After re-iterating five well-known theorems about the properties of conditional expectations in stationary settings—such as providing unbiased minimum mean square error predictions despite in- complete information, and the law of iterated expectations—we clarify unpredictability and illustrate its prevalence empirically.
We then relate unpredictability to imperfect knowledge about location shifts, and derive its implications. These include refuting the relevance of the five theorems about conditional expectations for the real world, entailing the failure of rational expectations and the inva- lidity of the inter-temporal mathematics underpinning dynamic stochastic general equilibrium mod- els (DSGEs). Finally, we describe how to empirically model ever-changing worlds despite imperfect knowledge thereof.
