Many recent studies in macroeconomics have focused on the estimation of DSGE models using a system of loglinear approximations to the models' nonlinear equilibrium conditions. The term macroeconometric equivalence encapsulates the idea that estimates using aggregate data based on first-order approximations to the equilibrium conditions of a DSGE model will not be able to distinguish between alternative underlying preferences and technologies. The concept of microeconomic dissonance refers to the fact that the underlying microeconomic differences become important when optimal monetary policy is analyzed in a nonlinear setting. The relevance of these concepts is established by analysis of optimal steady-state inflation and optimal policy in the stochastic economy using a small-scale New Keynesian model. Microeconomic and financial datasets are promising tools with which to overcome the equivalence problem.