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Dear all, I have a question regarding welfare evaluation in rational expectations models. If agents are risk averse, their welfare is supposed to be lower under 2nd order approximation (compared to 1st order approximation). If the opposite happens, does it mean that the Jensen's inequality matters here? How should we deal with the Jensen's inequality?

Thanks in advance.

Jensen's Inequality is always at work in nonlinear models. That is why welfare at second order is CETERIS PARIBUS lower if agents are risk-averse. However, there may be compensating non-linearities at work. For example, if you use lognormal TFP, the average TFP increases in volatility. You need to understand the economic intuition of your model-