Adaptive Continuous time Markov Chain Approximation Model to General Jump-Diusions

We propose a non-equidistant Q rate matrix formula and an adaptive numerical algorithm for a continuous time Markov chain to approximate jump-diffusions with affine or non-affine functional specifications. Our approach also accommodates state-dependent jump intensity and jump distribution, a flexibility that is very hard to achieve with other numerical methods. The Kolmogorov-Smirnov test shows that the proposed Markov chain transition density converges to the one given by the likelihood expansion formula as in Ait-Sahalia (2008). We provide numerical examples for European stock option pricing in Black and Scholes (1973), Merton (1976) and Kou (2002).

The Taylor Principle and (In-) Determinacy in a New Keynesian Model with hiring Frictions and Skill Loss

We introduce duration dependent skill decay among the unemployed into a New-Keynesian model with hiring frictions developed by Blanchard/Gali (2008). If the central bank responds only to (current, lagged or expected future) inflation and quarterly skill decay is above a threshold level, determinacy requires a coefficient on inflation smaller than one. The threshold level is plausible with little steady-state hiring and firing ("Continental European Calibration") but implausibly high in the opposite case ("American calibration"). Neither interest rate smoothing nor responding to the output gap helps to restore determinacy if skill decay exceeds the threshold level. However, a modest response to unemployment guarantees determinacy. Moreover, under indeterminacy, both an adverse sunspot shock and an adverse technology shock increase unemployment extremely persistently.

Ordering Policy Rules with an Unconditional Welfare Measure

The unconditional expectation of social welfare is often used to assess alternative macroeconomic policy rules in applied quantitative research. It is shown that it is generally possible to derive a linear - quadratic problem that approximates the exact non-linear problem where the unconditional expectation of the objective is maximised and the steady-state is distorted. Thus, the measure of pol icy performance is a linear combinat ion of second moments of economic variables which is relatively easy to compute numerically, and can be used to rank alternative policy rules. The approach is applied to a simple Calvo-type model under various monetary policy rules.