Whether we would like to model imports and exports, or forecast inflation, structural variation in an economy frequently causes problems. This thesis examines such variation in two dimensions: first, in a cross-section of individuals, and secondly, over time. A panel of manufacturing industries in several developed countries reveals that there is substantial variation across sectors, in the response of trade to changes in prices and incomes. Ignoring this heterogeneity can render conventional results biased and inconsistent, so a number of robust methods are used to obtain reliable estimates of long-run and short-run trade relationships. The findings point to common behaviour across sectors, which could be due to similarities in technology. The impact of structural breaks over time is examined in the second part of the thesis. Unpredictable shifts in deterministic terms such as the mean of a process are shown to generate significant forecast failure, and even the methods used to evaluated forecast accuracy are affected. Using the Kullback-Leibler discrepancy to measure the size of forecast errors, various robust mechanisms are discussed, that do not fail systematically after a break. Although they can provide a degree of insurance if a shift does occur, this comes at a cost if there is no change, and in the presence of measurement error they can exacerbate the uncertainty surrounding a forecast. An empirical illustration with a model of UK money demand provides some support for the automatic correction mechanisms, although there does seem to be a role for direct modeling of a break process.