Cointegrating Polynomial Regressions: Fully Modified Ols Estimation and Inference

Abstract

This paper develops a fully modified OLS estimator for cointegrating polynomial regressions, i.e. for regressions including deterministic variables, integrated processes and powers of integrated processes as explanatory variables and stationary errors. The errors are allowed to be serially correlated and the regressors are allowed to be endogenous. The paper thus extends the fully modified approach developed in Phillips and Hansen (1990). The FM-OLS estimator has a zero mean Gaussian mixture limiting distribution, which is the basis for standard asymptotic inference. In addition Wald and LM tests for specification as well as a KPSS-type test for cointegration are derived. The theoretical analysis is complemented by a simulation study which shows that the developed FM-OLS estimator and tests based upon it perform well in the sense that the performance advantages over OLS are by and large similar to the performance advantages of FM-OLS over OLS in cointegrating regressions.

A cointegrating polynomial regression analysis of the material kuznets curve hypothesis

“…These variables are frequently found to be integrated of order one (I(1)). Hence, before assessing the existence of any nexus between metal use and economic growth, it is imperative to individually test for each country (i) whether (log) GDP per capita is an I(1) process using unit-root tests and, if this holds true, (ii) whether the error term in Equation 1 is stationary using, e.g., tests for nonlinear cointegration developed by Wagner (2013) and Wagner and Hong (2016), rather than standard cointegration tests. In contrast to these tests for nonlinear cointegration, classical cointegration tests are based on the assumption that all stochastic regressors appearing in Equation 1, i. e. y t and y 2 t , as well as the dependent variable m t , are I(1).…”

“…To test whether Equation 1 is a cointegrating polynomial relationship, we use the tests developed by Wagner (2013) and Wagner and Hong (2016). First, we employ the extension of the non-cointegration test of Phillips and Ouliaris (1990) to cointegrating polynomial regressions (CPRs) of Wagner (2013), denoted here by Pû.…”

“…log GDP per capita, are not integrated processes of any order -for more details on this fact see Müller-Fürstenberger and Wagner (2007) and Wagner (2008Wagner ( , 2012. To prevent misplaced conclusions with respect to the existence of an MKC, both unit-root and cointegration tests, as well as cointegration estimation techniques, need to be modified to suit to the, in the words of Wagner and Hong (2016), cointegrating polynomial regression (CPR) context, thereby accounting for the fact that the MKC hypothesis necessitates powers of economic indicators as regressors. 2…”

“…By applying the cointegration tests of Wagner (2013), together with estimation techniques from Saikkonen and Choi (2004) as well as Wagner and Hong (2016), and employing metal use data spanning from about 1900 to 2006 for aluminum, lead and zinc, this paper tests the MKC hypothesis between a country's GDP per capita and the ratio of metal consumption to GDP (intensity of use, IOU) for eight OECD countries, including highly industrialized countries such as the US, Japan, and Germany. Our empirical analysis demonstrates that, similar to the conclusions drawn from the EKC analysis by Wagner (2015), the evidence for a MKC relationship is strongly diminished compared to that resulting from applying standard tests for linear cointegration.…”

Desarrollo desigual y trabajo potenciado en la eurozona

“…Para la estimación del vector de cointegración se utilizan el modelo de MCO dinámico (en adelante DOLS, por sus siglas en inglés) y el modelo de MCO totalmente modificado (en adelante FMOLS, por sus siglas en inglés). Con dichos modelos de regresión dinámica es factible interpretar el signo de la correlación entre la variable dependiente y las variables explicativas (Stock y Watson, 1993;Pedroni, 1999Pedroni, y 2001Wagner y Hong, 2016).…”