Spurious relationships in high-dimensional systems with strong or mild persistence

This paper is concerned with the interactions of persistence and dimensionality in the context of the eigenvalue estimation problem of large covariance matrices arising in cointegration and principal component analysis. Following a review of the early and more recent developments in this area, we investigate the behaviour of these eigenvalues in a vector autoregression setting that blends pure unit root, local to unit root and mildly integrated components. Our results highlight the seriousness of spurious relationships that may arise in such big data environments even when the degree of persistence of the variables involved is mild and affects only a small proportion of a large data matrix, with important implications for forecasts based on principal component regressions and related methods. We argue that, prior to principal component analysis, first-differencing may be suitable even in stationary or nearly stationary environments.     

Nonparametric estimation of conditional distribution functions with longitudinal data and time-varying parametric models

Nonparametric estimation and inferences of conditional distribution functions with longitudinal data have important applications in biomedical studies. We propose in this paper an estimation approach based on time-varying parametric models. Our model assumes that the conditional distribution of the outcome variable at each given time point can be approximated by a parametric model, but the parameters are smooth functions of time. Our estimation is based on a two-step smoothing method, in which we first obtain the raw estimators of the conditional distribution functions at a set of disjoint time points, and then compute the final estimators at any time by smoothing the raw estimators. Asymptotic properties, including the asymptotic biases, variances and mean squared errors, are derived for the local polynomial smoothed estimators. Applicability of our two-step estimation method is demonstrated through a large epidemiological study of childhood growth and blood pressure. Finite sample properties of our procedures are investigated through simulation study.     

Nonparametric estimation and inference about the overlap of two distributions

This paper develops methodology for nonparametric estimation of a measure of the overlap of two distributions based on kernel estimation techniques. This quantity has been proposed as a measure of economic polarization between two groups, Anderson (2004) and Anderson et al. (2010). In ecology it has been used to measure the overlap of species. We give the asymptotic distribution theory of our estimator, which in some cases of practical relevance is nonstandard due to a boundary value problem. We also propose a method for conducting inference based on estimation of unknown quantities in the limiting distribution and show that our method yields consistent inference in all cases we consider. We investigate the finite sample properties of our methods by simulation methods. We give an application to the study of polarization within China in recent years using household survey data from two provinces taken in 1987 and 2001. We find a big increase in polarization between 1987 and 2001 according to monetary outcomes but less change in terms of living space.     

Difference‐in‐differences when the treatment status is observed in only one period

This paper considers the difference‐in‐differences (DID) method when the data come from repeated cross‐sections and the treatment status is observed either before or after the implementation of a program. We propose a new method that point‐identifies the average treatment effect on the treated (ATT) via a DID method when there is at least one proxy variable for the latent treatment. Key assumptions are the stationarity of the propensity score conditional on the proxy and an exclusion restriction that the proxy must satisfy with respect to the change in average outcomes over time conditional on the true treatment status. We propose a generalized method of moments estimator for the ATT and we show that the associated overidentification test can be used to test our key assumptions. The method is used to evaluate JUNTOS, a Peruvian conditional cash transfer program. We find that the program significantly increased the demand for health inputs among children and women of reproductive age.     

Estimation of the change point of a distribution based on the number of failed test items

This paper discusses the family of life distributions with failure rate functions which decrease initially until a change point and remain constant thereafter. The paper focuses on the estimation for the change point of the failure rate function. While point estimation of the change point of the failure rate function has been discussed by some authors, one can hardly find any existing work on the interval estimation of the change point. In this paper, a method for constructing approximate confidence intervals for the change point is proposed. The proposed approximate confidence intervals are based on the number of failed test items at or before a fixed inspection time. Received: September 1999     

Outlier‐Robust Bayesian Multinomial Choice Modeling

A Bayesian method for outlier‐robust estimation of multinomial choice models is presented. The method can be used for both correlated as well as uncorrelated choice alternatives and guarantees robustness towards outliers in the dependent and independent variables. To account for outliers in the response direction, the fat‐tailed multivariate Laplace distribution is used. Leverage points are handled via a shrinkage procedure. A simulation study shows that estimation of the model parameters is less influenced by outliers compared to non‐robust alternatives. An analysis of margarine scanner data shows how our method can be used for better pricing decisions. Copyright © 2015 John Wiley & Sons, Ltd.     

Some remarks on measurement errors and the identification of panel data models*

We demonstrate that despite the common worry about the possible correlations between the unobserved individual effects and the explanatory variables in panel data models the likelihood approach can provide a unified framework towards the study of the identification of a panel data model subject to measurement errors. In fact, it can also serve as a basis for deriving efficient estimation methods.     

Bayesian portfolio selection using a multifactor model

This article develops a new portfolio selection method using Bayesian theory. The proposed method accounts for the uncertainties in estimation parameters and the model specification itself, both of which are ignored by the standard mean-variance method. The critical issue in constructing an appropriate predictive distribution for asset returns is evaluating the goodness of individual factors and models. This problem is investigated from a statistical point of view; we propose using the Bayesian predictive information criterion. Two Bayesian methods and the standard mean-variance method are compared through Monte Carlo simulations and in a real financial data set. The Bayesian methods perform very well compared to the standard mean-variance method.     

Nonparametric dynamic panel data models: Kernel estimation and specification testing

Motivated by the first-differencing method for linear panel data models, we propose a class of iterative local polynomial estimators for nonparametric dynamic panel data models with or without exogenous regressors. The estimators utilize the additive structure of the first-differenced model—the fact that the two additive components have the same functional form, and the unknown function of interest is implicitly defined as a solution of a Fredholm integral equation of the second kind. We establish the uniform consistency and asymptotic normality of the estimators. We also propose a consistent test for the correct specification of linearity in typical dynamic panel data models based on the _L2$L_2$ distance of our nonparametric estimates and the parametric estimates under the linear restriction. We derive the asymptotic distributions of the test statistic under the null hypothesis and a sequence of Pitman local alternatives, and prove its consistency against global alternatives. Simulations suggest that the proposed estimators and tests perform well for finite samples. We apply our new method to study the relationships among economic growth, the initial economic condition and capital accumulation, and find a significant nonlinear relation between economic growth and the initial economic condition.     

部分线性单指数动态面板模型的惩罚二次推断函数估计

本文将个体效应与模型的线性部分和非线性部分同时进行估计,构建了惩罚二次推断函数估计法,估计了个体内具有自相关结构的随机效应部分线性单指数动态面板模型。该方法的优点是能够克服由个体效应引起的内生性问题,因此无论滞后因变量处于线性部分还是处于非参数部分均可得到一致有效的估计。进一步,本文证明了该估计方法的一致性和渐近正态性,同时还用Monte Carlo模拟实验评估了该估计方法在有限样本下的表现。     

Panel data models with multiple time-varying individual effects

This paper considers a panel data model with time-varying individual effects. The data are assumed to contain a large number of cross-sectional units repeatedly observed over a fixed number of time periods. The model has a feature of the fixed-effects model in that the effects are assumed to be correlated with the regressors. The unobservable individual effects are assumed to have a factor structure. For consistent estimation of the model, it is important to estimate the true number of individual effects. We propose a generalized methods of moments procedure by which both the number of individual effects and the regression coefficients can be consistently estimated. Some important identification issues are also discussed. Our simulation results indicate that the proposed methods produce reliable estimates.     

The effect of estimation method and sample size in multilevel structural equation modeling

Multilevel structural equation modeling (multilevel SEM) has become an established method to analyze multilevel multivariate data. The first useful estimation method was the pseudobalanced method. This method is approximate because it assumes that all groups have the same size, and ignores unbalance when it exists. In addition, full information maximum likelihood (ML) estimation is now available, which is often combined with robust chi‐squares and standard errors to accommodate unmodeled heterogeneity (MLR). In addition, diagonally weighted least squares (DWLS) methods have become available as estimation methods. This article compares the pseudobalanced estimation method, ML(R), and two DWLS methods by simulating a multilevel factor model with unbalanced data. The simulations included different sample sizes at the individual and group levels and different intraclass correlation (ICC). The within‐group part of the model posed no problems. In the between part of the model, the different ICC sizes had no effect. There is a clear interaction effect between number of groups and estimation method. ML reaches unbiasedness fastest, then the two DWLS methods, then MLR, and then the pseudobalanced method (which needs more than 200 groups). We conclude that both ML(R) and DWLS are genuine improvements on the pseudobalanced approximation. With small sample sizes, the robust methods are not recommended.     

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.     

Nonlinear IV unit root tests in panels with cross-sectional dependency

We propose a unit root test for panels with cross-sectional dependency. We allow general dependency structure among the innovations that generate data for each of the cross-sectional units. Each unit may have different sample size, and therefore unbalanced panels are also permitted in our framework. Yet, the test is asymptotically normal, and does not require any tabulation of the critical values. Our test is based on nonlinear IV estimation of the usual augmented Dickey–Fuller type regression for each cross-sectional unit, using as instruments nonlinear transformations of the lagged levels. The actual test statistic is simply defined as a standardized sum of individual IV t-ratios. We show in the paper that such a standardized sum of individual IV t-ratios has limit normal distribution as long as the panels have large individual time series observations and are asymptotically balanced in a very weak sense. We may have the number of cross-sectional units arbitrarily small or large. In particular, the usual sequential asymptotics, upon which most of the available asymptotic theories for panel unit root models heavily rely, are not required. Finite sample performance of our test is examined via a set of simulations, and compared with those of other commonly used panel unit root tests. Our test generally performs better than the existing tests in terms of both finite sample sizes and powers. We apply our nonlinear IV method to test for the purchasing power parity hypothesis in panels.     

Large time-varying parameter VARs

In this paper, we develop methods for estimation and forecasting in large time-varying parameter vector autoregressive models (TVP-VARs). To overcome computational constraints, we draw on ideas from the dynamic model averaging literature which achieve reductions in the computational burden through the use forgetting factors. We then extend the TVP-VAR so that its dimension can change over time. For instance, we can have a large TVP-VAR as the forecasting model at some points in time, but a smaller TVP-VAR at others. A final extension lies in the development of a new method for estimating, in a time-varying manner, the parameter(s) of the shrinkage priors commonly-used with large VARs. These extensions are operationalized through the use of forgetting factor methods and are, thus, computationally simple. An empirical application involving forecasting inflation, real output and interest rates demonstrates the feasibility and usefulness of our approach.     

Smoothing and Benchmarking for Small Area Estimation

Small area estimation is concerned with methodology for estimating population parameters associated with a geographic area defined by a cross-classification that may also include non-geographic dimensions. In this paper, we develop constrained estimation methods for small area problems: those requiring smoothness with respect to similarity across areas, such as geographic proximity or clustering by covariates, and benchmarking constraints, requiring weighted means of estimates to agree across levels of aggregation. We develop methods for constrained estimation decision theoretically and discuss their geometric interpretation. The constrained estimators are the solutions to tractable optimisation problems and have closed-form solutions. Mean squared errors of the constrained estimators are calculated via bootstrapping. Our approach assumes the Bayes estimator exists and is applicable to any proposed model. In addition, we give special cases of our techniques under certain distributional assumptions. We illustrate the proposed methodology using web-scraped data on Berlin rents aggregated over areas to ensure privacy.     

Nonparametric estimation of structural change points in volatility models for time series

We propose a hybrid estimation procedure that combines the least squares and nonparametric methods to estimate change points of volatility in time series models. Its main advantage is that it does not require any specific form of marginal or transitional densities of the process. We also establish the asymptotic properties of the estimators when the regression and conditional volatility functions are not known. The proposed tests for change points of volatility are shown to be consistent and more powerful than the nonparametric ones in the literature. Finally, we provide simulations and empirical results using the Hong Kong stock market index (HSI) series.     

Estimation of spatial autoregressive panel data models with fixed effects

This paper establishes asymptotic properties of quasi-maximum likelihood estimators for SAR panel data models with fixed effects and SAR disturbances. A direct approach is to estimate all the parameters including the fixed effects. Because of the incidental parameter problem, some parameter estimators may be inconsistent or their distributions are not properly centered. We propose an alternative estimation method based on transformation which yields consistent estimators with properly centered distributions. For the model with individual effects only, the direct approach does not yield a consistent estimator of the variance parameter unless T is large, but the estimators for other common parameters are the same as those of the transformation approach. We also consider the estimation of the model with both individual and time effects.     

An information-theoretic approach for forecasting interval-valued SP500 daily returns

We develop an iterative and efficient information-theoretic estimator for forecasting interval-valued data, and use our estimator to forecast the SP500 returns up to five days ahead using moving windows. Our forecasts are based on 13 years of data. We show that our estimator is superior to its competitors under all of the common criteria that are used to evaluate forecasts of interval data. Our approach differs from other methods that are used to forecast interval data in two major ways. First, rather than applying the more traditional methods that use only certain moments of the intervals in the estimation process, our estimator uses the complete sample information. Second, our method simultaneously selects the model (or models) and infers the model’s parameters. It is an iterative approach that imposes minimal structure and statistical assumptions.     

Does the labor-income process contain a unit root? Evidence from individual-specific time series

Calibrations of models related to life-cycle behavior of consumption and saving often invoke the important assumption of a unit root in individuals׳ labor-income process. We for the first time test this assumption using methods for univariate time series. Based on longitudinal register data from 1968 to 2005, we first estimate an autoregressive model for each individual using a method for approximately median-unbiased estimation. We then exploit the resulting distribution of the individual-specific estimates to draw inference about the presence of a unit root. Results indicate that earnings for the representative worker are governed by a process where shocks to earnings have moderate persistence and are both economically and statistically significantly different from having permanent effects. These results question the heavy use of unit-root processes for earnings.