Partial rank estimation of duration models with general forms of censoring

In this paper we propose estimators for the regression coefficients in censored duration models which are distribution free, impose no parametric specification on the baseline hazard function, and can accommodate general forms of censoring. The estimators are shown to have desirable asymptotic properties and Monte Carlo simulations demonstrate good finite sample performance. Among the data features the new estimators can accommodate are covariate-dependent censoring, double censoring, and fixed (individual or group specific) effects. We also examine the behavior of the estimator in an empirical illustration.     

The second-order bias and mean squared error of estimators in time-series models

We develop analytical results on the second-order bias and mean squared error of estimators in time-series models. These results provide a unified approach to developing the properties of a large class of estimators in linear and nonlinear time-series models and they are valid for both normal and nonnormal samples of observations, and where the regressors are stochastic. The estimators included are the generalized method of moments, maximum likelihood, least squares, and other extremum estimators. Our general results are applied to four time-series models. We investigate the effects of nonnormality on the second-order bias results for two of these models, while for all four models, the second-order bias and mean squared error results are given under normality. Numerical results for some of these models are also presented.     

Weighted least squares estimators in possibly misspecified nonlinear regression

The behavior of estimators for misspecified parametric models has been well studied. We consider estimators for misspecified nonlinear regression models, with error and covariates possibly dependent. These models are described by specifying a parametric model for the conditional expectation of the response given the covariates. This is a parametric family of conditional constraints, which makes the model itself close to nonparametric. We study the behavior of weighted least squares estimators both when the regression function is correctly specified, and when it is misspecified and also involves possible additional covariates.     

A theory of robust long-run variance estimation

Long-run variance estimation can typically be viewed as the problem of estimating the scale of a limiting continuous time Gaussian process on the unit interval. A natural benchmark model is given by a sample that consists of equally spaced observations of this limiting process. The paper analyzes the asymptotic robustness of long-run variance estimators to contaminations of this benchmark model. It is shown that any equivariant long-run variance estimator that is consistent in the benchmark model is highly fragile: there always exists a sequence of contaminated models with the same limiting behavior as the benchmark model for which the estimator converges in probability to an arbitrary positive value. A class of robust inconsistent long-run variance estimators is derived that optimally trades off asymptotic variance in the benchmark model against the largest asymptotic bias in a specific set of contaminated models.     

A new class of asymptotically efficient estimators for moment condition models

In this paper, we propose a new class of asymptotically efficient estimators for moment condition models. These estimators share the same higher order bias properties as the generalized empirical likelihood estimators and once bias corrected, have the same higher order efficiency properties as the bias corrected generalized empirical likelihood estimators. Unlike the generalized empirical likelihood estimators, our new estimators are much easier to compute. A simulation study finds that our estimators have better finite sample performance than the two-step GMM, and compare well to several potential alternatives in terms of both computational stability and overall performance.     

Estimation with overidentifying inequality moment conditions

This paper derives limit distributions of empirical likelihood estimators for models in which inequality moment conditions provide overidentifying information. We show that the use of this information leads to a reduction of the asymptotic mean-squared estimation error and propose asymptotically uniformly valid tests and confidence sets for the parameters of interest. While inequality moment conditions arise in many important economic models, we use a dynamic macroeconomic model as a data generating process and illustrate our methods with instrumental variable estimators of monetary policy rules. The results obtained in this paper extend to conventional GMM estimators.     

Maximum likelihood and restricted maximum likelihood estimation for a class of Gaussian Markov random fields

This work describes a Gaussian Markov random field model that includes several previously proposed models, and studies properties of its maximum likelihood (ML) and restricted maximum likelihood (REML) estimators in a special case. Specifically, for models where a particular relation holds between the regression and precision matrices of the model, we provide sufficient conditions for existence and uniqueness of ML and REML estimators of the covariance parameters, and provide a straightforward way to compute them. It is found that the ML estimator always exists while the REML estimator may not exist with positive probability. A numerical comparison suggests that for this model ML estimators of covariance parameters have, overall, better frequentist properties than REML estimators.     

On Maximum Likelihood Estimation of Dynamic Panel Data Models

We analyse the finite sample properties of maximum likelihood estimators for dynamic panel data models. In particular, we consider transformed maximum likelihood (TML) and random effects maximum likelihood (RML) estimation. We show that TML and RML estimators are solutions to a cubic first‐order condition in the autoregressive parameter. Furthermore, in finite samples both likelihood estimators might lead to a negative estimate of the variance of the individual‐specific effects. We consider different approaches taking into account the non‐negativity restriction for the variance. We show that these approaches may lead to a solution different from the unique global unconstrained maximum. In an extensive Monte Carlo study we find that this issue is non‐negligible for small values of T and that different approaches might lead to different finite sample properties. Furthermore, we find that the Likelihood Ratio statistic provides size control in small samples, albeit with low power due to the flatness of the log‐likelihood function. We illustrate these issues modelling US state level unemployment dynamics.     

Functional coefficient instrumental variables models

We consider estimation of nonparametric structural models under a functional coefficient representation for the regression function. Under this representation, models are linear in the endogenous components with coefficients given by unknown functions of the predetermined variables, a nonparametric generalization of random coefficient models. The functional coefficient restriction is an intermediate approach between fully nonparametric structural models that are ill posed when endogenous variables are continuously distributed, and partially linear models over which they have appreciable flexibility. We propose two-step estimators that use local linear approximations in both steps. The first step is to estimate a vector of reduced forms of regression models and the second step is local linear regression using the estimated reduced forms as regressors. Our large sample results include consistency and asymptotic normality of the proposed estimators. The high practical power of estimators is illustrated via both a Monte Carlo simulation study and an application to returns to education.     

Dynamic Panel Data Models With Irregular Spacing: With an Application to Early Childhood Development

With the increased availability of longitudinal data, dynamic panel data models have become commonplace. Moreover, the properties of various estimators of such models are well known. However, we show that these estimators break down when the data are irregularly spaced along the time dimension. Unfortunately, this is an increasingly frequent occurrence as many longitudinal surveys are collected at non‐uniform intervals and no solution is currently available when time‐varying covariates are included in the model. In this paper, we propose two new estimators for dynamic panel data models when data are irregularly spaced and compare their finite‐sample performance to the näive application of existing estimators. We illustrate the practical importance of this issue in an application concerning early childhood development. Copyright © 2016 John Wiley & Sons, Ltd.     

Connections between Survey Calibration Estimators and Semiparametric Models for Incomplete Data

Survey calibration (or generalized raking) estimators are a standard approach to the use of auxiliary information in survey sampling, improving on the simple Horvitz–Thompson estimator. In this paper we relate the survey calibration estimators to the semiparametric incomplete‐data estimators of Robins and coworkers, and to adjustment for baseline variables in a randomized trial. The development based on calibration estimators explains the “estimated weights” paradox and provides useful heuristics for constructing practical estimators. We present some examples of using calibration to gain precision without making additional modelling assumptions in a variety of regression models.     

ESTIMATION OF CENSORED PANEL‐DATA MODELS WITH SLOPE HETEROGENEITY

This paper considers estimation of censored panel‐data models with individual‐specific slope heterogeneity. The slope heterogeneity may be random (random slopes model) or related to covariates (correlated random slopes model). Maximum likelihood and censored least‐absolute deviations estimators are proposed for both models. The estimators are simple to implement and, in the case of maximum likelihood, lead to straightforward estimation of partial effects. The rescaled bootstrap suggested by Andrews (Econometrica 2000; 68 : 399–405) is used to deal with the possibility of variance parameters being equal to zero. The methodology is applied to an empirical study of Dutch household portfolio choice, where the outcome variable (portfolio share in safe assets) has corner solutions at zero and one. As predicted by economic theory, there is strong evidence of correlated random slopes for the age profiles, indicating a heterogeneous age profile of portfolio adjustment that varies significantly with other household characteristics. Copyright © 2013 John Wiley & Sons, Ltd.     

On MLEs in an extended multivariate linear growth curve model

In this paper the extended growth curve model is considered. The literature comprises two versions of the model. These models can be connected by one-to-one reparameterizations but since estimators are non-linear it is not obvious how to transmit properties of estimators from one model to another. Since it is only for one of the models where detailed knowledge concerning estimators is available (Kollo and von Rosen, Advanced multivariate statistics with matrices. Springer, Dordrecht, 2005) the object in this paper is therefore to present uniqueness properties and moment relations for the estimators of the second model. One aim of the paper is also to complete the results for the model presented in Kollo and von Rosen (Advanced multivariate statistics with matrices. Springer, Dordrecht, 2005). The presented proofs of uniqueness for linear combinations of estimators are valid for both models and are simplifications of proofs given in Kollo and von Rosen (Advanced multivariate statistics with matrices. Springer, Dordrecht, 2005).     

Estimation strategies for the regression coefficient parameter matrix in multivariate multiple regression

We consider improved estimation strategies for the parameter matrix in multivariate multiple regression under a general and natural linear constraint. In the context of two competing models where one model includes all predictors and the other restricts variable coefficients to a candidate linear subspace based on prior information, there is a need of combining two estimation techniques in an optimal way. In this scenario, we suggest some shrinkage estimators for the targeted parameter matrix. Also, we examine the relative performances of the suggested estimators in the direction of the subspace and candidate subspace restricted type estimators. We develop a large sample theory for the estimators including derivation of asymptotic bias and asymptotic distributional risk of the suggested estimators. Furthermore, we conduct Monte Carlo simulation studies to appraise the relative performance of the suggested estimators with the classical estimators. The methods are also applied on a real data set for illustrative purposes.     

Choosing instrumental variables in conditional moment restriction models

Properties of GMM estimators are sensitive to the choice of instrument. Using many instruments leads to high asymptotic asymptotic efficiency but can cause high bias and/or variance in small samples. In this paper we develop and implement asymptotic mean square error (MSE) based criteria for instrument selection in estimation of conditional moment restriction models. The models we consider include various nonlinear simultaneous equations models with unknown heteroskedasticity. We develop moment selection criteria for the familiar two-step optimal GMM estimator (GMM), a bias corrected version, and generalized empirical likelihood estimators (GEL), that include the continuous updating estimator (CUE) as a special case. We also find that the CUE has lower higher-order variance than the bias-corrected GMM estimator, and that the higher-order efficiency of other GEL estimators depends on conditional kurtosis of the moments.     

Discrete factor approximations in simultaneous equation models: estimating the impact of a dummy endogenous variable on a continuous outcome

This paper contains a Monte Carlo evaluation of estimators used to control for endogeneity of dummy explanatory variables in continuous outcome regression models. When the true model has bivariate normal disturbances, estimators using discrete factor approximations compare favorably to efficient estimators in terms of precision and bias; these approximation estimators dominate all the other estimators examined when the disturbances are non-normal. The experiments also indicate that one should liberally add points of support to the discrete factor distribution. The paper concludes with an application of the discrete factor approximation to the estimation of the impact of marriage on wages.     

Relative efficiencies of some simple Bayes estimators of coefficients in a dynamic equation with serially correlated errors - II

Generalized least squares estimators, with estimated variance-covariance matrices, and maximum likelihood estimators have been proposed in the literature to deal with the problem of estimating autoregressive models with autocorrelated disturbances. In this paper we compare the small sample efficiencies of these estimators with those of some approximate Bayes estimators. The comparison is done with the help of a sampling experiment applied to a model specification. Though these Bayes estimators utilize very weak prior information, they out-perform the sampling theory estimators in every case we consider.     

Approximate inference in multivariate nonlinear functional relationships

An estimation procedure based on estimating equations is presented for the parameters in a multivariate functional relationship model, where all observations are subject to error. The covariance matrix of the observational errors may be parametrized and is allowed to be different for different sets of observations. Estimators are defined for the unknown relation parameters and error parameters.
For linear models (i.e. where the model function is linear in the incidental parameters) the estimators are consistent and asymptotically normal. A consistent expression for the covariance matrix of the estimators is derived. The results are valid for general error distributions.
For nonlinear models the estimators are based on locally linear approximations to the model function. The afore mentioned properties of the estimators are now only approximately valid. The adequacy of the approximate inference, based on asymptotic theory for the linearized model, needs at least informal check. Some examples are given to illustrate the estimation procedure.     

Examining bias in estimators of linear rational expectations models under misspecification

Most rational expectations models involve equations in which the dependent variable is a function of its lags and its expected future value. We investigate the asymptotic bias of generalized method of moment (GMM) and maximum likelihood (ML) estimators in such models under misspecification. We consider several misspecifications, and focus more specifically on the case of omitted dynamics in the dependent variable. In a stylized DGP, we derive analytically the asymptotic biases of these estimators. We establish that in many cases of interest the two estimators of the degree of forward-lookingness are asymptotically biased in opposite direction with respect to the true value of the parameter. We also propose a quasi-Hausman test of misspecification based on the difference between the GMM and ML estimators. Using Monte-Carlo simulations, we show that the ordering and direction of the estimators still hold in a more realistic New Keynesian macroeconomic model. In this set-up, misspecification is in general found to be more harmful to GMM than to ML estimators.     

Fixed effects estimation of structural parameters and marginal effects in panel probit models

Fixed effects estimators of nonlinear panel models can be severely biased due to the incidental parameters problem. In this paper, I characterize the leading term of a large-T expansion of the bias of the MLE and estimators of average marginal effects in parametric fixed effects panel binary choice models. For probit index coefficients, the former term is proportional to the true value of the coefficients being estimated. This result allows me to derive a lower bound for the bias of the MLE. I then show that the resulting fixed effects estimates of ratios of coefficients and average marginal effects exhibit no bias in the absence of heterogeneity and negligible bias for a wide variety of distributions of regressors and individual effects in the presence of heterogeneity. I subsequently propose new bias-corrected estimators of index coefficients and marginal effects with improved finite sample properties for linear and nonlinear models with predetermined regressors.