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on Econometrics |
| By: | Skinner, Chris J. |
| Abstract: | This paper reviews methods for handling complex sampling schemes when analysing categorical survey data. It is generally assumed that the complex sampling scheme does not affect the specification of the parameters of interest, only the methodology for making inference about these parameters. The organisation of the paper is loosely chronological. Contingency table data is emphasized first before moving on to the analysis of unit-level data. Weighted least squares methods, introduced in the mid 1970s along with methods for two-way tables, receive early attention. They are followed by more general methods based on maximum likelihood, particularly pseudo maximum likelihood estimation. Point estimation methods typically involve the use of survey weights in some way. Variance estimation methods are described in broad terms. There is a particular emphasis on methods of testing. The main modelling methods considered are log-linear models, logit models, generalized linear models and latent variable models. There is no coverage of multilevel models. |
| Keywords: | pseudo maximum likelihood; Rao-Scott adjustment; score test; survey weight; weighted least squares; EP/K032208/1 |
| JEL: | C1 |
| Date: | 2018–09–19 |
| URL: | http://d.repec.org/n?u=RePEc:ehl:lserod:89707&r=all |
| By: | Shakeeb Khan; Arnaud Maurel; Yichong Zhang |
| Abstract: | We study the informational content of factor structures in discrete triangular systems. Factor structures have been employed in a variety of settings in cross sectional and panel data models, and in this paper we formally quantify their identifying power in a bivariate system often employed in the treatment effects literature. Our main findings are that imposing a factor structure yields point identification of parameters of interest, such as the coefficient associated with the endogenous regressor in the outcome equation, under weaker assumptions than usually required in these systems. In particular, we show that an exclusion restriction, requiring an explanatory variable in the outcome equation to be excluded from the treatment equation, is no longer necessary for identification. Under such settings, we propose a rank estimator for both the factor loading and the causal effect parameter that are root-n consistent and asymptotically normal. The estimator's finite sample properties are evaluated through a simulation study. We also establish identification results in models with more general factor structures, that are characterized by nonparametric functional forms and multiple idiosyncratic shocks. |
| Date: | 2019–10 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1910.01318&r=all |
| By: | Jau-er Chen; Jia-Jyun Tien |
| Abstract: | The aim of this paper is to investigate estimation and inference on a low-dimensional causal parameter in the presence of high-dimensional controls in an instrumental variable quantile regression. The estimation and inference are based on the Neyman-type orthogonal moment conditions, that are relatively insensitive to the estimation of the nuisance parameters. The Monte Carlo experiments show that the econometric procedure performs well. We also apply the procedure to reinvestigate two empirical studies: the quantile treatment effect of 401(k) participation on accumulated wealth, and the distributional effect of job-training program participation on trainee earnings. |
| Date: | 2019–09 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1909.12592&r=all |
| By: | Jiangtao Duan; Wei Gao; Hao Qu; Hon Keung Tony |
| Abstract: | In this paper, a statistical model for panel data with unobservable grouped factor structures which are correlated with the regressors and the group membership can be unknown. The factor loadings are assumed to be in different subspaces and the subspace clustering for factor loadings are considered. A method called least squares subspace clustering estimate (LSSC) is proposed to estimate the model parameters by minimizing the least-square criterion and to perform the subspace clustering simultaneously. The consistency of the proposed subspace clustering is proved and the asymptotic properties of the estimation procedure are studied under certain conditions. A Monte Carlo simulation study is used to illustrate the advantages of the proposed method. Further considerations for the situations that the number of subspaces for factors, the dimension of factors and the dimension of subspaces are unknown are also discussed. For illustrative purposes, the proposed method is applied to study the linkage between income and democracy across countries while subspace patterns of unobserved factors and factor loadings are allowed. |
| Date: | 2019–09 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1909.09928&r=all |
| By: | Jun Ma; Vadim Marmer; Artyom Shneyerov; Pai Xu |
| Abstract: | We propose a new nonparametric estimator for first-price auctions with independent private values that imposes the monotonicity constraint on the estimated inverse bidding strategy. We show that our estimator has a smaller asymptotic variance than that of Guerre, Perrigne and Vuong's (2000) estimator. In addition to establishing pointwise asymptotic normality of our estimator, we provide a bootstrap-based approach to constructing uniform confidence bands for the density function of latent valuations. |
| Date: | 2019–09 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1909.12974&r=all |
| By: | Isaiah Andrews; Jonathan Roth; Ariel Pakes |
| Abstract: | We consider inference based on linear conditional moment inequalities, which arise in a wide variety of economic applications, including many structural models. We show that linear conditional structure greatly simplifies confidence set construction, allowing for computationally tractable projection inference in settings with nuisance parameters. Next, we derive least favorable critical values that avoid conservativeness due to projection. Finally, we introduce a conditional inference approach which ensures a strong form of insensitivity to slack moments, as well as a hybrid technique which combines the least favorable and conditional methods. Our conditional and hybrid approaches are new even in settings without nuisance parameters. We find good performance in simulations based on Wollmann (2018), especially for the hybrid approach. |
| Date: | 2019–09 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1909.10062&r=all |
| By: | Takaaki Koike; Marius Hofert |
| Abstract: | We propose a novel framework of estimating systemic risk measures and risk allocations based on a Markov chain Monte Carlo (MCMC) method. We consider a class of allocations whose j-th component can be written as some risk measure of the j-th conditional marginal loss distribution given the so-called crisis event. By considering a crisis event as an intersection of linear constraints, this class of allocations covers, for example, conditional Value-at-Risk (CoVaR), conditional expected shortfall (CoES), VaR contributions, and range VaR (RVaR) contributions as special cases. For this class of allocations, analytical calculations are rarely available, and numerical computations based on Monte Carlo methods often provide inefficient estimates due to the rare-event character of crisis events. We propose an MCMC estimator constructed from a sample path of a Markov chain whose stationary distribution is the conditional distribution given the crisis event. Efficient constructions of Markov chains, such as Hamiltonian Monte Carlo and Gibbs sampler, are suggested and studied depending on the crisis event and the underlying loss distribution. Efficiency of the MCMC estimators are demonstrated in a series of numerical experiments. |
| Date: | 2019–09 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1909.11794&r=all |
| By: | Marcel Bräutigam (LabEx MME-DII - UCP - Université de Cergy Pontoise - Université Paris-Seine, LPSM UMR 8001 - Laboratoire de Probabilités, Statistique et Modélisation - UPD7 - Université Paris Diderot - Paris 7 - SU - Sorbonne Université - CNRS - Centre National de la Recherche Scientifique, CREAR - Center of Research in Econo-finance and Actuarial sciences on Risk / Centre de Recherche Econo-financière et Actuarielle sur le Risque - Essec Business School); Marie Kratz (SID - Information Systems, Decision Sciences and Statistics Department - Essec Business School, LabEx MME-DII - UCP - Université de Cergy Pontoise - Université Paris-Seine, CREAR - Center of Research in Econo-finance and Actuarial sciences on Risk / Centre de Recherche Econo-financière et Actuarielle sur le Risque - Essec Business School) |
| Abstract: | In this study, we derive the joint asymptotic distributions of functionals of quantile estimators (the non-parametric sample quantile and the parametric location-scale quantile) and functionals of measure of dispersion estimators (the sample standard deviation, sample mean absolute deviation, sample median absolute deviation) - assuming an underlying identically and independently distributed sample. Additionally, for location-scale distributions, we show that asymptotic correlations of such functionals do not depend on the mean and variance parameter of the distribution. Further, we compare the impact of the choice of the quantile estimator (sample quantile vs. parametric location-scale quantile) in terms of speed of convergence of the asymptotic covariance and correlations respectively. As application, we show in simulations a good finite sample performance of the asymptotics. Further, we show how the theoretical dependence results can be applied to the most well-known risk measures (Value-at-Risk, Expected Shortfall, expectile). Finally, we relate the theoretical results to empirical findings in the literature of the dependence between risk measure prediction (on historical samples) and the estimated volatility. |
| Keywords: | asymptotic distribution,sample quantile,measure of dispersion,non-linear dependence,VaR,ES,correlation |
| Date: | 2018–12 |
| URL: | http://d.repec.org/n?u=RePEc:hal:wpaper:hal-02296832&r=all |
| By: | Yi Huang; Ishanu Chattopadhyay |
| Abstract: | Recognizing subtle historical patterns is central to modeling and forecasting problems in time series analysis. Here we introduce and develop a new approach to quantify deviations in the underlying hidden generators of observed data streams, resulting in a new efficiently computable universal metric for time series. The proposed metric is in the sense that we can compare and contrast data streams regardless of where and how they are generated and without any feature engineering step. The approach proposed in this paper is conceptually distinct from our previous work on data smashing, and vastly improves discrimination performance and computing speed. The core idea here is the generalization of the notion of KL divergence often used to compare probability distributions to a notion of divergence in time series. We call this the sequence likelihood (SL) divergence, which may be used to measure deviations within a well-defined class of discrete-valued stochastic processes. We devise efficient estimators of SL divergence from finite sample paths and subsequently formulate a universal metric useful for computing distance between time series produced by hidden stochastic generators. |
| Date: | 2019–09 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1909.12243&r=all |
| By: | Clément de Chaisemartin; Luc Behaghel |
| Abstract: | Oversubscribed treatments are often allocated using randomized waiting lists. Applicants are ranked randomly, and treatment offers are made following that ranking until all seats are filled. To estimate causal effects, researchers often compare applicants getting and not getting an offer. We show that those two groups are not statistically comparable. Therefore, the estimator arising from that comparison is inconsistent when the number of waitlists goes to infinity. We propose a new estimator, and show that it is consistent, provided the waitlists have at least two seats. Finally, we revisit an application, and we show that using our estimator can lead to significantly different results from those obtained using the commonly used estimator. |
| JEL: | C21 C26 |
| Date: | 2019–09 |
| URL: | http://d.repec.org/n?u=RePEc:nbr:nberwo:26282&r=all |
| By: | Majid M. Al-Sadoon; Piotr Zwiernik |
| Abstract: | We consider the problem of the identification of stationary solutions to linear rational expectations models from the second moments of observable data. Observational equivalence is characterized and necessary and sufficient conditions are provided for: (i) identification under affine restrictions, (ii) generic identification under affine restrictions of analytically parametrized models, and (iii) local identification under non-linear restrictions. The results strongly resemble the classical theory for VARMA models although significant points of departure are also documented. |
| Keywords: | identification, linear rational expectations models, linear systems, vector autoregressive moving average models |
| JEL: | C10 C22 C32 |
| Date: | 2019–09 |
| URL: | http://d.repec.org/n?u=RePEc:bge:wpaper:1114&r=all |
| By: | Tzougas, George; Yik, Woo Hee; Mustaqeem, Muhammad Waqar |
| Abstract: | This paper is concerned with presenting the Exponential-Lognormal (ELN) regression model as a competitive alternative to the Pareto, or Exponential-Inverse Gamma, regression model that has been used in a wide range of areas, including insurance ratemaking. This is the first time that the ELN regression model is used in a statistical or actuarial context. The main contribution of the study is that we illustrate how maximum likelihood estimation of the ELN regression model, which does not have a density in closed form, can be accomplished relatively easily via an Expectation-Maximisation type algorithm. A real data application based on motor insurance data is examined in order to emphasise the versatility of the proposed algorithm. Finally, assuming that the number of claims is distributed according to the classic Negative Binomial and Poisson-Inverse Gaussian regression models, both the a priori and a posteriori, or Bonus–Malus, premium rates resulting from the ELN regression model are calculated via the net premium principle and compared to those determined by the Pareto regression model that has been traditionally used for modelling claim sizes. |
| Keywords: | Exponential-Lognormal regression model; EM Algorithm; Motor Third Party Liability Insurance; ratemaking |
| JEL: | F3 G3 |
| Date: | 2019–06–26 |
| URL: | http://d.repec.org/n?u=RePEc:ehl:lserod:101729&r=all |
| By: | Marc S. Paolella (University of Zurich - Department of Banking and Finance; Swiss Finance Institute); Pawel Polak (Stevens Institute of Technology, Department of Mathematical Sciences); Patrick S. Walker (University of Zurich, Department of Banking and Finance) |
| Abstract: | Covariance matrix forecasts for portfolio optimization have to balance sensitivity to new data points with stability in order to avoid excessive rebalancing. To achieve this, a new robust orthogonal GARCH model for a multivariate set of non-Gaussian asset returns is proposed. The conditional return distribution is multivariate generalized hyperbolic and the dispersion matrix dynamics are driven by the leading factors in a principle component decomposition. Each of these leading factors is endowed with a univariate GARCH structure, while the remaining eigenvalues are kept constant over time. Joint maximum likelihood estimation of all model parameters is performed via an expectation maximization algorithm, and is applicable in high dimensions. The new model generates realistic correlation forecasts even for large asset universes and captures rising pairwise correlations in periods of market distress better than numerous competing models. Moreover, it leads to improved forecasts of an eigenvalue-based financial systemic risk indicator. Crucially, it generates portfolios with much lower turnover and superior risk-adjusted returns net of transaction costs, outperforming the equally weighted strategy even under high transaction fees. |
| Keywords: | Dynamic Conditional Correlations; Multivariate GARCH; Multivariate Generalized Hyperbolic Distribution; Principle Component Analysis; Financial Systemic Risk |
| JEL: | C32 C53 G11 G17 |
| Date: | 2019–09 |
| URL: | http://d.repec.org/n?u=RePEc:chf:rpseri:rp1951&r=all |
| By: | Jose Apesteguia; Miguel Ángel Ballester; Angelo Gutierrez |
| Abstract: | We develop a simple, tractable and sound stochastic framework for the joint treatment of risk and time preferences, in order to facilitate the estimation of risk and time attitudes. In so doing we: (i) study deterministic models of risk and time preferences paying special attention to their comparative statics, (ii) embed the deterministic models and their comparative statics within the random utility framework, and (iii) show how to estimate them, illustrating this exercise on several experimental datasets. |
| Keywords: | risk preferences, time preferences, comparative statics, stochastic choice; random utility models, discrete choice |
| JEL: | C01 D01 |
| Date: | 2019–09 |
| URL: | http://d.repec.org/n?u=RePEc:bge:wpaper:1117&r=all |
| By: | Laura Garcia-Jorcano (Department of Economic Analysis and Finance (Area of Financial Economics), Facultad de Ciencias Jurídicas y Sociales Universidad de Castilla-La Mancha, Toledo, Spain.); Alfonso Novales (Instituto Complutense de Análisis Económico (ICAE), and Department of Economic Analysis, Facultad de Ciencias Económicas y Empresariales, Universidad Complutense, 28223 Madrid, Spain.) |
| Abstract: | We introduce three dominance criteria to compare the performance of alternative VaR forecasting models. The three criteria use the information provided by a battery of VaR validation tests based on the frequency and size of exceedances, offering the possibility of efficiently summarizing a large amount of statistical information. They do not require the use of any loss function defined on the difference between VaR forecasts and observed returns, and two of the criteria are not conditioned on any significance level for the VaR tests. We use them to explore the potential for 1-day ahead VaR forecasting of some recently proposed asymmetric probability distributions for return innovations, as well as to compare the APARCH and FGARCH volatility specifications with more standard alternatives. Using 19 assets of different nature, the three criteria lead to similar conclusions, suggesting that the unbounded Johnson SU, the skewed Student-t and the skewed Generalized-t distributions seem to produce the best VaR forecasts. The added flexibility of a free power parameter in the conditional volatility in the APARCH and FGARCH models leads to a better fit to return data, but it does not improve upon the VaR forecasts provided by GARCH and GJR-GARCH volatilities. |
| Keywords: | Value at risk; Backtesting; Forecast evaluation; Dominance; Conditional volatility models; Asymmetric distributions. |
| JEL: | C52 C58 G17 G32 |
| Date: | 2019–09 |
| URL: | http://d.repec.org/n?u=RePEc:ucm:doicae:1923&r=all |
| By: | Laura Garcia-Jorcano (Department of Economic Analysis and Finance (Area of Financial Economics), Facultad de Ciencias Jurídicas y Sociales, Universidad de Castilla-La Mancha, Toledo, Spain.); Alfonso Novales (Instituto Complutense de Análisis Económico (ICAE), and Department of Economic Analysis, Facultad de Ciencias Económicas y Empresariales, Universidad Complutense, 28223 Madrid, Spain.) |
| Abstract: | We provide evidence suggesting that the assumption on the probability distribution for return in- novations is more influential for Value at Risk (VaR) performance than the conditional volatility specification. We also show that some recently proposed asymmetric probability distributions and the APARCH and FGARCH volatility specifications beat more standard alternatives for VaR fore- casting, and they should be preferred when estimating tail risk. The flexibility of the free power parameter in conditional volatility in the APARCH and FGARCH models explains their better performance. Indeed, our estimates suggest that for a number of financial assets, the dynamics of volatility should be specified in terms of the conditional standard deviation. We draw our results on VaR forecasting performance from i) a variety of backtesting approaches, ii) the Model Confi- dence Set approach, as well as iii) establishing a ranking among alternative VaR models using a precedence criterion that we introduce in this paper. |
| Keywords: | Value-at-risk; Backtesting; Evaluating forecasts; Precedence; APARCH model; Asym- metric distributions. |
| Date: | 2019–09 |
| URL: | http://d.repec.org/n?u=RePEc:ucm:doicae:1926&r=all |
| 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, called particle rolling Markov chain Monte Carlo (MCMC)with double block sampling. In our method, which is based on Sequential Monte Carlo(SMC), particles are sequentially updated to approximate the posterior distribution foreach window by learning new information and discarding old information from obser-vations. Th particles are refreshed with an MCMC algorithm when the importanceweights degenerate. To avoid degeneracy, which is crucial for reducing the computa-tion time, we introduce a block sampling scheme and generate multiple candidates bythe algorithm based on the conditional SMC. The theoretical discussion shows thatthe proposed methodology with a nested structure is expressed as SMC sampling forthe augmented space to provide the justification. The computational performance isevaluated in illustrative examples, showing that the posterior distributions of the modelparameters are accurately estimated. The proofs and additional discussions (algorithmsand experimental results) are provided in the Supplementary Material. |
| Date: | 2019–09 |
| URL: | http://d.repec.org/n?u=RePEc:tky:fseres:2019cf1126&r=all |