Lecture notes for a course of Introductory Econometrics (linear regression model and ordinary least squares, including concepts of Linear Algebra and Inferential Statistics), and for a second course of Econometrics (simultaneous equations, instrumental variables, limited and full information...

With most of the available software packages, estimates of the parameter covariance matrix in a GARCH model are usually obtained from the outer products of the first derivatives of the log-likelihoods (BHHH estimator). However, other estimators could be defined and used, analogous to the...

Starting from a consistent and asymptotically normally distributed structural estimate of a dynamic econometric model, this paper provides an analytical derivation of the asymptotic distribution of spectra and cross spectra of the jointly dependent variables. A numerical example is provided on...

When the coefficients of a Tobit model are estimated by maximum likelihood their covariance matrix is typically, even if not necessarily, associated with the algorithm employed to maximize the likelihood. Covariance estimators used in practice are derived by: (1) the Hessian (observed...

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...

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...

In econometric models, estimates of the asymptotic covariance matrix of FIML coefficients are traditionally computed in several different ways: with a generalized least squares type matrix; using the Hessian of the concentrated log-likelihood; using the outer product of the first derivatives of...

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...

Financial returns exhibit conditional heteroscedasticity, asymmetric responses of their volatility to negative and positive returns (leverage effects) and fat tails. The α-stable distribution is a natural candidate for capturing the tail-thickness of the conditional distribution of financial...