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We propose a quasi–maximum likelihood estimator for the location parameters of a linear regression model with bounded and symmetrically distributed errors. The error outcomes are restated as the convex combination of the bounds, and we use the method of maximum entropy to derive the quasi–log likelihood function. Under the stated model assumptions, we show that the proposed estimator is unbiased, consistent, and asymptotically normal. We then conduct a series of Monte Carlo exercises designed to illustrate the sampling properties of the quasi–maximum likelihood estimator relative to the least squares estimator. Although the least squares estimator has smaller quadratic risk under normal and skewed error processes, the proposed QML estimator dominates least squares for the bounded and symmetric error distribution considered in this paper.

This article examines the history, development, and application of the sandwich estimate of variance. In describing this estimator, we pay attention to applications that have appeared in the literature and examine the nature of the problems for which this estimator is used. We describe various adjustments to the estimate for use with small samples, and illustrate the estimator’s construction for a variety of models. Finally, we discuss interpretation of results.

We formulate generalized maximum entropy estimators for the general linear model and the censored regression model when there is first order spatial autoregression in the dependent variable. Monte Carlo experiments are provided to compare the performance of spatial entropy estimators relative to classical estimators. Finally, the estimators are applied to an illustrative model allocating agricultural disaster payments.

Standard stratified sampling (SSS) is a popular non-random sampling scheme. Maximum likelihood estimator (MLE) is inconsistent if some sampled strata depend on the response variable Y (‘endogenous samples’) or if some Y-dependent strata are not sampled at all (‘truncated sample’ – a missing data problem). Various versions of MLE have appeared in the literature, and this paper reviews practical likelihood-based estimators for endogenous or truncated samples in SSS. Also a new estimator ‘Estimated-EX MLE’ is introduced using an extra random sample on X (not on Y) to estimate the distribution EX of X. As information on Y may be hard to get, this estimator's data demand is weaker than an extra random sample on Y in some other estimators. The estimator can greatly improve the efficiency of ‘Fixed-X MLE’ which conditions on X, even if the extra sample size is small. In fact, Estimated-EX MLE does not estimate the full FX as it needs only a sample average using the extra sample. Estimated-EX MLE can be almost as efficient as the ‘Known-FX MLE’. A small-scale simulation study is provided to illustrate these points.

This paper is concerned with estimation of the parameters of a high-frequency VAR model using mixed-frequency data, both for the stock and for the flow case. Extended Yule–Walker estimators and (Gaussian) maximum likelihood type estimators based on the EM algorithm are considered. Properties of these estimators are derived, partly analytically and by simulations. Finally, the loss of information due to mixed-frequency data when compared to the high-frequency situation as well as the gain of information when using mixed-frequency data relative to low-frequency data is discussed.

One way to control for the heterogeneity in panel data is to allow for time-invariant, individual specific parameters. This fixed effect approach introduces many parameters into the model which causes the “incidental parameter problem”: the maximum likelihood estimator is in general inconsistent. Woutersen (2001) shows how to approximately separate the parameters of interest from the fixed effects using a reparametrization. He then shows how a Bayesian method gives a general solution to the incidental parameter for correctly specified models. This paper extends Woutersen (2001) to misspecified models. Following White (1982), we assume that the expectation of the score of the integrated likelihood is zero at the true values of the parameters. We then derive the conditions under which a Bayesian estimator converges at rate N where N is the number of individuals. Under these conditions, we show that the variance-covariance matrix of the Bayesian estimator has the form of White (1982). We illustrate our approach by the dynamic linear model with fixed effects and a duration model with fixed effects.

In the spirit of White’s (1982) paper, this paper examines the consequences of model misspecification using a panel data regression model. Maximum likelihood, random and fixed effects estimators are compared using Monte Carlo experiments under normality of the disturbances but with a possibly misspecified variance-covariance matrix. We show that the correct GLS (ML) procedure is always the best according to MSE performance, but the researcher does not have perfect foresight on the true form of the variance covariance matrix. In this case, we show that a pretest estimator is a viable alternative given that its performance is a close second to correct GLS (ML) whether the true specification is a two-way, a one-way error component model or a pooled regression model. Incorrect GLS, ML or fixed effects estimators may lead to a big loss in MSE.

In this chapter we approach the estimation of dynamic stochastic general equilibrium models through a moments-based estimator, the empirical likelihood. We attempt to show that this inference process can be a valid alternative to maximum likelihood, which has been one of the preferred choices of the related literature to estimate these models. The empirical likelihood estimator is characterized by a simple setup and only requires knowledge about the moments of the data generating process of the model. In this context, we exploit the fact that these economies can be formulated as a set of moment conditions to infer on their parameters through this technique. For illustrational purposes, we consider a standard real business cycle model with a constant relative risk averse utility function and indivisible labor, driven by a normal technology shock.