Firms provide substantial insurance against wage fluctuations and job loss. This paper studies how the interaction between shock size and persistence affects the firm’s ability to insure workers against idiosyncratic firm-level shocks. Using linked employer-employee data from Germany, I find...

We propose a simple modification of the time series filter by Hamilton (2018b) that yields reliable and economically meaningful real-time output gap estimates. The original filter relies on 8-quarter ahead forecasts errors of an autoregression. While this approach yields a cyclical component of...

In this chapter, we first explain what we mean by a signal, and then we describe some characteristics such as energy, frequency, phase, power spectrum, etc. We show how to analyse it by the means of spectral analysis and Fourier transform. Moreover, as the Fourier transform does not provide any...