Specifically, I am looking for the standard neoclassical growth model, but the labour decision is based on either search or matching theory instead of a Walrasian labour mechanism.
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Search and matching models are fairly standard in macroeconomics. I guess this is fair to say since Peter Diamond, Dale Mortensen, and Christopher Pissarides won the Nobel prize in 2010. These are the names behind the canonical DMP model that most graduate students have to study in their first year. Although I am not a macroeconomist, I am confident to say that search models recognized as a key ingredient to explain unemployment in equilibrium. I suggest to watch the interview with Per Krusell on the Nobel prize homepage and read the scientific background.
