A Poisson Ridge Regression Estimator

The standard statistical method for analyzing count data is the Poisson regression model, which is usually estimated using maximum likelihood (ML). The ML method is very sensitive to multicollinearity. Therefore, we present a new Poisson ridge regression estimator (PRR) as a remedy to the problem of instability of the traditional ML method. To investigate the performance of the PRR and the traditional ML approaches for estimating the parameters of the Poisson regression model, we calculate the mean squared error (MSE) using Monte Carlo simulations. The result from the simulation study shows that the PRR method outperforms the traditional ML estimator in all of the different situations evaluated in this paper.Poisson regression; maximum likelihood; ridge regression; MSE; Monte Carlo simulations; Multicollinearity

Performance of Some Ridge Parameters for Probit Regression: with Application on Swedish Job Search Data

In ridge regression the estimation of the ridge parameter is an important issue. This paper generalizes some methods for estimating the ridge parameter for probit ridge regression (PRR) model based on the work of Kibria et al. (2011). The performance of these new estimators are judged by calculating the mean square error (MSE) using Monte Carlo simulations. In the design of the experiment we chose to vary the sample size and the number of regressors. Furthermore, we generate explanatory variables that are linear combinations of other regressors, which is a common situation in economics. In an empirical application regarding Swedish job search data we also illustrate the benefits of the new method.probit regression; maximum likelihood; multicollinearity; ridge regression; MSE; job search

A New Ridge Regression Causality Test in the Presence of Multicollinearity

This paper analyzes and compares the properties of the most commonly applied versions of the Granger causality (GC) test to a new ridge regression GC test (RRGC), in the presence of multicollinearity. The investigation has been carried out using Monte Carlo simulations. A large number of models have been investigated where the number of observations, strength of collinearity, and data generating processes have been varied. For each model we have performed 10000 replications and studied seven different versions of the test. The main conclusion from our study is that the traditional OLS version of the GC test over-rejects the true null hypothesis when there are relatively high (but empirically common levels of) multicollinearity, while it is established that the new RRGC test will remedy or substantially decrease this problem.Granger causality test; multicollinearity; ridge parameters; size and power

New Liu Estimators for the Poisson Regression Model: Method and Application

A new shrinkage estimator for the Poisson model is introduced in this paper. This method is a generalization of the Liu (1993) estimator originally developed for the linear regression model and will be generalised here to be used instead of the classical maximum likelihood (ML) method in the presence of multicollinearity since the mean squared error (MSE) of ML becomes inflated in that situation. Furthermore, this paper derives the optimal value of the shrinkage parameter and based on this value some methods of how the shrinkage parameter should be estimated are suggested. Using Monte Carlo simulation where the MSE and mean absolute error (MAE) are calculated it is shown that when the Liu estimator is applied with these proposed estimators of the shrinkage parameter it always outperforms the ML. Finally, an empirical application has been considered to illustrate the usefulness of the new Liu estimators.Estimation; MSE; MAE; Multicollinearity; Poisson; Liu; Simulation

Improved Ridge Regression Estimators for Binary Choice Models: An Empirical Study

This paper suggests some new estimators of the ridge parameter for binary choice models that may be applied in the presence of a multicollinearity problem. These new ridge parameters are functions of other estimators of the ridge parameter that have shown to work well in the previous research. Using a simulation study we investigate the mean square error (MSE) properties of these new ridge parameters and compare them with the best performing estimators from the previous research. The results indicate that we may improve the MSE properties of the ridge regression estimator by applying the proposed estimators in this paper, especially when there is a high multicollinearity between the explanatory variables and when many explanatory variables are included in the regression model. The benefit of this paper is then shown by a health related data where the effect of some risk factors on the probability of receiving diabetes is investigated

A New Liu Type of Estimator for the Restricted SUR Estimator

A new Liu type of estimator for the seemingly unrelated regression (SUR) models is proposed that may be used when estimating the parameters vector in the presence of multicollinearity if the it is suspected to belong to a linear subspace. The dispersion matrices and the mean squared error (MSE) are derived. The new estimator may have a lower MSE than the traditional estimators. It was shown using simulation techniques the new shrinkage estimator outperforms the commonly used estimators in the presence of multicollinearity

A new estimator for the multicollinear Poisson regression model: simulation and application

The maximum likelihood estimator (MLE) suffers from the instability problem in the presence of multicollinearity for a Poisson regression model (PRM). In this study, we propose a new estimator with some biasing parameters to estimate the regression coefficients for the PRM when there is multicollinearity problem. Some simulation experiments are conducted to compare the estimators\u27 performance by using the mean squared error (MSE) criterion. For illustration purposes, aircraft damage data has been analyzed. The simulation results and the real-life application evidenced that the proposed estimator performs better than the rest of the estimators

Modified almost unbiased two-parameter estimator for the Poisson regression model with an application to accident data

Due to the large amount of accidents negatively affecting the wellbeing of the survivors and their families, a substantial amount of research is conducted to determine the causes of road accidents. This type of data come in the form of non-negative integers and may be modelled using the Poisson regression model. Unfortunately, the commonly used maximum likelihood estimator is unstable when the explanatory variables of the Poisson regression model are highly correlated. Therefore, this paper proposes a new almost unbiased estimator which reduces the instability of the maximum likelihood estimator and at the same time produce smaller mean squared error. We study the statistical properties of the proposed estimator and a simulation study has been conducted to compare the performance of the estimators in the smaller mean squared error sense. Finally, Swedish traffic fatality data are analyzed to show the benefit of the proposed method

Essays on Nonlinearities and Time Scales in Macroeconomics and Finance

This thesis consists of four chapters concerning the topics of nonlinearities and time scales in economics. The focus is on market frictions and price rigidities that may cause nonlinearities and different relationships between economic variables over time. It also focuses on applying robust econometrical methods. Chapter two evaluates the size and power of some nonlinear tests for panel unit roots in the presence of cross-sectional dependency and spatial dependency. Based on the simulated results some robust tests for nonlinear panel unit roots have been found. Chapter three applies robust linear and nonlinear tests for panel unit roots in order to investigate the purchasing power parity theory in developing regions. The main finding is that nonlinearities is an important phenomenon in the real effective exchange rates in developing regions and that support for several regions may be found by applying the nonlinear panel unit root test. Chapter four investigates if positive asymmetric price transmission (APT) exists in the Swedish mortgage loan market. Here robust quantile regression is used on data for the Swedish SEB bank. The main contribution is that positive APT effects are found, which implies that there is a higher propensity for the bank to rapidly increase its mortgage interest rates for customers following an increase in its borrowing costs, compared with the propensity for the bank to decrease its customers’ mortgage rates subsequent to a corresponding borrowing cost decrease. Chapter five investigates the causal relations between exchange rates and interest rate differentials using wavelets. Also the sign of the relationship between the two variables is studied using impulse response functions. The data used is for seven country pairs in which Sweden is included in all of the different combinations. In this chapter one key empirical finding is that the causal relationship between the two variables becomes stronger as the time scale increases. The other key empirical finding is that more evidence of negative relationships is found at the shorter time scales and more positive relationships at the longer time scales

Issues of multicollinearity and conditional heteroscedasticy in time series econometrics

This doctoral thesis consists of four chapters all related to the field of time series econometrics. The main contribution is firstly the development of robust methods when testing for Granger causality in the presence of generalized autoregressive conditional heteroscedasticity (GARCH) and causality-in-variance (i.e. spillover) effects. The second contribution is the development of different shrinkage estimators for count data models which may be used when the explanatory variables are highly inter-correlated. The first essay investigated the effect of spillover on some tests for causality in a Granger sense. As a remedy to the problem of over-rejection caused by the spillover effects White’s heteroscedasticity consistent covariance matrix is proposed. In the second essay the effect of GARCH errors on the statistical tests for Granger causality is investigated. Here some wavelet denoising methods are proposed and by means of Monte Carlo simulations it is shown that the size properties of the tests based on wavelet filtered data is better than the ones based on raw data. In the third and fourth essays ridge regression estimators for the Poisson and negative binomial (NB) regression models are investigated respectively. Then finally in the fifth essaya Liu type of estimator is proposed for the NB regression model. By using Monte Carlo simulations it is shown that the estimated MSE is lower for the ridge and Liu type of estimators than maximum likelihood (ML)