Nonparametric Panel Estimation of Labor Supply

In this article, we estimate structural labor supply with piecewise-linear budgets and nonseparable endogenous unobserved heterogeneity. We propose a two-stage method to address the endogeneity issue that comes from the correlation between the covariates and unobserved heterogeneity. In the first stage, Evdokimov’s nonparametric de-convolution method serves to identify the conditional distribution of unobserved heterogeneity from the quasi-reduced model that uses panel data. In the second stage, the conditional distribution is plugged into the original structural model to estimate labor supply. We apply this methodology to estimate the labor supply of U.S. married men in 2004 and 2005. Our empirical work demonstrates that ignoring the correlation between the covariates and unobserved heterogeneity will bias the estimates of wage elasticities upward. The labor elasticity estimated from a fixed effects model is less than half of that obtained from a random effects model.     

A Test for Slope Heterogeneity in Fixed Effects Models

Typical panel data models make use of the assumption that the regression parameters are the same for each individual cross-sectional unit. We propose tests for slope heterogeneity in panel data models. Our tests are based on the conditional Gaussian likelihood function in order to avoid the incidental parameters problem induced by the inclusion of individual fixed effects for each cross-sectional unit. We derive the Conditional Lagrange Multiplier test that is valid in cases where N → ∞ and T is fixed. The test applies to both balanced and unbalanced panels. We expand the test to account for general heteroskedasticity where each cross-sectional unit has its own form of heteroskedasticity. The modification is possible if T is large enough to estimate regression coefficients for each cross-sectional unit by using the MINQUE unbiased estimator for regression variances under heteroskedasticity. All versions of the test have a standard Normal distribution under general assumptions on the error distribution as N → ∞. A Monte Carlo experiment shows that the test has very good size properties under all specifications considered, including heteroskedastic errors. In addition, power of our test is very good relative to existing tests, particularly when T is not large.     

Exponential class of dynamic binary choice panel data models with fixed effects

ABSTRACT

This paper proposes an exponential class of dynamic binary choice panel data models for the analysis of short T (time dimension) large N (cross section dimension) panel data sets that allow for unobserved heterogeneity (fixed effects) to be arbitrarily correlated with the covariates. The paper derives moment conditions that are invariant to the fixed effects which are then used to identify and estimate the parameters of the model. Accordingly, generalized method of moments (GMM) estimators are proposed that are consistent and asymptotically normally distributed at the root-N rate. We also study the conditional likelihood approach and show that under exponential specification, it can identify the effect of state dependence but not the effects of other covariates. Monte Carlo experiments show satisfactory finite sample performance for the proposed estimators and investigate their robustness to misspecification.     

Importance sampling for signal extraction model in time series analysis

In time series analysis, signal extraction model (SEM) is used to estimate unobserved signal component from observed time series data. Since parameters of the components in SEM are often unknown in practice, a commonly used method is to estimate unobserved signal component using the maximum likelihood estimates (MLEs) of parameters of the components. This paper explores an alternative way to estimate unobserved signal component when parameters of the components are unknown. The suggested method makes use of importance sampling (IS) with Bayesian inference. The basic idea is to treat parameters of the components in SEM as a random vector and compute a posterior probability density function of the parameters using Bayesian inference. Then IS method is applied to integrate out the parameters and thus estimates of unobserved signal component, unconditional to the parameters, can be obtained. This method is illustrated with a real time series data. Then a Monte Carlo study with four different types of time series models is carried out to compare a performance of this method with that of a commonly used method. The study shows that IS method with Bayesian inference is computationally feasible and robust, and more efficient in terms of mean square errors (MSEs) than a commonly used method.     

Testing for Slope Heterogeneity Bias in Panel Data Models

ABSTRACT

Standard econometric methods can overlook individual heterogeneity in empirical work, generating inconsistent parameter estimates in panel data models. We propose the use of methods that allow researchers to easily identify, quantify, and address estimation issues arising from individual slope heterogeneity. We first characterize the bias in the standard fixed effects estimator when the true econometric model allows for heterogeneous slope coefficients. We then introduce a new test to check whether the fixed effects estimation is subject to heterogeneity bias. The procedure tests the population moment conditions required for fixed effects to consistently estimate the relevant parameters in the model. We establish the limiting distribution of the test and show that it is very simple to implement in practice. Examining firm investment models to showcase our approach, we show that heterogeneity bias-robust methods identify cash flow as a more important driver of investment than previously reported. Our study demonstrates analytically, via simulations, and empirically the importance of carefully accounting for individual specific slope heterogeneity in drawing conclusions about economic behavior.     

Nonparametric Discrete Choice Models With Unobserved Heterogeneity

In this research, we provide a new method to estimate discrete choice models with unobserved heterogeneity that can be used with either cross-sectional or panel data. The method imposes nonparametric assumptions on the systematic subutility functions and on the distributions of the unobservable random vectors and the heterogeneity parameter. The estimators are computationally feasible and strongly consistent. We provide an empirical application of the estimator to a model of store format choice. The key insights from the empirical application are: (1) consumer response to cost and distance contains interactions and nonlinear effects, which implies that a model without these effects tends to bias the estimated elasticities and heterogeneity distribution, and (2) the increase in likelihood for adding nonlinearities is similar to the increase in likelihood for adding heterogeneity, and this increase persists as heterogeneity is included in the model.     

Semiparametric Analysis of Network Formation

ABSTRACT

We consider a statistical model for directed network formation that features both node-specific parameters that capture degree heterogeneity and common parameters that reflect homophily among nodes. The goal is to perform statistical inference on the homophily parameters while treating the node-specific parameters as fixed effects. Jointly estimating all parameters leads to incidental-parameter bias and incorrect inference. As an alternative, we develop an approach based on a sufficient statistic that separates inference on the homophily parameters from estimation of the fixed effects. The estimator is easy to compute and can be applied to both dense and sparse networks, and is shown to have desirable asymptotic properties under sequences of growing networks. We illustrate the improvements of this estimator over maximum likelihood and bias-corrected estimation in a series of numerical experiments. The technique is applied to explain the import and export patterns in a dense network of countries and to estimate a more sparse advice network among attorneys in a corporate law firm.     

Common Correlated Effects Estimation of Dynamic Panels with Cross-Sectional Dependence

We derive inconsistency expressions for dynamic panel data estimators under error cross-sectional dependence generated by an unobserved common factor in both the fixed effect and the incidental trends case. We show that for a temporally dependent factor, the standard within groups (WG) estimator is inconsistent even as both N and T tend to infinity. Next we investigate the properties of the common correlated effects pooled (CCEP) estimator of Pesaran (2006) which eliminates the error cross-sectional dependence using cross-sectional averages of the data. In contrast to the static case, the CCEP estimator is only consistent when next to N also T tends to infinity. It is shown that for the most relevant parameter settings, the inconsistency of the CCEP estimator is larger than that of the infeasible WG estimator, which includes the common factors as regressors. Restricting the CCEP estimator results in a somewhat smaller inconsistency. The small sample properties of the various estimators are analyzed using Monte Carlo experiments. The simulation results suggest that the CCEP estimator can be used to estimate dynamic panel data models provided T is not too small. The size of N is of less importance.     

贝叶斯隐马尔科夫异质面板模型及应用研究

针对不可观测异质性非时变假设导致的删失变量偏差及推断无效问题,构建贝叶斯隐马尔科夫异质面板模型,刻画截面个体间的动态时变不可观测异质性,诊断经济系统环境中可能存在的隐性变点,设计相应的马尔科夫链蒙特卡洛抽样算法估计模型参数,并对中国各地区的金融发展与城乡收入差距关系进行实证分析,捕捉到金融发展与城乡收入差距间长期稳定关系的隐性变化,发现了区域个体不可观测异质性存在的动态时变特征。研究结果表明各参数的迭代轨迹收敛且估计误差非常小,验证了贝叶斯隐马尔科夫异质面板模型的有效性。     

Simple heterogeneity variance estimation for meta-analysis

Summary.  A simple method of estimating the heterogeneity variance in a random-effects model for meta-analysis is proposed. The estimator that is presented is simple and easy to calculate and has improved bias compared with the most common estimator used in random-effects meta-analysis, particularly when the heterogeneity variance is moderate to large. In addition, it always yields a non-negative estimate of the heterogeneity variance, unlike some existing estimators. We find that random-effects inference about the overall effect based on this heterogeneity variance estimator is more reliable than inference using the common estimator, in terms of coverage probability for an interval estimate.     

Small-Sample Methods for Cluster-Robust Variance Estimation and Hypothesis Testing in Fixed Effects Models

ABSTRACT

In panel data models and other regressions with unobserved effects, fixed effects estimation is often paired with cluster-robust variance estimation (CRVE) to account for heteroscedasticity and un-modeled dependence among the errors. Although asymptotically consistent, CRVE can be biased downward when the number of clusters is small, leading to hypothesis tests with rejection rates that are too high. More accurate tests can be constructed using bias-reduced linearization (BRL), which corrects the CRVE based on a working model, in conjunction with a Satterthwaite approximation for t-tests. We propose a generalization of BRL that can be applied in models with arbitrary sets of fixed effects, where the original BRL method is undefined, and describe how to apply the method when the regression is estimated after absorbing the fixed effects. We also propose a small-sample test for multiple-parameter hypotheses, which generalizes the Satterthwaite approximation for t-tests. In simulations covering a wide range of scenarios, we find that the conventional cluster-robust Wald test can severely over-reject while the proposed small-sample test maintains Type I error close to nominal levels. The proposed methods are implemented in an R package called clubSandwich. This article has online supplementary materials.     

Exact inference and prediction for k-sample exponential case under type-ii censoring

The exact inference and prediction intervals for the K-sample exponential scale parameter under doubly Type-II censored samples are derived using an algorithm of Huffer and Lin [Huffer, F.W. and Lin, C.T., 2001, Computing the joint distribution of general linear combinations of spacings or exponen-tial variates. Statistica Sinica, 11, 1141–1157.]. This approach provides a simple way to determine the exact percentage points of the pivotal quantity based on the best linear unbiased estimator in order to develop exact inference for the scale parameter as well as to construct exact prediction intervals for failure times unobserved in the ith sample. Similarly, exact prediction intervals for failure times of units from a future sample can also be easily obtained.     

Treating unobserved heterogeneity in PLS path modeling: a comparison of FIMIX-PLS with different data analysis strategies

In the social science disciplines, the assumption that the data stem from a single homogeneous population is often unrealistic in respect of empirical research. When applying a causal modeling approach, such as partial least squares path modeling, segmentation is a key issue in coping with the problem of heterogeneity in the estimated cause–effect relationships. This article uses the novel finite-mixture partial least squares (FIMIX-PLS) method to uncover unobserved heterogeneity in a complex path modeling example in the field of marketing. An evaluation of the results includes a comparison with the outcomes of several data analysis strategies based on a priori information or k-means cluster analysis. The results of this article underpin the effectiveness and the advantageous capabilities of FIMIX-PLS in general PLS path model set-ups by means of empirical data and formative as well as reflective measurement models. Consequently, this research substantiates the general applicability of FIMIX-PLS to path modeling as a standard means of evaluating PLS results by addressing the problem of unobserved heterogeneity.     

Statistical inference for oscillation processes

ABSTRACT

A new model for time series with a specific oscillation pattern is proposed. The model consists of a hidden phase process controlling the speed of polling and a nonparametric curve characterizing the pattern, leading together to a generalized state space model. Identifiability of the model is proved and a method for statistical inference based on a particle smoother and a nonparametric EM algorithm is developed. In particular, the oscillation pattern and the unobserved phase process are estimated. The proposed algorithms are computationally efficient and their performance is assessed through simulations and an application to human electrocardiogram recordings.     

Keep it simple: estimation strategies for ordered response models with fixed effects

By running Monte Carlo simulations, we compare different estimation strategies of ordered response models in the presence of non-random unobserved heterogeneity. We find that very simple binary recoding schemes deliver parameter estimates with very low bias and high efficiency. Furthermore, if the researcher is interested in the relative size of parameters the simple linear fixed effects model is the method of choice.     

Estimation and Inference for Linear Panel Data Models Under Misspecification When Both n and T are Large

This article considers fixed effects (FE) estimation for linear panel data models under possible model misspecification when both the number of individuals, n, and the number of time periods, T, are large. We first clarify the probability limit of the FE estimator and argue that this probability limit can be regarded as a pseudo-true parameter. We then establish the asymptotic distributional properties of the FE estimator around the pseudo-true parameter when n and T jointly go to infinity. Notably, we show that the FE estimator suffers from the incidental parameters bias of which the top order is O(T^{? 1}), and even after the incidental parameters bias is completely removed, the rate of convergence of the FE estimator depends on the degree of model misspecification and is either (nT)^{? 1/2} or n^{? 1/2}. Second, we establish asymptotically valid inference on the (pseudo-true) parameter. Specifically, we derive the asymptotic properties of the clustered covariance matrix (CCM) estimator and the cross-section bootstrap, and show that they are robust to model misspecification. This establishes a rigorous theoretical ground for the use of the CCM estimator and the cross-section bootstrap when model misspecification and the incidental parameters bias (in the coefficient estimate) are present. We conduct Monte Carlo simulations to evaluate the finite sample performance of the estimators and inference methods, together with a simple application to the unemployment dynamics in the U.S.     

Gamma shared frailty model based on reversed hazard rate

Abstract

Frailty models are used in survival analysis to account for unobserved heterogeneity in individual risks to disease and death. To analyze bivariate data on related survival times (e.g., matched pairs experiments, twin, or family data), shared frailty models were suggested. Shared frailty models are frequently used to model heterogeneity in survival analysis. The most common shared frailty model is a model in which hazard function is a product of random factor(frailty) and baseline hazard function which is common to all individuals. There are certain assumptions about the baseline distribution and distribution of frailty. In this paper, we introduce shared gamma frailty models with reversed hazard rate. We introduce Bayesian estimation procedure using Markov Chain Monte Carlo (MCMC) technique to estimate the parameters involved in the model. We present a simulation study to compare the true values of the parameters with the estimated values. Also, we apply the proposed model to the Australian twin data set.     

Interest-Rate Arbitrage in Currency Baskets: Forecasting Weights and Measuring Risk

This article addresses the problem of the bias of income and expenditure elasticities estimated on pseudopanel data caused by measurement error and unobserved heterogeneity. We gauge these biases empirically by comparing cross-sectional, pseudo-panel, and true panel data from both Polish and U.S. expenditure surveys. Our results suggest that unobserved heterogeneity imparts a downward bias to cross-section estimates of income elasticities of at-home food expenditures and an upward bias to estimates of income elasticities of away-from-home food expenditures. “Within” and first-difference estimators suffer less bias, but only if the effects of measurement error are accounted for with instrumental variables.     

Parameter estimation approaches to tackling measurement error and multicollinearity in ordinal probit models

Abstract

The regression model with ordinal outcome has been widely used in a lot of fields because of its significant effect. Moreover, predictors measured with error and multicollinearity are long-standing problems and often occur in regression analysis. However there are not many studies on dealing with measurement error models with generally ordinal response, even fewer when they suffer from multicollinearity. The purpose of this article is to estimate parameters of ordinal probit models with measurement error and multicollinearity. First, we propose to use regression calibration and refined regression calibration to estimate parameters in ordinal probit models with measurement error. Second, we develop new methods to obtain estimators of parameters in the presence of multicollinearity and measurement error in ordinal probit model. Furthermore we also extend all the methods to quadratic ordinal probit models and talk about the situation in ordinal logistic models. These estimators are consistent and asymptotically normally distributed under general conditions. They are easy to compute, perform well and are robust against the normality assumption for the predictor variables in our simulation studies. The proposed methods are applied to some real datasets.