Long difference instrumental variables estimation for dynamic panel models with fixed effects

This paper proposes a new instrumental variables estimator for a dynamic panel model with fixed effects with good bias and mean squared error properties even when identification of the model becomes weak near the unit circle. We adopt a weak instrument asymptotic approximation to study the behavior of various estimators near the unit circle. We show that an estimator based on long differencing the model is much less biased than conventional implementations of the GMM estimator for the dynamic panel model. We also show that under the weak instrument approximation conventional GMM estimators are dominated in terms of mean squared error by an estimator with far less moment conditions. The long difference (LD) estimator mimics the infeasible optimal procedure through its reliance on a small set of moment conditions.     

Properties of shrinkage estimators in linear regression when disturbances are not normal

This paper considers a class of recently developed biased estimators of regression coefficients and studies its sampling properties when the disturbances are not normally distributed. It has been found that the conditions of dominance of these estimators over the least squares estimator, under non-normality, are quite different than their well-known dominance conditions under normality. Some implications of the results are also discussed.     

A Comparative Analysis of Different IV and GMM Estimators of Dynamic Panel Data Models

It is well known that the usual procedures for estimating panel data models are inconsistent in the dynamic setting. A large number of consistent estimators however, have been proposed in the literature. This paper provides a survey of the majority of mainstream estimators, which tend to consist of IV and GMM ones. It also considers a newly proposed extension to the promising Wansbeek–Bekker estimator (Harris & Mátyás, 2000). To provide guidance to the applied researcher working on micro-datasets, the small sample performance of these estimators is evaluated using a set of Monte Carlo experiments.     

Nonparametric estimators of the bivariate survival function under random censoring

A large number of proposals for estimating the bivariate survival function under random censoring have been made. In this paper we discuss the most prominent estimators, where prominent is meant in the sense that they are best for practical use; Dabrowska's estimator, the Prentice–Cai estimator, Pruitt's modified EM-estimator, and the reduced data NPMLE of van der Laan. We show how these estimators are computed and present their intuitive background. The asymptotic results are summarized. Furthermore, we give a summary of the practical performance of the estimators under different levels of dependence and censoring based on extensive simulation results. This leads also to a practical advise.     

Regression analysis with dichotomous regressors and misclassification

We discuss a regression model in which the regressors are dummy variables. The basic idea is that the observation units can be assigned to some well-defined combination of treatments, corresponding to the dummy variables. This assignment can not be done without some error, i.e. misclassification can play a role. This situation is analogous to regression with errors in variables. It is well-known that in these situations identification of the parameters is a prominent problem. We will first show that, in our case, the parameters are not identified by the first two moments but can be identified by the likelihood. Then we analyze two estimators. The first is a moment estimator involving moments up to the third order, and the second is a maximum likelihood estimator calculated with the help of the EM algorithm. Both estimators are evaluated on the basis of a small Monte Carlo experiment.     

Estimation of a nonlinear panel data model with semiparametric individual effects

This paper investigates identification and estimation of a class of nonlinear panel data, single-index models. The model allows for unknown time-specific link functions, and semiparametric specification of the individual-specific effects. We develop an estimator for the parameters of interest, and propose a powerful new kernel-based modified backfitting algorithm to compute the estimator. We derive uniform rates of convergence results for the estimators of the link functions, and show the estimators of the finite-dimensional parameters are root-N$N$ consistent with a Gaussian limiting distribution. We study the small sample properties of the estimator via Monte Carlo techniques.     

Some identification and estimation results for regression models with stochastically varying coefficients

Although various theoretical and applied papers have appeared in recent years concerned with the estimation and use of regression models with stochastically varying coefficients, little is available in the literature on the properties of the proposed estimators or the identifiability of the parameters of such models. The present paper derives sufficient conditions under which the maximum likelihood estimator is consistent and asymptotically normal and also provides sufficient conditions for the estimation of regression models with stationary stochastically varying coefficients. In many instances these requirements are found to have simple, intuitively appealing interpretations. Consistency and asymptotic normality is also proven for a two-step estimator and a method suggested by Rosenberg for generating initial estimates.     

Effective nonparametric estimation in the case of severely discretized data

Often economic data are discretized or rounded to some extent. This paper proposes a regression and a density estimator that work especially well when discretization causes conventional kernel-based estimators to behave poorly. The estimator proposed here is a weighted average of neighboring frequency estimators, and the weights are composed of cubic B-splines. Interestingly, we show that this estimator can have both a smaller bias and variance than frequency estimators. As a means to obtain asymptotic normality and rates of convergence, we assume that the discreteness becomes finer as the sample size increases.     

Asymptotically efficient recursive estimation for incomplete data models using the observed information

For a recursive maximum-likelihood estimator with step lengths decaying as 1/n, an adaptive matrix needs to be incorporated to obtain asymptotic efficiency. Ideally, this matrix should be chosen as the inverse Fisher information matrix, which is usually very difficult to compute for incomplete data models. In this paper we give conditions under which the observed information can be incorporated into the recursive procedure to yield an efficient estimator, and we also investigate the finite sample properties of these estimators by simulation.     

Shrinkage estimation for the mean of the inverse Gaussian population

We consider improved estimation strategies for a two-parameter inverse Gaussian distribution and use a shrinkage technique for the estimation of the mean parameter. In this context, two new shrinkage estimators are suggested and demonstrated to dominate the classical estimator under the quadratic risk with realistic conditions. Furthermore, based on our shrinkage strategy, a new estimator is proposed for the common mean of several inverse Gaussian distributions, which uniformly dominates the Graybill–Deal type unbiased estimator. The performance of the suggested estimators is examined by using simulated data and our shrinkage strategies are shown to work well. The estimation methods and results are illustrated by two empirical examples.     

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.     

A new class of limited-information estimators for simultaneous equations systems

The TSLS and LIML estimators are evaluated by means of a new class of limited-information estimators, the so-called Ω-class estimators. Under certain assumptions the Ω-class estimator is a maximun-likelihood estimator. These assumptions are superfluous, however, if we view the Ω-class as a class of minimun-distance estimators; all the members are shown to be consistent under general conditions. Besides the TSLS and the LIML estimators some other interesting members are introduced, and it is shown that, under certain conditions, the Ω-class estimators are weighted averages of different TSLS estimators. The use of TSLS in small samples is criticized; an alternative estimator is proposed.     

The Estimation of Pareto Distribution by a Weighted Least Square Method

The two-parameter Pareto distribution provides reasonably good fit to the distributions of income and property value, and explains many empirical phenomena. For the censored data, the two parameters are regularly estimated by the maximum likelihood estimator, which is complicated in computation process. This investigation proposes a weighted least square estimator to estimate the parameters. Such a method is comparatively concise and easy to perceive, and could be applied to either complete or truncated data. Simulation studies are conducted in this investigation to show the feasibility of the proposed method. This report will demonstrate that the weighted least square estimator gives better performance than unweighted least square estimators with simulation cases. We also illustrate that the weighted least square estimator is very close to maximum likelihood estimator with simulation studies.     

A minimum chi-squared method for indirect parameter estimation from Poisson data

In this paper, we introduce a new algorithm for estimating non-negative parameters from Poisson observations of a linear transformation of the parameters. The proposed objective function fits both a weighted least squares (WLS) and a minimum χ² estimation framework, and results in a convex optimization problem. Unlike conventional WLS methods, the weights do not need to be estimated from the datas, but are incorporated in the objective function. The iterative algorithm is derived from an alternating projection procedure in which "distance" is determined by the chi-squared test statistic, which is interpreted as a measure of the discrepancy between two distributions. This may be viewed as an alternative to the Kullback-Leibler divergence which corresponds to the maximum likelihood (ML) estimation. The algorithm is similar in form to, and shares many properties with, the expectation maximization algorithm for ML estimation. In particular, we show that every limit point of the algorithm is an estimator, and the sequence of projected (by the linear transformation into the data space) means converge. Despite the similarities, we show that the new estimators are quite distinct from ML estimators, and obtain conditions under which they are identical.     

Linear regression using both temporally aggregated and temporally disaggregated data

Economists frequently encounter data which are subject to different temporal aggregation. In this paper we give a maximum likelihood approach to these problems with a minimum of mathematical manipulation. We show that the best prediction of the data by related series and efficient estimation of parameters are inseparable. The relative efficiency of the maximum likelihood estimator to other estimators are also indicated.     

Quasi-maximum likelihood estimation for conditional quantiles

In this paper, we construct a new class of estimators for conditional quantiles in possibly misspecified nonlinear models with time series data. Proposed estimators belong to the family of quasi-maximum likelihood estimators (QMLEs) and are based on a new family of densities which we call ‘tick-exponential’. A well-known member of the tick-exponential family is the asymmetric Laplace density, and the corresponding QMLE reduces to the Koenker and Bassett's (Econometrica 46 (1978) 33) nonlinear quantile regression estimator. We derive primitive conditions under which the tick-exponential QMLEs are consistent and asymptotically normally distributed with an asymptotic covariance matrix that accounts for possible conditional quantile model misspecification and which can be consistently estimated by using the tick-exponential scores and Hessian matrix. Despite its non-differentiability, the tick-exponential quasi-likelihood is easy to maximize by using a ‘minimax’ representation not seen in the earlier work on conditional quantile estimation.     

Least absolute deviations estimation for the censored regression model

This paper proposes an alternative to maximum likelihood estimation of the parameters of the censored regression (or censored ‘Tobit’) model. The proposed estimator is a generalization of least absolute deviations estimation for the standard linear model, and, unlike estimation methods based on the assumption of normally distributed error terms, the estimator is consistent and asymptotically normal for a wide class of error distributions, and is also robust to heteroscedasticity. The paper gives the regularity conditions and proofs of these large-sample results, and proposes classes of consistent estimators of the asymptotic covariance matrix for both homoscedastic and heteroscedastic disturbances.     

Mostly harmless simulations? Using Monte Carlo studies for estimator selection

We consider two recent suggestions for how to perform an empirically motivated Monte Carlo study to help select a treatment effect estimator under unconfoundedness. We show theoretically that neither is likely to be informative except under restrictive conditions that are unlikely to be satisfied in many contexts. To test empirical relevance, we also apply the approaches to a real‐world setting where estimator performance is known. Both approaches are worse than random at selecting estimators that minimize absolute bias. They are better when selecting estimators that minimize mean squared error. However, using a simple bootstrap is at least as good and often better. For now, researchers would be best advised to use a range of estimators and compare estimates for robustness.     

Instrumental variables estimation of a nearly nonstationary,heterogeneous error component model

This paper studies instrumental variables (IV) estimation for an error component model with stationary and nearly nonstationary regressors. It is assumed that the numbers of cross section and time series observations are infinite. Furthermore, autoregressive disturbances are assumed for the error component model, the structure of which may vary with individuals. The estimators considered are the Within-IV-OLS, Within-IV-GLS and IV-GLS estimators. The GLS estimators use Gohberg's formula, which is particularly useful when autoregressive structures are imposed on the disturbance terms. Sequential limit theories for the estimators are derived, and it is shown that all of the estimators have normal distributions in the limit. Additionally, Wald tests for coefficient vectors are shown to have chi-square distributions in the limit. Simulation results regarding the estimator efficiency and the size of the Wald tests are also reported. The results show that the Within-IV-GLS and IV-GLS estimators are more efficient than the Within-IV-OLS estimator in most cases and that the Wald tests keep nominal size reasonably well. The relation between the trade and budget deficits of 23 OECD nations is examined using the panel IV estimators. The empirical results support the view that the budget and trade deficits move in the same direction.     

The econometric analysis of models with risk terms

In this paper we have attempted to provide an integrated approach to the estimation of models with risk terms. It was argued that there exist orthogonality conditions between variables in the information set and higher-order moments of the unanticipated variable density. These could be exploited to provide consistent estimators of the parameters associated with the risk term. Specifically, it was recommended that an IV estimator should be applied, with instruments constructed from the information set. Four existing methods commonly used to estimate models with risk terms are examined, and applications of the techniques are made to the estimation of the risk term in the $US/$C exchange market, and the effects of price uncertainty upon production.