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Highlights
• Six Newton methods for solving matrix quadratic equations in linear DSGE models.
• Compared to QZ using 99 different DSGE models including Smets and Wouters (2007).
• Newton methods more accurate than QZ with comparable computation burden.
• Apt for refining solutions from alternative methods or nearby parameterizations.
Abstract
This paper presents and compares Newton-based methods from the applied mathematics literature for solving the matrix quadratic that underlies the recursive solution of linear DSGE models. The methods are compared using nearly 100 different models from the Macroeconomic Model Data Base (MMB) and different parameterizations of the monetary policy rule in the medium-scale New Keynesian model of Smets and Wouters (2007) iteratively. We find that Newton-based methods compare favorably in solving DSGE models, providing higher accuracy as measured by the forward error of the solution at a comparable computation burden. The methods, however, suffer from their inability to guarantee convergence to a particular, e.g. unique stable, solution, but their iterative procedures lend themselves to refining solutions either from different methods or parameterizations.
The Russian war of aggression against Ukraine since 24 February 2022 has intensified the discussion of Europe’s reliance on energy imports from Russia. A ban on Russian imports of oil, natural gas and coal has already been imposed by the United States, while the United Kingdom plans to cease imports of oil and coal from Russia by the end of 2022. The German Federal Government is currently opposing an energy embargo against Russia. However, the Federal Ministry for Economic Affairs and Climate Action is working on a strategy to reduce energy imports from Russia. In this paper, the authors give an overview of the German and European reliance on energy imports from Russia with a focus on gas imports and discuss price effects, alternative suppliers of natural gas, and the potential for saving and replacing natural gas. They also provide an overview of estimates of the consequences on the economic outlook if the conflict intensifies.
High-frequency changes in interest rates around FOMC announcements are an important tool for identifying the effects of monetary policy on asset prices and the macroeconomy. However, some recent studies have questioned both the exogeneity and the relevance of these monetary policy surprises as instruments, especially for estimating the macroeconomic effects of monetary policy shocks. For example, monetary policy surprises are correlated with macroeconomic and financial data that is publicly available prior to the FOMC announcement. The authors address these concerns in two ways: First, they expand the set of monetary policy announcements to include speeches by the Fed Chair, which essentially doubles the number and importance of announcements in our dataset. Second, they explain the predictability of the monetary policy surprises in terms of the “Fed response to news” channel of Bauer and Swanson (2021) and account for it by orthogonalizing the surprises with respect to macroeconomic and financial data. Their subsequent reassessment of the effects of monetary policy yields two key results: First, estimates of the high-frequency effects on financial markets are largely unchanged. Second, estimates of the macroeconomic effects of monetary policy are substantially larger and more significant than what most previous empirical studies have found.
Debt levels in the eurozone have reached new record highs. The member countries have tried to cushion the economic consequences of the corona pandemic with a massive increase in government spending. End of 2021 public debt in relation to GDP will approach 100% on average. There are various calls to abolish or soften the Maastricht rules of limiting sovereign debt. We see the risk of a new sovereign debt crisis in this decade if it is not possible to bring public debt down to an acceptable level. Our new fiscal rule would be suitable and appropriate for this purpose, because obviously the Maastricht criteria have failed. In contrast to the rigid 3% Maastricht-criterion, our rule is flexible and it addresses the main problem: excessively high public debt ratios. And it lowers the existing incentives for highly indebted governments to exert expansionary pressure on monetary policy. If obeyed strictly, our rule reinforces the snowball effect and reduces the excessively high debt ratios within a manageable period, even if nominal growth is weak. This is confirmed by simulations with different scenarios as well as with the hypothetical application of the new fiscal rule to eurozone economies from 2022 to 2026. Finally, we take up the recent proposal by ESM economists to increase the permissible debt ratio from 60 to 100% of GDP in the eurozone.
The purpose of the data presented in this article is to use it in ex post estimations of interest rate decisions by the European Central Bank (ECB), as it is done by Bletzinger and Wieland (2017) [1]. The data is of quarterly frequency from 1999 Q1 until 2013 Q2 and consists of the ECB's policy rate, inflation rate, real output growth and potential output growth in the euro area. To account for forward-looking decision making in the interest rate rule, the data consists of expectations about future inflation and output dynamics. While potential output is constructed based on data from the European Commission's annual macro-economic database, inflation and real output growth are taken from two different sources both provided by the ECB: the Survey of Professional Forecasters and projections made by ECB staff. Careful attention was given to the publication date of the collected data to ensure a real-time dataset only consisting of information which was available to the decision makers at the time of the decision.
Ein Freibrief für die Notenbank bedeutet, genau genommen, die Bankrotterklärung des demokratischen Verfassungsstaates vor technokratischen Beliebigkeiten, schreibt Helmut Siekmann in diesem Namensbeitrag. Er betont, dass die Europäische Union eine unverzichtbare Einrichtung ist und ein echter Bundesstaat sein sollte. Sie sei aber im Wesentlichen (nur) ein Rechtskonstrukt, weshalb es umso wichtiger sei, dass die rechtlichen Regeln, auf denen sie beruht, genauestens beachtet werden.
Notenbanken haben heute nicht die Aufgabe die Geldmenge zu kontrollieren. Ihr Job ist es, den Wert des Geldes – und damit den Preis der Wirtschaftsgüter in der jeweiligen Währung – zu stabilisieren. Doch wie ist diese Preisstabilität am besten herzustellen? Muß man dabei nicht doch die Geldmenge im Auge behalten? Unter monetären Ökonomen gibt es dazu eine wissenschaftliche Debatte.
Credit boom detection methodologies (such as threshold method) lack robustness as they are based on univariate detrending analysis and resort to ratios of credit to real activity. I propose a quantitative indicator to detect atypical behavior of credit from a multivariate system - a monetary VAR. This methodology explicitly accounts for endogenous interactions between credit, asset prices and real activity and detects atypical credit expansions and contractions in the Euro Area, Japan and the U.S. robustly and timely. The analysis also proves useful in real time.
In this paper, we provide some reflections on the development of monetary theory and monetary policy over the last 150 years. Rather than presenting an encompassing overview, which would be overambitious, we simply concentrate on a few selected aspects that we view as milestones in the development of this subject. We also try to illustrate some of the interactions with the political and financial system, academic discussion and the views and actions of central banks.