We consider the inverse problem of identifying a moving source in a linear advection–dispersion–reaction equation. The main application, but not the only one, is the identification of an environmental pollution source in a river. An identifiability result is established and an identification method proposed using measurement records at two locations, one upstream and the other downstream from the source. Finally, numerical simulations are performed to assess the identification process.

The Flexible System of Global Models (FSGM) is a group of models developed by the Economic Modeling Division of the IMF for policy analysis. A typical module of FSGM is a multi-region, forward-looking semi-structural global model consisting of 24 regions. Using the three core modules focused on the G-20, the euro area, and emerging market economies, this paper outlines the theory underpinning the model, and illustrates its macroeconomic properties by presenting its responses under a wide range of experiments, including monetary, financial, demand, supply, fiscal and international shocks.

We develop a semi-structural new-Keynesian open-economy model, with separate food and nonfood inflation dynamics, for forecasting and monetary policy analysis in low-income countries and apply it to Kenya. We use the model to run several policy-relevant exercises. First, we filter international and Kenyan data (on output, inflation and its components, exchange rates and interest rates) to recover a model-based decomposition of most variables into trends (or potential values) and temporary movements (or gaps)-including for the international and domestic relative price of food. Second, we use the filtration exercise to recover the sequence of domestic and foreign macroeconomic shocks that account for business cycle dynamics in Kenya over the last few years, with a special emphasis on the various factors (international food prices, monetary policy) driving inflation. Third, we perform an out-of-sample forecast to identify where the economy-and therefore policy-was likely headed given the inflationary pressures at the end of our sample (2011Q2). We find that while imported food price shocks have been an important source of inflation, both in 2008 and more recently, accommodating monetary policy has also played a role, most notably through its effect on the nominal exchange rate. The model correctly predicted that a policy tightening was required, although the actual interest rate increase was larger. We discuss implications for the use of model-based policy analysis in low income countries.

We consider the inverse problem of identifying multiple moving pollution sources in a linear advection-dispersion-reaction equation. Although we consider the specific application of pollution source identification in surface waters or atmospheric media, this problem has many other important applications in ecological and diffusive systems. We establish an identifiability result using observations on a non-empty subset of the domain boundary and develop an identification method by reformulating the inverse problem into a minimization problem. Finally, we provide numerical results to support the theoretical results.