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The objective of this paper is to examine the Wagner's law validity, and whether it can explain the U.K. public spending expansion for the period 1850-2010. According to Wagner's Law, economic development is the key determinant to public sector growth. Accordingly, the public sector grows overproportionally compared to national income when economies develop. We test this hypothesis for the UK. The data covers a period in which the U.K. economy experienced increased economic growth, government spending and met most of the assumption of Wagner's Law (industrialisation, urbanisation, increased population). Furthermore, the long data set ensures the reliability of our results in terms of statistical and economic conclusions. We apply unit root tests, unit root tests with structural breaks, cointegration techniques and the Granger causality test. Our results indicate a presence of a long run relationship between national income and government spending, while the causality is bi-directional, thus we find support for Wagner's and Keynesian hypotheses.

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The matrix pencil method is an eigenvalue based approach for the parameter identification of sparse exponential sums. We derive a reconstruction algorithm for multivariate exponential sums that is based on simultaneous diagonalization. Randomization is used and quantified to reduce the simultaneous diagonalization to the eigendecomposition of a single random matrix. To verify feasibility, the algorithm is applied to synthetic and experimental fluorescence microscopy data.2010 Mathematics Subject Classification. 65T40, 42C15, 30E05, 65F30.