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on Econometrics |
| By: | Abonazel, Mohamed R. |
| Abstract: | This paper considers the estimation methods for dynamic panel data (DPD) models with fixed effects which suggested in econometric literature, such as least squares (LS) and generalized method of moments (GMM). These methods obtain biased estimators for DPD models. The LS estimator is inconsistent when the time dimension (T) is short regardless of the cross sectional dimension (N). Although consistent estimates can be obtained by GMM procedures, the inconsistent LS estimator has a relatively low variance and hence can lead to an estimator with lower root mean square error after the bias is removed. Therefore, we discuss in this paper the different methods to correct the bias of LS and GMM estimations. The analytical expressions for the asymptotic biases of the LS and GMM estimators have been presented for large N and finite T. Finally, we display new estimators that presented by Youssef and Abonazel (2015) as more efficient estimators than the conventional estimators. |
| Keywords: | Bias-corrected estimators; First-order autoregressive panel model; Generalized method of moments estimators; Kantorovich inequality; Least squares dummy variable estimators. |
| JEL: | C01 C1 C23 C4 C5 C87 |
| Date: | 2016–04–11 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:70628&r=ecm |
| By: | Tran, M-N.; Kohn, R.; Quiroz, M.; Villani, M. |
| Abstract: | The pseudo-marginal Metropolis-Hastings approach is increasingly used for Bayesian inference in statistical models where the likelihood is analytically intractable but can be estimated unbiasedly, such as random effects models and state-space models, or for data subsampling in big data settings. In a seminal paper, Deligiannidis et al. (2015) show how the pseudo-marginal Metropolis-Hastings (PMMH) approach can be made much more e cient by correlating the underlying random numbers used to form the estimate of the likelihood at the current and proposed values of the unknown parameters. Their proposed approach greatly speeds up the standard PMMH algorithm, as it requires a much smaller number of particles to form the optimal likelihood estimate. We present a closely related alternative PMMH approach that divides the underlying random numbers mentioned above into blocks so that the likelihood estimates for the proposed and current values of the likelihood only di er by the random numbers in one block. Our approach is less general than that of Deligiannidis et al. (2015), but has the following advantages. First, it provides a more direct way to control the correlation between the logarithms of the estimates of the likelihood at the current and proposed values of the parameters. Second, the mathematical properties of the method are simplified and made more transparent compared to the treatment in Deligiannidis et al. (2015). Third, blocking is shown to be a natural way to carry out PMMH in, for example, panel data models and subsampling problems. We obtain theory and guidelines for selecting the optimal number of particles, and document large speed-ups in a panel data example and a subsampling problem. |
| Keywords: | Intractable likelihood; Unbiasedness; Panel data; Data subsampling; |
| Date: | 2016–03–30 |
| URL: | http://d.repec.org/n?u=RePEc:syb:wpbsba:2123/14595&r=ecm |
| By: | Xiaohong Chen (Cowles Foundation, Yale University); Yin Jia Qiu (Dept. of Economics, Yale University) |
| Abstract: | This paper reviews recent advances in estimation and inference for nonparametric and semiparametric models with endogeneity. It first describes methods of sieves and penalization for estimating unknown functions identified via conditional moment restrictions. Examples include nonparametric instrumental variables regression (NPIV), nonparametric quantile IV regression and many more semi-nonparametric structural models. Asymptotic properties of the sieve estimators and the sieve Wald, quasi-likelihood ratio (QLR) hypothesis tests of functionals with nonparametric endogeneity are presented. For sieve NPIV estimation, the rate-adaptive data-driven choices of sieve regularization parameters and the sieve score bootstrap uniform confidence bands are described. Finally, simple sieve variance estimation and over-identification test for semiparametric two-step GMM are reviewed. Monte Carlo examples are included. |
| Keywords: | Conditional moment restrictions containing unknown functions, (Quantile) Instrumental variables, Linear and nonlinear functionals, Sieve minimum distance, Sieve GMM, Sieve Wald, QLR, Bootstrap, Semiparametric two-step GMM, Numerical equivalence |
| JEL: | C12 C14 C32 |
| Date: | 2016–03 |
| URL: | http://d.repec.org/n?u=RePEc:cwl:cwldpp:2032&r=ecm |
| By: | David Hendry; Felix Pretis; Lea Schneider; Jason E. Smerdon |
| Abstract: | Abstract: We present a methodology for detecting structural breaks at any point in time-series regression models using an indicator saturation approach. Building on recent developments in econometric model selection for more variables than observations, we saturate a regression model with a full set of designed break functions. By selecting over these break functions using an extended general-to-specific algorithm, we obtain unbiased estimates of the break date and magnitude. Monte Carlo simulations confirm the approximate properties of the approach. We assess the methodology by detecting volcanic eruptions in a time series of Northern Hemisphere mean temperature spanning roughly 1200 years, derived from a fully-coupled global climate model simulation. Our technique demonstrates that historic volcanic eruptions can be statistically detected without prior knowledge of their occurrence or magnitude- and hence may prove useful for estimating the past impact of volcanic events using proxy-reconstructions of hemispheric or global mean temperature, leading to an improved understanding of the effect of stratospheric aerosols on temperatures. The break detection procedure can be applied to evaluate policy impacts as well as act as a robust forecasting device. |
| Keywords: | Indicator Saturation, Model Selection, Location Shifts, Climate,Temperature, Volcanic Eruptions |
| JEL: | C22 C52 Q54 |
| Date: | 2016–02–12 |
| URL: | http://d.repec.org/n?u=RePEc:oxf:wpaper:780&r=ecm |
| By: | Sílvia Gonçalves; Benoit Perron; Antoine Djogbenou |
| Abstract: | We propose bootstrap prediction intervals for an observation h periods into the future and its conditional mean. We assume that these forecasts are made using a set of factors extracted from a large panel of variables. Because we treat these factors as latent, our forecasts depend both on estimated factors and estimated regression coefficients. Under regularity conditions, Bai and Ng (2006) proposed the construction of asymptotic intervals under Gaussianity of the innovations. The bootstrap allows us to relax this assumption and to construct valid prediction intervals under more general conditions. Moreover, even under Gaussianity, the bootstrap leads to more accurate intervals in cases where the cross-sectional dimension is relatively small as it reduces the bias of the OLS estimator as shown in a recent paper by Gonçalves and Perron (2014). |
| Keywords: | factor model, bootstrap, forecast, conditional mean, |
| Date: | 2016–04–11 |
| URL: | http://d.repec.org/n?u=RePEc:cir:cirwor:2016s-19&r=ecm |
| By: | Barigozzi, Matteo; Lippi, Marco; Luciani, Matteo |
| Abstract: | We develop the econometric theory for Non-Stationary Dynamic Factor models for large panels of time series, with a particular focus on building estimators of impulse response functions to unexpected macroeconomic shocks. We derive conditions for consistent estimation of the model as both the cross-sectional size, n, and the time dimension, T, go to infinity, and whether or not cointegration is imposed. We also propose a new estimator for the non-stationary common factors, as well as an information criterion to determine the number of common trends. Finally, the numerical properties of our estimator are explored by means of a MonteCarlo exercise and of a real-data application, in which we study the effects of monetary policy and supply shocks on the US economy. |
| Keywords: | Dynamic Factor model ; , common trends ; impulse response functions ; unit root processes |
| JEL: | C00 C01 E00 |
| Date: | 2016–03–04 |
| URL: | http://d.repec.org/n?u=RePEc:fip:fedgfe:2016-24&r=ecm |
| By: | Molina, Isabel; Guadarrama, María; Rao, J.N.K. |
| Abstract: | When the probabilities of selecting the individuals for the sample depend on the outcome values, we say that the selection mechanism is informative. Under informative selection, individuals with certain outcome values appear more often in the sample and therefore the sample is not representative of the population. As a consequence, usual model-based inference based on the actual sample without appropriate weighting might be strongly biased. For estimation of general non-linear parameters in small areas, we propose a model-based pseudo empirical best (PEB) method that incorporates the sampling weights and reduces considerably the bias of the unweighted empirical best (EB) estimators under informative selection mechanisms. We analyze the properties of this new method in simulation experiments carried out under complex sampling designs, including informative selection. Our results confirm that the proposed weighted PEB estimators perform significantly better than the unweighted EB estimators in terms of bias under informative sampling, and compare favorably under non-informative sampling. In an application to poverty mapping in Spain, we compare the proposed weighted PEB estimators with the unweighted EB analogues. |
| Keywords: | Unit level models; Pseudo empirical best estimator; Poverty mapping; Nested-error model; Empirical best estimator |
| Date: | 2016–04 |
| URL: | http://d.repec.org/n?u=RePEc:cte:wsrepe:22731&r=ecm |
| By: | Isabelle Charlier; Davy Paindaveine; Jérôme Saracco |
| Abstract: | Charlier et al. (2015a,b) developed a new nonparametric quantile regression method based on the concept of optimal quantization and showed that the resulting estimators often dominate their classical, kernel-type, competitors. The construction, however, remains limited to single-output quantile regression. In the present work, we therefore extend the quantization-based quantile regression method to the multiple-output context. We show how quantization allows to approximate the population multiple-output regression quantiles introduced in Hallin et al. (2015), which are conditional versions of the location multivariate quantiles from Hallin et al. (2010). We prove that this approximation becomes arbitrarily accurate as the size of the quantization grid goes to infinity. We also consider a sample version of the proposed quantization-based quantiles and establish their weak consistency for their population version. Through simulations, we compare the performances of the proposed quantization-based estimators with their local constant and local bilinear kernel competitors from Hallin et al. (2015). We also compare the corresponding sample quantile regions. The results reveal that the proposed quantization-based estimators, which are local constant in nature, outperform their kernel counterparts and even often dominate their local bilinear kernel competitors. |
| Date: | 2016–04 |
| URL: | http://d.repec.org/n?u=RePEc:eca:wpaper:2013/229118&r=ecm |
| By: | Campbell R. Harvey; Yan Liu |
| Abstract: | We show that the standard equation-by-equation OLS used in performance evaluation ignores information in the alpha population and leads to severely biased estimates for the alpha population. We propose a new framework that treats fund alphas as random effects. Our framework allows us to make inference on the alpha population while controlling for various sources of estimation risk. At the individual fund level, our method pools information from the entire alpha distribution to make density forecast for the fund's alpha, offering a new way to think about performance evaluation. In simulations, we show that our method generates parameter estimates that universally dominate the OLS estimates, both at the population and at the individual fund level. While it is generally accepted that few if any mutual funds outperform, we find that the fraction of funds that generate positive alphas is accurately estimated at over 10%. An out-of-sample forecasting exercise also shows that our method generates superior alpha forecasts. |
| JEL: | G10 G11 G12 G14 G23 |
| Date: | 2016–03 |
| URL: | http://d.repec.org/n?u=RePEc:nbr:nberwo:22134&r=ecm |
| By: | Tingting Cheng; Jiti Gao; Xibin Zhang |
| Abstract: | As conventional cross-validation bandwidth selection methods do not work properly in the situation where the data are serially dependent time series, alternative bandwidth selection methods are necessary. In recent years, Bayesian based methods for global bandwidth selection have been studied. Our experience shows that a global bandwidth is however less suitable than a localized bandwidth in kernel density estimation based on serially dependent time series data. Nonetheless, a difficult issue is how we can consistently estimate a localized bandwidth. This paper presents a nonparametric localized bandwidth estimator, for which we established a completely new asymptotic theory. Applications of this new bandwidth estimator to the kernel density estimation of Eurodollar deposit rate and the S&P 500 daily return demonstrate the effectiveness and competitiveness of the proposed localized bandwidth. |
| Keywords: | Density estimation, localized bandwidth, GARCH model |
| JEL: | C13 C14 C21 |
| Date: | 2016 |
| URL: | http://d.repec.org/n?u=RePEc:msh:ebswps:2016-7&r=ecm |
| By: | Alberto Abadie; Kasy, Maximilian |
| Abstract: | We study the properties of machine learning procedures which are based on (i) regularized estimation, and (ii) data-driven choice of regularization parameters. Popular estimators covered by our results include ridge, lasso, and pretest estimators. For such regularized estimators, we characterize their finite sample risk functions (mean squared error), and provide analytic expressions which allow to compare the performance of alternative estimators. These expressions provide guidance for applied researchers to choose an estimation procedure in a given context. We show uniform risk consistency results for alternative ways of choosing regularization parameters, including Stein's unbiased risk estimate and cross-validation. Under regularity conditions, these empirical selection procedures of regularization parameters produce estimators with risk uniformly close to the risk of estimators that use the infeasible optimal (``oracle'') choice of regularization parameters. We illustrate the applicability of our results using simulated data, as well as data from the literature, on the causal effect of locations on intergenerational mobility, and on illegal trading by arms companies with conflict countries under an embargo. |
| Date: | 2016–01 |
| URL: | http://d.repec.org/n?u=RePEc:qsh:wpaper:383316&r=ecm |
| By: | Ole E. Barndorff-Nielsen (Aarhus University, THIELE Center and CREATES) |
| Abstract: | This paper reviews the roles of gamma type kernels in the theory and modelling for Brownian and Lévy semistationary processes. Applications to financial econometrics and the physics of turbulence are pointed out. |
| Keywords: | Ambit Stochastics; autocorrelation functions; Brownian semistationary processes; financial econometrics; fractional differentiation; identification; Levy semistationary processes; path properties; turbulence modelling; volatility/intermittency. |
| JEL: | C1 C5 |
| Date: | 2016–04–05 |
| URL: | http://d.repec.org/n?u=RePEc:aah:create:2016-09&r=ecm |
| By: | Takaya Fukui (Graduate School of Economics, University of Tokyo); Seisho Sato (Graduate School of Economics, University of Tokyo); Akihiko Takahashi (Graduate School of Economics, University of Tokyo) |
| Abstract: | This paper proposes a new approach to style analysis by applying a general state space model and Monte Carlo filter. Particularly, we regard coefficients of style indices as state variables in the state space model and employ Monte Carlo filter as an estimation method. Moreover, we utilize a generalized simulated annealing for estimating parameters, which seems the first attempt in particle filtering methods. Finally, an empirical analysis with actual funds' data confirms the validity of our approach. |
| Date: | 2016–03 |
| URL: | http://d.repec.org/n?u=RePEc:cfi:fseres:cf383&r=ecm |
| By: | David Hendry; Andrew B. Martinez |
| Abstract: | Abstract: This paper develops a new approach for evaluating multi-step system forecasts with relatively few forecast-error observations. It extends Clements and Hendry (1993a) using Abadir et al.(2014) to generate "design-free" estimates of the general matrix of the forecast-error second-moment when there are relatively few forecast-error observations. Simulations show that the usefulness of alternative methods deteriorates when their assumptions are violated. The new approach compares well against these methods and provides correct forecast rankings. |
| Keywords: | Invariance, Forecast Evaluation, Forecast Error, Moment Matrices, MSFE, GFESM |
| JEL: | C22 C32 C53 |
| Date: | 2016–03–08 |
| URL: | http://d.repec.org/n?u=RePEc:oxf:wpaper:784&r=ecm |
| By: | Xun Lu (Department of Economics, Hong Kong University of Science and Technology); Liangjun Su (Singapore Management University); Halbert White (University of California) |
| Abstract: | Granger non-causality in distribution is fundamentally a probabilistic conditional independence notion that can be applied not only to time series data but also to cross-section and panel data. In this paper, we provide a natural de nition of structural causality in cross-section and panel data and forge a direct link between Granger (G-) causality and structural causality under a key conditional exogeneity assumption. To put it simply, when structural e¤ects are well de ned and identi able, G-non-causality follows from structural non-causality, and with suitable conditions (e.g., separability or monotonicity), structural causality also implies G-causality. This justi es using tests of G-non- causality to test for structural non-causality under the key conditional exogeneity assumption for both cross-section and panel data. We pay special attention to heterogeneous populations, allowing both structural heterogeneity and distributional heterogeneity. Most of our results are obtained for the general case, without assuming linearity, monotonicity in observables or unobservables, or separability between observed and unobserved variables in the structural relations. |
| Keywords: | Granger causality, Structural causality, Structural heterogeneity, Distributional heterogeneity, Cross-section, Panel data |
| JEL: | C14 C33 C36 |
| Date: | 2016–02 |
| URL: | http://d.repec.org/n?u=RePEc:siu:wpaper:04-2016&r=ecm |
| By: | Medovikov, Ivan; Prokhorov, Artem |
| Abstract: | We propose a new nonparametric measure of association between an arbitrary number of random vectors. The measure is based on the empirical copula process for the multivariate marginals, corresponding to the vectors, and is insensitive to the within-vector dependence. It is bounded by the [0, 1] interval, covering the entire range of dependence from vector independence to a vector version of a monotone relationship. We study the properties of the new measure under several well-known copulas and provide a nonparametric estimator of the measure, along with its asymptotic theory, under fairly general assumptions. To illustrate the applicability of the new measure, we use it to assess the degree of interdependence between equity markets in North and South America, Europe and Asia, surrounding the financial crisis of 2008. We find strong evidence of previously unknown contagion patterns, with selected regions exhibiting little dependence before and after the crisis and a lot of dependence during the crisis period. |
| Keywords: | copula; measures of vector dependence; nonparametric statistics; Hoeffding's Phi-square; |
| Date: | 2016–03–11 |
| URL: | http://d.repec.org/n?u=RePEc:syb:wpbsba:2123/14490&r=ecm |
| By: | Leopoldo Catania (DEF, University of Rome "Tor Vergata"); Anna Gloria Billé (DEF, University of Rome "Tor Vergata") |
| Abstract: | We propose a new class of models specifically tailored for spatio{temporal data analysis. To this end, we generalize the spatial autoregressive model with autoregressive and heteroskedastic disturbances, i.e. SARAR(1,1), by exploiting the recent advancements in Score Driven (SD) models typically used in time series econometrics. In particular, we allow for time{varying spatial autoregressive coefficients as well as time{varying regressor coefficients and cross{sectional standard deviations. We report an extensive Monte Carlo simulation study in order to investigate the finite sample properties of the Maximum Likelihood estimator for the new class of models as well as its exibility in explaining several dynamic spatial dependence processes. The new proposed class of models are found to be economically preferred by rational investors through an application in portfolio optimization. |
| Keywords: | SARAR, time varying parameters, spatio{temporal data, score driven models |
| Date: | 2016–03–31 |
| URL: | http://d.repec.org/n?u=RePEc:rtv:ceisrp:375&r=ecm |