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on Econometrics |
| By: | Babii, Andrii |
| Abstract: | This paper provides novel methods for inference in a very general class of ill-posed models in econometrics, encompassing the nonparametric instrumental regression, different functional regressions, and the deconvolution. I focus on uniform confidence sets for the parameter of interest estimated with Tikhonov regularization, as in Darolles, Fan, Florens, and Renault (2011). I first show that it is not possible to develop inferential methods directly based on the uniform central limit theorem. To circumvent this difficulty I develop two approaches that lead to valid confidence sets. I characterize expected diameters and coverage properties uniformly over a large class of models (i.e. constructed confidence sets are honest). Finally, I illustrate that introduced confidence sets have reasonable width and coverage properties in samples commonly used in applications with Monte Carlo simulations and considering application to Engel curves. |
| Keywords: | nonparametric instrumental regression, functional linear regression, density deconvolution, honest uniform confidence sets, non-asymptotic inference, ill-posed models, Tikhonov regularization |
| JEL: | C14 |
| Date: | 2017–05 |
| URL: | http://d.repec.org/n?u=RePEc:tse:wpaper:31687&r=ecm |
| By: | Morais, Joanna; Thomas-Agnan, Christine; Simioni, Michel |
| Abstract: | When the aim is to model market-shares as a function of explanatory variables, the marketing literature proposes some regression models which can be qualified as attraction models. They are generally derived from an aggregated version of the multinomial logit model widely used in econometrics for discrete choice modeling. But aggregated multinomial logit models (MNL) and the so-called market-share models or generalized multiplicative competitive interaction models (GMCI) present some limitations: in their simpler version they do not specify brand-specific and cross-effect parameters. Introducing all possible cross effects is not possible in the MNL and would imply a very large number of parameters in the case of the GMCI. In this paper, we consider alternative models which are the Dirichlet covariate model (DIR) and the compositional model (CODA). DIR allows to introduce brand-specific parameters and CODA allows additionally to consider cross-effect parameters. We show that these last two models can be written in a similar fashion, called attraction form, as the MNL and the GMCI models. As market-share models are usually interpreted in terms of elasticities, we also use this notion to interpret the DIR and CODA models. We compare the main properties of the models in order to explain why CODA and DIR models can outperform traditional market-share models. The benefits of highlighting these relationships is on one hand to propose new models to the marketing literature and on the other hand to improve the interpretation of the CODA and DIR models using the elasticities of the econometrics literature. Finally, an application to the automobile market is presented where we model brands market-shares as a function of media investments, controlling for the brands average price and a scrapping incentive dummy variable. We compare the goodness-of-fit of the various models in terms of quality measures adapted to shares. |
| Keywords: | Multinomial logit; Market-shares models; Compositional data analysis; Dirichlet regression. |
| JEL: | C10 C25 C35 C46 D12 M31 |
| Date: | 2017–05 |
| URL: | http://d.repec.org/n?u=RePEc:tse:wpaper:31699&r=ecm |
| By: | Babii, Andrii; Florens, Jean-Pierre |
| Abstract: | We develop a uniform asymptotic expansion for the empirical distribution function of residuals in the nonparametric IV regression. Such expansion opens a door for construction of a broad range of residual-based specification tests in nonparametric IV models. Building on obtained result, we develop a test for the separability of unobservables in econometric models with endogeneity. The test is based on verifying the independence condition between residuals of the NPIV estimator and the instrument and can distinguish between the non-separable and the separable specification under endogeneity. |
| Keywords: | separability test, distribution of residuals, nonparametric instrumental regression,Sobolev scales |
| JEL: | C12 C14 |
| Date: | 2017–05 |
| URL: | http://d.repec.org/n?u=RePEc:tse:wpaper:31686&r=ecm |
| By: | Iacone, Fabrizio; Leybourne, Stephen J; Taylor, A M Robert |
| Abstract: | We develop a test, based on the Lagrange multiplier [LM] testing principle, for the value of the long memory parameter of a univariate time series that is composed of a fractionally integrated shock around a potentially broken deterministic trend. Our proposed test is constructed from data which are de-trended allowing for a trend break whose (unknown) location is estimated by a standard residual sum of squares estimator. We demonstrate that the resulting LM-type statistic has a standard limiting null chi-squared distribution with one degree of freedom, and attains the same asymptotic local power function as an infeasible LM test based on the true shocks. Our proposed test therefore attains the same asymptotic local optimality properties as an oracle LM test in both the trend break and no trend break environments. Moreover, and unlike conventional unit root and stationarity tests, this asymptotic local power function does not alter between the break and no break cases and so there is no loss in asymptotic local power from allowing for a trend break at an unknown point in the sample, even in the case where no break is present. We also report the results from a Monte Carlo study into the finite-sample behaviour of our proposed test. |
| Keywords: | Fractional integration; trend break; Lagrange multiplier test; asymptotically locally most powerful test |
| Date: | 2017–05 |
| URL: | http://d.repec.org/n?u=RePEc:esy:uefcwp:19654&r=ecm |
| By: | Hsu, Yu-Chin; Huber, Martin; Lai, Tsung Chih |
| Abstract: | Using a sequential conditional independence assumption, this paper discusses fully nonparametric estimation of natural direct and indirect causal effects in causal mediation analysis based on inverse probability weighting. We propose estimators of the average indirect effect of a binary treatment, which operates through intermediate variables (or mediators) on the causal path between the treatment and the outcome, as well as the unmediated direct effect. In a first step, treatment propensity scores given the mediator and observed covariates or given covariates alone are estimated by nonparametric series logit estimation. In a second step, they are used to reweigh observations in order to estimate the effects of interest. We establish root-n consistency and asymptotic normality of this approach as well as a weighted version thereof. The latter allows evaluating effects on specific subgroups like the treated, for which we derive the asymptotic properties under estimated propensity scores. We also provide a simulation study and an application to an information intervention about male circumcisions. |
| Keywords: | causal mechanisms; direct effects; indirect effects; causal channels; mediation analysis; causal pathways; series logit estimation; nonparametric estimation; inverse probability weighting; propensity score |
| JEL: | C21 |
| Date: | 2017–05–01 |
| URL: | http://d.repec.org/n?u=RePEc:fri:fribow:fribow00482&r=ecm |
| By: | Ferman, Bruno |
| Abstract: | We analyze the properties of matching estimators when the number of treated observations is fixed while the number of treated observations is large. We show that, under standard assumptions, the nearest neighbor matching estimator for the average treatment effect on the treated is asymptotically unbiased, even though this estimator is not consistent. We also provide a test based on the theory of randomization tests under approximate symmetry developed in Canay et al. (2014) that is asymptotically valid when the number of control observations goes to infinity. This is important because large sample inferential techniques developed in Abadie and Imbens (2006) would not be valid in this setting. |
| Keywords: | matching estimator, treatment effect, hypothesis testing, randomization inference |
| JEL: | C12 C13 C21 |
| Date: | 2017–05–04 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:78940&r=ecm |
| By: | John Aston; Florent Autin; Gerda Claeskens; Jean-Marc Freyermuth; Christophe Pouet |
| Abstract: | We present a novel method for detecting some structural characteristics of multidimensional functions. We consider the multidimensional Gaussian white noise model with an anisotropic estimand. Using the relation between the Sobol decomposition and the geometry of multidimensional wavelet basis we can build test statistics for any of the Sobol functional components. We assess the asymptotical minimax optimality of these test statistics and show that they are optimal in presence of anisotropy with respect to the newly determined minimax rates of separation. An appropriate combination of these test statistics allows to test some general structural characteristics such as the atomic dimension or the presence of some variables. Numerical experiments show the potential of our method for studying spatio-temporal processes. |
| Keywords: | Adaptation, Anisotropy, Atomic dimension, Besov spaces, Gaussian noise model, Hyperbolic wavelets, Hypothesis testing, Minimax rate, Sobol decomposition, Structural modeling |
| Date: | 2017–05 |
| URL: | http://d.repec.org/n?u=RePEc:ete:kbiper:582277&r=ecm |
| By: | Stavros J. Sioutis |
| Abstract: | The accuracy of least squares calibration using option premiums and particle filtering of price data to find model parameters is determined. Derivative models using exponential L\'evy processes are calibrated using regularized weighted least squares with respect to the minimal entropy martingale measure. Sequential importance resampling is used for the Bayesian inference problem of time series parameter estimation with proposal distribution determined using extended Kalman filter. The algorithms converge to their respective global optima using a highly parallelizable statistical optimization approach using a grid of initial positions. Each of these methods should produce the same parameters. We investigate this assertion. |
| Date: | 2017–05 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1705.04780&r=ecm |
| By: | Hiroyuki Kasahara (Vancouver School of Economics, University of British Columbia); Katsumi Shimotsu (Faculty of Economics, The University of Tokyo) |
| Abstract: | Testing the number of components in multivariate normal mixture models is a long-standing challenge. This paper develops a likelihood-based test of the null hypothesis of M 0 components against the alternative hypothesis of M 0 + 1 components. We derive a local quadratic approximation of the likelihood ratio statistic in terms of the polynomials of the parameters. Based on this quadratic approximation, we propose an EM test of the null hypothesis of M 0 components against the alternative hypothesis of M 0 + 1 components, and derive the asymptotic distribution of the proposed test statistic. The simulations show that the proposed test has good finite sample size and power properties. |
| Date: | 2017–03 |
| URL: | http://d.repec.org/n?u=RePEc:tky:fseres:2016cf1044&r=ecm |
| By: | Morais, Joanna; Thomas-Agnan, Christine; Simioni, Michel |
| Abstract: | Regression models have been developed for the case where the dependent variable is a vector of shares. Some of them, from the marketing literature, are easy to interpret but they are quite simple and can only be complexified at the expense of a very large number of parameters to estimate. Other models, from the mathematical literature, are called compositional regression models and are based on the simplicial geometry (a vector of shares is called a composition, shares are components, and a composition lies in the simplex). These models are transformation models: they use a log-ratio transformation of shares. They are very flexible in terms of explanatory variables and complexity (component-specific and cross-effect parameters), but their interpretation is not straightforward, due to the fact that shares add up to one. This paper combines both literatures in order to obtain a performing market-share model allowing to get relevant and appropriate interpretations, which can be used for decision making in practical cases. For example, we are interested in modeling the impact of media investments on automobile manufacturers sales. In order to take into account the competition, we model the brands market-shares as a function of (relative) media investments. We furthermore focus on compositional models where some explanatory variables are also compositional. Two specifications are possible: in Model A, a unique coefficient is associated to each compositional explanatory variable, whereas in Model B a compositional explanatory variable is associated to component-specific and cross-effect coefficients. Model A and Model B are estimated for our application in the B segment of the French automobile market, from 2003 to 2015. In order to enhance the interpretability of these models, we present different types of impact assessment measures (marginal effects, elasticities and odds ratios) and we show that elasticities are particularly useful to isolate the impact of an explanatory variable on a particular share. We show that elasticities can be equivalently computed from the transformed model and from the model in the simplex and that they are linked to directional C-derivatives of simplex-valued function of a simplex variable. Direct and cross effects of media investments are computed for both models. Model B shows interesting non-symmetric synergies between brands, and Renault seems to be the most elastic brand to its own media investments. In order to determine if component-specific and cross-effect parameters are needed to improve the quality of the model (Model B) or if a global parameter is reasonable (Model A), we compare the goodness-of-fit of the two models using (out-of-sample) quality measures adapted for share data. |
| Keywords: | Elasticity, odds ratio, marginal effect, compositional model, compositional differential calculus, market-shares, media investments impact |
| JEL: | C10 C25 C35 C46 D12 M31 |
| Date: | 2017–05 |
| URL: | http://d.repec.org/n?u=RePEc:tse:wpaper:31701&r=ecm |
| By: | Ziegel, Johanna F.; Krueger, Fabian; Jordan, Alexander; Fasciati, Fernando |
| Abstract: | Motivated by the Basel 3 regulations, recent studies have considered joint forecasts of Value-at-Risk and Expected Shortfall. A large family of scoring functions can be used to evaluate forecast performance in this context. However, little intuitive or empirical guidance is currently available, which renders the choice of scoring function awkward in practice. We therefore develop graphical checks (Murphy diagrams) of whether one forecast method dominates another under a relevant class of scoring functions, and propose an associated hypothesis test. We illustrate these tools with simulation examples and an empirical analysis of S&P 500 and DAX returns. |
| Date: | 2017–05–12 |
| URL: | http://d.repec.org/n?u=RePEc:awi:wpaper:0632&r=ecm |
| By: | Galeano San Miguel, Pedro; Ausín Olivera, María Concepción; Nguyen, Hoang |
| Abstract: | Copula densities are widely used to model the dependence structure of financial time series. However, the number of parameters involved becomes explosive in high dimensions which results in most of the models in the literature being static. Factor copula models have been recently proposed for tackling the curse of dimensionality by describing the behaviour of return series in terms of a few common latent factors. To account for asymmetric dependence in extreme events, we propose a class of dynamic one factor copula where the factor loadings are modelled as generalized autoregressive score (GAS) processes. We perform Bayesian inference in different specifications of the proposed class of dynamic one factor copula models. Conditioning on the latent factor, the components of the return series become independent, which allows the algorithm to run in a parallel setting and to reduce the computational cost needed to obtain the conditional posterior distributions of model parameters. We illustrate our approach with the analysis of a simulated data set and the analysis of the returns of 150 companies listed in the S&P500 index. |
| Keywords: | Parallel estimation; Generalized hyperbolic skew Student-t copula; GAS model; Factor copula models; Bayesian inference |
| Date: | 2017–05 |
| URL: | http://d.repec.org/n?u=RePEc:cte:wsrepe:24552&r=ecm |
| By: | JIN SEO CHO (Yonsei University); HALBERT WHITE (University of California, San Diego) |
| Abstract: | The current paper examines the limit distribution of the quasi-maximum likelihood estimator obtained from a directionally differentiable quasi-likelihood function and represents its limit distribution as a functional of a Gaussian stochastic process indexed by direction. In this way, the standard analysis that assumes a differentiable quasi-likelihood function is treated as a special case of our analysis. We also examine and redefine the standard quasi-likelihood ratio, Wald, and Lagrange multiplier test statistics so that their null limit behaviors are regular under our model framework. |
| Keywords: | directionally differentiable quasi-likelihood function, Gaussian stochastic process, quasilikelihood ratio test, Wald test, and Lagrange multiplier test statistics. |
| JEL: | C12 C13 C22 C32 |
| Date: | 2017–04 |
| URL: | http://d.repec.org/n?u=RePEc:yon:wpaper:2017rwp-103&r=ecm |
| By: | JIN SEO CHO (Yonsei University); HALBERT WHITE (University of California, San Diego) |
| Abstract: | We illustrate analyzing directionally differentiable econometric models and provide technical details which are not included in Cho and White (2017). |
| Keywords: | directionally differentiable quasi-likelihood function, Gaussian stochastic process, quasilikelihood ratio test, Wald test, and Lagrange multiplier test statistics, stochastic frontier production function, GMM estimation, Box-Cox transform. |
| JEL: | C12 C13 C22 C32 |
| Date: | 2017–04 |
| URL: | http://d.repec.org/n?u=RePEc:yon:wpaper:2017rwp-103a&r=ecm |
| By: | Thomas Gueuning; Gerda Claeskens |
| Abstract: | The focused information criterion for model selection is constructed to select the model that best estimates a particular quantity of interest, the focus, in terms of mean squared error. We extend this focused selection process to the high-dimensional regression setting with potentially a larger number of parameters than the size of the sample. We distinguish two cases: (i) the case where the considered submodel is of low-dimension and (ii) the case where it is of high-dimension. In the former case, we obtain an alternative expression of the low-dimensional focused information criterion that can directly be applied. In the latter case we use a desparsified estimator that allows us to derive the mean squared error of the focus estimator. We illustrate the performance of the high-dimensional focused information criterion with a numerical study and a real dataset. |
| Keywords: | Desparsified estimator, Focused information criterion, High-dimensional data, Variable selection |
| Date: | 2017–05 |
| URL: | http://d.repec.org/n?u=RePEc:ete:kbiper:582649&r=ecm |
| By: | Johanna F. Ziegel; Fabian Kr\"uger; Alexander Jordan; Fernando Fasciati |
| Abstract: | Motivated by the Basel 3 regulations, recent studies have considered joint forecasts of Value-at-Risk and Expected Shortfall. A large family of scoring functions can be used to evaluate forecast performance in this context. However, little intuitive or empirical guidance is currently available, which renders the choice of scoring function awkward in practice. We therefore develop graphical checks (Murphy diagrams) of whether one forecast method dominates another under a relevant class of scoring functions, and propose an associated hypothesis test. We illustrate these tools with simulation examples and an empirical analysis of S&P 500 and DAX returns. |
| Date: | 2017–05 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1705.04537&r=ecm |
| By: | Aurélien Poissonnier |
| Abstract: | Structural gravity models for trade stem from agnostic models of bilateral trade flows. Although more theoretically sound, they are much more complex to estimate. This difficulty is due to the multilateral resistance terms which account for the general equilibrium constraints of global trade and must be inferred from the rest of the model. In the present paper, I show that solving for these terms explicitly is a valid econometric approach for gravity models, including in panel data. I propose iterative solutions in Stata based on three different techniques. An example of these solutions on real data is presented. The results from this test confirm the necessity to account for the multilateral resistance terms in the estimation and raise some questions on the alternative solution using dummies. |
| JEL: | C13 F14 |
| Date: | 2016–12 |
| URL: | http://d.repec.org/n?u=RePEc:euf:dispap:040&r=ecm |
| By: | Li, Zhiyong; Lambe, Brendan; Adegbite, Emmanuel |
| Abstract: | In this paper, we introduce two low frequency bid-ask spread estimators using daily high and low transaction prices. The range of mid-prices is an increasing function of the sampling interval, while the bid-ask spread and the relationship between trading direction and the mid-price are not constrained by it and are therefore independent. Monte Carlo simulations and data analysis from the equity and foreign exchange markets demonstrate that these models significantly out-perform the most widely used low-frequency estimators, such as those proposed in Corwin and Schultz (2012) and most recently in Abdi and Ranaldo (2017). We illustrate how our models can be applied to deduce historical market liquidity in NYSE, UK, Hong Kong and the Thai stock markets. Our estimator can also effectively act as a gauge for market volatility and as a measure of liquidity risk in asset pricing. |
| Keywords: | High-low spread estimator; effective spread; transaction cost; market liquidity |
| JEL: | C02 C13 C15 |
| Date: | 2017–05 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:79102&r=ecm |
| By: | Chris J. Skinner; Jon Wakefield |
| Abstract: | We give a brief overview of common sampling designs used in a survey setting, and introduce the principal inferential paradigms under which data from complex surveys may be analyzed. In particular, we distinguish between design-based, model-based and model-assisted approaches. Simple examples highlight the key differences between the approaches. We discuss the interplay between inferential approaches and targets of inference and the important issue of variance estimation. |
| Keywords: | Design-based inference; model-assisted inference; model-based inference; weights; variance estimation. |
| JEL: | C1 |
| Date: | 2017 |
| URL: | http://d.repec.org/n?u=RePEc:ehl:lserod:76991&r=ecm |