Robust Hierarchical Bayes Small Area Estimation for the Nested Error Linear Regression Model

Standard model‐based small area estimates perform poorly in presence of outliers. Sinha & Rao ( 2009 ) developed robust frequentist predictors of small area means. In this article, we present a robust Bayesian method to handle outliers in unit‐level data by extending the nested error regression model. We consider a finite mixture of normal distributions for the unit‐level error to model outliers and produce noninformative Bayes predictors of small area means. Our modelling approach generalises that of Datta & Ghosh ( 1991 ) under the normality assumption. Application of our method to a data set which is suspected to contain an outlier confirms this suspicion, correctly identifies the suspected outlier and produces robust predictors and posterior standard deviations of the small area means. Evaluation of several procedures including the M‐quantile method of Chambers & Tzavidis ( 2006 ) via simulations shows that our proposed method is as good as other procedures in terms of bias, variability and coverage probability of confidence and credible intervals when there are no outliers. In the presence of outliers, while our method and Sinha–Rao method perform similarly, they improve over the other methods. This superior performance of our procedure shows its dual (Bayes and frequentist) dominance, which should make it attractive to all practitioners, Bayesians and frequentists, of small area estimation.     

Modelling Group Heterogeneity for Small Area Estimation Using M‐Quantiles

Small area estimation typically requires model‐based methods that depend on isolating the contribution to overall population heterogeneity associated with group (i.e. small area) membership. One way of doing this is via random effects models with latent group effects. Alternatively, one can use an M‐quantile ensemble model that assigns indices to sampled individuals characterising their contribution to overall sample heterogeneity. These indices are then aggregated to form group effects. The aim of this article is to contrast these two approaches to characterising group effects and to illustrate them in the context of small area estimation. In doing so, we consider a range of different data types, including continuous data, count data and binary response data.     

Benchmarked Estimators for a Small Area Mean Under a Onefold Nested Regression Model

In this paper, we modify small area estimators, based on the unit‐level model, so that they add up to reliable higher‐level estimates of population totals. These modifications result in benchmarked small area estimators. We consider two benchmarking procedures. One is based on augmenting the unit‐level model with a suitable variable. The other one uses the calibrated weights of the direct estimators that are reliable at the higher levels. These weights are used in estimators that are based on the aggregation of the unit‐level model for each small area. The mean squared error estimators of the proposed benchmarked estimators are obtained by suitably modifying those associated with the corresponding non benchmarked estimators. The properties of the estimators are evaluated via simulation.     

Estimation of Randomisation Mean Square Error in Small Area Estimation

In this article, we propose a new method for estimating the randomisation (design‐based) mean squared error (DMSE) of model‐dependent small area predictors. Analogously to classical survey sampling theory, the DMSE considers the finite population values as fixed numbers and accounts for the MSE of small area predictors over all possible sample selections. The proposed method models the true DMSE as computed for synthetic populations and samples drawn from them, as a function of known statistics and then applies the model to the original sample. Several simulation studies for the linear area‐level model and the unit‐level mixed logistic model illustrate the performance of the proposed method and compare it with the performance of other DMSE estimators proposed in the literature.     

Small Area Quantile Estimation

Sample surveys are widely used to obtain information about totals, means, medians and other parameters of finite populations. In many applications, similar information is desired for subpopulations such as individuals in specific geographic areas and socio‐demographic groups. When the surveys are conducted at national or similarly high levels, a probability sampling can result in just a few sampling units from many unplanned subpopulations at the design stage. Cost considerations may also lead to low sample sizes from individual small areas. Estimating the parameters of these subpopulations with satisfactory precision and evaluating their accuracy are serious challenges for statisticians. To overcome the difficulties, statisticians resort to pooling information across the small areas via suitable model assumptions, administrative archives and census data. In this paper, we develop an array of small area quantile estimators. The novelty is the introduction of a semiparametric density ratio model for the error distribution in the unit‐level nested error regression model. In contrast, the existing methods are usually most effective when the response values are jointly normal. We also propose a resampling procedure for estimating the mean square errors of these estimators. Simulation results indicate that the new methods have superior performance when the population distributions are skewed and remain competitive otherwise.     

Weak and Strong Cross‐Sectional Dependence: A Panel Data Analysis of International Technology Diffusion

This paper provides an econometric examination of technological knowledge spillovers among countries by focusing on the issue of error cross‐sectional dependence, particularly on the different ways—weak and strong—that this dependence may affect model specification and estimation. A preliminary analysis based on estimation of the exponent of cross‐sectional dependence provides a clear result in favor of strong cross‐sectional dependence. This result has relevant implications in terms of econometric modeling and suggests that a factor structure is preferable to a spatial error model. The common correlated effects approach is then used because it remains valid in a variety of situations that are likely to occur, such as the presence of both forms of dependence or the existence of nonstationary factors. According to the estimation results, richer countries benefit more from domestic R&D and geographic spillovers than poorer countries, while smaller countries benefit more from spillovers originating from trade. The results also suggest that when the problem of (possibly many) correlated unobserved factors is addressed the quantity of education no longer has a significant effect. Finally, a comparison of the results with those obtained from a spatial model provides interesting insights into the bias that may arise when we allow only for weak dependence, despite the presence of strong dependence in the data. Copyright © 2016 John Wiley & Sons, Ltd.     

Robust Small Area Estimation under Spatial Non‐stationarity

The effective use of spatial information in a regression‐based approach to small area estimation is an important practical issue. One approach to account for geographic information is by extending the linear mixed model to allow for spatially correlated random area effects. An alternative is to include the spatial information by a non‐parametric mixed models. Another option is geographic weighted regression where the model coefficients vary spatially across the geography of interest. Although these approaches are useful for estimating small area means efficiently under strict parametric assumptions, they can be sensitive to outliers. In this paper, we propose robust extensions of the geographically weighted empirical best linear unbiased predictor. In particular, we introduce robust projective and predictive estimators under spatial non‐stationarity. Mean squared error estimation is performed by two analytic approaches that account for the spatial structure in the data. Model‐based simulations show that the methodology proposed often leads to more efficient estimators. Furthermore, the analytic mean squared error estimators introduced have appealing properties in terms of stability and bias. Finally, we demonstrate in the application that the new methodology is a good choice for producing estimates for average rent prices of apartments in urban planning areas in Berlin.     

Building micro‐foundations for the routines,capabilities, and performance links

Micro‐foundations have become an important emerging theme in strategic management. This paper addresses micro‐foundations in two related ways. First, we argue that the kind of macro (or ‘collectivist') explanation that is presently utilized in the capabilities view in strategic management—which implies a neglect of micro‐foundations—is incomplete. There are no mechanisms that work solely on the macro‐level, directly connecting routines and capabilities to firm‐level outcomes. While routines and capabilities are useful shorthand for complicated patterns of individual action and interaction, ultimately they are best understood at the micro‐level. Second, we provide a formal model that shows precisely why macro‐explanation is incomplete and which exemplifies how explicit micro‐foundations may be built for notions of routines and capabilities and how these impact firm performance. Copyright © 2008 John Wiley & Sons, Ltd.     

Two applications of wild bootstrap methods to improve inference in cluster‐IV models

Microeconomic data often have within‐cluster dependence, which affects standard error estimation and inference. When the number of clusters is small, asymptotic tests can be severely oversized. In the instrumental variables (IV) model, the potential presence of weak instruments further complicates hypothesis testing. We use wild bootstrap methods to improve inference in two empirical applications with these characteristics. Building from estimating equations and residual bootstraps, we identify variants robust to the presence of weak instruments and a small number of clusters. They reduce absolute size bias significantly and demonstrate that the wild bootstrap should join the standard toolkit in IV and cluster‐dependent models.     

crs: A PACKAGE FOR NONPARAMETRIC SPLINE ESTIMATION IN R

crs is a library for R written by Jeffrey S. Racine (Maintainer) and Zhenghua Nie. This add‐on package provides a collection of functions for spline‐based nonparametric estimation of regression functions with both continuous and categorical regressors. Currently, the crs package integrates data‐driven methods for selecting the spline degree, the number of knots and the necessary bandwidths for nonparametric conditional mean, IV and quantile regression. A function for multivariate density spline estimation with mixed data is also currently in the works. As a bonus, the authors have also provided the first simple R interface to the NOMAD (‘nonsmooth mesh adaptive direct search’) optimization solver which can be applied to solve other mixed integer optimization problems that future users might find useful in other settings. Although the crs package shares some of the same functionalities as its kernel‐based counterpart—the np package by the same author—it currently lacks some of the features the np package provides, such as hypothesis testing and semiparametric estimation. However, what it lacks in breadth, crs makes up in speed. A Monte Carlo experiment in this review uncovers sizable speed gains compared to its np counterpart, with a marginal loss in terms of goodness of fit. Therefore, the package will be extremely useful for applied econometricians interested in employing nonparametric techniques using large amounts of data with a small number of discrete covariates. Copyright © 2014 John Wiley & Sons, Ltd.     

Regional dimensions of factor and fuel substitution in U.S. manufacturing

This paper analyzes the regional responses to price increases in U.S. manufacturing in the form of fuel and factor substitution. A translog specification of a production process with eight inputs organized into a two stage optimization process — optimizing the mix of four fuels that constitute the energy input and then optimizing the input mix of physical capital, working capital, labor and aggregate energy — is used. Sectoral and regional variations in factor and fuel substitutions as evident from econometric estimation of the model at the level of 50 states and four census regions are discussed and interpreted.     

Structural estimation of behavioral heterogeneity

We develop a behavioral asset pricing model in which agents trade in a market with information friction. Profit‐maximizing agents switch between trading strategies in response to dynamic market conditions. Owing to noisy private information about the fundamental value, the agents form different evaluations about heterogeneous strategies. We exploit a thin set—a small sub‐population—to point identify this nonlinear model, and estimate the structural parameters using extended method of moments. Based on the estimated parameters, the model produces return time series that emulate the moments of the real data. These results are robust across different sample periods and estimation methods.     

Spatial clustering of time series via mixture of autoregressions models and Markov random fields

Time series data arise in many medical and biological imaging scenarios. In such images, a time series is obtained at each of a large number of spatially dependent data units. It is interesting to organize these data into model‐based clusters. A two‐stage procedure is proposed. In stage 1, a mixture of autoregressions (MoAR) model is used to marginally cluster the data. The MoAR model is fitted using maximum marginal likelihood (MMaL) estimation via a minorization–maximization (MM) algorithm. In stage 2, a Markov random field (MRF) model induces a spatial structure onto the stage 1 clustering. The MRF model is fitted using maximum pseudolikelihood (MPL) estimation via an MM algorithm. Both the MMaL and MPL estimators are proved to be consistent. Numerical properties are established for both MM algorithms. A simulation study demonstrates the performance of the two‐stage procedure. An application to the segmentation of a zebrafish brain calcium image is presented.     

A Unifying Framework for Marginalised Random‐Intercept Models of Correlated Binary Outcomes

We demonstrate that many current approaches for marginal modelling of correlated binary outcomes produce likelihoods that are equivalent to the copula‐based models herein. These general copula models of underlying latent threshold random variables yield likelihood‐based models for marginal fixed effects estimation and interpretation in the analysis of correlated binary data with exchangeable correlation structures. Moreover, we propose a nomenclature and set of model relationships that substantially elucidates the complex area of marginalised random‐intercept models for binary data. A diverse collection of didactic mathematical and numerical examples are given to illustrate concepts. Copyright © 2013 John Wiley & Sons, Ltd.     

Planning an emergency department holding unit

A generalized computer simulation model of the queuing process in an emergency department holding unit has been developed to evaluate the effects of changes in demand and utilization policies upon the congestion level in the unit. Bed utilization percentages, census level and daily service level are the criteria used to measure congestion. The model is also used to determine when additional staff are needed and to investigate the extent to which economies of scale exist. The Springfield Hospital Medical Center holding unit is used to demonstrate how this model may be utilized.     

Combining Time Variation and Mixed Frequencies: an Analysis of Government Spending Multipliers in Italy

In this paper, we propose a time‐varying parameter vector autoregression (VAR) model with stochastic volatility which allows for estimation on data sampled at different frequencies. Our contribution is twofold. First, we extend the methodology developed by Cogley and Sargent (Drifts and volatilities: monetary policies and outcomes in the post WWII U.S. Review of Economic Studies 2005; 8 : 262–302) and Primiceri (Time varying structural vector autoregressions and monetary policy. Review of Economic Studies 2005; 72 : 821–852) to a mixed‐frequency setting. In particular, our approach allows for the inclusion of two different categories of variables (high‐frequency and low‐frequency) into the same time‐varying model. Second, we use this model to study the macroeconomic effects of government spending shocks in Italy over the 1988:Q4–2013:Q3 period. Italy—as well as most other euro area economies—is characterized by short quarterly time series for fiscal variables, whereas annual data are generally available for a longer sample before 1999. Our results show that the proposed time‐varying mixed‐frequency model improves on the performance of a simple linear interpolation model in generating the true path of the missing observations. Second, our empirical analysis suggests that government spending shocks tend to have positive effects on output in Italy. The fiscal multiplier, which is maximized at the 1‐year horizon, follows a U‐shape over the sample considered: it peaks at around 1.5 at the beginning of the sample; it then stabilizes between 0.8 and 0.9 from the mid 1990s to the late 2000s, before rising again to above unity during the recent crisis. Copyright © 2015 John Wiley & Sons, Ltd.     

Is gravity linear?

Despite the solid theoretical foundation on which the gravity model of bilateral trade is based, empirical implementation requires several assumptions which do not follow directly from the underlying theory. First, unobserved trade costs are assumed to be a (log‐)linear function of observables. Second, the effects of trade costs on trade flows are assumed to be constant across country pairs. Maintaining consistency with the underlying theory, but relaxing these assumptions, we estimate gravity models—in levels and logs—using two data sets via nonparametric methods. The results are striking. Despite the added flexibility of the nonparametric models, parametric models based on these assumptions offer equally or more reliable in‐sample predictions and out‐of‐sample forecasts in the majority of cases, particularly in the levels model. Moreover, formal statistical tests fail to reject either parametric functional form. Thus, concerns in the gravity literature over functional form appear unwarranted, and estimation of the gravity model in levels is recommended. Copyright © 2008 John Wiley & Sons, Ltd.     

Discrete choice models and the housing price and travel to work elasticities of location demand

Multinomial logit and nested logit models of mode choice in travel to work and housing location choice are estimated from 1970 U.S. census data aggregated to small zones of the Chicago SMSA. The estimated models are then used to derive the “housing rent,” “travel time,” and “travel cost” elasticities of location demand. The effects of sampling variation, sample size, attribute inclusion, model specification, and estimation method on the estimated elasticities are evaluated and found to be important. The elasticities are also compared and found to agree with those obtained from other discrete choice models and, in the case of “housing rent,” with estimates obtained from models based on other theoretical structure.     

Efficient estimation of factor models with time and cross‐sectional dependence

This paper studies the efficient estimation of large‐dimensional factor models with both time and cross‐sectional dependence assuming (N,T) separability of the covariance matrix. The asymptotic distribution of the estimator of the factor and factor‐loading space under factor stationarity is derived and compared to that of the principal component (PC) estimator. The paper also considers the case when factors exhibit a unit root. We provide feasible estimators and show in a simulation study that they are more efficient than the PC estimator in finite samples. In application, the estimation procedure is employed to estimate the Lee–Carter model and life expectancy is forecast. The Dutch gender gap is explored and the relationship between life expectancy and the level of economic development is examined in a cross‐country comparison.     

Asymmetry and nonstationarity for a seasonal time series model

Tests for symmetry and seasonal unit roots are developed for an extended model of Hylleberg et al. (1990. Seasonal integration and cointegration. Journal Econometrics 44, 215–238.) which can represent both partial seasonal unit roots and threshold effects. Methods based on ordinary least squares (OLS) estimation and instrumental variable (IV) estimation are proposed and compared. For adjusting mean functions, ordinary mean adjustment and recursive mean adjustment are both considered. Several tests are constructed from various combination of estimation schemes and mean adjustment schemes. Among the tests, the tests based on IV-estimation are recommended because they have very simple limiting null distributions and have finite sample power properties comparable to those based on the OLSE. The recommended tests are applied to a US unemployment rate data set and find evidences for both nonstationarities associated with zero frequency and threshold effects.