Multicollinearity and Modular Maximum Entropy Leuven Estimator

A high degree of multicollinearity often has a detrimental effects on the estimation of a linear econometric (regression) model due to an intricate internecine sharing among the estimated regression coefficients (beta). Paris (2001) introduced the Maximum Entropy Leuven (MEL) estimator. It exploits the information available in the sample data more efficiently than the OLS does, and unlike GME estimator, it does not require any additional information to be supplied by the researcher. Paris concludes: "under any level of multicollinearity, MEL estimator uniformly dominates the OLS estimator according to the mean squared error criterion. It rivals also the GME estimator without requiring any subjective additional information." Paris used the Euclidean norm to obtain prob(beta). In this paper we obtain prob(beta) using the absolute norm of beta and investigate into its effects on the performance of the Maximum Entropy estimator. We obtain a new estimator of regression coefficients by solving the reformulated problem. This new estimator is not fully a la Paris (2001) and hence we name it as the Modular Maximum Entropy Leuven (MMEL) estimator. Monte Carlo study has been conducted to compare the performance of the MEL estimator (Paris) and the new MMEL estimator. We observe that overall, the performance of MMEL (in terms of mean estimated coefficients as well as the RMS values) is much superior to that of the MEL estimator. It is pertinent to note that obtaining prob(beta) is the most crucial task before the scientist if he chooses to use the maximum entropy estimator (MEL, MMEL or any variant thereof). After all, the mathematics of probability suggests us that given a sample description space S, probability is a function which assigns a non-negative real number to every event A, denoted by P(A) and it is called the probability of the event A. The probability function is defined on a Borel field of events conformal to the axioms of positiveness, certainty and union. Under these axioms, there could be several different rules of assignment, ranging from subjective judgement backed up by a rational belief (JM Keynes) to counting the number of success in the repeated trials. In our study MEL does this assignment in the one way and the MMEL does that in the other way. There could be many more (possibly better) rules of assignment of probability. Thus, the subjective (or exogenous) element that was explicit in Golan et al. reappears in the MEL family of estimators, although in another garb