Penalized Quantile Regression with Semiparametric Correlated Effects: An Application with Heterogeneous Preferences

This paper proposes new ?₁‐penalized quantile regression estimators for panel data, which explicitly allows for individual heterogeneity associated with covariates. Existing fixed‐effects estimators can potentially suffer from three limitations which are overcome by the proposed approach: (i) incidental parameters bias in nonlinear models with large N and small T ; (ii) lack of efficiency; and (iii) inability to estimate the effects of time‐invariant regressors. We conduct Monte Carlo simulations to assess the small‐sample performance of the new estimators and provide comparisons of new and existing penalized estimators in terms of quadratic loss. We apply the technique to an empirical example of the estimation of consumer preferences for nutrients from a demand model using a large transaction‐level dataset of household food purchases. We show that preferences for nutrients vary across the conditional distribution of expenditure and across genders, and emphasize the importance of fully capturing consumer heterogeneity in demand modeling. Copyright © 2016 John Wiley & Sons, Ltd.     

Model‐Assisted Regression Estimators for Longitudinal Data with Nonignorable Dropout

Estimation with longitudinal Y having nonignorable dropout is considered when the joint distribution of Y and covariate X is nonparametric and the dropout propensity conditional on (Y,X) is parametric. We apply the generalised method of moments to estimate the parameters in the nonignorable dropout propensity based on estimating equations constructed using an instrument Z, which is part of X related to Y but unrelated to the dropout propensity conditioned on Y and other covariates. Population means and other parameters in the nonparametric distribution of Y can be estimated based on inverse propensity weighting with estimated propensity. To improve efficiency, we derive a model‐assisted regression estimator making use of information provided by the covariates and previously observed Y‐values in the longitudinal setting. The model‐assisted regression estimator is protected from model misspecification and is asymptotically normal and more efficient when the working models are correct and some other conditions are satisfied. The finite‐sample performance of the estimators is studied through simulation, and an application to the HIV‐CD4 data set is also presented as illustration.     

Real‐time detection of regimes of predictability in the US equity premium

We propose new real‐time monitoring procedures for the emergence of end‐of‐sample predictive regimes using sequential implementations of standard (heteroskedasticity‐robust) regression t‐statistics for predictability applied over relatively short time periods. The procedures we develop can also be used for detecting historical regimes of temporary predictability. Our proposed methods are robust to both the degree of persistence and endogeneity of the regressors in the predictive regression and to certain forms of heteroskedasticity in the shocks. We discuss how the monitoring procedures can be designed such that their false positive rate can be set by the practitioner at the start of the monitoring period using detection rules based on information obtained from the data in a training period. We use these new monitoring procedures to investigate the presence of regime changes in the predictability of the US equity premium at the 1‐month horizon by traditional macroeconomic and financial variables, and by binary technical analysis indicators. Our results suggest that the 1‐month‐ahead equity premium has temporarily been predictable, displaying so‐called “pockets of predictability,” and that these episodes of predictability could have been detected in real time by practitioners using our proposed methodology.     

Estimating the conditional mode of a stationary stochastic process from noisy observations

Let {(X _i, Y _i,)}, i≥1, be a strictly stationary process from noisy observations. We examine the effect of the noise in the response Y and the covariates X on the nonparametric estimation of the conditional mode function. To estimate this function we are using deconvoluting kernel estimators. The asymptotic behavior of these estimators depends on the smoothness of the noise distribution, which is classified as either ordinary smooth or super smooth. Uniform convergence with almost sure convergence rates is established for strongly mixing stochastic processes, when the noise distribution is ordinary smooth. Received: April 1998     

A Survey of L1 Regression

L₁ regularization, or regularization with an L₁ penalty, is a popular idea in statistics and machine learning. This paper reviews the concept and application of L₁ regularization for regression. It is not our aim to present a comprehensive list of the utilities of the L₁ penalty in the regression setting. Rather, we focus on what we believe is the set of most representative uses of this regularization technique, which we describe in some detail. Thus, we deal with a number of L₁‐regularized methods for linear regression, generalized linear models, and time series analysis. Although this review targets practice rather than theory, we do give some theoretical details about L₁‐penalized linear regression, usually referred to as the least absolute shrinkage and selection operator (lasso).     

Estimation and testing of crossing‐points in fixed design regression

Many phenomena in the life sciences can be analyzed by using a fixed design regression model with a regression function m that exhibits a crossing‐point in the following sense: the regression function runs below or above its mean level, respectively, according as the input variable lies to the left or to the right of that crossing‐point, or vice versa. We propose a non‐parametric estimator and show weak and strong consistency as long as the crossing‐point is unique. It is defined as maximizing point arg max of a certain marked empirical process. For testing the hypothesis H₀ that the regression function m actually is constant (no crossing‐point), a decision rule is designed for the specific alternative H₁ that m possesses a crossing‐point. The pertaining test‐statistic is the ratio max/argmax of the maximum value and the maximizing point of the marked empirical process. Under the hypothesis the ratio converges in distribution to the corresponding ratio of a reflected Brownian bridge, for which we derive the distribution function. The test is consistent on the whole alternative and superior to the corresponding Kolmogorov–Smirnov test, which is based only on the maximal value max. Some practical examples of possible applications are given where a certain study about dental phobia is discussed in more detail.     

Dose–response modelling for bivariate covariates with and without a spike at zero: theory and application to binary outcomes

In epidemiology and clinical research, there is often a proportion of unexposed individuals resulting in zero values of exposure, meaning that some individuals are not exposed and those exposed have some continuous distribution. Examples are smoking or alcohol consumption. We will call these variables with a spike at zero (SAZ). In this paper, we performed a systematic investigation on how to model covariates with a SAZ and derived theoretical odds ratio functions for selected bivariate distributions. We consider the bivariate normal and bivariate log normal distribution with a SAZ. Both confounding and effect modification can be elegantly described by formalizing the covariance matrix given the binary outcome variable Y. To model the effect of these variables, we use a procedure based on fractional polynomials first introduced by Royston and Altman (1994, Applied Statistics 43: 429–467) and modified for the SAZ situation (Royston and Sauerbrei, 2008, Multivariable model‐building: a pragmatic approach to regression analysis based on fractional polynomials for modelling continuous variables, Wiley; Becher et al., 2012, Biometrical Journal 54: 686–700). We aim to contribute to theory, practical procedures and application in epidemiology and clinical research to derive multivariable models for variables with a SAZ. As an example, we use data from a case–control study on lung cancer.     

Missing Data: A Unified Taxonomy Guided by Conditional Independence

Recent work (Seaman et al., 2013 ; Mealli & Rubin, 2015 ) attempts to clarify the not always well‐understood difference between realised and everywhere definitions of missing at random (MAR) and missing completely at random. Another branch of the literature (Mohan et al., 2013 ; Pearl & Mohan, 2013 ) exploits always‐observed covariates to give variable‐based definitions of MAR and missing completely at random. In this paper, we develop a unified taxonomy encompassing all approaches. In this taxonomy, the new concept of ‘complementary MAR’ is introduced, and its relationship with the concept of data observed at random is discussed. All relationships among these definitions are analysed and represented graphically. Conditional independence, both at the random variable and at the event level, is the formal language we adopt to connect all these definitions. Our paper covers both the univariate and the multivariate case, where attention is paid to monotone missingness and to the concept of sequential MAR. Specifically, for monotone missingness, we propose a sequential MAR definition that might be more appropriate than both everywhere and variable‐based MAR to model dropout in certain contexts.     

Automobile insurance ratemaking in the presence of asymmetrical information

Automobile insurance is an example of a market where multi-period contracts are observed. This form of contract can be justified by asymmetrical information between the insurer and the insured. Insurers use risk classification together with bonus-malus systems. In this paper we show that the actual methodology for the integration of these two approaches can lead to inconsistencies. We develop a statistical model that adequately integrates risk classification and experience rating. For this purpose we present Poisson and negative binomial models with regression component in order to use all available information in the estimation of accident distribution. A bonus-malus system which integrates a priori and a posteriori information on an individual basis is proposed, and insurance premium tables are derived as a function of time, past accidents and the significant variables in the regression. Statistical results were obtained from a sample of 19,013 drivers.     

Characterizations of probability distributions via bivariate regression of record values

Bairamov et al. (Aust N Z J Stat 47:543–547, 2005) characterize the exponential distribution in terms of the regression of a function of a record value with its adjacent record values as covariates. We extend these results to the case of non-adjacent covariates. We also consider a more general setting involving monotone transformations. As special cases, we present characterizations involving weighted arithmetic, geometric, and harmonic means.     

Estimating Bayesian Decision Problems with Heterogeneous Expertise

We consider the recent novel two‐step estimator of Iaryczower and Shum (American Economic Review 2012; 102 : 202–237), who analyze voting decisions of US Supreme Court justices. Motivated by the underlying theoretical voting model, we suggest that where the data under consideration display variation in the common prior, estimates of the structural parameters based on their methodology should generally benefit from including interaction terms between individual and time covariates in the first stage whenever there is individual heterogeneity in expertise. We show numerically, via simulation and re‐estimation of the US Supreme Court data, that the first‐order interaction effects that appear in the theoretical model can have an important empirical implication. Copyright © 2015 John Wiley & Sons, Ltd.     

Plug‐in bandwidth selector for recursive kernel regression estimators defined by stochastic approximation method

In this paper, we propose an automatic selection of the bandwidth of the recursive kernel estimators of a regression function defined by the stochastic approximation algorithm. We showed that, using the selected bandwidth and the stepsize which minimize the mean weighted integrated squared error, the recursive estimator will be better than the non‐recursive one for small sample setting in terms of estimation error and computational costs. We corroborated these theoretical results through simulation study and a real dataset.     

Regression‐Kink Approach for Wage Effect on Male Work Hours

In finding the effect of after‐tax wage rate on work hours, the main difficulty is the endogeneity of after‐tax wage rate that equals ‘one minus average tax rate’ times wage rate. To overcome this endogeneity problem, we take advantage of jumps in the marginal income tax rate, which is a regression discontinuity (RD) idea. This RD, in turn, makes the average income tax rate ‘kink‐continuous’, which is a regression kink (RK) idea. We provide a simple economic model resulting in the RD and RK features, explain how to implement RK in practice, and then apply our methods to Korean male data. Our main RK‐based labour supply elasticity estimate 7.16% turned out to be insignificant with t‐value 1.52, but it is much larger than most estimates in the literature. This may be attributed to, among other things, the facts that the RK instrument is unique, that RK identifies only the local elasticity at the kink point and that RK requires large data as regression derivatives are estimated.     

Intergenerational Transmission of Fertility Patterns*

Recent studies by economists have focused on cultural transmission from the origin country rather than the origin family. Our paper extends this research by investigating how family‐specific‘cultural transmission’ can affect fertility rates. Following Machado and Santos Silva [Journal of the American Statistical Association (2005) Vol. 100, p. 1226] and Miranda [Journal of Population Economics (2008) Vol. 21, p. 67], we estimate count data quantile regression models using the British Household Panel Survey. We find that a woman's origin‐family size is positively associated with completed fertility in her destination family. A woman's country of birth also matters for her fertility. For a sub‐sample of continuously partnered men and women, both partners’ origin‐family sizes significantly affect destination‐family fertility.     

The Economic Consequences of Increased Disclosure: Evidence from Cross-Listings of Chinese Firms

In this paper, we investigate the impact of cross‐listings on information asymmetry risk, the cost of capital and firm value of a group of cross‐listed Chinese companies. Our paper is the first to examine the effect of cross‐listing on information asymmetry risk. Because cross‐listed firms are subject to increased disclosure requirements, increased regulatory scrutiny and increased legal liability, we propose that Chinese cross‐listed firms have lower information asymmetry risk, lower cost of capital and higher firm value than their non‐cross‐listed counterparts. We find in both univariate and multivariate tests that cross‐listed firms enjoyed lower information asymmetry risk in the domestic market compared with the non‐cross‐listed firms. We also find that cross‐listed firms have lower cost of capital in the cross‐listing market than non‐cross‐listed firms in the domestic markets. Finally, we find that cross‐listed firms are associated with higher firm value as measured by Tobin's Q. These results have implications for international investors and companies seeking cross‐listing opportunities.     

The Role of Corporate Sustainability in a Low‐Cost Business Model – A Case Study in the Scandinavian Fashion Industry

This multi‐level case study illustrates how corporate sustainability contributes to the low‐cost business model of a Scandinavian fashion company. Contrary to parts of the extant literature, we do not find that corporate sustainability directly adds measurable value (e.g. a better brand image); neither does it exert coercive control over critical supplier relationships. However, corporate sustainability minimizes the downside risk of the business model. It does so by (1) creating implicit contracts that reach beyond traditional ‘shareholder value’, (2) transferring risk to suppliers and (3) improving leadership by motivating management and employees, and by directing their attention to critical issues. For companies, we offer the insight that corporate sustainability is a necessary complement to shareholder value, even if the relationship is not obvious at first sight. We also suggest that concerted actions of companies or a positive connotation of certification create effective control over suppliers. As to public policy, we conclude that regulators could introduce mandatory disclosure of suppliers to facilitate controls through stakeholders, or alternatively an industry‐wide comply‐or‐explain code of conduct. We also address how regulators can take direct actions against countries with unsustainable labor policies. Last, we suggest future research topics, e.g. expanding the notion of a business model by interpreting ‘adding value’ as prevention of losses. Copyright © 2013 John Wiley & Sons, Ltd and ERP Environment.     

Existence of equilibria in economies with externalities and non-convexities in an infinite-dimensional commodity space

We prove an equilibrium existence theorem for economies with externalities, general types of non-convexities in the production sector, and infinitely many commodities. The consumption sets, the preferences of the consumers, and the production possibilities are represented by set-valued mappings to take into account the external effects. The firms set their prices according to general pricing rules which are supposed to have bounded losses and may depend upon the actions of the other economic agents. The commodity space is L_∞(M,M,μ), the space of all μ-essentially bounded M-measurable functions on M.As for our existence result, we consider the framework of Bewley (1972). However, there are four major problems in using this technique. To overcome two of these difficulties, we impose strong lower hemi-continuity assumptions upon the economies. The remaining problems are removed when the finite economies are large enough.Our model encompasses previous works on the existence of general equilibria when there are externalities and non-convexities but the commodity space is finite dimensional and those on general equilibria in non-convex economies with infinitely many commodities when no external effect is taken into account.     

Relative Value Relevance of Alternative Accounting Treatments for Unrealized Gains: Implications for the IASB

We investigate the relative value relevance of the alternative accounting methods for unrealized gains on investment properties in New Zealand (NZ). Using both the Likelihood‐ratio test and the F‐test, we find that, while preferred by the NZ standard setter, recognition of unrealized gains in the income statement is not superior to (or significantly different from) recognition of unrealized gains in revaluation reserve in terms of their value relevance. The results are robust to the different research methods we used. Our results have implications for the International Accounting Standards Board in terms of: (i) recognizing changes in fair values of investment properties in the income statement under the revised IAS 40: Investment Property in countries where “realization” refers to net income available for distribution; (ii) its intent to issue a standard on a single statement of comprehensive income; and (iii) its initiative to reduce or eliminate alternative accounting treatments for similar fact situations in its standards.     

Estimating the Kullback–Liebler risk based on multifold cross‐validation

This paper concerns a class of model selection criteria based on cross‐validation techniques and estimative predictive densities. Both the simple or leave‐one‐out and the multifold or leave‐m‐out cross‐validation procedures are considered. These cross‐validation criteria define suitable estimators for the expected Kullback–Liebler risk, which measures the expected discrepancy between the fitted candidate model and the true one. In particular, we shall investigate the potential bias of these estimators, under alternative asymptotic regimes for m. The results are obtained within the general context of independent, but not necessarily identically distributed, observations and by assuming that the candidate model may not contain the true distribution. An application to the class of normal regression models is also presented, and simulation results are obtained in order to gain some further understanding on the behavior of the estimators.     

On the Lp error of the Grenander-type estimator in the Cox model

We consider the Cox regression model and study the asymptotic global behavior of the Grenander-type estimator for a monotone baseline hazard function. This model is not included in the general setting of Durot (2007). However, we show that a similar central limit theorem holds for L_p-error of the Grenander-type estimator. As an illustration of application of our main result, we propose a test procedure for a Weibull baseline distribution, based on the L_p-distance between the Grenander estimator and a parametric estimator of the baseline hazard. Simulation studies are performed to investigate the performance of this test.