Identification of linear time-invariant systems with Dynamic Mode Decomposition

Dynamic mode decomposition (DMD) is a popular data-driven framework to extract linear dynamics from complex high-dimensional systems. In this work, we study the system identification properties of DMD. We first show that DMD is invariant under linear transformations in the image of the data matrix. If, in addition, the data are constructed from a linear time-invariant system, then we prove that DMD can recover the original dynamics under mild conditions. If the linear dynamics are discretized with the Runge–Kutta method, then we further classify the error of the DMD approximation and detail that for one-stage Runge–Kutta methods; even the continuous dynamics can be recovered with DMD. A numerical example illustrates the theoretical findings

Going Deep: The Trade and Welfare Effects of TTIP

Since July 2013, the EU and the US have been negotiating a preferential trade agreement (PTA), the Transatlantic Trade and Investment Partnership (TTIP). We use a multi-country, multi-industry Ricardian trade model with national and international input-output linkages to quantify its potential economic consequences. We structurally estimate the sectoral trade flow elasticities of trade costs and of existing PTAs. We simulate the trade, value added, and welfare effects of the TTIP, assuming that the agreement would eliminate all transatlantic tariffs and reduce non-tariff barriers as other deep PTAs have. The long-run level of real per capita income would change by 2.12% in the EU, by 2.68% in the US, and by -0.03% in the rest of the world relative to the status quo. However, there is substantial heterogeneity across the 134 geographical entities that we investigate. Gross value of EU-US trade could triple, but its value added would grow by substantially less. Moreover, trade diversion effects are more pronounced in value added trade than in gross trade. This signals a deepening of the transatlantic value chain