Imputation of continuous variables missing at random using the method of simulated scores

For multivariate datasets with missing values, we present a procedure of statistical inference and state its "optimal" properties. Two main assumptions are needed: (1) data are missing at random (MAR); (2) the data generating process is a multivariate normal linear regression. Disentangling the problem of convergence of the iterative estimation/imputation procedure, we show that the estimator is a "method of simulated scores" (a particular case of McFadden's "method of simulated moments"); thus the estimator is equivalent to maximum likelihood if the number of replications is conveniently large, and the whole procedure can be considered an optimal parametric technique for imputation of missing data.Simulates scores; missing data; estimation/imputation; structural form; reduced form

Negative variance estimates in panel data models

Negative values for estimated variances can arise in a panel data context. Empirical and theoretical literature dismisses the problem as not serious and a practical solution is to replace negative variances by its boundary value, i.e. zero. While this is not a concern when the individual variance components is "small" with respect to idiosyncratic variance component (making it indistinguishable from zero in practice), we claim that a negative estimated variance can also arise with a "large" individual variance component, when the orthogonality condition between the individual effects and regressors fails. Estimation problems are considered in the (feasible) generalized least squares and maximum likelihood frameworks.Panel data, random effect estimation, negative variances, maximum likelihood

Identification of linear panel data models when instruments are not available

One of the major virtues of panel data models is the possibility to control for unobserved and unobservable heterogeneity at the unit (individual, firm, sector...) level, even when this is correlated with the variables included on the right hand side of the equation. By assuming an additive error structure, identification of the model parameters spans from transformations of the data that wipe out the individual component. We propose an alternative identification strategy, where the equation of interest is embedded in a structural system that properly accounts for the endogeneity of the variables on the right hand side (without distinguishing correlation with the individual component or the idiosyncratic term). We show that, under certain conditions, the system is identified even in the case where no exogenous variable is available, due to the presence of cross-equation restrictions. Estimation of the model parameters can rely on an iterated Zellner-type estimator, with remarkable performance gains over traditional GMM approaches.panel data, identification, cross-equation restrictions

Poor identification and estimation problems in panel data models with random effects and autocorrelated errors

A dramatically large number of corner solutions occur when estimating by (Gaussian) maximum likelihood a simple model for panel data with random effects and autocorrelated errors. This can invalidate results of applications to panel data with a short time dimension, even in a correctly specified model. We explain this unpleasant effect (usually underestimated, almost ignored in the literature) showing that the expected log-likelihood is nearly flat, thus rising problems of poor identification.panel data, maximum likelihood, identification.

Moment Conditions and Neglected Endogeneity in Panel Data Models

This paper develops a new moment condition for estimation of linear panel data models. When added to the set of instruments devised by Anderson, Hsiao (1981, 1982) for the dynamic model, the proposed approach can outperform the GMM methods customarily employed for estimation. The proposal builds on the properties of the iterated GLS, that, contrary to conventional wisdom, can lead to a consistent estimator in particular cases where endogeneity of the explanatory variables is neglected. The targets achieved are a reduction in the number of moment conditions and a better performance over the most widely adopted techniques.panel data, dynamic model, GMM estimation, endogeneity

Autocorrelation and masked heterogeneity in panel data models estimated by maximum likelihood

In a panel data model with random effects, when autocorrelation in the error is considered, (Gaussian) maximum likelihood estimation produces a dramatically large number of corner solutions: the variance of the random effect appears (incorrectly) to be zero, and a larger autocorrelation is (incorrectly) assigned to the idiosyncratic component. Thus heterogeneity could (incorrectly) be lost in applications to panel data with customarily available time dimension, even in a correctly specified model. The problem occurs in linear as well as nonlinear models. This paper aims at pointing out how serious this problem can be (largely neglected by the panel data literature). A set of Monte Carlo experiments is conducted to highlight its relevance, and we explain this unpleasant effect showing that, along a direction, the expected log-likelihood is nearly flat. We also provide two examples of applications with corner solutions.Panel data, autocorrelation, random effects, maximum likelihood, expected log-likelihood

Individual wage and reservation wage: efficient estimation of a simultaneous equation model with endogenous limited dependent variables

We consider a simultaneous equation model with two endogenous limited dependent variables (individual wage and reservation wage) characterized by a selection mechanism determining a two-regimes endogenous-switching. We extend the FIML procedure proposed by Poirier-Ruud (1981) for a single equation switching model providing a stochastic specification for both equations and for the selection criterion. An accurate Monte Carlo experiment shows that the relative efficiency of the FIML estimator over to the Two-Stage procedure is remarkably high in presence of a high degree of endogeneity in the selection equation.Selection bias; endogenous switching

THE SCORE OF CONDITIONALLY HETEROSKEDASTIC DYNAMIC REGRESSION MODELS WITH STUDENT T INNOVATIONS, AN LM TEST FOR MULTIVARIATE NORMALITY

We provide numerically reliable analytical expressions for the score of conditionally heteroskedastic dynamic regression models when the conditional distribution is multivariate $t$. We also derive one-sided and 2-sided LM tests for multivariate normality versus multivariate $t$ based on the first two moments of the (squared) norm of the standardised innovations evaluated at the Gaussian quasi-ML estimators of the conditional mean and variance parameters. We reinterpret them as specification tests for multivariate excess kurtosis, and show that they have power against leptokurtic alternatives. Finally, we analyse UK stock returns, and confirm that their conditional distribution has fat tails.Kurtosis, Inequality Constraints, ARCH, Financial Returns.

CONSTRAINED EMM AND INDIRECT INFERENCE ESTIMATION

We develop generalised indirect inference procedures that handle equality and inequality constraints on the auxiliary model parameters. We obtain expressions for the optimal weighting matrices, and discuss as examples an MA(1) estimated as AR(1), an AR(1) estimated as MA(1), and a log-normal stochastic volatility process estimated as a GARCH(1,1) with Gaussian or t distributed errors. In the first example, the constraints have no effect, while in the second, they allow us to achieve full efficiency. As for the third, neither procedure systematically outperforms the other, but equality restricted estimators are better when the additional parameter is poorly estimated.