JBNST - Vol. 241/1 - 2021

We analyze whether, and since when, East and West German business cycles are synchronised. We investigate real GDP, unemployment rates and survey data as business cycle indicators and we employ several empirical methods. Overall, we find that the regional business cycles have synchronised over time. GDP-based indicators and survey data show a higher degree of synchronisation than the indicators based on unemployment rates. However, synchronisation among East and West German business cycles seems to have become weaker again recently.

We develop and analyze an intertemporal cost of living index (ICOLI), also referred to as lifetime cost of living or cost of life index. The ICOLI is a geometric weighted average of effective prices, derived from constrained consumer utility maximization. Effective prices are both, money valued marginal utilities of the final unit consumed, and present values of prices for future consumption. Using the concept of duration, we derive analytical elasticities of the ICOLI with respect to consumer prices and interest rates and show their impact on lifetime welfare of consumers. We also provide empirical evidence for Germany, compute an ex post time series of the ICOLI, and gauge the welfare effects of low interest rate scenarios. We find that the financial repression policy of the ECB since 2010 contributed to substantial losses in the purchasing power of money and led to lasting welfare losses for consumers in Germany, in particular for the cohorts of young consumers. The ICOLI complements conventional price and inflation statistics and could serve as a valuable information tool for monetary policy.

This paper is concerned with the applications of discrete Fourier transforms in identification of the number of common factors of static approximate factor models. We report and explain the effects of discrete Fourier transforms to matrices, and show how the effects can be used to improve the performance of a number of eigenvalue-based estimators. In addition, we develop a set of pseudo-eigenvalues using cross-sectional discrete Fourier transforms, and use them to develop new estimators. Mathematical proofs of the consistency of the new estimators are provided, and Monte Carlo experiments are conducted to compare the new estimators with some existing ones in the literature.