Productivity shocks and Optimal Monetary Policy in a Unionized Labor Market Economy

In this paper we analyze a general equilibrium DSNK model characterized by labor indivisibilities, unemployment and a unionized labor market. The presence of monopoly unions introduces real wage rigidities in the model. We show that as in Blanchard Galì (2005) the so called "divine coincidence" does not hold and a trade-off between inflation stabilization and the output stabilization arises. In particular, a productivity shock has a negative effect on inflation, while a reservation-wage shock has an effect of the same size but with the opposite sign. We derive a welfare-based objective function for the Central Bank as a second order Taylor approximation of the expected utility of the economy's representative household, and we analyze optimal monetary policy under discretion and under commitment. Under discretion a negative productivity shock and a positive exogenous wage shock will require an increase in the nominal interest rate. An operational instrument rule, in this case, will satisfy the Taylor principle, but will also require that the nominal interest rate does not necessarily respond one to one to an increase in the rate of interest that supports the efficient equilibrium. The model is calibrated under different monetary policy rules and under the optimal rule. We show that the correlation between productivity shocks and employment is strongly influenced by the monetary policy regime. The results of the model are consistent with a well known empirical regularity in macroeconomics, i.e. that employment volatility is relatively larger than real wage volatility.