Using the HEGY Procedure When Not All Roots Are Present

Empirical studies have shown little evidence to support the presence of all unit roots present in the filter in quarterly seasonal time series. This paper analyses the performance of the Hylleberg, Engle, Granger and Yoo (1990) (HEGY) procedure when the roots under the null are not all present. We exploit the Vector of Quarters representation and cointegration relationship between the quarters when factors 4 (1 L),(1+ L), (1+ L2 ), (1 L2 ) and (1+ L + L2 + L3 ) are a source of nonstationarity in a process in order to obtain the distribution of tests of the HEGY procedure when the underlying processes have a root at the zero, Nyquist frequency, two complex conjugates of frequency / 2 and two combinations of the previous cases. We show both theoretically and through a Monte-Carlo analysis that the t-ratios and and the F-type tests used in the HEGY procedure have the same distribution as under the null of a seasonal random walk when the root(s) is/are present, although this is not the case for the t-ratio tests associated with unit roots at frequency 1 t 2 t / 2 .hegy tests, vector of quarters, unit root tests, seasonality

The determinants of university patenting: Do incentives matter?

In recent years various studies have examined the factors that may explain academic patents. Existing analyses have also underlined the substantial differences to be found in European countries in the institutional framework that defines property rights for academic patents. The objective of this study is to contribute to the empirical literature on the factors explaining academic patents and to determine whether the incentives that universities offer researchers contribute towards explaining the differences in academic patenting activity. The results of the econometric analysis for the Spanish universities point towards the conclusion that the principal factor determining the patents is funding of R&D while royalty incentives to researchers do not appear to be significant.Patents, University, R&D

The geography of innovation: the effects of university research

Applied studies on the relationship between geography and technological innovation for United States, Germany, France and Italy have shown the positive effects that academic research exerts on the innovative output of firms at a spatial level. The purpose of this paper is to look for new evidence on the possible effects of the university research for the case of Spain. To do so, within the framework of a Griliches-Jaffe knowledge production function, and using panel data and count models, the relationship between innovative inputs and patents, in the case of the Spanish regions is explored.geography of innovation, patents, r&d

Using the HEGY Procedure When Not All Roots Are Present

Les fòrmules matemàtiques del resum estan representades en LaTeX.Empirical studies have shown little evidence to support the presence of all unit roots present in the Δ4 filter in quarterly seasonal time series. This paper analyses the performance of the Hylleberg, Engle, Granger and Yoo (1990) (HEGY) procedure when the roots under the null are not all present

Breaking the panels. An application to the GDP per capita

This paper proposes a test statistic for the null hypothesis of panel stationarity that allows for the presence of multiple structural breaks. Two different specications are considered depending on the structural breaks affecting the individual effects and/or the time trend. The model is exible enough to allow the number of breaks and their position to differ across individuals. The test is shown to have an exact limit distribution with a good nite sample performance. Its application to a typical panel data set of real per capita GDP gives support to the trend stationarity of these series.stationarity test, multiple structural changes, gdp per capita, panel data

Regression-based seasonal unit root tests

The contribution of this paper is three-fold. Firstly, a characterisation theorem of the sub-hypotheses comprising the seasonal unit root hypothesis is presented which provides a precise formulation of the alternative hypotheses against which regression-based seasonal unit root tests test. Secondly, it proposes regressionbased tests for the seasonal unit root hypothesis which allow a general seasonal aspect for the data and are similar both exactly and asymptotically with respect to initial values and seasonal drift parameters. Thirdly, limiting distribution theory is given for these statistics where, in contrast to previous papers in the literature, in doing so it is not assumed that unit roots hold at all of the zero and seasonal frequencies. This is shown to alter the large sample null distribution theory for regression t-statistics for unit roots at the complex frequencies, but interestingly to not affect the limiting null distributions of the regression t-statistics for unit roots at the zero and Nyquist frequencies and regression Fstatistics for unit roots at the complex frequencies. Our results therefore have important implications for how tests of the seasonal unit root hypothesis should be conducted in practice. Associated simulation evidence on the size and power properties of the statistics presented in this paper is given which is consonant with the predictions from the large sample theory.Seasonal unit root tests; seasonal drifts; characterisation theorem

The determinants of University patenting: do incentives matter?

In recent years various studies have examined the factors that may explain academic patents. Existing analyses have also underlined the substantial differences to be found in European countries in the institutional framework that defines property rights for academic patents. The objective of this study is to contribute to the empirical literature on the factors explaining academic patents and to determine whether the incentives that universities offer researchers contribute towards explaining the differences in academic patenting activity. The results of the econometric analysis for the Spanish universities point towards the conclusion that the principal factor determining the patents is funding of R&D while royalty incentives to researchers do not appear to be significant