FAQ: How do I estimate the output gap?

I investigate the properties of output gaps in New Keynesian DSGE models and study the relationship between theory-based quantities and the estimates obtained with standard approaches. Theoretical gaps display low frequency variations, have similar frequency domain representation as potentials and are generally correlated with them. Potentials have important business cycle variability. Existing statistical approaches fail to recognize these features and generate distorted estimates. Gaps are best estimated with a Polynomial filter. Explanations for the outcomes are given. I propose a statistical procedure reducing estimation biases.