New Keynesian model with technology shocks: Consider a New Keynesian economy with equilibrium conditions given by
where and are in ation and aggregate output in period t, xt = yt- ytn is the output gap, ytn is the natural rate of output, Ρ is the exogenous discount rate, and σ > 0, k > 0 and 0< β < 1. Monetary policy is described by a simple rule of the form
with ΦΠ > 1. Labour productivity is given by
where is employment and is an exogenous technology parameter that evolves according to
where is a mean-zero process and persistence parameter paε [0 1). The underlying RBC model is assumed to imply a natural output level proportional to technology
where Ψy>1
(a) Discuss the real output and in ation expressions verbally.
(b) Determine the equilibrium response of output, employment and in ation to a technology shock.
(c) Describe how these responses depend on the value of ΦΠ and k. Provide economic intuition. What happens when ΦΠ -> ∞ ? What happens when the elasticity of labour supply (HINT: one of the ingredients of parameter k) increases ?
(d) Analyse the joint response of employment and output to a technology shock and discuss briefly the implications of the role of technology as the source of business cycles.