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on Econometrics |
| By: | Xiaohong Chen (Cowles Foundation, Yale University); Timothy Christensen (New York University); Elie Tamer (Harvard University) |
| Abstract: | In complicated/nonlinear parametric models, it is generally hard to know whether the model parameters are point identified. We provide computationally attractive procedures to construct confidence sets (CSs) for identified sets of full parameters and of subvectors in models defined through a likelihood or a vector of moment equalities or inequalities. These CSs are based on level sets of optimal sample criterion functions (such as likelihood or optimally-weighted or continuously-updated GMM criterions). The level sets are constructed using cutoffs that are computed via Monte Carlo (MC) simulations directly from the quasi-posterior distributions of the criterions. We establish new Bernstein-von Mises (or Bayesian Wilks) type theorems for the quasi-posterior distributions of the quasi-likelihood ratio (QLR) and profile QLR in partially-identified regular models and some non-regular models. These results imply that our MC CSs have exact asymptotic frequentist coverage for identified sets of full parameters and of subvectors in partially-identified regular models, and have valid but potentially conservative coverage in models with reduced-form parameters on the boundary. Our MC CSs for identified sets of subvectors are shown to have exact asymptotic coverage in models with singularities. We also provide results on uniform validity of our CSs over classes of DGPs that include point and partially identified models. We demonstrate good finite-sample coverage properties of our procedures in two simulation experiments. Finally, our procedures are applied to two non-trivial empirical examples: an airline entry game and a model of trade flows. |
| Date: | 2016–05 |
| URL: | http://d.repec.org/n?u=RePEc:cwl:cwldpp:2037r2&r=ecm |
| By: | Liu, Cheng (Economics and Management School of Wuhan University); Xia, Ningning (School of Statistics and Management, Shanghai University of Finance and Economics); Yu, Jun (School of Economics, Singapore Management University) |
| Abstract: | This paper examines the usefulness of high frequency data in estimating the covariance matrix for portfolio choice when the portfolio size is large. A computationally convenient nonlinear shrinkage estimator for the integrated covariance (ICV) matrix of financial assets is developed in two steps. The eigenvectors of the ICV are first constructed from a designed time variation adjusted realized covariance matrix of noise-free log-returns of rel- atively low frequency data. Then the regularized eigenvalues of the ICV are estimated by quasi-maximum likelihood based on high frequency data. The estimator is always positive definite and its inverse is the estimator of the inverse of ICV. It minimizes the limit of the out-of-sample variance of portfolio returns within the class of rotation-equivalent estimators. It works when the number of underlying assets is larger than the number of time series ob- servations in each asset and when the asset price follows a general stochastic process. Our theoretical results are derived under the assumption that the number of assets (p) and the sample size (n) satisfy p/n -> y > 0 as n -> 8. The advantages of our proposed estimator are demonstrated using real data. |
| Keywords: | Portfolio Choice; High Frequency Data; Integrated Covariance Matrix; Shrinkage Function |
| JEL: | C13 C22 C51 G12 G14 |
| Date: | 2016–11–18 |
| URL: | http://d.repec.org/n?u=RePEc:ris:smuesw:2016_014&r=ecm |
| By: | Mohamad Kazem Shirani Faradonbeh; Ambuj Tewari; George Michailidis |
| Abstract: | Identification of the parameters of stable linear dynamical systems is a well-studied problem in the literature, both in the low and high-dimensional settings. However, there are hardly any results for the unstable case, especially regarding finite time bounds. For this setting, classical results on least-squares estimation of the dynamics parameters are not applicable and therefore new concepts and technical approaches need to be developed to address the issue. Unstable linear systems reflect key real applications in control theory, econometrics, and finance. This study establishes finite time bounds for the identification error of the least-squares estimates for a fairly large class of heavy-tailed noise distributions, and transition matrices of such systems. The results relate the time length required as a function of the problem dimension and key characteristics of the true underlying transition matrix and the noise distribution. To obtain them, appropriate concentration inequalities for random matrices and for sequences of martingale differences are leveraged. |
| Date: | 2017–10 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1710.01852&r=ecm |
| By: | Espasa Terrades, Antoni; Carlomagno Real, Guillermo |
| Abstract: | The objective of this paper is to propose a strategy to exploit short-run commonalities in the sectoral components of macroeconomic variables to obtain better models and more accurate forecasts of the aggregate and of the components. Our main contribution concerns cases in which the number of components is large, so that traditional multivariate approaches are not feasible. We show analytically and by Monte Carlo methods that subsets of components in which all the elements share a single common cycle can be discovered by pairwise methods. As the procedure does not rely on any kind of cross-sectional averaging strategy: it does not need to assume pervasiveness, it can deal with highly correlated idiosyncratic components and it does not need to assume that the size of the subsets goes to infinity. Nonetheless, the procedure works both with fixed N and T going to infinity, and with T and N both going to infinity. |
| Keywords: | Pairwise tests; Disaggregation; Factor Models; Common features |
| JEL: | C53 C32 C22 C01 |
| Date: | 2017–09–01 |
| URL: | http://d.repec.org/n?u=RePEc:cte:wsrepe:25392&r=ecm |
| By: | Chuan Goh |
| Abstract: | This paper presents a new estimator of the intercept of a sample-selection model in which the joint distribution of the unobservables is unspecified. The intercept is often in this context of inherent interest; for example, in a program evaluation context, the difference between the intercepts in outcome equations for participants and non-participants can be interpreted as the difference in average outcomes of participants and their counterfactual average outcomes if they had chosen not to participate. The new estimator can under mild conditions exhibit a rate of convergence in probability equal to $n^{-(p-1)/(2p-1)}$, where $p\ge 2$ is an integer that indexes the strength of certain smoothness assumptions. This rate of convergence is in this context the optimal rate of convergence for estimation of the intercept parameter in terms of a minimax criterion. The new estimator is an adaptation of a nearest-neighbours estimator of a conditional mean (Yang, 1981; Stute, 1984), and is under mild conditions consistent and asymptotically normal with a rate of convergence that is the same regardless of the degree to which selection depends on unobservables in the outcome equation. The first-order behaviour of the new estimator, unlike those of other proposals in the literature, does not depend on explicit assumptions regarding the relative tail behaviours of the determinants of selection. Simulation evidence and an empirical example are included. |
| Date: | 2017–10 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1710.01423&r=ecm |
| By: | Dare, Wale; Fengler, Matthias |
| Abstract: | We propose a non-parametric procedure for estimating the realized spot volatility of a price process described by an Itô semimartingale with Lévy jumps. The procedure integrates the threshold jump elimination technique of Mancini (2009) with a frame (Gabor) expansion of the realized trajectory of spot volatility. We show that the procedure converges in probability in L2([0, T]) for a wide class of spot volatility processes, including those with discontinuous paths. Our analysis assumes the time interval between price observations tends to zero; as a result, the intended application is for the analysis of high frequency financial data. |
| Keywords: | Nonparametric estimation, Itô semimartingale, Lévy jumps, Gabor frames, realized spot volatility |
| JEL: | C13 C14 |
| Date: | 2017–09 |
| URL: | http://d.repec.org/n?u=RePEc:usg:econwp:2017:15&r=ecm |
| By: | Anand Acharya (Carleton University); Lynda Khalaf (Carleton University); Marcel Voia (Carleton University); Myra Yazbeck (University of Ottawa); David Wensley (University of British Columbia) |
| Abstract: | Endogeneity or unmeasured confounding is a nontrivial complication in duration data models, for which there are relatively few existing methods. I develop two related, but methodologically distinct, identification-robust instrumental variable estimators to address the complications of endogeneity in an accelerated life regression model. The two unique methods generalize the Anderson-Rubin statistic to (1) lifetime data distributions in the case of the least squares estimator and (2) distribution-free censored models in the case of the rank estimator. Valid confidence sets, based on inverting the pivotal least-squares statistic and the linear rank statistic, form the basis for identification-robust inference using the Mata programming language via exact simulation-based methods. The finite sample performance of the proposed statistics is evaluated using the built-in features of Stata combined with the original Mata code. I provide an empirical analysis, utilizing an original prospectively collected clinical patient dataset in which the trauma status of a pediatric critical care patient instruments a possibly confounded illness severity index in a length of stay regression for a specific pediatric intensive care population. Results suggest a clinically relevant bias correction for routinely collected patient risk indices that is meaningful for informing policy in the healthcare setting. |
| Date: | 2017–09–20 |
| URL: | http://d.repec.org/n?u=RePEc:boc:csug17:15&r=ecm |
| By: | Olivier Ledoit; Michael Wolf |
| Abstract: | This paper introduces a nonlinear shrinkage estimator of the covariance matrix that does not require recovering the population eigenvalues first. We estimate the sample spectral density and its Hilbert transform directly by smoothing the sample eigenvalues with a variable-bandwidth kernel. Relative to numerically inverting the so-called QuEST function, the main advantages of direct kernel estimation are: (1) it is much easier to comprehend because it is analogous to kernel density estimation; (2) it is only twenty lines of code in Matlab — as opposed to thousands — which makes it more verifiable and customizable; (3) it is 200 times faster without significant loss of accuracy; and (4) it can handle matrices of a dimension larger by a factor of ten. Even for dimension 10, 000, the code runs in less than two minutes on a desktop computer; this makes the power of nonlinear shrinkage as accessible to applied statisticians as the one of linear shrinkage. |
| Keywords: | Kernel estimation, Hilbert transform, large-dimensional asymptotics, nonlinear shrinkage, rotation equivariance |
| JEL: | C13 |
| Date: | 2017–09 |
| URL: | http://d.repec.org/n?u=RePEc:zur:econwp:264&r=ecm |
| By: | Luo, Ye; Spindler, Martin |
| Abstract: | In the recent years more and more highdimensional data sets, where the number of parameters p is high compared to the number of observations n or even larger, are available for applied researchers. Boosting algorithms represent one of the major advances in machine learning and statistics in recent years and are suitable for the analysis of such data sets. While Lasso has been applied very successfully for highdimensional data sets in Economics, boosting has been underutilized in this field, although it has been proven very powerful in fields like Biostatistics and Pattern Recognition. We attribute this to missing theoretical results for boosting. The goal of this paper is to fill this gap and show that boosting is a competitive method for inference of a treatment effect or instrumental variable (IV) estimation in a high-dimensional setting. First, we present the L2Boosting with componentwise least squares algorithm and variants which are tailored for regression problems which are the workhorse for most Econometric problems. Then we show how L2Boosting can be used for estimation of treatment effects and IV estimation. We highlight the methods and illustrate them with simulations and empirical examples. For further results and technical details we refer to (?) and (?) and to the online supplement of the paper. |
| JEL: | C21 C26 |
| Date: | 2017 |
| URL: | http://d.repec.org/n?u=RePEc:zbw:vfsc17:168194&r=ecm |
| By: | Giuseppe Pandolfo; Davy Paindaveine; Giovanni Porzio |
| Abstract: | Directional data are constrained to lie on the unit sphere of Rq, for some q ≥ 2. To address the lack of a natural ordering for such data, depth functions have been defined on spheres. However, the depths available either lack flexibility or are so computationally expensive that they can only be used for very small dimensions q. In this work, we improve on this by introducing a class of distance-based depths for directional data. Irrespective of the distance adopted, these depths can easily be computed in high dimensions, too. We derive the main structural properties of the proposed depths and study how they depend on the distance used. We discuss the asymptotic and robustness properties of the corresponding deepest points. We show the practical relevance of the proposed depths in two inferential applications, related to (i) spherical location estimation and (ii) supervised classification. For both problems, we show through simulation studies that distance-based depths have strong advantages over their competitors. |
| Date: | 2017–10 |
| URL: | http://d.repec.org/n?u=RePEc:eca:wpaper:2013/258549&r=ecm |
| By: | Victor Chernozhukov; Denis Chetverikov; Mert Demirer; Esther Duflo; Christian Hansen; Whitney Newey; James Robins |
| Abstract: | Most modern supervised statistical/machine learning (ML) methods are explicitly designed to solve prediction problems very well. Achieving this goal does not imply that these methods automatically deliver good estimators of causal parameters. Examples of such parameters include individual regression coefficients, average treatment effects, average lifts, and demand or supply elasticities. In fact, estimates of such causal parameters obtained via naively plugging ML estimators into estimating equations for such parameters can behave very poorly due to the regularization bias. Fortunately, this regularization bias can be removed by solving auxiliary prediction problems via ML tools. Specifically, we can form an orthogonal score for the target low-dimensional parameter by combining auxiliary and main ML predictions. The score is then used to build a de-biased estimator of the target parameter which typically will converge at the fastest possible 1/root(n) rate and be approximately unbiased and normal, and from which valid confidence intervals for these parameters of interest may be constructed. The resulting method thus could be called a "double ML" method because it relies on estimating primary and auxiliary predictive models. In order to avoid overfitting, our construction also makes use of the K-fold sample splitting, which we call cross-fitting. This allows us to use a very broad set of ML predictive methods in solving the auxiliary and main prediction problems, such as random forest, lasso, ridge, deep neural nets, boosted trees, as well as various hybrids and aggregators of these methods. |
| Date: | 2016–07 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1608.00060&r=ecm |
| By: | Victor Chernozhukov; Iv\'an Fern\'andez-Val; Tetsuya Kaji |
| Abstract: | Extremal quantile regression, i.e. quantile regression applied to the tails of the conditional distribution, counts with an increasing number of economic and financial applications such as value-at-risk, production frontiers, determinants of low infant birth weights, and auction models. This chapter provides an overview of recent developments in the theory and empirics of extremal quantile regression. The advances in the theory have relied on the use of extreme value approximations to the law of the Koenker and Bassett (1978) quantile regression estimator. Extreme value laws not only have been shown to provide more accurate approximations than Gaussian laws at the tails, but also have served as the basis to develop bias corrected estimators and inference methods using simulation and suitable variations of bootstrap and subsampling. The applicability of these methods is illustrated with two empirical examples on conditional value-at-risk and financial contagion. |
| Date: | 2016–12 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1612.06850&r=ecm |
| By: | Victor Chernozhukov; Iv\'an Fern\'andez-Val; Whitney Newey |
| Abstract: | Multinomial choice models are fundamental for empirical modeling of economic choices among discrete alternatives. We analyze identification of binary and multinomial choice models when the choice utilities are nonseparable in observed attributes and multidimensional unobserved heterogeneity with cross-section and panel data. We show that derivatives of choice probabilities with respect to continuous attributes are weighted averages of utility derivatives in cross-section models with exogenous heterogeneity. In the special case of random coefficient models with an independent additive effect, we further characterize that the probability derivative at zero is proportional to the population mean of the coefficients. We extend the identification results to models with endogenous heterogeneity using either a control function or panel data. In time stationary panel models with two periods, we find that differences over time of derivatives of choice probabilities identify utility derivatives "on the diagonal," i.e. when the observed attributes take the same values in the two periods. We also show that time stationarity does not identify structural derivatives "off the diagonal" both in continuous and multinomial choice panel models. |
| Date: | 2017–06 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1706.08418&r=ecm |
| By: | Eric Beutner; Alexander Heinemann; Stephan Smeekes |
| Abstract: | To quantify uncertainty around point estimates of conditional objects such as conditional means or variances, parameter uncertainty has to be taken into account. Attempts to incorporate parameter uncertainty are typically based on the unrealistic assumption of observing two independent processes, where one is used for parameter estimation, and the other for conditioning upon. Such unrealistic foundation raises the question whether these intervals are theoretically justified in a realistic setting. This paper presents an asymptotic justification for this type of intervals that does not require such an unrealistic assumption, but relies on a sample-split approach instead. By showing that our sample-split intervals coincide asymptotically with the standard intervals, we provide a novel, and realistic, justification for confidence intervals of conditional objects. The analysis is carried out for a general class of Markov chains nesting various time series models. |
| Date: | 2017–10 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1710.00643&r=ecm |
| By: | Pedro H. C. Sant'Anna |
| Abstract: | In a unified framework, we provide estimators and confidence bands for a variety of treatment effects when the outcome of interest, typically a duration, is subjected to right censoring. Our methodology accommodates average, distributional, and quantile treatment effects under different identifying assumptions including unconfoundedness, local treatment effects, and nonlinear differences-in-differences. The proposed estimators are easy to implement, have close-form representation, are fully data-driven upon estimation of nuisance parameters, and do not rely on parametric distributional assumptions, shape restrictions, or on restricting the potential treatment effect heterogeneity across different subpopulations. These treatment effects results are obtained as a consequence of more general results on two-step Kaplan-Meier estimators that are of independent interest: we provide conditions for applying (i) uniform law of large numbers, (ii) functional central limit theorems, and (iii) we prove the validity of the ordinary nonparametric bootstrap in a two-step estimation procedure where the outcome of interest may be randomly censored. |
| Date: | 2016–04 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1604.02642&r=ecm |
| By: | Hepsag, Aycan |
| Abstract: | In this paper, we develop a new unit root testing procedure which considers jointly for structural breaks and nonlinear adjustment. The structural breaks are modeled by means of a logistic smooth transition function and nonlinear adjustment is modeled by means of an ESTAR model. The empirical size of test is quite close to the nominal one and in terms of power, the new unit root test is generally superior to the alternative test. |
| Keywords: | Smooth Transition, nonlinearity, unit root, ESTAR |
| JEL: | C12 C22 |
| Date: | 2017–10–05 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:81788&r=ecm |
| By: | Jianqing Fan; Yuan Ke; Yuan Liao |
| Abstract: | We provide an econometric analysis for the factor models when the latent factors can be explained partially by several observed explanatory proxies. In financial factor models for instance, the unknown factors can be reasonably well predicted by a few observable proxies, such as the Fama-French factors. In diffusion index forecasts, identified factors are strongly related to several directly measurable economic variables such as consumption-wealth variable, financial ratios, and term spread. To incorporate the explanatory power of these observed characteristics, we propose a new two-step estimation procedure: (i) regress the data onto the observables, and (ii) take the principal components of the fitted data to estimate the loadings and factors. The proposed estimator is robust to possibly heavy-tailed distributions, which are encountered by many macroeconomic and financial time series. With those proxies, the factors can be estimated accurately even if the cross-sectional dimension is mild. Empirically, we apply the model to forecast US bond risk premia, and find that the observed macroeconomic characteristics contain strong explanatory powers of the factors. The gain of forecast is more substantial when these characteristics are incorporated to estimate the common factors than directly used for forecasts. |
| Date: | 2016–03 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1603.07041&r=ecm |
| By: | Ramazan Gencay (Simon Fraser University); Ege Yazgan (Istanbul Bilgi University) |
| Abstract: | When data exhibit high volatility and jumps, which are common features in most high frequency financial time series, forecasting becomes even more challenging. Using high frequency exchange rate data, we show that wavelets, which are robust to high volatility and jumps, are useful forecasters in high frequency settings when high volatility is a dominant feature that affects estimation zones, forecasting zones or both. The results indicate that decomposing the time series into homogeneous components that can then be used in time series forecast models is critical. Different components become more useful than others for different data features associated with a volatility regime. We cover a wide range of linear and nonlinear time series models for forecasting high frequency exchange rate return series. Our results indicate that when data display nonstandard features with high volatility, nonlinear models outperform linear alternatives. However, when data are in low volatility ranges for both estimations and forecasts, simple linear autoregressive models prevail, although considerable denoising of the data via wavelets is required. |
| Keywords: | Wavelets; Forecasting; High Frequency Data; Nonlinear Models; Maximum Overlap; Discrete Wavelet Transformation |
| JEL: | C12 C22 |
| Date: | 2017–09 |
| URL: | http://d.repec.org/n?u=RePEc:bli:wpaper:1704&r=ecm |
| By: | Tao, Yubo (Singapore Management University); Yu, Jun (Singapore Management University) |
| Abstract: | This paper examines the limit properties of information criteria for distinguishing between the unit root model and the various kinds of explosive models. The information criteria include AIC, BIC, HQIC. The explosive models include the local-to-unit-root model, the mildly explosive model and the regular explosive model. Initial conditions with different order of magnitude are considered. Both the OLS estimator and the indirect inference estimator are studied. It is found that BIC and HQIC, but not AIC, consistently select the unit root model when data come from the unit root model. When data come from the local-to-unit-root model, both BIC and HQIC select the wrong model with probability approaching 1 while AIC has a positive probability of selecting the right model in the limit. When data come from the regular explosive model or from the mildly explosive model in the form of 1+n^{\alpha}/n with \alpha \in (0; 1), all three information criteria consistently select the true model. Indirect inference estimation can increase or decrease the probability for information criteria to select the right model asymptotically relative to OLS, depending on the information criteria and the true model. Simulation results confirm our asymptotic results in finite sample. |
| Keywords: | Model Selection; Information Criteria; Local-to-unit-root Model; Mildly Explosive Model; Unit Root Model; Indirect Inference. |
| Date: | 2016–03–29 |
| URL: | http://d.repec.org/n?u=RePEc:ris:smuesw:2016_006&r=ecm |
| By: | Chu-An Liu (Institute of Economics, Academia Sinica, Taipei, Taiwan); Biing-Shen Kuo (Department of International Business, National Chengchi University); Wen-Jen Tsay (Institute of Economics, Academia Sinica, Taipei, Taiwan) |
| Abstract: | This paper considers model averaging in spectral density estimation. We construct the spectral density function by averaging the autoregressive coefficients from all potential autoregressive models and investigate the autoregressive spectral averaging estimator using weights that minimize the Mallows and jackknife criteria. We extend the consistency of the autoregressive spectral estimator in Berk (1974) to the autoregressive spectral averaging estimator under a condition that imposes a restriction on the relationship between the model weights and autoregressive coefficients. Simulation studies show that the autoregressive spectral averaging estimator compares favorably with the AIC and BIC model selection estimators, and the bias of the averaging estimator approaches zero as the sample size increases. |
| Keywords: | Model averaging, Model selection, Spectral density estimator |
| Date: | 2017–09 |
| URL: | http://d.repec.org/n?u=RePEc:sin:wpaper:17-a013&r=ecm |
| By: | Timo Teräsvirta (Aarhus University and CREATES, C.A.S.E., Humboldt-Universität zu Berlin) |
| Abstract: | This article contains a short review of nonlinear models that are applied to modelling macroeconomic time series. Brief descriptions of relevant models, both univariate, dynamic single-equation, and vector autoregressive ones are presented. Their application is illuminated by a number of selected examples. |
| Keywords: | Markov-switching model, nonlinear time series, random coefficient model, smooth transition model, threshold autoregressive model, vector autoregressive model |
| JEL: | C32 C51 E00 |
| Date: | 2909 |
| URL: | http://d.repec.org/n?u=RePEc:aah:create:2017-32&r=ecm |
| By: | Xiao, Weilin (Zhejiang University); Yu, Jun (School of Economics, Singapore Management University) |
| Abstract: | This paper develops the asymptotic theory for the least squares (LS) estimator of the persistent parameter in the fractional Vasicek model when a continuous record of observations is available. The fractional Vasicek model is assumed to be driven by the fractional Brownian motion with a known Hurst parameter greater than or equal to one half. It is shown that the asymptotic properties depend on the sign of the persistent parameter, corresponding to the stationary case, the explosive case and the null recurrent case. The strong consistency and the asymptotic distribution are obtained in all three cases. |
| Keywords: | Least squares estimation; Fractional Vasicek model; Stationary process; Explosive process; Consistency; Asymptotic distribution |
| JEL: | C15 C22 C32 |
| Date: | 2017–09–25 |
| URL: | http://d.repec.org/n?u=RePEc:ris:smuesw:2016_013&r=ecm |
| By: | George Daniel Mateescu (Institute for Economic Forecasting, Romanian Academy) |
| Abstract: | In some previous papers ([3],[4]) we introduced and used a regression suitable for data series where the depended variable is not a value but a set of values. These values may be a discrete set or a continuous data. The economic correspondent of this mathematical approach is the exchange rate, where values are spread into an interval, during one day. Also, the stock exchange market is an example where indicators values are continuously variable during a day, etc. |
| Keywords: | regression |
| JEL: | C02 C22 C58 |
| Date: | 2017–09 |
| URL: | http://d.repec.org/n?u=RePEc:rjr:wpiecf:170901&r=ecm |
| By: | Naoki Awaya (Graduate School of Economics, The University of Tokyo); Yasuhiro Omori (Faculty of Economics, The University of Tokyo) |
| Abstract: | An efficient simulation-based methodology is proposed for the rolling window esti- mation of state space models. Using the framework of the conditional sequential Monte Carlo update in the particle Markov chain Monte Carlo estimation, weighted particles are updated to learn and forget the information of new and old observations by the forward and backward block sampling with the particle simulation smoother. These particles are also propagated by the MCMC update step. Theoretical justifications are provided for the proposed estimation methodology. As a special case, we obtain a new sequential MCMC based on Particle Gibbs. It is a exible method alternative to SMC2 that is based on Particle MH. The computational performance is evaluated in illustrative examples, showing that the posterior distributions of model parameters and marginal likelihoods are estimated with accuracy. |
| Date: | 2017–09 |
| URL: | http://d.repec.org/n?u=RePEc:tky:fseres:2017cf1066&r=ecm |
| By: | Igor Halperin |
| Abstract: | We propose an analytical approach to the computation of tail probabilities of compound distributions whose individual components have heavy tails. Our approach is based on the contour integration method, and gives rise to a representation of the tail probability of a compound distribution in the form of a rapidly convergent one-dimensional integral involving a discontinuity of the imaginary part of its moment generating function across a branch cut. The latter integral can be evaluated in quadratures, or alternatively represented as an asymptotic expansion. Our approach thus offers a viable (especially at high percentile levels) alternative to more standard methods such as Monte Carlo or the Fast Fourier Transform, traditionally used for such problems. As a practical application, we use our method to compute the operational Value at Risk (VAR) of a financial institution, where individual losses are modeled as spliced distributions whose large loss components are given by power-law or lognormal distributions. Finally, we briefly discuss extensions of the present formalism for calculation of tail probabilities of compound distributions made of compound distributions with heavy tails. |
| Date: | 2017–10 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1710.01227&r=ecm |
| By: | Pedro H. C. Sant'Anna; Xiaojung Song |
| Abstract: | This paper introduces new nonparametric diagnostic tools for detecting propensity score misspecification. These tests may be applied to assess the validity of different treatment effects estimators that rely on the correct specification of the propensity score. Our tests do not suffer from the "curse of dimensionality" when the vector of covariates is of high-dimensionality, are fully data-driven, do not require tuning parameters such as bandwidths, and are able to detect a broad class of local alternatives converging to the null at the parametric rate $n^{-1/2}$, with $n$ the sample size. We show that the use of an orthogonal projection on the tangent space of nuisance parameters both improves power and facilitates the simulation of critical values by means of a multiplier bootstrap procedure. The finite sample performance of the tests are examined by means of a Monte Carlo experiment and an empirical application. Open-source software is available for implementing the proposed tests. |
| Date: | 2016–11 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1611.06217&r=ecm |
| By: | Pedro H. C. Sant'Anna |
| Abstract: | This article proposes different tests for treatment effect heterogeneity when the outcome of interest, typically a duration variable, may be right-censored. The proposed tests study whether a policy 1) has zero distributional (average) effect for all subpopulations defined by covariate values, and 2) has homogeneous average effect across different subpopulations. The proposed tests are based on two-step Kaplan-Meier integrals, and do not rely on parametric distributional assumptions, shape restrictions, nor on restricting the potential treatment effect heterogeneity across different subpopulations. Our framework is suitable not only to exogenous treatment allocation, but can also account for treatment noncompliance, an important feature in many applications. The proposed tests are consistent against fixed alternatives, and can detect nonparametric alternatives converging to the null at the parametric $n^{-1/2}$-rate, $n$ being the sample size. Critical values are computed with the assistance of a multiplier bootstrap. The finite sample properties of the proposed tests are examined by means of a Monte Carlo study, and an application about the effect of labor market programs on unemployment duration. Open-source software is available for implementing all proposed tests. |
| Date: | 2016–12 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1612.02090&r=ecm |
| By: | James G. MacKinnon (Queen’s University); Matthew D. Webb (Carleton University) |
| Abstract: | Many datasets involve observations which are grouped, or clustered, and often in several dimensions. While robust inference with single-way or multiway clustering is possible with a large number of clusters, reliable inference with few clusters and multiway clustering has otherwise proved challenging. We propose a bootstrap method that improves inference considerably. |
| Date: | 2017–09–20 |
| URL: | http://d.repec.org/n?u=RePEc:boc:csug17:06&r=ecm |
| By: | Laura Liu; Hyungsik Roger Moon; Frank Schorfheide |
| Abstract: | This paper considers the problem of forecasting a collection of short time series using cross sectional information in panel data. We construct point predictors using Tweedie's formula for the posterior mean of heterogeneous coefficients under a correlated random effects distribution. This formula utilizes cross-sectional information to transform the unit-specific (quasi) maximum likelihood estimator into an approximation of the posterior mean under a prior distribution that equals the population distribution of the random coefficients. We show that the risk of a predictor based on a non-parametric estimate of the Tweedie correction is asymptotically equivalent to the risk of a predictor that treats the correlated-random-effects distribution as known (ratio-optimality). Our empirical Bayes predictor performs well compared to various competitors in a Monte Carlo study. In an empirical application we use the predictor to forecast revenues for a large panel of bank holding companies and compare forecasts that condition on actual and severely adverse macroeconomic conditions. |
| Date: | 2017–09 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1709.10193&r=ecm |
| By: | Gordon Anderson; Alessio Farcomeni; Grazia Pittau; Roberto Zelli |
| Abstract: | A latent Markov model admitting variation in the number of latent states at each time period is introduced. The model facilitates subjects switching latent states at each time period according to an inhomogeneous first-order Markov process, wherein transition matrices are generally rectangular. As a consequence, latent groups can merge, split, or be re-arranged. An application analyzing the progress of well-being of nations, as measured by the three dimensions of the Human Development Index over the last 25 years illustrates the approach. |
| Keywords: | group merging, group splitting, Human Development Index, latent transitions. |
| JEL: | C1 I3 |
| Date: | 2017–09–22 |
| URL: | http://d.repec.org/n?u=RePEc:tor:tecipa:tecipa-589&r=ecm |
| By: | Khai X. Chiong; Hyungsik Roger Moon |
| Abstract: | Gaussian graphical models are recently used in economics to obtain networks of dependence among agents. A widely-used estimator is the Graphical Lasso (GLASSO), which amounts to a maximum likelihood estimation regularized using the $L_{1,1}$ matrix norm on the precision matrix $\Omega$. The $L_{1,1}$ norm is a lasso penalty that controls for sparsity, or the number of zeros in $\Omega$. We propose a new estimator called Structured Graphical Lasso (SGLASSO) that uses the $L_{1,2}$ mixed norm. The use of the $L_{1,2}$ penalty controls for the structure of the sparsity in $\Omega$. We show that when the network size is fixed, SGLASSO is asymptotically equivalent to an infeasible GLASSO problem which prioritizes the sparsity-recovery of high-degree nodes. Monte Carlo simulation shows that SGLASSO outperforms GLASSO in terms of estimating the overall precision matrix and in terms of estimating the structure of the graphical model. In an empirical illustration using a classic firms' investment dataset, we obtain a network of firms' dependence that exhibits the core-periphery structure, with General Motors, General Electric and U.S. Steel forming the core group of firms. |
| Date: | 2017–09 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1709.10038&r=ecm |