A search model that (a) produces the right cyclical elasticity of wages but (b) does not produce the right cyclical volatility of employment has the wrong microfoundations. It is producing the right cyclical elasticity of wages because it is producing the wrong cyclical volatility of employment. Thus I think this approach is pretty much tapped out: Christopher A Pissarides: The Unemployment Volatility Puzzle: Is Wage Stickiness the Answer?: "An equilibrium search model... focus on the model’s failure to match the observed cyclical volatility of unemployment...

...Job creation in the model is influenced by wages in new matches. I summarize microeconometric evidence on wages in new matches and show that the key model elasticities are consistent with the evidence. Therefore explanations of the unemployment volatility puzzle have to preserve the cyclical volatility of wages. I discuss some extensions of the model that can increase cyclical unemployment volatility through mechanisms other than wage stickiness...


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