: | Bayesian VAR, Forecasting, Time-varying parameters, Stochastic volatility |
| JEL: | E17 C11 C33 C53 |
| Date: | 2014–09–11 |
| URL: | http://d.repec.org/n?u=RePEc:bno:worpap:2014_13&r=ecm |
| By: | Paola Cerchiello (Department of Economics and Management, University of Pavia); Paolo Giudici (Department of Economics and Management, University of Pavia) |
| Abstract: | Systemic risk modelling concerns the estimation of the interrelationships between financial institutions, with the aim of establishing which of them are more central and, therefore, more contagious/subject to contagion. The aim of this paper is to develop a novel systemic risk model. A model that, differently from existing ones, employs not only the information contained in financial market prices, but also big data coming from financial tweets. From a methodological viewpoint, the novelty of our paper is the estimation of systemic risk models using two different data sources: financial markets and financial tweets, and a proposal to combine them, using a Bayesian approach. From an applied viewpoint, we present the first systemic risk model based on big data, and show that such a model can shed further light on the interrelationships between financial institutions. |
| Keywords: | Twitter data analysis, Graphical Gaussian models, Graphical Model selection, Banking and Finance applications, Risk Management |
| Date: | 2014–09 |
| URL: | http://d.repec.org/n?u=RePEc:pav:demwpp:086&r=ecm |
| By: | Phoebe Koundouri; Nikolaos Kourogenis (Department of Banking and Financial Management, University of Piraeus.); Nikitas Pittis (University of Piraeus, Greece) |
| Abstract: | The purpose of this paper is twofold: first, to survey the statistical models of stock returns that have been suggested in the finance literature since the middle of the twentieth century; second, to examine under the prism of the contemporary philosophy of science, which of the aforementioned models can be classified as explanatory and which as descriptive. Special emphasis is paid on tracing the interactions between the motivation for the birth of statistical models of stock returns in any given historical period and the concurrent changes of the theoretical paradigm in financial economics, as well as those of probability theory. |
| Keywords: | Stock Returns, Statistical Model, Explanatory Model, Scientific Explanation, Market Efficiency, Brownian Motion. |
| JEL: | C58 C51 G17 |
| Date: | 2014–09–17 |
| URL: | http://d.repec.org/n?u=RePEc:aue:wpaper:1410&r=ecm |
| By: | Leandro Prados de la Escosura |
| Abstract: | Comparisons of economic performance over space and time largely depend on how statistical evidence from national accounts and historical estimates are spliced. To allow for changes in relative prices, GDP benchmark years in national accounts are periodically replaced with new and more recent ones. Thus, a homogeneous long-run GDP series requires linking different temporal segments of national accounts. The choice of the splicing procedure may result in substantial differences in GDP levels and growth, particularly as an economy undergoes deep structural transformation. An inadequate splicing may result in a serious bias in the measurement of GDP levels and growth rates. Alternative splicing solutions are discussed in this paper for the particular case of Spain, a fast growing country in the second half of the twentieth century. It is concluded that the usual linking procedure, retropolation, has serious flows as it tends to bias GDP levels upwards and, consequently, to underestimate growth rates, especially for developing countries experiencing structural change. An alternative interpolation procedure is proposed. |
| Keywords: | Growth measurement, Splicing GDP, Historical national accounts, Spain |
| JEL: | C82 E01 N13 O47 |
| Date: | 2014–09 |
| URL: | http://d.repec.org/n?u=RePEc:cte:whrepe:wp14-04&r=ecm |