We examine the performance and robustness properties of alternative monetary policy rules in the presence of structural change that renders the natural rates of interest and unemployment uncertain. Using a forward-looking quarterly model of the U.S. economy, estimated over the 1969-2002 period, we show that the cost of underestimating the extent of misperceptions regarding the natural rates significantly exceeds the costs of overestimating such errors. Naive adoption of policy rules optimized under the false presumption that misperceptions regarding the natural rates are likely to be small proves particularly costly. Our results suggest that a simple and effective approach for dealing with ignorance about the degree of uncertainty in estimates of the natural rates is to adopt difference rules for monetary policy, in which the short-term nominal interest rate is raised or lowered from its existing level in response to inflation and changes in economic activity. These rules do not require knowledge of the natural rates of interest or unemployment for setting policy and are consequently immune to the likely misperceptions in these concepts. To illustrate the differences in outcomes that could be attributed to the alternative policies we also examine the role of misperceptions for the stagflationary experience of the 1970s and the disinflationary boom of the 1990s.