21,592 research outputs found
Bayesian Semiparametric Hierarchical Empirical Likelihood Spatial Models
We introduce a general hierarchical Bayesian framework that incorporates a
flexible nonparametric data model specification through the use of empirical
likelihood methodology, which we term semiparametric hierarchical empirical
likelihood (SHEL) models. Although general dependence structures can be readily
accommodated, we focus on spatial modeling, a relatively underdeveloped area in
the empirical likelihood literature. Importantly, the models we develop
naturally accommodate spatial association on irregular lattices and irregularly
spaced point-referenced data. We illustrate our proposed framework by means of
a simulation study and through three real data examples. First, we develop a
spatial Fay-Herriot model in the SHEL framework and apply it to the problem of
small area estimation in the American Community Survey. Next, we illustrate the
SHEL model in the context of areal data (on an irregular lattice) through the
North Carolina sudden infant death syndrome (SIDS) dataset. Finally, we analyze
a point-referenced dataset from the North American Breeding Bird survey that
considers dove counts for the state of Missouri. In all cases, we demonstrate
superior performance of our model, in terms of mean squared prediction error,
over standard parametric analyses.Comment: 29 pages, 3 figue
Counterfactual Sensitivity and Robustness
Researchers frequently make parametric assumptions about the distribution of
unobservables when formulating structural models. Such assumptions are
typically motived by computational convenience rather than economic theory and
are often untestable. Counterfactuals can be particularly sensitive to such
assumptions, threatening the credibility of structural modeling exercises. To
address this issue, we leverage insights from the literature on ambiguity and
model uncertainty to propose a tractable econometric framework for
characterizing the sensitivity of counterfactuals with respect to a
researcher's assumptions about the distribution of unobservables in a class of
structural models. In particular, we show how to construct the smallest and
largest values of the counterfactual as the distribution of unobservables spans
nonparametric neighborhoods of the researcher's assumed specification while
other `structural' features of the model, e.g. equilibrium conditions, are
maintained. Our methods are computationally simple to implement, with the
nuisance distribution effectively profiled out via a low-dimensional convex
program. Our procedure delivers sharp bounds for the identified set of
counterfactuals (i.e. without parametric assumptions about the distribution of
unobservables) as the neighborhoods become large. Over small neighborhoods, we
relate our procedure to a measure of local sensitivity which is further
characterized using an influence function representation. We provide a suitable
sampling theory for plug-in estimators and apply our procedure to models of
strategic interaction and dynamic discrete choice
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Econometrics: A bird's eye view
As a unified discipline, econometrics is still relatively young and has been transforming and expanding very rapidly over the past few decades. Major advances have taken place in the analysis of cross sectional data by means of semi-parametric and non-parametric techniques. Heterogeneity of economic relations across individuals, firms and industries is increasingly acknowledge and attempts have been made to take them into account either by integrating out their effects or by modeling the sources of heterogeneity when suitable panel data exists. The counterfactual considerations that underlie policy analysis and treatment evaluation have been given a more satisfactory foundation. New time series econometric techniques have been developed and employed extensively in the areas of macroeconometrics and finance. Non-linear econometric techniques are used increasingly in the analysis of cross section and time series observations. Applications of Bayesian techniques to econometric problems have been given new impetus largely thanks to advances in computer power and computational techniques. The use of Bayesian techniques have in turn provided the investigators with a unifying framework where the tasks and forecasting, decision making, model evaluation and learning can be considered as parts of the same interactive and iterative process; thus paving the way for establishing the foundation of the "real time econometrics". This paper attempts to provide an overview of some of these developments
Lower Bounds on Exponential Moments of the Quadratic Error in Parameter Estimation
Considering the problem of risk-sensitive parameter estimation, we propose a
fairly wide family of lower bounds on the exponential moments of the quadratic
error, both in the Bayesian and the non--Bayesian regime. This family of
bounds, which is based on a change of measures, offers considerable freedom in
the choice of the reference measure, and our efforts are devoted to explore
this freedom to a certain extent. Our focus is mostly on signal models that are
relevant to communication problems, namely, models of a parameter-dependent
signal (modulated signal) corrupted by additive white Gaussian noise, but the
methodology proposed is also applicable to other types of parametric families,
such as models of linear systems driven by random input signals (white noise,
in most cases), and others. In addition to the well known motivations of the
risk-sensitive cost function (i.e., the exponential quadratic cost function),
which is most notably, the robustness to model uncertainty, we also view this
cost function as a tool for studying fundamental limits concerning the tail
behavior of the estimation error. Another interesting aspect, that we
demonstrate in a certain parametric model, is that the risk-sensitive cost
function may be subjected to phase transitions, owing to some analogies with
statistical mechanics.Comment: 28 pages; 4 figures; submitted for publicatio
Inverse Probability Weighted Generalised Empirical Likelihood Estimators: Firm Size and R&D Revisited
The inverse probability weighted Generalised Empirical Likelihood (IPW-GEL) estimator is proposed for the estimation of the parameters of a vector of possibly non-linear unconditional moment functions in the presence of conditionally independent sample selection or attrition.The estimator is applied to the estimation of the firm size elasticity of product and process R&D expenditures using a panel of German manufacturing firms, which is affected by attrition and selection into R&D activities.IPW-GEL and IPW-GMM estimators are compared in this application as well as identification assumptions based on independent and conditionally independent sample selection.The results are similar in all specifications.research and development;generalised emperical likelihood;inverse probability weighting;propensity score;conditional independence;missing at random;selection;attrition
A Globally Flexible Model for Crop Yields Under Weather Risk
The literature on climate change and crop yields recognizes the need to allow for highly non-linear marginal effects. This study combines these two areas of the literature by using Flexible Fourier Transforms (FFT’s) to ensure flexibility for both the time trend and the weather effects. This study also illustrates how FFT’s can be combined with quantile regression (QR) to provide both robustness to outliers and information on the scale effects of time and weather variables. For U.S. county level data on corn, soybeans, and winter wheat, we estimate the relationship between yield and temperature and precipitation using a traditional parametric expected-yield estimator, our quantile-FFT regression evaluated at the median, and our QR-FFT regression that incorporates information on the tails of the distribution. We find that quadratic terms are not sufficient for capturing nonlinearities in the relationship between yield and the explanatory variables.Crop yield distributions, flexible fourier transforms, quantile regression, Crop Production/Industries, Risk and Uncertainty,
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