The relationship between budgetary expenditure and economic growth in Poland Abstract This paper investigates the association between different kinds of budgetary expenditure and economic growth of Poland. The empirical analysis makes use of linear and nonlinear Granger causality tests to evaluate the applicability of Wagnerxe2x80x99s Law and that of the contrasting Keynesian theory.We employ aggregate and disaggregate data with the subcategories of most important budgetary expenditure, including health care and social security, education and science, national defence and public security expenditure and government administration expenditure for the period Q1 2000 to Q3 2008. This causality analysis indicates that total relation between budgetary expenditure and economic growth is consistent with Keynesian theory. The results of our computations have important policy implications. In case of Poland the health care expenditure was found to be as important for economic growth as expenditures on education and science. Furthermore, in order to stimulate economic growth, Polish government should consider reallocating some of national defence, public security and government administration expenditure to health care, social security, education and science expenditure.

VariableLag Granger Causality for Time Series Analysis Granger causality is a fundamental technique for causal inference in time series data, commonly used in the social and biological sciences. Typical operationalizations of Granger causality make a strong assumption that every time point of the effect time series is influenced by a combination of other time series with a fixed time delay. However, the assumption of the fixed time delay does not hold in many applications, such as collective behavior, financial markets, and many natural phenomena. To address this issue, we develop variablelag Granger causality, a generalization of Granger causality that relaxes the assumption of the fixed time delay and allows causes to influence effects with arbitrary time delays. In addition, we propose a method for inferring variablelag Granger causality relations. We demonstrate our approach on an application for studying coordinated collective behavior and show that it performs better than several existing methods in both simulated and realworld datasets. Our approach can be applied in any domain of time series analysis.