Matching Models and Nominal Rigidities
Various authors have attempted to embed matching models in the RBC framework or to incorporate new Keynesian nominal rigidities in matching models.
Merz [1995] and Andolfatto [1996] were the first to introduce labor market frictions in an otherwise standard RBC model.
In both cases, the focus was on the dynamic effects of productivity shocks, and in both cases, the model was solved using simulations.Cheron and Langot [2000], Walsh [2003], and Trigari [2006] have allowed for Calvo staggered pricing by firms, to study the effects of nominal shocks. Those models are also too large to be analytically tractable and so are solved using simulations. Walsh [2005], Moyen and Sahuk [2005], Andres et al. [2006], and Trigari [2009], among others, introduce extensions that range from habit persistence in preferences, to capital accumulation, to the implications of Taylor rules. The models in these papers are relatively complex DSGE models, which need to be studied through calibration and simulations. Shimer [2005] and Hall [2005] were the first to introduce real wage ridigities. Shimer argued that, in the standard matching model with Nash bargaining, wages are too flexible, and the response of unemployment to productivity shocks is too small. Gertler and Trigari [2009] have explored the implications of introducing real wage staggering à la Calvo. Thomas [2008] and Gertler et al. [2008] have explored models in a staggered nominal wage setting rather than real wage rigidity. Krause and Lubik [2007], Faia [2008], Christoffel and Linzert [2010], and Blanchard and Gali [2010] explore models with matching frictions and both real and nominal wage and price rigidities. More recently, Michaillat [2012] and Michaillat and Saez [2015] have introduced matching frictions in rationing models with nominal wage and price rigidities of the Barro and Grossman [1971] variety. With few exceptions (such as the Blanchard and Gali [2010] model), all these models are quite complicated and can only be solved by using numerical methods.
The quest to produce analytically tractable DSGE models that incorporate both matching frictions and nominal rigidities is an active area of current research.
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