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 generalized 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.

This paper considers the estimation of parameters for the Poisson regression model in the presence of high, but imperfect multicollinearity. To mitigate this problem, we suggest using the Poisson Liu Regression Estimator (PLRE) and propose some new approaches to estimate this shrinkage parameter. The small sample statistical properties of these estimators are systematically scrutinized using Monte Carlo simulations. To evaluate the performance of these estimators, we assess the Mean Square Errors (MSE) and the Mean Absolute Percentage Errors (MAPE). The simulation results clearly illustrate the benefit of the methods of estimating these types of shrinkage parameters in finite samples. Finally, we illustrate the empirical relevance of our newly proposed methods using an empirically relevant application. Thus, in summary, via simulations of empirically relevant parameter values, and by a standard empirical application, it is clearly demonstrated that our technique exhibits more precise estimators, compared to traditional techniques-at least when multicollinearity exist among the regressors.

According to previous research, standard unit root tests are considered robust to stationary GARCH distortions. These conclusions are in fact correct when the number of observations is extraordinarily high. However, simulation experiments in this study, using more normal sample sizes, reveal that eight of the most commonly applied unit root tests exhibit considerable bias in the size in the presence of fairly moderate GARCH distortions. As a remedy for the disturbances from GARCH, this article presents size-corrected unbiased critical values for all these examined tests. Nevertheless there is still reduced power in the presence of stationary GARCH distortions. As a solution, a completely new test is formulated which simultaneously models unit roots and the interconnected parameters of GARCH risk. For empirically relevant sample sizes, this new test exhibits superior size and power properties compared with all the traditional unit root tests in the presence of GARCH disturbances.

Månsson and Shukur (Econ Model 28:1475–1481, 2011) proposed a Poisson ridge regression estimator (PRRE) to reduce the negative effects of multicollinearity. However, a weakness of the PRRE is its relatively large bias. Therefore, as a remedy, Türkan and Özel (J Appl Stat 43:1892–1905, 2016) examined the performance of almost unbiased ridge estimators for the Poisson regression model. These estimators will not only reduce the consequences of multicollinearity but also decrease the bias of PRRE and thus perform more efficiently. The aim of this paper is twofold. Firstly, to derive the mean square error properties of the Modified Almost Unbiased PRRE (MAUPRRE) and Almost Unbiased PRRE (AUPRRE) and then propose new ridge estimators for MAUPRRE and AUPRRE. Secondly, to compare the performance of the MAUPRRE with the AUPRRE, PRRE and maximum likelihood estimator. Using both simulation study and real-world dataset from the Swedish football league, it is evidenced that one of the proposed, MAUPRRE ($$ \hat{k}_{q4} $$ k ^ q 4 ) performed better than the rest in the presence of high to strong (0.80–0.99) multicollinearity situation.

PurposeIn what seems as an infinitely ongoing debate regarding the purchasing power parity (PPP) theory, this paper seeks to question the strength of the scientific “evidence” put forward by the PPP revisionistsDesign/methodology/approachIn this paper, the validity of the PPP revisionists' scientific evidence supporting long‐run PPP is questioned based on the replication of an influential review study that is considered by PPP revisionists to exhibit “some of the strongest evidence” in favour of the PPP theory.FindingsBy simulation experiments it is demonstrated that the traditional PPP unit root tests are non‐robust to the empirically identified (G)ARCH distortions. Due to (G)ARCH distortions, over‐rejections for the traditional unit root tests are shown to be a problem that potentially misleads researchers to believe that long‐run PPP holds under circumstances when it is in fact not valid. As a potential remedy to this problem, a new unit root test is introduced which is robust to conditional heteroscedasticity disturbances, and in contrast to traditional unit root tests, it exhibits no significant empirical support for the PPP theory.Originality/valueThe study illustrates that the PPP revisionists' unit root tests cannot reliably test the PPP hypothesis in the presence of (G)ARCH distortions, due to bad power and size properties. Perhaps it is time to conclude that, based on the currently existing research, it is virtually impossible to empirically come to a credible conclusion regarding whether long‐run PPP holds or not.